PEH:Petrophysical Applications

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 3H – Petrophysical Applications

H.R. (Hal) Warner Jr., Warner Consulting Services and Richard Woodhouse, Independent Consultant

Pgs. 421-493

ISBN 978-1-55563-120-8
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This chapter discusses the determination of lithology, net pay, porosity, water saturation, and permeability from wellbore core and log data. The chapter deals with "Development Petrophysics" and emphasizes the integration of core data with log data; the adjustment of core data, when required, to reservoir conditions; and the calibration and regression line-fitting of log data to core data. The goal of the calculations is to use all available data, calibrated to the best standard, to arrive at the most accurate quantitative values of the petrophysical parameters (i.e., lithology, net pay, porosity, water saturation, and permeability). Log analysis, cased-hole formation evaluation, and production logging are not covered here.

The following topics are covered in this chapter: petrophysical data sources and databases, lithology determination, net-pay (or pay/nonpay) determination, porosity determination, fluid-contacts identification, water-saturation determination, permeability calculations, case studies, other considerations in petrophysical calculations, and summary and conclusions. This chapter concerns the foot-by-foot calculations of the five petrophysical parameters at the wellbore. It does not cover the propagation of the wellbore values, or "populating" of static or dynamic reservoir models, vertically and areally over the whole of the reservoir volume. Because other chapters in this section of the Handbook discuss the technical details of various well logs and coring, these details are generally assumed as the basis for this chapter and are referenced accordingly.

In practical terms, petrophysics is used for two types of calculations: determination of original hydrocarbons in place [original oil in place (OOIP) or original gas in place (OGIP)] and their distribution, and reservoir-engineering dynamic flow calculations. For the development geoscientists (geologists, geophysicists, and geostatisticians), petrophysics means developing the detailed stratigraphic, depositional, and diagenetic descriptions of the reservoir, both vertically and areally. To make accurate calculations of OOIP or OGIP and the various flow calculations, accurate foot-by-foot calculations of lithology, net pay, porosity, water saturation, and permeability are necessary. These calculations need to be made not only as overall calculations, but also so that the variation and distribution of these parameters are determined appropriately.

Some of the petrophysical calculations can be made in several ways, particularly for porosity and water saturation. One key to arriving at an accurate petrophysical calculation is to obtain the same quantitative result with a variety of techniques. An important consideration is the acquisition and handling of the various types of petrophysical data and, for each reservoir, the preparation of its unique petrophysical database. Petrophysical data take many forms and, for many reservoirs, may not be as comprehensive as desired. The technical personnel working with these data have to review what data are available, their quality, and what additional data might be acquired from the existing wellbores and from preserved and unpreserved cores. Finally, if there are sufficient financial stakes, new wells might be drilled, cores cut, various additional sample measurements made, and both conventional and special logs run to obtain other desired petrophysical information.

As mentioned previously, this chapter does not deal with log analysis, the petrophysical evaluations made when no core, mud log, or tester data are available. Log analysis is used universally and is generally successful in the identification of oil and gas reservoirs and in the preliminary estimation of their volumes.  However, log analysis augmented and calibrated with core and other data provides the most accurate quantification of oil and gas volumes present in a well and best represents the practice of petrophysics.

This chapter is focused on petrophysical calculations at the reservoir level, where there are several to hundreds of wells with logs and significant amounts of core data that need to be integrated to develop the most accurate overall values for the petrophysical parameters over the whole of the reservoir. The techniques discussed also apply to single wellbores, but many of the complications are not a concern in single-well evaluation.

This chapter does not cover some special cases, such as oil shales, tight gas-sand reservoirs, or coalbed-methane reservoirs. Petrophysical calculations for tight gas-sand reservoirs and coalbed-methane reservoirs are discussed in separate chapters on these topics in the Emerging and Peripheral Technologies volume of this Handbook.

Petrophysical Data Sources and Databases

In making the petrophysical calculations of lithology, net pay, porosity, water saturation, and permeability at the reservoir level, the development of a complete petrophysical database is the critical first step. This section describes the requirements for creating such a database before making any of these calculations. The topic is divided into four parts: inventory of existing petrophysical data; evaluation of the quality of existing data; conditioning the data for reservoir parameter calculations; and acquisition of additional petrophysical data, where needed. The overall goal of developing the petrophysical database is to use as much valid data as possible to develop the best standard from which to make the calculations of the petrophysical parameters.

Inventory of Existing Petrophysical Data

To start the petrophysical calculations, the data that have been gathered previously from various wellbores throughout the reservoir must be identified, organized, and put into electronic form for future calculations.

In a typical reservoir, several "generations" of wells have been drilled. The exploration wells that discover and delineate the reservoir constitute the first generation of wells. These wells are usually drilled with scant knowledge of formation pressure, which results in deep mud-filtrate invasion in the reservoir interval for which there may be significant hole-washout problems. For this series of wells, the muds used may vary from one well to the next, and this phase may take from 1 to 10 years to complete. The second generation is the group of wells drilled during initial reservoir development. These wells are likely to be drilled with a common mud system, which might be either water-based or oil-based and will be tailored to help minimize the near-wellbore damage caused by detrimental mud-filtrate/reservoir-rock interactions. Third-generation wells may also be available. These wells would be those from later field-development activities and may have been drilled 5 to 15 years after the initial development wells were drilled.

The logs from these various generations of wells can vary in several regards. First, the logs may have been run by various service companies and may not be directly comparable to each other, even if they were from the same time period. Secondly, if the logs were run by the same service company, they may still have significant differences because different generations of logging tools were used for each set of wells. An additional difference may be between logging-while-drilling (LWD) logs and those run on wireline. LWD logging is often associated with high-angle wells. This geometry can lead to significantly different responses from zones previously seen in vertical wells and may lead to petrophysical mapping issues for high-angle-well evaluations, if not correctly accounted for.

Many of these same caveats hold for core data. The early wells may or may not have been completely cored through the reservoir interval. Later wells are more likely to be fully cored, although some zones of particular interest may have a greater concentration of cores. The routine data acquisition from cores also may vary because of different laboratories performing the core analysis on each well and because of changes in laboratory procedures and equipment over the intervening years. Also, different portions of the reservoir interval may have been analyzed with different techniques because they differ in degree of consolidation or rock heterogeneity. Special-core-analysis (SCAL) data are likely to be a variety of information because the SCAL programs for each well’s cores will be unique to the perceived data needs when each well was drilled. With respect to the geologists’ core descriptions, there may be differences between wells because different individuals prepared the various core descriptions with different techniques and emphasis. The number of petrographic measurements on cores [e.g., thin sections, scanning electron microscope (SEM), and X-ray diffraction (XRD)] is likely to vary widely from well to well.

First, the technical team must prepare several spreadsheets tabulating the basic information about each of the drilled wells. Tables 3H.1 through 3H.3 show templates for a spreadsheet for the log data and two for the core data, respectively. These spreadsheets provide quick access by the technical team to see what data are available, what form the data are in, how much of each type of data is available, and where gaps exist in the database. Separate sets of spreadsheets should be prepared for each of the reservoirs, if there are several separate reservoirs in a particular oil or gas field.

• 

  Table 3H.3

 Next, as much as possible of these detailed log and core data should be obtained in electronic form. There are a number of commercially available software packages that are useful for this purpose and can be used to access the log data and the routine-core-analysis data. However, the routine-core-analysis data may also be entered into spreadsheet form for easy use by the engineers and geoscientists. To the extent possible, the geologists’ core descriptions and petrographic measurements should be converted to electronic form for use with the other types of petrophysical data. The SCAL data will require special spreadsheet formats because each of these types of data is unique.

Core and log databases should be considered as a part of the overall reservoir database. In establishing and maintaining the overall reservoir database, controls should be in place to ensure high quality of the data and the timely inclusion of all data that are obtained.

Evaluation of the Quality of Existing Data

The second step in working with the petrophysical data is to evaluate the quality of each of these types of data. This step requires that the data inventory and database preparation steps are completed first so that this second step can occur as a systematic and complete process. The evaluation process is a "compare and contrast" exercise.

Log Data. The evaluation of log-data quality has many aspects.  First, the drilling-mud and hole-condition effects may lead to no valid readings being recorded on the logs. This should be noted in the petrophysical database. "Flags" of various types should be stored, for example, to denote intervals where the hole size exceeds some limit, or where there is cycle-skipping on the sonic logs. Logging tools sometimes become temporarily stuck as a log is being run. This results in constant readings on each of the several detectors on the tool string. When the tool is stationary, each detector on it becomes stuck at a different depth, so the interval of "stuck" log will vary for each log curve. For example, the neutron log typically sticks over an interval approximately 10 ft above the stuck interval on a density log. It may be possible to "splice" in a replacement section of log from a repeated log section, or the invalid readings may simply be deleted.

Second, each log is formally calibrated before the start of each logging run by various calibration standards. The logs are also checked again after the run. Calibration records may assist in determining the quality of the logs. Perhaps of equal importance are the written comments on the log heading made immediately after the job by the logging engineer.

Third, systematic influences on the quality of log readings should be corrected. For example, if some of the wells are drilled with water-based mud (WBM), the effect of WBM-filtrate invasion on various resistivity logs can be quantified. This is done by computations made using the various resistivity logs in the same wellbore; however, where deep invasion of WBM filtrate occurs, offsetting wells drilled with oil-based mud (OBM) give a good comparison. The induction logs in OBM wells can provide accurate true reservoir resistivity values in thick hydrocarbon zones. See the chapter on resistivity and SP logging in this volume of the Handbook for more information on how invasion effects can be handled. Boreholes are not always right cylinders. Holes sometimes become spiral shaped during the drilling process, and their logs show sinusoidal responses.

Routine-Core Analysis Data. The evaluation of the quality of routine-core-analysis data starts with crossplot comparisons of various wells’ porosity, permeability, grain density, and saturation data on a reservoir or zone basis. With various wells’ data presented on the same plot (permeability vs. porosity, grain density vs. porosity, S_w vs. permeability, or S_w vs. porosity), one can determine if there are significantly different trends from one well to the next. Differences may exist, and there may be good geologic reasons for such differences; however, some laboratory data may be of suspect quality and may require further review and inquiry.

With respect to core’s fluid-saturation data, the evaluation process must be an end-to-end review process. This evaluation begins with knowledge of the drilling mud used and whether the cores were specially cut and preserved to try to obtain undisturbed connate S_w. Second, review the core sampling and routine-core-analysis laboratory procedures to understand how those steps impacted the final fluid-saturation data reported. Well-preserved OBM cores that are analyzed using the Dean-Stark water-extraction procedure typically provide the most valid values for connate S_w in the hydrocarbon column above the mobile gas/water or oil/water transition zone. In aquifers and other mobile-water intervals, OBM-filtrate invasion displaces mobile water during core cutting, and fluid "bleeding" occurs during core surfacing. As a result, OBM-core water saturations are too low and not representative of true resident saturations. They may also be more uncertain in very poor quality, high-S_w rock intervals in which it is difficult to make accurate porosity and water-volume determinations.

WBM cores can provide a qualitative measure of residual-oil saturations in the oil column after accounting for oil shrinkage and bleeding.  WBM cores in oil reservoirs may also provide information about oil/water contacts (OWCs) and the S_w of low-quality rock intervals above the OWC into which oil has never entered because the entry capillary pressure, P_ce, has not been exceeded.

The OBM and WBM routine-core-analysis data should be compared and contrasted to identify how each alone, and in combination, can be used to answer certain petrophysical issues. Also, the trends of these sets of data (e.g., permeability vs. porosity) should be compared as one of the evaluation tools.

Coring in friable, uncemented, and unconsolidated sands demands special coring, handling, and analysis techniques so that the grain structure is not altered. Modern practice is to use rapid drilling rates and fiberglass or aluminum inner core barrels to minimize the friction as the core enters the barrel. The core is tripped to surface slowly and smoothly to allow dissolved gas to exit the core without disruption. The last two stands of drillpipe are the most critical because during this time the volume of gas doubles, then quadruples. During the laying down of the inner core barrel, precautions are needed to prevent bending and core deformation. For transporting the core, the inner core barrel can be cut into short (1-m/3-ft) lengths, the ends sealed with caps, then the voids between the core and the sections of the inner core barrel filled with resin. Freezing the cores in their segments before transportation is sometimes used to prevent damage, but is not very effective when there is little formation water. The costs are also higher. Cross-section X-raying of the tubes reveals which cores are damaged and which are suitable for measurements in the laboratory. See the American Petroleum Institute’s (API) RP 40 Recommended Practices for Core Analysis for details about the various types of core analysis and details of the laboratory procedures. 

Special Core Analysis Laboratory Data. SCAL-data evaluation begins with a comparison of the same type of data from different laboratories and whether data from each laboratory are internally consistent. SCAL data are much more difficult to measure, and the procedures often differ from laboratory to laboratory. The challenge is to determine which of these data are more correct and should be used to make various petrophysical-parameter calculations. With SCAL data, the best approach is to have those individuals who are expert in taking and evaluating these types of data review the procedures of the various laboratories and the reported data and provide an opinion about which of these data should be used and which should be discarded.

Capillary pressure (P_c/S_w) data can be susceptible to not being taken to fully equilibrated conditions because it occasionally takes longer for equilibrium to occur than typical laboratory procedures require. This is because the relative permeability of the wetting phase becomes so low that equilibrium is very slowly reached. Additionally, the porous-plate method is susceptible to loss of capillary contact between the core plug and the porous plate. In both situations at higher capillary pressure, P_c, reported S_w values will be too high. 

For the rock electrical-property laboratory measurements and how they are reported, the raw laboratory data should be reviewed very carefully to ensure that the data are of high quality and are properly reported for later S_w calculations. These measurements, as a function of brine saturation, again have the potential problem of nonequilibrium saturation distributions. Sometimes the saturation exponent, n, is a function of brine saturation, but this nonlinear behavior is typically not reported as such by the reporting laboratory. Restoration of the in-situ brine-saturation distribution is absolutely required for making laboratory rock-electrical-property and P_c measurements that lead to accurate reservoir S_w calculations, so it is best if any restored-state core-plug measurements agree with similar measurements made on native-state core plugs. Finally, the resistivity index (I_R) vs. S_w data should be taken over a range of S_w values equivalent to those found in the particular reservoir. Sometimes these data are taken only down to 30% pore volume (PV) S_w, yet some of the in-situ S_w values may be in the 5 to 20% PV saturation range. If this is the case, laboratory electrical-property measurements may not lead to accurate in-situ S_w calculations from resistivity logs for the low S_w values.

Internal consistency in a laboratory’s reported results is a very good "first test" to determine if some of the data are immediately suspect. For example, if the measurements of the reduction in porosity from surface to reservoir stress vary from one set of measurements to another for a particular laboratory, then those measurements must be discarded or used very carefully. As another example, with respect to P_c/ saturation measurements, there is an immediate concern if the air/water and air/oil P_c/ saturation measurements do not reasonably overlay after accounting for the interfacial-tension (IFT) and contact angle difference between these fluid pairs. There would be a similar concern when mercury-injection P_c data are available. Again, experts in taking and using these types of data should evaluate the quality of the various sets of laboratory measurements.

Conditioning the Data for Reservoir Parameter Calculations

Conditioning the log and core data for calculations of the various petrophysical parameters includes adjustments from surface-to-reservoir conditions, normalization, and environmental-correction factors. The emphasis here is on obtaining, at reservoir conditions, a set of reliable petrophysical data that involve many wells with many sets of log data and a variety of routine and SCAL core measurements.

Log Data. Each type of log data may need to be conditioned in unique ways for the subsequent petrophysical-parameter calculations. The purpose of each of these preliminary sets of calculations is to put that portion of the overall petrophysical database on a common basis.

The log data, as a whole for each well, must be depth aligned so that the various log measurements at each depth refer, as closely as possible, to the same rock volume. Differences in log response characteristics and in each tool’s path in the hole make this a complex task. Lining up the bed boundaries is particularly important. Some commercial software programs have automatic routines that perform the depth-alignment process, but, more often, shifts are made manually. Borehole-size corrections are required for most logs, while the readings of some tools require correction for other factors, such as temperature, mud density, and mud resistivity.

Histograms are often used to compare the log values of one well with the typical field values of the same log type. This process can identify logs that are miscalibrated, and it may indicate by how much they should be corrected. Bad logs that cannot be corrected by reasonable-sized shifts should be discarded from the database.

Gamma Ray Logs. For reservoir-wide petrophysical calculations, gamma ray (GR) logs are often normalized to reduce the variation in their values from one well to the next in intervals that are considered to have the same rock properties, usually clean sands and specific thick shale intervals.

Density and Neutron Logs. Log calibrations can be checked in situ because they read nearly constant values in certain formations. Anhydrite has a density value of 2.98 g/cm³ and close to zero neutron porosity, while salt has a density value of 2.04 g/cm³ and zero neutron porosity. There are few "marker" beds in which higher neutron-log readings can be verified. (See the chapter on Nuclear Logging in this volume of the Handbook.)

Sonic Logs. Sonic logs read near-constant velocity values inside steel casing (57 μsec/ft) and in evaporate formations such as anhydrite (50 μsec/ft) and salt (67 μsec/ft). Where they occur, these constant values are used to check the correct operation of the compressional-wave travel-time tool.

Resistivity (Laterolog and Induction) Logs. One of the main goals in developing the reservoirwide petrophysical database is to provide the most accurate true resistivity values for subsequent S_w calculations. (See the chapter on resistivity and SP logging in this section of the Handbook for information on electric logging.) Often there are several generations of laterolog and induction-logging devices that were run in the various wellbores, and this leads to a variety of data sources with different depths of investigation. Also, over the past two decades, various calculation techniques have been published to deconvolve the reported foot-by-foot resistivity values to obtain more-accurate estimates of true resistivity, R_t. Some of the more modern induction tools incorporate deconvolution into the wellsite processing. 

Routine-Core Analysis and SCAL Data. To prepare the routine-core-analysis data for use in reservoir petrophysical calculations, most of these data require adjustment from surface to reservoir conditions.

One of the first steps is aligning core data to depth-aligned log data. Frequently, a GR log of the core is measured in the laboratory, and this is used to depth match the core to the in-situ GR log. Also, in a sandstone with occasional shale intervals of low permeability, the core-analysis data must be aligned with those obvious from the downhole GR log. The log data are often digitized on a half-foot basis, but the core data are typically on a one-foot basis. As these different types of data are included in the same electronic database, care must be taken to ensure that some of the individual data points are not lost. This is likely to require a significant degree of user intervention. The core data for a particular well are really several subsets of data, each of which comes from an individual core-barrel run. These subsets of data must be kept together, and each may need to be individually depth-shifted to the log data.

Porosity Data. For the routine-core-analysis porosity data, SCAL measurements of core samples’ porosity at various confining-stress levels are used as the basis for making compaction corrections. Historically, routine-core-analysis porosity measurements were taken at low stress conditions, and SCAL measurements on a small set (10 to 30) of core plugs were made to determine the relationship of porosity to overburden-stress level. Stressed-porosity values are plotted vs. laboratory stressed-porosity values to determine the relationship between the two. Regression of the porosity difference vs. surface porosity gives the same result as regressing stressed porosity vs. surface porosity. Two factors are important to consider in analyzing these plots: whether or not there is a systematic "baseline" laboratory effect related to the equipment’s coreholder tightening against the core plug at the start of the test procedure, and whether there is a systematic relationship. Theoretically, the change in porosity is a function of porosity level; however, many sets of SCAL experimental data indicate the "baseline" effect can dominate the second effect.

In the past decade, an unsteady-state style of equipment has come into fairly common usage in which routine porosity measurements can be made at both low-stress and high-stress conditions.  With this equipment, reservoir-stress-level porosity measurements can be made on each and every core plug during the routine-core-analysis testing; however, typically, high-stress porosity measurements are made only on every fifth or tenth sample for later use in making the porosity adjustment from surface to reservoir conditions.

For some oil reservoirs, or OBM cores, there is a second adjustment that may need to be applied. This effect is that the routine-core-analysis procedures did not clean all of the heavy hydrocarbons from the pore space, and, hence, the measured porosity values are understated. This effect can be evaluated two ways: first, the measured grain densities may appear to be lower than expected for the particular rock type (i.e., grain densities of less than 2.65 g/cm 3 for clean sandstones); and second, if some of the routine core plugs are retested later, the cleaning solvent is found to discolor, and subsequent porosity values are found to be systematically higher than the original values. This second effect [0.5 to 1.0% bulk volume (BV)] can be as large as the stress-related porosity-reduction effect discussed in the previous paragraphs.

Permeability Data. For the routine-core-analysis permeability data, SCAL measurements of core samples’ permeability at various stress levels are used as the basis for making compaction corrections. Historically, routine-core-analysis permeability measurements were taken at low-stress conditions, and SCAL measurements on a small set (10 to 30) of core plugs were made to determine the relationship of permeability to stress level. The "permeability ratio" values (stressed permeability divided by surface permeability) need to be plotted vs. surface-permeability values to determine the relationship, likely to be nonlinear, between the two. Determination of permeability at reservoir conditions is especially important in rocks with air permeabilities of less than 20 md. For low-permeability samples (<2 1="" 2="" reductions="" in="" permeability="" of="" to="" orders="" magnitude="" have="" been="" observed="" between="" values="" at="" ambient="" conditions="" and="" those="" reservoir="" stress="" />
OBM S_W Data. For routine-core-analysis S_w data from OBM cores, the adjustment from the surface values to those at reservoir conditions requires the application of several factors. First, the pore-volume reduction, as a result of the porosity adjustment discussed previously and because of the change in size of the core plug at stressed conditions, must be applied to the S_w data. Second, the water volume and S_w must be increased because of the effects of reservoir temperature and pressure, salinity, and gas in solution.

Other SCAL Measurements. For other SCAL measurements, some conditioning of these data may be required. For example, for the P_c/S_w data, the data must be converted from surface to reservoir conditions and a height-above-the-OWC (H_owc) basis by accounting for the oil/water or gas/water density difference at reservoir conditions and the change in IFT and contact angle between surface and reservoir conditions.

The SCAL electrical-property measurements of a, m, and n (and possibly Q_v, a*, m*, and n*) will need to be considered in the light of the theoretical model that will be used to make S_w calculations from resistivity-log data. Many shaly-sand relationships for estimating S_w from R_t have been proposed.  These parameters are sometimes measured at overburden conditions.

Other Relevant Data. There are various other types of wellbore data that may need to be inventoried, organized, reviewed, and considered when making the various petrophysical calculations. Other wellbore data that can be particularly important include mud-log data, formation-pressure surveys, formation-tester fluid samples, drillstem-test fluid samples, and 3D-seismic data. Sections 3H.6 and 3H.7 discuss the uses of these data for the fluids-contact identification and for the S_w calculations.

Acquisition of Additional Petrophysical Data, Where Critically Needed

Often when a new petrophysical evaluation of a reservoir is undertaken, there are significant gaps in the overall database after the existing data have been inventoried and evaluated. It is possible that an acceptable petrophysical evaluation can be completed within the constraints and limitations of the available data, but sometimes additional data are needed. These new data, typically additional SCAL data or possibly routine-core-analysis data, can be obtained from two sources: additional experimental measurements on core plugs taken from existing cores; and drilling, logging, and coring new wells to obtain the needed data. The second approach is used only if such expensive data gathering is required and economically justified.

To obtain additional data from existing cores, geologists can redescribe existing cores as needed. Additional porosity and permeability measurements can be made on newly cut core plugs from any of these cores. Additional valid fluid-saturation measurements might be made on well-preserved core samples; however, such measurements have to be checked carefully because such core samples often dry out over the years. Samples can be cut for more SCAL measurements if the experts consider that the rock samples can be restored for such testing.

In some cases, the need for additional data can justify the drilling of one or more new wells in which cores are cut and routine and special logs are run. In certain equity-redetermination situations, additional wells at specific locations have been drilled to gather additional data about the reservoir interval to more accurately calculate net pay, porosity, and water saturation. For some proposed reservoir-development projects, expensive new data, often of a special nature, can be economically justified because a new well can reduce risk and improve the likelihood of project success.

Lithology Determination

Understanding reservoir lithology is the foundation from which all other petrophysical calculations are made. To make accurate petrophysical calculations of porosity, S_w, and permeability, the various lithologies of the reservoir interval must be identified and their implications understood. Lithology means "the composition or type of rock such as sandstone or limestone."  These few words belie a host of details about reservoir rocks, their depositional and diagenetic history, pore structure, and mineralogy. Geologists are trained to describe rocks, based on outcrops, cuttings, cores, and more-detailed mineralogical measurements, and they identify certain log-curve characteristics related to particular depositional environments (i.e., coarsening upwards, fining upwards, massive bedding, and the scales of interbedding). For reservoir petrophysical evaluations, a geologist must be on the technical team, and there must be cooperation between the geologists and engineers.

The lithology of a new oil or gas reservoir is understood on a preliminary basis by the wellsite geologist’s description of mud-shaker cuttings and possibly by a few cores that are cut if the reservoir interval is sufficiently long. Lithology is also determined from the logs, because each main reservoir lithology has characteristic responses. Frequently, lithologies are derived by pattern recognition of the GR-, density-, and neutron-log responses.

Some subsequent delineation wells are likely to be cored over the entire of the reservoir interval. The geologist will make detailed descriptions of these cores and order a number of thin-section, SEM, XRD, and mercury-injection capillary pressure (MICP) or pore-size measurements on various rock types that have been identified. From these data and the routine-core-analysis data, geologists can construct their interpretation of the reservoir’s depositional environment and insights into the nature of its pore system and mineralogy. Geologists typically prepare reservoir cross sections with seismic traces, well logs, and core descriptions to illustrate the depositional environments, rock types, and internal geometries. See the chapter on Reservoir Geology in this volume of the Handbook for additional discussion of geologic aspects of oil and gas reservoirs.

The lithology of a reservoir impacts the petrophysical calculations in numerous ways. The depositional environment and sediments being deposited will define the grain size, its sorting, and its distribution within the reservoir interval. In most sandstone reservoirs, the depositional environment controls the porosity/permeability relationship (see the chapter on permeability in the General Engineering volume of this Handbook for additional details about the controls on the absolute permeability because of grain size and rock sorting).

The mineralogy of a reservoir results from a combination of its depositional and diagenetic histories. For a sandstone reservoir, the depositional environment controls the percentages of quartz, chert, feldspar, and detrital clay-mineral grains and the other matrix material. These materials must be measured and their variations within the reservoir interval quantified. The diagenetic history determines the extent to which portions of the grains have been leached away; cements such as calcite, siderite, or pyrite have been deposited; and authigenetic clay minerals formed. The diagenetic history can be complicated and can be impacted by differences in burial history from one part of a reservoir to other parts, or by aspects of the hydrocarbon-filling history.

For carbonate reservoirs, most of the same factors as discussed for sandstones come into play, but the mineralogical considerations are different. For carbonate formations, the rock formations typically consist of interbedded sequences of carbonates, dolomites, anhydrite, salt, and shale layers. The keys to reservoir development within the carbonate layers are the original grain size and how it has been altered by chemical diagenetic processes. As these chemical reactions take place, the pore-size distribution and porosity level will change (e.g., by dolomitization). Carbonate-reservoir porosity is also greatly enhanced by weathering, dissolution, and fracturing.

As well as the basic mineralogy, clay-mineral properties are also of particular importance to the petrophysical calculations in the reservoir intervals. There are many types of clay minerals, and their impacts on well logs are quite different. Particularly, there may be differences between clay minerals that form shale layers and claystones and those that occur within sandstone intervals. While the detrital clay minerals in sandstones will likely be the same as the clay minerals in the shales, the authigenetic clay minerals in the sandstone pore system can be quite different. The types and amounts of the various clay minerals impact the rock pore system by affecting its electrical properties and permeability characteristics (see Sec. 3H.3.1). A few of the aspects of mineralogy that impact the petrophysical calculations are the extent to which various heavy minerals (e.g., anhydrite, calcite, dolomite, granites, pyrite, siderite) impact the density log; various light minerals (e.g., coal, halite salt) impact the density, neutron, and sonic logs; various radioactive minerals (e.g., uranium, thorium, and potassium salts such as K-feldspar) impact the GR log; and various electrically conductive minerals (e.g., clay minerals and pyrite) impact the resistivity logs.

Clay-Mineral Properties

Clay minerals are, in general, composed of layered alumina and silicate molecules,  and the properties of the various clay minerals vary widely. Some swell when wet, are plastic, and can easily deform, while others are hard and dense. Clay minerals are extremely fine-grained, and those with the smallest grain size have a very high surface-area-to-volume ratio. Clay minerals (e.g., chlorite, illite, kaolinite, smectites, and mixed-layer clays) generally impair the permeability and porosity of the pores in which they reside; the permeability is sometimes impacted by an order of magnitude or more. However, it is the smectites (one of which is montmorillonite) that often cause very significant effects on the petrophysical measurements of porosity and water saturation.

In smectites, exchange cations and adsorbed water molecules are loosely bound between the silicate layers. Dehydration occurs whenever there is low humidity or an elevated temperature (e.g., in a dried-up lakebed or in a brick kiln). Loss of this adsorbed water is even more rapid at temperatures above the boiling point of water. For smectites, this is a problem during core analysis because the extraction and drying of the core samples is an essential step in the measurement procedures.

For resistivity logging, smectite clay minerals pose a further problem. The exchange cations and adsorbed water molecules lead to smectite exhibiting excess electrical conductivity. This occurs as exchange cations (e.g., sodium, calcium) migrate from site to site on the clay surfaces. The clays thus exhibit a lower resistivity and, in most cases, depress the bulk resistivity of reservoir rocks in which they reside. Cation exchange also occurs with the other clay minerals, but to a lesser extent.

Rock formations of pure clay minerals are rare. More typically, several species of clay mineral are associated together with clay-sized and silt-sized quartz, mica, and other rock grains. This association is known widely as "shale." In sandstone reservoirs, clay-mineral content typically ranges from 0 to approximately 10% BV. In shales, clay minerals occupy approximately 20 to 40% BV, and the remainder is often very-fine-grained quartz, volcanic minerals, carbonates, and organic matter. Besides the adsorbed water on the clay minerals, shales and authigenetic clay minerals also include additional formation water held in their micron-sized pore system by capillary retention. This water cannot be produced from the formation and is referred to as "capillary water."

During the burial of the sediments over geological time, the overburden stress and the pore-fluid pressures increase. The net result is that water is expelled from the shale beds into surrounding permeable beds. Young clay-mineral-bearing sediments at shallow burial depths are likely to be smectites (e.g., gumbo shale in the submerged Mississippi delta of Louisiana, U.S.A.). Clay minerals in deeply buried shales become less hydrated, and their forms can be altered by higher temperatures and pressures. Low-salinity water is sometimes observed in reservoir-rock pores adjacent to the shales and where clay-mineral-expelled water cannot escape from the permeable bed. This formation may become overpressured and can cause severe problems during drilling if not predicted or detected in time to alter the drilling program.

Although shale formations are not usually of commercial importance, the measurement and evaluation of core and log data in partly shaly reservoirs presents many difficulties that are not present in clay-mineral-free (clean) formations. A large body of technical literature addresses shaly-formation analysis because the shale, to one degree or another, affects all log and core measurements. Because these shaly rocks are so variable, a single model usually cannot fully describe all of their behaviors.

Reservoirs with a fractional shale content, V_sh, are common, and the clay minerals/shales take several physical forms, including laminated, structural, and pore-filling.  Laminated shales are thin detrital shale layers interbedded within a reservoir interval. Each represents short periods of deposition where the suspended finest sediments could settle out of the original sediment-rich river, lake, or seawater. Laminated shales may range from approximately one hundredth of a centimeter to 1 m thick. Shale deposits can be broken up and reworked after their original deposition and become "grains" in the same manner as quartz grains. Structural, or detrital, shale grains become a part of the grain composition of sandstone. As well as the clay minerals that are deposited directly as solids from lakes and marine environments, they also may be deposited from in-situ formation-water solutions that are rich in dissolved minerals. These clay minerals are called "authigenetic." By this mechanism, the pores of sandstone may become partly filled with various clay minerals and other minerals. Of this type, illite, kaolinite, chlorite, and smectite clays are most common. Each can take several physical and chemical forms within a pore. Several generations of pore-filling clay minerals may be present, representing different periods of geological time when changes occurred in formation-water composition or depth of burial.

Evaluation of Shale Volume

Geological techniques, like XRD, are available to identify clay-mineral species and to quantify rock-component volumes in physical specimens. Such analyses can help calibrate the log-based methods for estimating V_sh, the bulk-volume fraction of shale. V_sh from the GR log is frequently used to determine nonpay.

Shale content can be estimated from well logs by many techniques, because shale affects the readings of most logs. The task for a particular field is to identify an evaluation technique that is reasonably accurate and as simple as possible. A method using a combination of the neutron and density logs is often applied for practical log analysis. Modern optimized simultaneous-equations log solutions attempt to identify individual clay species. Nevertheless, for petrophysical studies for field development, it is the GR log that is probably used most frequently to evaluate V_sh. The GR-log readings are normalized to reduce hole-size variations and mud effects and differences among the tools. Normalization is achieved by finding typical GR values in the 100% "clean" sand and 100% shale formations for each well. These different endpoint values in each well are then equalized. The GR values in between the sand and shale levels are scaled to give V_sh values. The scaling is often linear, but nonlinear alternatives are available, if appropriate. Occasionally the GR log is affected by radioactive components that are not shale, and these need to be identified and assigned a revised V_sh. Water-based drilling muds sometimes contain high concentrations of potassium salts, and these may also lead to GR interpretation problems, such as invasion of potassium salts into the near-wellbore region.

The uncertainty of V_sh log evaluations is moderate to high. At low values, less than 30% BV, the authors estimate that V_sh may typically be accurate to approximately ± 10% BV at one standard deviation (SD). At values greater than 30% BV, the uncertainty increases. The uncertainties affect nonpay bed-boundary evaluations; however, the V_sh uncertainty also seriously impacts the accuracy of the effective-porosity and S_w estimates when smectites, with their high clay-mineral adsorbed-water fraction, are present. If the clay species is different (illite or chlorite with little or no adsorbed water), then the V_sh uncertainty has a much-reduced impact on porosity, as is discussed in Sec. 3H.5.3.

Reservoir Zonation or Layering

An important conclusion from the geologists’ technical studies is a definition of the extent to which the reservoir needs to be subdivided either vertically or areally. Besides all of the information developed by the geologists from the detailed core descriptions, the routine-core-analysis and SCAL data need to be analyzed for such effects. This is accomplished by preparing, for different possible layering within the reservoir interval, a variety of crossplots such as log₁₀ (permeability) vs. porosity and OBM-core S_w vs. porosity or log₁₀ (permeability) and comparing the data clouds and trends of those plots from one possible layer to the next. Significant differences should be expected between reservoir intervals with different depositional environments and differences in grain size and sorting. Areal variations may occur across a given vertical zone within the reservoir because of varying distances from the sediment source, differences in the depositional environment in various areas, or varying diagenetic effects.

For accurate petrophysical calculations, most large reservoirs will probably require a number of vertical subdivisions, usually termed zones or layers. Typical zones for a reservoir are 50 to 150 ft (15 to 45 m) thick. Areally, several square miles of reservoir can usually be included together; however, if the reservoir covers tens of square miles, it is likely to require some areal subdivision for accurate petrophysical calculations.

A second consideration is the amount of available data of various types. If a reservoir has a large database of log and core data from many wells, then the number of these subdivisions is not impacted by the quantity of data. However, if some types of data are very limited, then this consideration may control the degree of vertical and areal subdivision that can be used for various petrophysical calculations. The same degree of subdivision may not be required for net-pay calculations relative to porosity calculations or for porosity calculations relative to S_w calculations. In summary, more-accurate vertical and areal petrophysical calculations are made if the reservoir is appropriately subdivided.  Fig. 3H.1 shows the vertical zonation used for the Prudhoe Bay field’s Sadlerochit reservoir. Figs. 3H.2 through 3H.4 are example plots based on real reservoir data that show how rock properties within the same field can vary from one reservoir to another and from one vertical portion of a reservoir interval to other parts.

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  Fig. 3H.1 – Reservoir zonation of the Sadlerochit reservoir, Prudhoe Bay field, Alaska, U.S.A.

Net-Pay (or Pay.Nonpay) Determination

The goal of the net-pay calculations is to eliminate nonproductive rock intervals and, from these calculations at the various wellbores, provide a solid basis for a quality 3D reservoir description and quantitative hydrocarbons-in-place and flow calculations. The determination of net pay is a required input to calculate the hydrocarbon pore feet, F_HCP, at a wellbore and its input to the overall reservoir OOIP or OGIP calculations. The total F_HCP at a well is the point-by-point summation over the reservoir interval with Eq. 3H.1. The top and base of the reservoir interval are defined by geologists on the basis of core descriptions and log characteristics.

[[File:Vol5 page 0434 eq 001.png|RTENOTITLE]]....................(3H.1)

In the F_HCP calculation, net pay, h_ni, at each data point has a value of either 1 (pay) or 0 (nonpay). The "net-to-gross ratio" or "net/gross" (N/G) is the total amount of pay footage divided by the total thickness of the reservoir interval (for simplicity, the well is assumed here to be vertical). A N/G of 1.0 means that the whole of the reservoir interval is pay footage. In this formula, any foot (or half foot) that is defined as nonpay contributes absolutely nothing to the subsequent reservoir-engineering OOIP (or OGIP) and reserves calculations, even if it contains some amount of hydrocarbons. The net-pay determination should be performed in a reasonable practical manner, but it should be recognized that when any cutoff is used, the result will, to some extent, be arbitrary (see the chapter on reserves determination in this volume of the Handbook).

Conceptual Bases for Net-Pay Calculations

Several conceptual bases for the petrophysical calculations of net pay are described here. At one limit, the whole of the reservoir interval can be treated as net pay (i.e., N/G equals 1.0). Another reasonable engineering approach is to define some lower limit on flow, below which each foot or half foot of the reservoir interval is deemed to be nonpay. A third approach is to use one or more log cutoffs that have been used historically within the petroleum industry. The advantages and disadvantages of these various approaches will be discussed in this section.

N/G = 1.0. One approach is to calculate the OOIP or OGIP assuming that all the reservoir interval is pay to determine the total volume of hydrocarbons present within the reservoir interval. When using an N/G = 1 approach, the technical team needs to ensure that the calculations of porosity, permeability, and S_w are quantitatively reasonable over the whole range of values for each of these parameters. This calculation could be called a determination of the "total hydrocarbon resource" within the reservoir interval, and it provides a value for the total hydrocarbon potential of the reservoir. Some of these hydrocarbons will have low mobilities and will contribute little or nothing to hydrocarbon recovery. But, with this value available, the engineer has a measure of how well the reservoir is producing overall and what resources should be considered for improved-recovery-project evaluations. This value can be viewed as the ultimate "prize."

Another reason for setting N/G to 1.0 is that, with modern reservoir-engineering tools, it is technically feasible to treat the entire reservoir interval as pay. For example, with modern reservoir-engineering tools, a million (or more) cell reservoir-simulation model can be constructed in which a very detailed description of the vertical and horizontal variations in the reservoir-rock properties are incorporated. In this approach, the very-poor-quality portions of the reservoir are assigned low porosities, low permeabilities, and higher water-saturation values. Then, in the OOIP or OGIP calculations, these portions contain only small volumes of hydrocarbons and will contribute their appropriate, albeit small, share to pressure maintenance and recoverable hydrocarbons. This is in contrast to defining these poor-quality intervals as nonpay and defining a priori that they contribute nothing to OOIP or OGIP or reserves.

Mobility or Permeability Cutoff Approach. From first-principle calculations using Darcy’s law, a reservoir engineer can define net pay by applying a fluid-flow cutoff. The choice of this cutoff would be related directly to the hydrocarbon mobility (rock permeability divided by hydrocarbon viscosity) in the different portions of the reservoir interval. With this approach, the net-pay permeability cutoff used in the point-by-point log calculations would be quite different between that for a gas reservoir (very low gas viscosity of approximately 0.02 cp), that for a light-oil reservoir (oil viscosity of 1 to 10 cp), and that for a heavy oil reservoir (oil viscosity of 10,000 cp or more).  Any portion of the reservoir interval that has a permeability at reservoir conditions below the cutoff would be defined to be nonpay. In the next section, the gas-reservoir situation is discussed separately from that for oil reservoirs.

The arbitrary nature of any net-pay cutoff is apparent when one notes the flow implications of using a permeability cutoff. If a rock interval has a permeability 1% greater than the cutoff value, it is included as net pay. However, if another rock interval has a permeability 1% less than the cutoff value, it is excluded as nonpay. The difference between the fluid-flow contributions from these two rock intervals is only 2%, yet one is allowed to contribute to the subsequent OOIP or OGIP and reserves calculations, while the other is not.

If a permeability cutoff is chosen, its application to the various wellbore data (cores and logs) generally takes three steps.  The first step is to apply the permeability cutoff to the routine-core-analysis permeability data. In this step, there are two checks that need to be made. First, a permeability/porosity plot needs to be prepared and outlier points identified. The outlier points need to be individually checked for validity. For example, a very-low-porosity shale sample may have dried out and a parting developed between the shale layers. This may lead to a very high permeability value that is not consistent with the rest of the rock characteristics. Bad routine-core-analysis data points should be excluded from the database. A second consideration is that often during the routine core analysis, the shale intervals are not sampled at the same frequency of core plugs as the other lithologies. This likelihood must be kept in mind in reviewing the routine-core-analysis database and in comparing the results of pay/nonpay calculations between cores and logs. The subsequent steps—the conversion of a permeability cutoff to a porosity or V_sh cutoff including the calibration of logs to the core standard, and the calculations from the logs of net pay for all wells over the reservoir interval—are discussed later in this section.

Gas Reservoirs

For a gas reservoir being produced under pressure-depletion drive, any permeability cutoff applied should be very low. This is quite evident by the successful development of tight gas-sandstone reservoirs producing nearly 10 Bcf/D from 85,000 wells in the United States, some with average permeabilities in the microdarcy range (see the chapter on tight gas sands in the Emerging and Peripheral Technologies volume of this Handbook for additional details). In conventional gas reservoirs in which higher-quality rock intervals are interbedded with the poorer-quality ones, gas in the poorer-quality rocks will flow to the higher-quality rock intervals if there is any permeability between the two. An example calculation for gas flow from a 1-microdarcy layer with a pressure difference of 2,000 psi, over a thickness of 10 ft for an area of 10 acres, and for a period of 1 year shows that this layer would contribute 1 Bcf per year.

Because pressure-depletion-drive gas reservoirs are produced for decades and, if found at significant depths, have abandonment pressures less than 10% of their initial pressures, there are both long times and large pressure differentials to cause gas to flow from very-low-permeability and low-porosity rock intervals into higher-permeability conduits and on to the production wellbores. In many instances, the distance traveled to reach a higher-permeability layer is just a few feet vertically.

Oil Reservoirs

For oil reservoirs, any permeability cutoff will be significantly higher than that for a gas reservoir, generally by a factor of 10 or 100 or more. A second aspect of oil reservoirs is that typically, only 10 to 20% of the OOIP will be produced by pressure-depletion drive (without assistance from gravity drainage) in which the pressure differential will affect all portions of the reservoir. However, during waterflooding, overall oil/water displacement efficiency will depend, in part, on how much of this displacement process occurs in poorer-quality oil-bearing rock intervals. Hence, the choice of oil-reservoir permeability cutoff needs to account for the oil/water relative permeability effects. Interwell injector/producer connectivity (or "floodability") is not a topic of this chapter. Connectivity will affect recovery but is considered a separate issue apart from individual-wellbore calculations of net pay.

Any permeability cutoff cannot be directly applied to foot-by-foot log calculations of net pay because there is no log that quantitatively measures permeability. A permeability cutoff typically is converted to a porosity cutoff and is subsequently applied to the logs through log porosity, bulk density, GR, or V sh cutoffs. The procedures for applying a permeability cutoff to the logs are discussed later in this section.

Other Historical Net Pay Cutoffs

The technical literature shows that a number of net-pay-cutoff approaches have been used over the years by petrophysicists, geologists, and reservoir engineers.  These cutoffs are often simply stated as a particular value for porosity, V_sh, and/or S_w. The justification for those cutoffs is rarely stated. Geologists often provide their foot-by-foot pay/nonpay identifications ("picks") with their detailed core descriptions.

In all cases, chosen cutoffs generally exclude poorer-quality rock intervals. The key issues become whether the cutoff is applied in an accurate, consistent, and systematic manner through net-pay calculations using log data and the volume of hydrocarbons that are excluded in the net-pay calculations. For example, geologists often define shales, and possibly siltstones and very shaly sandstones, as nonpay intervals; then the GR logs can be calibrated to this nonpay standard. A value of the geologists’ core descriptions in the net-pay determination is that core descriptions are generally more continuous than are the routine-core-analysis data.

Like the geologist’s criteria, porosity and V_sh cutoffs also exclude poorer-quality rocks because lower-porosity rocks also generally have lower permeability, higher water saturations, and little, if any, mobile oil. Higher V_sh values are generally indicative of more clay-mineral-rich rocks that also tend to have lower porosities, lower permeabilities, higher water saturations, and little, if any, mobile oil. If these two cutoffs are applied without consideration for flow implications, then some rock intervals containing significant volumes of hydrocarbons that can contribute significantly to production may be excluded before OOIP, OGIP, or reserves calculations.

An S_w cutoff is sometimes also used as a nonpay cutoff, often in addition to a porosity and/or V_sh cutoff. An S_w cutoff is typically justified on the basis that, at high S_w, gas or oil is immobile on the basis of relative permeability considerations. This approach does not account for, at original reservoir conditions, high-S_w rock intervals that contain lower hydrocarbon saturations but with those hydrocarbons in the larger pores of the rock. These hydrocarbons will have mobility and contribute to production, particularly for gas reservoirs in which, as the pressure declines, the gas phase expands (and gas saturation increases) and results in gas flow toward the production-well pressure sinks.

The difficulty with the use of porosity, V_sh, or S_w cutoffs, without reference to flow considerations, is that rock intervals evaluated to contain hydrocarbons may be excluded from the other reservoir-engineering calculations. Each of these approaches, when applied to the logs, requires that underlying physical relationships between log readings and these cutoffs be understood. Also, complications on logs (e.g., intervals of heavy minerals, radioactive minerals other than clay minerals, or hole washouts) need to be quantified and treated appropriately in net-pay calculations.

Geologic Considerations in Net-Pay Determination 

The primary geological considerations in determining pay and nonpay in the reservoir interval are depositional environment and hydrocarbon and structural history. The depositional environment provides a picture of whether the overall reservoir interval is sand rich (high N/G) or shale rich (low N/G) and the nature of the interbedding of high-quality rock with poor-quality rock. If the reservoir interval is quite interbedded with high-quality rock intimately layered with poor-quality rock on the scale of a few inches to a few feet, the poor-quality rock intervals, if they contain hydrocarbons, will likely contribute to production. However, if the layering is on a much larger scale with thick high-quality rock intervals separated from thick low-quality rock intervals, then the poor-quality rock intervals are much less likely to contribute significantly to production.

Regarding hydrocarbon and structural history considerations in net pay calculations, several fields have relict-oil intervals below the current OWC (e.g., Prudhoe Bay, Alaska North Slope, U.S.A.; San Andres carbonate reservoirs, west Texas, U.S.A.)  or relict-gas intervals below the current gas/water contact (GWC) (e.g., North Morecambe field, Irish Sea, U.K.).  These relict-oil columns would generally be considered to be nonpay intervals because of their high mobile-water saturations and lack of oil mobility. This is true for either primary production or waterflooding; however, for CO₂ enhanced oil recovery, the west Texas San Andres relict-oil intervals have been considered for development. A more significant situation is that of relict-gas saturations below the current GWC. This gas does not have immediate mobility; but if the aquifer is not strong, this gas will expand and can contribute to production as the reservoir pressure declines. Hence, a relict-gas interval should not necessarily be excluded in net-pay calculations.

George and Stiles published an excellent example of the complications of net-pay calculations concerning the heterogeneous Clearfork carbonate oil reservoirs in west Texas, U.S.A. Their approach was to develop an empirical relationship between "actual pay" and "apparent pay" as a function of porosity in order to redetermine net pay to improve OOIP calculations and to obtain a reasonable distribution of net pay. They defined two net-pay cutoffs. The "actual pay" was defined as the net thickness of core samples with permeabilities greater than 0.1 md, and an "apparent pay" was defined as the net thickness of core samples with porosity greater than a specific cutoff. Fig. 3H.5 shows the relationship of actual pay to apparent pay as a function of porosity. On the basis of this analysis, at a porosity level of 8% BV, 75% of the rock samples would be pay, while at a porosity level of 1% BV, 50% of the rock samples would be pay. By this methodology, wells with low porosity levels will not be all nonpay, but will be given a limited amount of pay. The purpose of their method was "to achieve a better distribution of porosity-feet" and "both total original oil in place and distribution of PV throughout the field will be realistic." 

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  Fig. 3H.5 – Apparent and actual pay for Robertson Upper Clearfork unit, West Texas, U.S.A.

 Finally, the technical team needs to determine the implications of any net-pay cutoff. This is best done by plotting the cumulative hydrocarbon pore feet (F_HCP) percentage as a function of porosity and as a function of permeability (see Figs. 3H.6 and 3H.7 for respective examples of these two types of plots). In this way, it is possible to determine what percentage of the hydrocarbons within the reservoir interval would be excluded by any particular net-pay cutoff. While this net-pay sensitivity method is a logical approach, the evaluation of porosity and water saturation is more uncertain in low-porosity rocks. Log calculations may indicate hydrocarbon saturations in rocks where no hydrocarbon actually exists.

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  Fig. 3H.7 – Illustrative plot of cumulative F_HCP vs. permeability for two types of reservoirs(one mainly good-quality rock, the other mainly poor-quality rock). The total F_HCP of the “good” reservoir is three times the total F_HCP of the “poor” reservoir.

Application of Net-Pay Cutoffs to Well Logs

The four main steps in the application of a net-pay cutoff to a particular reservoir interval are to establish a standard, calibrate one or more logs to the chosen standard, confirm that the calibration step produces results consistent with the standard, and apply the calibrated model to all wells.

Establish a Standard. As discussed previously, the choice of the standard for the net-pay calculations should be reasonable but is, to some degree, arbitrary. The choice should be a single concept, such as a permeability cutoff, a porosity cutoff, or geologists’ calls of pay/nonpay from core descriptions. The use of multiple cutoffs will lead to a very conservative result that eliminates rock intervals that are likely to contribute to production, particularly for gas reservoirs. This underestimation occurs because each of the individual cutoffs will, to some extent, define different datapoints as nonpay. Even after the best possible depth matching of the logs involved, remaining depth mismatches always occur, resulting in the double counting of nonpay at bed boundaries. The following discussion assumes that an air-permeability cutoff of 0.1 md has been chosen.

Calibrate One or More Logs to the Chosen Standard. Once the 0.1-md air-permeability cutoff has been chosen, it needs to be converted into a methodology that can be applied to foot-by-foot log calculations. Typically, this is done by converting the permeability-cutoff value into a porosity-cutoff value by a permeability-vs.-porosity semilog crossplot of routine-core-analysis data converted to reservoir conditions. Also, plots are made of the core permeability data vs. the various available log parameters to determine if there is a strong correlation that can be used. Alternatively, a multivariate regression technique might be used to calibrate multiple logs to permeability. If a porosity cutoff is developed from the permeability cutoff, then it needs to be defined as a log-related cutoff, such as a log-derived porosity or density log cutoff, or a V_sh or GR-log cutoff. There are several variations on how this calibration step can be undertaken. The alternatives are not discussed here because each reservoir situation has unique characteristics.

Confirm That the Calibration Step Produces Results Consistent With the Standard. After the calibration step is completed, the resulting log calculations of pay/nonpay need to be checked against the core standard in the cored wells. This is needed to determine that the log calculations and their cutoffs do not overstate or understate the calibration standard of net pay of the reservoir interval. The goal is to develop the "best estimate" values in the reservoir-engineering calculations, not the "low estimate" or the "high estimate."

Apply the Calibrated Model to All Wells Over the Reservoir Interval. After the first steps have been successfully completed, the finalized net-pay log model can be applied to all wells’ valid log data in the reservoir interval to develop point-by-point pay/nonpay determinations. For optimal results, it may be necessary to have different models in different areas of the reservoir. The results for each zone over the reservoir should be quality controlled. Maps should be examined looking for "bulls-eyes" that may represent either real geological effects, artifacts in the database, or bad calculations.

In the subsequent steps of calculating porosity, S_w, and permeability, those calculations will be made only for pay intervals. The nonpay intervals will be excluded from the core and SCAL database and the log database. In cases in which the depth matching of cores and logs presents difficulties, it is prudent to retain both core- and log-defined nonpay in the database. This will enable appropriate samples to be selected for various analyses, such as the evaluation of SCAL petrophysical properties.

Porosity Determination

The accurate calculation of porosity at the wellbore is essential for an accurate calculation of OOIP or OGIP throughout the reservoir. The porosity and its distribution also need to be calculated as accurately as possible because they are almost always directly used in the S_w and permeability calculations and, possibly, in the net pay calculations. In most OOIP and OGIP studies, only the gross-rock-volume uncertainties have a greater influence on the result than porosity does. Occasionally, where porosity estimates are difficult, porosity is the leading uncertainty. Fractured and clay-mineral-rich reservoirs remain a challenge.

This section describes the methods that can be used to make porosity calculations at the wellbore with the available core and log data. For this discussion, it is assumed that the core data have been properly adjusted to reservoir conditions, that the data from various logs have been reviewed and validated as needed, and that all of the required depth-alignment work has been completed. Sec. 3H.2 discusses the specifics of these topics. This section discusses the use of core porosity data, total and effective porosity, core-log calculation approaches, consistency of calculations, and uncertainty.

Use of Core Porosity Data

There are a few preliminary steps in the use of routine core porosity data over the reservoir interval. First, this data set needs to be restricted to those porosity measurements made in pay intervals; the nonpay porosity measurements should be excluded from the porosity calculations. Second, if more than one type of porosity measurements are made, then a hierarchy of these measurements needs to be developed for use in subsequent log/core porosity calculations. For example, it is possible that whole-core Boyles-law porosity measurements, core-plug Boyles-law porosity measurements, and sum-of-fluids porosity measurements are made with several of these measurements made on the same feet of core.  (See the chapter on petrophysical measurements in the General Engineering volume of this Handbook.) Also, if enough of two data types are taken for the same footage of cores, then these data need to be crossplotted to determine if there are any systematic differences between the various types of core porosity data. If more than one porosity measurement are available for a given depth, then only the highest priority in the hierarchy should be included in the log/core porosity calculations; otherwise, there will be unequal weighting in the statistical calculations.

The core porosity measured in shaly sands may include some volume that is associated with the dehydration of certain types of clay minerals (see Sec. 3H.3.1).  When smectite (montmorillonite) clay mineral is present as a significant fraction [e.g., a V_cl (not V_sh) of 40% BV], the core porosity may be increased, by approximately 12% BV, solely because of the smectite present. However, when other species of clay are present that have much less clay-mineral physically bound water (e.g., chlorite, illite, kaolinite), the clay water will add little to the core porosity. The effects of the presence of shale and clay minerals must be understood to yield the correct evaluation of the hydrocarbon and water content of a reservoir’s pore network.

Total and Effective Porosity

The estimation of porosity and water saturation in shaly formations is, where possible, based on various types of laboratory core data. Where core measurements are not available, estimates based wholly on log measurements and selected interpretation models are widely used. Rock models are based on "total" or "effective" porosity and "total" or "effective" S_w definitions. Both definitions account for the usual grain volume and hydrocarbon and capillary-water volumes seen in the porosity of nonshaly sands, and both models include volumes for the clay-mineral physically adsorbed water (sometimes known as clay-bound water) and the volume of dry clay minerals. Fig. 3H.8 is a schematic of a shaly-sand-reservoir model. It indicates the various solid and fluid volumes and pore networks to which core measurements, density, and neutron logs correspond.

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  Fig. 3H.8 – Total, effective, and core porosities and their associated water saturations in shaly sands (after Woodhouse and Warner

 Core Analysis. This discussion is restricted to siliciclastic rocks; carbonate rocks are not discussed. The porosity measured on core plugs containing clay minerals is dependent on the methods used to clean and dry the sample before it is measured. Cleaning removes oil from the pores. It is widely, if not universally, accepted that drying the core in a vacuum oven at temperatures just above the boiling point of water (110°C) will remove most, or all, of the clay-mineral adsorbed water and the capillary water, but not the chemically bonded hydroxyl groups within the clay minerals. The standard reported core porosity, ϕ_c, is, therefore, a total porosity including the effective porosity, ϕ_e, and the clay-mineral adsorbed water volume, V_clϕ_cl or V_shϕ_sh.

[[File:Vol5 page 0443 eq 001.png|RTENOTITLE]]....................(3H.2)

OBM-core S_w determined using Dean-Stark water-volume extraction is also accomplished with boiling toluene at approximately 110°C. Subsequent preparation of the OBM-core sample to measure porosity uses the same maximum temperature.

The core total porosity, ϕ_c, and core water saturation, S_wc, are, therefore, fully compatible with each other.  They are used together to accurately quantify hydrocarbon pore volume (V_HCP) [the "core" V_HCP = ϕ_c×(1-S_wc) ]. When smectite clays are present, the core total porosity will be higher than the effective porosity, ϕ_e, as defined in the previous paragraph. However, for the same sample, the core water saturation, S_wt (capillary water plus clay-mineral adsorbed water volumes as a fraction of ϕ_t), will also be greater than S_we (capillary water volume as a fraction of the effective porosity) and will fully compensate the V_HCP for the increased porosity.

V_HCP is used instead of F_HCP in the following discussion because the equalities apply at all scales.

[[File:Vol5 page 0443 eq 002.png|RTENOTITLE]]....................(3H.3)

For porosity,

[[File:Vol5 page 0443 eq 003.png|RTENOTITLE]]....................(3H.4)

For water saturation,

[[File:Vol5 page 0444 eq 001.png|RTENOTITLE]]....................(3H.5)

"Humidity-dried" cores, extracted at temperatures lower than boiling water and partially dried, retain some, or all, of the clay-mineral physically bound water and, therefore, approximate the effective porosity. There is, however, no generally accepted way to measure accurately the values of effective porosity on shaly-formation cores. In smectite-rich shaly sands, humidity-dried porosity is incompatible with the Dean-Stark S_w, and, if combined, the result will understate V_HCP.

Cores extracted at much higher temperatures may give compatible porosity and S_w results, but other problems can sometimes occur. The mineral gypsum dehydrates between 110 and 120°C and must be corrected for in the retort method of water-volume measurements. At 110°C, the structural, chemically bound hydroxyl groups that are part of the clay-mineral lattice are not liberated.  However, at very high temperature (500°C or more), these hydroxyl groups react to form water and condense as water in the collecting tubes of a high-temperature retort apparatus. This "structural water" is not captured during standard core analysis but is the hydrogen component of clay minerals that is detected by the neutron porosity log even though it is a part of the solid mineral (Fig. 3H.8).

Log Analysis. Log-interpretation methods for porosity and S_w all seek the same end result in terms of porosity and hydrocarbon volume. They are divided into methods that model the effective porosity and the clay-mineral adsorbed water separately and methods that model the total porosity containing both clay-mineral adsorbed water and capillary water. The total porosity is often calculated from the density log and the core grain density, as Fig. 3H.8 shows. Estimates of interconnected porosity (effective porosity) at reservoir conditions come from combinations of many different logs, but all of them attempt to quantify the clay-water volume fraction and subtract it from the total porosity.

Log Calculation Approaches

In calculating porosity values from the core and log data, the first step is to create depth plots and crossplots of the core data against the various log data, like those in Figs. 3H.9 and 3H.10, respectively. These crossplots visually show which of the logs has the strongest correlation with the core porosity measurements. For example, the density log readings vs. core porosity data may have a less-scattered data cloud than the sonic log vs. core porosity data, or, if there are heavy-mineral complications, the opposite may be the case. These crossplots show, and the correlation coefficient, r , of each correlation indicates which of the log/core combinations should be used for the log/core calibration step discussed next. Where possible, it is best to use a single-log porosity estimator because multiple-log estimators will have problems at bed boundaries because of imperfect depth matching. The volumes sampled by different logs also vary, with the neutron log "seeing" a larger volume than the density log.

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  Fig. 3H.9 – Well-log and core data from gas-bearing sandstone with predicted porosity and permeability(South Morecambe gas field, offshore U.K.) After Woodhouse.

 The variance of core-plug data is always larger than the equivalent variance of a log because of the small plug volume compared with the larger volume seen by the running-average log reading. One way to reduce the core-plug variance is to create a modified core property curve that is the running average of the core data (a 1-2-1 filter may be appropriate). Core data modified in this way are considered by some to be a superior calibration standard.

Calibration Line-Fitting. The generally recommended method for obtaining a line-fit for porosity prediction is the "y-on-x" ordinary least-squares regression method.  The recommendation presumes that the calibration data set has accurate depth adjustments and is fully representative in all respects of the environment of the equation’s future use. The dependent-variable calibration data, y, the values wanted in the future (e.g., core porosity), are regressed against the selected independent x-variable data [the values available to make the future prediction (e.g., the density log values)]. The same x-variable must be used when the calibration line is applied in the uncored wells. Multiple regression uses more than one independent variable (e.g., the density and GR logs).

For y-on-x regression lines, removal of x-y data outliers, far from the general trend, must be considered. The y-on-x method assumes that the y and x measurements apply to the same rock sample, so data pairs that are not likely to represent similar rocks must be edited from the data set.

Although straight (linear) regression lines are often created with the data in their original form, the regression method applies equally to curved relationships. These are achieved by transforming one or more of the variables. For example, it is common to transform permeability to a logarithm, thereby creating a log 10 (permeability) and linear porosity relationship. This transform preserves the geometric averages of the permeability. As an alternative, a permeability and exponential porosity relationship should be considered because this will preserve the arithmetic averages of permeability, instead of the geometric averages.

To some observers, the y-on-x line-fit initially is awkward and less central than some other line-fits. The reduced-major-axis (RMA) line-fit, for example, follows the intuitive middle ground along the major axis of the data cloud (see Fig. 3H.10). The "structural" line-fits estimate the relationship that would be observed if both the y and x variables were error-free. The RMA line provides this relationship for the particular case when y and x have equal fractional errors. These structural line-fits are not generally used in practice because, for their future use, they apply to error-free x-input data, not the real measured data. The RMA slope is defined by the ratio of the SDs of y and x together with the sign of r. The y-on-x slope is equal to the RMA slope multiplied by the correlation coefficient r.

• 

  Fig. 3H.10 – Core-plug porosity vs. well-log bulk density with y-on-x and RMA line fits (South Morecambe gas field, offshore U.K.) After Woodhouse.

 The initial impression of y-on-x does not weaken its status as the method with the lowest overall residual error in the required y estimates. When viewed from any position on the x-axis, the y-on-x line is central within the y-data values near that x-position (see Fig. 3H.11). Providing average y-estimates from measured x-data is the main feature of y-on-x lines; however, the y-variance of the calibration data is not preserved by y-on-x predictions and the extremes of the y-range are averaged. The RMA line-fit does honor the y-variance; but if y and x are only moderately correlated, high porosity values are overestimated and low porosity values are underestimated (see Fig. 3H.12). The depths of the RMA-predicted high and low y-values will not be at the same depths as the core high and low values.

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  Fig. 3H.11 – Residual plot for y-on-x predicted porosity vs. well-log bulk density. Residuals are evenly distributed around zero (South Morecambe gas field, offshore U.K.) After Woodhouse.</ref>

 Cores are not always regularly sampled (e.g., at one per foot) and are typically sampled at a lower frequency in the shale intervals. In these cases, the plotted data can sometimes have no trend, for example, in a high-porosity reservoir. External information, not in the standard log/core variables, can be used to provide a useful line-fit. The zero-porosity end of the line might be derived from the core grain-density data. Calibration lines may be calculated by joining this grain density to the means (arithmetic averages) of the x-y data, or a fixed-point regression might be used.

There are circumstances when line-fits such as RMA should be considered. Some reservoirs (e.g., carbonates and finely laminated sandstones) are so heterogeneous that it is difficult, if not impossible, to make accurate core-to-log depth adjustments. In these cases, where the data pairs do not reliably sample similar rocks, core porosity vs. log plots have a poor correlation, and the y-on-x line-fit has a low slope. Here, the RMA line can be a better practical approximation of the underlying core/log relationship. If the core/log correlation is very poor, deterministic or simultaneous-equations log analysis —without using the core—remain useful options.

Calibration lines should be determined for a single population, not a mixture of two or more populations. For example, when density logs are used to predict porosity, if two zones in a well have significantly different lithologies or grain densities, they should, where possible, be separated into different population groups. Likewise, significant grain-density trends across the reservoir area should be honored; however, this process must not be taken to an extreme. Calibration lines with excellent apparent correlations can be achieved with very fine subdivisions of the calibration sample data. Unfortunately, when they are applied in prediction mode to the uncored wells, these "overfitted" calibrations will not yield robust and accurate porosity estimates.

Density Log. The density log is often the best log for making porosity estimates.  In their simplest form, the density-log readings are considered to be a linear relationship between the zero-porosity limit where the density log reads the rock-matrix density and the 100% BV porosity limit where the density log reads the fluid density.

[[File:Vol5 page 0447 eq 001.png|RTENOTITLE]]....................(3H.6)

where ϕ = porosity, ρ_ma = matrix density, ρ_b = formation bulk density, and ρ_fl = fluid density.

This physical relationship assumes constant matrix density and insignificant variation in the fluid saturation and fluid density within the pore system. These are not necessarily the case in real reservoirs. Where core measurements and regression analysis are used to quantify the relationship, the regression coefficients (slope and intercept) do not represent true matrix and fluid-density properties. The regression coefficients are "catch-all" fitted parameters without a physical meaning.

When using the density log for porosity calculations, it should be expected that a different log/core relationship will be found for the aquifer, the oil column, and the gas column because of the different fluid densities in these various fluid environments. Also, there may be curvature of the relationship if the near-wellbore gas saturations increase as porosity increases. This curvature does not always occur, and gas saturations "seen" by the density tool (up to 4 in. into the borehole wall) may be fairly constant. Differences in the core/log relationship are also expected for WBM vs. OBM wells.

In a density-log vs. core-porosity crossplot, the low-porosity portion of the data cloud needs to be handled carefully. Typically, these rocks have lower porosity because of either a much higher clay-mineral content or various cements filling some of the pore system, either of which is likely to alter the average matrix density. Also, the lower-porosity rocks within the hydrocarbon column will have significantly higher S_w. Hence, either of these effects can cause curvature of this crossplot that will need to be accounted for in the correlation of log and core data.

For reservoirs that are buried sufficiently deep and in which no smectite clay mineral is present, the sandstone and shale core grain densities are often similar, and the core porosity of the shale is low, less than approximately 5% BV. In these particular conditions, there are very small volumes of adsorbed water in the clay molecules, ϕ_cl and ϕ_sh in Eq. 3H.2 are low, and it is possible to use the density log alone to estimate effective porosity. Neutron logs usually do not indicate such low apparent shale porosities because of chemically bound hydroxyl groups in clay-mineral structures and neutron-adsorbing elements. Sonic logs in shales usually read higher than quartz travel-time. The sonic and neutron are, therefore, not satisfactory single-log effective-porosity predictors in shaly sands.

Other Approaches. Evaluations based on the sonic log follow a logic similar to that of the density-log methods described previously. The sonic-derived porosities are particularly useful when conditions are adverse for the density log, such as in caved holes or when heavy minerals are present. See the chapter on acoustic logging in this volume of the Handbook.

Two-log combination solutions, such as density/neutron or density/GR, are useful in carbonate and siliciclastic reservoirs, including shaly sands. Gas-bearing sands may require multiple-log methods. Multiple-log and multivariate regression methods can be used but are often difficult to apply in practice. All multilog methods will have problems where one of the input logs reads incorrectly (e.g., hole washouts, tool sticking, cycle skipping, GR statistical variations, and poor depth alignment).

Some prefer to use core data for nonquantitative, visual comparison with log-analysis porosity developed from a variety of methods. When the volume of core data is low, making simple qualitative presentations of the measured core may be satisfactory. When there is sufficient core data to provide a representative sample of the formations in one or more wells, quantitative use will lead to more accurate OOIP and OGIP. It is not possible to provide strong guidance on the amount of core required, because the geological and engineering issues of each reservoir differ greatly. However, as a starting point, one might consider coring one well in approximately every 10 if this fits sensibly with the unique parameters of the reservoir under study.

Consistency of Calculations and Uncertainty

Calculations of porosity and S_w must be compatible with each other. They must both be evaluated within the "total ϕ/S_w system," or both be evaluated within the "effective ϕ/S_w system" (see the discussion in the following S_w section). When preserved OBM ("native") core measurements of both porosity and water saturation are available, the core sample F_HCP [ = ϕ × (1 – S_w)] is, after a few small standard adjustments, usually the best estimate of the V_HCP at each cored depth. This core-based V_HCP can be used to validate, or calibrate, the V_HCP given by either the "effective" or the "total" ϕ/S_w evaluation systems, as calculated from the log data (see Eq. 3H.3).

The uncertainty of porosity evaluations varies from case to case. The porosity of a single cleaned core plug can be repeated to within approximately ± 0.2% BV, where this uncertainty refers to one SD.  This very small instrument-repeatability uncertainty does not, however, include the many other noninstrumental variables that affect the systematic uncertainty and overall accuracy. Before the measurement is made, there may be core-plug cleaning problems from native salt in the pore space and incomplete oil removal. The drying time of water-adsorbing clay minerals adds further uncertainty. Surface roughness causes the plug volume to be uncertain especially when there are large grains and vugs. The uncertainty of the average core porosity will be improved when many plugs are selected at approximately one per foot without regard for the rock quality (i.e., randomly). However, because of commercial pressures and common sense, plug samples are not always selected at random, so care must be exercised, especially concerning the porosity values predicted at depths where core is not available. It must also be remembered that 1-in. core-plug samples, taken from each foot of whole core, sample only approximately 2% of the whole core volume.

Log readings are also uncertain, and, for example, the bulk-density-log random uncertainty may be approximately ± 0.015 g/cm³ or approximately ± 1% BV.  Systematic errors, such as poor density-tool pad contact with the borehole wall, increase the uncertainty in some wells. Further uncertainty in the final calculated porosity arises from the grain- and fluid-density values (or the related regression coefficients) and from mixed-mineral and shaly-sand effects.

The evaluations of zone-average porosity in the net-pay intervals in a single well that has relevant core control might have an accuracy of approximately ± 1.0% BV. This is largely the result of systematic uncertainty because the random uncertainties will be very small for zone-average values. In other words, an average porosity of 20% BV has an uncertainty range of 19 to 21% BV. This is a one SD estimate. In 32% of cases, zone-average uncertainties of greater than ± 1.0% BV are considered likely. Where core control is not available, these accuracy estimates should probably be doubled. Effective-porosity accuracy in very shaly sands is also more uncertain because of the associated V_sh estimates.

For fractured reservoirs, imaging tools now provide better visualizations of the borehole wall, but quantification of the open-fracture porosity, which may be approximately 0.1 to 1.0% BV, is highly uncertain. Production testing and test analysis are recommended to determine the nature and extent of any fracture system within the reservoir interval.

Fluid-Contacts Identification

Defining the depths of the fluid contacts, GWC, OWC, and gas/oil contact (GOC), or defining both of the latter in some reservoir situations, is essential for volumetrics calculations and important for detailed petrophysical calculations. For example, for more-accurate porosity calculations, the reservoir’s vertical interval needs to be subdivided by fluid type to account for differences in the average fluid saturation and, hence, differences in fluid density or sonic travel time in the various fluid intervals: gas cap, oil column, or aquifer. For the S_w calculations, the depth of the OWC or GWC, or more particularly the related free water level (FWL), is a required input for any S_w calculations using capillary pressure, P_c, data. These depths need to be defined in every wellbore, to the extent that they occur. This section addresses the methods used to make the most accurate determination of the GOC, OWC, and/or GWC depths at the wellbores. This section does not address the larger topic of how these fluid contacts may vary over the whole of the reservoir either because of faults, rock-quality variations, isolated sands, a reservoir’s hydrocarbon-filling history, or hydrodynamics of the reservoir-aquifer system.

There are four types of data that can be used to define the fluid-contact depths in a wellbore: mud logs, cores (geologists’ descriptions and routine-core-analysis data), resistivity and neutron logs, and formation-tester pressure surveys. These are listed approximately in the order in which these data are gathered from a wellbore. Each has its own strengths and weaknesses. Each is an independent source of information; therefore, the most accurate fluid contact is obtained by using all of the data available for a particular well. The first step in using any and all of these data sources is to align their depths as accurately as possible.

Mud Logs

Mud logs record mud gas compositions and quantities and descriptions and analyses of drill cuttings. These provide information about the fluid content and lithology of the rock as it is drilled. These data have some depth uncertainty because of the lag time between a rock interval being drilled and the time the cuttings are recovered at the surface. The field personnel work to minimize this uncertainty by periodically dropping a bit of "carbide" into the drilling mud and then determining how long it takes for it to show up on the mud-returns gas-chromatograph output. The mud log gas-analysis data plotted vs. drilled depth, and adjusted for drilling rate, is a semiquantitative measure of the gas content over the reservoir interval. It can be used to determine a GWC or OWC because the background gas content per unit volume of aquifer brine is so low compared with that of free gas or gas dissolved in oil. The methane-concentration log is most useful for defining the top of the reservoir and the GWC for a gas reservoir, and the detailed gas analyses can also identify a GOC from increasing ratios of the heavier hydrocarbon components compared with methane as depth increases.

Direct observation of oil staining, and yellow or brown ultraviolet (UV) fluorescence on drill cuttings, identifies oil. When drill cuttings are crushed in solvents, mobile oil migrates to the solvent, which then fluoresces. Gas condensate has a bright white fluorescence. These characteristics assist in identifying oil and gas reservoirs, the top of the reservoir, GOC and OWC, and, possibly, the base of the reservoir.

Water-Based-Mud Cores

WBM cores can provide direct observations of the OWCs and GOCs. Because of differences in the colors of the oil staining, the depths of gas, oil, tar, and relict-oil intervals can often be determined visually from the cores, especially when they are cut at a high rate of penetration. It is common practice to photograph cores in both white and UV light to provide an accessible, permanent visual record. These visual observations are typically complemented by the routine-core-analysis S_o data over the same depth ranges.  Gas and aquifer intervals have low core oil saturations, and tar intervals often have high core oil saturations.

Log-Based Methods

The use of resistivity-log data is another method of determining OWC and GWC depth in a wellbore.  The resistivity logs are used to calculate S_w, and where there is a significant decrease in the S_w values (decreasing from near 100% PV as one moves up through the reservoir interval), that depth is defined as the fluid-contact depth. Also, the invasion profile of the shallow- vs. deeper-reading resistivity tools can be used to help define the depth interval in which the fluid contact occurs. This is true of either WBM- or OBM-drilled wells. Also in WBM-drilled wells, tar intervals can be defined by those depths over which the shallow- and deep-reading resistivity tools show a lack of oil-saturation change, which indicates that the hydrocarbons in the pore space are too viscous to be displaced by the WBM filtrate. If the reservoir is not too shaly, neutron logs can be one of the keys to identifying gas-bearing intervals.  A GOC, or a GWC, can be defined at the depth at which the neutron porosity significantly decreases and the density and sonic porosities slightly increase as one moves up through the reservoir interval.

Formation-Pressure Surveys

The best data from which to determine FWL fluid contacts are given by the formation-pressure-testing tools (e.g., RFT, formation multitester, MDT, and RCI) that measure pressure surveys over reservoir intervals.  In going vertically from the gas cap into the oil column, or from the hydrocarbon column into the aquifer, there will be breaks in the formation-pressure vs. depth trends as one moves from a very low gas pressure gradient (0.10 psi/ft or less) to the higher oil pressure gradient (typically 0.25 to 0.35 psi/ft) and then to the water pressure gradient (0.40 to 0.55 psi/ft). When adequate data can be collected, the fluid contacts can be determined very accurately by identifying the depths at which the characteristic pressure gradients change. See the chapter on reservoir pressure and temperature in this volume of the Handbook for additional information on fluid-contact depth determination using pressure information.

Overall, the formation-pressure-survey data should be the primary source of data for defining the FWL fluid contacts. The other data should be used to complement these pressure data, or should be used together to define the fluid contacts if no pressure-survey data are available. In reservoirs with sand/shale sequences, sometimes the fluid contact is determined to be within a shale interval, even if that interval is only 10 ft thick or less. If this is the case, the best estimate depth of the fluid contact is at the mid-depth of the shale interval (unless the pressure-survey data indicate otherwise). The fluid contact may be different from the FWL, and it is the FWL depth that is important commercially and important when making S_w calculations from P_c/S_w data.

Since the introduction of 3D-seismic surveys, acoustic-impedance contrasts between gas-, oil- and water-bearing formations are increasingly used. The impedance is dependent on the density and acoustic velocity of each fluid. Many reservoirs exhibit a significant change of acoustic impedance at the fluid contacts, allowing the contacts defined at the wells to be propagated, with data control, into the undrilled areas of the reservoir. These impedance maps show visual "haloes" around a GWC or OWC. These same impedance changes may also be seen in vertical seismic sections and assist in identifying the top of the reservoir, GOC, GWC, and OWC.

Water-Saturation Determination

S_w determination is the most challenging of petrophysical calculations and is used to quantify its more important complement, the hydrocarbon saturation (1 – S_w). Complexities arise because there are a number of independent approaches that can be used to calculate S_w. The complication is that often, if not typically, these different approaches lead to somewhat different S_w values that may equate to considerable differences in the OOIP or OGIP volumes. The challenge to the technical team is to resolve and to understand the differences among the S_w values obtained using the different procedures, and to arrive at the best calculation of S_w and its distribution throughout the reservoir vertically and areally. In OOIP and OGIP calculations, it is important to remember the relative importance of porosity and S_w. A 10% PV change in S_w has the same impact as a 2% BV change in porosity (in a 20% BV porosity reservoir).

Techniques for Calculating S_w

S_w in wellbores can be determined by the following primary methods: *S_w calculations from resistivity well logs by application of a model relating S_w to porosity, connate-water resistivity, and various rock electrical properties. *S_w calculations from laboratory capillary pressure/saturation (P_c/S_w) measurements by application of a model relating S_w to various rock and fluid properties and height above the free-water level. *S_w calculations using OBM-core-plug Dean-Stark water-volume determinations. *Combinations of these methods. This listing is the chronological order in which data are likely to become available, not in a ranked order based on the accuracy of the various methods. In fact, the use of S_w values from properly handled and preserved OBM cores is superior to the other techniques in the oil (or gas) column above the mobile-water part of the oil/water (or gas/water) transition zone. The OBM cores are superior because the water-volume measurements on these core plugs are a direct determination of S_w. The extracted water is the reservoir’s connate water. The resistivity-log data are inferential measurements that have to be converted to S_w values by a conceptual, theoretical, or empirical model. The use of P_c/S_w data requires other models and a number of input parameters whose values at reservoir conditions cannot be directly determined and, hence, must be estimated.

The choice of which S_w-calculation approach to use is often controlled by the availability of the various types of data. If no OBM cores have been cut, then this technique cannot be used unless funds are spent to acquire such data from one or more newly drilled wells. This is not a high incremental cost when OBM use is planned for other purposes. Resistivity logs are run in all wells, so these data are available for making standard-log-analysis S_w calculations. A key consideration when making calibrated S_w calculations is the availability of SCAL data on core samples from the particular reservoir; that is, the number of laboratory electrical-property and P_c/S_w core-plug measurements that have been made.

The technique chosen to calculate S_w is often a hybrid that combines the use of two of these basic data sources. For example, the OBM-core S_w data can be used in combination with the resistivity logs to expand the data set used to include all wells and the whole of the hydrocarbon column. Alternatively, the OBM-core S_w data can be used in combination with the P_c/S_w data. In this way, the OBM-core S_w data define the S_w values for the majority of the reservoir, whereas the P_c/S_w data define the S_w values in the interval just above the fluid contact and perhaps in areas of the field where P_c data are available but OBM-core data are not.

Data Availability and Data Quality

This section discusses the input-data availability and data-quality issues for each S_w technique. Details of the S_w physical-models equations are given in the next section. These considerations often control the initial choice of methodology to calculate S_w and need to be addressed at the start of the project to determine whether it is practically possible to fill gaps in the database in order to use a more accurate S_w-calculation approach. This discussion assumes that accurate porosity values are available from the routine-core-analysis database and that porosity is calculated point by point from the well logs. The discussion focuses on particular aspects that affect the choice of S_w methodology. Many of the database considerations were discussed in Sec. 3H.2.

Resistivity Logs. Wells generally have one variety or another of laterolog or induction resistivity log because they are broadly useful and because government regulations typically demand that they be recorded. This generally provides point-by-point data from the top of the hydrocarbon column down through any aquifer intervals that are present. However, in many fields, the early wells are spread thinly over the reservoir area, but the later development wells are drilled only in areas chosen to maximize rate and recovery while minimizing costs. This means that, often, few wells are drilled downdip where the hydrocarbon column thins because of an underlying aquifer, or in the potentially thin updip limits of the reservoir. In such areas, there may, therefore, be few resistivity logs.

Laterologs are preferred to induction logs when the drilling mud has moderate to high salinity. This limitation of induction tools arises because of the excessive conductivity signal from the borehole and the mud-filtrate-invaded zone. Deep laterolog tools read too high when measuring immediately beneath anhydrite and salt,  and alternative resistivity curves should be selected. When formation resistivity, R_t, is very high, previous generations of induction tools had limited accuracy, but current tools are much improved. Although the deep induction measurement is a running average over many vertical feet, modern tools include systems to deconvolve the raw log and provide a final log with a good vertical resolution.

Deep invasion of WBM filtrate affects all resistivity logs, and, in the extreme, the available resistivity log may be used only qualitatively. At the opposite extreme, when OBM filtrate invades a hydrocarbon reservoir, the invading OBM filtrate generally displaces only the reservoir oil and gas, leaving the S_w unchanged. Here, invasion of OBM does not usually change the deep-formation or the invaded-zone resistivity. For moderate invasion depths, the logging company charts are sometimes used to correct the deep-reading log to provide a better estimate of R_t.

Pad-mounted shallow-reading microresistivity logs measure R_xo, the resistivity of the mud-filtrate-invaded zone. When used together with the deeper-reading tools, these logs provide valuable information about the mobility of the reservoir fluids, including the presence of tar. In WBM wells, they also provide an estimate of the residual-hydrocarbon saturation, S_orw.

Connate-Brine Resistivity Data. An accurate value of connate-brine resistivity, R_w, or its values and distribution throughout the reservoir, are required for accurate S_w calculations using resistivity logs. Temperature estimates are also required.

A first check on the R_w of the aquifer is to back-calculate the apparent R_w with the Archie equation using the invasion-corrected resistivity logs and the best estimates of a and m parameters. Because S_w is typically 100% PV in the aquifer interval, the n value is not relevant here.

The spontaneous-potential (SP) log provides a second method to calculate R_w in wells drilled with WBM. Information on the mud-filtrate composition and temperature is used with the SP deflection to calculate R_w. The moderately accurate calculation process is valid in the aquifer but is also valid in the hydrocarbon column if high resistivity does not suppress the SP response. When OBM-core salinity measurements are not available, the SP log provides the only evidence of possible R_w variations in the hydrocarbon column.

A third estimate of aquifer-water composition and R_w is often taken from samples recovered during flow tests of the aquifer interval; however, the R_w of the oil and/or gas column is not always the same as that of the aquifer interval.  Aquifer-interval flow tests must be validated and checked for contamination from mud-filtrate invasion.

For the oil or gas column, the determination of the R_w value or values is far more of a challenge because the reservoir water will not flow. The typical, but not necessarily correct, first assumption is that the hydrocarbon-column R_w is the same as that of the underlying aquifer. If wells have been cored with OBM, core plugs from the hydrocarbon- and water-bearing intervals can be analyzed for both their water volume and their salt content, particularly the chloride ion that in almost all cases dominates the anion side of the salinity determination. 

Fig. 3H.13 shows variation of chloride concentration with depth for a reservoir in Ecuador.  The chloride value can generally be used to quantify the reservoir-water salinity, from which the R_w at reservoir conditions can be calculated using standard water-resistivity vs. chloride charts or algorithms. For reservoirs in which there is a considerable CO₂ content (3+ mol%), the ion distribution at surface conditions will differ from that at reservoir temperature and pressure. Equilibrium ion-distribution calculations need to be made when adjusting the surface-salinity measurement to reservoir conditions.

• 

  Fig. 3H.13 – Formation-water salinity variation within the hydrocarbon column (Villano oil field, Ecuador).

 Formation temperature affects the S_w estimates because, for constant formation-water composition, R_w varies with temperature.  Maximum downhole temperature is measured with most log runs and drillstem-tool (DST) tests, and these are widely used to estimate a temperature vs. depth profile. It can be argued that the temperature required for resistivity-derived S_w estimates is the prevailing temperature in the rock volume seen by the tool at the time of logging. At this time, the relevant rock is likely to be cooler than the original formation temperature. The error induced by the usual maximum temperature simplification is not large, and the cooling issue is generally ignored.

Electrical-Property SCAL Data. The third aspect of making these S_w calculations is the choice of the model for the "electrical network" within the rock. These models relate S_w to several formation variables including the bulk-formation resistivity and the formation-water resistivity. A number of models have been published [e.g., Archie, Waxman-Smits-Thomas (WST), dual-water (DW), and Indonesia].  Laboratory measurements of two or more types of electrical properties are taken. All of these models assume a homogeneous rock sample.

Archie Exponents. First, a set of cleaned core plugs with a range of porosities are fully saturated with brine of known resistivity, and the bulk resistivity of each core plug is measured. For this simplest model, the slope of a line fitted to a log-log plot of the data set gives the cementation exponent, m, and the intercept is the cementation constant,  a (see Fig. 3H.14, where a = 1 and m = 1.77). These parameters are used to predict point-by-point F from porosity; leading to predictions of R₀ and S_w.

[[File:Vol5 page 0454 eq 001.png|RTENOTITLE]]....................(3H.7)

where F = formation factor, R_w = brine-water resistivity, and R₀ = rock resistivity with zero oil and gas saturation (100% PV S_w). The plotted logarithmic data (log₁₀F and log₁₀ϕ) are fitted with a linear model of the form,

[[File:Vol5 page 0454 eq 002.png|RTENOTITLE]]....................(3H.8)

where ϕ = porosity, a = cementation constant, and m = cementation exponent. Therefore, m = − change in log₁₀F/change in log₁₀ϕ (the slope of the line-fit) and a = F at 100% BV porosity (the line-fit intercept).

• 

  Fig. 3H.14 – Laboratory-measured formation resistivity factor (F) vs. porosity for core plugs from Dulang field, Malaysia.

 This model was developed by Archie,  who proposed a = 1.0 and m = 1.8 to 2.0 for his data set. Subsequent work by Exxon researchers for several sandstone rocks recommended a = 0.61 and m = 2.15 (the Humble formula).  Carbonates also have been studied and yielded a recommendation to use m = 1.87 + 0.019/ϕ below 9% BV (the Shell formula).  However, carbonate pore and fracture networks vary greatly, and m values from 1.0 to 3.0 may be required. Clearly, m is not a constant, but varies with rock type.

When plotting these formation-factor data, it is typically assumed that the rock samples have similar pore geometry, but with differing levels of porosity and diagenesis. Reservoir-specific exponent values are likely to provide more-accurate S_w results than worldwide correlations. However, before reservoir-specific values are determined, descriptive and experimental data need to be studied to determine whether they need to be subdivided into various groupings that relate to distinct differences in lithological properties (grain size, sorting, or clay-mineral content).

In partially brine-saturated rocks, a related experimental study involves measuring electrical properties as a function of water saturation. In these experiments, the resistivity index (I_R), the ratio of the desaturated-rock resistivity to the 100% PV brine-saturated rock resistivity (R_t/R₀), is measured as a function of brine saturation. For example, in a porous-plate apparatus, S_w is changed by increasing gas pressure, and therefore capillary pressure, at the gas/water interface in the pores. Brine flows from the base of the plug via a porous-plate. From the measurements on each core plug, a log-log plot of I_R vs. S_w is made (see Fig. 3H.15, where n = 1.64). The slope of the line (almost always forced through I_R = 1.0 at S_w = 100% PV) is the Archie saturation exponent n (see Eqs 3H.9 and 3H.10). On the basis of experimental data, Archie recommended that n = 2.0, and this value is still widely used when no experimental data are available. Although cementation exponents can be determined from log analysis, saturation exponents cannot and, therefore, require external information from core data.

[[File:Vol5 page 0456 eq 001.png|RTENOTITLE]]....................(3H.9)

and [[File:Vol5 page 0457 eq 001.png|RTENOTITLE]]....................(3H.10)

where n = saturation exponent, the slope from the origin of a line-fit of several data points; I_R = resistivity index; and S_w = fractional brine water saturation.

• 

  Fig. 3H.15 – Laboratory-measured formation resistivity index (I_R) vs. brine saturation for core plugs from Dulang, Malaysia.

 A straight line-fit is usually used, but curved line-fits can be considered where necessary. Curvature is often the result of the clay-mineral content but may also result from an inhomogeneous water distribution at the pore scale (e.g., when microporous rock grains are present). When significant amounts of clay minerals are present in the rocks, other models are required to extend the Archie relationships. The WST model, discussed next, is based on laboratory SCAL measurements including cation-exchange capacity (CEC).

Waxman-Smits-Thomas Exponents and Cation-Exchange Capacity. WST cementation and saturation exponents (m* and n*) are required to apply the WST shaly-sand-model equation discussed in Sec. 3H.7.3. The quantity of cation-exchange sites per gram of rock sample (CEC) may be measured in the laboratory by several methods and, after converting to CEC per unit PV, is used as the model parameter Q_V. The most reliable measurement of Q_V involves carrying out bulk-rock resistivity, R₀, tests at several brine resistivities and, therefore, is time consuming. The rock conductivity values (1/R₀) are plotted vs. brine conductivity (1/R_w) to identify the excess conductivity resulting from the shales and clay minerals. The slope of the fitted line is the reciprocal of F*, the WST formation factor. The excess conductivity is modeled as being equal to BQ_v/F*, and B is presumed in this model to be always positive. The parameter B is the equivalent counter-ion conductance,  which is a function of temperature and the free-water resistivity. Q_v is estimated from the values of F* and B. Core resistivities are also measured when S_w is less than 100% PV and both the WST exponents m* and n* are derived (see Fig. 3H.16 and Fig. 3H.17, respectively). It should be noted that m* > m and n* > n, except in "clean" sands.

• 

  Fig. 3H.16 – Laboratory-measured formation resistivity factor (F) vs. porosity for core plugs from the Shannon sand, Wyoming, U.S.A. (after Keelan and McGinley</ref>

 Other CEC methods require the breaking up, disaggregation, and consequent partial loss of the real geometry of the rock’s electrical network. These simpler methods, such as the ammonia method, use analytical-chemistry methods to measure CEC. After measuring porosity and grain density, this practical laboratory unit is converted to the required Q_v parameter.  These simpler CEC measurements are often made on sidewall cores and are used together with exponent values measured on cores from neighboring wells.

Numerous other shaly-sand models have been developed, and, unlike WST, many are calculated from effective porosity. These types of models are generally applied using Archie exponents. When using SCAL electrical-property data, there must be consistency between the electrical-network model used to derive the laboratory parameters and the model used in the final S_w calculations from the porosity and the resistivity logs (e.g., if the laboratory provides standard Archie n values, these are not appropriate input to the WST equation).

Capillary Pressure SCAL Data. P_c data are a different type of SCAL data that can be taken experimentally in several ways. All P_c saturation tests respond to the pore-size distribution of the rock and the interfacial properties of the various solid/fluid systems. These data are obtained by desaturating core plugs, either using a centrifuge or a porous-plate apparatus. Initially, cleaned and dry plugs are saturated with either water or oil. The liquid is then displaced by air or nitrogen. Because air is very nonwetting compared with either water or oil, using these fluid pairs (air/water or air/oil) means that, as the P_c increases, the air will first occupy the largest pores. As the P_c and air saturation increase, the air will occupy smaller and smaller pores. The core plug begins the experiment saturated with the wetting phase, so the desaturation process provides data for the drainage P_c curve. After completing the drainage process, the core plug can be spun under the liquid in a centrifuge experiment, the liquid saturation will increase, and the imbibition P_c curve will be generated. Usually, only drainage P_c/S_w data are taken, and for most reservoir situations, these are the relevant data because they correspond to the original oil (or gas) trap-filling process.

MICP data are taken on cleaned and dried irregular core pieces. The core pieces are evacuated to a low vacuum, and mercury is injected with increasing pressure, up to 20,000 psi and sometimes higher. Corrections for clay-mineral adsorbed-water removed during drying can be made with the Hill-Shirley-Klein method.  The MICP experiment has the advantage of being run rapidly but is not a true wetting/nonwetting system. The sample cannot be used for subsequent SCAL tests because some mercury is retained within the core pieces at the end of the testing sequence. MICP data are widely used to measure pore-size distribution, but, when considering whether they should be used for accurate S_w calculations, MICP should be compared with air/water or air/oil P_c/S_w data.

The P_c/S_w data are usually compared first on a Leverett "J-function" basis.  The P_c data are converted to the J-function basis by multiplying each P_c value by the square root of its permeability divided by porosity and then dividing by the fluid-pair IFT multiplied by the contact angle (see Eq. 3H.11). J-function values differ depending on whether they are calculated in oilfield or metric units. The J-function approach assumes similar pore-size distribution in all cores tested. In this way, the various P_c/S_w data tend to converge when the underlying assumptions are met; however, there may still be enough scatter to suggest that the data need to be divided into two or more groupings (see Fig. 3H.18).

[[File:Vol5 page 0460 eq 001.png|RTENOTITLE]]....................(3H.11)

From a J-function vs. S_w plot, the technical team can determine whether enough data have been obtained, whether new data need to be gathered to fill in portions of the data ranges, and whether the data indicate that subgroupings are appropriate and needed. Also, this plot indicates whether there are significant outliers that should be excluded or examined in more detail. A drawback to this averaging method is the introduction into S_w determination of four measured parameters and their associated errors (i.e., porosity, permeability, IFT, and contact angle).

• 

  Fig. 3H.18 – Example plots of centrifuge air/brine capillary pressure (P_c/S_w) data and its conversion to a J-function basis; data from an Asian gas field. The air/brine P_c value of 100 psi is equivalent to a height above free-water level of 200 to 350 ft, depending on the reservoir fluid’s properties and the temperature and pressure conditions.

 Capillary pressure data may also be averaged by various models.  The relationship of S_w with permeability, and then porosity, is examined and is followed by examination of the height dependency.

The last type of S_w data discussed here is that obtained from routine core analysis of core plugs cut from OBM cores, either preserved as whole cores or else with core plugs cut at the wellsite and preserved individually. These data are taken foot-by-foot and are direct measurements of reservoir S_w values.  Many fields may never have had any wells cored with OBM; others may have only one or two OBM-cored wells. Even a single OBM coring of the full reservoir interval offers significant data that may impact the technical team’s methodology for making the S_w calculations. It is better to have at least two wells fully cored with OBM from different areas of the reservoir.

To evaluate the OBM-core S_w data, they should be plotted as S_w vs. log₁₀ (permeability) or vs. porosity to identify outliers and trends in the data. Particularly, the low-porosity/low-permeability data range should be examined for potential measurement problems. Sometimes, the raw laboratory measurements of water volume and PV data need to be reviewed for problem points and recalculations made where appropriate. Finally, the data should be divided into various possible interval groupings so that any needed zonation can be identified.

If reservoir connate water has flowed out of the core plug at any stage before the laboratory measurement, the OBM-core S_w data are clearly not representative of the in-situ reservoir S_w. This certainly occurs in water-bearing formations and can also occur in the lowest intervals of the oil/water or gas/water transition zones. These lowest intervals, which may be a few feet to approximately 30-ft thick, are precisely the same intervals in which a water cut is expected with the initial oil production. The mobile-water intervals can be identified in OBM wells where the shallow-reading induction-log resistivity is higher than the deep-reading induction-log resistivity. This pattern indicates higher oil saturations in the invaded zone compared with the original oil saturations. Where mobile water is observed, the OBM-core S_w measurements do not represent in-situ S_w and are too low.

Application of Each S_w Technique and Its Strengths and Weaknesses =

Methodologies for quantifying S_w at the wellbore are discussed here. The main features of each approach are described; however, in some cases, there are variations that are not addressed. For each technique, its strengths and weaknesses are discussed.

Calculating S_w from Resistivity Well Logs by Applying a Model Relating S_w to Porosity, Connate-Water Resistivity, and Various Rock Electrical Properties. The most common technique for calculating S_w is the use of resistivity logs with a model (empirical or theoretical) that relates S_w to R_t, R_w, and porosity. As mentioned previously, a large number of R_t/S_w models have been published. The models are applied at every data point in the reservoir where deep resistivity, porosity, and shale-volume estimates, if required, are available. The evaluation of all other necessary parameters (constant or variable R_w values, a, m, n, Q_V, V_sh, R₀ = F • R_w, etc.) has also been discussed previously. Several commercial software packages are available that perform these S_w calculations for a variety of log models.

Clean Sand (Archie) Model.

[[File:Vol5 page 0461 eq 001.png|RTENOTITLE]]....................(3H.12a)

and, alternatively,

[[File:Vol5 page 0461 eq 002.png|RTENOTITLE]]....................(3H.12b)

This model is used for field studies in the many sandstone and carbonate reservoirs in which the clay-mineral content is low. This decision is strengthened after SCAL data have demonstrated that the simplest solution is satisfactory. When a significant fraction of smectite (montmorillonite) is present and where finely laminated sand and shale sequences occur, one of the shaly-sand models is very likely to be required. Low-resistivity pay is an issue in several oil-producing areas, such as the U.S. Gulf Coast, Egypt, and Indonesia, and hydrocarbon reserves can be missed and left undiscovered as a result of the resistivity suppression by clay minerals and shales.

Shaly-Sand Models. In the clean-sand model, the formation water is the only electrically conductive medium. In shaly rocks, R_t is suppressed and Archie S_w calculations are too high. As clay-mineral-rich rocks were studied and experimentally tested, more-complicated electrical models were developed to account for the effects of the geometries of conductive clay minerals and shale on rock resistivity. The primary goal of the shaly-sand models is to determine a working relationship between S_w using parameters similar to the Archie model, but also incorporating the quantity and specific electrical properties of the clay-mineral/shale. All of the shaly-sand models reduce to the Archie equation when the shale component is zero. For simplicity, in all of the shaly-sand models, the cementation constant, a, is taken to be 1.0 but, if required, can be easily associated again with the R_w term.

Laminated Sand/Shale Model. A parallel resistor model might be used for laminated sands, with multiple thin parallel layers of 100% shale interbedded with clean-sand layers. Thin, in this context, means that there are several beds within the vertical resolution of the resistivity-logging tool.

[[File:Vol5 page 0462 eq 001.png|RTENOTITLE]]....................(3H.13)

where the clean-sand resistivity [[File:Vol5 page 0462 inline 001.png|RTENOTITLE]]. For this laminated shale/sand model, effective porosity depends simply on the sand fraction of the bulk volume:

[[File:Vol5 page 0462 eq 002.png|RTENOTITLE]]....................(3H.14)

[[File:Vol5 page 0462 eq 003.png|RTENOTITLE]]....................(3H.15)

The value of ϕ_sd may be assumed from neighboring thick sands, and all of the parameters, except the S_w of the sand, S_wsd, can be estimated.

Poupon-Leveaux (Indonesia) Model. The Indonesia model was developed by field observation in Indonesia rather than by laboratory experimental measurement support.  It remains useful because it is based on readily available standard log-analysis parameters and gives reasonably reliable results. The formula was empirically modeled with field data in water-bearing shaly sands, but the detailed functionality for hydrocarbon-bearing sands is unsupported, except by common sense and long-standing use. S_w results from the formula are comparatively easy to calculate and, because it is not a quadratic equation, it gives results that are always greater than zero. Several of the other quadratic and iterative-solution models can calculate unreasonable negative S_w results.

[[File:Vol5 page 0462 eq 004.png|RTENOTITLE]]....................(3H.16)

[[File:Vol5 page 0463 eq 001.png|RTENOTITLE]]....................(3H.17)

The Indonesia model,  and other similar models, are often used when field-specific SCAL rock electrical-properties data are unavailable but are also sometimes used where the SCAL exponents do not measure the full range of shale volumes. Although it was initially modeled on the basis of Indonesian data, the Indonesia model can be applied everywhere. The inputs are the effective porosity, ϕ_e, shale volume and resistivity (V_sh and R_sh), and water and deep resistivities (R_w and R_t). The S_w output is usually taken to be the water saturation of the effective porosity, but it has been recently suggested that the output is likely to estimate S_wt. Many other log-based shaly-sand models have been proposed but, for brevity, are not discussed here.

Waxman-Smits-Thomas and Dual-Water Models. S_wt, the water saturation of the total porosity, is calculated at each reservoir data point by iterative solution of the complex multiparameter WST and DW equations (Eqs. 3H.18 and 3H.19). For brevity, the details of the solution methods are not presented here. The WST and DW models are total-porosity/S_w system models.

The WST model is based on laboratory measurements of resistivity, porosity, and saturation of real rocks.  Q_v is the CEC per unit PV.

[[File:Vol5 page 0463 eq 002.png|RTENOTITLE]]....................(3H.18)

where S_wt = water saturation of the total porosity as shown schematically in Fig. 3H.8, B = specific cation conductance in (1/ohm•m)/(meq/mL), and Q_V = CEC in meq/mL of total PV. The exponents m* and n* apply to the total PV.

The DW model is also based on the WST data. It uses clay-bound-water conductivity instead of WST’s BQ_v factor (see Eqs. 3H.18 and 3H.19) and an alternative shale-volume descriptor, S_wb, the saturation of physically bound water in the total PV (see Fig. 3H.8).  When V_sh is zero, S_wb is zero; and when V_sh is 100% BV, S_wb and S_wt are also 100% PV.

[[File:Vol5 page 0463 eq 003.png|RTENOTITLE]]....................(3H.19)

where R_wb = resistivity of clay-bound water [[File:Vol5 page 0463 inline 001-2.png|RTENOTITLE]] in the shales, and R_wf = resistivity of free formation water [[File:Vol5 page 0463 inline 001-2.png|RTENOTITLE]] in the shale-free water zones. Because of the different model assumptions, DW exponents m_o and n_o must always be smaller than the WST exponents and may be values similar to "clean" sand exponents. Where the WST and DW models have been properly applied, the V HCP results should be equal. All S_wt calculations from the WST and DW methods must be checked to ensure that they are greater than S_wb. After this check, they are used with ϕ_t to obtain the V_HCP. For the DW model, when the outputs require conversion to effective porosity, ϕ_e, and effective water saturation, S_we, the properties are converted with Eqs. 3H.20 and 3H.21, respectively.

[[File:Vol5 page 0463 eq 004.png|RTENOTITLE]]....................(3H.20)

and [[File:Vol5 page 0463 eq 005.png|RTENOTITLE]]....................(3H.21)

Strengths and Weaknesses of R_t-Based S_w Calculations. The greatest strength of S_w calculations from the R_t logs is that these calculations can be made at each net-pay depth with valid data for all wells within the log database. The calculations can account for any subsets of input parameters related to the individual zones.

The weaknesses of the R_t-based S_w calculations are that one has to select a model to describe the relationship of S_w to R_t, R_w, and a variety of other input parameters. Any model is an approximation to the real nature of the reservoir pore system and, typically, has limitations such as how the clay-mineral conductivity is modeled. Log-analysis estimates of V_sh are rather uncertain, so sands that are substantially free of clay minerals can easily, and incorrectly, be assigned significant clay volumes. In these circumstances, complex shaly-sand models may have been applied when it is more appropriate to model the sand as clean sand. Effective porosity is also impacted by the uncertain V_sh estimates. The R_w is often assumed to be constant within the hydrocarbon column, and usually there is little data regarding R_w other than from aquifer samples. In several cases in which the R_w distribution has been studied in depth, it was found to vary in systematic ways within the hydrocarbon column and not necessarily be the same as in the underlying aquifer. 

CEC can be measured in the laboratory, but in the reservoir it must be estimated by correlations with porosity or V_sh. For the laboratory CEC measurements, there are fundamental uncertainties such as the degree to which the clay-mineral geometry is altered by the disaggregation of the core. The total surface area and CEC may be enhanced by comminution (i.e., grinding to grain-size particles). 

The other input parameters for the S_w/R_t models are either based on "worldwide experience" (such as default exponent parameters in commercial software packages) or developed from SCAL rock-electrical-property measurements on a relatively small number of core plugs from the reservoir interval. Hence, there are relatively few data determining the parameters that are used for the log point-by-point S_w calculations. It has to be assumed that the manner in which the water saturation is distributed in the core plugs during these laboratory experiments is like that of the real reservoir. Because water is present during the laboratory measurements, clay minerals are rehydrated at the time of the tests.

Calculating S_w From Laboratory Capillary-Pressure/Saturation Measurements. A second S_w method that is totally independent of the resistivity logs uses laboratory-measured P_c/S_w data. The underlying concept of the use of capillary pressure data is that the reservoir has come to capillary equilibrium over geologic time (the millions of years since hydrocarbons have entered and filled the reservoir trap). This equilibrium is reproduced in laboratory experiments using the centrifuge, porous-plate, and MICP methods. The P_c/S_w data are measured on a selected set of reservoir core plugs representing a range of porosity and permeability values (and possibly also lithologies).

Centrifuge experiments are typically made on 1-in. core plugs over a period of several days in the intense gravitational field (up to 1000 G) of the centrifuge and are assumed to be equivalent to what occurs in a hydrocarbon reservoir over millions of years in a 1-G gravitational field and over lengths of 10 to hundreds of feet. These assumptions are broadly accepted as being reasonable, provided that the samples are not damaged during testing in the centrifuge. The reported P_c/S_w values are not the raw laboratory data. In the laboratory, the average saturation is determined at each centrifuge speed, and those raw data are input to a mathematical model to convert them to a tabulation of endface saturations and P_c values.

Porous-plate P_c tests are made on core plugs at several different gas pressures and are generally carried out at the same time as the resistivity experiments. After reaching equilibrium with no further brine flow at each pressure, the S_w is constant along each plug and is calculated from its weight loss.

MICP tests are made on dried core pieces and the volume of injected mercury, the nonwetting phase, is converted to an S_w value. This is considered to be total S_w if, at high enough pressures, mercury enters both the microporosity and dry clay-mineral porosity. Conversely, for centrifuge or porous-plate tests, where brine is present as the wetting phase, clay minerals probably hydrate, and their physically bound water is unlikely to be displaced during the test. Brine-related P_c/S_w measurements may give total or effective S_w, depending on the specific porosity measurement method used (i.e., whether the porosity occupied by the clay-mineral physically-bound water is included or excluded from the porosity calculation). Effective S_w values are always lower than total S_w values and should be very low at high capillary pressures if there is little nonclay-mineral-related microporosity. 

The conversion of the laboratory P_c/S_w data to reservoir conditions requires knowledge of the IFT and contact angle of the fluid pair used in the laboratory and properties of the brine and hydrocarbon fluids at reservoir conditions. These are needed to calculate the density of each phase and to estimate the IFT between the fluid pair at reservoir conditions. The P_c values (in psi) are converted to vertical height above the hydrocarbon/water contact, H_hwc (in feet), with the following formula:

[[File:Vol5 page 0465 eq 001.png|RTENOTITLE]]....................(3H.22)

where fluid densities (ρ) are in g/cm³, and the subscripts are r = reservoir, s = surface, h = hydrocarbon, and w = water. Table 3H.4 lists some typical values for IFT, σ, and contact angle, θ, used in Eq. 3H.  and provides approximate ranges for the factors for converting P_c-laboratory data to height above a reservoir free-water level. Height-P_c conversion factors are similar for many oil and gas reservoirs; the footnotes in Table 3H.4 describe the values that were assumed to calculate these ranges. More details of correlations for brine/hydrocarbon IFT as a function of oil or gas gravity have been published.  The reservoir-condition contact angle, θ, is usually taken as 0 for gas reservoirs and 0 or 30° for oil reservoirs because, generally, data are not available at reservoir conditions.

• 

  Table 3H.4

 The suite of P_c/S_w data is typically converted to a mathematical relationship between S_w as the dependent variable and the independent variables—porosity, permeability, and H_owc or H_gwc. Because permeability is usually determined as a function of porosity, it is often not included as an independent variable. Two of the mathematical forms that have been used are

[[File:Vol5 page 0466 eq 001.png|RTENOTITLE]]....................(3H.23)

and [[File:Vol5 page 0466 eq 002.png|RTENOTITLE]]....................(3H.24)

where A, B, C, D, and E are curve-fit constants. In Eq. 3H.24, B permits the removal of singularities at zero height.

In developing the coefficients for these relationships, any zonation of the reservoir intervals needs to be applied, and then separate sets of coefficients developed for each zone. The zonation can be based on geological interpretation of the reservoir depositional and diagenetic history and/or variation in the P_c/S_w curves for different parts of the reservoir interval.

The depth of the reservoir’s OWC or GWC must be known in order to make S_w calculations using the P_c/S_w methodology. The calculations of S_w are made only above this depth. In reality, the H_owc or H_gwc is referenced to the FWL (i.e., the depth at which P_c =0 and which is deeper than the observed OWC or GWC). For a gas reservoir consisting of good-quality rocks, the difference between the FWL and the GWC is typically 1 ft or less. However, for an oil reservoir containing a heavier oil, this difference can be 10 feet or more, and, given four-way closure on an anticlinal structure, the impact on the OOIP volume between using the FWL vs. the observed OWC as the H_owc = 0 depth can equal a few percent of OOIP.

Once the various sets of coefficients have been developed and the P_c to H_owc (or H_gwc) conversion made, an S_w value can be calculated at each data point within the log database that has a valid porosity value and is above the OWC or GWC. Hence, there will be the same number of, or more, S_w values available from this S_w methodology as when using the R_t logs.

Strengths and Weaknesses of P_C/Sw-Based Sw Calculations. The strength of S_w calculations from P_c/S_w data is that, after making a correlation with porosity and height, a unique S_w value is available for all wells at all net-pay depths with valid porosity values in the log database. This also applies to the whole hydrocarbon column anywhere in the reservoir once the wellbore porosity values have been propagated into the full geocellular model grid. These calculations can account for any zonation and subsets of input parameters related to the individual zones.

A potential weakness in the P_c approach to S_w calculations is whether the laboratory measurements have been allowed sufficient time to reach equilibrium. If not, the S_w values, particularly at high P c values, will be too high. Another potential weakness is the accuracy of the IFT value used in converting from surface to reservoir conditions; fortunately, these values vary over a limited range for most hydrocarbon/brine pairs. A third potential weakness is the definition of the FWL depth compared with the observed OWC or GWC. A fourth potential weakness is whether enough data have been taken to be representative, both vertically and areally, of the zones in the reservoir. 

The fifth potential weakness concerns the complexity of the reservoir’s hydrocarbon-filling and structural history. In simple oil-reservoir situations and most gas-reservoir situations, this is not an issue. However, for oil reservoirs with tar mats and heavy-oil zones there is a complication because of the varying oil density near the OWC, including the possibility that the tar mat has a hydrocarbon density very close to that of the connate brine. Another aspect may be whether all or portions of the hydrocarbon column are on the imbibition cycle where imbibition P_c/S_w data are needed for the S_w calculations, not the typical drainage P_c/S_w data. 

Calculating S_w With OBM-Core-Plug Dean-Stark Water-Volume Determinations. The third method for determining the S_w in a reservoir’s hydrocarbon column is to cut OBM cores and perform Dean-Stark water-volume determinations on the routine core plugs. Foot-by-foot S_w values can be calculated from these water volumes and the associated core-plug PVs. OBM cores are typically cut only in a few wells in a particular field. These S_w data can be applied to other, uncored wells in the reservoir if strong correlations between these values and porosity and/or permeability are identified. These data are not valid in the oil/water or gas/water transition zone or in the aquifer, intervals in which the connate brine is mobile. OBM-core S_w values may be found to be either higher or lower than those from the other two methods described previously.

Strengths and Weaknesses of OBM-Core S_w Values. The strength of S_w values from routine-core-analysis Dean-Stark S_w data is that these data are the most direct measure of reservoir connate S_w values above the oil/water or gas/water transition zone. Relative to the two methods discussed previously and the variations of these methods, the OBM-core S_w approach is a direct S_w determination and the other methods are indirect S_w-calculation approaches that require many more assumptions and inferences.

The weaknesses of the OBM S_w method are that it does not apply to the lowest parts of the oil/water or gas/oil transition zone where the brine phase has mobility and that, generally, the amount of OBM core S_w data is limited because the operator cuts cores with OBM only in a limited number of wells because of the expense. The first of these weaknesses can be overcome if the OBM S_w data are used in combination with either the resistivity logs or with P_c/S_w data.

Another consideration is that the whole project, from the mud formulation to the core-handling and -preservation procedures on through the routine-core-analysis measurements, needs to be monitored and reviewed in detail to ensure all steps were executed properly. This demands that considerable time and effort be spent by the technical team to ensure success; however, to some extent the same comment applies to the P_c/S_w and resistivity-log/S_w calculation approaches discussed previously.

Integration of S_w Data From the Different Methods

Depending on the data availability in a particular reservoir situation, a combination of the various S_w approaches may prove superior to the use of a single type of data. The first step in going to a combination approach is to review the reservoir’s database to identify any significant gap in vertical, or areal, coverage. The most obvious gap often occurs near the fluid contact, because there is little reason to drill wells in downdip locations, particularly during a reservoir’s development phase. Three examples of combination approaches are described here.

Resistivity-Log Data With P_c/S_w Data. Resistivity-log-derived S_w results may not be available throughout the hydrocarbon column of a reservoir. To fill gaps and average the point-by-point data set, it is common practice to plot S_w as a function of height, to omit nonpay points, and to identify various porosity ranges by coding the data points. Resistivity-log-derived S_w data frequently shows V- or U-shaped patterns on these plots because of the shoulder/bed effects near nonpay sections (shales). The most accurate S_w values in such patterns are usually at the lowest S_w values where the thin-bed correction is minimized. In a manner similar to that described in the previous P_c/S_w section, height/saturation curves are often fitted to these resistivity-log-derived S_w data to enable reservoir hydrocarbons-in-place volumes to be calculated. The function forms are similar to or are the same as those described in the P_c/S_w section. 

Routine OBM Core S_w Data With P_c/S_wData. Because there is a need to define the S_w characteristics of the oil/water or gas/water transition zone and because the OBM-core S_w data can be incorrect and too low in this interval, one approach is to use P_c/S_w data in combination with the routine OBM-core S_w data. This can be done by first correlating the OBM-core S_w data to porosity and assuming that this relationship is valid above the oil/water or gas/water transition zone. The functional form of this first relationship might be

[[File:Vol5 page 0468 eq 001.png|RTENOTITLE]]....................(3H.25)

The second step is to create a tabular data set in which the S_w/porosity correlation is used to calculate an array of S_w values for large H_owc or H_gwc values and a range of porosity values. For this part of the data set, S_w is assumed to be independent of the H_owc or H_gwc values. The P_c/S_w data converted to reservoir conditions is used to provide data points for low H_owc or H_gwc values and various porosity values. Statistical calculations are applied to the whole of this data set. The functional form of this second relationship might be

[[File:Vol5 page 0468 eq 002.png|RTENOTITLE]]....................(3H.26)

With this functional form, the boundary conditions of the first step are automatically met in the second step.

Routine OBM-Core S_w Data With Resistivity-Log Data. To address the lack of valid OBM-core S_w data in the oil/water or gas/water transition zone discussed previously, it is also possible to combine OBM-core S_w data with the resistivity-log data to develop an overall S_w methodology. This approach assumes that a number of wells have been drilled through the OWC or GWC so that there are log resistivity values through the oil/water or gas/water transition zone. In this approach, the OBM-core S_w data are used to back-calculate the saturation-exponent, n, values over each zone so that the core-based V_HCP value equals that calculated from the resistivity logs (see Eq. 3H.26). Then the core-based saturation-exponent, n, values are applied to the noncored well’s resistivity logs to calculate S_w point-by-point throughout the reservoir interval in all wells.  This approach assumes that the R_w, a, and m values have been determined from other experimental and fluid-sample data so that R₀ can be calculated.

[[File:Vol5 page 0468 eq 003.png|RTENOTITLE]]....................(3H.27)

where R₀ is the bulk resistivity at S_w = 100% PV and is calculated with Eqs. 3H.7 and 3H.8. R_t is the deep-reading resistivity-log reading, and S_wc is the OBM-core S_w above the mobile-water transition zone. The resulting back-calculated n values at the core-plug depths are averaged for the zone. In some instances, n may be found to have an areal variation within a zone that should be taken into account in subsequent calculations.

Adjustments to S_w Data From Different Methods. In the previous section, a number of methodologies for S_w calculations have been described. These are basically three independent methods; hence, they can be used together to determine the accuracy of the S_w calculations throughout the hydrocarbon column. Because the methods are based on very different technical approaches and assumptions, if the different methods give essentially the same S_w answer, then it is highly likely that this is the correct S_w.

However, the challenge comes when, as is often the case, the different methods result in different S_w values and distributions. The OBM-core S_w values might be either higher or lower than those from the other two methods. The common misunderstanding that OBM-core S_w is likely to be too low is unsubstantiated. In a very large reservoir, it could go both ways depending on where one is in the reservoir.  If the values are quite different, two aspects of the calculations need to be reviewed in depth. First, the quality of the input laboratory data needs to be checked and how it was converted from raw data into the input values to the S_w calculations needs to be reviewed. Second, the assumptions and models used for the S_w calculations need to be checked. For example, with the P_c/S_w data, the assumed oil/water density difference may be considerably in error, or the shaly-sand S_w model may be inappropriate for the particular reservoir. As well as the S_w averages, the zone-average V_HCP values from the various methods should be compared, which includes porosity in the comparison calculations.

Core, Total, and Effective Systems Compatibility. The Archie R_t-based S_w equation models "clean" sands. Various other shaly-sand models use either the effective or the total-porosity systems. It is well known that these basic models, if applied properly to the same formation, must produce the same final V_HCP from their different calculation procedures (see Fig. 3H.8 and Eqs. 3H.3 through 3H.5 in Sec. 3H.5).  ϕ_t is greater than or equal to ϕ_e; however, at the same time, S_wt is greater than or equal to S_we and, when used together, the appropriate combinations must give the same V_HCP result. For the total-porosity system, V_HCP = ϕ_t × (1-S_wt), whereas for the effective-porosity system, V_HCP = ϕ_e × (1-S_we).

The V_HCP can also be estimated from a combination of core porosity and Dean-Stark S_w measured on preserved OBM cores. The several systems—core, total, and effective—must all give the same fundamental results, and the most accurate of them (the OBM-core method) can be used to calibrate and test the less accurate methods. When properly adjusted and applied (e.g., by improving the V_sh estimates or IFT values), all three methods give the same final V_HCP. If they do not agree, the likely sources of uncertainty and error must be examined.

It is clearly inconsistent and incorrect to mix the systems by, for example, reporting an effective porosity with a total S_w, a total porosity with an effective S_w, or a standard-core porosity with an effective S_w. System compatibility must also be maintained by correct use of the SCAL measurements and log-analysis formulae, when these are used to calibrate the resistivity logs and P_c/S_w methods. The differences should be resolved as much as possible. To the extent that they are not, the differences can be considered to be a measure of the uncertainty in the S_w calculations.

Uncertainties

It is the uncertainty of the hydrocarbon saturation (1 − S_w) that is economically important, not the absolute uncertainty in S_w. When uncertainties in S_w are evaluated, their importance in terms of S_o and S_g should be accounted for. The uncertainties of the several S_w-evaluation methods vary widely.

OBM-Core S_w Data. The water volume extracted from a single core plug may have a random and known systematic uncertainty of ± 0.05 cm³, where each uncertainty refers to one SD. The PV of a typical 1-in. core plug is 4.0 cm³ if the porosity is 20% BV. The water-volume uncertainty alone equates to an S_w uncertainty of ± 1% PV (0.05/4.0). The uncertainties in porosity have a further effect on this calculation.  An OBM-core S_w of 20% PV, therefore, has a combined 1-SD range from approximately 18 to 22% PV. At lower porosities and higher S_w values, the water-volume uncertainty may be ± 0.1 cm³, leading to an S_w uncertainty of ± 3% PV, when the porosity is 15% BV. As porosity decreases, the uncertainty grows. Before the measurements are made, any water in the toluene and the Dean-Stark apparatus must be removed, or the S_w values will be overstated. The extraction time required to recover the water adsorbed on the clay minerals adds to the uncertainty.

The uncertainty of the average core S_w will be improved when plugs are selected at one or two per foot with equal spacing and without regard for the rock quality. However, as discussed previously, plug samples are not always selected at random, so care must be exercised, especially regarding the S_w values predicted at depths where core is not available. From a broader perspective, it must also be remembered that 1-in. core plugs only sample approximately 2% of the full-core volume. Because of these many factors, the authors estimate that uncertainties similar to those given concerning porosity also propagate to the zone-average OBM-core S_w values. Measurements in which larger core plugs are analyzed will reduce several of the uncertainties.

Resistivity-Log-Derived S_w Values. The log readings, typical SCAL-derived Archie exponents, and all of the other associated parameters are uncertain. For example, the resistivity-log uncertainty may be ± 50% when R t is 500 ohm•m. The most important uncertainty contributors at low S_w values are likely to be R_t and n. S_w uncertainty in this circumstance is estimated at ± 5% PV (i.e., if S_w is calculated as 10% PV, the 1-SD range is 5 to 15% PV).  At lower porosity values and higher water saturations, similar methods led to uncertainty estimates of ± 9% PV. Given that further uncertainty in the final calculated S_w may arise from shaly-sand effects and many other sources, the authors believe that the ranges given apply equally to the overall systematic uncertainty of the S_w zone-average values. These estimates are all 1 SD; therefore, in 32% of cases, zone-average uncertainties are considered likely to be greater than the ranges given.

P_c-Derived S_wValues. The uncertainty estimates are the sum of several factors. Most of these factors have their greatest impact on the S_w calculations in the first 100 to 200 ft of the hydrocarbon column above the fluid contact. Therefore, because the transition zone is considerably longer in many oil reservoirs than in a gas reservoir, their impacts will be greater in most oil reservoirs. Above 200 ft, the S_w values are usually only changing slowly; hence, the primary consideration above the transition zone is whether the laboratory measurements are taken at equilibrium conditions.

The first factor in the uncertainty analysis is the fundamental assumption as to whether the drainage or imbibition P_c/S_w data should be used. In most cases, the drainage curves should be used, but, in a few situations, the reservoir may be on the imbibition cycle. In these situations, the improper choice of using the drainage P_c curve can lead to a +5 to 20% PV S_w error in the first 100 to 200 ft above the OWC. 

The second factor concerns the laboratory P_c/S_w measurements. If the measurements are not taken to equilibrium, then the S_w values at a particular P_c value will be too high. This can be +1 to 10% PV effect for the large H_owc or H_gwc range. The other key aspects for reported centrifuge laboratory results are how the raw laboratory measurements of water volumes were determined and how these data have been converted to the reported endface saturations. The water-volume measurements have the same-size potential error as discussed for the OBM Dean-Stark S_w measurements (± 1 to 3% PV). Differences in the laboratory calculation procedures can result in further variations of ± 1 to 3% PV in reported P_c/S_w results when using the same raw laboratory data. For porous-plate tests and others, the repeated handling of poorly cemented or uncemented core plugs can cause grain loss, which, after the final calculations, translates into small errors in S_w.

The third factor is how the suite of raw laboratory data for a particular reservoir interval are curve-fitted and presented in the final laboratory report as tabulations of P_c/S_w values for each core plug. Uncertainty in the application arises from how these reported values are averaged for use in the S_w calculations over the full range of reservoir porosity and permeability values. This uncertainty includes how the data are weighted and whether some potential outlier data from one or two core plugs distorts the averaged P_c/S_w curves. These uncertainties primarily affect the first 100 to 200 ft above the H_owc or H_gwc so that their impact depends on how thick the hydrocarbon column is and its distribution as a function of H_owc or H_gwc.

The final factor is the conversion of the averaged P_c/S_w curves (or equation) from surface to reservoir conditions, all of which affect the conversion of P_c values to H_owc or H_gwc values. This includes a number of subfactors, each with its own uncertainty level: IFT at surface and reservoir conditions, fluid-pair density difference at reservoir conditions, contact angles, and depth of the actual in-situ FWL compared with the OWC or GWC. The contact angles at surface and reservoir conditions are generally taken to be the same because no data are available to proceed otherwise. For these other factors, the uncertainty is considerably greater for an oil reservoir than for a gas reservoir; because the IFT values can be low and compared with those for a gas reservoir, the density differences are significantly less particularly if there is a vertical oil-gravity variation that results in a heavy-oil interval just above the OWC. All of these factors affect the H_owc or H_gwc values; therefore, their impact on the S w calculations is predominantly in the first 100 to 200 ft above the fluid contact.

In summary, the use of P_c/S_w data can result in S_w uncertainty of ± 5 to 15% PV in the oil/water or gas/water transition zone. Above that transition zone, the uncertainty is related to whether the laboratory data were taken at equilibrium conditions and how the various P_c/S_w curves have been averaged together. In this range, the uncertainty is likely to be 3 to 10% PV.

Permeability Determination

Point-by-point permeability values are needed over the reservoir interval at the wellbores for several purposes. First, the distribution and variation of the permeabilities are needed by the engineers to develop completion strategies. Second, this same information is needed as input to the geocellular model and dynamic-flow calculations (e.g., numerical reservoir-simulation models). For both of these, the first consideration is the location of shales and other low-permeability layers that can act as barriers or baffles to vertical flow. A second consideration is the nature of the permeability variation (i.e., whether the high-permeability rock intervals occur in specific layers and the low-permeability intervals occur in other layers, or that there is so much heterogeneity that the high- and low-permeability intervals are intimately interbedded with each other).

When good-quality core data are not available, estimates of permeability can be made from empirical equations. Permeability is controlled by such factors as pore size and pore-throat geometry, as well as porosity. To take some account of these factors, the widely used Timur equation relates permeability to irreducible S_w and porosity, and therefore can be applied only in hydrocarbon-bearing zones. This form of his equation applies to a medium-gravity oil zone:

[[File:Vol5 page 0471 eq 001.png|RTENOTITLE]]....................(3H.28)

where k = absolute permeability in millidarcies, ϕ_e = effective (not total) porosity as a bulk volume fraction, and S_w = effective water saturation above the transition zone as a fraction of PV. Estimates that are based only on porosity are likely to have large prediction errors, especially in carbonate reservoirs. Equations of the following form, or a logarithmic-linear form, are useful particularly in sandstones:

[[File:Vol5 page 0471 eq 002.png|RTENOTITLE]]....................(3H.29)

where parameters C and D are very approximate and equal to about 7, and k and ϕ_e are as defined following Eq. 3H.28. They should be adjusted according to local knowledge.

In field evaluation, the starting point for calculations of permeability is the routine-core-analysis data. These data, and the associated SCAL measurements of permeability and porosity as a function of overburden stress, are input to calculations to develop permeability values at reservoir conditions and the permeability vs. porosity correlation. The permeability vs. porosity correlation is often taken as semilogarithmic but usually with a steeper slope at low-porosity values. Figs. 3H.19 and 3H.20 demonstrate the characteristics of these relationships. Fig. 3H.19 presents a typical permeability vs. porosity relationship from routine-core-analysis data (the scatter in these data increases at the lower-porosity levels). Fig. 3H.20 shows the permeability ratio (stressed permeability divided by unstressed permeability) vs. unstressed permeability. This ratio is much smaller for low-permeability values and approaches a value of 1.0 for the high-permeability values.

• 

  Fig. 3H.20 – Crossplots of core permeability at stressed vs. surface conditions and core permeability ratio vs. core permeability at surface conditions; data from an Asian gas field. “Stressed” refers to the rock being subjected to simulated overburden pressure of approximately 4,500 psia. The permeability correction is larger at low permeabilities.

 In developing the permeability vs. porosity relationships, the technical team needs to identify the extent to which the reservoir interval needs to be subdivided into zones or layers. The subdividing of the core data over the reservoir interval should be into logical subdivisions that are strongly influenced by the geologists’ understanding of the depositional environment. This will naturally account for major differences in grain size, sorting, and key mineralogical factors. Alternatively, a sufficiently thick reservoir interval can be subdivided into layers of 50 to 100 ft each. A superior petrophysical methodology will be developed if a thick reservoir is appropriately subdivided, compared with treating the full reservoir interval with a single permeability vs. porosity correlation. A single permeability vs. porosity correlation for a reservoir interval with different depositional environments can lead to underprediction of permeability by an order of magnitude in an interval of better-sorted rocks compared with poorly sorted rocks (see Fig. 3H.3). Identifying the location and correct values of highest-permeability rocks is very important for reservoir flow modeling.

The result of modeling the relationship with the least-squares regression method is that the range of predicted permeability values is smaller than that of the original routine-core permeability data. This loss of range is made worse when the logarithm of permeability is used as the y-variable because the logarithmic model is a predictor of the geometric-average permeability.  While the permeability vs. porosity relationship is developed from the routine and SCAL core-analysis data, the application to the point-by-point well-log database requires the use of porosity values calculated from the logs. It is preferable to model the prediction equation directly with core permeability and the basic log values (see Fig. 3H.21 and the calibration line-fitting in Sec. 3H.5.3). The y-on-x (dashed) line-fit in Fig. 3H.21 follows a curved trend on the logarithmic-linear plot and uses an arctangent function as the transformation. The solid line gives arithmetic average permeabilities at various bulk-density values. The arithmetic averages, which may be more appropriate in some reservoirs, are 2 to 3 times larger than the geometric averages. Alternative predictions of permeability may also be estimated using two-log or multiple regression analysis methods.

• 

  Fig. 3H.21 – Nonlinear regression relationships for core permeability and bulk density log (South Morecambe gas field, offshore U.K.). After Woodhouse

 After the permeability values have been calculated point-by-point over the reservoir interval from the various wells’ logs, these permeability values need to be compared with those derived at each well from the pressure-transient analysis (PTA) of the pressure-buildup (PBU) or falloff data. The PBU permeability values are average values for the interval open to flow into the wellbore. The type of average (arithmetic, geometric, harmonic, or somewhere in between) to use with the point-by-point permeability values depends on the nature of the depositional environment and whether the perforated intervals are a small fraction of the full reservoir interval. If there are significant differences between the two sets of average permeability values, then the technical team needs to determine the likely cause of the differences—small-scale fractures, relative permeability effects, or some other geological factors. The point-by-point permeability values may need to be adjusted on the basis of the technical teams’ conclusions.

Petrophysical Case Studies

>This section presents brief summaries of detailed petrophysical evaluations of several fields that have been described in the SPE and Soc. of Professional Well Log Analysts (SPWLA) technical literature. These case studies cover some of the complications that occur when making net-pay, porosity, and S_w calculations.

Prudhoe Bay Field

Prudhoe Bay is the largest oil and gas field in North America with more than 20 billion bbl of OOIP and an overlying 30 Tscf gas cap. In the early 1980s, the unit operating agreement required that a final equity determination be undertaken. In the course of this determination, an extensive field coring program was conducted, which resulted in more than 25 OBM cores being cut in all areas of the field and some conventional WBM and bland-mud cores in other wells. Also, several major laboratory programs were run to address various technical issues regarding the correct approach to calculate porosity and water saturation. The background geologic understanding of the major reservoir, the Ivishak or Sadlerochit, and various technical studies have been presented in a number of technical papers. 

Geologically, the Sadlerochit reservoir is a combination structural/stratigraphic trap consisting of a 500-ft reservoir interval covering an area of 15×35 square miles at a depth of 8,000 to 9,000 ft. This reservoir is mainly very high quality deltaic Permo-Triassic sandstones deposited in a braided stream environment, ranging from fine-grained to conglomeratic, with some limited intervals of shales found in various areas of the reservoir. The reservoir has been divided vertically into eight zones on the basis of differences in rock types (see Fig. 3H.1). The grains are primarily quartz, quartzite, and chert. Over geologic time, there have been significant leaching and cementation. The chert grains have been leached to varying degrees, resulting in a significant intragranular component (10 to 60%) of the pore system. There are considerable amounts of siderite and pyrite cementation, together with quartz overgrowth and kaolinite cementation. 

The structural and hydrocarbon-filling histories of Prudhoe Bay are very complicated; this is clearly evident from a visual examination of the cores, the routine-core-analysis fluid-saturation data, and an interpretation of the seismic data.  Oil initially filled this trap 40 million years ago. Since that time, because of differential burial, there has been a change in the configuration of the trap. Where there was previously a 2,000-ft closure, currently there is less than 1,000-ft maximum closure. The reservoir "tilting" resulted in a relict-oil zone systematically varying in thickness, which underlies the current oil column particularly to the southeast. At its base, the relict-oil zone had a flat OWC at the end of the original oil filling. Later, gas migrated into the trap creating a large gas cap over the main area of the field, but also smaller ones in the west-end area of the field. At discovery, a 40- to 60-ft heavy-oil-tar (HOT) layer was found above the current OWC with the oil gravity decreasing upwards from there. No relict-oil interval and essentially no HOT interval are found in the western part of the reservoir (see Figs. 3H.22 and 3H.23).

• 

  Fig. 3H.22 – Areal structure map showing gas-cap and oil-column distribution in the Sadlerochit reservoir, Prudhoe Bay field, Alaska, U.S.A.</ref>

 The net pay was based on defining the shale and siltstone intervals as nonpay.  Except for the inclusion of a small number of highly cemented sandstone intervals, this is effectively equivalent to a permeability cutoff of 0.6 md on the basis of routine-core-analysis permeability data, unadjusted to reservoir conditions. The net pay was determined from geologists’ core descriptions. A GR-log model was used to define the pay/nonpay intervals within the Sadlerochit reservoir interval using the more than 450 logged wells’ normalized GR logs. Radioactive sandstone intervals had previously been edited out of the core-log database. This GR-log model had to account for both thick and thin shale intervals, which it did by using three parameters—GR-sand, GR-thin, and GR-thick. The reservoir area was subdivided to account for areal variations when calibrating the GR-log model to the geologists’ core picks of shale and siltstone intervals.

Porosity in the Sadlerochit interval was based on use of routine-core-analysis porosity data and sonic logs. The density log was not used because of the heavy-mineral effects discussed previously. The porosity data were not adjusted for overburden stress at reservoir conditions because it was found that the highly asphaltic crude oil had not been thoroughly cleaned from the core plugs during the routine laboratory procedures. Because there were generally both full-diameter Boyles-law and sum-of-fluids porosity measurements on the pebbly-sandstone and conglomeratic intervals (and both core-plug Boyles-law and sum-of-fluids porosity measurements for the other intervals), a hierarchy of these data was used when preparing the core standard for use with the sonic logs. The sonic log was calibrated linearly to the core porosity data. The calculations were performed individually for each of the eight zones and the different fluid intervals (gas cap, oil column, and aquifer). Finally, the reservoirwide porosity solution for each of these zone/fluid combinations was arealized to account for remaining systematic differences.

The OBM cores indicated that there is a wide range of S_w values, from less than 5% PV in the updip oil column and its overlying gas cap to as high as 50 to 70% PV in the west-end and southwestern portions of the Sadlerochit reservoir. Conventional log-analysis and capillary pressure methods suggested a much narrower range of S_w values. For these reasons, major studies were undertaken to identify the reasons for these differences and to determine if the OBM-core S_w data were valid. The primary conclusions were as follows: *The OBM-core S_w data are valid.  This was confirmed by detailed observations and measurements at the wellsite at the time of coring some of the wells and at the commercial laboratory where the routine-core-analysis measurements were made. *The centrifuge P_c data were found to agree with the OBM-core S_w data after the following effects were accounted for: the laboratory P_c/S_w measurements were run sufficiently long to reach equilibrium, it was recognized that various portions of the Sadlerochit reservoir were on different drainage and imbibition cycles on the basis of either the ancient or the current OWC, and the vertical variation of oil densities and the effect of the HOT interval were accounted for.  *The S_w calculations from the SCAL measurements of rock electrical properties agreed with the OBM-core S_w values after the following effects were included: native-state rock electrical properties were measured at the wellsite and restored-state rock electrical properties were measured in the same S_w range as found from the OBM cores; and the variations in the R_w in the oil column and gas cap were included in these S_w calculations.  The n parameter was found to vary significantly as a function of S_w because of the complicated intergranular/intragranular (inhomogeneous) nature of the Sadlerochit pore system.  *An independent in-situ measurement of S_w using the single-well chemical-tracer test produced results consistent with the OBM-core S_w at two updip well locations.  The S_w methodology for the Sadlerochit reservoir was a combined use of the OBM-core S_w data with R_t values from the deconvolved deep induction logs. Because of the low clay-mineral content of the Sadlerochit reservoir, an Archie S_w equation was used with n values derived for each zone at the OBM-cored wells and then trended over the reservoir. This results in foot-by-foot S_w calculations for the whole hydrocarbon column in the more than 450 logged wells. This very large database of S_w values was converted into a relationship involving porosity and H_owc and subdivided to account for systematic variations from one area to the next, before making the OOIP and OGIP calculations.

In summary, the Prudhoe Bay field shows that accurate petrophysical calculations can be complex, particularly in large reservoirs. If a typical approach had been used to make the various petrophysical calculations, the OOIP, OGIP, and the distribution of the hydrocarbons would have been significantly in error. Only through detailed core review by the geologists and by working through a number of complicated laboratory studies was closure reached. The same S_w values were then calculated using the various independent S_w methods.

West Howard-Glasscock Unit Oil Field

This west Texas San Andres oil reservoir is an example of the petrophysical evaluation of a carbonate reservoir.  It is one of many San Andres oil reservoirs found in the Permian Basin of west Texas, U.S.A., and is presented to show that good-quality core/log petrophysical calculations can be undertaken even when a reservoir covers only a few square miles.

This study was performed in the 1970s after this unit was formed, and the waterflood of the San Andres reservoir was expanded. A total of 40 new wells was drilled with WBM and logged. Ten wells were extensively cored. The new wells were primarily for water injection and added to the existing 80 wells. This coring program was instituted because of the reservoir’s complex and heterogeneous lithology and to aid log interpretation, geological mapping, and injection-well planning.

The routine-core-analysis measurements were primarily performed on whole core samples. Fig. 3H.24 displays, through a permeability vs. porosity plot, the very heterogeneous nature of this reservoir. A number of plug samples (1.5 in. in diameter and 2 in. long) were cut for SCAL studies. Figs. 3H.25 and 3H.26 show a comparison of the SCAL samples’ permeability and porosity data with those from the adjacent whole-core data and show how heterogeneous this reservoir is. Previously published San Andres P_c/S_w correlations were used to calculate the irreducible S_w in the log calculations. 

• 

  Fig. 3H.24 – Core-permeability/core-porosity data for Zone D, West Howard-Glasscock Unit, west Texas, U.S.A.</ref></ref>

 The reported SCAL measurements focused on lithology, grain-density, and electrical-property measurements. The grain densities of the vast majority of the tested samples (82%) were in the 2.84- to 2.86-g/cm³ range. The average m from tests on 32 core plugs was 2.1 (assuming a = 1.0). The average for n was 2.2; however, the data were quite scattered (see Fig. 3H.27).

• 

  Fig. 3H.27 – Laboratory-measured formation resistivity index (I_R) vs. brine saturation for core plugs from West Howard-Glasscock unit, west Texas, U.S.A.

 Log computation software was used to calculate lithology and porosity. The volume of shale present was computed from the sonic and density logs because the GR log was not a good shale indicator because of the presence of many radioactive zones containing little or no shale. Variables calculated were primary porosity, secondary-porosity index, dolomite, sand, anhydrite, and shale. Fig. 3H.28 presents a comparison of the computed and the core porosity values. The permeability, S_w, and S_wi were calculated from the logs on the basis of relationships derived from core data.

• 

  Fig. 3H.28 – Agreement of core-analysis and Bitri-computed porosity for West Howard-Glasscock unit, west Texas, U.S.A.

Oil Fields-Offshore Peninsular Malaysia

Several technical papers have been written about the combined use of core and log data to increase the reliability of the petrophysical calculations for the various oil reservoirs found in this basin.  These papers particularly address how the calculations of fluid saturations were improved, and the uncertainty reduced, by a variety of coring and core-analysis studies. The bottom line to the technical work regarding the Dulang oil field was that the best estimate of OOIP was increased by approximately 30%, which led to management being more confident regarding further development.

The oil fields of the Malay basin consist of stacked sequences of laminated sands and shales. Dispersed clay minerals are present in the sands in the form of kaolinite, illite, and mixed-layer clays. The connate waters are generally of low salinity and impacted by the presence of meteoric (surface) waters. The resistivity-log readings in the sand intervals are suppressed because of the thin-bed effects.

For the reasons described in the previous paragraph, OBM- and bland-mud-coring programs were undertaken in the stacked oil reservoirs of several of these fields. These coring programs’ design and execution paid great attention to all of the details before, during, and after the coring operations. The cores were generally cut at high rates of penetration (60 to 90 ft/hr) and with low overbalance pressure (maximum of 200 psi). Because of the friable and unconsolidated nature of some of the sands, full-diameter cores were frozen in dry ice before plug cutting with liquid nitrogen. Special testing, including the use of mud-system tracers, was conducted to determine that OBM filtrate had not impacted the connate-water saturations. Because some unpublished studies suggested that some of the connate water might be displaced as far as 100 to 150 ft above the OWC, core-layering tests were run to determine the depth and concentration of mud tracers within the cross section of the core. The layering tests found that OBM-filtrate invasion was insignificant.

The routine-core-analysis measurements of OBM cores included Dean-Stark S_w determinations and water-salinity studies. Sponge cores were analyzed for residual-oil saturations. SCAL core samples were taken for rock electrical-property measurements. Fig. 3H.29 presents an example plot showing a comparison of the core results and the results calculated from the logs. 

• 

  Fig. 3H.29 – Plots of core- and log-calculated hydrocarbon pore volume, porosities, and S_w vs. depth for a Malaysian shaly-sandstone reservoir-Core #3.

 The results from the analysis of the Dulang field’s various studies were as follows:  *The Dulang reservoirs’ connate S_w was found, from OBM cores, to range from 20.1 to 43.1% PV with an average of 33.6% PV, compared with the previous range of 19 to 61% PV with an average of 39% PV. Also, the S_w varies from reservoir to reservoir, as controlled by the reservoir quality and depositional environments. *The measurements of water salinity and R_w indicated that R_w varied with reservoir depth and was not constant as previously assumed (see Table 3H.5). *The rock electrical-property measurements indicated that m and n have values of 1.77 and 1.64, respectively (assuming a = 1.0). n was significantly lower than the previously used value of 1.89 (see Table 3H.5). *The authors used these core data to calibrate the DW model. *The residual-oil saturation data indicated that S_orw ranged from 25.8 to 29% PV with an average of 27.5% PV. Recovery factors ranged from 37.8 to 49.4% for the various reservoirs. The effect of these changes in the petrophysical calculations for the various reservoirs was that S_w had been previously overestimated. The impact of the revised calculations and new core data for the Dulang field’s OOIP was that it increased from 550 to 685 million STB.

• 

  Table 3H.5

Block A-18, Gas/Condensate Field, Malaysia-Thailand Joint Development Area

This example used core P_c and log data to increase the reliability of the petrophysical calculations for gas/condensate reservoirs found offshore near the Thailand-Malaysia border.  It addresses how the S_w calculations were improved by the integrated use of resistivity logs in a shaly-sand model and P_c data measured on core plugs. The calibration method led to the resistivity model reproducing the S_w given by the core-measured P_c data. The end result of the work was a well-supported increase in OGIP estimates for the A-18 gas field, leading to a greater confidence in the development viability. The best estimate of gas reserves was increased by more than 20%.

In the first part of the calibration method, the shaly-sand sequence is classified into several facies according to the clay distribution. Initially, 10 facies are identified in the cores, but they are reduced to four petrophysical facies consisting of clean sands, sands with discontinuous clay, bioturbated and heterolithics, and poor reservoir mainly consisting of mudstones and coals. The electrical continuity of the shale components increases with each facies. Where core is not available, the facies type is estimated, preferably from resistivity imaging logs. P_c data were acquired on 1.5-in.-diameter plugs using the centrifuge method and spanned the full range of reservoir parameters. A multiple-linear-regression prediction of S_w from P_c, porosity, and permeability was used to estimate S_w at every routine-core-plug depth.

In the second part of the calibration, the P_c-predicted S_w values were correlated with the Waxman-Smits shaly-sand model and the deep-resistivity log values at each foot of the core. The Waxman-Smits model and the resistivity log were forced to match the P_c-based S_w by back-calculation of the n* value at each foot in a way similar to that described for OBM cores in the main S_w section of this chapter (Sec. 3H.7). A mean back-calculated n* is then determined for each of the four facies. Table 3H.6 gives the n* mean values, along with the usual SCAL electrical-properties n* values acquired by measuring core-plug resistivities in the laboratory. The P_c-calibrated n* values are significantly lower than the SCAL electric-property n* values, leading to significant increases in effective hydrocarbon column, especially in the bioturbated and heterolithic sands.

• 

  Table 3H.6

 

Total porosity at every logged foot was calculated from the density-log force fitting the line-fit through the core grain density. Fig. 3H.30 shows mainly raw data with the S_w results at the right side.

• 

  Fig. 3H.30 – Water saturation S_wws calibrated to capillary pressure P_c core data and S_wsca calibrated to standard core-electrical-properties n*.

Whitney Canyon-Carter Creek Gas Field

This Wyoming, U.S.A., gas field produces from a 1,000-ft-thick complex carbonate with a wide range of minerals including dolomite, anhydrite, limestone, and quartz.  The study hoped to examine significant differences in well performance and to provide recommendations to increase recovery.

The main reservoir is in dolomitic rocks where there is a full continuum from slightly to fully dolomitized limestones. There is little or no relationship between permeability and porosity. Four rock types were identified by high-pressure mercury injection (HPMI) and, because this reservoir has very high P_c (deriving from the 1,000-ft-thick gas column), even the poorest dolomitic rock has some gas saturation in the small pores. Table 3H.7 gives a summary of the petrophysical properties of the four rock types.

• 

  Table 3H.7

 Porosity and mineralogy were evaluated with a probabilistic simultaneous-equation method.  Gas corrections were required and had a significant effect on the results because, while the density-log reading is shallow, the neutron log is much deeper. Boron, a neutron absorber, is present in the dolomites and required a correction. S_w was calibrated to Dean-Stark initial S_w measurements and to the HPMI P_c measurements (Fig. 3H.31 because the laboratory Archie n measurements (1.1 to 1.5) were unreliable in the "tight" rocks. Force-fitted Archie exponents of m = 2.18 and n = 2.0 were used in the evaluations, and provided similar results to the OBM core S_w and HPMI P_c data.

• 

  Fig. 3H.31 – High pressure mercury injection (HPMI) plots for Whitney Canyon-Carter Creek field, Wyoming, U.S.A. for Rock Types 1, 2, and 3 (See Table 3H.6): (a) mercury intrusion as pore-throat radius changes and (b) wetting-phase saturation as height above free-water level (H_GWC) changes (after Gunter et al.

 Gas saturations up to 75% PV were calculated for the poorest rock type and represented a significant prize for the production team. Positive steps were taken to ensure that this gas was accessed by production wells. The study determined that, as well as the usual acid stimulation of the higher-quality rock, the poorer rocks should also be separately stimulated with acid. Acid diversion to lower-permeability zones was used in new infill wells.

Other Considerations in Petrophysical Calculations

While this chapter focuses on the calculations of various petrophysical properties using core and log data, there are other types of data obtained from oil and gas reservoirs that need to be considered when making petrophysical calculations. This section briefly discusses some of those data and how they can be used to improve the petrophysical evaluation. Sec. 3H.6 discussed some of these data sources, as used for determining fluid-contact depths.

Mud-Log Gas and Oil Shows

The information gathered by the mud logger regarding lithology, oil and gas shows, and gas composition should be integrated with the petrophysical calculations. In a gas reservoir, the mud log gas shows can be used to reasonably locate the GWC. In an oil reservoir, this same information can be used to identify the depth of the OWC. These data are useful to determine whether there is a relict-gas or -oil interval below the current GWC or OWC.

Pressure Measurements and Fluid Samples From Formation-Tester Logging Runs

At the time wells are drilled, a suite of pressure measurements are often made over the reservoir interval, and sometimes, a few fluid samples are taken. These pressure data can aid the petrophysical interpretation by indicating whether the vertical pressures are in equilibrium throughout the reservoir interval. If not, then the reservoir may actually be several different compartments with different OWCs, GWCs, or GOCs. The fluid samples are useful in defining which fluid is flowing in each of the tested intervals and the extent of compositional differences. In addition to pressure data, modern wireline formation-tester tools can determine hydrocarbon type, GOR, and API gravity from spectroscopic measurements before taking fluid samples. 

Drillstem-Test Data

The pressure and flow data from DST tests must also be considered when performing a reservoir petrophysical evaluation. These tests provide information about the flowing fluids in different portions of the reservoir. Also, the pressure-transient-analysis calculations from the flow-rate and pressure data are used to calculate an average value for reservoir permeability. This needs to be compared with that calculated from the routine-core-analysis permeability data and the well logs. The permeability values determined from these two sources of data often disagree, with the value from the DST testing almost always taken to be more correct. The DST results can be used to develop adjustments to the methodology for calculating permeability from core and log data, but also to determine the underlying technical reason for the need for the adjustments. If a DST is run long enough, it may yield information on the drainage limits of a reservoir.

Three-Dimensional Seismic Data

The interpretation of the 3D-seismic data provides complementary data to that gathered at the wellbores and, with the rapidly improving data quality and interpretation techniques, can add significantly to reservoir-characterization calculations. The depositional, diagenetic, structural, and hydrocarbon-filling histories of a reservoir can be better understood by including the broad picture available from the 3D-seismic data. Locations of major faults that may compartmentalize the reservoir can be identified and the extent and location of channel-sand deposits is possible. Seismic attributes may be correlated with rock properties and fluid contents, allowing prediction of properties at proposed well locations.

Summary and Conclusions

The purpose of this chapter is to acquaint the reader with the various aspects of the quantitative petrophysical determination of lithology, net pay, porosity, fluid contacts, water saturation, and permeability. To make these calculations as accurately as possible, core and log data need to be integrated. The routine-core-analysis data adjusted to reservoir conditions should be used to calibrate the logs for more-accurate calculations at the various wells. The conclusions of this chapter are as follows: *Lithology is determined by geologists working with cores and rock cuttings. This information can be combined with log characteristics to identify depositional environments and characterize how these change vertically and areally throughout the reservoir. *The clay minerals present in the shales and the sandstone intervals, both as detrital and authigenic components, must be identified and quantified so that their effects on the logs and routine-core-analysis data can be adequately understood. Radioactive components present in the reservoir rocks must be identified and quantified so that the clay-mineral volumes derived from the GR log are not overstated. *Net pay calculations determine how much of the reservoir interval contributes to the technical calculations of in-place hydrocarbon volumes and fluid flow. With modern reservoir engineering tools, it is possible to set N/G to 1.0 and work the various engineering calculations from that basis. If some portion of the reservoir interval is to be excluded as nonpay, the choice of cutoff should be based on flow considerations with a systematic and consistent approach. Whatever nonpay cutoff is used, that cutoff will be somewhat arbitrary. *Porosity can be computed from a variety of well logs (density, sonic, or neutron) in combination with routine-core data adjusted to reservoir conditions. In sandstones in which the mineralogy and the hole conditions permit, foot-by-foot porosity calculations from the density log, calibrated to core, are likely to be the most accurate. Correct fluid values are an integral part of the log evaluation. Porosity needs to be calculated accurately because, as well as its primary use, these values are also required for S_w and permeability estimates used directly in the volumetrics and flow calculations. Minerals that affect the porosity calculations, such as clay and heavy minerals, need to be identified as part of the lithology determination. *Water saturation can be computed by a number of independent methods using routine-core-analysis OBM-core Dean-Stark S_w data, SCAL capillary pressure data, resistivity logs used in combination with SCAL rock electrical-property measurements, or some combination of these three datasets. Adjusted OBM-core Dean-Stark S_w data are likely to be the most accurate method. Integrated use of these various technical approaches will result in the most accurate S_w solution overall. The relevant uncertainty here is not in S_w itself; it is the uncertainty in the complement, the hydrocarbon saturation (1 − S_w), that is important. *In the water-saturation calculation using resistivity logs, the connate-brine salinity and its resistivity, R_w, can vary within the hydrocarbon column, but the extent of this variation is often not measured. Also, the rock electrical properties may be a function of S_w. In most conventional S_w calculations using well logs, these are both assumed to be constant, and those assumptions can lead to significant errors in the calculated S_w values. The S_w calculations from the resistivity logs and the various Archie parameters can be partially checked in aquifer intervals where S_w is known to be 100% PV. *In the S_w calculation using P_c measurements, the laboratory tests are measurements of fluid volumes associated with cleaned and restored core plugs. For application, the reservoir values of the IFT, contact angle, and the wetting state of the reservoir generally must be estimated, along with several other factors. P_c laboratory tests do not always achieve the equilibrium water saturation, or the same water distribution within the pore network as is present in the real reservoir. *Permeability is typically calculated from porosity logs through a permeability/porosity transform. Permeability values need to be adjusted to reservoir conditions. This adjustment is nonlinear, with poor-quality rocks having larger adjustments compared with those applied to high-quality rocks. Also, the calculated permeabilities at the wells should be compared with those obtained from PBU analysis of flow tests. *The statistical correlation and calibration of core and log data requires that these data are properly depth aligned, have outliers deleted, and, if required, are mathematically transformed. A variety of line-fitting techniques are available, but the "y-on-x" approach generally results in the most accurate predictor, except in highly variable, heterogeneous rocks. *In any reservoir with a thick hydrocarbon column and large areal extent, more accurate-petrophysical calculations are made if the reservoir is vertically zoned or layered. Different parameters for different areas of the reservoir may also be required for the most accurate solution.

Nomenclature

a	=	Archie cementation constant
a*	=	Waxman-Smits cementation constant
A	=	Coefficient in various equations of this chapter
A′	=	Coefficient of term of Eq. 3H.26
B	=	Specific cation conductance, [(1/ohm•m) / (meq/mL)]
B′	=	Coefficient of term of Eq. 3H.26
C	=	Coefficient in various equations
C′	=	Coefficient of term in Eq. 3H.26
D	=	Coefficient in various equations
E	=	Coefficient in various equations
F	=	Archie formation factor
F*	=	Waxman-Smits-Thomas formation factor
FHCP	=	hydrocarbon pore feet, L, ft [m]
Hgwc	=	height above the gas/water contact, L, ft [m]
Hhwc	=	height above the hydrocarbon/water contact, L, ft [m]
Howc	=	height above the oil/water contact, L, ft [m]
IR	=	resistivity index
J(Sw)	=	Leverett J-function
k	=	permeability, L2, md [μm2]
m	=	Archie cementation exponent
m*	=	Waxman-Smits-Thomas cementation exponent
mo	=	dual-water cementation exponent
n	=	Archie saturation exponent
n*	=	Waxman-Smits-Thomas saturation exponent
no	=	dual-water saturation exponent
Pc	=	capillary pressure, m/Lt2, psi
Pce	=	entry capillary pressure, m/Lt2, psi
Qv	=	cation-exchange capacity of total PV, meq/mL
r	=	correlation coefficient
R0	=	rock resistivity with 100% PV water saturation, ohm•m
Rsd	=	clean-sand resistivity, ohm•m
Rsh	=	shale resistivity, ohm•m
Rt	=	true resistivity of uninvaded, deep formation, ohm•m
Rw	=	connate-brine resistivity, ohm•m
Rwb	=	clay-bound water resistivity, ohm•m
Rwf	=	free-formation-water resistivity, ohm•m
Rxo	=	shallow-reading invaded-zone microresistivity, ohm•m
Sg	=	gas saturation, %PV
So	=	oil saturation, %PV
Sorw	=	residual-oil saturation to water displacement, %PV
Sw	=	water saturation, %PV
Swb	=	saturation of clay-bound water in the total porosity, %PV
Swc	=	connate water saturation, %PV
Swc	=	core water saturation, %PV
Swe	=	water saturation of the effective porosity, %PV
Swsd	=	sand water saturation, %PV
Swt	=	water saturation of the total porosity, %PV
Vcl	=	clay content, %BV
VHCP	=	hydrocarbon pore volume, L3, ft3 [m3]
Vsh	=	shale content, %BV
θ	=	contact angle, degrees
ρb	=	formation bulk density, m/L3, g/cm3
ρfl	=	fluid density, m/L3, g/cm3
ρh	=	hydrocarbon density, m/L3, g/cm3
ρma	=	matrix or grain density, m/L3, g/cm3
ρw	=	water density, m/L3, g/cm3
σ	=	interfacial tension, m/t2, dynes/cm
ϕ	=	porosity, %BV
ϕc	=	core porosity, %BV
ϕcl	=	clay porosity, %BV
ϕe	=	effective porosity, %BV
ϕsd	=	sand porosity, %BV
ϕsh	=	shale porosity, %BV
ϕt	=	total porosity, %BV

References

SI Metric Conversion Factors

acre	×	4.046 856	E + 03	=	m2
bbl	×	1.589 873	E − 01	=	m3
Btu	×	1.055 056	E + 00	=	kJ
cp	×	1.0*	E − 03	=	Pa•s
dyne	×	1.0*	E − 02	=	mN
ft	×	3.048*	E − 01	=	m
°F		(°F − 32)/1.8		=	°C
in.	×	2.54*	E + 00	=	cm
mile	×	1.609 344*	E + 00	=	km
psi	×	6.894 757	E + 00	=	kPa

*

Conversion factor is exact.