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PEH:Tight Gas Reservoirs
Petroleum Engineering Handbook
Larry W. Lake, Editor-in-Chief
Volume VI – Emerging and Peripheral Technologies
H.R. Warner Jr., Editor
Copyright 2007, Society of Petroleum Engineers
Chapter 7 – Tight Gas Reservoirs
Tight gas is the term commonly used to refer to low permeability reservoirs that produce mainly dry natural gas. Many of the low permeability reservoirs that have been developed in the past are sandstone, but significant quantities of gas are also produced from low permeability carbonates, shales, and coal seams. Production of gas from coal seams is covered in a separate chapter in this handbook. In this chapter, production of gas from tight sandstones is the predominant theme. However, much of the same technology applies to tight carbonate and to gas shale reservoirs.
Tight gas reservoirs have one thing in common—a vertical well drilled and completed in the tight gas reservoir must be successfully stimulated to produce at commercial gas flow rates and produce commercial gas volumes. Normally, a large hydraulic fracture treatment is required to produce gas economically. In some naturally fractured tight gas reservoirs, horizontal wells and/or multilateral wells can be used to provide the stimulation required for commerciality.
To optimize the development of a tight gas reservoir, the geoscientists and engineers must optimize the number of wells drilled, as well as the drilling and completion procedures for each well. Often, more data and more engineering manpower are required to understand and develop tight gas reservoirs than are required for higher permeability, conventional reservoirs. On an individual well basis, a well in a tight gas reservoir will produce less gas over a longer period of time than one expects from a well completed in a higher permeability, conventional reservoir. As such, many more wells (or smaller well spacing) must be drilled in a tight gas reservoir to recover a large percentage of the original gas in place (OGIP), when compared to a conventional reservoir.
In this chapter, we discuss all aspects of data collection and the analyses required to evaluate and develop tight gas reservoirs. Many more details can be found in the referenced papers and books.
Definition of Tight Gas
In the 1970s, the United States government decided that the definition of a tight gas reservoir is one in which the expected value of permeability to gas flow would be less than 0.1 md. This definition was a political definition that has been used to determine which wells would receive federal and/or state tax credits for producing gas from tight reservoirs. Actually, the definition of a tight gas reservoir is a function of many factors, each relating to Darcy's law.
The main problem with tight gas reservoirs is that they do not produce at economic flow rates unless they are stimulated—normally by a large hydraulic fracture treatment. Eq. 7.1 illustrates the main factors controlling flow rate. Eq. 7.1 clearly shows that the flow rate, q, is a function of permeability k; net pay thickness h; average reservoir pressure p¯; flowing pressure pwf; fluid properties β¯μ¯ drainage area re; wellbore radius rw; and skin factor s. Thus, to choose a single value of permeability to define "tight gas" is not wise. In deep, high pressure, thick reservoirs, excellent completions can be achieved when the formation permeability to gas is in the microdarcy range (0.001 md). In shallow, low pressure, thin reservoirs, permeabilities of several millidarcies, might be required to produce the gas at economic flow rates, even after a successful fracture treatment.
The best way to define tight gas is that "the reservoir cannot be produced at economic flow rates nor recover economic volumes of natural gas unless a special technique is used to stimulate production." Specifically, large hydraulic fracture treatments, a horizontal wellbore, or multilateral wellbores must be used to stimulate flow rates and increase the recovery efficiency in the reservoir.
So what is a typical tight gas reservoir? There are no "typical" tight gas reservoirs. They can be deep or shallow; high pressure or low pressure; high temperature or low temperature; blanket or lenticular; homogeneous or naturally fractured; and single layered or multilayered.
The optimum drilling, completion and stimulation methods for each well are a function of the reservoir characteristics and the economic situation. Some tight gas reservoirs are in south Texas, while others are in the deserts of Egypt. The costs to drill, complete and stimulate the wells, plus the gas price and the gas market affect how tight gas reservoirs are developed. As with all engineering problems, the technology used is a function of the economic conditions surrounding the project.
The Resource Triangle
The concept of the resource triangle was used by Masters and Grey to find a large gas field and build a company in the 1970s. The concept is that all natural resources are distributed log-normally in nature. If you are prospecting for gold, silver, iron, zinc, oil, natural gas, or any resource, you will find that the best or highest-grade deposits are small in size and, once found, are easy to extract. The hard part is finding these pure veins of gold or high permeability gas fields. Once you find the high-grade deposit, producing the resource is rather easy and straightforward. Fig. 7.1 illustrates the principle of the resource triangle.
As you go deeper into the gas resource triangle, the reservoirs are lower grade, which usually means the reservoir permeability is decreasing. These low permeability reservoirs, however, are much larger in size than the higher quality reservoirs. The scale on the right side of Fig. 7.1 illustrates typical values of formation permeability for tight gas sands or carbonates. Other low quality resources, such as coalbed methane, gas shales, and gas hydrates would likely have different permeability scales.
The common theme is that low quality deposits of natural gas require improved technology and adequate gas prices before they can be developed and produced economically. However, the size of the deposits can be very large when compared to conventional or high quality reservoirs. The concept of the resource triangle applies to every hydrocarbon-producing basin in the world. One should be able to estimate the volumes of oil and gas trapped in low quality reservoirs in a specific basin by knowing the volumes of oil and gas that exist in the higher quality reservoirs.
Tight Gas in the United States
Since the 1950s, the oil and gas industry has been completing and fracture treating low permeability wells in the United States. However, it was the natural-gas price increase in the 1970s that spurred significant activity in low permeability gas reservoirs. Since the 1970s, sustained increases in natural gas prices, along with advances in evaluation, completion and stimulation technology, have led to substantial development of low quality gas reservoirs. Fig. 7.2 is a map showing the location of the major tight gas basins in the United States.
Some people believe that producing natural gas from unconventional reservoirs is not important now but could likely be important in the future. Actually, significant production from unconventional gas is occurring in the United States. Production from tight gas is important to both the natural gas consumer and the producer. During the later part of the 1900s, there were approximately 85,000 producing tight gas wells; 29,000 producing gas shale wells; and 10,000 producing coalbed methane wells. The following statistics indicate the importance of these unconventional wells to the gas produced and consumed in the United States for the year 1999.
- Gas consumption in the United States = 21.8 Tcf.
- Gas production (net) in the United States = 18.8 Tcf.
- Gas production from tight reservoirs = 3.4 Tcf.
- Gas production from shales = 0.4 Tcf.
- Gas production from coal seams = 1.2 Tcf.
As these statistics indicate, 15.6% of the consumption and 18.1% of the gas production in the United States came from tight gas reservoirs. If one considers all three unconventional reservoir types, then 23% of consumption and 25% of production came from unconventional reservoirs. The logical conclusion is that tight gas reservoirs were very important to the United States in 1999 and will be even more important in coming decades.
Tight Gas Outside the United States
The purposes for discussing tight gas in the United States in such detail are to provide statistics to validate the resource triangle concept and to provide information on how important tight gas production currently is to the United States. The next logical question is to ask, "Can we extrapolate what we know about tight gas in the United States to the other oil and gas basins around the world?" The answer is yes. The resource triangle concept is valid for all natural resources in all basins in the world, so it is logical to believe that enormous volumes of gas in unconventional reservoirs will be found, developed, and produced in every basin that now produces significant volumes of gas from conventional reservoirs. Unfortunately, no organization has published a comprehensive review and estimate of the volume of gas that might be found in tight reservoirs around the world. In fact, the volume of gas in conventional reservoirs around the world is still being revised upward as exploration for natural gas increases.
If we use the concept of the resource triangle, the volume of gas-in-place in tight reservoirs could be orders of magnitude higher than the volume of gas known to exist in conventional reservoirs, in every basin. The information in Fig. 7.4 shows that the current estimate of world gas reserves is about 5,250 Tcf. By comparing the ratio of current conventional gas reserves in the United States (133 Tcf) to the potential for gas production from tight reservoirs in the United States (569 Tcf), one could envision that eventually 20,000+ Tcf of gas will be produced from tight reservoirs around the world, given proper economic conditions and technology improvements.
Without question, interest in tight gas reservoirs around the world increased substantially during the 1990s. In many countries, tight gas is defined by flow rate and not by permeability. Development activities and production of gas from tight reservoirs in Canada, Australia, Mexico, Venezuela, Argentina, Indonesia, China, Russia, Egypt, and Saudi Arabia have occurred during the past decade. Large hydraulic fracture treatments are being used more commonly around the world to stimulate gas flow from low permeability reservoirs. Such activity will only increase during the coming decades.
The analysis of any reservoir, including a tight gas reservoir, should always begin with a thorough understanding of the geologic characteristics of the formation. The important geologic parameters for a trend or basin are the structural and tectonic regime, the regional thermal gradients, and the regional pressure gradients. Knowing the stratigraphy in a basin is very important and can affect the drilling, evaluation, completion, and stimulation activities. Important geologic parameters that should be studied for each stratigraphic unit are the depositional system, the genetic facies, textural maturity, mineralogy, diagenetic processes, cements, reservoir dimensions, and presence of natural fractures.
According to Fisher and McGowan,  a depositional system is a group of lithogenetic facies linked by depositional environment and associated processes. Each lithogenetic facies has certain attributes, including porosity, permeability, and special relations to other facies, that affect the migration and distribution of hydrocarbons. The nine principal clastic depositional systems reviewed by Fisher and Brown can be classified into three major groups, as illustrate in Table 7.1. According to the information from GTI,  most tight gas sandstones that are being developed and produced in the United States are located in barrier-strandplains, deltaic systems, or fluvial systems. A few plays are found in shelf and fan delta systems. Knowing the depositional system is important because it will affect the reservoir morphology and both the lateral and vertical continuity one expects in a reservoir. Details concerning clastic depositional systems can be found in books by Galloway and Hobday and Berg.  Also see the chapter on Reservoir Geology in the Reservoir Engineering and Petrophysics volume of this Handbook.
When most sands are deposited, the pores and pore throats are well connected, resulting in high permeability. As explained by Berg,  sands are composed of mineral particles called grains, which usually consist of quartz, feldspars, and rock fragments. The finer particles between the grains are called matrix. The original porosity and permeability of a sandstone is determined by characteristics such as mineral composition, pore type, grain size, and texture. After deposition and burial, the grains and matrix are commonly altered by the physical effects of compaction and by chemical changes. These changes are broadly referred to as diagenesis. Table 7.2 describes common diagenetic changes as explained by Berg.
Table 7.2—Common Diagenetic Changes in Sandstones
In addition to the grains and the matrix, cement is normally introduced into the rock during diagenesis. Cement is precipitated between the grains and holds the rock together. Virtually every low permeability gas reservoir has been severely altered by diagenesis. Clay and quartz overgrowths are commonly found to be filling some of the original porosity and reducing the size of the pore throats. Normally, quartz overgrowths cause the most severe permeability reduction in tight sands. Pore-filling clays reduce the permeability more than pore-lining clays. Detailed geologic analyses are required to understand the effects of diagenesis on the formation and determine how diagenesis information can be used to optimize the completion and stimulation fluids.
One of the most difficult parameters to evaluate in tight gas reservoirs is the drainage area size and shape of a typical well. In tight reservoirs, months or years of production are normally required before the pressure transients are affected by reservoir boundaries or well-to-well interference. As such, the engineer often has to estimate the drainage area size and shape for a typical well in order to estimate reserves. Knowledge of the depositional system and the effects of diagenesis on the rock are needed to estimate the drainage area size and shape for a specific well.
In blanket, tight gas reservoirs, the average drainage area of a well largely depends on the number of wells drilled, the size of the fracture treatments pumped on the wells, and the time frame being considered. In lenticular or compartmentalized tight gas reservoirs, the average drainage area is likely a function of the average sand-lens size or compartment size, and may not be a strong function of the size of the fracture treatment.
A main factor controlling the continuity of the reservoir is the depositional system. Generally, reservoir drainage per well is small in continental deposits and larger in marine deposits. Fluvial systems tend to be more lenticular. Barrier-strandplain systems tend to be more blanket and continuous. If one looks at the tight gas plays that have been more successfully developed, such as the Vicksburg in south Texas, the Cotton Valley Taylor in east Texas, the Mesa Verde in the San Juan Basin, and the Frontier in the Green River Basin, just to name a few, all of these sandstones are marine deposits. Marine deposits tend to be more blanket and continuous. Most of the more successful tight gas plays are those in which the formation is a thick, continuous, marine deposit.
There are other formations, such as the Travis Peak in east Texas, the Abo in the Permian Basin, and the Mesa Verde in parts of the Rocky Mountains that are fluvial systems and tend to be very lenticular. The Wilcox Lobo in south Texas is highly compartmentalized because of faulting. In lenticular or compartmentalized reservoirs, the drainage area is controlled by the geology and must be estimated by the geologist or engineer.
The best way to determine the depositional system is to cut and analyze cores. Cutting cores in the shales, mudstones, and nonreservoir rock above and below the main pay interval is recommended. A geologist can tell much more about the depositional system by studying the entire stratigraphic sequence. The core descriptions can be correlated with openhole logging data to determine the logging signature for various depositional environments. Once these correlations are made, logs from additional wells can be analyzed to generate maps of the depositional patterns in a specific area. These maps can be useful in developing field optimization plans.
Tectonic activity during deposition can affect reservoir continuity and morphology. In addition, regional tectonics affect the horizontal stresses in all rock layers. The horizontal stresses, in turn, affect faulting, rock strength, drilling parameters, hydraulic fracture propagation, natural fracturing and borehole stability. The main concerns for tight gas reservoirs are the effects of regional tectonics on hydraulic fracture propagation and natural fracturing in the formation.
Natural fractures affect both the overall level of permeability in a reservoir and the degree of permeability anisotropy in the reservoir. If a reservoir is naturally fractured, it is possible that a horizontal well or multilateral wellbores will be more effective in producing gas than a vertical well with a hydraulic fracture. If a fracture treatment is performed in a reservoir containing an abundance of natural fractures, problems with multiple hydraulic fractures near wellbore, tortuosity problems, and excessive fluid leakoff can occur during the fracture treatment.
The engineer and geologist should work together to understand the current and past tectonic activity in a basin. Knowledge of the tectonic history is important in designing the field optimization plan and developing drilling and completion procedures. A good way to begin is to study the fault systems in a basin. Hydraulic fractures tend to parallel normal faults and run perpendicular to reverse faults. The engineer should use data from openhole caliper logs, injection tests, and prior hydraulic fracture treatments to better understand the total in-situ stresses and the tectonic stress component in a given area. By combining engineering data with geologic data, a team of geologists and engineers can develop an understanding of the regional tectonics in an area. This understanding is important to the analysis and development of any tight gas reservoir.
Normally, a tight gas reservoir can be described as a layered system. In a clastic depositional system, the layers are composed of sandstone, siltstone, mudstone, and shale. In carbonate systems, layers of limestone, dolomite, shale, and, perhaps, halite or anhydrite occur. To optimize the development of a tight gas reservoir, a team of geoscientists, petrophysicists, and engineers must fully characterize all the layers of rock above, within, and below the pay zones in the reservoir. Data concerning gross pay thickness, net pay thickness, permeability, porosity, water saturation, pressure, in-situ stress, and Young's modulus for all layers are required to use 3D reservoir and fracture propagation models to evaluate the formation, design the fracture treatment, and forecast production rates and ultimate recovery.
The speed at which pressure transients move through porous media is a function of the formation permeability, the fluid viscosity, and fluid compressibility, as well as other variables. In a high permeability gas reservoir (say, 100 md), a pressure transient will reach the reservoir boundary in a matter of hours or days. Well-to-well interference in high permeability, blanket gas reservoirs is quite common. However, in a gas reservoir with a permeability of 0.1 md, the pressure transients move 1,000 times slower than the transients in a 100-md reservoir. As such, it might take years of production before well-to-well interference or a boundary can be recognized by studying pressure transient or production data.
In high permeability gas reservoirs, the semisteady-state form of Darcy's law works well. Methods such as the McGuire and Sikora graph and Prat's equations can be used to design and analyze hydraulic fractures in medium to high permeability gas reservoirs. Short (24 to 72 hours) pressure buildups, analyzed using a Horner graph, can provide accurate estimates of formation properties in medium to high permeability gas reservoirs.
However, in tight gas reservoirs, semisteady-state analysis methods cannot be used alone to analyze short-term (days, weeks or months) data. The best methods for analyzing transient production or pressure data are type curves, analytical models, or finite-difference models.  Transient flow analyses can be used to estimate values of formation permeability, skin, fracture half-length, fracture conductivity, and a minimum value of drainage area.
Drilling and Completion Considerations
The most important part of drilling a well in a tight gas reservoir is to drill a gauge hole. A gauge hole is required to obtain an adequate suite of openhole logs and to obtain an adequate primary cement job. In low porosity, shaly reservoirs, the analyses of gamma ray (GR), spontaneous potential (SP), porosity, and resistivity logs to determine accurate estimates of shale content, porosity, and water saturation can be difficult. If the borehole is washed out ("out of gauge"), the log readings will be affected, and it will be even more difficult to differentiate the pay from the nonpay portions of the formation. If the borehole is washed out, obtaining a primary cement seal is difficult, which could affect zonal isolation and cause the well to have to be cement squeezed prior to running tests or pumping stimulation treatments.
Formation damage and drilling speed should be a secondary concern. Some wells are drilled underbalanced to increase the bit penetration rate or to minimize mud filtrate invasion. However, if the wellbore is severely washed out because the well was drilled underbalanced, it is probable that a lot of money will be wasted because the logs are not accurate and the primary cement job might not be adequate. It is best to drill a tight gas well near balanced to minimize borehole washouts and mud filtrate invasion.
The completion strategy and stimulation strategy required for a tight gas reservoir very much depends on the number of layers of net gas pay and the overall economic assessment of the reservoir. In almost every case, a well in a tight gas reservoir is not economic to produce unless the optimum fracture treatment is both designed and pumped into the formation. The well can be perfectly drilled, cased, and perforated, but will be uneconomic until the optimum fracture treatment is pumped. As such, the entire well prognosis should be focused on how to drill and complete the well so that it can be successfully fracture treated. The hole sizes, casing sizes, tubing sizes, wellhead, flowlines, and perforation scheme should be designed to accommodate the fracture treatment.
To properly complete, fracture treat, and produce a tight gas reservoir, each layer of the pay zone and the formations above and below the pay zone must be thoroughly evaluated. The most important properties that must be known are pay zone thickness, porosity, water saturation, permeability, pressure, in-situ stress, and Young's modulus. The raw data that are used to estimate values for these important parameters come from logs, cores, well tests, drilling records, and production from offset wells.
Because tight gas reservoirs are normally also low porosity reservoirs, the importance of detailed log analyses becomes critical to understanding the reservoir. For example, if an error of 2 porosity units (p.u.) occurs when the porosity is 30%, it is normally not critical. The difference between 28 or 30% porosity will not lead to much error in net gas pay, water saturation, or gas in place. However, the same 2 p.u. error applied to a reservoir in which the porosity is 8% is a much more significant problem. The difference between 6 and 8% porosity can cause significant errors in estimates of net gas pay, water saturation, and gas in place. As such, careful preprocessing of log data and detailed petrophysical analyses of all openhole logging data are very important in the analyses of tight gas reservoirs.
The logs provide the most economical and complete source of data for evaluating layered, complex, low porosity, tight gas reservoirs. The recommended logging suite for a tight gas reservoir consist of the spontaneous potential, GR, density (FDC), neutron (CNL), sonic (SON), and dual (or array) induction logs (DIL). All openhole logging data should be preprocessed before the data are used in any detailed computations. The steps required to preprocess the logs are (1) digitize all log data; (2) depth shift the data as required; (3) perform all environmental corrections; and (4) normalize data so that all logs from different wells are reading the same in zones, such as thick marine shales in which one expects the log readings to be consistent from well to well. 
Once the data have been preprocessed and stored in a digital database, a series of statistical analyses must be conducted to quantify certain evaluation parameters. These statistical analyses consist of a Picket plot to determine estimates of water resistivity (Rw), cementation factor (m), and saturation exponent (n); shale histograms to find the shale endpoints on all logs; sand and/or limestone histograms to determine the clean zone endpoints on all the logs; linear regressions between each porosity log and any core data to establish correlation constants; and linear regressions among the porosity logs to develop correlations that can be used to correct for bad hole effects on one or more of the logs. The series of articles by Hunt et al. clearly describes the steps required to preprocess the logs; develop the correlation parameters; and analyze logs in shaly, low porosity formations.
Computing PorosityTo correctly compute porosity in tight, shaly (clay-rich) reservoirs, one of the first values to compute is the volume of clay in the rock. The clay volume is normally computed using either the SP or the GR log readings. The following equations are commonly used to compute the clay volume in a formation.
The SP provides reasonable estimates of VSH if the formation water and the mud filtrate do not have the same salinities. The GR log provides reasonable estimates of VSH as long as all the radioactive materials in the formation are part of the clays and not part of the sandstone, such as potassium feldspar.
Once the values of VSH are known as a function of depth, then the petrophysicist can compute values of clay-corrected porosity from the density, neutron, and sonic logs with Eqs. 7.6, 7.7, or 7.8.
If the petrophysicist only has a density, sonic, or neutron log, the clay-corrected estimates of porosity from Eqs. 7.6, 7.7, or 7.8 should be used to determine the porosity. However, if two or all three logs are available, crossplots should be used to determine the best estimate of porosity.
There have been numerous water saturation equations published in the petroleum engineering and petrophysical literature. Worthington published a complete review of all the commonly used water-saturation equations. For tight gas sandstones, the best method to compute the value of water saturation is normally the dual-water model. Eq. 7.9 and Fig. 7.6 illustrate the dual-water model.
It is possible to use a clay-corrected Archie equation, the Simandeaux equation, the Waxman-Smits equation, or any number of other equations as described by Worthington; however, for many situations, the dual-water model provides accurate estimates of water saturation.
In the Archie equation, all the electrical conductivity in the formation is assumed to be transmitted through the water in the pore space. The rock is assumed to be an insulator and does not conduct current. However, in clay-rich formations, the clays conduct an electric current. The Simandeaux and Waxman-Smits equations provide for a conductive rock but assume that the water associated with the pore space and the water associated with the clays have the same properties. In the dual-water model, there is free water and bound water. The free water is in the pores, and the bound water is associated with the clays. More accurate estimates of water saturation can be achieved by taking into account the current conducted by the clays using the dual-water model.
When the formation permeability in a gas reservoir is between 0.01 and 10 md, mud filtrate invasion from freshwater mud into a formation with saline interstitial water can substantially alter the resistivity profile near the wellbore during the time period before the openhole logs are normally run. In such cases, dual-induction logs or array-induction logs should be run and used to make corrections to determine the true resistivity, Rt, of the formation. The log readings change with time because of mud filtrate invasion.
Most tight gas reservoirs are tight because they are highly cemented and have low porosity. The low porosity and cementation cause many tight gas reservoirs to become hard and abrasive, which may prevent the use of logging while drilling (LWD) equipment. In addition, the flow rates and ultimate recovery from individual wells are low, and the operator must control drilling, completion, and operating costs to improve the profitability of each well. For these reasons, LWD is not often used when drilling tight gas reservoirs. Most of the logging data come from openhole logs run after the well reaches total depth. See more discussion on logging practices in the chapter on petrophysics in the Reservoir Engineering section of this Handbook.
Obtaining and analyzing cores is crucial to the proper understanding of any layered, complex reservoir system. To obtain the data needed to understand the fluid flow properties, the mechanical properties and the depositional environment of a specific reservoir requires that cores be cut, handled correctly, and tested in the laboratory using modern and sophisticated laboratory methods. Of primary importance is measuring the rock properties under restored reservoir conditions. The effect of net overburden pressure (NOB) must be reproduced in the laboratory to obtain the most accurate quantitative information from the cores.
To provide all the data needed to characterize the reservoir and depositional system, a core should be cut in the pay interval and in the layers of rock above and below the pay interval. Core from the shales and mudstones above and below the pay interval help the geologist determine the environment of deposition. Knowing more about the deposition allows the reservoir engineer to better estimate the morphology and size of the gas-bearing reservoir layers. Also, mechanical property tests can be run on the shales to determine estimates of Poisson's ratio and Young's modulus. Additional tests can be run to measure the shale density and the sonic travel time in the shale to assist in the analyses of the density- and sonic-log data.
After cutting the cores in the field, it is important to handle the core properly. The core should not be hammered out of the barrel. It should be pumped out. Once the core is laid out on the pipe racks, it should be wiped with rags to remove the mud (do not wash with water), then described as quickly as possible. Bedding features, natural fractures, and lithology should be described foot by foot. Permanent markers should be used to label the depth of the core and clearly mark the up direction on the core. As quickly as feasible, the core should be wrapped in heat shrinking plastic, then sealed in paraffin for the trip to the core analysis laboratory. Precautions should be taken to minimize alteration of the core properties while retrieving and describing the core in the field.
Once in the laboratory, the core is unwrapped and slabbed, and plugs are cut for testing. Normally, a core plug should be cut every foot in the core, trying to properly sample all the rock—not just the cleaner pay zones. Routine core analyses can be run on these core plugs. Once the routine core analyses are completed, additional core plugs are cut for special core analyses. Sometimes samples of whole core are used for testing. Both the routine and the special core analyses are required to calibrate the openhole logging data, and to prepare the data sets required to design the optimum completion. The core plugs must also be treated with care. For example, if a core plug from a shaly sand is placed in a standard oven, it is likely that the clays in the pores will be altered as they dry out. A more accurate core analysis usually is achieved if the core plugs are dried in a humidity controlled oven in which the free water is evaporated, but the bound clay water is not affected.
Routine Core AnalysesRoutine core analyses should be run on core plugs cut every foot along the core. Routine core analyses should consist of measurements of grain density, porosity and permeability to air (both unstressed and stressed), cation exchange capacity, and fluid saturations analysis. In addition, each core plug should be described in detail to understand the lithology and grain size and to note any natural fractures and other details that could be of importance to the geologist, petrophysicist, or engineer.
The porosity is used to determine values of gas in place and to develop correlations with permeability. The grain density should be used to determine how to correlate the density log values and to validate any calculation of lithology from log data. The cation exchange capacity can be used to determine how much electric current can be transmitted by the rock rather than the fluid in the pore space. The cation exchange capacity must be measured in the laboratory, using samples of rock, and is a function of the amount and type of clay in the rock. Saturation analysis measures the amount of water, oil, and gas in the core plugs in the laboratory. Saturation analysis can be misleading in rocks that are cored with water based mud because of mud filtrate invasion during the coring process and problems that occur with core retrieval and handling prior to running the laboratory tests. However, the values of water saturation from the core analysis of cores cut with an oil-based mud can be used to calibrate the log data and to estimate values of gas in place in the reservoir.
The measurements of porosity and permeability are a function of the net stress applied to the rock when the measurements are taken. For low porosity rock, it is very important to take measurements at different values of net stress to fully understand how the reservoir will behave as the gas is produced and the reservoir pressure declines. The data in Fig. 7.7 illustrate how the values of porosity changed in Travis Peak sandstone cores when the cores were tested both at low net stress and at simulated net overburden pressure (NOB). Notice that the measurements of porosity are one to two porosity units less when measured under net overburden pressure than when measured under minimal stress.
Special Core AnalysesTo fully understand the properties of tight gas formations, special core analyses must be run on selected core plugs to measure values of gas permeability vs. water saturation, resistivity index, formation factor, capillary pressure, acoustic velocity, and the rock mechanical properties. The values of resistivity index and formation factor are used to better analyze the porosity and resistivity logs. The acoustic velocity can be used to better estimate porosity and to determine how to estimate the mechanical properties of the rock from log data. The mechanical properties are measured and correlated to log measurements and lithology. The capillary pressure measurements and the gas permeability vs. water saturation relative permeability measurements are required to properly simulate fluid flow in the reservoir and to design hydraulic fracture treatments.
It is important to choose the correct core samples for conducting the special core analyses. Special core analysis tests are expensive and require weeks or months of special laboratory measurements. As such, the core samples must be chosen with care to provide the optimum data for designing the well completion and the well stimulation treatment and forecasting future gas recovery. A good way to select the core samples for special core analysis testing is to get a team of geologists, engineers, and petrophysicists in a room; lay out the core on a table; have the routine core analysis and log analysis available; determine how many rock types or lithology types that are contained in the core are important to the completion and stimulation process; and pick three to six locations for each rock type or lithology where core plugs are cut for testing.
In the SFE No. 3 well that was part of the Gas Research Institute (GRI) Tight Gas Sands Project, special core analyses were run and described in detail. Fig. 7.10 shows how the log analysis, the routine core analysis, and the special core analysis can be combined to develop a detailed description of a layered, tight gas reservoir.
Mud Filtrate Invasion
In many tight gas formations, drilling mud mixed with fresh water is used to drill. Commonly, the formation water is more saline than the water in the drilling mud. When the drill bit penetrates a permeable formation, filtrate from the drilling mud invades the formation. The factors that affect mud filtrate invasion are mud cake properties, reservoir pressure, mud weight, formation permeability, formation porosity, relative permeability, and capillary pressure. The factors that affect the resistivity profile around the well, in addition to the above factors, are the formation water salinity, the mud filtrate salinity, and the initial water saturation in the formation.
In low permeability gas reservoirs, mud filtrate invasion during drilling can affect the results from both drillstem tests and from openhole logs.  The mud filtrate invades the permeable zones, and the mud filtrate invasion profile changes with time. Therefore, the values recorded by logging tools are a function of when those logs are run. In addition, values such as mud weight, mud filtrate salinity, and mud circulation rate can change hourly or daily. As such, it is important to measure the mud properties daily and to keep accurate records during drilling operations.
The fact that mud filtrate invasion in low porosity rocks does affect openhole logs can be used to the advantage of the log analyst. Semmelbeck et al. explained how mud filtrate invasion in low permeability formations affect the deep induction (Rild) and the medium induction log (Rilm) differently as a function of time. Thus, if one has multiple logging runs, one can evaluate how the ratio of Rild /Rilm varies and can correlate that ratio with formation permeability. Fig. 7.11 shows simulated data that describes how the ratio of Rild /Rilm for one set of reservoir and drilling mud parameters varies over time as a function of reservoir permeability. Notice that the resistivity ratio changes with time as the mud filtrate continues to invade the formation. It is clear that the mud filtrate invasion affects the different resistivity logs more in high permeability formations than in low permeability formations. As such, evidence of mud filtrate invasion from log analyses can be used to estimate values of formation permeability
Mud filtrate invasion also affects the sonic velocities, the bulk densities, and the hydrogen content of the portion of the rock near the wellbore that is invaded. As such, mud filtrate invasion also affects the sonic, density, and neutron log readings. As mud filtrate invasion proceeds, the properties change with time, and the readings from the sonic, density and neutron logs will also change with time.
Formation Mechanical Properties
Many tight gas reservoirs are thick, layered systems that must be hydraulically fracture treated to produce at commercial gas flow rates. To optimize the completion, it is necessary to understand the mechanical properties of all the layers above, within, and below the gas pay intervals. Basic rock properties such as in-situ stress, Young's modulus and Poisson's ratio are needed to design a fracture treatment. The in-situ stress of each rock layer affects how much pressure is required to create and propagate a fracture within the layer. The values of Young's modulus relate to the stiffness of the rock and help determine the width of the hydraulic fracture. The values of Poisson's ratio relate to the lateral deformation of the rock when stressed. Poisson's ratio is a parameter required in several fracture design formulas. The definition of these mechanical properties, the importance of these parameters, and how to determine values for each property are discussed in the chapter on hydraulic fracturing in the Production Operations Engineering section of this Handbook.
The most important mechanical property is in-situ stress, often called the minimum compressive stress or the fracture closure pressure. When the pressure inside the fracture is greater than the in-situ stress, the fracture is open. When the pressure inside the fracture is less than the in-situ stress, the fracture is closed. We can determine values of in-situ stress using logs, cores, or injection tests. To optimize the completion, it is very important to know the values of in-situ stress in every rock layer.
In addition to knowing the values of in-situ stress, it is also extremely important to know the values of formation permeability in every rock layer. The values of permeability control everything from gas flow rate to fracture fluid leakoff. It is impossible to optimize the location of the perforations, the length of the hydraulic fracture, the conductivity of the hydraulic fracture, and the well spacing, if one does not know the values of formation permeability in every rock layer. In addition, one must know the formation permeability to forecast gas reserves and to analyze post-fracture pressure buildup tests. To determine the values of formation permeability, one can use data from logs, cores, production tests, and prefracture pressure buildup tests or injection falloff tests.
The most data that are available vs. depth comes from openhole logs. If the logs are analyzed correctly, it is often possible to generate estimates of formation permeability vs. depth using the logging data. However, the correlations used must be calibrated with core, production data, or pressure transient data to ensure the values are representative of the permeability of the particular formation. The following equations have been used in the industry over the years to correlate logs with permeability. 
Kozeny (1927) and Carman (1938):
To use these equations, the values of porosity, water saturation, and irreducible water saturation are obtained from logging data. The various authors suggested ways of determining the values of surface area, grain diameter, and relative permeability. The equations of Timur and Coates are the most widely used correlations.
In 1993, a paper was published that presented another method for correlating formation permeability with log data, as shown in Eq. 7.15.
Notice that once the correlation is developed, only log data from the GR, dual induction, and porosity logs are used to estimate permeability.
In summary, obtaining permeability from logging data is very useful because it provides the engineer with estimates of permeability vs. depth. However, to be accurate, the engineer must correlate the logging data with permeabilities measured from core or computed from production or pressure buildup data.
Production Data Analyses
Usually, production data are available for technical calculations. Production data can be measured from a well after it is perforated and before it is fracture treated. Also, production data could be available from other nearby wells producing from similar intervals. Using a computer model based on Darcy's law, one can estimate values of formation permeability. The model can be a simple single-layer, single-phase, single-well analytical model,  or it can be a complicated, multiwell, multilayered, multiphase finite difference model. For a typical tight gas reservoir, the simple analytical model is usually adequate.
Fetkovich published type curves that are commonly used to analyze production data, as illustrated in Fig. 7.14. One can either manually analyze production data using the type curves or one can use an analytical model. Fig. 7.15 illustrates how one set of production data were analyzed to determine estimates of formation permeability, skin factor, and drainage area using an analytical model. Several papers have been written to better explain how to analyze production data using models. 
In tight gas reservoirs, especially when analyzing prefracture production data, it is often difficult to flow the well to produce at rates high enough to measure. In addition, because the well has to be fracture treated to be economic, prefracture flow tests are often not even run, or if they are run, the flow period is very short. As such, the main goal is to measure flow rates and pressures and to analyze those data to determine an estimate of formation permeability and, perhaps, the skin factor. Seldom do we have enough data to estimate the drainage area, as shown in Fig. 7.15.
Pressure Buildup TestingPerhaps the most accurate method to determine the value of formation permeability is to run a prefracture pressure buildup (PBU) test. The literature is voluminous on pressure transient testing. That material is not repeated here. Instead, this chapter discusses several issues concerning PBU testing that are important when testing low permeability gas reservoirs.
A PBU test works well when the formation is well connected to the wellbore, the flow rate is large enough for accurate measurement, and there are no liquid loading effects in the wellbore. The well must be produced long enough so that the radius of investigation of the test is meaningful. Eq. 7.17 is used to estimate the radius of investigation of any transient in the reservoir for radial flow.
Thus, to determine the length of the production test to sample a reasonable portion of the reservoir, followed by the PBU test, one can select a desired radius and then determine the duration of the test using the "best guess" for the value of permeability. Obviously, the permeability is unknown prior to running the test. Table 7.3 illustrates typical test times required based on the desired radius and the best guess at formation permeability.
As seen in Table 7.3, substantial flow times, followed by equal PBU times, are required to sample a large portion of the reservoir in low permeability gas reservoirs. In most cases, the engineer trying to analyze the reservoir would like the production and PBU test to be run as long as possible. On the other hand, because the well is more than likely producing at uneconomic flow rates, and a fracture treatment is required to improve productivity, the operations personnel want to minimize the duration of these tests to minimize costs and get the well producing to sales as soon as possible.
In addition to running the test long enough, the PBU tests in tight gas reservoirs should be analyzed using modern concepts such as pseudopressure, pseudotime, effective pseudotime, producing pseudotime, adjusted pressure, and adjusted time Using these concepts helps increase accuracy when large pressure drawdowns exist in the reservoir and changing wellbore storage constants complicate the analyses of the PBU data.
One Point Testing
In many cases, there are no long-term production data, and operational or cost-related problems prevent one from running a long-term PBU to quantify the formation permeability. However, it is very important to get a rough estimate of formation permeability prior to designing the fracture treatment. Sometimes, the well can be perforated and produced for several hours or days prior to designing and pumping the fracture treatment. If the production and flowing data are accurately measured, the one point method can be used to estimate the value of formation permeability. 
In this method, the semisteady-state gas-flow equation and the radius of investigation equation are solved simultaneously for both permeability and radius of investigation. The semisteady-state gas-flow equation is
Four steps are used to solve Eqs. 7.18 through 7.20.
- Assume a value of s and D on the basis of the well completion history, then compute a value for s′ with the measured flow rate.
- Estimate a value for the permeability. An assumption of 1 md for a tight gas reservoir is usually a reasonable guess.
- Using the values of s′ and k, solve Eq. 7.19 for rd.
- The value of rd can be used in Eq. 7.18 to compute a new estimate of permeability.
One can iterate until the value of rd and k converge. A weakness in this method is that one has to estimate the value of skin factor; therefore, the procedure should be repeated by assuming different values of skin, s. One can generate a range of permeabilities for a range of assumed values of skin factor.
Tight gas reservoirs generate many difficult problems for geologists, engineers, and managers. Cumulative gas recovery (thus income) per well is limited because of low gas flow rates and low recovery efficiencies when compared to most high permeability wells. To make a marginal well into a commercial well, the engineer must increase the recovery efficiency by using optimal completion techniques and decrease the costs required to drill, complete, stimulate, and operate a tight gas well.
To minimize the costs of drilling and completion, many managers want to reduce the amount of money spent to log wells and totally eliminate money spent on extras such as well testing. However, in these low-permeability layered systems, the engineers and geologists often need more data than is required to analyze high permeability reservoirs. To balance the need for more data with the need to minimize costs, the logical solution is to spend money gathering accurate data on a few wells, then use correlations developed from that data to evaluate the wells that will be drilled and completed thereafter. Once acceptable correlations are developed for specific reservoirs in specific geographic areas, the correlations can be applied to all wells in the area. By using these "calibrated" correlations, accurate datasets can be developed for new wells at a minimal cost.
For example, if one spends $100,000 to cut cores, analyze the cores, and generate core-log correlations, and these correlations can be used to plan and conduct an infill drilling plan for 100 wells, the cost per well to generate accurate datasets is only $1,000. Normally, the most critical data items are formation permeability and in-situ stress. If accurate correlations, in which logs can be used to estimate permeability and in-situ stress, can be developed, the well completion and stimulation plans can be optimized.
Correlating Core and Log DataAll cores from tight gas reservoirs must be properly handled and tested to obtain the accurate data required for developing useful correlations between log and core data. Information concerning how to cut and test core plug samples was discussed earlier in the chapter. Also, information concerning how to develop correlations for determining permeability from logs has been previously discussed. One can use Eqs. 7.10 through 7.16 to generate accurate correlations between log data and formation permeability derived from core or well tests. These correlations can then be used to determine values of formation permeability using log data from wells that have not been cored or well tested.
To generate valid correlations in most layered, tight gas reservoirs, the core and log data normally must be subdivided by lithology, rock type or flow units prior to finalizing the correlations. If one tries to correlate the core and log data for the entire reservoir, the correlation coefficient is usually not very high. For example, consider the dataset in Fig. 7.16 that contains 1,078 data points from a large Travis Peak dataset. The correlation coefficient between core permeability at net overburden pressure is only 0.692. However, if the cores containing visible natural or coring induced fractures are removed and only cores from clean, fluvial-deltaic channel sands are correlated, the correlation coefficient between permeability and porosity increases to 0.865, as illustrated in Fig. 7.9.
Some have used flow units to segregate core and log data to develop better correlations.  Amaefule et al. used the same Travis Peak data set as illustrated in Fig. 7.16 and analyzed the data using a flow unit concept. In their paper, Amaefule et al. defined a rock quality index (RQI) and a flow zone indicator (FZI). Using these two parameter groups, they developed a scheme to correlate formation permeability with effective porosity as a function of the FZI.
Original Gas-in-Place(OGIP) Distribution
As suggested by the Resource Triangle, Fig. 7.1, the distribution of any natural resource is skewed in nature. For natural gas, the distribution is log-normal. As the value of reservoir permeability decreases, the value of OGIP increases exponentially. There is obviously a difference between OGIP and reserves. The OGIP represents all the gas in the rocks that comprise the reservoir layers. Reserves represent the amount of gas that can be produced economically. The value of reserves is a function of gas prices, costs, and the level of technology used to develop the resource.
Often the amount of OGIP is computed by using porosity, water saturation, and shale volume cutoffs. In high permeability reservoirs, using such cutoffs may be appropriate, especially if the reservoir produces water above a certain water saturation cutoff and the OGIP estimates are not very sensitive to the cutoff values chosen. However, in most tight gas reservoirs, only dry gas and small volumes of water that condense in the wellbore are produced. Very seldom are large volumes of water produced in tight gas reservoirs.
A good rule of thumb for selecting cutoffs to determine net pay to determine gas-in-place for tight gas reservoirs is to use 3% gas porosity. The first step is to compute the value of porosity after making clay correlations with Eqs. 7.6 through 7.8. The porosity can then be used to compute the water saturation, normally using the dual-water saturation model. One can compute gas porosity and include all zones with gas porosity values of 3% or greater in the net pay count. In the tight gas sands research project sponsored by the Gas Research Inst., special core analyses on numerous core samples indicated that gas could flow at 3% gas saturation in typical tight gas cores.
Permeability DistributionPermeability within a gas reservoir, field, or basin is distributed log-normally. To illustrate this concept, four data sets obtained from public records are presented for discussion. The data in Fig. 7.17 are from the Travis Peak Formation in east Texas, the Cotton Valley Formation in east Texas, the Wilcox Lobo Formation in south Texas, and the Cleveland Formation in northwest Texas. These reservoirs are in different basins but, remarkably, have very similar log-normal permeability distributions. More information concerning the permeability distribution for these four data sets is presented in Table 7.4. The median permeability for all four formations ranges from 0.028 to 0.085 md, while the arithmetic mean values of permeability range from 0.179 to 7.378 md.
Reserves DistributionEven though the permeability distribution and the OGIP distribution are log-normally distributed, the distribution of reserves may or may not be log normally-distributed because of the changing recovery efficiency vs. permeability and the number of wells drilled in each permeability range. Reserves represent the volume of gas that can be produced economically using existing technology. Reserves are a function of the permeability, net gas pay, porosity, drainage area, initial reservoir pressure, flowing bottomhole pressure, gas prices, operating costs, effective fracture half-length, effective fracture conductivity, and other economic factors such as taxation rates and overhead charges. The data in Figs. 7.21, 7.22, and 7.23 illustrate how the abandonment pressure and recovery efficiency varies as functions of permeability, net gas pay, and fracture half-length for a specific set of Vicksburg data.  At the time the graphs were generated, an economic limit of 250 Mcf/D was being used in the Vicksburg because of low gas prices. If these same cases were computed with a lower value of economic limit, the abandonment pressure would decrease, and the recovery efficiency would increase. These examples illustrate how one should use reservoir engineering to evaluate the effects of drainage area, hydraulic fracture properties, and economic parameters to determine values of recovery efficiency and, thus, the distribution of reserves.
Fig. 7.21 shows that as the permeability increases and the net gas pay increases, the abandonment pressure in the reservoir, when the economic limit is reached, decreases. The data in Fig. 7.22 illustrate the recovery efficiencies for the same cases as shown in Fig. 7.21. For thick, high permeability reservoirs, the recovery efficiency can be 80% or more of the OGIP. However, as the value of permeability decreases below a value of 0.1 md, the recovery efficiency decreases substantially. For the case in which the net gas pay was only 25 ft and the permeability was between 0.02 and 0.1 md, the recovery efficiency varied from 0 to 45% of the OGIP. The data in Figs. 7.21 and 7.22 are for semisteady-state radial flow. Fig. 7.23 illustrates the effect of a hydraulic fracture on the recovery efficiency for the 25 feet of net gas pay case. It is clear that a hydraulic fracture that extends out to 40% of the drainage area substantially increases the recovery of gas in a tight gas reservoir.
In-Situ Stress Correlations
It is important to generate correlations between logs, cores, and measured values of in-situ stress. The values of in-situ stress are very important to the engineer planning the well completion and stimulation treatment. The engineer can usually correlate values of in-situ stress measured from pump-in tests with data measured using logs and cores. A common equation used to correlate lithology (using Poisson's ratio) with the in-situ stress is given in Eq. 7.21.
|σmin||=||the minimum horizontal stress (in-situ stress),|
|σp||=||reservoir fluid pressure (pore pressure),|
The correlations included in this chapter were generated using log, core, and well-test data for the Travis Peak formation; hence, one cannot use these correlations for other formations in other basins around the world. These correlations are included in this chapter to illustrate how values of permeability and in-situ stress can be correlated with log and core data. The methods explained in this chapter can be used to generate other correlations in other formations in other basins.
Once specific correlations have been developed and verified, they can be used to evaluate layered, tight gas reservoirs to make basic decisions, such as whether the casing should be set. Once the casing is set, the correlations can be used to generate the data required to design the completion and the stimulation treatment for the reservoir layers that are determined to be commercially viable.
To evaluate a layered, tight gas reservoir and design the well completion, the operator must use both a reservoir model and a hydraulic fracture propagation model. The data required to run both models are similar and can be divided into two groups. One group consists of data that can be "controlled." The second group reflects data that must be measured or estimated but cannot be controlled.
The primary data that can be controlled by the engineer are the well completion details and the fracture treatment details, such as fluid volume and injection rate. The data that must be measured or estimated by the design engineer are formation depth, formation permeability, in-situ stresses in the pay zone, in-situ stresses in the surrounding layers, formation modulus, reservoir pressure, formation porosity, formation compressibility, and the thickness of the reservoir. There are actually three thicknesses that are important to the design engineer: the gross thickness of the reservoir; the net thickness of the gas producing interval; and the permeable thickness that accepts fluid loss during the hydraulic fracture treatment.
Data for Reservoir Simulation ModelsThe data required to run a reservoir model depends on the type of model one chooses to use. The engineer can use (listed in order of simplest to most complex) semisteady-state flow equations, materials balance methods, single-layer analytical solutions, multilayered analytical solutions, or numerical reservoir simulation models. As one might expect, the amount and complexity of the data required to use these models increases as the complexity of the model increases.
Interestingly, most of the data required to run a reservoir simulation model are also required to run a 3D hydraulic fracture propagation model. Table 7.9 lists the data required to run both the reservoir model and the fracture treatment design model. Because a typical tight gas reservoir is a layered formation, it is necessary to determine values of reservoir properties, such as permeability, net pay, porosity, and water saturation on a layer-by-layer basis. Many problems can be solved using a single-layer model; however, in other cases, better completions are achieved by developing multilayer models of the reservoir.
Hydraulic Fracture Propagation Models
The fracture propagation model requires information on the rock mechanical properties, such as in-situ stress, modulus, and Poisson's ratio. We also need data on the fracture fluid properties and the propping agent properties.
The most critical data for the design of a fracture treatment are, roughly in order of importance, the in-situ stress profile; formation permeability; fluid loss characteristics; total fluid volume pumped; propping agent type and amount; pad volume size; fracture fluid viscosity; injection rate; and formation modulus. The design engineer should focus his/her time on the most important parameters. In hydraulic fracture treatment design, by far the two most important parameters are the in-situ stress profile and the permeability profile of the zone to be stimulated, plus the layers of rock above and below the target zone that affect fracture height growth.
In new fields or reservoirs, most operating companies are normally willing to spend money to run logs, cut cores, and run well tests to determine important factors such as the in-situ stress and the permeability of the reservoir layers. By using such data, along with fracture treatment records and production records, accurate data sets for a given reservoir in a given field can normally be compiled. These data sets can be used on subsequent wells to optimize the fracture treatment designs. It is normally not practical to cut cores and run well tests on every well. Thus, the data obtained from cores and well tests from a few wells must be correlated to log parameters, so the logs on subsequent wells can be used to compile accurate data.
Vertical ProfilesTo use either a multilayered reservoir model or a pseudo-three-dimensional (P3D) hydraulic fracture propagation model, the data must be entered by reservoir layer. Fig. 7.26 illustrates the profiles of important input data required by either the reservoir or the P3D model. For the situation in Fig. 7.26, the well is completed and the fracture treatment is initiated in the sandstone reservoir. The fracture typically grows up and down until a barrier is reached to prevent vertical fracture growth. In many cases, thick marine shales, which tend to have in-situ stresses that are higher than the sandstones, are barriers to vertical fracture growth. In other cases, coal seams prevent fractures from growing vertically. Many coal seams are highly cleated, and when the fracture fluid enters the coal seam, it remains contained within the coal seam.
The data used to design a fracture treatment can be obtained from a number of sources, such as drilling records, completion records, well files, openhole logs, cores and core analyses, well tests, production data, geologic records, and other public records, such as publications. In addition, service companies provide data on their fluids, additives, and propping agents.
Economic ModelsTo design the optimum well completion and fracture-treatment design in a tight gas reservoir, detailed economic calculations must be conducted. The first decision is usually to determine if there is enough net gas pay, porosity, and permeability to justify setting casing after the well reaches total depth. Once casing is set, engineering and economic calculations are required to determine the optimum completion method and the optimum fracture-treatment design. The data required to run an economic model are given in Table 7.10. Essentially, one must determine the net cash flow for a variety of completion scenarios. The net cash flow can then be evaluated using a number of ways to determine the optimum completion design. The data required to run an economics model is specific to each situation. Gas prices, operating costs, royalty payments, taxes, and many other factors can vary widely among leases in the same field and, especially, in different geologic basins in different countries or even continents. Hence, it is extremely important to gather the appropriate economic data and performed detailed economic calculations to design the optimum well completion.
Well construction is a term used to incorporate the activities required to drill, complete, and stimulate a well as it goes from spud to a producing well. Well construction is a very broad topic, and to discuss every aspect in detail is outside the scope of this chapter. Instead, we concentrate on the aspects of well construction that are unique to tight gas reservoirs. Many of the items discussed next are also found in the Drilling Engineering volume of this Handbook.
Drilling and CompletionThe definition of a tight gas reservoir is that the reservoir does not produce at commercial gas flow rates, or recover commercial volumes of natural gas, unless a hydraulic-fracture treatment is properly designed and pumped. As such, the entire drilling and completion procedures should focus on making sure the optimum fracture treatment can be designed and pumped in the field.
When drilling a tight gas well, the most important aspect of the drilling operation is to drill a gauge hole. Many times this means the well should be drilled at a balanced mud weight or slightly overbalanced. In other cases, air drilling or underbalanced drilling works best, as long as the hole remains in gauge. If a gauge hole is drilled, we can run openhole logs and obtain valid data that are required to properly evaluate the formation and to design the completion. If the hole is washed out and rugose, the logs are difficult or impossible to accurately evaluate, and the net gas pay is difficult to identify. Also, if the borehole is in gauge, the chances of obtaining a satisfactory primary cement job on the production casing increase when compared to trying to cement casing in a washed-out borehole. Obtaining a good primary cement job is extremely important when completing a well in a multilayered reservoir that must be fracture treated.
Some drilling personnel want to drill underbalanced in tight gas reservoirs because the penetration rate is faster, formation invasion of mud filtrate is minimized, and there is little chance of a gas kick because of the low permeability nature of the formations. However, underbalanced drilling is only acceptable if a gauge hole can be maintained. Speed to reach total depth is not important if the borehole is washed out and we cannot properly evaluate the reservoir layers or obtain an adequate primary cement job. Also, formation damage is not an important consideration in tight gas reservoirs. It does not matter whether or not the near-wellbore formation has been damaged during drilling. In every case, we still use multiple pump trucks and pump rather large fracture treatments. The hydraulic fracture breaks through any near-wellbore damage.
Completion Strategy.'''' To complete a tight gas well successfully, the engineer should consider the items included in Table 7.11. The ideal completion is the one that produces the most gas for the lowest cost—considering both the initial completion cost and the subsequent operating costs. This definition implies that a prudent engineer will attempt to provide a functional completion for many years to come at the lowest possible cost to the operator.
Of concern in the design of the completion is always the number of producing zones that are separated in the reservoir by vertical flow barrier layers. To determine whether different producing intervals should actually be treated as a single reservoir, one must first determine if these various intervals are all connected by a single hydraulic fracture. If a particular zone is separated from another pay zone by a thin silt or shale layer with little in-situ stress contrast among the layers, one can use a model to determine if all the zones can be connected by a single hydraulic fracture. If a single fracture treatment is used to stimulate multiple layers, and no reservoir damage occurs by commingling the different zones, the well should be completed as if all the layers are actually a single reservoir. Normally, in dry gas reservoirs, no reservoir damage occurs by commingling zones. In fact, it is likely that more gas will be recovered by producing all the layers commingled because the abandonment pressure is lower at any given economic limit when the zones are commingled vs. producing the zones one at a time.
If two or more productive intervals are separated by a thick, clean shale (say, 50 ft or more) and this shale has enough in-situ stress contrast to be a barrier to vertical fracture growth, the design engineer might need to design the completion and stimulation treatments to consider the fact that multiple hydraulic fractures will be created. In such cases, fracture treatment diverting techniques must be used to properly stimulate all producing intervals. More information concerning completion design in multilayered reservoirs is available in the technical literature. 
Tubular Concerns. The two main concerns with tubular design are pumping the optimum fracture treatment and liquid loading as the gas flow rate declines. These two concerns must be balanced to achieve the optimum well completion. As previously stated, a tight gas well is uneconomic to drill, complete, and produce unless a successful fracture treatment is designed and pumped. In general, fracture treatments are more successful when pumped at higher injection rates. Therefore, to pump a treatment at a high injection rate, we normally like to use large tubulars.
Once the treatment is pumped and the well is put on production, the gas flow rate begins to decline. All wells, even dry gas wells, produce liquids in the form of condensate or water. Regardless of how little liquid is produced, the well eventually loads up with liquids as the flow rate declines. Liquid loading is a function of gas velocity. Therefore, to minimize liquid-loading problems, we must use small tubing.
Thus, the dilemma: we need large tubulars to pump the fracture treatment and small tubulars to minimize liquid loading. The solutions to this dilemma can be as varied as the number of fields in which we work. Many considerations and computational techniques needed to solve these problems are presented in Gidley, et al. In some cases, when the reservoir pressure is at or below normal pressure, we can fracture treat the formation down casing, then run small tubing after the treatment to produce the well. If the reservoir is geopressured, we might have to fracture treat the well down tubing at injection rates less than optimum.
The topic of how to design casing and tubing and how to design the optimum tubular configuration in a tight gas well is too large to deal with completely in this chapter. The completion engineer should, however, try to design the fracture treatment and the completion prior to spudding the well. If, during the design, the engineer determines that a certain size casing or a certain size tubing is required to implement an optimal design, the completion engineer should provide that feedback to the drilling engineer. The drilling engineer can then design the bit program and casing program to accommodate the needs of the completion engineer. Once the hole is drilled and the production casing is set and cemented, it is too late to redesign the completion if you discover you needed larger casing to implement the optimum completion.
In the same manner, the fracture treatment should be designed prior to spudding the well, so a reasonable estimate of fracture treatment pressures, from bottomhole to the surface, can be estimated as a function of the casing size, the injection rate, and the fracture fluid friction and density properties. It is very important to know the maximum injection pressure during the fracture treatment for a variety of completion scenarios. The drilling engineer can use that information to select the correct size, weight, and grade of casing. A fracture treatment is usually not successful if the injection rate or fluid viscosity is compromised when the casing cannot withstand the desired injection pressure. Again, working the problem prior to spudding and designing the casing correctly can prevent problems and allow the service company to actually pump the optimum fracture treatment.
Perforating Concerns. Perhaps the least understood part of well completions and hydraulic fracturing revolves around how to perforate a well. Again, there is no simple solution, and the best perforating scheme varies depending on the specific reservoir situation. Two factors seem to be very important. First, the number of layers and the number of fracture treatment stages affect how we perforate the well. Second, the in-situ stress anisotropy plus the presence or lack of natural fractures have a strong bearing on how we perforate the well.
A problem associated with hydraulic fracture treatment problems has been recently identified in the petroleum literature as "near-wellbore tortuosity."  Near-wellbore tortuosity occurs when multiple hydraulic fractures are created near the wellbore. These multiple hydraulic fractures are usually caused by the presence of natural fractures or the fact that too many perforations are shot in multiple directions over a long, perforated interval. When multiple fractures occur near the wellbore, each fracture is narrower than a single fracture, and problems occur when trying to pump the propping agent down the narrow fractures. In many cases, a near-wellbore screenout occurs when near-wellbore tortuosity problems occur.
There are several ways to minimize near-wellbore tortuosity problems. The best solution might be to minimize the length of the perforated interval and to orient the perforations 180° in the same direction that the fracture propagates (which is perpendicular to the minimum principle horizontal stress, for a vertical fracture). More information concerning stresses and stress orientations is found in Gidley, et al.
Again, the main concern when perforating a tight gas well is to perforate in such a way that the optimum fracture treatment(s) can be successfully pumped. The completion engineer must be concerned with choosing the correct zones and perforating those zones to accommodate any diversion techniques that will be used in multistaged fracture treatments.
In the perforating literature, there are many papers discussing how many holes are needed per foot of casing so that the productivity index is not reduced because of too few holes. In a tight gas well that is fracture treated, the number of holes per foot of casing is really not much of a consideration. More importantly, the number of holes with respect to the fracture treatment injection rate should control the perforation operation. A good rule of thumb is that the number of holes should be such that the injection rate per hole is between 0.25 and 0.5 barrels per minute per perforation. For example, if you plan to pump the fracture treatment at 20 barrels per minute, then you should consider putting between 40 and 80 holes in the pipe in the zone where you want the fracture to initiate. In general, the more compact the perforated interval the better, and perforations oriented 180° in the direction of maximum horizontal stress provide the best situation for hydraulic fracturing. The worst situation is to shoot 4 or 6 shots per foot over a long interval. When too many holes are shot over too long an interval, the engineer loses control of where the fracture initiates, and the chances of creating multiple fractures at the wellbore increases substantially.
Hydraulic Fracture Treatment Considerations
As stated many times in this chapter, the definition of a tight gas reservoir is one that must be successfully fracture treated to produce economic volumes of gas at economic flow rates. In this chapter, we will discuss a few basic considerations for fracture treatment design and application. More information can be found in the chapter on Hydraulic Fracturing in the Production Operations Engineering volume of this Handbook.
Candidate Selection. The success or failure of a hydraulic fracture treatment often depends on the quality of the candidate well selected for the treatment. Choosing an excellent candidate for stimulation often ensures success, while choosing a poor candidate normally results in economic failure. To select the best candidate for stimulation, the design engineer must consider many variables. The most critical parameters for hydraulic fracturing are formation permeability, the in-situ stress distribution, reservoir fluid viscosity, skin factor, reservoir pressure, reservoir depth, and the condition of the wellbore. The skin factor refers to whether the reservoir is already stimulated or, perhaps, damaged. If the skin factor is positive, the reservoir is damaged and will likely be an excellent candidate for stimulation.
The best candidate wells for hydraulic fracturing treatments in a tight gas reservoir have a substantial volume of OGIP and good barriers to vertical fracture growth above and below the net pay intervals. Such reservoirs have a thick pay zone, medium to high pressure, in-situ stress barriers to minimize vertical height growth, and substantial areal extent.
Tight gas reservoirs that are not good candidates for hydraulic fracturing are those with small volume of gas in place because of thin reservoirs, low reservoir pressure, or small areal extent. Also, reservoirs that do not have enough clean shale above or below the pay interval to suppress vertical fracture growth are considered to be poor candidates. Reservoirs with extremely low permeability might not produce enough hydrocarbons to pay all the drilling and completion costs, even if successfully stimulated; thus, such reservoirs would not be good candidates for stimulation.
Fracture Treatment Optimization. The goal of every design engineer is to design the optimum fracture treatment for each and every well. Holditch et al. discuss the optimization of both the propped fracture length and the drainage area (well spacing) for low permeability gas reservoirs. Fig. 7.27 illustrates the method used to optimize the size of a fracture treatment.  Fig. 7.27 clearly shows the following:
- As the propped length of a fracture increases, the cumulative production increased, and the revenue from hydrocarbon sales increase.
- As the fracture length increases, the incremental benefit ($ of revenue per foot of additional propped fracture length) decreases.
- As the treatment volume increases, the propped fracture length increases.
- As the fracture length increases, the incremental cost of each foot of fracture ($ of cost per foot of additional propped fracture length) increases.
- When the incremental cost of the treatment is compared to the incremental benefit of increasing the treatment volume, an optimum propped fracture length can be found for every situation.
Additional economic calculations can be made to determine the optimum fracture treatment design. However, in all cases, the design engineer must consider the effect of the fracture upon flow rates and recovery, the cost of the treatment, and the investment guidelines of the company that owns and operates the well.
Fracture Treatment Design Considerations. The most important data for designing a fracture treatment are the in-situ stress profile, formation permeability, fluid loss characteristics, total fluid volume pumped, propping agent type and amount, pad volume, fracture fluid viscosity, injection rate, and formation modulus. It is very important to quantify the in-situ stress profile and the permeability profile of the zone to be stimulated, plus the layers of rock above and below the target zone that influence fracture height growth.
There is a structured method that should be followed by the engineer to design, optimize, execute, evaluate, and re-optimize the fracture treatments in any reservoir.  The first step is always the construction of a complete and accurate data set. Table 7.9 lists the sources for the data required to run fracture propagation and reservoir models. Notice that the design engineer must be capable of analyzing logs, cores, production data, well-test data, and reviewing well files to obtain all the information needed to design and evaluate the well that is to be hydraulically fracture treated.
Design Procedures. To design the optimum treatment, the engineer must determine the effect of fracture length and fracture conductivity upon the productivity and the ultimate recovery from the well. As in all engineering problems, sensitivity runs must be made to evaluate uncertainties, such as estimates of formation permeability and drainage area. The production data obtained from the reservoir model should be used in an economics model to determine the optimum fracture length and conductivity. Then, a fracture treatment must be designed using a fracture propagation model to achieve the desired length and conductivity at minimum cost. The most important concept is to design a fracture using all data and appropriate models that results in the optimum economic benefit to the operator of the well, as shown in Fig. 7.27. A hydraulic fracture propagation model should be run to determine what needs to be mixed and pumped into the well to achieve the optimum values of propped fracture length and fracture conductivity. The base data set should be used to make a base case run. Then, the engineer determines which variables are the most uncertain. Many times, the values of in-situ stress, Young's modulus, permeability, and fluid loss coefficient, for example, are not known with certainty and have to be estimated. The design engineer should acknowledge these uncertainties and makes sensitivity runs with the fracture propagation model to determine the effect of these uncertainties on the design process. As databases are developed, the number and magnitude of the uncertainties will diminish.
In practice, the design engineer should simulate the fracture treatment of the well many times on his or her computer. Making these sensitivity runs leads to a better design, while also educating the design engineer on how certain variables affect both the created and the propped fracture dimensions.
Fracture Fluid Selection. A critical decision by the design engineer is the selection of the fracture fluid for the treatment. Economides et al. developed a flow chart that can be used to select the category of fracture fluid required to stimulate a gas well on the basis of factors such as reservoir temperature, reservoir pressure, the expected value of fracture half-length, and a determination of whether the reservoir is water sensitive. That chart is included in the chapter on hydraulic fracturing in the Production Operations section of this Handbook.
Propping Agent Selection. Economides et al. also produced a flow chart for selecting propping agents. Their flow chart is also included in the chapter on hydraulic fracturing in this Handbook. The selection of the propping agent is based on the maximum effective stress that is applied to the propping agent during the life of the well. The maximum effective stress depends on the minimum value of flowing bottomhole pressure that one expects during the life of the well. If the maximum effective stress is less than 6,000 psi, sand is usually recommended as the propping agent. If the maximum effective stress is between 6,000 and 12,000 psi, one should use either resin-coated sand or intermediate strength proppant, depending on the temperature. For cases in which the maximum effective stress is greater than 12,000 psi, high-strength bauxite should be used as the propping agent.
Of course, any rule of thumb should only be used as a guide, as there will be exceptions. For example, even if the maximum effective stress is less than 6,000 psi, the design engineer may choose to use resin-coated sand or other additives to "lock" the proppant in place when proppant flowback becomes an issue. Also, in high flow rate gas wells, intermediate strength proppants may be needed because of inertial flow. For fracture treatments in countries that do not mine sand for fracturing, the largest cost for the proppant is often the shipping charges. Thus, if one has to import the propping agent, one may choose to use intermediate strength proppants, even for relatively shallow wells, because the cost differential between the intermediate strength proppants and sand is not a significant factor.
Once the optimum fracture half-length has been determined and the fracture fluid and fracture propping agent have been selected, the design engineer needs to use a P3D model to determine the details of the design, such as the optimum injection rate, the optimum pad volume, the need for fluid loss additives, the proper location for the perforations, and other details. After designing the optimum treatment, the design engineer must compute the costs of the proposed treatment to be certain the costs are not too different from the costs assumed during the treatment optimization process. If the treatment costs are substantially different, the entire optimization loop (Fig. 7.27) should be retraced using the correct cost data.
Fracture Treatment Execution in the Field. After the optimum fracture treatment has been designed, it must be pumped into the well successfully. A successful field operation requires planning, coordination, and cooperation of all parties. Treatment supervision and the use of quality-control measures improve the successful application of hydraulic fracturing. Safety is always the primary concern in the field. Safety begins with a thorough understanding by all parties of their duties in the field. A safety meeting is always held to review the treatment procedure, establish a chain of command, make sure everyone knows his/her job responsibilities for the day, and to establish a plan for emergencies.
The safety meeting also should be used to discuss the well completion details and the maximum allowable injection rate and pressures, as well as the maximum pressures to be held as backup in the annulus. All casing, tubing, wellheads, valves, and weak links, such as liner tops, should be thoroughly tested prior to beginning the fracturing treatment. Mechanical failures during a treatment can be costly and dangerous. All mechanical problems should be discovered during testing and repaired prior to pumping the fracture treatment.
Prior to pumping the treatment, the engineer in charge should conduct a detailed inventory of all the equipment and materials on location. The inventory should be compared to the design and the prognosis. After the treatment is concluded, the engineer should conduct another inventory of all the materials left on location. In most cases, the difference in the two inventories can be used to verify what was mixed and pumped into the wellbore and the hydrocarbon-bearing formation.
In addition to an inventory, samples of the base fracturing fluid (usually water) should be taken and analyzed. Typically, a water analysis is done on the base fluid to determine the minerals present and the type of bacteria in the water. The data from the water analysis can be used to select the additives required to mix the viscous fracture fluid required to create a wide fracture and to transport the propping agent into the fracture. In addition to testing the water, samples of the additives used during a treatment, and the fracture fluid after all additives have been added, should be taken during the job and saved in case future analyses are required.
Post-Fracture Reservoir Evaluation Methods
Analyzing post-fracture production and pressure data requires a thorough understanding of the flow patterns in the reservoir.  The technique applied to analyze the data must be compatible with the flow regime that is occurring when the data are collected. For a well containing a finite conductivity hydraulic fracture, the flow regimes that occur consist of bilinear flow, linear flow, transitional flow, and pseudoradial flow. These flow regimes can be defined in terms of dimensionless time. The times that encompass bilinear flow, linear flow, and transitional flow can be termed "transient flow." The pseudoradial flow data can be analyzed using semisteady-state methods. In most tight gas reservoirs containing a finite conductivity hydraulic fracture, the flow rate and pressure data measured during well tests fall somewhere in the transient flow category. Seldom can semisteady-state analyses techniques, such as the Horner analyses of PBU data, be used to successfully analyze well-test data in tight gas reservoirs containing a hydraulic fracture. As such, transient flow analyses methods should be used to analyze such data. If long-term (years) production data are available, semisteady-state methods can be used successfully to analyze the production and pressure data.
Transient Flow ConsiderationsIn the 1950s and 1960s, several papers were published containing semisteady-state analysis methods to analyze wells containing hydraulic fractures.  During the time those papers were published, most wells that were hydraulically fracture treated were moderate to high permeability wells that had been damaged during drilling or production. The fracture treatments were designed to be short and only break through the near-wellbore damaged zone. For such situations, the wells would reach semisteady-state flow in a matter of days or weeks, and the semisteady-state analysis methods of Horner, Prats, or McGuire and Sikora could be used successfully to analyze the production and pressure data. However, in low permeability gas reservoirs containing long hydraulic fractures, months or years of production must occur before the well approaches pseudoradial flow.
The flow regimes of a vertical well containing a finite conductivity vertical fracture can be defined using the dimensionless time equation.
In a paper by Lee and Holditch,  it was shown that linear flow occurs between dimensionless times of 0.0225 and 0.1156. Pseudo-radial flow of a well containing a finite conductivity hydraulic fracture does not begin until a dimensionless time of 2 to 5, depending on the value of dimensionless fracture conductivity. Prior to reaching linear flow, the flow is often characterized as bilinear flow. Between the end of linear flow and the beginning of pseudo-radial flow, the regime is often called transitional flow. The data in Table 7.12 illustrate the actual times required to reach linear flow and pseudo-radial flow for typical reservoir situations.
Notice that for gas reservoirs with permeabilities of 1.0 md containing short hydraulic fractures, linear and pseudoradial flow techniques can be used to analyze data during the first month of production. However, as the permeability decreases below the value of 0.1 md, long, hydraulic fractures are required to produce the well at commercial flow rates, and years worth of data are required to use linear and pseudoradial flow analysis procedures.
So how do we analyze early time data from low permeability gas reservoirs containing finite conductivity fractures? The answer is that we must use analytical or numerical solutions of Darcy's law to properly analyze data in the transient flow period, which is all the pressure and flow-rate data prior to reaching pseudoradial flow. Many analytical transient-flow solutions for hydraulically fractured wells have been derived and published. In fact, there are too many to list in the references, but the first and most important analytical solutions were published by Russell and Truitt,  Gringarten et al.,  Cinco et al.,  and Agarwal. 
In addition to the analytical solutions, Lee and Holditch showed that finite difference modeling could be used to analyze data from tight gas reservoirs containing a finite conductivity hydraulic fracture. Actually, the ideal solution is to first use the analytical models to analyze the data to determine first-order estimates of formation permeability, fracture half-length, and fracture conductivity, and then take those values and use them as input into a realistic finite difference model. The finite difference model can be used to determine the final estimates of the formation and fracture properties, taking into account effects such as non-Darcy flow, fracture closure, and formation compaction. The key is to use transient-flow models to analyze transient-flow data. If one tries to analyze data in linear flow with a pseudoradial flow model (such as the Horner graph), one gets incorrect estimates of formation and fracture properties.
Types of Models
As briefly discussed, there are several types of models that can be used to analyze flow and pressure data from a tight-gas-well containing a finite conductivity hydraulic fracture.
Early models by Horner, Prats, and McGuire and Sikora, or simply the semisteady-state flow equation, can be used successfully to analyze data from wells that actually reach pseudoradial flow. In the 1950s and 1960s, very few wells with permeabilities less than 1.0 md were completed because of the low gas prices at the time. As illustrated in Table 7.12, the time required to reach pseudoradial flow in reservoirs of 1.0 md or greater was short enough so that semisteady-state models could be used successfully to analyze the data.
Semianalytical Models. Analytical and semianalytical models published in the 1960s and 1970s allowed the engineer to analyze both production and pressure data during the transient flow period. Originally, these semianalytical solutions were presented in the form of type curves. To analyze the field data, the data had to be plotted on a log/log graph, made of transparent paper, and then the field data would be placed on top of the type curve and shifted horizontally and vertically until the "shape of the field data" could be matched with the "shape of one of the type curves." At the time, even though the solution method was time consuming, type curves revolutionized pressure transient analyses by allowing engineers to analyze transient-flow data from wells containing a finite conductivity hydraulic fracture. A complete discussion on how to use type curves to analyze data from wells containing a hydraulic fracture is found in Gidley, et al.
Even though the use of type curves has proven to be very useful, type curves (semianalytical solutions) do have their limitations. For example, most semianalytical solutions were derived using the following assumptions:
- There is single-phase Darcy flow.
- There is a single-layer, horizontal, homogeneous, isotropic reservoir.
- The reservoir is under pressure depletion drive and no water drive or water influx is included.
- The reservoir permeability is constant with time.
- The hydraulic fracture conductivity is constant with both time and distance.
These assumptions do fit many reservoir situations; hence, the engineer analyzing the data must realize these limitations. In most cases, the semianalytical solutions can be used to analyze transient-flow data and derive first-order estimates of formation permeability, fracture half-length, and fracture conductivity.
Finite Difference Models. Finite difference or numerical models can also be used to analyze transient-flow data from a well containing a finite conductivity hydraulic fracture.  Finite difference models can be used to overcome many of the limitations that accompany the semianalytical solutions. For example, if a finite difference reservoir model is used, we can model multiphase flow, water influx, multiple layers,  and anisotropic reservoir properties. In addition, the finite difference reservoir model can be used to simulate non-Darcy flow and fracture closure because of the crushing and embedment of the propping agent.  Other factors such as water blocking, caused by the fracture fluid,  and the effects of fracture fluid on the cleanup behavior of the reservoir after the fracture treatment can also be investigated.
Finite difference reservoir models are more difficult to use and more time consuming than the semianalytical models, especially if multiphase flow and multilayered reservoirs are going to be simulated. However, when these properties are important, the extra time and effort to use a finite difference reservoir model results in a better understanding of the reservoir and better estimates of the reservoir and fracture properties. The best solution technique is normally to use the semianalytical reservoir models to obtain a first-order estimate of the formation and fracture properties and then use those values as input to the finite difference reservoir model. The finite difference model can then be used to determine the final answers.
Analyzing Post-Fracture Production Data
In many cases, after a well is fracture treated (especially in the early days of fracturing), the well is produced to a pit until the fracture fluid is cleaned up sufficiently to turn the well to sales. After the well quits making proppant and fracture fluid, a test separator is installed to measure the gas flow rate. The gas flow rate and flowing pressures are subsequently analyzed using transient-flow models to estimate values of the reservoir and fracture properties. If lucky, the engineer talks management into shutting in the well to run a pressure buildup test.
In the 1980s, we found that we could better analyze the hydraulic fracture and the reservoir if all of the pressure and flow-rate data were measured from the time the well is opened for cleanup. The Gas Research Inst. (GRI) sponsored a multiyear research project to learn how to evaluate fracture treatments in tight gas reservoirs. The research was focused on four staged field experiments (SFE) in which four wells named SFE Nos. 1, 2, 3, and 4 were drilled and tested extensively. During the GRI tight-gas-sands research project, it was learned that we need to measure all flow rates (gas, water, and condensate) and the flowing pressures from the time the well is opened for cleanup. Especially in SFE No. 1,  it was found that the only acceptable match of the pressure transient data could be obtained by modeling multiphase flow and fracture fluid cleanup in a multilayer reservoir. Such a complicated analysis can only be done using a finite difference reservoir simulator.
If a finite difference reservoir simulator is used to analyze field data or just to do parametric studies, it is clear that the production and pressure transient data, if measured accurately, can lead to a much better characterization of the reservoir and the hydraulic fracture.  The very early flow-rate data are mostly affected by the fracture conductivity, often called bilinear flow. Later, during linear flow, the flow-rate data are most affected by the fracture half-length. If pseudoradial flow is reached, the flow-rate data are most affected by the formation permeability. As such, if the early time flow-rate and pressure data, during the first few days and weeks, are not measured accurately, it is possible that one may not truly understand the properties of the hydraulic fracture.
Post-fracture production data can be analyzed with decline curves, type curves, semianalytical reservoir models, or finite difference reservoir models. When analyzing the production data, the analyst tries to determine the values of formation permeability, fracture half-length, and fracture conductivity. Experience has shown that it is best to measure the formation permeability using prefracture well testing. Then, when analyzing the post-fracture data, one is only trying to determine the properties of the hydraulic fracture.
Experience has also shown that the analysis of post-fracture production data only provides estimates of the length of the fracture that "has cleaned up."  After the fracture treatment has been pumped, the hydraulic fracture is filled with fluid. The fracture fluid either flows into the wellbore, imbibes into the formation, or stays in the fracture.  If the fracture fluid stays in the fracture, that part of the fracture does not allow gas to flow into the fracture from the formation. Consequently, only the part of the fracture near the wellbore that has been cleaned up is seen by the analysis of production or pressure transient data. In essence, there are three fracture lengths: the created fracture length, the propped fracture length, and the effective fracture length. The propped fracture length is the part of the created fracture that contains propping agent at the end of the treatment. The effective fracture length is that part of the propped fracture length that has cleaned up enough to allow gas flow. When we analyze production and pressure transient data, we only obtain estimates of the effective fracture length.
Post-Fracture Pressure Transient Analysis
Lee and Holditch presented discussions concerning how to analyze post-fracture pressure transient data. In most cases, the analysis of post-fracture pressure buildup data, along with the analysis of the post-fracture production data, leads to accurate descriptions of the formation and the hydraulic fracture only if the correct portion of the data are analyzed with the correct model. For example, the analyst must be sure to use only the linear-flow data when analyzing the transient test using a linear-flow model. It might be possible, when one is analyzing data from moderate permeability reservoirs containing short fractures, that linear flow or pseudoradial flow methods can be used to correctly analyze the pressure buildup data. However, in most cases involving tight gas reservoirs containing long hydraulic fractures, transient-flow methods, such as type curves, semianalytical reservoir models, or finite difference reservoir models, must be used to correctly analyze the post-fracture pressure buildup data. To account for factors such as multiphase flow, multilayered reservoirs, non-Darcy flow, and fracture closure effects, the analyst should use a finite difference reservoir model that is capable of modeling a finite conductivity fracture, plus the other features previously listed.
Estimating Reserves in Tight Gas Reservoirs
The resource triangle, Fig. 7.1, describes the distribution of OGIP in a typical basin.  At the top of the triangle are the high permeability reservoirs. These reservoirs are small, and, once discovered, as much as 80 to 90% of the OGIP can be produced using conventional drilling and completion methods. As we go deeper into the resource triangle, the permeability decreases, but the size of the resource increases. Higher gas prices and better technology are required to produce significant volumes of gas from these tight gas reservoirs.
The recovery efficiency is computed by dividing the cumulative gas produced by the OGIP volume. In a tight gas reservoir, the recovery efficiency varies from less than 10% to more than 50% of the OGIP. The recovery efficiency is a function of permeability, net gas pay thickness, drainage area, effective fracture half-length, economic limit, and well life.
Reserve Evaluation MethodsThe most common methods used by reservoir engineers to determine reserves are volumetric, materials balance, decline curves, and reservoir models. Table 7.13 presents information concerning how these methods are used to evaluate high and low permeability gas reservoirs
In tight gas reservoirs, the volumetric method might provide reasonable estimates of OGIP; however, estimates of gas reserves are not as reliable because it is very difficult to estimate both the drainage area of a given well and the recovery efficiency. Because the drainage area and recovery efficiency are so difficult to estimate in tight gas reservoirs, the volumetric method of estimating reserves should only be used prior to drilling any wells and only as a last resort. Once drilling and production data are available, production data analyses should be used to estimate reserves.
Material Balance Method. The material balance method should be used only in high permeability gas reservoirs when accurate gas production and reservoir pressure data are available. In high permeability gas reservoirs, the wells can be shut in for hours or days, and accurate estimates of the average reservoir pressure can be measured or computed using Horner graphs. If the high permeability reservoir is connected to a strong aquifer, or the reservoir rock is very compressible, material balance methods can still be used but are less accurate because of the complexity of the problem and the difficulty in developing an accurate data set.
In tight gas reservoirs, material balance methods should never be used because it is impossible to obtain accurate data to describe how the reservoir pressure declines as gas is produced. In a tight gas reservoir, a well (or the entire reservoir) must be shut in for months or years before enough pressure data are collected to accurately estimate the average reservoir pressure. As such, virtually all shut-in pressure measurements in tight gas reservoirs underestimate the value of average reservoir pressure. If the data are used, the estimate of OGIP and ultimate gas recovery will be too low.
Decline Curve Method. In most gas reservoirs, the decline curve analysis method can be used to estimate reserves. For high permeability reservoirs, the decline curve method works even with limited production data using the exponential equation, which is written as
where a is the (constant) instantaneous decline factor; q is the flow rate at time, t; and qo is the initial flow rate. When Eq. 7.23 applies, a graph of gas flow rate vs. the logarithm of time is a straight line. The straight line can be extrapolated to an economic limit or a fixed well life to determine the ultimate gas recovery. Fig. 7.28 illustrates typical data that can be described using an exponential decline.
where ao is the initial instantaneous decline factor. The decline factor, a, decreases with time, as given by
Near the end of the life of the well, the decline becomes exponential again. Usually, if the decline rate decreases below 6 to 8%, the user sets the decline rate constant (at 6 to 8%) for the remaining life of the well. Fig. 7.29 illustrates a typical exponential decline for a tight gas well. This well is a Cotton Valley well in east Texas that was originally completed and fracture treated in the early 1980s in the lower Cotton Valley zone called the Taylor sand. In the early 1990s, the well was completed and fracture treated in the upper Cotton Valley. The gap in gas production data in the early 1980s was because of the gas market and curtailment of production.
Reservoir Modeling Method. The most accurate method of estimating gas reserves in tight gas reservoirs is to use a reservoir model, such as a semianalytical model or a numerical-reservoir model, to history match production data from the well. The model should be capable of simulating layered reservoirs, a finite conductivity hydraulic fracture, and a changing flowing tubing pressure. In some cases, the analyst might also need to simulate non-Darcy flow, fracture closure, and/or fracture fluid cleanup effects.
Normally, a reasonable approach to estimating reserves is to use decline curves to review and quality-check the data; semianalytical models to history match existing data and estimate reserves; and finite difference models to analyze the data, especially if factors such as non-Darcy flow, fracture closure, and fracture fluid cleanup need to be included in the analysis. Fig. 7.30 illustrates how the saturation profile around a hydraulic fracture can be simulated to better understand fracture fluid cleanup and its effect on gas production vs. time.
|ao||=||initial instantaneous decline factor|
|D||=||diameter (for grain size) or constant for computing s′|
|h||=||net pay, ft|
|L||=||fracture half length, ft|
|q||=||flow rate, Mcf/D|
|qo||=||initial flow rate|
|s′||=||effective skin factor|
|t||=||time, hours or days|
|β||=||formation volume factor, rcf/scf|
|Δt||=||travel time, μsec/ft|
|μ||=||gas viscosity, cp|
|a||=||instantaneous decline rate|
|DC||=||density corrected for shale|
|e||=||at the extremity of the reservoir|
|f||=||fluid or fracture|
|g||=||grain or gas (for flow rate)|
|i||=||investigation (for radius)|
|ild||=||induction log deep|
|ilm||=||induction log medium|
|NC||=||neutron corrected for shale|
|o||=||original (for flow rate)|
|rh||=||relative to hydrocarbon flow|
|sfl||=||spherically focused log|
|t||=||true (for conductivity); total (for compressibility)|
|w||=||wellbore (for radius); water (for saturation)|
|wb||=||bound water (for conductivity and water saturation)|
|wf||=||well flowing; free water (for conductivity)|
- Masters, J.A. 1979. Deep Basin Gas Trap, Western Canada. AAPG Bulletin 63 (2): 152–181.
- Tight Gas Resource Map of the United States. 2001. Gas Technology Inst. Report, GTI-01/0114, Quicksilver Resources.
- Fisher, W.L. and McGowen, J.H.: "Depositional Systems in the Wilcox Group of Texas and Their Relationship to Occurrence of Oil and Gas," AAPG Bulletin (1969) 53, No. 1, 30.
- Fisher, W.L. and Brown, L.F. Jr. 1972. Clastic Depositional Systems—A Genetic Approach to Facies Analysis. Bur. Econ. Geol., U. of Texas at Austin.
- Galloway, W.E. and Hobday, D.K. 1983. Terrigeneous Clastic Depositional Systems. New York City: Springer-Verlag.
- Berg, R.R. 1986. Reservoir Sandstones. New Jersey: Prentice-Hall, Inc.
- McGuire, W.J. and Sikora, V.J. 1960. The Effect of Vertical Fractures on Well Productivity. J Pet Technol 12 (10): 72-74. SPE-1618-G. http://dx.doi.org/10.2118/1618-G.
- Prats, M. 1961. Effect of Vertical Fractures on Reservoir Behavior—Incompressible Fluid Case. SPE J. 1 (2). SPE-1575-G. http://dx.doi.org/10.2118/1575-G.
- Horner, D.R. 1951. Pressure Build-Up in Wells. Proc., Third World Petroleum Congress, The Hague, Sec. II, 503-523.
- Lee, W.J. and Holditch, S.A. 1981. Fracture Evaluation With Pressure Transient Testing in Low-Permeability Gas Reservoirs. J Pet Technol 33 (9): 1776–1792. SPE-9975-PA. http://dx.doi.org/10.2118/9975-PA.
- Cinco-Ley, H., Samaniego-V., F., and A.N., D. 1978. Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture. SPE J. 18 (4): 253–264. SPE-6014-PA. http://dx.doi.org/10.2118/6014-PA.
- Agarwal, R.G., Carter, R.D., and Pollock, C.B. 1979. Evaluation and Performance Prediction of Low-Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing. J Pet Technol 31 (3): 362–372. SPE-6838-PA. http://dx.doi.org/10.2118-6838-PA.
- Aly, A.M., Hunt, E.R., Pursell, D.A. et al. 1997. Application of Multi-Well Normalization of Open Hole Logs in Integrated Reservoir Studies. Presented at the SPE Western Regional Meeting, Long Beach, California, 25-27 June 1997. SPE-38263-MS. http://dx.doi.org/10.2118/38263-MS.
- Howard, W.E. and Hunt, E.R. 1986. Travis Peak: An Integrated Approach to Formation Evaluation. Presented at the SPE Unconventional Gas Technology Symposium, Louisville, Kentucky, 18-21 May 1986. SPE-15208-MS. http://dx.doi.org/10.2118/15208-MS.
- Hunt, E.R. et al. 1996. Fundamentals of Log Analysis. 12-part article in World Oil (June, July, September, October, November, December 1996 and March, July, September, October, November, December 1997).
- Worthington, P.F. 1985. The Evolution of Shaly-Sand Concepts in Reservoir Evaluation. The Log Analyst (January/February): 23.
- Clavier, C., Coates, G., and Dumanoir, J. 1984. Theoretical and Experimental Bases for the Dual-Water Model for Interpretation of Shaly Sands. SPE J 24 (2): 153-168. SPE-6859-PA. http://dx.doi.org/10.2118/6859-PA.
- Semmelbeck, M.E. and Holditch, S.A. 1988. The Effects of Mud-Filtrate Invasion on the Interpretation of Induction Logs. SPE Form Eval 3 (2): 386-392. SPE-14491-PA. http://dx.doi.org/10.2118/14491-PA.
- Thomas, R.D. and Ward, D.C. 1972. Effect of Overburden Pressure and Water Saturation on Gas Permeability of Tight Sandstone Cores. J Pet Technol 24 (2): 120-124. SPE-3634-PA. http://dx.doi.org/10.2118/3634-PA.
- Jones, F.O. and Owens, W.W. 1980. A Laboratory Study of Low-Permeability Gas Sands. J Pet Technol 32 (9): 1631–1640. SPE-7551-PA. http://dx.doi.org/10.2118/7551-PA.
- Soeder, D.J. and Randolph, P.L. 1987. Porosity, Permeability, and Pore Structure of the Tight Mesaverde Sandstone, Piceance Basin, Colorado. SPE Form Eval 2 (2): 129-136. SPE-13134-PA. http://dx.doi.org/10.2118/13134-PA.
- Staged Field Experiment No. 3: Application of Advanced Technologies in Tight Gas Sandstones—Travis Peak and Cotton Valley Formations, Waskom Field, Harrison County, Texas. 1991. Gas Research Inst. Report, GRI-91/0048, CER Corp. and S.A. Holditch & Assocs. Inc., February.
- Ferguson, C.K. and Klotz, J.A. 1954. Filtration from Mud During Drilling. Trans., AIME 201, 29.
- Holditch, S.A., Lee, W.J., Lancaster, D.E. et al. 1983. Effect of Mud Filtrate Invasion on Apparent Productivity in Drillstem Tests in Low-Permeability Gas Formations. J Pet Technol 35 (2): 299-305. SPE-9842-PA. http://dx.doi.org/10.2118/9842-PA.
- Tobola, D.P. and Holditch, S.A. 1991. Determination, of Reservoir Permeability From Repeated Induction Logging. SPE Form Eval 6 (1): 20-26. SPE-19606-PA. http://dx.doi.org/10.2118/19606-PA.
- Yao, C.Y. and Holditch, S.A. 1996. Reservoir Permeability Estimation From Time-lapse Log Data. SPE Form Eval 11 (1): 69–74. SPE-25513-PA. http://dx.doi.org/10.2118/25513-PA.
- Berg, R.R. 1970. Method for Determining Permeability from Reservoir Rock Properties. Trans., GCAGS, 20, 303.
- Timur, A. 1968. An Investigation of Permeability, Porosity, and Residual Water Saturation Relationships. The Log Analyst (July/August): 8.
- Coates, G.R. and Dumanoir, J.L. 1974. A New Approach to Improved Log-Derived Permeability. The Log Analyst (January/February): 17.
- Schlumberger Log Interpretation Principles/Application, 10. Houston, Texas: Schlumberger Educational Services.
- Ahmed, U., Crary, S.F., and Coates, G.R. 1991. Permeability Estimation: The Various Sources and Their Interrelationships. J Pet Technol 43 (5): 578-587. SPE-19604-PA. http://dx.doi.org/10.2118/19604-PA.
- Yao, C.Y. and Holditch, S.A. 1993. Estimating Permeability Profiles Using Core and Log Data. Presented at the SPE Eastern Regional Meeting, Pittsburgh, Pennsylvania, 2-4 November 1993. SPE-26921-MS. http://dx.doi.org/10.2118/26921-MS.
- Holditch, S.A., Gatens III, J.M., McVay, D.A. et al. 1984. An Automated Method of Matching Production Performance Using Dimensionless Solutions. Presented at the SPE Unconventional Gas Recovery Symposium, Pittsburgh, Pennsylvania, 13-15 May 1984. SPE-12846-MS. http://dx.doi.org/10.2118/12846-MS.
- Fetkovich, M.J. 1980. Decline Curve Analysis Using Type Curves. J Pet Technol 32 (6): 1065–1077. SPE 4629-PA. http://dx.doi.org/10.2118/4629-PA.
- Watson, T.A., Lane, S.H., and III, M.J.G. 1990. History Matching With Cumulative Production Data. J Pet Technol 42 (1): 96-100. SPE-17063-PA. http://dx.doi.org/10.2118/17063-PA.
- Fetkovich, M.D., Guerrero, E.T., Fetkovich, M.J. et al. 1986. Oil and Gas Relative Permeabilities Determined From Rate-Time Performance Data. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 5-8 October 1986. SPE-15431-MS. http://dx.doi.org/10.2118/15431-MS.
- Ansah, J., Knowles, R.S., and Blasingame, T.A. 1996. A Semi-Analytic (p/z) Rate-Time Relation for the Analysis and Prediction of Gas Well Performance. Presented at the SPE Mid-Continent Gas Symposium, Amarillo, Texas, 28-30 April 1996. SPE-35268-MS. http://dx.doi.org/10.2118/35268-MS.
- Gidley, J.L., Holditch, S.A., Nierode, D.E. et al. 1989. Recent Advances in Hydraulic Fracturing, No. 12, 39-56. Richardson, Texas: Monograph Series, SPE.
- Lee, W.J., Kuo, T.B., Holditch, S.A. et al. 1984. Estimating Formation Permeability From Single-Point Flow Data. Presented at the SPE Unconventional Gas Recovery Symposium, Pittsburgh, Pennsylvania, 13-15 May 1984. SPE-12847-MS. http://dx.doi.org/10.2118/12847-MS.
- Amaefule, J.O., Altunbay, M., Tiab, D. et al. 1993. Enhanced Reservoir Description: Using Core and Log Data to Identify Hydraulic (Flow) Units and Predict Permeability in Uncored Intervals/Wells. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. SPE 26436. http://dx.doi.org/10.2118/26436-MS.
- Al-Ajmi, F.A. and Holditch, S.A. 2000. Permeability Estimation Using Hydraulic Flow Units in a Central Arabia Reservoir. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, 1-4 October 2000. SPE-63254-MS. http://dx.doi.org/10.2118/63254-MS.
- Rollins, J.B., Holditch, S.A., and Lee, W.J. 1992. Characterizing, Average Permeability in Oil and Gas Formations (includes associated papers 25286 and 25293 ). SPE Form Eval 7 (1): 99-105. SPE-19793-PA. http://dx.doi.org/10.2118/19793-PA.
- Holditch, S.A., Lin, Z.-S., and Spivey, J.P. 1991. Estimating the Recovery From an Average Well in a Tight Gas Formation. Presented at the SPE Gas Technology Symposium, Houston, Texas, 22–24 January. SPE-21500-MS. http://dx.doi.org/10.2118/21500-MS.
- Holditch, S.A. and Spivey, J.P. 1993. Estimate Recovery from Tight Gas Formation Wells. Pet. Eng. Intl. (August): 20.
- Veatch Jr., R.W. 1983. Overview of Current Hydraulic Fracturing Design and Treatment Technology--Part 1. J Pet Technol 35 (4): 677-687. SPE-10039-PA. http://dx.doi.org/10.2118/10039-PA.
- Holditch, S.A. 1974. Economic Production of Tight Gas Reservoirs Look Better. Oil & Gas J. (4 February): 99.
- Gongora, C. 1995. Correlations to Determine In-Situ Stress from Open-Hole Logging Data in Sandstone Reservoirs. MS thesis, Texas A&M University, College Station, Texas (1995).
- Holditch, S.A. and Rahim, Z. 1994. Developing Data Sets for 3D Fracture Propagation Models. SPE Prod & Oper 9 (4): 257-261. SPE-26155-PA. http://dx.doi.org/10.2118/26155-PA.
- Gidley, J.L., Holditch, S.A., Nierode, D.E. et al. 1989. Recent Advances in Hydraulic Fracturing, 12, 245-262. Richardson, Texas: Monograph Series, SPE.
- Rahim, Z. and Holditch, S.A. 1995. The Effects of Mechanical Properties and Selection of Completion Interval Upon the Created and Propped Fracture Dimensions in Layered Reservoirs. J. Pet. Science & Eng. 13 (1): 29-45 http://dx.doi.org/10.1016/0920-4105(94)00061-8.
- Cleary, M.P., Johnson, D.E., Kogsbøll, H.-H. et al. 1993. Field Implementation of Proppant Slugs To Avoid Premature Screen-Out of Hydraulic Fractures With Adequate Proppant Concentration. Presented at the Low Permeability Reservoirs Symposium, Denver, Colorado, 26-28 April 1993. SPE-25892-MS. http://dx.doi.org/10.2118/25892-MS.
- Holditch, S.A., Jennings, J.W., Neuse, S.H. et al. 1978. The Optimization of Well Spacing and Fracture Length in Low Permeability Gas Reservoirs. Presented at the SPE Annual Fall Technical Conference and Exhibition, Houston, Texas, 1-3 October 1978. SPE-7496-MS. http://dx.doi.org/10.2118/7496-MS.
- Britt, L.K. 1985. Optimized Oilwell Fracturing of Moderate-Permeability Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, USA, 22–26 September. SPE-14371-MS. http://dx.doi.org/10.2118/14371-MS.
- Gidley, J.L., Holditch, S.A., Nierode, D.E. et al. 1989. Recent Advances in Hydraulic Fracturing, 12, 317. Richardson, Texas: Monograph Series, SPE.
- Economides, M.J. and Nolte, K.G. 2000. Reservoir Stimulation, third edition. West Sussex, England: John Wiley & Sons, Ltd., West Sussex, England.
- Lee, W.J. and Holditch, S.A. 1981. Fracture Evaluation With Pressure Transient Testing in Low-Permeability Gas Reservoirs. J Pet Technol 33 (9): 1776–1792. SPE-9975-PA. http://dx.doi.org/10.2118/9975-PA.
- Russell, D.G. and Truitt, N.E. 1964. Transient Pressure Behavior in Vertically Fractured Reservoirs. J Pet Technol 16 (10): 1159–1170. SPE-967-PA. http://dx.doi.org/10.2118/967-PA.
- Gringarten, A.C., Henry J. Ramey, J., and Raghavan, R. 1974. Unsteady-State Pressure Distributions Created by a Well With a Single Infinite-Conductivity Vertical Fracture. Society of Petroleum Engineers Journal 14 (4): 347-360. SPE-4051-PA. http://dx.doi.org/10.2118/4051-PA.
- Cinco-Ley, H., Samaniego-V., F., and A.N., D. 1978. Transient Pressure Behavior for a Well With a Finite-Conductivity Vertical Fracture. SPE J. 18 (4): 253–264. SPE-6014-PA. http://dx.doi.org/10.2118/6014-PA.
- Agarwal, R.G., Carter, R.D., and Pollock, C.B. 1979. Evaluation and Performance Prediction of Low-Permeability Gas Wells Stimulated by Massive Hydraulic Fracturing. J Pet Technol 31 (3): 362–372. SPE-6838-PA. http://dx.doi.org/10.2118-6838-PA.
- Rahim, Z., Holditch, S.A., Zuber, M.D. et al. 1998. Evaluation of Fracture Treatments Using a Layered-Reservoir Description: Field Examples. SPE Prod & Oper 13 (1): 21-28. SPE-26187-PA. http://dx.doi.org/10.2118/26187-PA.
- Holditch, S.A. and Morse, R.A. 1976. The Effects of Non-Darcy Flow on the Behavior of Hydraulically Fractured Gas Wells. J Pet Technol 28 (10): 1169–1179. SPE-5586-PA. http://dx.doi.org/10.2118/5586-PA.
- Holditch, S.A. 1979. Factors Affecting Water Blocking and Gas Flow From Hydraulically Fractured Gas Wells. J Pet Technol 31 (12): 1515–1524. SPE-7561-PA. http://dx.doi.org/10.2118/7561-PA.
- Voneiff, G.W., Robinson, B.M., and Holditch, S.A. 1996. The Effects of Unbroken Fracture Fluid on Gaswell Performance. SPE Prod & Oper 11 (4): 223-229. SPE-26664-PA. http://dx.doi.org/10.2118/26664-PA.
- Holditch, S.A., Robinson, B.M., Whitehead, W.S. et al. 1988. The GRI Staged Field Experiment. SPE Form Eval 3 (3): 519-533. SPE-16429-PA. http://dx.doi.org/10.2118/16429-PA.
- Robinson, B.M., Holditch, S.A., and Peterson, R.E. 1991. The Gas Research Institute's Second Staged Field Experiment: A Study of Hydraulic Fracturing. Presented at the SPE Gas Technology Symposium, Houston, Texas, 22-24 January 1991. SPE-21495-MS. http://dx.doi.org/10.2118/21495-MS.
- Robinson, B.M., Holditch, S.A., Whitehead, W.S. et al. 1992. Hydraulic Fracturing Research in East Texas: Third GRI Staged Field Experiment. J Pet Technol 44 (1): 78-87. SPE-22878-PA. http://dx.doi.org/10.2118/22878-PA.
- Saunders, B.F., Robinson, B.M., Holditch, S.A. et al. 1992. Hydraulic Fracturing Research in the Frontier Formation Through the Gas Research Institute's Fourth Staged Field Experiment. Presented at the SPE Annual Technical Conference and Exhibition, Washington, D.C., 4-7 October 1992. SPE-24854-MS. http://dx.doi.org/10.2118/24854-MS.
- Montgomery, K.T., Holditch, S.A., and Berthelot, J.M. 1990. Effects of Fracture Fluid Invasion on Cleanup Behavior and Pressure Buildup Analysis. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 23–26 September. SPE-20643-MS. http://dx.doi.org/10.2118/20643-MS.
- Sherman, J.B. and Holditch, S.A. 1991. Effect of Injected Fracture Fluids and Operating Procedures on Ultimate Gas Recovery. Presented at the SPE Gas Technology Symposium, Houston, Texas, 22-24 January 1991. SPE-21496-MS. http://dx.doi.org/10.2118/21496-MS.
SI Metric Conversion Factors
|acre||×||4.046 873||E + 03||=||m2|
|°API||141.5/(131.5 + °API)||=||g/cm3|
|bbl||×||1.589 873||E – 01||=||M3|
|cp||×||1.0*||E – 03||=||Pa•s|
|ft||×||3.048*||E – 01||=||m|
|°F||(°F – 32)/1.8||=||°C|
|in.||×||2.54*||E + 00||=||cm|
|psi||×||6.894 757||E + 00||=||kPa|
Conversion factor is exact.