PEH:Estimation of Primary Reserves of Crude Oil, Natural Gas, and Condensate

Publication Information

Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume V – Reservoir Engineering and Petrophysics

Edward D. Holstein, Editor

Copyright 2007, Society of Petroleum Engineers

Chapter 18 – Estimation of Primary Reserves of Crude Oil, Natural Gas, and Condensate

Ron Harrell, SPE, Ryder Scott Co., Chap Cronquist, SPE Consultant

Pgs. 1479-1570

ISBN 978-1-55563-120-8
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Most exploration and production companies’ assets consist of the resources and reserves owned by that entity. Resources typically are classified as either contingent (discovered but presently uneconomic) or undiscovered, but their quantification is outside the scope of this work. This chapter discusses primary reserves, which are discovered quantities of hydrocarbons that can be produced at a profit and are classified by level of uncertainty. The discussion of estimated reserves in this chapter excludes limitations imposed by the terms of ownership.

Since publication of the first two petroleum handbooks, the international petroleum industry has increased its understanding of the need to develop more reliable estimates of petroleum reserves and to quantify the uncertainty associated with the classifications of reserves. Furthermore, the regulatory authorities of many countries, particularly of the U.S.A., have found it necessary to accommodate the increasing internationalization of the industry and to manage their increasing involvement and influence in the industry.

With this global expansion of the petroleum industry has come ongoing technological development that provides better tools and techniques for analyzing reservoirs and reservoir fluids as well as greater understanding of how reservoir geology affects reservoir performance. In developing mathematical models that replicate the geologic environment, the reservoir engineer must incorporate all available hard technical data and work closely with and use fully the experience of multidisciplinary teams of geophysicists, geologists, petrophysicists, and other specialists. The engineer must develop a working knowledge of the skills contributed by each member of the reserves assessment team and apply the professional judgment of each team member to the estimation and classification of reserves.

The estimation of reserves is more than just a periodic, statutory calculating and reporting of company assets (although those are important functions); it is an essential element of investment planning and resource management for every prudent operator. Estimating reserves begins with identifying a drillable prospect, and it continues while the prospect is developed and placed on production, and thereafter as warranted by well and/or reservoir performance, new geologic data, competitor (offset) operations, unitization, contract renegotiation, improved technology, and/or changing economic conditions.

Fig. 18.1 illustrates the entire spectrum of in-place and recoverable hydrocarbons, the total resource base that is contained within the subsurface of the Earth. The vertical scale represents the total resource base, including cumulative production, reserves, and the unrecoverable portions of the discovered and economic quantities, as well as the recoverable and unrecoverable portions of the two categories of resources.

• 

  Fig. 18.1 – Resource classification system, showing possible project status categories (after Ross).

The horizontal scale reflects the increasing degrees of uncertainty of reserves quantities, showing (left to right) reserves classifications of proved through possible and resource-estimates categories of low to high. A project status column on the far right contains terms typically used to describe the stage of exploration and development associated with the various degrees of uncertainty. The classifications of proved plus probable and proved plus probable plus possible reserves are consistent with those used with probabilistic methods of reserves estimation and classification.

Fig. 18.2 adapts the so-called McKelvey box to show the relationship between USGS reserves classifications and those of the 1997 Society of Petroleum Engineers/World Petroleum Congress (SPE/WPC), which are quoted in a subsequent section. USGS (McKelvey ) classifications of identified (discovered) reserves (measured, indicated, and inferred) are approximately equivalent to the 1997 SPE/WPC classifications of proved, probable, and possible, respectively. The integration of this concept with the 2001 SPE/WPC/AAPG (American Assn. of Petroleum Geologists) resource definitions 4 led to the development of Fig 18.1.

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  Fig. 18.2 – The McKelvey box, illustrating the relationship between the U.S. Geological Survey (USGS) classification of resources and the 1997 SPE/WPC classification of reserves. (After McKelvey.)

Reserves are the quantities that remain to be commercially produced as of a given date, under stated economic and operating conditions. Ultimate reserves are the sum of cumulative production and quantities (reserves) yet to be commercially produced. Terms such as "remaining reserves" and "recoverable reserves" are redundant. Terms such as "exploratory reserves," "geologic reserves," "potential reserves," and "technical reserves" often are used in conversation, but are misleading. The use of such terms is discouraged.

For this chapter discussion, reserves are quantities that are available for sale following lease or platform separation. Oil and condensate quantities do not reflect any reduction for field losses or field use. Natural-gas reserves typically are reported net after field condensate removal, but no consideration is given herein to gas volume reduction resulting from the extraction of natural-gas liquids or for the removal of contaminants. (See McMichael and Spencer for a discussion of these issues.)

Reserves Definitions

1997 SPE/WPC Petroleum Reserves Definitions*

Reserves are those quantities of petroleum which are anticipated to be commercially recovered from known accumulations from a given date forward. All reserves estimates involve some degree of uncertainty. The uncertainty depends chiefly on the amount of reliable geologic and engineering data available at the time of the estimate and the interpretation of these data. The relative degree of uncertainty may be conveyed by placing reserves into one of two principal classifications, either proved or unproved. Unproved reserves are less certain to be recovered than proved reserves and may be further subclassified as probable and possible reserves to denote progressively increasing uncertainty regarding their recoverability.

The intent of the SPE and WPC in approving additional classifications beyond proved reserves is to facilitate consistency among professionals using such terms. In presenting these definitions, neither organization is recommending public disclosure of reserves classified as unproved. Public disclosure of the quantities classified as unproved reserves is left to the discretion of the countries or companies involved.

Estimation of reserves is done under conditions of uncertainty. The method of estimation is called deterministic [our emphasis] if a single best estimate of reserves is made based on known geological, engineering, and economic data. The method of estimation is called probabilistic [our emphasis] when the known geological, engineering, and economic data are used to generate a range of estimates and their associated probabilities. Identifying reserves as proved, probable, and possible has been the most frequent classification method and gives an indication of the probability of recovery. Because of potential differences in uncertainty, caution should be exercised when aggregating reserves of different classifications.

Reserves estimates will generally be revised as additional geologic or engineering data become available or as economic conditions change. Reserves do not include quantities of petroleum being held in inventory, and they may be reduced for usage or processing losses if required for financial reporting.

Reserves may be attributed to either natural energy or improved recovery methods. Improved recovery methods include all methods for supplementing natural energy or altering natural forces in the reservoir to increase ultimate recovery. Examples of such methods are pressure maintenance, cycling, waterflooding, thermal methods, chemical flooding, and the use of miscible and immiscible displacement fluids. Other improved recovery methods may be developed in the future as petroleum technology continues to evolve.

Proved Reserves. Proved reserves are those quantities of petroleum which, by analysis of geological and engineering data, can be estimated with reasonable certainty to be commercially recoverable, from a given date forward, from known reservoirs and under current economic conditions, operating methods, and government regulations. Proved reserves can be categorized as developed or undeveloped.

If deterministic methods are used, the term reasonable certainty is intended to express a high degree of confidence that the quantities will be recovered. If probabilistic methods are used, there should be at least a 90% probability that the quantities actually recovered will equal or exceed the estimate.

Establishment of current economic conditions should include relevant historical petroleum prices and associated costs and may involve an averaging period that is consistent with the purpose of the reserves estimate, appropriate contract obligations, corporate procedures, and government regulations involved in reporting these reserves.

In general, reserves are considered proved if the commercial producibility of the reservoir is supported by actual production or formation tests. In this context, the term "proved" refers to the actual quantities of petroleum reserves and not just the productivity of the well or reservoir. In certain cases, proved reserves may be assigned on the basis of well logs and/or core analysis that indicate the subject reservoir is hydrocarbon-bearing and is analogous to reservoirs in the same area that are producing or have demonstrated the ability to produce on formation tests.

The area of the reservoir considered as proved includes (1) the area delineated by drilling and defined by fluid contacts, if any, and (2) the undrilled portions of the reservoir that can reasonably be judged as commercially productive on the basis of available geological and engineering data. In the absence of data on fluid contacts, the lowest known occurrence of hydrocarbons controls the proved limit unless otherwise indicated by definitive geological, engineering, or performance data.

Reserves may be classified as proved if facilities to process and transport those reserves to market are operational at the time of the estimate or there is a reasonable expectation that such facilities will be installed. Reserves in undeveloped locations may be classified as proved undeveloped provided (1) the locations are direct offsets to wells that have indicated commercial production in the objective formation, (2) it is reasonably certain such locations are within the known proved productive limits of the objective formation, (3) the locations conform to existing well spacing regulations where applicable, and (4) it is reasonably certain the locations will be developed. Reserves from other locations are classified as proved undeveloped only where interpretations of geological and engineering data from wells indicate with reasonable certainty that the objective formation is laterally continuous and contains commercially recoverable petroleum at locations beyond direct offsets.

Reserves that are to be produced through the application of established improved recovery methods are included in the proved classification when (1) successful testing by a pilot project or favorable response of an installed program in the same or an analogous reservoir with similar rock and fluid properties provides support for the analysis on which the project was based, and (2) it is reasonably certain that the project will proceed. Reserves to be recovered by improved recovery methods that have yet to be established through commercially successful applications are included in the proved classification only (1) after a favorable production response from the subject reservoir from either (a) a representative pilot or (b) an installed program where the response provides support for the analysis on which the project is based and (2) it is reasonably certain the project will proceed.

Unproved Reserves. Unproved reserves are based on geologic and/or engineering data similar to those used in estimates of proved reserves; but technical, contractual, economic, or regulatory uncertainties preclude such reserves being classified as proved. Unproved reserves may be further classified as probable reserves and possible reserves.

Unproved reserves may be estimated assuming future economic conditions different from those prevailing at the time of the estimate. The effect of possible future improvements in economic conditions and technological developments can be expressed by allocating appropriate quantities of reserves to the probable and possible classifications.

Probable Reserves. Probable reserves are those unproved reserves which analysis of geological and engineering data suggests are more likely than not to be recoverable. In this context, when probabilistic methods are used, there should be at least a 50% probability that the quantities actually recovered will equal or exceed the sum of estimated proved plus probable reserves.

In general, probable reserves may include (1) reserves anticipated to be proved by normal step-out drilling where subsurface control is inadequate to classify these reserves as proved, (2) reserves in formations that appear to be productive based on well log characteristics but lack core data or definitive tests and which are not analogous to producing or proved reserves in the area, (3) incremental reserves attributable to infill drilling that could have been classified as proved if closer statutory spacing had been approved at the time of the estimate, (4) reserves attributable to improved recovery methods that have been established by repeated commercially successful applications when (a) a project or pilot is planned but not in operation and (b) rock, fluid, and reservoir characteristics appear favorable for commercial application, (5) reserves in an area of the formation that appears to be separated from the proved area by faulting and the geologic interpretation indicates the subject area is structurally higher than the proved area, (6) reserves attributable to a future workover, treatment, retreatment, change of equipment, or other mechanical procedures, where such procedure has not been proved successful in wells which exhibit similar behavior in analogous reservoirs, and (7) incremental reserves in proved reservoirs where an alternative interpretation of performance or volumetric data indicates more reserves than can be classified as proved.

Possible Reserves. Possible reserves are those unproved reserves which analysis of geological and engineering data suggests are less likely to be recoverable than probable reserves. In this context, when probabilistic methods are used, there should be at least a 10% probability that the quantities actually recovered will equal or exceed the sum of estimated proved plus probable plus possible reserves.

In general, possible reserves may include (1) reserves which, based on geological interpretations, could possibly exist beyond areas classified as probable, (2) reserves in formations that appear to be petroleum-bearing based on log and core analysis but may not be productive at commercial rates, (3) incremental reserves attributed to infill drilling that are subject to technical uncertainty, (4) reserves attributed to improved recovery methods when (a) a project or pilot is planned but not in operation and (b) rock, fluid, and reservoir characteristics are such that a reasonable doubt exists that the project will be commercial, and (5) reserves in an area of the formation that appears to be separated from the proved area by faulting and geological interpretation indicates the subject area is structurally lower than the proved area.

Reserves Status Categories. Reserves status categories define the development and producing status of wells and reservoirs.

Developed Reserves. Developed reserves are expected to be recovered from existing wells including reserves behind pipe. Improved recovery reserves are considered developed only after the necessary equipment has been installed, or when the costs to do so are relatively minor. Developed reserves may be subcategorized as producing or nonproducing.

Producing. Reserves subcategorized as producing are expected to be recovered from completion intervals that are open and producing at the time of the estimate. Improved recovery reserves are considered producing only after the improved recovery project is in operation.

Nonproducing. Reserves subcategorized as nonproducing include shut-in and behind-pipe reserves. Shut-in reserves are expected to be recovered from (1) completion intervals that are open at the time of the estimate but that have not started producing, (2) wells which were shut in for market conditions or pipeline connections or (3) wells not capable of production for mechanical reasons. Behind-pipe reserves are expected to be recovered from zones in existing wells that will require additional completion work or future recompletion prior to the start of production.

Undeveloped Reserves. Undeveloped reserves are expected to be recovered (1) from new wells on undrilled acreage, (2) from deepening existing wells to a different reservoir, or (3) where a relatively large expenditure is required to (a) recomplete an existing well or (b) install production or transportation facilities for primary or improved recovery projects.

The 1997 SPE/WPC definitions quoted above evolved over many years through the efforts of several organizations. The Soc. of Petroleum Evaluation Engineers (SPEE) contributed significantly to the 1981 and 1987 SPE Petroleum Reserves definitions. The 1981 definitions refer only to proved reserves; the 1987 definitions introduce the concept of unproved reserves and the subclassifications of probable and possible reserves.

The 1997 SPE/WPC definitions recognize both the deterministic and probabilistic methods and establish relative standards for each. The SPE and the WPC continue to work together to improve these definitions in light of several unresolved ambiguities. Such ambiguities include reconciliation of the terms "reasonable certainty" and "at least a 90% probability" used to describe proved reserves. For deterministic estimates, quantities for each of the three reserves categories of proved, probable, and possible are estimated, and the evaluator is cautioned not to add these quantities together because of the differing degrees of uncertainty associated with each. Conversely, the probabilistic approach requires the addition of "proved plus probable" or "proved plus probable plus possible" categories to comply with the stated numerical levels of uncertainty. Further, definitions place certain specified limitations on the "lowest known occurrence of hydrocarbons," average prices, and conformance to regulatory well spacing (where applicable), thus reducing the variables that are subject to classic probabilistic reserves assessment.

* Definitions here are quoted from SPE/WPC Petroleum Reserves Definitions. Cronquist has provided comments regarding interpretation of some of the terms used in these definitions. New definitions were approved in 2007.

1978 U.S. Securities and Exchange Commission (SEC) Oil and Gas Reserves Definitions

The U.S. SEC Regulation S X Rule 4 10 paragraph (a) defines proved reserves as follows: *

Proved Oil and Gas Reserves. Proved oil and gas reserves are the estimated quantities of crude oil, natural gas, and natural gas liquids which geological and engineering data demonstrate with reasonable certainty to be recoverable in future years from known reservoirs under existing economic and operating conditions; i.e., prices and costs as of the date the estimate is made. Prices include consideration of changes in existing prices provided only by contractual arrangements, but not on escalations based upon future conditions.

1. Reservoirs are considered proved if economic producibility is supported by either actual production or conclusive formation test. The area of a reservoir considered proved includes:

   (A) that portion delineated by drilling and defined by gas/oil and/or oil/water contacts, if any; and

   (B) the immediately adjoining portions not yet drilled, but which can be reasonably judged as economically productive on the basis of available geological and engineering data. In the absence of information on fluid contacts, the lowest known structural occurrence of hydrocarbons controls the lower proved limit of the reservoir.

2. Reserves which can be produced economically through application of improved recovery techniques (such as fluid injection) are included in the "proved" classification when successful testing by a pilot project, or the operation of an installed program in the reservoir, provides support for the engineering analysis on which the project or program was based.
3. Estimates of proved reserves do not include the following:

   (A) oil that may become available from known reservoirs but is classified separately as "indicated additional reserves";

   (B) crude oil, natural gas, and natural gas liquids, the recovery of which is subject to reasonable doubt because of uncertainty as to geology, reservoir characteristics, or economic factors;

   (C) crude oil, natural gas, and natural gas liquids, that may occur in undrilled prospects; and

   (D) crude oil, natural gas, and natural gas liquids, that may be recovered from oil shales, coal,^† gilsonite and other such sources.

Proved Developed Oil and Gas Reserves. Proved developed oil and gas reserves are reserves that can be expected to be recovered through existing wells with existing equipment and operating methods. Additional oil and gas expected to be obtained through the application of fluid injection or other improved recovery techniques for supplementing the natural forces and mechanisms of primary recovery should be included as "proved developed reserves" only after testing by a pilot project or after the operation of an installed program has confirmed through production response that increased recovery will be achieved.

Proved Undeveloped Oil and Gas Reserves. Proved undeveloped oil and gas reserves are reserves that are expected to be recovered from new wells on undrilled acreage, or from existing wells where a relatively major expenditure is required for recompletion. Reserves on undrilled acreage shall be limited to those drilling units offsetting productive units that are reasonably certain of production when drilled. Proved reserves for other undrilled units can be claimed only where it can be demonstrated with certainty that there is continuity of production from the existing productive formation. Under no circumstances should estimates for proved undeveloped reserves be attributable to any acreage for which an application of fluid injection or other improved recovery technique is contemplated, unless such techniques have been proved effective by actual tests in the area and in the same reservoir.

* Subsection formatting in this section follows that of the SEC. †SAB12, following, modifies this ruling.

U.S. SEC Staff Accounting Bulletins (SABs)

Certain SABs published after Regulation S X concern the application of financial accounting and disclosure rules for oil and gas producing activities. In particular, the following interpretations extracted from a recent SEC compilation of SABs set forth the Commission staff’s view on specific questions pertaining to proved oil and gas reserves:

Economic producibility of estimated proved reserves can be supported to the satisfaction of the Office of Engineering if geological and engineering data demonstrate with reasonable certainty that those reserves can be recovered in future years under existing economic and operating conditions. The relative importance of the many pieces of geological and engineering data which should be evaluated when classifying reserves cannot be identified in advance. In certain instances, proved reserves may be assigned to reservoirs on the basis of a combination of electrical and other type logs and core analyses which indicate the reservoirs are analogous to similar reservoirs in the same field which are producing or have demonstrated the ability to produce on a formation test.

In determining whether "proved undeveloped reserves" encompass acreage on which fluid injection (or other improved recovery technique) is contemplated, is it appropriate to distinguish between (i) fluid injection used for pressure maintenance during the early life of a field and (ii) fluid injection used to effect secondary recovery when a field is in the late stages of depletion? The Office of Engineering believes that the distinction identified in the above question may be appropriate in a few limited circumstances, such as in the case of certain fields in the North Sea. The staff will review estimates of proved reserves attributable to fluid injection in the light of the strength of the evidence presented by the registrant in support of a contention that enhanced recovery will be achieved.

Companies should report reserves of natural gas liquids which are net to their leasehold interest; i.e., that portion recovered in a processing plant and allocated to the leasehold interest. It may be appropriate in the case of natural gas liquids not clearly attributable to leasehold interests ownership to follow instruction (b) of Item 2(b)(3) of Regulation S K and report such reserves separately and describe the nature of the ownership.

The staff believes that since coalbed methane gas can be recovered from coal in its natural and original location, it should be included in proved reserves, provided that it complies in all other respects with the definition of proved oil and gas reserves as specified in Rule 4 10(a)(2) including the requirement that methane production be economical at current prices, costs, (net of the tax credit) and existing operating conditions.

SAB statements are not rules or interpretations of the Commission, nor are they published as bearing the Commission’s official approval. They represent interpretations and practices followed by the U.S. SEC’s Div. of Corporation Finance and Office of the Chief Accountant in administering the disclosure requirements of the U.S. securities laws.

Unproved Oil and Gas Reserves

U.S. SEC Regulation S K prohibits the disclosure of estimated quantities of probable and possible reserves of oil and gas and any estimated value thereof in any documents publicly filed with the Commission.

Website Release

In a 21 February 2001 website release, the U.S. SEC addressed several topics relative to the reporting of proved reserves. No changes were made to the 1978 definitions, but the U.S. SEC engineering staff modified its application and interpretation of those definitions in light of the widespread technological advances in over the previous 20 years. The most significant of these application changes are discussed below.

Significance of the 1997 SPE/WPC and the 1978 U.S. SEC Reserves Definitions

The 1997 SPE/WPC definitions have been proposed as the technical standards for the international petroleum industry. Regulatory authorities worldwide have been encouraged to use these definitions as much they reasonably can for their specific purposes.

When the U.S. SEC definitions were approved (1978), virtually all regulated companies were in the U.S.A. and most reported reserves were located in North America, neither of which is now the case. Also, virtually all natural gas then was sold through long-term contracts with a defined pricing structure. Oil prices were less volatile then, compared with price swings seen over the past 10 to 15 years. Privatization of numerous national or state-owned oil and gas companies, with the sale of their securities within the U.S.A., has greatly enlarged the effective reach and importance of the U.S. SEC. The U.S. SEC’s petroleum-engineering staff has been increased in recent years to enable the agency to monitor more effectively the reserves-reporting activities of an increasing number of oil and gas companies subject to the jurisdiction of the agency.

1997 SPE/WPC and 1978 U.S. SEC Definitions Comparison

Reasonable Certainty. The SPE/WPC and the U.S. SEC definitions both use "reasonable certainty" to describe the controlling condition for proved reserves, but neither offers quantification of the term. Most engineers now accept that reasonable certainty indicates relatively high confidence. The 1997 SPE/WPC definitions require that for proved reserves estimated using probabilistic methods there be at least 90% probability (a "P90" estimate) that the quantity recovered will equal or exceed the estimated quantity. At least 50% probability (a "P50" estimate) is required for proved plus probable reserves estimated using probabilistic methods.

Proved reserves estimated using deterministic methods seldom, if ever, will meet a P90 requirement. Most volumetric estimates use average porosity, average water saturation, and recovery efficiencies (REs) that are consistent with expected reservoir drive mechanisms and operating conditions.

If an oil/water contact (OWC) or gas/water contact (GWC) is known, the resultant volumetric reserves estimate logically may be described as the "most likely" estimate, which might approach a P50 (probabilistic) estimate. For another example, when using a conservative RE because of an unknown drive mechanism and a lowest known limit of oil (LKO) or gas (LKG), the equivalent confidence level may be between P50 and P90.

For performance estimates using trend analysis, the engineer typically will extrapolate a "best fit" from the historical information, which essentially reflects a P50 estimate. 3 Extrapolations could be prepared for P90, P50, and P10 estimates, but this seldom is done.

In summary, reasonable certainty for deterministic estimates will represent confidence levels approaching P50 in most instances, but will seldom approach the P90 level as defined in the 1997 SPE/WPC definitions.

Known Accumulations. The 1997 SPE/WPC definitions use the term known accumulations, which the U.S. SEC definitions refer to as known reservoirs. In the industry, a known accumulation is an underground collection of moveable petroleum—one or more reservoirs confirmed through the drilling and gathering of reservoir data from one or more wells. A known accumulation must be considered commercial before reserves of any classification may be assigned.

Economic Conditions. The U.S. SEC definitions specify that proved reserves are to be reported consistent with "existing economic and operating conditions; i.e., prices and costs as of the date the estimate is made." This is intended to be the contract price for the sale of oil and gas as of the report date, which typically is 31 December. For products sold in a spot market, the pricing available on the report date should be used. Operating costs typically are costs averaged over the preceding 12 months, unless a change material to the estimate has occurred during the preceding 6 months. In the estimation of proved reserves, the 1997 SPE/WPC definitions allow the use of a historical oil and gas price averaged over a time period that is "consistent with the purpose of the estimate."

According to the 1997 SPE/WPC definitions, probable and possible reserves also must be considered commercial before they can be classified, but they may be based on more favorable economic conditions than those existing at the effective date of the estimate.

Development Status. The U.S. SEC continues to enforce the 1978 definitions regarding undeveloped well locations, requiring that the proved classification be given only to those locations beyond one offset from a productive well where "it can be demonstrated with certainty that there is continuity of production" [emphasis added] from the existing productive formation. A subsequent clarification released by the U.S. SEC in 2001 stated that "there is no mitigating modifier for the word certainty."

These provisions are troublesome in at least three regards. First, the term "offset" refers to regulatory-controlled well spacing in North America and to few areas, if any, elsewhere. Second, and more importantly, the term "certainty" is used here by the U.S. SEC to describe undeveloped reserves, whereas the controlling term in the first sentence of the U.S. SEC definitions is "reasonable certainty." Third, the expression "continuity of production" is undefined, but is used in a context of a higher standard than reservoir continuity.

The 1997 SPE/WPC definitions leave the classification of reserves from undrilled locations to the discretion of the evaluator using good engineering practices.

Requirement for Flow Testing. Both the U.S. SEC definitions and the 1997 SPE/WPC definitions require evidence of producibility through actual production or conclusive formation tests. Both definitions also permit exceptions in certain cases. The U.S. SEC may grant an exception for a definitive flow test for a particular reservoir if core and log data indicate commercial productivity and the reservoir is analogous to one or more flow-tested or producing reservoir(s) in the same field. The 1997 SPE/WPC definitions have a similar but less restrictive flow-test exemption that requires favorable core and/or log data for the subject reservoir compared to an analogous reservoir(s) in the same area that has demonstrated commercial productivity.

There is increasing interest by evaluators using both the U.S. SEC and the 1997 SPE/WPC reserves definitions in certain instances, particularly for the deepwater areas of the U.S. Gulf of Mexico, where physical well testing is impractical because of costs and environmental concerns. Many of these discoveries are not close to other fields, but may be characterized by thick sections of highly permeable sandstones saturated with high-API-gravity, low-viscosity crudes and exhibiting reservoir pressures in excess of 8,000 psia. In such scenarios, flow calculations can confirm production rates that are considerably higher than the minimum commercial rates, and are adequate for producers to make commercial decisions about facility sizing and project sanctioning. The evaluator determines on a case-specific basis whether such indirect data are adequate to confirm commercial flow rates (without a physical flow test) in consideration of the applicable definitions.

Areal Extent of a Reservoir. The U.S. SEC definitions mandate the use of a recognized OWC, gas/oil contact (GOC), and GWC to define structural limits of proved reserves. In the absence of such contacts, limits are imposed by the LKO or LKG, which typically are defined as the subsea depth of the base of the (permeable) reservoir, as recorded on well logs. Only in recent years has the U.S. SEC begun to consider indirect measurements or calculations of controlling contacts. The U.S. SEC’s acceptance of indirect indicators such as pressure/depth calculations, seismic information, pressure-gradient calculations, and capillary-pressure computations has been only in exceptional cases in which the quality of the data was excellent and the presentation of the interpretation was compelling. In their acceptance of a limiting contact below the base of the lowest logged interval, the U.S. SEC engineering staff may further consider the materiality of the quantity of reserves added through the use of pressure-gradient data. They provide no definition of materiality. Also, agreement between two or more indirect measurements would be required as the basis for establishing proved reserves. Such agreement also applies to 1997 SPE/WPC definitions.

Enhanced-Recovery Reserves. The U.S. SEC traditionally has required that the proved designation be limited to reservoirs where enhanced-recovery (improved-recovery) methods have been demonstrated through a successful pilot project or an installed program "in the reservoir." This requirement was reinterpreted in 2001 to allow successful, operating analog reservoirs in the same geologic area to be used as support for assigning proved enhanced-recovery reserves. The subject reservoir should have reservoir and fluid parameters that are equal to or more favorable than those of the analog reservoir(s). The 1997 SPE/WPC definitions also permit the use of successful analogs in the area as the basis for establishing proved enhanced-recovery reserves.

Other Differences. The 1997 SPE/WPC and 1978 U.S. SEC definitions contain many other wording differences regarding proved reserves, but those cited above are of major importance. For questions of interpretation or application, however, the U.S. SEC typically will respond to inquiries by interested parties.

Other Reserves Definitions

Other petroleum-producing countries and regulatory authorities have promulgated petroleum reserves definitions that are recognized and based on years of development and sound engineering judgment, but none—however important in their sphere of influence—with such far-reaching consequences as the 1978 U.S. SEC and the 1997 SPE/WPC definitions. (See Cronquist for a summary of many of these other definitions.)

Calculation Procedures

Although reserves estimates for known accumulations historically have used deterministic calculation procedures, the 1997 SPE/WPC definitions allow either deterministic or probabilistic procedures. Each of these is discussed briefly in the next two sections. Thereafter—except for another section on probabilistic procedures near the end—the chapter will focus on deterministic procedures because they still are more widely used. Both procedures need the same basic data and equations.

Deterministic Procedures

Deterministic calculations of oil and/or gas initially in place (O/GIP) and reserves are based on best estimates of the true values of pertinent parameters, although it is recognized that there may be considerable uncertainty in such values. Reserves calculated using such procedures are classified subjectively on the basis of professional judgments of the uncertainty in each reserve estimate and/or of pertinent regulatory and/or corporate guidelines.

Probabilistic Procedures

Probabilistic procedures recognize that uncertainties in input data and equations to calculate reserves may be significant. Accordingly, each input parameter uses a reasonable range of values, from which a set of reserves calculations is made. Reserves calculated using this procedure are classified on the basis of specified percentile rankings of reserves estimates within the calculated set and/or of pertinent regulatory and/or corporate guidelines.

Estimation Methods

Methods to estimate reserves may be categorized as either static or dynamic. Static methods typically are used before production is initiated in a subject reservoir, and include analogy methods and volumetric methods. Computer simulation that is used before production initiation is considered a static method. Dynamic methods might be used after sustained production has been initiated, and include production trend analysis, material-balance calculations, and computer simulation. Because dynamic methods typically consider well and/or reservoir performance, they generally are considered more reliable than static methods. A specific reserves estimate might involve one or more such methods. What method (or methods) are used depends on several factors, including production history of the area, if any; stage of development on the date of the estimate; geologic complexity; quality and quantity of data; maturity of production for the subject reservoir; and the purpose of the estimate. Each estimate should be corroborated using an alternate, preferably independent, method.

Analogy Methods

Analogy methods typically are used to estimate ultimate recovery—or unit recovery factors—of oil and/or gas for undrilled locations and to supplement volumetric methods of estimating reserves in the early stages of development and production. The analogy method assumes that the analogous reservoir or well is comparable to the subject reservoir or well in those aspects that control ultimate recovery of oil and/or gas. The method’s weakness is that this assumption’s validity cannot be determined until the subject reservoir or well has been produced long enough to estimate reserves using dynamic methods.

In some scenarios, analogy may be the only feasible method until there are sufficient pressure and/or production data for a reliable analysis of performance. Such scenarios include areas of widely spaced development, where subsurface information might be too sparse to facilitate reliable volumetric mapping, and reservoirs where log, core, and/or test data are insufficient for reliable characterization.

There are two broad categories of analogy methods: analytical and statistical. Regardless of the method used, however, analogous and subject reservoirs should be similar in their structural configuration; lithology and depositional environment of the reservoir rock; nature and degree of principal heterogeneity; average net thickness and ratio of net pay to gross pay; petrophysics of the rock/fluid system; initial pressure and temperature; reservoir-fluid properties and drive mechanism; spatial relationship between free gas (if any), oil, and aquifer at initial conditions ("stacked" vs. "en echelon"); well spacing; and economic scenario. Because all these reservoir aspects seldom, if ever, are similar, judicious compensating adjustments from analogous to subject reservoir usually are needed. Such adjustments require considerable local knowledge and reservoir engineering experience.

Analytical (analogy) methods include using recovery factors (e.g., STBO/acre-ft of reservoir) or recovery efficiencies (percent recovery) from analogous reservoirs to estimate oil and/or gas reserves for wells or reservoirs being studied. Basic rock and/or fluid parameters—porosity, water saturation, and formation volume factor (FVF)—may be used with, or as modifiers to, these recovery factors or recovery efficiencies. For example, the recovery factor observed in an analogous reservoir (F_RA) might be adjusted by:

....................(18.1)

where the terms (ФS_hi)_S and (ФS_hi)_A refer to subject and analogous reservoirs, respectively.

Depending on circumstances, more complex relations might be appropriate, such as one or more of the factorial groups in Eqs. 18.14 and 18.15, which are discussed in the Recovery Efficiency section below.

In many areas, estimates of rock properties—porosity, initial water saturation, and net pay—made from wireline logs are subject to considerable uncertainty. Without core data or definitive formation tests, analogy may be the only method available initially to estimate reserves. Analogies can be drawn from mature reservoirs in comparable geologic and engineering settings. Several examples are provided for mature areas in the U.S.A.

Using American Petroleum Institute (API) data, aggregate REs were estimated for groups of oil reservoirs in various regions in the U.S.A. (Table 18.1). (Comparable data on natural gas reservoirs in the U.S.A. have not been published.) From Table 18.1, one might note (1) for northern and southern Louisiana, for example, the respective influence of lithology and drive mechanism on RE; (2) for Oklahoma and Pennsylvania, for example, the significant difference in waterflood (ultimate) RE, which probably results from the Pennsylvania waterfloods’ significantly poorer rock quality; (3) for southern Louisiana and the Texas Gulf Coast, for example, the reasonable agreement in waterdrive RE. The slightly higher-quality sands in the Louisiana Gulf Coast probably cause small differences.

• 

  Table 18.1

From a review of these (admittedly limited) data, it appears that variations in aggregate oil RE between regions are attributable principally to differences in reservoir rock/fluid systems and reservoir drive mechanisms. SPEE has published additional, useful summary discussions of regional variations in rock quality and reservoir drive mechanism for various areas in the U.S.A.

In 1984, the API published estimates of oil initially in place (OIP) and primary RE for 533 reservoirs in the U.S.A. and estimates of primary and waterflood RE for 230 reservoirs in the U.S.A. (Table 18.2). Estimates such as these can be developed for other areas using detailed data published annually by most U.S.A. state oil and gas regulatory commissions, the Alberta Energy Resource Conservation Board (ERCB) [which since 1995 has been part of the Alberta Energy and Utilities Board (EUB)], the Saskatchewan Dept. of Energy and Mines, various regional geological societies, and other such agencies. This type of regional data might be useful in making preliminary estimates of reserves, pending development of specific data for the well/reservoir in question.

• 

  Table 18.2

Information presented in Tables 18.1 and 18.2 is included only as reference information and should be considered only in the absence of definitive data available from specific wells or reservoirs.

Statistical (analogy) methods include using per-well recoveries of oil and/or gas from analogous wells in the same producing trend or in analogous geologic settings to estimate recoveries from wells being studied. Two types of statistical (analogy) methods are discussed here: isoultimate recovery maps and analysis of observed frequency distributions of ultimate recovery. Additional comments are provided in the Recovery Efficiency section below.

When analogy methods are used to estimate reserves for individual wells, the analogous and subject wells should be similar regarding well completion, including stimulation type (if any); production method; initial absolute open-flow potential for gas wells; initial potential and/or productivity index for oil wells; well spacing; and economic limit.

In some producing areas, ultimate recovery of oil or gas from individual wells may be controlled by geologic trends such as depositional environment, intensity of fracturing, or degree of diagenesis. In such cases, an isoultimate recovery map can be made by posting and contouring estimated ultimate recovery from individual wells in the area of interest. Such a map can be used to estimate reserves for undrilled tracts, but one should use this technique cautiously! Nongeologic factors might control ultimate recovery of oil or gas.

Different completion and stimulation procedures may yield different ultimate recoveries from individual wells. For example, for wells in several areas of the U.S.A., a correlation has been observed between size of fracture treatment and ultimate recovery. Thus, before relying on isoultimate recovery maps, one should determine whether there is a statistically valid relation between ultimate recovery and the completion or stimulation method or another parameter. Wells in the area of interest may be capable of draining more than a "spacing unit." In this case, wells that are adjacent to undrilled tracts and those placed on production early in reservoir life may exhibit higher ultimate recoveries than wells in central locations and those placed on production late in reservoir life. One should investigate these possibilities before using an isoultimate recovery map to estimate reserves for undrilled tracts.

An alternative to isoultimate recovery maps is the use of "bubble maps," in which the size of the circle drawn around a wellbore is proportional to the parameter or measurement being compared.

Factors such as well spacing, completion technique, operating cost, and operating procedure can affect ultimate recovery of oil and/or gas significantly. If there are significant differences in these factors from one property to the next, be careful in making comparisons or statistical analyses of wells between such properties.

If other factors are more or less the same, the RE of oil and/or gas generally will be greater in areas with low operating costs and closely spaced wells than in areas with high operating costs and widely spaced wells. Most statistical data on RE in the U.S.A. have come from operations with onshore properties, which historically have had relatively low operating costs and closely spaced wells. These are not typical conditions in other areas of the world, especially offshore areas; thus, one should exercise caution when using REs determined from U.S.A. reservoirs to estimate REs from otherwise analogous reservoirs elsewhere.

Volumetric Methods

Volumetric methods to estimate reserves generally are used early in the life of a reservoir, before there are sufficient production and/or pressure data to use the performance method, and for behind-pipe zones, which might not be placed on production until the current completion zone is abandoned. Although volumetric methods are the most widely used methods for estimating reserves, results from their use might be subject to considerable uncertainty, depending on the geologic setting and the amount and quality of geologic and engineering data. Thus, it is recommended that an evaluator compare reserves estimated by volumetric methods against well and reservoir performance at the earliest practical stage of production and make adjustments as warranted.

Volumetric methods for estimating reserves involve three steps:

1. Use volumetric mapping or another procedure to determine net volume of the reservoir.
2. Determine rock/fluid parameters to calculate unit volumes of oil, gas, and/or condensate initially in place (O/G/CIP).
3. Estimate REs for oil, gas, and/or condensate. Step 1 may involve the use of gross-rock-volume isopach maps and a net-to-gross net-pay ratio to obtain the net volume of the reservoir.

For oil reservoirs, initial reserves of oil and solution gas can be calculated using Eq. 18.2. and Eq. 18.4, respectively. (Remember, however, that all calculations of reserves must be considered estimates, and are accurate to no more than two significant figures.)

....................(18.2)

where 7,758 = bbl/acre-ft (but if units in Eqs. 18.2 and 18.3 are ha and m, this constant becomes 1.0).

For analyses where A_oh_no is determined from planimetry of isopach maps:

....................(18.3)

Eq. 18.3 assumes a gross-pay isopach and would be modified for a net-pay isopach by setting R_ngo = 1.

Initial reserves of solution gas can be calculated by:

....................(18.4)

For gas reservoirs—either gas caps or nonassociated gas—initial gas and condensate reserves can be calculated by:

....................(18.5)

and

....................(18.6)

where 43,560 = ft³/acre-ft (but if units in Eq. 18.5 are ha and m, this constant becomes 1.0). Gas initially in place (GIP) may, alternatively, be calculated with an equation analogous to Eq. 18.3.

Reservoir Maps. Most volumetric methods begin with determining the bulk reservoir volume that contains hydrocarbons. This usually involves preparing structure maps of the top and base of the reservoir and an isopach map of the reservoir. The reliability of results derived from the construction of reservoir maps is directly related to the geologic complexity of the reservoir, the number of wells drilled, the quality and extent of seismic data, information gathered through the drilling and completion of wells, and the evaluator’s ability to accurately integrate all data into such maps.

Structure maps should be clearly marked to indicate reservoir limits related to faulting, fluid contacts, and/or facies changes, as well as to indicate all wellbores that penetrate the subject formation. The location of relevant seismic lines and shot points should be shown on all reservoir maps. Subsea depths (ft or m) typically are used to represent formation depths and fluid contacts. Structure maps prepared by explorationists often relate more to structural "markers" or log features that are recognizable over large areas. These lithological interval "tops" may be used to better define structural influences that may control hydrocarbon trapping forces and depositional trends; however, the reserves geologist should prepare reservoir structure maps that describe the top (and sometimes the base) of the reservoir interval in the mapped formation. Both logs and core data can be used in defining the mapped interval. Contouring may be hand drawn or accomplished using geologic mapping software.

The construction of isopach maps should incorporate the same level of detail as do structure maps, as described above. Net pay should be clearly marked for each well penetration. Failure to calculate gross reservoir volumes properly can lead to serious errors in the preparation of reservoir development plans, unwise expenditure of capital budget amounts, and seriously distorted estimates of reserves. Some of these concerns are discussed further in the Pitfalls section of this chapter.

Net Pay. Estimating net pay is one of the most important steps in volumetric mapping, but unfortunately, it also is one of its most subjective steps. Among the factors that influence it are the amount and quality of log, core, and test data; the nature of the rock/fluid system; and the anticipated drive/recovery mechanism. In the following discussion, the term "net pay" refers to "true vertical net pay"—logged net pay thickness that is corrected for borehole inclination and formation dip. [The correction procedure assumes that volumetric mapping is based on vertical projection of dipping formations onto a horizontal (mapping) plane. For steeply dipping formations, kh so derived must be corrected for calculations of fluid flow parallel to the formation bedding surface.]

Net pay in a given reservoir might be determined for different purposes, for each of which the procedure and results might be different. For example:

• In an initial well-log evaluation to determine whether to run production casing and attempt a completion, net pay typically includes only intervals that are judged likely to contribute to well inflow at commercial rates. The log analyst might estimate net pay conservatively to minimize the monetary risk of a subcommercial completion.
• When evaluating a reservoir to determine total hydrocarbons in place (e.g., as an independent check on material-balance calculations), net pay usually includes all hydrocarbon-bearing intervals that are likely to contribute to the "energy balance." Net pay for this purpose generally will be more than that estimated during initial completion.
• When considering a waterflood, net pay should include only intervals considered "floodable," a criterion that implies interwell continuity. Also, the methods used to define floodable intervals are subjective and may exclude intervals that will contribute to recovery by imbibition. Net pay for waterflooding might be less than for initial well-log evaluation or for determining total hydrocarbons in place.
• If a reservoir is to be unitized and net pay is part of the unitization formula, the determination of net pay may be subject to arbitrary rules to ensure "uniformity," which might require determination of net pay that is unrelated to the considerations above.

To facilitate visualization of pertinent data, prepare composite logs for all wells in the reservoir that is under study. Regional and individual variations are expected, but generally the two steps are:

1. Determine "gross interval" by establishing the top and bottom of the zone of interest. In sand/shale sequences, the inflection points of the spontaneous, or self, potential or the gamma ray curves usually are considered zone boundaries. For carbonates, establishing the zone boundaries might involve using one or more of the porosity curves to establish a minimum porosity (porosity cutoff) or using a combination of logs to determine lithologic top and bottom. (Choice of minimum porosity typically is quite subjective and is related to the minimum permeability that is considered productive in the area, which depends on petrophysics, reservoir fluid, and drive mechanism.)
2. Exclude nonpay intervals within the gross interval on the basis of maximum shaliness, minimum porosity, maximum water saturation, specified degree of reversal in either the spontaneous-potential or the gamma ray curve, or a combination of these.

The Petroleum Soc. of the Canadian Inst. of Mining provides a list of "generally accepted (minimum) cutoffs" (Table 18.3). Local cutoff data for other regions are available in sources such as the Schlumberger* Well Evaluation Conference (WEC) publications for various regions (e.g., Venezuela Well Evaluation Conference). Engineers should use published cutoff data only as general guidelines, however, and only when information for a specific reservoir or project is unavailable. There may be circumstances for which no minimum permeability, porosity, and/or saturation cutoffs are appropriate.

• 

  Table 18.3

Historically, the objective of initially estimating net pay has been to determine which intervals in each well zone could be expected to contribute to fluid flow into the wellbore under the anticipated method of well and/or reservoir operation. (This is not a proposed definition of net pay; indeed, there is more than one recognized definition of net pay.). The criteria for determining net pay under primary drive should include fluid mobility (k_e/μ) and pressure differential. Permeability data, however, seldom are available on all wells in a reservoir. Typically, permeability is estimated using correlations between porosity and permeability measured in cores from the subject reservoir, empirical correlations based on global data, low-frequency acoustic log interpretation,** and/or nuclear magnetic resonance (NMR) log response.

In some cases (e.g., shaly, laminated, sand reservoirs and many carbonate reservoirs), it may be difficult, at best, to determine net pay with an acceptable degree of confidence. [For examples of log response in shaly, laminated, sand reservoirs (known as low-resistivity, low-contrast), see publications of the Houston Geological Soc., the New Orleans Geological Soc., and the Rocky Mountain Assn. of Geologists.]

A net-pay isopach made with considerable interpretation uncertainty might have to be revised frequently when interpretive procedures are revised or when new data become available. In this situation, it might be desirable to map gross pay and apply an average net-to-gross ratio to account for nonproductive rock. The net-to-gross ratio can be revised as warranted, thereby avoiding the need to remap the entire reservoir; however, this procedure is not appropriate if there are significant spatial variations in the net-to-gross ratio.

Depending on circumstances, it might be appropriate to classify net pay as proved, probable, or possible to recognize the degree of uncertainty in such estimates and to provide a basis for classifying reserves associated with each estimate. Regardless of the method used to determine net pay, the porosity and water-saturation values used in the volumetric equations (Eqs. 18.2, 18.3, and 18.5) should be consistent with the cutoff values used to determine net pay.

Volumetric-Mapping Example. Figs. 18.3 through 18.6 illustrate several mapping and reserves-classification principles. Fig. 18.3 is a structure map of an oil reservoir along the upthrown side of a west/northwest dipping fault. A well log and core taken in Well 1 indicate that the sandstone section is oil-filled throughout the logged interval, thereby defining the highest known oil (HKO) at 10,500 ft subsea (ss) and LKO at 10,550 ft ss. A flow test indicated commercial rates of oil production. Pressure/volume/temperature (PVT) data indicate that the oil is gas-saturated. It is assumed that three wells (Well 1 and Locations A and B) are needed to effectively drain the oil reservoir, although B is contingent on the geologic interpretation after drilling A.

• 

  Fig. 18.3 – Structure map on top of porosity.

• 

  Fig. 18.4 – Isopach map of total net sand.

• 

  Fig. 18.5 – Isopach of total net (oil) sand.

• 

  Fig. 18.6 – Net oil isopach above HKW.

Although the production test in Well 1 does not indicate so, there is a possibility of a GOC just updip from the top of its logged interval, and of an OWC just below the base of the logged interval. Accordingly, on the basis of available information at the conclusion of the logging and testing of Well 2, only the reservoir volume between 10,500 and 10,550 ft ss can be considered to contain proved reserves—by either the 1978 U.S. SEC or the 1997 SPE/WPC reserves definitions. Conversely, if the crude oil is undersaturated, the volume of the reservoir above the HKO may be considered to be oil-filled. (This proved volume might need to be reduced further because of lateral limitations imposed by optimum well spacing and geological uncertainty. See the later discussion in the Reserves Classifications section in this chapter.)

Fig. 18.4 is a "net sand" isopach of a channel sand, and it is based on an interpretation of the geologic and geophysical data available at the mapping date. This interpretation is supported by regional studies and the 2D seismic lines indicated on the net sand isopach. Note that using mechanically derived contours when contouring the net sand thickness in each of the wellbores would yield an entirely different interpretation, which illustrates the importance of using all available information, including subsurface data, geophysical interpretations, and experiential/analog data from the area.

Fig. 18.5 integrates Figs. 18.3 and 18.4 as a net oil isopach map of the reservoir volume between HKO and LKO, using the spatially correct "Wharton’s method" of contouring the "wedge edges." "Wedging" of the net pay contours northwest of Well 1 and southeast of Well 3 reflects truncation of the net (oil) sand contours on Fig. 18.4 by the fault. Wedging in the crescent-shaped area on the northwest side reflects truncation of HKO by the fault. Wedging on the southeast side reflects loss of structure between HKO and LKO, whereas thinning of the net oil contours to the northeast and southwest reflects thinning of the net (oil) sand.

Fig. 18.6 is an isopach map of the entire reservoir volume that is interpreted to exist above highest known water (HKW) at 10,650 ft ss, as seen in Well 2. By assuming the reservoir volume above HKO at 10,500 ft ss to be oil-filled, rather than (possibly) partially gas-filled, oil reserves in this volume might be considered to be proved plus probable plus possible (3P).

A map similar to Fig. 18.6 could be prepared for a proved-plus-probable (2P) interpretation, using an arbitrary downdip limit of 10,600 ft ss, which is the midpoint between LKO and HKW. If 3D seismic or other data are available to define or otherwise indicate an OWC, an alternate 2P interpretation based on this limit might be appropriate, as discussed on the section on reservoir limits.

Reservoir volumes for the proved case (P1) reserves usually are calculated directly by planimetry of the proved volume defined by an isopach map. Incremental probable (P2) reservoir volumes typically are the result of subtracting P1 volumes from the isopach of 2P volumes. Similarly, incremental possible (P3) reservoir volumes are the result of subtracting the 2P isopach volume from the 3P isopach volume.

It may be appropriate to clarify the terms P1, P2, and P3 at this point and to distinguish these from the seemingly similar terms 1P, 2P, and 3P as most often used in reservoir engineering vernacular. As stated previously, P1, P2, and P3 reflect reserves quantities for the classifications of proved, probable, and possible, respectively. The term 1P is synonymous with P1 as it applies to proved reserves only. The term 2P is a cumulative expression for the sum of proved and probable reserves; the term 3P embraces the sum of proved, probable, and possible reserves.

Seismic information, especially when "calibrated" through comparison to well log information, is especially important when well-control information is sparse and when faulting has not been defined through fault cuts recognized in wellbores. One should be alert to all circumstances in which reservoir extent may be limited by faulting, permeability changes, depositional discontinuities, or any other condition that might interrupt fluid flow. Individual reservoir compartments might be difficult to define without performance information, especially pressure information.

Typically, faults with a throw of less than the thickness of the productive formation are assumed to be nonsealing. Caution! One should not assume this without supporting evidence, which should be evaluated over time by a skilled, experienced engineer.

Isopach maps are designed to determine one or more measures of reservoir volume, and for a single-phase oil reservoir, they might include:

1. Bulk reservoir volume above an observed OWC or LKO. A net-to-gross pay ratio is applied to the bulk reservoir volume to yield net oil reservoir volume.
2. Net reservoir volume determined from the contouring of net oil pay thickness on the basis of log analysis and/or core analysis.
3. Isopore volume maps that reflect the product of net pay and wellbore weighted average porosity, h_nФ.

Oil pore-volume (PV) maps that reflect the product of net pay, porosity, and oil saturation, h_nФ (1-S_w).

For an oil reservoir with a gas cap, similar maps might be prepared, which include:

1. Bulk volume of the reservoir above the GOC, and that between the GOC and the OWC (or LKO), with net-to-gross pay ratios applied separately to the oil and gas portions of the reservoir.
2. Net reservoir volumes from the contouring of net oil and net gas pays on the basis of log and/or core analyses.
3. Isopore volume maps that reflect the product of net oil and net gas pays and wellbore weighted average porosity h_nФ for each of the oil- and gas-filled portions of the reservoir.
4. PV maps of the oil- and gas-saturated portions of the reservoir that reflect the products of net pay, porosity, and oil saturation and of net pay, porosity, and gas saturation, respectively.

In each set of isopach map design objectives, each subsequent objective requires more data and effort to complete. The amount and quality of the available data and the purpose of the reserves estimate are important in determining what type of maps to construct.

For hand-drawn isopach maps, reservoir volumes are calculated using manually operated planimeters. If computer software is used in map preparation, reservoir volumes are generated within that software. All reservoir maps, whether manually or computer-prepared, should be constructed without bias, should be consistent with the geology of the area, and should use sound mathematical and spatial fundamentals.

Computer-Aided Mapping. Many commercial software programs are available to help prepare reservoir maps and calculate ranges and distributions of reservoir parameters. Such programs range from relatively simple, 2D contouring utilities to fully integrated applications that help construct and visualize the complex distribution of various reservoir parameters and attributes in 3D geostatistical models. Few reservoir engineers are trained to use the more complex software to describe the structural and stratigraphic complexities of a reservoir. Similarly, not all geologists and geophysicists are aware of the reservoir engineer’s concerns about the uncertainty of reservoir parameters in absolute terms and in the distribution of these parameters throughout the reservoir model.

For this and other reasons, the reservoir engineer must work closely with the geologists and/or geophysicists who have contributed data and interpretations to the models and have made critical decisions about the construction details. The quality, completeness, and unbiased use of the data are critical to the evaluation team’s ability to make decisions about in-place hydrocarbons, compartmentalization, expected recovery mechanisms, and REs that are consistent with the development and production plan approved for the project. These considerations enable reliable quantification and classification of reserves.

The phrase "computer-aided mapping" firmly conveys that all such programs are useful tools, but cannot substitute for the judgment and experience of their users. All the basic reservoir-mapping principles and reserves definitions must be integrated in all reservoir maps, whether hand-drawn or computer-created.

Areal Assignments. Frequently, available geologic information is inadequate to prepare volumetric maps, especially with discovery wells. In such cases, an estimated productive area may need to be "assigned" to the completion interval and other productive intervals where reserves are attributed. Typically, such areal assignments are used only until adequate geologic or performance data become available.

Initial areal assignments should reflect the expected drainage area for the well and should use all available analogous, geologic, and test information. The product of the expected drainage area or spacing pattern and two-thirds to three-fourths of the apparent wellbore thickness often is used to account for possible reservoir thinning away from the wellbore.

Reservoir Limits. In general, there are two types of reservoir limits, external and internal. External limits define the zero-isopach contour for either oil or free gas. Internal limits may affect the flow of fluids in the reservoir. The following discussion is related to external limits, which usually are major faults and/or fluid/fluid contacts. Internal limits are discussed in a later section.

In the absence of observation through wellbores, several methods might be used to calculate an OWC/GWC, including pressure/depth, 3D seismic mapping, pressure gradients, and capillary pressure. These are listed in order of their commonly recognized degree of reliability, but their true reliability is a direct function of the extent and quality of the data from which the limits are calculated.

Pressure/Depth Method. If there are sufficient accurate subsurface pressure measurements at a series of depths within a given reservoir, such measurements can be used to calculate definitively the depth of a GOC, GWC, and/or an OWC. The principle is illustrated in Figs. 18.7 and 18.8.

• 

  Fig. 18.7 - Structure on top of productive sand (after Dake).

• 

  Fig. 18.8 – BHP vs. depth, illustrating the pressure/depth method for estimating the FWL (after Cronquist).

Fig. 18.7 is a structure map on the top of a productive sand, and it shows the locations of an oil completion (Well B) and a wet well (Well A). Well B encountered commercial oil throughout the logged interval. Well A apparently was in the aquifer. Static bottomhole pressures (BHP), measured in the fluid columns of each well using a wireline formation tester (WLFT), are tabulated in Fig. 18.7.

From linear regression through each data set, a "most likely" free-water level (FWL) is estimated at 6,222 ft ss, which may be used to map proved plus probable oil reserves. This interpretation is based on several considerations:

• The backflow periods during the WLFTs in the oil column were sufficient to reconnect the oil in the filtrate-invaded zone, thereby ensuring valid BHP data.
• The oil gradient calculated from the regression is consistent with the reservoir oil density measured from PVT analysis.
• From available subsurface data, the fault separating the two wells at the eastern end of the structure appears to die out to the southwest, thereby supporting pressure communication between the two wells through the aquifer.
• Regional data support the assumption of constant oil density between LKO and the estimated FWL.

If appropriate, this analysis can be expanded through a probabilistic approach. From the regression results, the upper and lower bounds at 80% confidence can be used to estimate P10 and P90 projections of oil BHP vs. depth, respectively (Fig. 18.9). (At 80% confidence, oil gradients were calculated to range from 0.24 to 0.31 psi/ft, which is considered reasonable in light of other uncertainties in the data. Because the regression coefficient for the aquifer pressures is 0.9999, the projection of aquifer BHP vs. depth was considered error-free.) This analysis leads to a proved OWC at 6,140 ft ss, a most likely OWC at 6,222 ft ss, and a possible OWC at 6,349 ft ss. (Given the low density of the reservoir oil and the high quality of the reservoir rock in this example, the FWL is considered a reasonable approximation to the commercial OWC.) Note that the geologic interpretation (Fig. 18.7) would support an OWC at approximately 6,300 ft ss. Were there a significant disparity between the geologic and engineering interpretations, this analysis would have to be reviewed.

• 

  Fig. 18.9 – BHP vs. depth, including the upper and lower bounds of predictions at 80% confidence and illustrating the pressure depth/method for estimating proved, most likely, and possible FWLs (after Cronquist).

In more general applications of the pressure/depth method, be careful when estimating FWLs and commercial OWCs in cases where the density of the reservoir oil approaches that of the interstitial water in the aquifer, and/or the reservoir rock is of such low quality that there might be a significant vertical distance between the FWL and the 100% water level.

3D Seismic Mapping. The widespread use of 3D seismic methods has increased confidence in the guiding of development drilling and defining of reservoir size and extent, especially in certain geographic locations. One should be cautious in assigning proved reserves to the entire area indicated to be productive, unless there is corroborating support from other measurements and unless such areas can be drained with the anticipated development plan. To classify gas as proved reserves on the basis of the analysis of seismic bright spots or flat spots in a faulted accumulation, Robertson (quoted here) recommends that all the following conditions be met:

1. The flat spot and/or bright spot is clearly visible in the 3D seismic data.
2. The spatial mapping of the flat spot and/or downdip edge of the bright spot fits a structural contour, which usually will be the spill point of the reservoir.
3. A well penetrates the GWC in one fault block of the reservoir, so logs, pressure data, and test data provide a direct and unambiguous tie between the GWC in the well and the seismic flat spot and/or downdip edge of the bright spot; i.e., the borehole proves that there is producible gas, not residual gas, down to the seismic indicators of the GWC.
4. A well in another fault block penetrates the reservoir updip from the GWC.
5. This second well proves gas down to a lowest known depth, and pressure data show that this gas is in communication with the gas in the first fault block.
6. The seismic flat spot and/or downdip edge of the bright spot in the second fault block lies below the lowest known gas in the second well and is spatially continuous with and at the same depth as these seismic indicators in the first fault block.

Robertson further says that "[i]f all these conditions are met, the gas in the second fault block between the lowest known occurrence in the well and the seismic flat spot and/or downdip edge of the bright spot can reasonably be judged to be proved." Authors’ caution! This interpretation might not be accepted within all regulatory jurisdictions.

In exploration, good practice mandates the need for at least one well penetration into a seismic bright spot (amplitude anomaly) to demonstrate commercial producibility before the prospective resources in a pool defined by an amplitude anomaly can be classified as reserves.

There are recognized circumstances in which geophysical interpretations that are made using surveys designed for exploration can be considered reliable in determining reservoir thickness, certain petrophysical parameters, and fluid contacts, but these circumstances are few and currently apply minimally, if at all, to establishing proved reserves quantities. Using 3D surveys for reservoir evaluation increases opportunities for developing confidence in geophysical techniques to help quantify reservoir parameters and limits.

4D seismic analysis—a time sequence of 3D surveys—is an emerging technology that is beginning to be applied more widely to monitor the flow of hydrocarbons in a reservoir. 4D seismic interpretation analysis can benefit the understanding of reservoir compartmentalization and RE, but its greatest application might be in optimized reservoir management.

Pressure-Gradient Method. The pressure-gradient method for calculating a hydrocarbon/water contact is similar to that described in the Pressure/Depth section in this chapter, but it relies on the computation of fluid gradients from fluid analyses, rather than gradients calculated by repeat pressure measurements at different depths in a common reservoir. Extrapolation over a large depth interval will magnify slight errors in computing fluid gradients. Accordingly, one should not use the pressure gradient method to produce definitive results, but rather to provide approximations that will require confirmation by other sources.

The density of reservoir oil at the bubblepoint (lbm/bbl) can be calculated by:

....................(18.7)

Oil density calculated from Eq. 18.7 can be converted to oil gradient (in psi/ft) by multiplying it by 0.00124. For calculations of density and gradient for undersaturated oil, see McCain. Water gradients can be calculated from salinity or other compositional data.

The method discussed here and that in the Pressure Gradient section can be generalized to estimate the depths of 1P, 2P, and 3P GOCs and/or FWLs. The procedure is summarized in Table 18.4 and illustrated by Fig. 18.10.

• 

  Table 18.4

• 

  Fig. 18.10 – Pressure-gradient method (after Cronquist).

Capillary-Pressure Method. The capillary-pressure method to calculate the depth of an OWC or GWC is based on the principle that in a common reservoir the family of capillary-pressure curves for various rock types in the reservoir has a common FWL. The capillary-pressure method involves several equations:

....................(18.8)

....................(18.9)

....................(18.10)

....................(18.11)

and

....................(18.12)

In Eqs. 18.8 through 18.12, the operator ≈ denotes correlations, whereas = is reserved for analytical equations.

The capillary-pressure method has several limitations (discussed later) and involves four steps:

1. For each well log level for which porosity and permeability are known, calculate F_g using Eq. 18.8 and P_dm using Eq. 18.9. [The permeability value k_a in Eqs. 18.8 and 18.9 is absolute (air) permeability (md) and must be estimated independently from log-determined permeability, and typically is computed by logging-company interpretation programs, which assume that log-calculated water saturation is irreducible water saturation.]
2. Use the F_g and P_dm values and the log-determined value of S_w at the same level to calculate P_cm for that level, using Eq. 18.10.
3. Use Eq. 18.11 to convert from mercury/air capillary pressure—the basis for the Thomeer curves—to the fluid system of interest.
4. Use Eq. 18.12 to calculate the vertical distance from the level investigated to the FWL, using the fluid densities in the reservoir being evaluated. To reduce statistical scatter, make such calculations for multiple points within the interval being evaluated.

Fig. 18.11 illustrates the basic principle of the capillary-pressure method, showing a good-quality sand layer underlain by a poor-quality sand layer in a hypothetical well that logged LKO to the base of the poor-quality sand. The presence of variable-quality sand layers enhances the method’s reliability because more than one capillary-pressure curve must be fitted in the calculations.

• 

  Fig. 18.11 – Capillary pressure chart that illustrates the shift in capillary pressure across the boundary between good- and poor-quality sand (after Cronquist).

There are several limitations to the capillary-pressure method:

1. The well-log interval of interest must be within the part of the hydrocarbon/water transition zone (HWTZ) that exhibits a significant water-saturation vs. depth gradient.
2. There must be a robust correlation between permeability and porosity.
3. The Archie equation, frequently used in logging programs to calculate S_w, may not be the "correct" model for the log interval of interest because the value for S_w that is computed from log analysis is a function of the saturation and cementation exponents, each of which is a function of lithology, which might vary over the logged interval.
4. Reservoir fluid densities should not vary significantly between the observation well(s) and the FWL.
5. Although the FWL may reasonably approximate the initial hydrocarbon/water contact in reservoirs with good-quality rocks containing free gas or light oil, in reservoirs with poor-quality rocks and/or those containing heavy oil, the commercial hydrocarbon/water contact may be significantly shallower than the FWL.

Internal Limits. In addition to external limits discussed in a previous section, there might be internal limits that could significantly affect RE. Two of these internal limits are internal faulting and depositional/diagenetic discontinuities.

Internal faults can be partial or complete barriers to fluid flow along all or part of their length. Under pressure gradients imposed by production, such barriers might respond differently from how they would under static conditions. Usually internal faults exhibit smaller vertical displacements than do bounding faults. In many cases, such faulting might be undetectable using existing well-control, or even seismic, data. Furthermore, internal faults might only become apparent after a period of sustained production, as happened in the Cormorant field in the North Sea and in other fields in that area.

Depositional discontinuities internal to a reservoir might adversely affect RE. In the U.S.A. Gulf Coast, for example, in composite reservoirs that are producing by strong waterdrive, high-permeability (channel) sands typically flood out in preference to low-permeability (fringe) sands. Such occurrences are common in comparable geologic and reservoir settings.

Several methods are used to detect internal limits, including repeat formation tester (RFT) depth/pressure traverses, differences in hydrocarbon isotopes, ⁸⁷Sr/⁸⁶Sr isotope ratios, and differences in saturation pressure.

Volumetric Parameters. In addition to those determined from geologic mapping, volumetric parameters include petrophysical data (Ф , S_w) and formation volume factors, all of which should be averaged over the reservoir; initial pressure and formation temperature, which are arguments for formation volume factors and other parameters; and REs, which are discussed in a subsequent section.

Petrophysical data used in Eqs. 18.2, 18.3 , and18.5 can be determined by several methods, including well logging, transient pressure testing, and routine and special core analysis, each of which is discussed in detail in separate chapters of the Handbook. Accordingly, only brief comments are provided here.

Porosity. Although reservoir porosity is estimable from well logs, it is good practice to calibrate log-determined porosity against core data, corrected for compressibility effects, if appropriate. As denoted in Eqs. 18.2, 18.3, and18.5, porosity in the oil zone might differ from that in the gas zone. Depending on circumstances, procedures to estimate net pay (e.g., cutoff porosity and water saturation) might differ between the two zones. Accordingly, average porosity in each of the two zones should reflect such differences.

Water Saturation. In Eqs. 18.2, 18.3, and18.5, the saturation terms S_wo and S_wg should reflect average initial water saturation—which might be greater than the irreducible saturation—in the oil zone and gas zone, respectively. Depending on the petrophysics and geometry of the reservoir, some of the accumulation might be in an oil/water or gas/water transition zone. This might reasonably be expected in reservoirs with low-relief, heavy oil, poor-quality rock, or a combination of these. In any event, the saturation terms in Eqs. 18.2, 18.3, and18.5 should be consistent with the procedure(s) used to determine net pay and map the accumulation.

Compressibility Effects. For accumulations in geopressured reservoirs or friable, unconsolidated sands, it might be appropriate to correct properties measured at ambient conditions to those expected at reservoir conditions. For example, irreducible water saturation at reservoir conditions typically will be greater than that measured under ambient conditions in the same rock sample, and porosity and permeability will be less. Low-permeability rock, such as is seen in tight gas reservoirs, can have permeabilities of as much as two orders of magnitude less at reservoir conditions, compared to those measured at ambient conditions. (Geopressured reservoirs are discussed further in the Special Problems section of this chapter.)

Formation Volume Factor. In general, FVFs [expressed as reservoir volume/standard volume (RV/SV)] are a function of composition of the reservoir fluid, reservoir pressure and temperature, and surface separator(s) temperature(s) and pressure(s). As discussed in subsequent sections, such factors may be measured in a PVT cell; estimated from empirical correlations; or, for nonretrograde reservoir gases, calculated from the composition of the reservoir gas. The FVFs in Eqs. 18.2, 18.3, and 18.5 should reflect initial reservoir conditions and separator conditions that are anticipated over reservoir life.

Oil FVFs at a specified reservoir temperature and over a specified range of reservoir pressures and surface separator conditions can be measured in a PVT cell in a laboratory. Fluid samples used for these measurements are taken from the wellhead during carefully controlled flow and test conditions, or from bottomhole samples after careful conditioning of the sampled well. Such procedures are covered in detail by McCain and elsewhere in the Handbook.

If PVT data are unavailable, oil FVFs at initial conditions can be estimated from empirical correlations. Since publication of Standing’s correlation in 1947—still considered industry standard—there have been at least 10 such correlations published. Each yields slightly different results, and it might not be apparent which correlation is best for a specific application.

Gas reservoirs are either retrograde or nonretrograde. For retrograde gas reservoirs that are to be produced by pressure depletion below the dewpoint pressure, consider obtaining separator samples and running a PVT analysis at reservoir temperature and over an appropriate pressure range. For nonretrograde gas reservoirs, empirical correlations usually provide sufficient accuracy.

Gas Deviation Factor. The gas deviation factor—also called the supercompressibility factor or the z-factor—reflects the nonideal PVT behavior of real gases. Many engineers use this factor for the analysis of nonassociated gas reservoirs, as discussed later. The z-factor is a function of fluid composition, pressure, and temperature. Mathematically, it is the volume of a specific molar quantity of real gas, divided by the volume of the same molar quantity of an ideal gas, both measured at the same pressure and temperature:

....................(18.13)

To ensure accuracy, the z-factor should be measured in a PVT laboratory, using a gas sample from the reservoir being analyzed; however, the z-factor estimated using empirical correlations is acceptably accurate for most engineering calculations.

For nonretrograde gases, the reservoir fluid composition does not change, regardless of reservoir pressure changes, and the initial z-factor can be used for calculations over the reservoir life. For retrograde gases, however, the composition of the reservoir fluid—and the z-factor—will change if reservoir pressure goes below the dewpoint pressure, under which scenario the two-phase z-factor must be used. Correlations are available to estimate the two-phase z-factor, but using PVT data might be preferable.

Initial Pressure. The initial reservoir pressure is needed to determine the initial FVFs, and it is the basis for material balance calculations of O/GIP. An accurate estimate of initial reservoir pressure is particularly important for geopressured reservoirs and undersaturated oil reservoirs, especially those for which material balance calculations might be necessary.

Reservoir Temperature. Reservoir temperature also is needed to determine the initial FVFs. Accurate determination of reservoir temperature is especially important for reservoir fluids anticipated to be close to critical conditions.

Recovery Efficiency''''. Estimation of RE is one of the most difficult aspects of volumetric estimation of reserves and—unless there is considerable local experience and/or good analogs—is fraught with uncertainty. In approximate order of importance, RE for developed oil/gas reservoirs depends on drive mechanism, formation quality, degree and type of reservoir heterogeneity, well spacing, fluid type, operating and completion methods, reservoir geometry and well locations, and economics. The interaction between these factors—some of which are discussed below—is complex enough to preclude quantitative analysis during the static phase of reserves estimation, and to allow only qualitative guidelines to be provided here.

Depending on geologic setting, drive mechanism, and reservoir geometry, RE might be strongly influenced by well spacing. Such scenarios include thin oil columns producing by bottom waterdrive; heavy oil, in general; low-permeability gas reservoirs; and reservoirs with discontinuities.

Oil Reservoirs. The viscosity of the reservoir oil strongly influences RE for oil reservoirs, and roughly correlates to the stock-tank oil gravity. Reservoir oils are broadly classified as either heavy (stock-tank gravity less than approximately 25°API) or light (stock-tank gravity greater than approximately 25°API).

For light oils that are producing by solution gas drive with insignificant gravity segregation, REs from reasonably homogeneous reservoirs generally range from 5 to 35% OIP, depending on formation quality, initial solution gas/oil ratio (GOR), and stock-tank gravity.

For heavy oils that are producing by solution gas drive, REs from reasonably homogeneous reservoirs generally range from < 5 to 20% OIP, depending on production mechanism, formation quality, initial solution GOR, and stock-tank gravity. Additional comments about heavy oil are provided in the Special Problems section of this chapter.

Table 18.5 is based on analytical calculations for an assumed range of oil properties and gas/oil relative permeability characteristics. The calculations assume pressure depletion from the bubblepoint pressure to 10% of that pressure. For reservoirs developed on wide well spacing, especially those in poor-quality formations, it is conjectural whether average reservoir pressure can be reduced to such levels at commercial production rates. The calculations for Table 18.5 take no account of gravity segregation, which might increase RE; of possible heterogeneities, which might cause incomplete drainage; or of initially undersaturated reservoirs, where expansion of the rock/fluid system will contribute to overall RE when reservoir pressure is reduced from initial to bubblepoint pressure. Nevertheless, REs in Table 18.5 reasonably agree with many REs observed in the field.

• 

  Table 18.5

Eqs. 18.14 and18.15, published by the API in 1967, result from regression analyses of observed RE of oil vs. various rock/fluid properties. Eq. 18.14 was developed from 80 U.S.A. reservoirs that had produced by solution gas drive with no initial gas cap. Eq. 18.15 was developed from 70 U.S.A. reservoirs that had produced by waterdrive.

....................(18.14)

....................(18.15)

As with any correlation, these equations reflect the best fit through large data sets; there might be substantial errors when they are applied to a specific case. Accordingly, the user should seek independent corroboration.

Despite disclaimers regarding the reliability of these correlations, their applicability has been corroborated in enough scenarios to warrant continued, but cautious, application. Estimates based on these correlations can be adjusted when more information becomes available. Early life performance data might be helpful in determining the drive mechanism (which correlation to use) or might lead to a better analysis of reservoir fluid properties (bubblepoints and/or formation volume factors).

The nature of water influx (bottomwater vs. edge water) apparently was not considered in the development of Eq. 18.15. In bottom waterdrive reservoirs, suboptimal well spacing might cause significantly lower RE than indicated by that correlation. (For additional comments regarding bottom waterdrive, see Cronquist.)

Generalized application of these correlations to estimate REs outside onshore North America is limited by the absence of terms for well spacing and heterogeneity and by the economic scenario under which the reservoirs were operated. Data for these correlations were derived from onshore, U.S.A. reservoirs that generally were developed on relatively close spacing; thus, the reservoirs probably were produced under semisteady-state conditions, under which well spacing might not be a significant parameter. Also, with close well spacing, the effects of reservoir heterogeneity tend to be minimal. Operating costs and economic limits for onshore U.S.A. reservoirs tend to be significantly less than are typical elsewhere, such that REs tends to be greater.

Gravity Segregation. In nature, there always is some gravity segregation of free gas and oil during production of oil by solution gas drive. The relative importance of gravity segregation can be shown by a gravity number N_G:

....................(18.16)

The N_G and RE data in Table 18.6 were compiled from published studies of actual reservoirs, and they may be useful for guidance in making a preliminary estimate of the relative importance of gravity segregation. These data do not show a correlation between N_G and oil RE; however, they do indicate that, in an oil reservoir with a N_G greater than approximately 15, significant gravity segregation is a reasonable expectation.

• 

  Table 18.6

Gas was injected into some of these reservoirs. The term m_i indicates the volume injected as a multiple of initial gas-cap volume. In the presence of gravity segregation, gas-cap injection reasonably is expected to have the same effect as a large initial gas cap.

Solution Gas. Industry literature rarely discusses RE of solution gas from oil reservoirs. This is because of the historically low economic value of solution gas and the expense of commercializing it (installation of multistage compressors). For oil reservoirs produced by strong waterdrive, such that abandonment pressure is not significantly less than initial bubblepoint pressure, RE of solution gas should be comparable to that for the oil in the same reservoir. For oil reservoirs produced by solution gas drive, such that abandonment pressure approaches atmospheric, as a first approximation, RE of solution gas reasonably can be estimated at approximately 75% solution gas initially in place (SGIP).

Volatile Oils. In composition and PVT behavior, volatile oils are transitional between black oil and retrograde gas, and their FVFs from differential liberation are greater than 2.0 RB/STB. Their initial solution GOR ranges from approximately 1,750 to 3,200 scf/STB, and their stock-tank gravity ranges from approximately 40 to 60°API.

A significant volume of stock-tank liquids may be produced as condensate from the liberated solution gas. For a specific reservoir, the producing GOR and FVF strongly depend on separator conditions. Use the flash FVF that reflects anticipated separator conditions—not the differential liberation factor—to calculate OIP and reserves.

REs of volatile oils by primary drive mechanisms are comparable to those observed for light oils. Unless there are compelling data to the contrary, Eqs. 18.14 and/or18.15 may be used for a preliminary estimate of RE. Depending on the anticipated drive mechanism, volatile-oil/primary-drive-mechanism reservoirs frequently are operated under high-pressure gas injection. Cronquist discusses several such projects.

Depending on circumstances, some or all of the wellhead production from accumulations of volatile oils might be processed through an off-site plant. One should take care to allocate products properly between lease and plant because ownership of each may differ.

Volatile oils sometimes are classified—erroneously—as retrograde gases. The reservoir temperature in such accumulations may be only slightly less than critical temperature, and a small error in measuring formation temperature can cause laboratory PVT analysis to be conducted at an incorrect temperature. Also, because producing GOR depends on separator conditions, recombination ratios might be incorrect, causing the laboratory fluid to be nonrepresentative.

Gas Reservoirs. RE of gas from nonassociated gas reservoirs is influenced by the ratio of abandonment to initial reservoir pressure and the degree to which the accumulation has been invaded by water from the aquifer, among other factors. In general, RE can be calculated by

....................(18.17)

where

....................(18.18)

and where S_gr can be approximated by

....................(18.19)

If there is no water influx, E_V = 0 and Eq. 18.17 becomes

....................(18.20)

For moderate- to high-permeability reservoirs that are producing by pressure depletion with no water influx, an RE of 85% GIP frequently is assumed, pending observation of well and/or reservoir performance. In many such reservoirs, multiple-stage compression may be warranted, and REs exceeding 95% can be achieved. Caution! Without actual installation of such equipment and/or operating data to demonstrate the commerciality of such an installation, such REs should not be assumed in booking proved reserves. For poor- to low-permeability reservoirs, however, RE might be substantially less than 85%.

If there is a strong waterdrive (where R_pz ≈ 1.0), Eq. 18.17 reduces to

....................(18.21)

and gas RE can be approximated by the product of the volumetric sweep efficiency, E_V, and the displacement efficiency, E_D.

RE of gas from partial waterdrive gas reservoirs is rate-sensitive. Some engineers advocate producing such reservoirs at high rates to minimize abandonment pressure, thereby maximizing RE of GIP. Depending on the nature of permeability distribution in a reservoir, well spacing and location, and the strength of the aquifer, however, high production rates might cause irregular water encroachment, which could cause lower ultimate recovery than if the reservoir were produced at a lower rate.

Volumetric sweep efficiency is influenced by reservoir geometry, spatial distribution of permeability, horizontal/vertical permeability ratio, well spacing, and well positioning, among other factors. For example, in thin gas accumulations underlain by water, the volumetric sweep efficiency will be significantly less than in thick gas accumulations underlain by water. Accordingly, closer well spacing—if commercially feasible—might be required for efficient drainage of such thin gas accumulations. Regardless of well spacing, a high horizontal/vertical permeability ratio generally will be conducive to effective sweep efficiency in bottom waterdrive gas reservoirs. Also, sweep efficiency by bottom waterdrive generally will be higher in reservoirs where permeability increases toward the top of the reservoir (as in offshore barrier bars) than in ones where permeability decreases toward the top (as in alluvial channels). Well positioning in the reservoir also is important. A long, narrow reservoir that is developed by a single well at one end might not drain effectively, requiring additional wells to achieve a reasonable RE.

Gas-Cap Gas. Estimating RE of gas from gas caps can be more complex than might be inferred from Eqs. 18.17 through18.21. In addition to the factors discussed in the Gas Reservoirs section of this chapter, RE of gas from gas caps also depends on the thickness and spatial relation of the gas cap with respect to the oil column and on the completion and production practices for wells that are completed in the oil column. In general, estimation of RE of gas from gas caps using volumetric methods might be subject to considerable error, and such reserves should be checked against those estimated from well performance as soon as clearly defined, reliable production trends have been established.

In reservoirs with thin gas caps that are completely underlain by the oil column, making gas-well completions may be infeasible and, regardless of the drive mechanism, most of the gas-cap gas might be produced by downward coning into oil-well completions. In a strong-waterdrive reservoir, this scenario could lead to the presence of substantial volumes of unswept gas at crestal locations. In a depletion drive reservoir, if the oil-well completions can be operated to relatively low economic limits, RE of gas should be commensurate with that calculated from Eq. 18.20.

In reservoirs where the gas cap is en echelon to the oil column and where gas-well completions are feasible, RE of gas should be commensurate with that expected from a nonassociated free-gas accumulation.

Condensate. Condensate is defined here as a petroleum liquid consisting mostly of pentanes and heavier hydrocarbons that is in the gas (vapor) phase under initial reservoir conditions and that condenses to the liquid phase when the gas is produced through surface separation equipment operating under ambient conditions on a lease. (The definition of "condensate" has been controversial among OPEC countries. Less restrictive definitions that make it difficult to distinguish between condensate and light oil have been proposed.)

RE of condensate from gas reservoirs depends on composition of the reservoir gas, reservoir abandonment pressure relative to the dewpoint pressure, RE of gas from the same reservoir, and separation equipment used in the lease, among other factors. For nonretrograde reservoirs, RE of condensate should be comparable to that of the gas in the same reservoir, but either way, separator conditions might influence RE. For example, high-pressure gas wells—those with flowing tubing pressure (FTP) greater than approximately 1,000 psia—typically are produced through low-temperature separators (LTS). If FTP gradually decreases below approximately 1,000 psia because of pressure depletion, LTS equipment becomes progressively less efficient, which may lead to condensate carry-over.

For retrograde reservoirs, if PVT data are not available, the correlations in Eqs. 18.22 through18.26 may be used to calculate condensate/gas ratio (CGR) as a function of reservoir pressure, dewpoint pressure, and initial CGR. Caution! These correlations are based on limited data.

....................(18.22)

where R_cd = the CGR at the dewpoint pressure, STB/MMscf, and n and D are defined as follows:

....................(18.23)

....................(18.24)

....................(18.25)

....................(18.26)

If retrograde gas reservoirs are produced to reservoir pressures that are less than the dewpoint pressure, retrograde condensation might cause irreversible loss of condensate in the reservoir pore space. The loss will be proportionately greater for richer gases.

To illustrate this point, producing CGR vs. reservoir pressure (as calculated using Eqs. 18.22 through18.26 ) is plotted on Fig. 18.12 as dimensionless CGR (R_c/R_cd) vs. dimensionless pressure (p/p_d). For example, if a reservoir with an initial CGR of 100 STB/MMscf is produced to a reservoir pressure that is 80% of dewpoint pressure, the producing CGR is estimated from Fig. 18.12 to be 40 STB/MMscf.

• 

  Fig. 18.12 – Dimensionless CGR vs. dimensionless pressure (after Cronquist).

Eqs. 18.22 through 18.26 also are used here to calculate ultimate CGR for reservoirs produced to 10% of dewpoint pressure:

....................(18.27)

where R_cuD = dimensionless ultimate condensate production (C_pu/G_puR_ci). (In developing Eq. 18.27, it was necessary to assume z = 1, which may introduce intolerable errors.) For example, for a gas reservoir with an initial CGR of 100 STB/MMscf produced from dewpoint pressure to 10% of dewpoint pressure, from Eq. 18.27 the cumulative (ultimate) CGR is calculated to be 30 STB/MMscf.

These simple guidelines are adequate for retrograde gas reservoirs in good- formations; however, in poor-quality formations, estimating reserves from such reservoirs is a major problem. Producing such reservoirs by pressure depletion at reservoir pressures below the dewpoint pressure causes retrograde liquids to condense in the pore space. In the interwell areas of the reservoir, such condensation typically builds up to no more than a few percent of initial pore space, but around wellbores, it can build up to saturation levels that can substantially reduce the effective permeability to gas. Depending on circumstances, well productivity might be severely reduced, possibly causing premature abandonment.

A major difficulty continues to be reliable prediction of the depletion performance of such reservoirs, especially those with "rich gases" (high initial CGR) in low-permeability formations. Some of the problems are being overcome through advances in simulation technology, but as yet there are no simple guidelines in the open literature.

Classification of Volumetric Reserves. Classification of volumetric reserves may involve both updip/downdip limits and areal assignments.

Updip/Downdip Limits. The 1997 SPE/WPC and the 1978 U.S. SEC reserves definitions both limit proved reserves to a volume no deeper than GWC or OWC. The 1997 SPE/WPC definitions state: "In the absence of data on fluid contacts, the lowest known occurrence of hydrocarbons controls the proved limit unless otherwise indicated by definitive geological, engineering or performance data." Their use of "geological" embraces all facets of geology, including geophysics. Similarly, the U.S. SEC definitions state: "In the absence of information on fluid contacts, the lowest known structural occurrence of hydrocarbons controls the lower proved limit of the reservoir."

Until areal and vertical reservoir limits are defined by the drilling of enough wells, the location or depth of an OWC or a GWC may be subject to much uncertainty. The extent of this uncertainty often can be narrowed to the vertical distance between the HKW in an off–structure dry hole and the LKO or LKG that is demonstrated by an upstructure well. Without other information to define the hydrocarbon/water contact, LKO/LKG depths typically are used to limit the downdip volume of proved oil and gas reserves.

A deterministic approach might arbitrarily assign incremental probable reserves to the portion of the reservoir between the LKO/LKG and the midpoint between that depth and the HKW, and it might assign incremental possible reserves to the interval between this midpoint and the HKW.

A probabilistic approach in one case might ascribe various confidence values to different levels between the LKO/LKG and the HKW, or in another case might consider that the LKO/LKG and the HKW define the endpoints of a probabilistic distribution and use Monte Carlo analysis to calculate appropriate probabilities for 2P and 3P reserves. In the first case, for instance, the reservoir volume above the LKO/LKG might be assigned a 90% (P90) value, and the maximum possible reservoir size down to the HKW might be given a 5 to 10% (P5, P10) value. An intermediate depth between the LKO/LKG and the HKW can be established to define the 50% (P50) confidence level.

The six simplified reservoir cross sections included in Fig. 18.13 establish some basic guidelines in reserves classification, but do not include all potential variations. All examples in Fig. 18.13 assume adequate geologic data to support the structural interpretation. See Cronquist for additional guidelines.

• 

  Fig. 18.13 – Estimation of reservoir limits for classification of reserves.

Part A of Fig. 18.13 illustrates a one-well reservoir with the well interval fully saturated with oil or gas, but without direct evidence of a downdip GOC, GWC, OWC, or HKW. No other data are available. For gas or undersaturated crude, proved (P1) reserves are limited to the "lowest known occurrence" or the depth established by the base of the formation as seen in the well log. Some have assumed that one sand thickness below the LKG or LKO contains proved (P1) or probable (P2) reserves, even though little geologic data or logic typically supports this assumption. Possible (P3) reserves sometimes are assigned to the reservoir volume represented by one additional sand thickness below the assumed P2 limit, again often with little basis.

Part B of Fig. 18.13 is similar to part A, but includes data from a downdip wet well located below the LKO/LKG contact. This wet well establishes the HKW, which is considered equivalent to the deepest (and largest) possible accumulation of gas or oil in the reservoir. As in part A of Fig. 18.13, the volume of gas or oil above the LKG/LKO may be considered P1 reserves; the volume below the LKG/LGO, but above the HKW, often is split into P2 and P3 reserves.

Part C of Fig. 18.13 is similar to part A, but the depth and location of a reservoir structural spill point (SP) can be mapped. The SP depth establishes a maximum size of a hydrocarbon accumulation in much the same way as does the dry hole shown in part B of Fig. 18.13. The interval between the LKG/LKO and the SP may be subdivided into P2 and P3 intervals, assuming no other information to the contrary.

Part D of Fig. 18.13 is identical to part C in structural attributes, but illustrates a further complication for a saturated oil reservoir that might have a gas cap with a GOC that potentially is as deep as the HKO shown at the top of the logged interval. The engineer judges what portion of the reservoir volume above the HKO should be allocated to oil and/or gas. In any event, only the reservoir portion limited by the LKO and HKO can be classified as P1 reserves in most circumstances. This limitation might have a significant impact on the value of the reservoir because oil usually has a higher value than natural gas.

Part E of Fig. 18.13 is a simplified example to guide where seismic interpretations lead to a downdip limit below that calculated through the use of pressure/depth data. Although using pressure and seismic data lead to different conclusions, they can be useful in defining P2 and P3 reserves allocations. In some cases, the quality of the pressure/depth data may warrant assigning P1 reserves to the calculated hydrocarbon/water contact, especially if the 3D seismic interpretation supports a larger reserves quantity.

Part F of Fig. 18.13 is an idealized case in which a reservoir limit below the LKG/LKO is corroborated by both pressure and seismic interpretations, perhaps enough to support the designation of P1 reserves to the lower depth. Such a conclusion would be a function of the amount and quality of the pressure and seismic data.

These six examples are useful, but they are only guidelines. The reserves engineer should consider fully the quantity and quality of all data used in reserves quantifications and classification and look beyond the specifics of any individual reserves determination for guidance obtainable from area analogs.

Areal Assignments. Fig. 18.14 is identical to Fig. 18.3, except for the two dashed lines that suggest assignment of different classifications reserves from an areal perspective. Consistent with the Fig. 18.3 discussion, Locations A and B in Fig. 18.14 are required for effective drainage and depletion of the reservoir. Well 1 is classified as proved producing. Location A can be classified as proved (undeveloped) on the basis of reasonable certainty of the geologic interpretation and the adequacy of well control.

• 

  Fig. 18.14 – Structure map on top of porosity.

Location B cannot be classified as proved, given the uncertainty introduced by reservoir sand being absent in Well 4 and the structural uncertainty regarding the position of an LKO or an OWC. The southwest boundary of the interpreted channel sand is not defined and has been inferred through seismic interpretation (see Fig 18.4). Most would classify the reservoir volume southwest of the southern line and above 10,600 ft ss as probable undeveloped. Note that all or part of the reservoir volume above the HKO may be assumed to be oil-filled in the P2 or P3 cases.

* This reference is not intended to be limiting and does not imply endorsement.** Personal communication with E.C. Thomas, Bayou Petrophysics, 23 April 2002.

Performance Methods

Performance methods are used after a field, reservoir, or well has been on sustained production long enough to develop a trend of pressure and/or production data that can be analyzed, usually mathematically, to estimate O/GIP and/or future production. The analysis may involve material-balance calculations, computer simulation, or "fitting" historical trends of production rates [water/oil ratio (WOR), gas/oil ratio, water/gas ratio (WGR), condensate/gas ratio, and/or pressure], or some combination of these.

Material Balance. Classic material balance (CMB) is a computational procedure by which the fluid properties and pressure/performance history of a reservoir are averaged, thereby treating the reservoir as though it were a tank. Computer simulation (discussed in a subsequent section) uses material-balance principles, but segments the reservoir into numerous cells or gridblocks, rather than treating it as a tank. Also, simulation programs can be used to forecast production.

CMB equations are formulated to calculate volumes of O/GIP. These methods can be used when there are sufficient historical reservoir pressure and production data to perform reliable calculations. Computer simulation might seem to have rendered the CMB obsolete, but not so. For many scenarios, the CMB remains an essential adjunct to computer simulation. Indeed, the CMB sometimes is the only practical approach to reservoir analysis, such as in the following cases:

• In highly fractured reservoirs, which defy characterization needed for reliable computer simulation.
• In fractured/vugular carbonates where lost circulation problems preclude complete penetration and, accordingly, adequate characterization of the reservoir.
• In reservoirs (typically offshore-gas) that are developed from clusters of wells from widely spaced platforms, a scenario in which subsurface data may be inadequate to characterize the reservoir.

For reliable material-balance calculations, the reservoir must have reached semisteady-state conditions (pressure transients must have affected the entire hydrocarbon fluid system and contiguous aquifer, if any). Depending on reservoir fluid and formation properties and on reservoir drive mechanism, this could require cumulative production of as much as 5 to 10% of the O/GIP.

Reliable application of the material balance method requires accurate historical production data for all fluids (oil, gas, and water), accurate historical (static) bottomhole pressure data, and PVT data representative of initial reservoir conditions.

Limitations for CMB include reservoirs with strong waterdrives or large gas caps that maintain reservoir pressure close to initial pressure, a scenario in which reservoir-pressure errors cause erratic calculations of the expansion terms and, consequently, unstable solutions (discussed in the next section); thin, areally extensive, and/or low-permeability reservoirs that have wide areal variations in reservoir pressure and saturation conditions that cannot be averaged reliably; and volatile oils, in which the volumes of stock-tank liquids separated from the solution gas are unaccounted for. This last limitation might be overcome using procedures discussed by Walsh.

For gas reservoirs that are producing by pressure depletion, a graphical form of the material-balance equation (discussed in a subsequent section) can be used to estimate GIP and reserves. For oil reservoirs, the material-balance equation can be used to estimate O/GIP and likely drive mechanism. To estimate reserves from oil reservoirs, however, the material-balance equation must be used in a form that includes appropriate relative-permeability data and operating constraints in a predictive mode adapted for computer simulation. Otherwise, REs can be estimated by analogy.

Equations. In "expanded" form (including water influx), the material-balance equation may be stated as oil-and-gas production (plus water) equals expansion of oil and free gas initially in place plus water influx. Assuming an initial gas cap and, at this time, ignoring compressibility of PV and interstitial water, this relation may be written as:

....................(18.28)

and gathering terms,

....................(18.29)

In Eqs. 18.28 and18.29, units on both sides of the equal sign are RB. Also, units for B_g in these and subsequent equations in this section are RB/scf (whereas in Eq. 18.5, B_g is in Rcf/scf).

Depending on the magnitude of pore and water compressibility compared to overall system compressibility, it might be desirable to include compressibility terms for oil material balance calculations, both above and below the bubblepoint pressure. If compressibility terms were included for both the initial gas cap and the oil column, Eq. 18.29 would be written:

....................(18.30)

where the pore compressibility c_p = the integrated value between p_i and p, and where p = the pressure at which Eq. 18.30 is evaluated.

There are three unknowns in Eqs. 18.29 and18.30: OIP, N_i; size of the initial gas cap, m; and water influx, W_e. It is rarely possible to solve for all three with reasonable reliability, but depending on circumstances, it might be possible to eliminate m or W_e, or both. For example, if PVT data indicate an undersaturated oil reservoir, m may be eliminated, and if geologic and/or well-performance data indicate no water influx, W_e may be eliminated. In general, however, the engineer might be faced with determining all three unknowns. In practice, after appropriate modifications, Eq. 18.29 orEq. 18.30 is solved repeatedly and successively, using the cumulative production and pressure data corresponding to each time until stable solutions are achieved.

One approach to solving for all three unknowns is to group the terms in Eq. 18.30 to reflect the production and expansion:

....................(18.31)

....................(18.32)

....................(18.33)

....................(18.34)

(E_c, which accounts for expansion of PV and interstitial water in the gas cap, in addition to that in the oil column, is taken from Dake. Havlena and Odeh neglected to include a compressibility term for reservoirs with an initial gas cap.) Substituting these new terms in Eq. 18.30 yields:

....................(18.35)

Depending on pressure/production history and subsurface data, it might not be apparent in the early stages of the analysis whether a reservoir being studied had an initial gas cap or whether there is water influx, or both. Eq. 18.35 can be used in various forms to estimate the amount of O/GIP and the most likely reservoir-drive mechanism.

For example, if there is no initial gas cap, m = 0, and if there is no water influx, W_pB_w is dropped from Eq. 18.31. After dropping m and W_e, Eq. 18.35 reduces to

....................(18.36)

Without a gas cap and water influx, a plot of F_pR vs. (E_o + E_c) should be a straight line passing through the origin, as shown in Fig. 18.15. (For consolidated formations in normally pressured reservoirs, the compressibility term E_c may be ignored, and the plot would be of F_pR vs. E_o.) The points represent successive solutions of the fluid production and expansion terms, up to the date of evaluation. The origin is a must point; thus, one has a fixed point to guide the straight-line plot. The first few points might be erratic and may be ignored in constructing the straight line. As implied by Eq. 18.36, the slope of the line is F_pR / (E_o + E_c), dimensionally equal to RB/(RB/STB), which equals N_i (OIP, in STB).

• 

  Fig. 18.15 – Fluid production vs. compressibility (no gas cap and no water influs). (After Havlena and Odeh.)

There are three other possibilities: no gas cap and water influx, gas cap and no water influx, and gas cap and water influx. Each requires appropriate modifications to Eqs. 18.31 through 18.36 and the plotting of different groups. Havlena and Odeh, Dake, Tehrani, Sills, and Cronquist offer detailed discussion—and criticism—of these procedures.

p/z vs. Cumulative Wellhead Gas. For nonassociated gas reservoirs where there is no (or insignificant) aquifer influx, and where PV compressibility is negligible, the volume of the initial gas-bearing pore space typically is assumed to remain constant over life. For these volumetric gas reservoirs, the material-balance equation can be written as:

....................(18.37)

For such reservoirs, most engineers use a plot of p/z vs. G_p to monitor performance and estimate GIP and reserves, as shown by Fig. 18.16. In theory, such plots should be for a reservoir, which may involve averaging static BHPs for more than one well. Caution! G_p is cumulative wellhead gas, not just separator or pipeline gas, and should include the gaseous equivalent of stock-tank condensate (GEC).

• 

  Fig. 18.16 – Reservoir pressure vs. cumulative gas production for a volumetric reservoir.

Depending on the geologic setting and initial well spacing, however, it might not readily be apparent which wells are in a common reservoir, in which case it might be appropriate to plot initial static BHPs for the suspect wells vs. time on a common scale. It is good practice to maintain plots of p/z vs. G_p for each well until performance indicates which wells are in a common reservoir; however, even then it might be desirable to maintain a plot for each well because such plots might help to determine the drainage area of each well and to identify areas for infill drilling. In competitive reservoirs, well plots should be maintained over reservoir life.

Plots of p/z vs. G_p are among the most widely used reservoir engineering tools, as well as one of the most widely misused tools, as discussed in the Pitfalls section of this chapter.

Computer Simulation. Computer simulation is based, in part, on material balances, and can involve analysis of an entire reservoir, segments of a reservoir, or a single well. When such analysis includes a good-quality history match, future production forecasts might be considered proved reserves, depending on the constraints imposed on the forecast; however, if computer simulation is used to forecast production, considering such forecasts to be proved reserves is conjectural without a history match. More detailed comments regarding computer simulation are provided in a subsequent section.

Production/Decline Trend Analysis. Whereas material-balance methods focus on reservoirs, production/decline trend analysis (P/DTA) focuses on wells or aggregates of wells. In that sense, they are two fundamentally different, independent methods for estimating reserves. Depending on circumstances, their results might not agree, a situation that warrants further investigation. Pending resolution, the smaller of the reserves estimates might be classified as proved, and the larger one as proved plus probable or proved plus probable plus possible, depending on the degree of uncertainty.

Economic Limit. "Economic limit" generally refers to one or the other of the following:

• Producing characteristic(s) that typically are used locally to establish the practical limit of production—maximum WOR or maximum GOR—which are identified here as economic limit conditions.
• The minimum production rate at which income from such production is less than the cost of continued operation. This is known as the economic limit production rate or, simply, the economic limit.

The economic limit may refer to a single well; an aggregate of wells, a lease or unit, or other economic aggregation or financial grouping; or a production facility for an aggregate of wells with processing equipment that must be operated as a unit (e.g., offshore production platforms or fluid injection projects).

The economic limit generally is defined as the production rate at which the net revenue to the operator’s working interest that is attributable to production from a well, aggregate, or facility equals the "out-of-pocket" cost to operate the well, aggregate, or facility. Net revenue is gross revenue, less production and ad valorem taxes, royalties, transportation, and treating expense, if any. Out-of-pocket costs—sometimes called direct operating costs—are costs that would be saved if the well or facility were shut in (e.g., costs for power and materials). Accordingly, such costs include labor only if shutting in the well or facility would save that cost. State and federal income tax and corporate overhead usually are excluded from out-of-pocket costs.

The economic limit for an oil well can be calculated by

....................(18.38)

Application of production and ad valorem taxes varies from one jurisdiction to another, and Eq. 18.38 should be viewed only as an example.

Wellbore/Mechanical Problem vs. Reservoir Performance. A performance/decline trend in a well might, in some instances, be caused by a wellbore and/or mechanical problem, rather than by the performance of the well and/or reservoir. Extrapolation of such trends can lead to estimates that do not reflect production that might actually be recovered if the wellbore and/or mechanical problem were remedied.

Single Wells vs. Aggregates. Historical production data on single wells might not always be available, and reserves estimates might have to be made using production data aggregated to leases or to reservoir units that contain more than one well. Even if single-well data are available, such production might be volumes allocated from a common battery on the basis of periodic well tests.

In aggregates, various wells might be in different stages of decline and might have different GORs and/or different WORs. Remedial operations, infill drilling, and modifications to production equipment might have influenced the production history and may be expected to influence future trends. An evaluator should become familiar with past, current, and anticipated future operations before attempting to estimate reserves from production trends from multiwell aggregates. Routine lease operations that affect well performance might be reported only informally, if at all. Frequently, pumpers or lease foremen maintain records of well tests, pressures, and equipment changes in "daily gauge reports" that generally are not available elsewhere. Depending on circumstances, the engineer responsible for reserves estimates should consider making an on-site visit with field personnel to determine the nature of field operations and the possible influence of those operations on production rate.

The Pitfalls section of this chapter discusses some factors affecting production forecast reliability.

Production Curtailment. Production of oil and/or gas might be curtailed for many reasons, including capacity limitations on pipelines or plants, market restrictions, inability to handle all produced water or gas, limitations on treating facilities, contract arrangements, regulatory limits, and governmental interference. Here are several examples:

• If wellhead gas is being processed through a gasoline plant, total gas production might be limited by plant capacity. Wellhead gas may periodically bypass a processing plant if the relationship between oil and gas prices makes the sale of unprocessed gas more financially attractive.
• Production from low-pressure gas wells might have to be compressed before being sold, and such production might be constrained by available compressor capacity.
• Production from high-WOR oil wells might have to be limited because of limited capacity to separate, treat, and dispose of produced water.

Thus, before analyzing historical production trends, especially on multiwell aggregates, the engineer should determine whether there has been curtailment of production during the period being analyzed and whether there are facilities constraints that might cause curtailment in the future.

Regarding possible future curtailments, the reserves engineer should ensure that extrapolations of historical trends to estimate reserves do not generate future fluid production forecasts that are inconsistent with existing or anticipated processing capacity. For example, tacit in a future oil and gas production forecast from a waterdrive reservoir is the idea that, after breakthrough, water production will gradually increase until wells reach the economic limit; however, such forecasts might not be realistic because of physical limitations to handling the produced water.

Performance Indicators. One or more of the performance indicators of a well might exhibit a trend before the production rate of the principal product begins to decline. Depending on reservoir type and drive mechanism, these performance indicators include fractional flow of oil (f_o), WOR, WGR, GOR, CGR, BHP, FTP, and shut-in tubing pressure (SITP).

Several performance methods have been used to estimate oil reserves from individual wells in waterdrive reservoirs. Two of the most widely used methods involve plotting either f_o vs. N_p or WOR vs. N_p. These and other methods are discussed briefly here.

In waterdrive reservoirs, after breakthrough of water in individual wells, semilog plots of f_o vs. N_p for each well might exhibit linear trends, as illustrated by Fig. 18.17. Usually, the trend can be extrapolated to f_o at economic limit conditions to estimate reserves. The f_o at the economic limit will be governed by the total liquid capacity (oil plus water) of the well and the completion equipment used to produce the well.

• 

  Fig. 18.17 – Fraction of oil in total fluids vs. cumulative oil production for a typical well that is producing by waterdrive (after Cronquist).

For such wells produced at an approximately constant oil rate after breakthrough of water, the logarithm of the rate of total liquid production (oil plus water) typically increases linearly with time, as illustrated by Fig. 18.18. This behavior has been observed for high-capacity oil wells in waterdrive reservoirs being produced by gas lift. Oil reserves can be estimated by extrapolating the total liquids rate (oil plus water) to the maximum capacity of the well. Plots such as Figs 18.17 and18.18 should be prepared for each well that is producing significant water. In using plots such as Fig. 18.18 to estimate reserves, note that the production rate of oil will decrease after the production rate of total liquids increases to the maximum capacity of the well. As discussed in the Rate/Time Trends section, following, the nature of the decrease will depend on the trend of f_o vs. N_p.

• 

  Fig. 18.18 – Total liquids production vs. time for a typical waterdrive oil well (after Cronquist).

In many cases, a linear trend of f_o vs. N_p might turn downward as f_o becomes small. The downturn reportedly occurs at smaller f_o values for heavy (viscous) oils than it does for light oils, as illustrated by Fig. 18.19.

• 

  Fig. 18.19 – Observed gas RE vs kh (after Brons).

In areas with high-permeability sands and a favorable water/oil-mobility ratio (e.g., offshore Nigeria), a Cartesian plot of f_o vs. N_p, rather than a semilog plot, might provide a more reliable basis for extrapolation.

Occasionally, the completion interval may extend across a shale break, as shown schematically by part A of Fig. 18.20. In many cases in bottom waterdrive reservoirs with such completions, discontinuities have been observed in the trend of f_o vs. N_p , as shown by part B of Fig. 18.20. After water breakthrough (point "a" on both figures), the trend of f_o vs. N_p decreases while the perforations below the shale break water out (point "b"). The trend stabilizes until the encroaching water rises above the shale break (point "c"). After water breakthrough into the perforations above the shale break, the trend again declines. The rate of decline of f_o after the stabilization period might be greater or less than the rate of decline before the stabilization period, as discussed below. During period b–c, f_o should be approximately:

....................(18.39)

If such behavior is observed (trend a–b–c) and if well-completion geometry can be verified by Eq. 18.39, then, as a first approximation:

....................(18.40)

If h_n1> h_n2 , the rate of decline in f_o after the stabilization period usually will be less than the rate of decline before the stabilization period. Conversely, if h_n1 < h_n2 , the rate of decline after stabilization will be more than before.

• 

  Fig. 18.20 – Typical water encroachment and fractional flow behavior for a well in a bottom waterdrive oil reservoir with a shale break in the completion interval (after Cronquist). OOWC = original oil/water contact.

In a scenario like that shown by Fig. 18.20, extrapolation of trend a–b could lead to significant underestimation of reserves. Against such a possibility, one should check reserves from such an extrapolation against a reasonable volumetric estimate. In general, reserves estimated from any such extrapolation should be checked against those estimated from volumetric mapping and/or should be compared with reserves from analogous wells.

Trends of WOR vs. N_p also can be used to estimate reserves from waterdrive wells. In many scenarios, semilog plots of such data tend to become linear at WORs greater than approximately 1. In these cases, semilog plots of (WOR + 1) vs. N_p tend to be linear at WORs of less than 1, which might help to define trends at low WOR values. Be careful in using such plots, however, without first examining the nature of the fractional flow trend, as discussed in the Rate/Time Trends section, following.

Determining the correct performance plot to estimate reserves in waterdrive reservoirs is highly empirical. Many of the published procedures are based on the observation that a significant part of a semilog plot of (k_rw/ k_ro) vs. S_w is linear. The floodout performance of wells and reservoirs, however, is governed not only by relative permeability, but also by formation heterogeneity and gravity/viscous forces, among other factors; thus, consider different types of plots, determining the best plot type by experience in analogous scenarios. Remember, however, that the best plot at low water cuts might not be the best plot at high water cuts.

Formation heterogeneity can have a significant and, typically, unpredictable influence on the WOR trend. For example, in naturally fractured reservoirs, the WOR trends in specific wells have varied sharply as a function of cumulative production and/or production rate.

Rate/Time Trends. Historically, engineers have used what have come to be known as "Arps equations" to analyze behavior and predict future production of wells. Three types of equations have been used: hyperbolic, harmonic, and exponential. The rate/time equation for hyperbolic declines is:

....................(18.41)

Note that t, which should be written as Δt, is the incremental time (t₂ – t₁) required for the production rate to decline from q₁ to q₂.

After integrating with respect to time, Eq. 18.41 becomes the rate-cumulative equation for hyperbolic declines:

....................(18.42)

where ΔQ_p = denotes incremental cumulative production, ΔG_p or ΔN_p , as the production rate declines from q₁ to q₂ . Eq. 18.42 may be solved to determine the incremental time for the production rate to decline from q₂ to the economic limit rate, q_el:

....................(18.43)

The harmonic and exponential equations are special cases of a hyperbolic equation, where b is equal to 1 and 0, respectively. The three types of equations are compared graphically in Fig. 18.21, which shows Cartesian and semilog plots of rate vs. time and rate vs. cumulative production for b values of 0, 0.5, and 1.0. This range of b values reflects semisteady-state, cylindrical flow of a single fluid with small, constant compressibility. This is a reasonable approximation for many well/reservoir scenarios, but it is not universally applicable, and b values greater than 1 have been observed in many areas.

• 

  Fig. 18.21 – Three types of production-decline curves (after Arps).

Historically, the Arps equations have been considered as empirical fits to observed trends of production rate vs. time (or vs. cumulative production). As discussed by numerous authors, such equations should, in theory, be used only to fit the constant terminal pressure period of production—the semisteady-state period during which flowing BHP is maintained at a constant value; however, in practice, this operating condition is seldom maintained over long periods of time, which contributes to uncertainties in reserves estimation based on decline trend analysis.

As implied by Fig. 18.19, if the production rate of total liquids is maintained at a constant rate (a common practice), then a linear, semilog trend of f_o vs. N_p reflects a harmonic decline. In this scenario, a linear trend of log (WOR + 1) vs. cumulative oil may be observed, which also may be extrapolated to estimate reserves. Linear, Cartesian trends of f_o vs. N_p, however, have sometimes been observed, as mentioned previously, and such trends reflect exponential declines. Apparently linear trends of log (WOR + 1) vs. cumulative oil might be observed at low WORs, but they typically depart from linearity at high WORs and should not be extrapolated to estimate reserves.

Analysis and forward projection of rate/time trends (or rate/cumulative production or other trends) typically are handled with in-house or commercial software, as discussed in the next section.

Analysis, Forecasting, and Evaluation Software. In addition to in-house and other proprietary software, numerous commercial software products are available for analyzing historic trends and projecting future oil and gas production, or reserves. Typically, such products include a graphics module and an evaluation module. The graphics module is used to analyze historic trends and project future oil and gas production. These projections may be inserted into the evaluation module, together with prices, costs, taxes, ownership, and other pertinent data, to calculate the economic limit and the reserves of oil, gas, and condensate, and to generate a cash flow projection.

The graphics module can be used either to curve fit a historic trend of production and generate a production forecast of reserves on the basis of projection of the fitted trend, or to generate a production forecast of reserves that has been calculated by analogy and/or volumetric methods. Three curve-fitting/-projection parameters are most important: the initial decline rate D_i, the hyperbolic exponent b, and the terminal effective decline rate a.

Procedures for curve fitting depend on the production maturity of the well(s) being analyzed. For example, the production trend for an immature well might be so erratic as to require considerable local knowledge to ensure a curve fit that is consistent with analogous wells/reservoirs. If such a well is in the transient stage, apparent b factors from curve fitting might not represent of the semisteady-state stage. Projection of such curve fits might yield substantial overestimates of reserves. It might be appropriate to ignore the curve fit and impose a decline trend consistent with analogous wells in the area. The reasonableness of this procedure can be tested with volumetric and/or simulation analysis. In any event, the criterion of reasonable certainty should be observed in estimating proved reserves.

For wells in an advanced stage of production and in areas where there are good analogy wells, the appropriate b factors and terminal effective decline rates may be readily apparent.

For scenarios in which there is no production history, reserves can be estimated by analogy and/or volumetric methods, as discussed previously. The graphics module then can be used to compute a production forecast, given initial and final production rates, using any of the curve types (exponential, hyperbolic, or harmonic) that typically are programmed into the software. A constant rate period can be projected, followed by a prescribed decline period. Analogs are useful in selecting the decline curve parameters.

An evaluator should not automatically accept the best fit calculated by the software; rather, fully review and analyze the data it displays. Production histories can be affected by operational downtime, equipment modifications, market conditions, weather, and many other conditions that might distort the productive capacity of the property being reviewed. One should preview the pressure history, where relevant, to detect erroneous data. There might be a need to acquire missing data or to contact the operator for additional information.

The projection or forecast never should be made until the engineering analysis has been completed. Good engineering practice might require overriding the software-generated hyperbolic projection with an exponential projection.

Most graphics modules allow the user to exclude certain data points and to include all or a portion of the well history. One should use this feature cautiously and ensure that only erroneous or invalid data points are excluded.

Decline curves typically are used to forecast future production rates for properties that have some established performance history. In addition to monthly rates of oil and gas production, reservoir and surface pressure data and various fluid ratios can be analyzed and used in preparing reliable production forecasts. In most cases, the primary production stream volumes are forecast, and secondary products are estimated using constant or variable indices—primarily GOR or CGR. Gas and/or liquid handling constraints often are not considered in such projections. Iterative methods are available to assist in forecasting oil production from a mature waterflood where there are surface or subsurface limitations on water handling, and in gas lift oil operations where gas-handling equipment imposes limitations.

Reconciliation of Estimates. For each well or reservoir, the reserves engineer should attempt to reconcile the estimates by comparing ultimate recovery estimated using P/DTA to ultimate recovery estimated using volumetric methods. (This reconciliation also should include results from computer simulation, as appropriate, but this is not specifically included in this discussion.) Consider the following possibilities:

1. If ultimate recovery estimated using volumetric methods is significantly greater than that from P/DTA, then

   (a) The performance data might be representative only of the transient period (when the pressure sink around wells is still expanding) and not of semisteady-state conditions (when the drainage area has stabilized), which usually better represents well performance.

   (b) The volumetric parameters might not be representative of the well or reservoir.

   (c) Wells might need to be stimulated or equipped with higher-capacity equipment.

   (d) Infill wells might be needed.

   (e) Or, more than one of the foregoing factors may be relevant.

2. If ultimate recovery estimated using volumetric methods is significantly less than that from P/DTA, then

   (a) The volumetric parameters might not be representative of the well or reservoir.

   (b) The mapped area or volume might be too small and additional development might be warranted.

   (c) Or, both factors may be relevant.

3. Pending determination of the reason for the difference in ultimate recovery estimated using the two methods, assign proved reserves only to those quantities demonstrated to be recoverable from performance methods.

As discussed earlier, reservoir heterogeneities often have an adverse effect on the recovery of oil and/or gas. A significant difference between ultimate recovery estimated using volumetric methods and that from P/DTA might indicate inefficient drainage caused by reservoir heterogeneities.

Computer Simulation.Computer simulation is a sophisticated method for analyzing well/reservoir performance and/or projecting future production (reserves). The widespread commercial availability of simulation software and the greatly expanded capabilities of personal computers have increased use of this technology.

Engineers use models of varying complexity to guide reservoir development and production programs and to compare and evaluate well spacing, rate sensitivity, and improved recovery potential, as well as other scenarios. It is important to realize, however, that although computer simulation is widely used, these methods typically oversimplify representation of the spatial distribution of reservoir properties. Computer simulation results typically are sensitive to changes in reservoir characterization, and the degree of sensitivity may render moot an estimate of ultimate recovery that is based on this method.

Accordingly, check such estimates against simple models, as discussed by Richardson and Blackwell, and against actual performance in analogous reservoirs. Saleri and Toronyi observe that "determination of ultimate recovery through simulation is an unattainable goal, particularly for heterogeneous reservoirs that are coarsely gridded." Jacks notes that "an estimate of ultimate recovery from any single simulation is subject to considerable uncertainty, especially if it is developed early in the life of a reservoir." Many forecasts of future performance have been significantly in error, despite the users’ best efforts at reservoir characterization and history matching. In some cases, the reservoir characterization and history matching were sound, but the field development was not consistent with that modeled. Continuous monitoring of performance, then, is essential in reserve estimation by computer simulation—indeed, by any method!

Computer Simulation vs. Reserves Definitions. Despite its limitations, computer simulation may provide the only acceptable answer to analysis of complex reservoirs, but such use must be consistent with the purpose(s) for which a specific reserves estimate is made. For example, the presumed "most likely" case—consistent with proved plus probable reserves—is the case typically modeled by computer simulation. Such a case might not be appropriate for reporting reserves under U.S. SEC guidelines.

To ensure that simulation results will comply with SEC reserves definitions, either configure the model using the observed hydrocarbon/water contact or imposing the lowest known occurrences of oil or gas, or, if the constructed model does not comply with proved reserves definitions, make necessary adjustments to the model results to estimate the recovery that would approximate recovery reached using a model that meets proved reserves requirements. Many model runs might be needed to accomplish this. Manually adjusting the output data causes some of the rigorous nature of the simulation process to not be realized fully.

One should not construct a reservoir model solely to comply with proved reserves definitions unless warranted by special, and perhaps limited, circumstances. Constructing a (3P) model may be best initially, with the ability to modify it to assist in estimating proved or proved plus probable reserves.

Reservoir models that do not comply with the limitations inherent in proved reserves definitions can help in understanding the hydrocarbon REs likely with each reserves category. Sensitivities of various reservoir characteristics (e.g., relative permeability, drive mechanisms, and PV compressibilities) can be investigated to determine a range of recoveries that may comply with the "reasonable certainty" aspect of proved reserves.

In history matching, a fit typically is described as "poor," "good," or "excellent." Such subjective terms mean little in establishing a confidence level in predictions of future production (reserves). However, if a history match can be obtained that replicates individual well producing rates and pressures with reasonable tolerance, without illogical adjustments, the model might be appropriate for the estimating proved reserves.

Palke and Rietz observe (in part) that

• Although reservoir simulation is a sophisticated technique, it does not always produce reliable or applicable results suitable for reserves estimation.
• Reservoir simulation should be used to improve the understanding of a reservoir, but should not be used to circumvent the intent of U.S. SEC reserves definitions.
• Although reservoir simulation increasingly is being used as a tool for reserves estimation, the results do not necessarily constitute U.S. SEC reserves estimates.
• Models that do not comply with U.S. SEC reserves definitions can be modified to comply, but this process may be difficult.
• Results from models that are not consistent with U.S. SEC reserves definitions can be used through the alteration of the simulation output itself, which requires a great deal of simulation output and might provide less rigorous solutions.
• For immature reservoirs, simulation is useful primarily for estimating the oil and/or gas RE, and for testing the limits in terms of uncertain parameters (permeability, aquifer support, O/GIP).
• Models of mature reservoirs should exhibit reasonable history matches before they are accepted for reserves purposes.
• The uniqueness and quality of the history match affect the confidence to be placed in a model’s ability to predict future performance, and thus dictate the model’s appropriate usage in the process of estimating reserves.

Example Study. Rasor presents a field study comparing the results of a simulation study of a three-reservoir field with those of a classic reservoir-engineering approach. He uses a 3D compositional model and assumes gas processing to maximize liquid recovery. Laboratory PVT and special core analysis data are matched. The classic procedure is limited to a traditional volumetric study incorporating estimated REs based on the fluid and formation properties and the experience of the estimator. Fig. 18.22 is a schematic cross section of the three reservoirs, MA, B, and G, shallow to deep, respectively.

• 

  Fig. 18.22 – Schematic cross section with fluid contacts and DSTs (after Rasor).

OWCs for reservoirs MA and G were calculated using the pressure/depth relationships illustrated in Figs. 18.23 and 18.24. The GOC in B is based on PVT analysis, Fig. 18.25. Table 18.7 compares the results from the classic and simulation methods. The REs of oil and gas from reservoirs B and G are in reasonably close agreement. The oil REs for MA range from 24 to 42%. Without other information or suitable analogies, an engineer might assign a proved (P1) recovery of 24% OIP and a proved plus probable (2P) recovery of 42% OIP.

• 

  Fig. 18.23 – Reservoir MA fluid gradients (after Rasor).

• 

  Fig. 18.24 – Reservoir G fluid (after Rasor).

• 

  Fig. 18.25 – Reservoir B PVT analysis (after Rasor).

• 

  Table 18.7

The condensate REs are significantly different for all three reservoirs. In this situation, without reasonable explanation for the differences or compelling data to the contrary, the lower REs would be appropriate for booking proved reserves.

This study illustrates the range in results produced by the two methods—classic engineering and reservoir simulation—by a competent evaluator using a reasonable amount of data. It is a real-world example of the uncertainties of relying on computer simulation, without history matching, for the estimation of proved reserves.

Special Problems*

Some operating and/or reservoir scenarios are so complex as to defy conventional analysis and to require a high degree of skill and ingenuity. Because of the substantial degree of uncertainty, such scenarios may be better suited for probabilistic procedures than for conventional scenarios.

Coalbed Methane

Chap. 6 of the Emerging Technologies section of the Handbook discusses the development of coal deposits in the U.S.A. and around the world for recovery of natural gas. Such natural gas is predominantly methane, but it also may contain small amounts of ethane, carbon dioxide, and nitrogen.

Coalbed methane (CBM) is adsorbed onto the coal surfaces exposed through the matrix microporosity and the naturally occurring fracture or cleat system. This cleat system typically is water-filled, often with fresh or slightly saline water, but may also contain some free gas.

Calculation of gas in place for a unit volume of the coal layers being developed does not follow the "porous media" approach of determining effective porosity, saturations, pressures, temperatures, and gas quality. Instead, the gas in place is measured physically through the recovery of coal samples, the number and distribution of which are important to the estimation of total gas in place pertinent to the property being evaluated.

Cored samples are transferred carefully from the core barrel to canisters, which are sealed immediately and transported to an analysis laboratory. In analysis, two measurements are taken. First, free gas in the canister is measured, and then the coal sample is crushed and the liberated gas measured. These two measurements are combined with an estimate of gas lost during the core recovery operation. The lost gas volume is estimated as a function of the coal type and depth of burial and other factors. Total gas in place is calculated as the product of the unit gas in place—considering areal variations—and the mapped volume of the coal seams being developed.

A volumetric estimate of GIP (scf) in coalbed reservoirs can be calculated by

....................(18.44)

The first term in the square brackets of Eq. 18.44 is used to calculate the gas volume contained in the interconnected fracture or cleat system (if any) and is identical to the term used for porous media reservoirs. The second term in the square brackets is used to calculate the adsorbed gas in the coal matrix. The adsorbed gas quantity results from laboratory measurements of the adsorbed gas in a unit of dry, ash-free coal and other coal-quality factors.

In most cases, cleat porosity is water-filled, so that the free gas therein essentially is zero. Most engineers ignore the gas volume in solution in the water.

Most of the data on which the reservoir engineer must rely is gathered through core analysis, fluid analyses, and well tests. Table 18.8 presents certain pertinent data items and primary sources for each item.

• 

  Table 18.8

Seismic data historically has not been used in CBM project analysis because most of these projects have been in areas that had an abundance of subsurface data obtained as a result of underground mining (e.g., the Black Warrior basin) or oil and gas wells drilled to deeper objectives (e.g., the San Juan basin). As the industry advances into areas with a dearth of existing subsurface information, seismic information is expected to become more important in determining reservoir extent and structure. Section sequence is not intended to convey authors’ views of relative importance.

REs, typically up to 75% GIP, are related to well density, the degree of naturally occurring fractures, the effectiveness of wellbore hydraulic fracturing programs, and the ability to "dewater" the reservoir to reduce the reservoir pressure to a level where desorption can be effective. Laboratory measurements can be used to develop composited desorption isotherms, which are useful in estimating the rate of gas liberation while reservoir pressure is reduced.

Proved reserves can be assigned to an area where wells have been drilled and have demonstrated that commercial gas rates can be maintained. Well spacing in the U.S.A. ranges from approximately 40 to 160 acres per well. For coalbed projects in areas remote from comparable analog operations, the time to confirm commerciality may be as long as several years. Some projects dewater quickly, allowing commercial gas rates to be attained early; other projects might prove to be noncommercial because of dewatering failure. A cluster of wells might need to create a pressure sink large enough to overcome the influx of water from a large aquifer. High permeability, together with a large aquifer, might create enough water influx to cause project failure.

Fig. 18.26 illustrates a typical individual well decline curve exhibiting a 2-year period of dewatering that is characterized by increasing gas production rates. An exponential trend has been drawn through the approximate 1-year decline period.

• 

  Fig. 18.26 – Long-term forecast using exponential decline (after Zuber).

Confidence in the forecast would increase if there were nearby analog wells with more production history supporting the exponential projection. Lacking such support, however, the projection should be confirmed through volumetric means before booking the forecast volumes as proved reserves. Many (perhaps most) coalbed wells producing from coal that has low to moderate permeability will exhibit a wide range of hyperbolic declines, underscoring the need for suitable analogs.

Type curves (production vs. time) from successful analog operations are the most useful tools for predicting the production profile and reserves for completed wells. As in traditional reserves estimation, volumetric reserves estimates should be checked against performance-driven reserves estimates.

Assigning of proved undeveloped reserves to coalbed projects usually should be restricted to the "one-offset" limitation imposed by the 1978 U.S. SEC definitions, unless the engineer can demonstrate "certainty of production" beyond the one-offset location. The 1997 SPE/WPC definitions may, in some circumstances, permit a larger area to be classified as proved, but one should be cautious until both the presence of coal of commercial thickness and adequate permeability are determined with reasonable certainty.

Probable and possible reserves typically are assigned to acreage at increasing distances from the commercially developed portion of the project.

Fractured Reservoirs

Fractured reservoirs have been observed in most producing areas of the world, in igneous/metamorphic rocks, sandstones, carbonates, shales, and cherts. The two broad categories of fractured reservoirs are those with a porous matrix and those with a nonporous matrix. In the porous matrix type (the more common), most of the hydrocarbons are stored in the matrix porosity, and the fractures serve as the principal flow conduits. Such reservoirs typically are identified as "dual-porosity" systems. Examples include many of the Iranian fields, Ekofisk (North Sea), Palm Valley (Australia), and Spraberry (Texas, U.S.A.). Some cherts exhibit dual porosity and have significant storage capacity in the matrix but that contributes little to reserves. Fractured reservoirs with a nonporous matrix occur in fractured igneous and/or metamorphic rocks, fractured shales, and fractured cherts. Such reservoirs frequently are associated with basement rocks. Examples include the Bach Ho field (offshore Vietnam), the Augila field (Libya), the Edison field (California, U.S.A.), the Big Sandy gas field (Kentucky, U.S.A.), and the Santa Maria basin fields (California).

When they occur in carbonates, fractures tend to facilitate extensive leaching and diagenesis, which may lead to the development of vugular, sometimes karstic, porosity. Examples include the Albion Scipio trend (Michigan, U.S.A.) and the Rospo Mare field (offshore Italy).

Fractured reservoirs pose formidable difficulties for estimating reserves. These difficulties are attributable to the heterogeneity of the reservoir formation, which causes substantial uncertainties in estimates of O/GIP and RE. Because of uncertainties in determining the flow characteristics of dual-porosity systems, estimates of reserves using volumetric methods are subject to substantial uncertainty. When feasible, compare such estimates with observed recovery in analogous reservoirs.

In general, the following scenarios cause problems:

• Boreholes frequently are severely washed out, making log interpretation difficult or impossible.
• Core recovery frequently is fragmental, at best.
• Even in good-quality boreholes, detection of fractures and measurement of fracture porosity using logging devices is highly empirical, although significant improvements have been made using formation imaging tools.
• In accumulations with a severe loss of circulation, operators typically stop drilling at the top of the reservoir section, a practice that, while necessary for safe operations, precludes characterization of the objective section.
• Well performance frequently is strongly influenced by proximity to major fractures, which can extend surprising distances. Because of this, be extremely cautious in assigning reserves to undrilled tracts that offset tracts at a mature stage of production.
• Although transient pressure analysis provides useful data, applying modern interpretation techniques mandates using highly accurate quartz pressure transducers.
• The accuracy of type curve matching depends on the accuracy of the mathematical model used for the type curves. An invalid model cannot yield a valid interpretation. Even if the model is valid, analysis of results might not provide unique answers.
• In pressure-depletion reservoirs, the rate/time performance of wells typically is hyperbolic. The behavior of an average well might be used to estimate reserves, but one should expect wide variation in performance between wells.
• In reservoirs producing by pressure depletion, the early performance of wells typically is characterized by relatively rapid decline in the production rate, which usually is caused by transient pressure behavior. Reserves cannot be estimated with any degree of confidence using decline trend analysis until wells have passed through the transient pressure period and settled into semisteady-state conditions.

Aguilera provides guidelines for estimating RE in fractured reservoirs, classifying fractured reservoirs by pore type and "storage ratio"—the relative amount of storage in matrix vs. fractures. Table 18.9 is adapted from Aguilera’s Tables 2 and 3.

• 

  Table 18.9

Aguilera does not state so, but "oil" presumably means light oil—stock-tank gravities greater than approximately 25°API. Also, Aguilera does not mention the influence of well spacing on RE, which could be a major factor, depending on the nature of the fracture system.

Natural Gas From Fracured Scale

As reported in mid-2000, natural gas produced from shale in the U.S.A. has grown to be approximately 1.6% (0.3 Tcf annually) of total gas production. The first commercial production of natural gas from shale was developed to supply gas to the town of Fredonia, New York, U.S.A., in the late 1820s, predating Col. Drake’s first oil well by almost 40 years.

By 1979, some 60 Bcf/year was being produced from wells in the Appalachian (Ohio) basin. Production from the Antrim shale (Michigan basin) began in the mid-1980s and by 1994 had surpassed production of the Appalachian basin. Three other U.S.A. basins—San Juan (Colorado, New Mexico), Fort Worth (Texas), and Illinois (Illinois, Indiana, Kentucky) currently are producing from shale. Total U.S.A. gas-bearing shale resources are shown in Table 18.10.

• 

  Table 18.10

In a 1992 report, the Gas Research Inst. (GRI) describes the Antrim shale as being organically rich and says that the majority of the in-place gas was sorbed into the organic constituent. Productivity is achieved by reducing reservoir pressure, and is maximized by hydraulic fracturing to access and connect the wellbore to the natural microfractures and other permeability pathways.

As in coalbed methane reservoirs, the naturally occurring fracture system usually is water-filled, requiring artificial lift equipment to dewater the wells to reduce the bottomhole pressure to a level consistent with maximum gas desorption and production.

Shale gas volumes initially in place (scf) can be calculated by:

....................(18.45)

where 1,359 is a conversion factor to convert volume (acre-ft), shale density (g/cm³), and gas content (scf/ton) to scf gas in place.

Shale density and gas content can be measured directly through core analysis or indirectly through well logs, using correlations established between gas content and shale bulk density. Core samples are taken and preserved to minimize the release of original gas in place. The free gas in the core sample canisters plus the gas that is released during core crushing is measured in the laboratory. This volume of gas may be adjusted to account for the volume estimated to have been lost during core retrieval. The analysis procedures are similar to those used for CBM.

Gas-content/shale-density correlations are an outgrowth of studies in which the laboratory-measured shale densities and total organic content (TOC) of the samples were compared and related in a linear correlation. Similarly, gas content was found to have a linear relationship with TOC.

This research thus leads to the ability to measure bulk density from well logs and use this information to directly estimate gas content and log-derived gas in place.

Fig. 18.27 is an example of the relationship between gas content and shale density for the Antrim shale in a defined area.

• 

  Fig. 18.27 – Calculation of gas content from bulk density measurements from log, Antrim shale (after Gas Research Inst.

Gas REs vary widely and are related to many factors, including completion efficiency, reservoir pressure, water removal efficiency, and well spacing. The recoveries shown in Table 18.11 range from 5 to 60% GIP, but probably average approximately 40% GIP in the Michigan basin (Antrim). A typical well production profile is shown in Fig. 18.28.

• 

  Table 18.11

• 

  Fig. 18.28 – Typical production graph for an Antrim shale well.

The initial dewatering period of approximately 1 year is characterized by diminishing water production and increasing gas production. Following perhaps a year of relatively constant production, a decline rate of approximately 6% per year is typical for a Michigan-basin Antrim well. Most wells exhibit exponential decline during their economic life.

The booking of proved reserves must be delayed until the production rate reaches a commercial level and/or there is ample evidence from nearby analog wells. Undeveloped locations may be classified as proved if these locations are directly adjacent to commercial wells (1978 U.S. SEC definitions). Additional locations may be classified as proved under the 1997 SPE/WPC definitions if there is compelling evidence from nearby analogs and if the continuity of favorable reservoir conditions is reasonably certain. * Personal communication with Ed Holstein, retired, Exxon, 2 March 2002.

"Tight" Gas Reservoirs

As defined by the U.S. Federal Energy Regulatory Commission (U.S. FERC), low-permeability ("tight") gas reservoirs have an average in-situ permeability of 0.1 md or less. Others have placed the upper limit at 1 md. Such accumulations in the U.S.A. contain substantial resources. Estimates of ultimate recovery from these resources vary widely and depend chiefly on assumptions of wellhead gas price.

Methods for estimating gas reserves in moderate- to high-permeability reservoirs are unreliable in very-low-permeability reservoirs. The unreliability can be attributed to the geologic setting in which these reservoirs occur and the completion methods required to make them commercial. In general, their geologic setting is characterized by a high degree of permeability heterogeneity; lateral discontinuities in apparently blanket sands; stratigraphic, rather than structural, traps; and complex mineralogy, frequently with high-grain-density minerals randomly dispersed throughout the section as well as water-sensitive clays.

These attributes make it very difficult to determine porosity and interstitial water saturation by conventional log and core analysis. Petrophysical properties measured at ambient conditions (e.g., k and S_w) differ substantially from those at reservoir conditions, and corrections for formation compressibility are subject to considerable uncertainty. For example, permeabilities can be as much as two orders of magnitude greater at ambient conditions than at reservoir conditions. These problems and poor lateral continuity lead to substantial uncertainties in volumetric estimates of GIP. In many cases, it is impossible to distinguish between commercial and noncommercial intervals from log analysis alone. Drillstem tests rarely provide useful information because formations often are damaged during drilling.

Massive hydraulic fracturing usually is required to obtain commercial flow rates. Despite more than 35 years of experience with fracturing technology, however, the industry remains unable to design a treatment and predict the results with high confidence when relying solely on analytical methods. Typically, operators rely on analytical models coupled with analogy.

Along the U.S. Gulf Coast, tight-gas accumulations frequently occur in geopressured sections. In this environment, understanding the influence of reservoir stress on rock properties is important for differentiating between productive and nonproductive formations.

Over the life of a well completed in low-permeability gas reservoirs, the gas production rate typically exhibits a hyperbolic decline, with apparent b values generally >1. In addition to decline curve analysis, empirical log-log rate/time models might provide useful short-term information for such wells—before the onset of significant pressure depletion. The following equations, developed in the 1980s for more than 2,500 then-new wells in the U.S. Rocky Mountains, have been used to estimate flow rates (Eqs. 18.46 and 18.47) and near-term reserves (Eqs. 18.48 and 18.49) for damaged fracture flow:

....................(18.46)

....................(18.47)

....................(18.48)

and

....................(18.49)

where K_A and K_B are coefficients calculated during fitting these equations.

For an undamaged, fractured well, initial values of n should equal approximately –0.5. Because of damage, however, initial n values as small as –0.15 had been observed in the wells studied; the average was –0.34. With the onset of depletion, n decreases to –1.0 or more.

Eqs. 18.46 and 18.48 can be used to account for the effects of a damaged fracture by using the field-observed value of n for each such well. Depending on circumstances, however, Eqs. 18.47 and 18.49 might provide a better fit to the observed data.

RE of gas from some of these reservoirs vs. k_gh is shown in Fig. 18.29. Well spacing ranges from approximately 160 to 320 acres. For k_h of less than approximately 50 md-ft, there is a decrease in RE, albeit erratically so.

• 

  Fig. 18.29 – Observed gas RE as related to kh. (After Cronquist.)

Because of the high degree of permeability heterogeneity, drainage areas of individual wells vary widely. In the Green River basin (U.S.A.), for example, effective drainage areas reportedly have ranged from approximately 100 to 640 acres. Depending on economics, such situations can offer opportunities for significant increase in reserves by infill drilling.

Heavy Oil

Discovered resources of heavy and extraheavy crude oil are estimated to be approximately 4,600 billion bbl, two-thirds of which are in Canada and Venezuela. Bitumen and tar sands are excluded from this estimate. Published data on RE from this resource by primary drive mechanisms are sparse. Meyer and Mitchell estimated worldwide ultimate recovery from heavy and extraheavy crude oils to be 476 billion bbl, which is 10% of the Briggs et al. estimate of the discovered resource initially in place. Estimated primary RE ranges from 8 to 12% OIP for the Orinoco area of Venezuela, where stock-tank gravities range from 8 to 13°API. Estimated primary RE ranges from 3 to 8% OIP for the Lloydminster area of western Canada, where stock-tank gravities range from 13 to 17°API.

Primary RE vs. API gravity for heavy crude oil "pools" in Alberta and Saskatchewan* is plotted on Fig. 18.30. Data are from 69 "pools" with OIP > 10 6 m³ (6.3 million STB). The trend line is not weighted by resource size and is shown only for reference; the regression coefficient, 0.21, is too small to infer a statistically significant correlation between RE and oil gravity. Of interest, however, is that the trend line is consistent with REs shown on Table 18.5 for "average" sandstone for 15°API and slightly-higher-gravity oils. Also interesting (lack of correlation notwithstanding) is the large number of heavy-oil reservoirs with significantly greater REs than would be predicted using "conventional" solution gas drive calculations. Reportedly, such REs are attributed to two mechanisms: the simultaneous production of oil and sand known as "cold production," and "foamy oil."

• 

  Fig. 18.30 – Observed oil RE as related to oil gravity for 69 pools in Alberta and Saskatchewan (after Cronquist

Although there are reports of REs that range from 5 to 20% OIP, no general correlations are available that relate specific rock/fluid properties and REs for heavy oil; thus, for volumetric methods, reserves engineers typically rely on analogy. The performance of wells in heavy oil reservoirs is erratic, however, and is influenced by varying production practices, varying volumes of sand production, and frequent downtime, among other factors, so that analogy estimates are subject to considerable uncertainty.

Reserves estimates based on performance also are subject to considerable uncertainty. Production rates for single wells usually are erratic, thereby precluding meaningful trend analysis. Many engineers generate normalized production curves from groups of wells producing from zones comparable to those being analyzed.

In summary, the producing mechanisms for heavy oil are poorly understood; an optimum production strategy has yet to be developed; a priori prediction of the efficiency of the production mechanisms for heavy oil currently is impossible. Although progress is being made on computer modeling, it may be several years before sufficient data are compiled for reliable estimates of RE and/or reserves from heavy oil.

* Personal communication with Rajneesh Kumar, Ryder Scott Co., 2 April 2002.

Thin Oil Columns

Thin oil columns overlain by free gas and underlain by water pose difficult problems in well spacing and completion method, production policy, and reserves estimation. In this context, "thin" is a relative term. Whether an oil column is considered thin depends on costs to drill and produce the accumulation. For example, in the Bream field (Australia Bass Strait, 230 ft water depth), 44 ft was considered thin, whereas in the Troll field (offshore Norway, 980 ft water depth), 79 ft was considered thin. Onshore U.S.A., 20 ft is considered thin. Irrgang takes a pragmatic approach, defining thin oil columns as those that "will cone both water and gas when produced at commercial rates."

The overall RE of oil from such accumulations can be influenced by well spacing and completion method and by gas-cap management policy. Economics, though, tend to be controlled by individual well recoveries and production capacities, rather than by average RE from the reservoir; thus, development planning focuses on the economics of individual wells—the cost to drill, complete, and operate vs. the oil rate/time profile. Ultimate oil recovery from individual wells tends to be controlled by a number of factors, including the gross thickness of the oil column and the horizontal/vertical permeability ratio in the well’s drainage area. This ratio might vary significantly over the areal extent of the reservoir, depending on the depositional environment of the reservoir rock. Experience with such reservoirs indicates that this parameter typically is underestimated, causing underestimates of oil recovery. Localized shale breaks might contribute to suppressed coning of gas and/or water if wells can be completed to take advantage of these heterogeneities.

From limited data from conventional well completions in several such fields in Australia, Irrgang developed the relation

....................(18.50)

where the bracketed term is a correlating parameter.

Irrgang does not provide details on estimation of k_H; the median permeability probably is appropriate. Irrgang has observed, "a higher power may be appropriate for permeability—possibly even 2."* The vertical/horizontal permeability ratio, k_V /k_H, influences volumetric sweep efficiency in bottom waterdrive reservoirs. The absence of this term in Irrgang’s correlation is puzzling, but might be because of measurement difficulties.

Depending on the water/oil mobility ratio and the horizontal/vertical permeability ratio, oil wells completed in this type of accumulation might exhibit coning of the overlying gas and/or coning of the underlying water early in life. These phenomena might cause rapidly increasing GOR or WOR and relatively short economic life; thus, how efficiently this type of accumulation can be exploited depends on the degree to which premature coning of gas and/or water can be avoided by appropriate completion methods and production practices. In one of the earliest published analyses of this problem, Van Lookeren advocated perforating below the initial OWC to minimize gas coning; however, the simple isotropic model used in his analysis essentially negates the practical application of this approach. In the last few years, horizontal drainholes have been used to develop these accumulations. Because this technology is still evolving, consider apparent successes in analogous reservoirs with caution.

Determination of optimum well spacing and estimation of oil reserves in such reservoirs is subject to substantial uncertainty, at least until a reasonably well-defined performance trend has been established for each well. Before performance trends are established, however, reserves typically are estimated using a combination of volumetric mapping and analogy or analytical methods. In this context, computer simulation can be extremely useful in establishing sensitivity of RE to various assumed scenarios, thereby helping to determine optimum well spacing and commerciality. Potential analogs are provided in Table 18.12.

• 

  Table 18.12

A critical review of the more than 50 years of literature makes apparent that the industry has yet to develop a general treatment of coning that includes the influences of gas cap, aquifer influx, and other relevant parameters. For example, some authors investigate the problem of coning in the presence of an inactive aquifer, which is analogous to the classic coning problem first discussed by Muskat and Wyckoff, whereas others investigate it in the presence of an active aquifer. Clearly, the critical rate to avoid water coning would be less in the presence of an active aquifer than in the presence of an inactive aquifer, other factors being the same.

In addition to aquifer strength, another critical parameter to apply the correlations in the literature is the horizontal/vertical permeability ratio over each well’s drainage area. Laboratory measurements of vertical and horizontal permeability of small core samples are inadequate for estimating this parameter. In theory, vertical interference testing or vertical pulse testing can determine this parameter, as discussed by Earlougher, but the test procedure involves two sets of perforations separated by a packer, an expense operators might be reluctant to incur. Another possible approach for wells exhibiting coning is computer simulation to establish the horizontal/vertical permeability ratio that yields an acceptable match to observed behavior. Whether results from a few such wells would apply to all wells in the reservoir depends on the depositional environment of the reservoir formation and the degree of lateral heterogeneity; however, it is unlikely. It might be more practical to test wells at gradually increasing rates to determine a maximum rate at which each well can be produced without coning.

In the presence of a strong aquifer and a gas cap, the combination of water encroachment and gas-cap coning might cause displacement of part of the oil column into the gas cap. Depending on the size of the initial gas cap and the degree of gas-cap voidage, significant volumes of oil might be lost. In some cases, this loss might be minimized or avoided by injecting the produced free gas into the gas cap to maintain constant gas-cap volume.

* Personal communication with H.H. Irrgang, Command Petroleum Holdings (December 1994).

Geopressured Oil/Gas

The term "geopressure," introduced in the late 1950s by Charles Stuart of Shell Oil Co., refers to reservoir fluid pressure that significantly exceeds hydrostatic pressure (which is 0.4 to 0.5 psi/ft of depth), possibly approaching overburden pressure (approximately 1.0 psi/ft). Geopressured accumulations have been observed in many areas of the world.

Geologic Setting.In regressive tertiary basins (the geologic setting for most geopressured accumulations), such pressures in sand/shale sequences generally are attributed to undercompaction of thick sequences of marine shales. Reservoirs in this depositional sequence tend to be geologically complex and exhibit producing mechanisms that are not well understood. Both of these factors cause considerable uncertainty in reserves estimates at all stages of development/production and reservoir maturity. Geologic complexity contributes to uncertainty in estimates of O/GIP that are based on volumetric mapping. Poorly understood producing mechanisms contribute to uncertainty in estimates of reserves that are based on pressure/production performance. Each aspect is discussed below.

Geopressured reservoirs frequently are associated with substantial faulting and complex stratigraphy, which can make correlation, structural interpretation, and volumetric mapping subject to considerable uncertainty.

The resistivity of interstitial water in geopressured sections may approach that of fresh water, which may suppress the SP log. Under these conditions, it might be difficult to estimate net pay unless a gamma ray log also has been run. In addition, the relatively fresh waters frequently encountered in geopressured sections complicate interpretation of resistivity logs, especially in shaly sands. Cases have been reported in which reserves were booked on the basis of high resistivity observed in porous sands that later investigation proved bore fresh water.

Drive Mechanism(s).As discussed in the Material Balance section of this chapter, if gas production is attributed to gas expansion only, a plot of p/z vs. G_p should be a straight line. Because geologists considered them to be closed accumulations, during the early years of exploitation it was assumed that geopressured gas reservoirs would produce by pressure depletion and exhibit linear plots of p/z vs. G_p . Although this was observed to be true in many cases, it is not universally true. The p/z vs. G_p plots for many geopressured reservoirs initially appear to be linear, but curve downward as reservoir pressure approaches hydrostatic pressure. Extrapolation of the initial part of such a plot might yield an estimate of GIP that is approximately twice that estimated using volumetric methods. The anomalously low initial slope of the p/z vs. G_p plot has been attributed to several phenomena, including PV compression, expansion of interstitial water, and partial waterdrive. The downward curvature of the p/z vs. G_p plot has been attributed to other factors, including depletion of a limited protoshale water aquifer and rock collapse. [The American Geological Inst. (AGI) defines shale as an "indurated (hardened)...sedimentary rock formed by the consolidation...of clay." Because geopressures in tertiary basins generally are attributed to undercompaction, the term protoshale is adopted here to make that distinction.]

Producing mechanisms in a geopressured gas reservoir might include gas expansion; compressibility of the reservoir PV; expansion of the interstitial water; water influx because of water expansion from a contiguous aquifer; water influx because of dewatering of interbedded protoshale; and/or evolution of natural gas dissolved in interstitial and aquifer water. Any or all of these mechanisms may be active at various stages in the life of a geopressured gas reservoir. Pressure/production data typically are insufficiently diagnostic to distinguish one mechanism from another, so that there may be considerable uncertainty in analysis of historical data and estimation of reserves.

There is disagreement regarding the relative importance of these mechanisms, especially compressibility of reservoir PV and water influx from interbedded protoshale. Because it is difficult to analyze geopressure mechanisms separately for a specific reservoir, many engineers use Eq. 18.51 to make an aggregate adjustment to the p/z vs. G_p plot:

....................(18.51)

Eq. 18.51 differs from Eq. 18.37 by inclusion of a p/z adjustment factor, which is the left-side square-bracketed term. Eq. 18.51 sometimes is simplified by adjusting the apparent gas in place (AGIP)—that estimated by extrapolation of the initial part of the p/z vs. G_p plot—by multiplying the AGIP by the gas-compressibility/effective-compressibility ratio.

Both methods assume that PV compressibility remains constant over the life of the reservoir being evaluated, which is contrary to the findings of numerous investigators. In addition, neither accounts for possible water encroachment.

Regardless of the method used to adjust the p/z vs. G_p plot, always check a reserves estimate so derived against analogies and/or a volumetric estimate for the same well.

Analytical Methods.Analytical methods outlined in the literature typically require more information than usually is available. As an alternative, a method was proposed that parallels that of Havlena and Odeh. Under this method, Eq. 18.28 can be written for a gas reservoir as

....................(18.52)

Define

....................(18.53)

and

....................(18.54)

Substituting Eqs. 18.53 and 18.54 into Eq. 18.52 leads to

....................(18.55)

Divide by the gas-expansion and rock/fluid-compression term in brackets:

....................(18.56)

If the water-influx term and the rock/fluid expansion/compression terms are estimated correctly, a plot of the left-side term vs. the fractional part of the second right-side term of Eq. 18.56 will be a straight line. The y intercept should be equal to G_Fi. The slope of the line should equal C, the water-influx constant. Note that c_p is a function of pressure and is c_p(p) integrated over a change in net overburden pressure that corresponds to the value p_i-p.

The water-influx term probably will be the most difficult term to evaluate because water influx in a given reservoir could be attributable to expansion from a contiguous aquifer and/or to dewatering of interbedded protoshale. Favorable conditions for protoshale water influx include considerable interbedding of protoshale with the gas-bearing sand, a small contiguous aquifer, and a high initial fluid-pressure gradient. Opposite conditions would favor aquifer influx. Depending on the size and shape of the contiguous aquifer, W_e might be calculable using a limited linear aquifer model or a limited cylindrical aquifer model. If protoshale dewatering is suspected, a limited linear aquifer model might be more appropriate.

Geopressured gas reservoirs might exhibit retrograde behavior, a phenomenon discussed in the Condensate section of this chapter. Oil reservoirs are encountered less frequently than gas reservoirs in the geopressured section and rarely are discussed in the literature. Comments similar to those for geopressured gas reservoirs are appropriate regarding drive mechanism in geopressured oil reservoirs. Depending on circumstances, an approach analogous to that presented in Eqs. 18.52 through 18.56 might be appropriate for geopressured oil reservoirs.

PV Compressibility.On the basis of numerous studies of the influence of reservoir pressure on PV compressibility, it seems apparent that PV compressibility of porous rocks depends on the stress conditions in the reservoir, decreases as stress increases, decreases as rocks become more consolidated, and might increase as temperature increases.

There appears to be no correlation between compressibility and rock properties that is generally valid across a broad spectrum of lithologies and pressures. Hall’s correlation between compressibility and porosity—still widely cited—covers only a narrow range of stress conditions and apparently reflects only data from well-consolidated rocks.

Reportedly, some geopressured sands have compressibilities approaching those usually associated with consolidated rock; however, these data apparently were measured on rock samples taken from geopressured aquifers, rather than from hydrocarbon reservoirs. In the high temperatures usually associated with geopressured environments, sandstones undergo rapid diagenesis that can cause a geologically young rock to become tightly cemented. This is more likely to occur in aquifers (where the interstitial water is mobile) than in hydrocarbon reservoirs (where the interstitial water is immobile). Expect these tightly cemented sandstones to be less compressible than relatively uncemented sands; accordingly, measure compressibility on samples taken from the hydrocarbon-bearing zone, not from the aquifer. Take great care when using compressibility data from rocks that appear similar to the zone of interest or that have comparable porosity and permeability.

In the absence of laboratory data, the following correlation can be used to estimate PV compressibility:

....................(18.57)

where A, B, C, D, K₁, K₂, and K₃ depend on rock properties, as shown in Table 18.13.

• 

  Table 18.13

During pressure reduction of reservoir fluids, the resultant stresses on reservoir rocks differ from those on core samples during hydrostatic testing in the laboratory. In the subsurface, when production reduces reservoir fluid pressure, the weight of the overburden compacts the reservoir rock, which uniaxially reduces the bulk volume of the rock and, consequently, reduces PV. This process can be replicated in the laboratory, but such tests require special equipment that is not used by most commercial laboratories. Most laboratory compressibility data are measured using hydrostatic stress, which can be related to reservoir stress by

....................(18.58)

*

Section sequence is not intended to convey authors’ views of relative importance.

Probabilistic Procedures

Background

Experienced reservoir engineers know that uncertainty exists in geologic and engineering data and, consequently, in the results of calculations made with these data; however, the degree of uncertainty in most reservoir engineering calculations usually is not quantified.

Reserves estimates historically have been deterministic ("single-valued"), with the degree of uncertainty indicated by qualitative terms such as proved, probable, and possible. Additional information about the degree of uncertainty has been conveyed by describing producing category and development status (e.g., producing, behind-pipe, or not developed), as discussed in the Reserves Definitions section of this chapter.

Even now, deterministic estimates of reserves usually are considered appropriate in geologic settings and operating areas where there is substantial experience, and in fully developed, mature fields—situations having relatively little uncertainty; however, for new geologic settings (then, coalbed methane) and in new operating areas (then, the North Sea), the industry developed probabilistic procedures to estimate and classify reserves. These procedures have been used to quantify potential range of reserves attributed to risky ventures and their degree of uncertainty.

Probabilistic procedures have long been used to assess exploratory ventures, but have not been widely used to assess production ventures. There are, however, several considerations and potential application areas for probabilistic procedures discussed below.

Probabilistic Classification of Reserves

Probabilistic classifications of reserves for a specific entity usually are based on the cumulative density function of the quantities calculated for the entity. (Cronquist discusses basic principles of probabilistic methods.) As previously discussed, probabilistic classifications typically specify for proved reserves that

• There should be at least 90% probability that the quantities actually recovered will equal or exceed the estimate.
• There should be at least 50% probability that the quantities actually recovered will equal or exceed the sum of estimated proved plus probable reserves.
• There should be at least 10% probability that the quantities actually recovered will equal or exceed the sum of estimated proved plus probable plus possible reserves.

Caution! Probabilistic notation and concepts discussed here should not be confused with those used by many exploration geologists [e.g., Rose, in which probabilities refer to, among other considerations, prospect reserves distributions or field size distributions. In that context P_90% (Rose’s notation) refers to ultimate reserves in a yet to be discovered accumulation. After discovery, reserves in such an accumulation might be estimated and classified using the procedures discussed here.]

For the expectation curve (EC) in Fig. 18.31 , proved, proved plus probable, and proved plus probable plus possible quantities would be 17, 39, and 73, respectively.

• 

  Fig. 18.31 – Typical expectation curve for proved, proved plus probable, and proved plus probable plus possible reserves. X_a = the actual quantity of reserves and X_e = the estimated quantity of reserves.

The foregoing (probabilistic) definitions reflect a cumulative interpretation of the EC in Fig 18.31. An incremental interpretation is shown by the short dotted lines, which approximate the area under the EC having three rectangles with increments on the x-axis that are defined by the foregoing classifications; thus, for the EC in Fig. 18.31, it might be said that the probability of recovering proved reserves [Pr(Pv)] ≈ 0.97, the probability of recovering incremental probable reserves [Pr(Pb)] ≈ 0.70, and the probability of recovering incremental possible reserves [Pr(Ps)] ≈ 0.27.

Despite the 1997 SPE/WPC definitions’ emphasis on a cumulative approach to probabilistic estimation and classification, an incremental approach might be more appropriate in situations that involve undrilled and/or unproved reserves where incremental expenditures and/or regulatory approval are required to bring such reserves on production. Specific guidelines for these situations are enumerated in separate paragraphs in the 1997 SPE/WPC reserves definitions for probable and possible reserves, respectively, and are preceded by the phrases "In general, probable reserves may include..." and "In general, possible reserves may include...."

Applications

Despite the (still) widespread use of deterministic methods for reserves estimation, there are several scenarios in which a probabilistic approach might be more appropriate.

Analogy/Statistical Methods.Historically, analogy/statistical methods have involved arithmetic averages of pertinent parameters, which have been considered "best estimates," a procedure that assumes that such parameters are (approximately) normally distributed; however, there are scenarios in which arithmetic averages might lead to significant bias in reserves estimates, especially those intended to conform to a P90 standard. The statistical frequency distribution of ultimate recovery—initial reserves—for wells in a common reservoir or geologic trend typically can be approximated with a log-normal (frequency) distribution. Also, the frequency distribution of geologic and/or engineering parameters (e.g., net pay) typically can be approximated with log-normal distributions. Log-normal distributions generally exhibit positive (right) skew. Depending on the degree of skew, the arithmetic average of such a distribution might be significantly greater than the intended "best estimate," which usually is considered the median of the distribution; thus, estimates based on arithmetic averages of pertinent parameters may (inadvertently) be biased on the high side. The more skewed the distribution, the greater the bias. With skewed distributions of pertinent parameters, consider using the median value for each such distribution, rather than the arithmetic average.

These observations can be used to estimate reserves for new wells by analogy with data from older wells in the same trend. Before using this technique, however, determine whether per-well reserves are truly random, are not influenced by prior drainage, and are unrelated to a geologic or operating parameter. As drilling and production continue, update the analysis when reserves for existing and new wells are revised.

Random distributions of per-well reserves have been observed in many geologic/reservoir settings in the U.S.A. and elsewhere. In these areas, at the time of the analysis, there was no statistically valid correlation between ultimate production for individual wells and date of initial production, net pay, "frac" treatment, initial potential, or any other parameter for these same wells. In some of these areas, however, as infill drilling continued, correlations were observed between date of initial production and ultimate recovery; thus, in any mature area, one should be alert to similar possibilities.

Volumetric Methods.Depending on the geologic complexity, the stage of development, and the quality/quantity of subsurface and geophysical data, volumetric mapping might involve considerable uncertainty, including subsea depth of fluid/fluid contacts, location of bounding faults, position of sand pinchouts, and time/depth conversion(s) for seismic data, among other factors. Circumstances might make it appropriate to quantify one or more of these uncertainties using probabilistic procedures. There may be numerous perturbations and/or combinations, a subject that merits an entire chapter, but is only covered briefly here. (See Cronquist for a more in-depth discussion of this topic.)

As discussed in the Reservoir Limits section, the subsea depth(s) of fluid/fluid contacts in a specific reservoir—GOC, GWC, and/or OWC—might not have been penetrated by wells, and there might be considerable disparity between analyses based on pressure, seismic, and/or capillary pressure data. Given such a scenario, it might be appropriate to define the range of uncertainty in subsea depth using a triangular probability distribution, with the mode of the distribution determined by the analysis procedure considered the most robust.

Performance Methods.The analysis of performance data might involve, for example, regression analysis (a least squares fit) of a production trend vs. time or vs. cumulative production. Historically, production projections based on such analyses have been classified as proved reserves. Regression analysis, however, yields a "fit" through the "means" of the analyzed trend. Probabilistically, such a fit is a P50, and reserves so calculated might, accordingly, be classified as proved plus probable. In a scenario where there is a long history of settled production and, consequently, a regression coefficient approaching unity, such a distinction is insignificant; however, where there is a relatively short, erratic production history and, consequently, a regression coefficient significantly less than unity, the distinction might be significant. Reserves engineers might consider a probabilistic analysis of the data.

Pitfalls*

A pitfall is a hidden or not easily recognized danger or difficulty that catches one unawares. In engineering, pitfalls are fallen into through mistakes from carelessness or ignorance. The potential petroleum engineering pitfalls below are described from the perspectives of an engineer preparing a reserves estimate and an engineer reviewing the work product of another.

Bias is not usually considered a pitfall, but rather is a conscious effort to "shape" a result for a specific purpose. An engineer must guard against all forms of external or internal bias and be careful to avoid the pitfalls that can affect the reliability of any reserves estimate. Some of the material presented here has been covered, in part, earlier in this chapter but is expanded here in light of the seriousness of these potential pitfalls.

Analogy/Statistical Methods

Assuming that reservoirs on trend and in the same geologic formation are analogous is a common pitfall. Depending on the geologic setting, depositional environment and, consequently, reservoir quality, might vary significantly over relatively short distances. For example, in a clastic deltaic environment both channel and fringe sands occur. Reservoirs in channel sands exhibit better quality than those in fringe sands and the two cannot be considered analogous; for the same drive mechanism, recovery factors in the former typically are significantly larger than those in the latter.

Statistical correlations—for recovery factor, for example—usually reflect the geologic, engineering, operational, and economic settings in which the correlated data were observed. Application of such correlations between disparate settings is a common pitfall and might lead to significant errors in reserves estimates.

Statistical correlations for PVT properties reflect the geologic setting from which the reservoir fluids originated. Failure to recognize this is a common pitfall. For example, such correlations developed for fluids from California reservoirs might be inappropriate for estimating PVT properties of fluids from North-Sea reservoirs. Use of inappropriate correlations might cause significant errors in estimates of reserves of both gas and oil. Cronquist has provided additional guidelines regarding application of PVT correlations.

Volumetric Methods

Pitfalls in volumetric methods include failing to integrate subsurface (well) data with seismic data, incorrectly constructing net-pay isopachs, and applying global correlations without adjustments for local conditions. Some of these pitfalls are discussed in the following paragraphs.

Structural Mapping. Fig. 18.32 is a log section marked to indicate a structural top at 6,973 ft ss, top of first porosity at 7,018 ft ss, and an OWC at 7,133 ft ss. The three porosity intervals (at 7,018, 7,064, and 7,098 ft ss) might be part of a single pressure-connected reservoir, or they might be three separate reservoirs. Well log data alone usually are insufficient to resolve such uncertainties. If the single-reservoir scenario can be confirmed, a reservoir structure map incorporating the top of the first porosity (7,018 ft ss) and the OWC at 7,133 ft ss might be appropriate. Net-pay isopach maps of each pay interval could be constructed using a common OWC.

• 

  Fig. 18.32 – Well log section (after Mistrot).

An alternate geologic interpretation might indicate the likelihood of the continuation of the two 10-ft shale breaks over the area of the accumulation. Should this situation exist, it would be appropriate to recognize three separate reservoirs. The upper two would have P1 reserves limited to the LKO depths of 7,054 and 7,092 ft ss, respectively.

Additional wells might be required to confirm or deny the effectiveness of the intervening shale members. Assuming a single reservoir in similar circumstances might cause P1 reserves to be overstated significantly, should subsequent information support the presence of more than one reservoir. A structure map using a structural top of 6,973 ft ss, without adjusting for the distance between this top and the top of porosity, would lead to overstatement of the productive area and reserves through exaggeration of the reservoir area. Fig. 18.33 illustrates the potential overstatement of reservoir extent, using lowest known hydrocarbons (LKH) limits for three sand intervals, A, B, and C, that might be three individual reservoirs and the marker, M. Shaded areas above the individual LKH levels may be considered proved reserves. The crosshatched areas may be considered P2 or P3 reserves. Continued monitoring of performance history and/or development drilling would confirm the presence of a single accumulation or of two or three separate reservoirs.

• 

  Fig. 18.33 – Single-well cross section illustrating the possibility of three separate reservoirs.

Isopach Mapping.Isopach maps often are prepared improperly, which almost always leads to overstatement of O/GIP. Fig. 18.34 illustrates a common pitfall of assuming a net-pay buildup updip from well control. Given that the maximum net sand observed in the immediate area is only 45 ft, there is no justification to assume such a buildup. If the dry hole to the north had a total net sand thickness greater than 45 ft, then a buildup in net pay to the observed maximum net sand might be justified. Also, there is uncertainty regarding the position of the fault bounding the northwest side of the reservoir, and the geologist’s interpretation might have been optimistic.

• 

  Fig. 18.34 – Net gas isopach (after Gaston).

Fig. 18.35 is similar to Fig. 18.34, but the area updip from the highest productive wells is interpreted to be no more than 45 ft thick. Also, the fault has been shifted to the southeast as a result of an alternate fault interpretation, which results in significantly less reservoir volume than the original interpretation. Which is correct? Is the difference from a pitfall or bias? One should be vigilant in discerning the differences in reserves estimates resulting from either bias or a pitfall, and should make appropriate revisions as warranted.

• 

  Fig. 18.35 – Net gas isopach (after Gaston).

Performance Methods

Many pitfalls await the unwary who use performance methods to estimate reserves. Several of the more common pitfalls are discussed here: analysis of production decline trends to estimate reserves for wells still in the transient stage; extrapolation of performance indicators to unrealistic economic limit conditions; misuse of composite decline curves; physical life limitations; failure to recognize the effect of interference between wells; failure to reconcile results of volumetric and performance analyses; and miscalculation/misuse of p/z vs. G_p plots.

Analysis of Production Decline Trends During Transient Flow.An expanding drainage radius and (initially) steep, hyperbolic declines in production rate characterize transient flow from wells. Reserves estimates during this stage of production usually will be too low if they are based solely on decline-trend analysis, without appropriate adjustments. The problem is especially severe in shallow, low-permeability gas reservoirs, where wells may exhibit transient flow over a substantial part of their productive life.

Unrealistic Economic-Limit Conditions.Semilog plots of f_o vs. N_p commonly are used to estimate reserves for oil wells in waterdrive reservoirs. Such plots frequently are used before there is a clearly defined decline in oil production rate, which can be a pitfall. Plots of f_o vs. N_p can be extrapolated to a local average "f_o cutoff," but this cutoff might be too low for wells with low productivity. For example, in many areas, the average f_o cutoff is 0.01; however, if a well is capable of producing only 250 B/D (oil plus water) and the economic limit is 5 BOPD, then the f_o cutoff for this well should be 0.02, not 0.01.

Misuse of Composite Decline Curves.Projecting decline trends of composited production from multiple wells to estimate proved reserves often leads to an overstatement of reserves. Failure to thoroughly analyze the effects of operator efforts to sustain production rates, as well as of marketing limitation or transportation restriction influences, is a common pitfall. Production declines of individual wells and the composite production stream might have been mitigated by workovers, recompletions, new wells, stimulation, and/or compression equipment upgrade or other equipment and facility upgrades, the benefits of which might not be available during the forecast period to sustain the demonstrated production trend. The engineer should always try to evaluate the performance of individual wells or completions, even if the production history has been computed using an allocation of the composite production quantities.

Physical Life Limitations.The extrapolation of monthly production rates of oil and/or gas from a well can extend for 40, 60, or maybe 100 years, depending on the economic assumptions that are used. When estimating such reserves, consider the cost of drilling a replacement well and the replacement of infrastructure facilities. Some engineers arbitrarily limit future projection lives to 30 to 50 years, depending on the specific circumstances of each production area.

Failure To Recognize the Effect of Interference Between Wells.Analyzing each well in a common reservoir often is appropriate for estimating reserves, particularly for a fully developed reservoir being produced under the control of a single operator; however, when individual wells are not analyzed, be aware of the potential for interwell interference to affect individual well-drainage patterns. Examples are the drilling of infill wells, which might increase reserves or serve only to accelerate rate, and increased production, from competitor-operated wells.

Failure To Reconcile Results of Volumetric and Performance Analyses.During the early life of a reservoir, performance-data analysis might suggest more or less reserves than are indicated by volumetric methods. Depending on the degree of difference and the economic consequences thereof, it might be appropriate to review the performance and volumetric data, as well as the analysis methods, to resolve these discrepancies. Such a review might reveal one or more causes (e.g., inappropriate net-pay cutoffs, invalid drainage-volume estimates, poor assumptions regarding drive mechanism, and/or unrealistic decline-trend projections).

Misuse and/or Improper Calculation of p/z vs. Gp Plots.Plots of p/z vs. G_p are powerful tools for analyzing the performance of gas reservoirs; however, there are several reservoir scenarios in which these plots are misused or misinterpreted, including geopressured reservoirs, partial waterdrive, conjectural economics of multistage compression, and plot miscalculation.

Geopressured Reservoirs. In geopressured reservoirs, plots of p/z vs. G_p frequently exhibit an anomalously low initial slope, followed by a steeper slope. The initial low slope might be caused by water influx and/or PV compressibility. The steeper slope, which might not appear until later in reservoir life, might be because of depletion of a limited aquifer. As discussed in the Special Problems section of this chapter, depending on the stage of production maturity, it might not be possible to determine the dominant drive mechanism in such reservoirs. In such case, either adjust plots of p/z vs. G_p or use an alternate material-balance method.

Partial Waterdrive. In many cases, a plot of p/z vs. G_p is insufficient to determine whether there is water influx into a gas reservoir under study. Failure to recognize such influx may lead to substantial overestimates of gas reserves. The uncertainty in such cases might be resolved by using a procedure, discussed in the Geopressured Oil/Gas section of this chapter, that is based on the Havlena and Odeh method. Ignoring the rock-compressibility term and rearranging Eq. 18.52 yields:

....................(18.59)

If there is no water influx, the second right-side term equals zero and the left-side term vs. G_p should plot as a horizontal line, with the y-axis intercept equal to G_Fi. If there is water influx, however, the plot will be curved, with the degree and type of curvature dependent on the degree of water influx.

Conjectural Economics of Multistage Compression. In some operating and economic scenarios, RE of gas from volumetric reservoirs may exceed 95% GIP; however, such REs typically require multistage compression, the economics of which might be conjectural in the early stages of reservoir history. Be wary of assuming that installing such compression facilities can be justified economically, unless there is considerable experience in an analogous reservoir in a comparable operating and economic setting. On offshore platforms, for example, there may not be enough space to install such facilities, and major expansion may be infeasible, either structurally or economically.

Improper Calculations of p/z Values. Some of the more commonly seen problems associated with the determination of static reservoir pressures and related z-factor are:

• Nonrepresentative pressures obtained when some wells completed in the reservoir remain on production.
• Relying on shut-in wellhead pressures to calculate bottomhole pressures in the presence of water and hydrocarbon liquids.
• Shut-in time that is inadequate to achieve static pressure.
• Using inappropriate gas composition to compute z-factors.
• Not adjusting bottomhole pressures to a common subsea depth.

Each of these problems is discussed briefly in the following paragraphs.

Nonrepresentative pressures may occur when operators do not shut in certain wells because of high liquid ratios or other concerns. They allow these wells to continue to produce while other wells in the same reservoir are shut in for a pressure survey. Other operators might obtain static reservoir pressures in new wells being completed in a common reservoir at the same time when other reservoir wells continue to produce. Be cautious in relying on such pressure information in any circumstance wherein the reservoir is not allowed to approach an equilibrium pressure.

Shut-in wellhead pressures may be used to reliably calculate reservoir pressures only if the composition and relative volumes of the wellbore fluids are known. The range of error in the calculated values increases if there is a static liquid level (either condensate or water) in the wellbore at an unknown depth.

Inadequate shut-in time to achieve static reservoir pressure occurs commonly. Knowledge of actual shut-in time is important for assessing data reliability. Third-party engineers might not have full access to the operator’s data. In many cases, such data may have been lost or misplaced because of transfers of interest. For example, a reserves engineer might have only publicly reported pressure data for use in reservoir analysis, and might not be aware of the length of the shut-in period before the pressure measurement or of the consequences of this lack of knowledge.

Using an inappropriate gas composition to calculate z-factors usually is the result of assuming a constant gas composition throughout the life of a gas reservoir. While this might be appropriate for a dry-gas reservoir, it could cause serious errors for a retrograde gas reservoir if static reservoir pressure is reduced to less than the dewpoint pressure during production. Ignoring the resultant change in composition of the reservoir gas in retrograde accumulations can cause errors in calculation of the z-factor, in-place hydrocarbons, and reserves.

Not adjusting bottomhole pressures to a common depth in a given reservoir often is attributed to time constraints or carelessness. Although this might cause minor errors in low-pressure, low-relief, dry-gas reservoirs, it might be critical for high-relief oil reservoirs.
*

This section was inspired by a presentation by Harry Gaston Jr. at the 1992 Annual Convention of the SPEE on 13–16 June 1992 at Jackson Hole, Wyoming.

Nomenclature

a	=	terminal effective decline rate
a1	=	decline rate, initial, 1/t
A	=	area of reservoir or accumulation, acre
A	=	constant (in Eq. 18.57 and Table 18.13 only)
Ag	=	area of gas cap or gas reservoir, acre or hectare
Ao	=	area of the oil zone, acre or hectare
b	=	hyperbolic decline exponent (same as n, used by earlier authors)
B	=	constant
Bg	=	formation volume factor, gas, Rcf/scf
Bgi	=	initial formation volume factor, gas, Rcf/scf or RB/scf
Bo	=	formation volume factor, oil, RB/STB
Bob	=	formation volume factor at the bubblepoint, oil, RB/STB
Boi	=	initial formation volume factor, oil, RB/STB
Bt	=	formation volume factor, total, RB/STB
Bti		initial total formation volume factor, RB/STB
Bw	=	formation volume factor, water, RB/STB
cp	=	compressibility, pore volume, vol/vol/psi
cw	=	compressibility, water, vol/vol/psi
C	=	water-influx constant
C	=	constant (in Eq. 18.57 and Table 18.13 only)
CD	=	direct operating cost, U.S. dollar/well
Cgi	=	initial sorbed gas concentration, scf/ton, dry, ash-free coal or shale
Ci	=	condensate (distillate) initially in place, STB
Cpu	=	ultimate condensate production, STB
CRi	=	initial condensate reserves, STB
Ctp	=	transportation costs, U.S. dollar/bbl
D	=	curve-fit coefficient
D	=	curve-fit coefficient (in Eq. 18.57 and Table 18.13 only)
Di	=	initial decline rate
Ec	=	water, vol/vol/psi
ED	=	microscopic displacement efficiency, fraction
Eg	=	expansion of the initial gas cap, if one is present, RB/scf
Eo	=	expansion of a unit volume of oil and dissolved (solution) gas initially in place, RB/STB
ERc	=	recovery efficiency of condensate, fraction
ERg	=	recovery efficiency of gas, general, fraction
(ERg)pd	=	recovery efficiency of gas attributable to pressure depletion
(ERg)pwd	=	recovery efficiency of (free) gas attributable to partial waterdrive, fraction
(ERg)swd	=	recovery efficiency of (free) gas attributable to strong water drive, fraction
ERo	=	recovery efficiency of oil, general, fraction
(ERo)sg	=	recovery efficiency of oil attributable to solution gas drive, fraction
(ERo)wd	=	recovery efficiency of oil attributable to waterdrive, fraction
EV	=	fraction of the initially gas bearing volume swept by the aquifer (volumetric sweep efficiency), fraction
fa	=	average weight fraction of ash, fraction
fm	=	average weight fraction of moisture, fraction
fo	=	fractional flow of oil
Fg	=	Thomeer parameter for capillary pressure curves
FpR	=	volume of cumulative oil, gas, and water production, RB
Frg	=	royalty on gas, fraction
Fro	=	royalty on oil, fraction
FRA	=	recovery factor, analogous reservoir
FRS	=	recovery factor, subject reservoir
GFi	=	free gas initially in place, scf or m3
Gi	=	gas-in-place at initial reservoir conditions, scf
Gp	=	cumulative gas production, scf
Gpu	=	ultimate cumulative gas production, scf
GR	=	(remaining) gas reserves, scf
GRFi	=	initial free gas reserves, scf
GRi	=	initial gas reserves, scf
GRSi	=	initial solution gas reserves, scf
GSi	=	solution gas initially in place, scf
h	=	thickness, ft
hn	=	net pay thickness
hn1	=	net thickness of upper (oil) zone, ft
hn2	=	net thickness of the lower (oil) zone, ft
hng	=	average net thickness of gas cap or gas reservoir, ft or m
hno	=	average net oil pay, ft or m
hs	=	shale thickness, ft
ht	=	gross oil column thickness
k	=	permeability, md
ka	=	air permeability, md
ke	=	effective permeability
kg	=	effective gas permeability, md
kH	=	horizontal permeability
ko	=	effective oil permeability, md
kro	=	relative oil permeability, dimensionless
krw	=	relative oil permeability, dimensionless
kV	=	vertical permeability, md
kw	=	effective water permeability, md
KA	=	coefficient
KB	=	coefficient
K1	=	constant
K2	=	constant
K3	=	constant
m	=	ratio of initial gas cap volume to initial oil column volume, dimensionless
mi	=	volume of gas injected, multiple of initial gas cap volume, dimensionless
n	=	variable
NG	=	gravity number, dimensionless
Ni	=	oil initially in place, STB or m3
Np	=	cumulative oil production, STB
Npa	=	cumulative oil production at abandonment, STB
Npaw	=	cumulative oil production, well, at abandonment, STB
Npc	=	cumulative oil production at point "c," STB
Npu	=	ultimate oil production, STB
NRi	=	initial oil reserves, STB
p	=	pressure, static reservoir, general, psia
pa	=	abandonment pressure, psia
pb	=	bubblepoint pressure, psia
pd	=	dewpoint pressure, psia
pg	=	wellhead price of gas, U.S. dollar/STB
pi	=	initial reservoir pressure, psia
pn	=	laboratory net (hydrostatic) pressure (confining pressure minus pore pressure), psia
po	=	wellhead price of oil, U.S. dollar/STB
pob	=	overburden pressure, psia
PcL	=	capillary pressure at laboratory conditions, psia
Pcm	=	mercury (air) capillary pressure, psia
PcR	=	capillary pressure at reservoir conditions, psia
Pdm	=	mercury (air) displacement pressure, psia
q	=	production rate, general, STB/month or scf/month
q1	=	production rate at the beginning of a period
q2	=	production rate at the end of a period
qel	=	production rate at the economic limit, general, scf/D or STB/D
qg	=	gas production rate, scf/month
qoel	=	oil production rate at economic limit, BOPD
Q	=	cumulative production
R	=	gas/oil ratio, general, scf/STB
Rc	=	condensate/gas ratio, STB/MMscf
Rcd	=	condensate/gas ratio at dewpoint pressure, STB/MMscf
Rci	=	initial condensate/gas ratio, STB/MMscf
RcuD	=	cumulative condensate/gas ratio at abandonment divided by initial condensate/gas ratio, dimensionless
Rng	=	net-to-gross pay ratio, dimensionless
Rngo	=	average net-to-gross pay ratio in initially oil-bearing zone
Ro	=	vitrinite reflectance, %
Rp	=	cumulative (producing) gas/oil ratio, scf/STB
Rpz	=	ratio of abandonment p/z to initial p/z , or pazi/piza
Rs	=	gas/oil ratio, ft3/STB
Rsb	=	gas/oil ratio at bubblepoint pressure, scf/STB
Rsi	=	initial solution gas/oil ratio, scf/STB
Sgr	=	residual gas saturation, fraction
Shi	=	initial hydrocarbon saturation, fraction
So	=	oil saturation, fraction
Sor	=	residual oil saturation, fraction
Sw	=	water saturation, fraction
Swfi	=	interconnected fracture water saturation, fraction
Swg	=	water saturation in the free-gas zone, fraction
Swi	=	initial water saturation, fraction
Swo	=	water saturation in the oil zone, fraction
t	=	time, months or years
tel	=	(incremental) time for production to decline from current rate to economic limit rate, days, months, or years
t1	=	time 1
t2	=	time 2
TA	=	ad valorem tax, U.S. dollar/STB
TP	=	production tax, U.S. dollar/STB
VI	=	molar volume of ideal gas
VR	=	molar volume of real gas
Vto	=	gross volume of initially oil-bearing rock, acre-ft
We	=	cumulative water influx, RB
Wp	=	cumulative water production, STB
Xa	=	the actual quantity of reserves
Xe	=	the estimated quantity of reserves
z	=	gas compressibility factor, general, dimensionless
za	=	gas compressibility factor at the economic limit, dimensionless
Zfw	=	vertical distance above free-water level, ft
zi	=	gas compressibility factor at initial conditions, dimensionless
α	=	dip angle, degree
γg	=	specific gravity of solution gas (air = 1.0), dimensionless
γos	=	specific gravity of stock-tank oil, dimensionless
ΔGp	=	incremental cumulative gas production, scf
ΔNp	=	incremental cumulative oil production, STB
Δp	=	pressure, incremental, psi
ΔQp	=	incremental cumulative production, ΔGp or Δ Np, as the production rate declines from q1 to q2
Δt	=	incremental time between t1 and t2
θL	=	contact angle at laboratory conditions, degree
θR	=	contact angle at reservoir conditions, degree
μ	=	viscosity, general, cp
μo	=	oil viscosity, general, cp
μob	=	oil viscosity at the bubblepoint, cp
μoi	=	initial oil viscosity, cp
μw	=	viscosity, water, general, cp
μwi	=	initial water viscosity, cp
ρ	=	density, general, g/cm3
ρc	=	density, coal, g/cm3
ρg	=	density, gas, g/cm3
ρo	=	density, oil, psi/ft or g/cm3
ρor	=	density of reservoir oil, lbm/bbl
ρw	=	density, water, psi/ft
σL	=	interfacial tension at laboratory conditions, dyne/cm
σR	=	interfacial tension at reservoir conditions, dyne/cm
Ф	=	porosity, general, fraction
Фf	=	interconnected fracture (effective) porosity, fraction
Фg	=	porosity in gas zone, fraction
Фo	=	porosity in oil zone, fraction

References

SI Metric Conversion Factors

acre	×	4.046 856	E − 01	=	ha
acre-ft	×	1.233 489	E + 03	=	m3
°API		141.5/(131.5 + °API)		=	g/cm3
bbl	×	1.589 873	E − 01	=	m3
°F		(°F − 32)/1.8		=	°C
ft	×	3.048*	E − 01	=	m
ft3	×	2.831 685	E − 02	=	m3
lbm	×	4.535 924	E − 01	=	kg
mile	×	1.609 344*	E + 00	=	km
psi	×	6.894 757	E + 00	=	kPa
psia	×	6.894 757	E + 00	=	kPa
square mile	×	2.589 988	E + 06	=	m2
ton	×	9.071 847	E − 01	=	Mg

*

Conversion factor is exact.