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By P. N. McCreery, R. L. Slobod, B. J. Dotson, James W. Spurlock

A core sample porosity-check program is described. A number of laboratories participated in the investigation. which comprised measuring the porosities of ten selected natural and synthetic core samples. Each laboratory employed its own method (or methods) of measurement. These included Boyle's Law, water-saturation. and organic liquid-saturation methods. Brief descriptions of each method employed are given. In general, the measured values of porosity were in reasonably good agreement. The average deviation of porosity from the mean or average values for the group of samples was ±0.5 porosity per cent. The results of these measurements are compiled and presented in graphical form. INTRODUCTION The total hulk volume of a porous sample is derived from the sum of two volumes, the void or pore volume and the solid* or grain volume. The porosity fraction of the sample ia defined as the ratio of the void volume to the bulk volume. Multiplication of this ratio by 100 converts it to per cent porosity. Distinction is made here between total porosity and effective porosity. The former includes all void space, both interconnected and isolated, while the latter includes only those voids which are interconnected. This investigation deals only with the effective porosity.* Numerous cases had been noticed in which there appeared to be appreciable discrepancies in the results of porosity determinations on core samples. Differences of as much as 10 to 15 porosity per cent had been reported from different sources

Jan 1, 1951

By John S. Bell, J. M. Shepherd

pressure difference of 280 psi measured initially on opposite sides of the major fault in the Hawkins Field led to pressure determinations in the Woodbine sand throughout the East Texas basin. Considering the large area, there is unusually good correlation between pressure losses and points of major withdrawals, these losses indicating that the basin pressure has been materially reduced by withdrawals, primarily from the East Texas Field and secondarily from the old fault-line fields of Limestone and Navarro counties, with the pressure loss varying inversely with the log of the distance from these two main areas of basin withdrawals to the measurement points. Apparently faults located throughout the basin serve as local blocks to continuous pressure gradients. INTRODUCTION The pressure anomalies found in the Hawkins Field, Wood County, Texas,' shortly after discovery have led to an area-wide investigation of the pressure distribution within the Woodbine sand of the East Texas basin. These pressures were obtained by drill-stem tests made for that sole purpose while drilling wildcat wells to deeper horizons. The Woodbine sand of Gulf Cretaceous Age is or has been productive of oil and gas in 42 different fields, with the 28 oil fields currently active having produced 118,000,000 bbl of oil during 1949. With one exception, producing energy for all Woodbine reservoirs has been from water drive provided predominantly by expansion of the tremendous volume of water contained in the Woodbine sand. This producing mechanism was recognized at an early date and was described mathematically by

Jan 1, 1951

By John S. Bell, J. M. Shepherd

pressure difference of 280 psi measured initially on opposite sides of the major fault in the Hawkins Field led to pressure determinations in the Woodbine sand throughout the East Texas basin. Considering the large area, there is unusually good correlation between pressure losses and points of major withdrawals, these losses indicating that the basin pressure has been materially reduced by withdrawals, primarily from the East Texas Field and secondarily from the old fault-line fields of Limestone and Navarro counties, with the pressure loss varying inversely with the log of the distance from these two main areas of basin withdrawals to the measurement points. Apparently faults located throughout the basin serve as local blocks to continuous pressure gradients. INTRODUCTION The pressure anomalies found in the Hawkins Field, Wood County, Texas,' shortly after discovery have led to an area-wide investigation of the pressure distribution within the Woodbine sand of the East Texas basin. These pressures were obtained by drill-stem tests made for that sole purpose while drilling wildcat wells to deeper horizons. The Woodbine sand of Gulf Cretaceous Age is or has been productive of oil and gas in 42 different fields, with the 28 oil fields currently active having produced 118,000,000 bbl of oil during 1949. With one exception, producing energy for all Woodbine reservoirs has been from water drive provided predominantly by expansion of the tremendous volume of water contained in the Woodbine sand. This producing mechanism was recognized at an early date and was described mathematically by

Jan 1, 1951

By J. N. Breston, R. V. Hughes

Conclusions drawn by previous research workers with reSPect to the relation between Pressure gradients and/or velocity and oil recovery obtained by laboratory water flood tests have been in disagreement probably due to variable procedures and unnatural conditions and materials. The Bradford Laboratory of the Pennsylvania Grade Crude Oil Association as part of its secondary recovery research program has conducted nineteen water floods on two long cores of widely differing characteristics in an attempt to clarify this relationship and make it an aid in predicting flooding pressures in the field. Unlike previous research procedures the present experiments were conducted with the aim of duplicating field conditions as closely as possible by using long unextracted consolidated cores, a live crude, and natural brines for both flooding and, connate water content. Also, the pressure gradients and flooding velocities were representative of field conditions where similar sands were being flooded. Eleven floods on one core and eight floods on the other core showed increased recoveries and lower residual oil saturation with increased flood pressure gradients and flood velocities. A marked decrease in recovery was obtained from both cores at very low flood velocities. This pressure versus recovery relationship is shown to hold up to the point of water breakthrough and also up to the 100 and 1 produced water to oil ratio point. INTRODUCTION The possibility of water flooding oil sands was suggested by Carl1 of the Pennsylvania Geological Survey in 1880. It is not known when the practice was tried intentionally for the first time, but its beneficial effects were noted in the annual production rate of the Bradford field as early as 1907. The practice was illegal in Pennsylvania until 1921. Early water floods in the Bradford field usually consisted of shooting or splitting the casing secretly to permit subsurface waters to enter the producing sands under hydrostatic head. As it was noted that the benefits of water flooding seemed to be proportional to the quantity of water dumped into the well many also began to utilize surface sources after the practice became legal. It was probably during the middle 20's before many producers realized that the pressurehead of the water upon the producing sand determined the rate and quantity of water that would enter the sand. Hence, rate and quantity of production appeared to be a direct function of input pressures. By 1927 a few producers had ventured the installation of pressure pumps in order to increase water-input rates and production through the combination of hydrostatic and hydraulic pressures. The adoption of pressure flooding and the "five-spot" drilling pattern in the Bradford field were essentially simultaneous. Water-input pressures in 1930 seldom exceeded 300 p.s.i. at the well head or 1100 p.s.i. at the sand face. Since that time, water-flood producers in the Bradford-Allegany fields have gone to higher and higher pressure until today 600 p.s.i. at the well heads is called a low pressure flood. Many high pressure floods now operate at 1300-1400 p.s.i. at the well head. The limiting and advisable pressure at the sand face has been pronounced as that pressure just under what is required to lift the overburden or to cause formation parting: According to this rule any water flood operation utilizing well-head pressures nearly equal in pounds per sq. in. to 1.1 times the average depth in feet to the top of the producing sand would be considered as a high-pressure flood. Despite the higher pressure trends in the Bradford-Allegany field operations and the results of early laboratory water flooding research, the desirability and benefits of high input pressures are still questioned by many operators, particularly in midwestern water flood operations. The present paper recounts a series of 19 laboratory water floods using two long, consolidated cores of widely differing characteristics saturated with live crude and flooded with oil field brines in an effort to simulate field conditions under • various pressure gradients and flooding velocities. For both cores, higher recoveries and lower residual oil saturations were obtained at higher pressure gradients and flood velocities. This relationship is shown to hold up to the water breakthrough point and also up to the 100 to 1 produced water to oil ratio point.

Jan 1, 1949

By R. V. Hughes, J. N. Breston

Conclusions drawn by previous research workers with reSPect to the relation between Pressure gradients and/or velocity and oil recovery obtained by laboratory water flood tests have been in disagreement probably due to variable procedures and unnatural conditions and materials. The Bradford Laboratory of the Pennsylvania Grade Crude Oil Association as part of its secondary recovery research program has conducted nineteen water floods on two long cores of widely differing characteristics in an attempt to clarify this relationship and make it an aid in predicting flooding pressures in the field. Unlike previous research procedures the present experiments were conducted with the aim of duplicating field conditions as closely as possible by using long unextracted consolidated cores, a live crude, and natural brines for both flooding and, connate water content. Also, the pressure gradients and flooding velocities were representative of field conditions where similar sands were being flooded. Eleven floods on one core and eight floods on the other core showed increased recoveries and lower residual oil saturation with increased flood pressure gradients and flood velocities. A marked decrease in recovery was obtained from both cores at very low flood velocities. This pressure versus recovery relationship is shown to hold up to the point of water breakthrough and also up to the 100 and 1 produced water to oil ratio point. INTRODUCTION The possibility of water flooding oil sands was suggested by Carl1 of the Pennsylvania Geological Survey in 1880. It is not known when the practice was tried intentionally for the first time, but its beneficial effects were noted in the annual production rate of the Bradford field as early as 1907. The practice was illegal in Pennsylvania until 1921. Early water floods in the Bradford field usually consisted of shooting or splitting the casing secretly to permit subsurface waters to enter the producing sands under hydrostatic head. As it was noted that the benefits of water flooding seemed to be proportional to the quantity of water dumped into the well many also began to utilize surface sources after the practice became legal. It was probably during the middle 20's before many producers realized that the pressurehead of the water upon the producing sand determined the rate and quantity of water that would enter the sand. Hence, rate and quantity of production appeared to be a direct function of input pressures. By 1927 a few producers had ventured the installation of pressure pumps in order to increase water-input rates and production through the combination of hydrostatic and hydraulic pressures. The adoption of pressure flooding and the "five-spot" drilling pattern in the Bradford field were essentially simultaneous. Water-input pressures in 1930 seldom exceeded 300 p.s.i. at the well head or 1100 p.s.i. at the sand face. Since that time, water-flood producers in the Bradford-Allegany fields have gone to higher and higher pressure until today 600 p.s.i. at the well heads is called a low pressure flood. Many high pressure floods now operate at 1300-1400 p.s.i. at the well head. The limiting and advisable pressure at the sand face has been pronounced as that pressure just under what is required to lift the overburden or to cause formation parting: According to this rule any water flood operation utilizing well-head pressures nearly equal in pounds per sq. in. to 1.1 times the average depth in feet to the top of the producing sand would be considered as a high-pressure flood. Despite the higher pressure trends in the Bradford-Allegany field operations and the results of early laboratory water flooding research, the desirability and benefits of high input pressures are still questioned by many operators, particularly in midwestern water flood operations. The present paper recounts a series of 19 laboratory water floods using two long, consolidated cores of widely differing characteristics saturated with live crude and flooded with oil field brines in an effort to simulate field conditions under • various pressure gradients and flooding velocities. For both cores, higher recoveries and lower residual oil saturations were obtained at higher pressure gradients and flood velocities. This relationship is shown to hold up to the water breakthrough point and also up to the 100 to 1 produced water to oil ratio point.

Jan 1, 1949

By A. C. England, William F. Haney, Paul B. Crawford, Bobby L. Landrum

The creation of unsymmetrical vertical or horizontal fractures in a producing well will result in a unique distortion of the normal shut-in pressures existing at the four surrounding wells. An electrical model study has been made to show how the shut-in pressures at the wells surrounding the fractured producing well may he used to estimate the size and orientation of vertical or horizontal fractures. The pressure differences at the four surrounding wells are recorded during production from the fractured well. The resulting pressure dato are matched from a table of several hundred possible fracture combinations. The table refers to the figure showing the effective size and orientation of the commercially created fracture. INTRODUCTION The creation of commercial fractures about oil and gas wells has led to considerable speculation as to the size and shape of the fractures. It is important that the size and shape be known in certain instances, especially when pressure maintenance programs are to be initiated. It was shown that if knowledge of a vertical fracture could be found that such information may be utilized in planning a waterflooding or gas cycling program and that in some cases the fractures might be utilized very effectively.' Other work showed that it may be desirable to create "pancake" fractures in certain reservoirs but that they should exist in a desirable range.' If the fractures are too large, they should be plugged prior to initiating a pressure maintenance program. If an irregular shaped "pancake" fracture is created, it is desirable to know the orientation of this fracture because similar but unreported studies have shown that "pancake" fractures may or may not substantially affect the sweep efficiencies and performance of the flooding or cycling program. Consequently, it may be desirable in some instances to estimate the effective size and orientation of the fracture. ANALOG An electrical model was used in making this study. The electrical model consisted of a circular reservoir approximately 8 in. in diameter, 1 in. thick and was filled with a dilute salt solution. A copper band formed the periphery of the reservoir. A vertical fracture was simulated by a copper strip soldered to the wire well located in the center of the reservoir. Vertical copper strips of various lengths and orientation were soldered to the wire well to represent vertical fractures in the reservoir. In studies reported here on vertical fractures it was arbitrarily assumed that two fractures originated at the well and extended out into the reservoir. An electrical potential was imposed between the wire well and the periphery of the tank. Plots of the iso-potentials are shown in Figs. 1 through 9. This model provides the steady-state isopotentials existing in a uniform, homogeneous circular reservoir having a vertically fractured well at its center. The permeability of the fracture is much greater than the permeability of the matrix proper. The effects of gravity are neglected. In preparing Tables 1 and 2, four symmetrically located unfractured wells were assumed to exist around

Jan 1, 1956

By C. S. Matthews, H. C. Lefkovits

The purposes of this study are (a) to determine the accuracy of a previously proposed method for calclrlating average reservoir pressure and (b) to find a method for estimating the shape of the drainage area of each well in a bounded reservoir. Both numerical and experimental methods are used to determine the pressure distribution and the location of drainage bounrlaries in idealized reservoirs at steady state. A number of photographs are included which show flowlines and drainage areas in reservoir models of various shapes. Results from these studies are then compared with those from the previously proposed method for calculating average reservoir pressure.' It is concluded that the previously proposed method is sufficiently accurate for most reservoir engineering purposes. In addition, some simple methods are given for estimation of .shapes of drainage boundaries. INTRODUCTION A method for the determination of the average Pressure in a bounded reservoir was previously developed by Matthews, Brons, and Hazebroek,1 and presented at the Petroleum Branch Fall Meeting in 1953.† In aP- plying this method, the reservoir was first divided into drainage volumes; second, the average pressure in each drainage volume was calculated; and third, these drainage volume pressures were averaged volumetrically to give the average pressure in the reservoir. It was shown that each well's individual drainage volume, at steady state, is proportional to the well's production rate; however. the question of how to estimate accurately the shape of these drainage volumes could not be answered. Furthermore, in calculating the average pressure for each drainage area, the actual drainage areas, which are in general quite asymmetric in shape, are replaced with one of the symmetric prototypes given in T.P. 3876. A question may then be raised as to how accurately the symmetrical figures depict the pressure behavior of the actual unsymmetrical drainage areas. The study reported on in the present paper was made in an attempt to shed light on the above questions. METHODS It was shown in T.P. 3876 that after a period of steady rate of withdrawal the rate of pressure decline becomes constant at every point in a bounded reservoir containing a single-phase fluid whose compressibility is small and constant and whose viscosity is con-

Jan 1, 1956

By E. V. Watts

The D-7 zone of the Ventura Avenue field is of special interest because the initial reservoir pressure at 92.00 ft nearly equaled the pressure exerted by the overburden. While the phenomenon has been observed elsewhere in the world, there is no record of a previous case in California. Such high pressures have been attributed to sealing of the reservoir, followed either by emergence of the beds or by compaction of the sediments in various ways. Oil in the D-7 zone is undersaturated. At pressures above the bubble point, oil is recovered by the slight expansibility of the reservoir framework and its liquid contents. More than 40 pct as much oil probably will be recovered by this mechanism as will be recovered by internal gas drive after pressures pass below the bubble point. Operations are handicapped by sand and pipe troubles. Introduction The Ventura Avenue field has been under development since 1915. It has long been considered a "high-pressure" field, but interest was heightened by the extreme conditions encountered in the recent development of the so-called D-7 zone. The original reservoir pressure in this pool is estimated to have been 8300 psi at a depth of 9000 ft below sea level, or 9200± ft below the surface. A fluid pressure approaching that exerted by the overlying sediments has been encountered in other parts of the world, but never before in California to the degree observed in the D-7 pool. With few exceptions, the original pressure in California fields is about equivalent to the static head of water below the water table in the outcrop. Structure The Ventura anticline is a prominent feature of the Ventura basin, being traceable on the surface about 17 miles.' The Ventura Avenue field is at the apex of the anticline. It is about one mile wide and five miles long, the major axis lying in an east-west direction. The productive limits cover an area of about 2300 acres. The entire anticline has been severely folded and faulted. The productive portions in particular are broken up by three major thrust faults having a general east-west strike. The resultant four fault blocks are termed the A, B, C, and D blocks, respectively. Certain electric-log intervals are assigned numbers. Fig I is a diagrammatic north-south section of the field near the crest, looking west, and shows three of the four fault blocks. To the west, the upper fault divides into two branches, which define the B block. Wells penetrating a fault may duplicate over 1000 ft of formation. However, the greater fault movement is the strike shift, which is believed to exceed 2500 ft both between the A and C blocks and between the C and D blocks. The location of water is irregular and unpredictable. A few intermediate waters exist, while some strata have more than 2000 ft of productive closure.

Jan 1, 1948

By E. V. Watts

The D-7 zone of the Ventura Avenue field is of special interest because the initial reservoir pressure at 92.00 ft nearly equaled the pressure exerted by the overburden. While the phenomenon has been observed elsewhere in the world, there is no record of a previous case in California. Such high pressures have been attributed to sealing of the reservoir, followed either by emergence of the beds or by compaction of the sediments in various ways. Oil in the D-7 zone is undersaturated. At pressures above the bubble point, oil is recovered by the slight expansibility of the reservoir framework and its liquid contents. More than 40 pct as much oil probably will be recovered by this mechanism as will be recovered by internal gas drive after pressures pass below the bubble point. Operations are handicapped by sand and pipe troubles. Introduction The Ventura Avenue field has been under development since 1915. It has long been considered a "high-pressure" field, but interest was heightened by the extreme conditions encountered in the recent development of the so-called D-7 zone. The original reservoir pressure in this pool is estimated to have been 8300 psi at a depth of 9000 ft below sea level, or 9200± ft below the surface. A fluid pressure approaching that exerted by the overlying sediments has been encountered in other parts of the world, but never before in California to the degree observed in the D-7 pool. With few exceptions, the original pressure in California fields is about equivalent to the static head of water below the water table in the outcrop. Structure The Ventura anticline is a prominent feature of the Ventura basin, being traceable on the surface about 17 miles.' The Ventura Avenue field is at the apex of the anticline. It is about one mile wide and five miles long, the major axis lying in an east-west direction. The productive limits cover an area of about 2300 acres. The entire anticline has been severely folded and faulted. The productive portions in particular are broken up by three major thrust faults having a general east-west strike. The resultant four fault blocks are termed the A, B, C, and D blocks, respectively. Certain electric-log intervals are assigned numbers. Fig I is a diagrammatic north-south section of the field near the crest, looking west, and shows three of the four fault blocks. To the west, the upper fault divides into two branches, which define the B block. Wells penetrating a fault may duplicate over 1000 ft of formation. However, the greater fault movement is the strike shift, which is believed to exceed 2500 ft both between the A and C blocks and between the C and D blocks. The location of water is irregular and unpredictable. A few intermediate waters exist, while some strata have more than 2000 ft of productive closure.

Jan 1, 1948

By R. A. Morse, W. O. Keller

The properties of limestone reservoir rocks such as the distribution and degree of continuity of the pore systems, and the relative volumes and permeabilities of the systems making up the complex cause large variations between performance of individual limestone reservoirs and their susceptibility to secondary recovery methods. The effects of these factors on the mechanism of fluid flow cannot be adequately evaluated with presently developed concepts, laboratory data, and geological information. The observance and interpretation of the performance of individual limestone reservoirs provides, at present, the most adequate approach for evaluating the integrated effects upon performance of the many. now immeasurable variations in the properties of limestone reservoirs. INTRODUCTION The development and application of techniques for increasing the efficiency of oil recovery from natural reservoirs is a problem of primary importance to the industry. During the past several years, a great deal of effort has been expended by the technical personnel of the industry toward the improvement of present known methods of oil recovery. and evaluating the factors which control the susceptibility of particular reservoir types to economic application of secondary recovery methods. Providing adequate and accurate laboratory data on the properties of the reservoir rock and its contained fluids. together with good production statistics, are available, methods have been evolved for estimating with reasonable accuracy the performance of an oil reservoir under either continued natural depletion or conditions imposed by introducing additional displacing fluid into the reservoir from an extraneous source through the injection of gas and/or water. The susceptibility of limestone reservoirs to secondary recovery by gas injection is very much dependent upon gas-oil relative permeability relationships for the reservoir in question. In a rock formation in which the porosity is of the intergranular type such as is found in sand stones and some non-fractured dolomites, a representative sample of the pore structure can be obtained in a small core plug. In this type of reservoir, it has been shown that relative permeability data obtained from laboratory experiments can be Properly applied to evaluate the flow relationships actually observed during the depletion of a reservoir. In addition, a good idea of the fraction of the reservoir which will be swept by the injected gas may be obtained from the spacing pattern used and the permeability profile of cored wells. From these data, it has been demonstrated that reliable estimates of performance and recoveries under gas injection operations can be made for reservoirs in which the Porosity is of the intergranular type. Limestone reservoirs on the other hand often present much more complex problems. One reason that the performance of limestone reservoirs is so variable is that there may be, in reality. two or more pore systems, the integrated performance of which will depend upon the physical properties of each system and their inter-relationship. For instance, in a limestone reservoir, the main pore structure, as far as void spaces for storage of hydrocarbons is concerned, may be represented by the intergranular openings of the rock. Usually in limes and dolomites, the intergranular pore openings are very small and the matrix permeabilities extremely low. Often, as in the case of Many dolomite and oolitic lime reservoirs, this is the only pore system, and performance is observed to be very similar to that of a sand stone of similar permeability. However, in the great majority of' the limestone reservoirs, there is present, in addition to the intergranular pore system, a complementary system of openings caused by fracturing or solution.',' The openings in the latter system are usually many times more permeable than the intergranular pore system due to their much larger size, and may contribute almost all the fluid carrying capacity of the formation, even though their volume may be a very small part of the total pore space in the reservoir. Obviously, the performance of such a complex under either primary or secondary control will deend upon the distribution and degree of continuity of both systems, the relative volumes and permeabilities of the

Jan 1, 1949

By R. A. Morse, W. O. Keller

The properties of limestone reservoir rocks such as the distribution and degree of continuity of the pore systems, and the relative volumes and permeabilities of the systems making up the complex cause large variations between performance of individual limestone reservoirs and their susceptibility to secondary recovery methods. The effects of these factors on the mechanism of fluid flow cannot be adequately evaluated with presently developed concepts, laboratory data, and geological information. The observance and interpretation of the performance of individual limestone reservoirs provides, at present, the most adequate approach for evaluating the integrated effects upon performance of the many. now immeasurable variations in the properties of limestone reservoirs. INTRODUCTION The development and application of techniques for increasing the efficiency of oil recovery from natural reservoirs is a problem of primary importance to the industry. During the past several years, a great deal of effort has been expended by the technical personnel of the industry toward the improvement of present known methods of oil recovery. and evaluating the factors which control the susceptibility of particular reservoir types to economic application of secondary recovery methods. Providing adequate and accurate laboratory data on the properties of the reservoir rock and its contained fluids. together with good production statistics, are available, methods have been evolved for estimating with reasonable accuracy the performance of an oil reservoir under either continued natural depletion or conditions imposed by introducing additional displacing fluid into the reservoir from an extraneous source through the injection of gas and/or water. The susceptibility of limestone reservoirs to secondary recovery by gas injection is very much dependent upon gas-oil relative permeability relationships for the reservoir in question. In a rock formation in which the porosity is of the intergranular type such as is found in sand stones and some non-fractured dolomites, a representative sample of the pore structure can be obtained in a small core plug. In this type of reservoir, it has been shown that relative permeability data obtained from laboratory experiments can be Properly applied to evaluate the flow relationships actually observed during the depletion of a reservoir. In addition, a good idea of the fraction of the reservoir which will be swept by the injected gas may be obtained from the spacing pattern used and the permeability profile of cored wells. From these data, it has been demonstrated that reliable estimates of performance and recoveries under gas injection operations can be made for reservoirs in which the Porosity is of the intergranular type. Limestone reservoirs on the other hand often present much more complex problems. One reason that the performance of limestone reservoirs is so variable is that there may be, in reality. two or more pore systems, the integrated performance of which will depend upon the physical properties of each system and their inter-relationship. For instance, in a limestone reservoir, the main pore structure, as far as void spaces for storage of hydrocarbons is concerned, may be represented by the intergranular openings of the rock. Usually in limes and dolomites, the intergranular pore openings are very small and the matrix permeabilities extremely low. Often, as in the case of Many dolomite and oolitic lime reservoirs, this is the only pore system, and performance is observed to be very similar to that of a sand stone of similar permeability. However, in the great majority of' the limestone reservoirs, there is present, in addition to the intergranular pore system, a complementary system of openings caused by fracturing or solution.',' The openings in the latter system are usually many times more permeable than the intergranular pore system due to their much larger size, and may contribute almost all the fluid carrying capacity of the formation, even though their volume may be a very small part of the total pore space in the reservoir. Obviously, the performance of such a complex under either primary or secondary control will deend upon the distribution and degree of continuity of both systems, the relative volumes and permeabilities of the

Jan 1, 1949

By Alton B. Cook, G. B. Spencer, F. P. Bobrowski

In estimating production gas/oil ratios and oil recoveries from reservoirs containing highly volatile oils it is highly important to include condensate that may be recovered from the gas produced from the reservoir. The volume of the hydrocarbon liquid condensed from the production of the solution gas that has been liberated. in some reservoirs may equal or even exceed the volume of recoverable stock-tank oil as estimated by present methods. The usual procedure1, 2, 3 in estimating future reservoir performance includes use of relative permeability data of the reservoir rock to gas and oil and includes material-balance calculations utilizing data on the volume of the reservoir fluids, oil and gas production and reservoir pressure decline, and data on the physical properties of the initial reservoir fluids. The inaccuracy in the procedure results from the false assumption that all of the free or liberated gas that enters the well bore of reservoirs containing highly volatile oils remains in the gaseous phase as it is produced. This paper presents a method for estimating future reservoir performance and oil recoveries based on special labora. tory analyses of reservoir-oil samples and recognition of the additional volume of hydrocarbon liquid that will be recovered at various stages of depletion from a solution.gas.drive reservoir. The method also includes calculations of the volume and composition of the hydrocarbon liquids that can be recovered by processing the produced gas in a natural-gasoline plant. The development of the method resulted from a study of laboratory analyses of reservoir samples and of field data obtained from two reservoirs containing oil of the highly velatile type. Relatively high pressures and temperatures prevail in oil reservoirs discovered at the greater depths of present-day drilling. The contained fluids may have high saturation -Dressures and large volumes of gas in solution. The oils and gases under these conditions may be almost identical in compositions and densities.4,5 Also, engineers have noted that, for a number of oil reservoirs and especially the deeper reservoirs, the API gravity of the stock-tank oil increaees as the production gas/oil ratios increase. They attributed this increase in API gravity of the stock-tank oil to the formation of condensate as the liberated gas in the reservoir is being produced. SOURCE OF DATA FOR CALCULATIONS Subsurface oil samples and well-test data were obtained from the E. Constantin-Lambert Well No. 1 in the Elk City Field, Okla., to demonstrate the need for and a method of calculating future reservoir performance when consideration is given to the recoverable hydrocarbon liquid from the production of solution gas that has been or will be liberated in a reservoir. The Lambert well is located in C, SW 1/4, SW 1/4, Set- 18, T-l0-N, R-20-W, Washita County, Okla. At the time of completion it was on the east edge of the development and Was producing from conglomerate through 30 perforations in the 5 1/2-in. casing at a depth of 9,859 to 9,864 ft. The well Was completed on July 9, 1949, and subsurface oil samples were obtained July 29 and August 1, 1949. Production gas/oil ratio data were obtained during the operation in series of two Separators at high and low-pressures of 314 and 44 psia, respectively, and at an average temperature of approximately 60°F. The flowing bottom-hole pressure at the time of sampling was 3,934 psis. The static bottom-hole pressure was not obtained at the time of sampling, as the well could not be shut in long enough for testing because gas produced from the well was used for fuel at an offset drilling well. However, the initial reservoir pressure was calculated to be 4,364 psia from knowledge of pressure gradients in other wells in the field and the depth of the casing perforations in the Lambert NO. 1 well.

Jan 1, 1951

By F. P. Bobrowski, G. B. Spencer, Alton B. Cook

In estimating production gas/oil ratios and oil recoveries from reservoirs containing highly volatile oils it is highly important to include condensate that may be recovered from the gas produced from the reservoir. The volume of the hydrocarbon liquid condensed from the production of the solution gas that has been liberated. in some reservoirs may equal or even exceed the volume of recoverable stock-tank oil as estimated by present methods. The usual procedure1, 2, 3 in estimating future reservoir performance includes use of relative permeability data of the reservoir rock to gas and oil and includes material-balance calculations utilizing data on the volume of the reservoir fluids, oil and gas production and reservoir pressure decline, and data on the physical properties of the initial reservoir fluids. The inaccuracy in the procedure results from the false assumption that all of the free or liberated gas that enters the well bore of reservoirs containing highly volatile oils remains in the gaseous phase as it is produced. This paper presents a method for estimating future reservoir performance and oil recoveries based on special labora. tory analyses of reservoir-oil samples and recognition of the additional volume of hydrocarbon liquid that will be recovered at various stages of depletion from a solution.gas.drive reservoir. The method also includes calculations of the volume and composition of the hydrocarbon liquids that can be recovered by processing the produced gas in a natural-gasoline plant. The development of the method resulted from a study of laboratory analyses of reservoir samples and of field data obtained from two reservoirs containing oil of the highly velatile type. Relatively high pressures and temperatures prevail in oil reservoirs discovered at the greater depths of present-day drilling. The contained fluids may have high saturation -Dressures and large volumes of gas in solution. The oils and gases under these conditions may be almost identical in compositions and densities.4,5 Also, engineers have noted that, for a number of oil reservoirs and especially the deeper reservoirs, the API gravity of the stock-tank oil increaees as the production gas/oil ratios increase. They attributed this increase in API gravity of the stock-tank oil to the formation of condensate as the liberated gas in the reservoir is being produced. SOURCE OF DATA FOR CALCULATIONS Subsurface oil samples and well-test data were obtained from the E. Constantin-Lambert Well No. 1 in the Elk City Field, Okla., to demonstrate the need for and a method of calculating future reservoir performance when consideration is given to the recoverable hydrocarbon liquid from the production of solution gas that has been or will be liberated in a reservoir. The Lambert well is located in C, SW 1/4, SW 1/4, Set- 18, T-l0-N, R-20-W, Washita County, Okla. At the time of completion it was on the east edge of the development and Was producing from conglomerate through 30 perforations in the 5 1/2-in. casing at a depth of 9,859 to 9,864 ft. The well Was completed on July 9, 1949, and subsurface oil samples were obtained July 29 and August 1, 1949. Production gas/oil ratio data were obtained during the operation in series of two Separators at high and low-pressures of 314 and 44 psia, respectively, and at an average temperature of approximately 60°F. The flowing bottom-hole pressure at the time of sampling was 3,934 psis. The static bottom-hole pressure was not obtained at the time of sampling, as the well could not be shut in long enough for testing because gas produced from the well was used for fuel at an offset drilling well. However, the initial reservoir pressure was calculated to be 4,364 psia from knowledge of pressure gradients in other wells in the field and the depth of the casing perforations in the Lambert NO. 1 well.

Jan 1, 1951

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By Frank G. Miller

This report presents developments of fundamental equations for describing the flow and thermodynamic behavior of two-phase single-component fluids moving under steady conditions through porous media. Many of the theoretical considerations upon which these equations are premised have received little or no attention in oil-reservoir fluid-flow research. The significance of the underlying flow theory in oil-producing operations is indicated. In particular, the theoretical analysis pertains to the steady, adiabatic, macroscopically linear, two-phase flow of a single-component fluid through a horizontal column of porous medium. It is considered that the test fluid enters the upstream end of the column while entirely in the liquid state, moves downstream an appreciable distance, begins to vaporize, and then moves through the remainder of the column as a gas-liquid mixture. The problem posed is to find the total weight rate of flow and the pressure distribution along the column for a given inlet pressure and temperature, a given exit pres5ure or temperature and given characteristics of the test fluid and porous medium. In developing the theory, gas-liquid interfacial phenomena are treated. phase equilibrium is assumed and previous theoretical work of other investigators of the problem is modified. Laboratory experiments performed with specially designed apparatus. in which propane is used as the test fluid, substantiate the theory. The apparatus. materials and experimental procedure are described. Comparative experimental and theoretical results are presented and discussed. It is believed that the research findings contributed in this * paper should not only lead to a better understanding of oil-reservoir behavior, but also should be suggective in regard to future research in this field of study. INTRODUCTION In recent years much time and effort has been consumed in both theoretical and experimental studies of the static and . dvnamic behavior of oil-reservoir fluids in porous rocks. Although lack of sufficient basic oil-field data, principally concerning the properties and characteristics of reservoir rocks and fluids, largely precludes quantitative application of research results to oil-field problems, qualitative application has become common practice. In effect. oil-reservoir engineering research is serving as a firm foundation for oil-field development and production practices leading to increased economic recoveries of petroleum. This province of research. however, still poses many perplexing problems. The thermodynamic behavior of two-phase fluids moving through porous media constitutes one facet of reservoir-fluid-flow research that has not received the attention it deserves. This report embodies a theoretical discussion of this subject and a description of a series of related laboratory experiments. The significance of the problem to oil field operations is indicated but in articular the report centers around a theory and method for analyzing the steady. macroscopically linear, two-phase flow of a fluid (a single molecular species) through a horizontal column of porous medium. For simplicity in showing how the thermodynamic behavior of two-phase fluids moving through porous media affects oil-reservoir performance problems, attention is focused temporarily on a particular well producing petroleum from an idealized water-free solution-gas drive reservoir, the reservoir rock being a horizontal, thin, fairly homogeneous sandstone of large areal extent confined between two impermeable strata. The flowing hydrocarbon fluid is considered to exist entirely as a Iiquid at points in the reservoir remote from the well; however. the decline in fluid pressure in the direction of the well causes vaporization of the hydrocarbon to begin at a radial distance r from the well. Upstream from r the fluid moves entirely as a liquid and downstream from r it moves either entirely as a gas or as a gas-liquid mixture depending on the properties of the hydrocarbon and on the thermodynamic process it follows during flow. The distance r would be variable under transient flow conditions. but for purposes of analysis the flow is considered to l~e steady at the particular instant of observation during the flowing life of the well of interest. If the flow were isothermal and the hydrocarbon a pure substance, the fluid would be entirely gaseous downstream from r. Thus, this isothermal flow process for a pure substance would require that the heat of vaporization be supplied at r. over zero length of porous medium, at the precise rate necessary to maintain the constant temperature. This means that the solid matrix of the porous medium (reservoir rock) and the surroundings (impermeable strata confining the reservoir rock) would have to serve as infinite heat sources. Heat-transfer requirements would be somewhat less severe for the isothermal flow of a multicorn-ponent hydrocarbon as bubble and dew points at the same temperature correspond to different pressures. In this instance isothermal conditions would be sustained without complete vaporization of the fluid over zero length of porous medium. Nevertheless. as the flow is in the direction of decreasing

Jan 1, 1951

By John C. Calhoun, Raymond G. Loper

Theoretical calculations for the decline of pressure and the variation of instantaneous producing gas-oil ratio with increased cumulative production have been made for reservoir systems under various producing drawdown values and for various spacings. These variables have been included by a modification of previously Published techniques. This consists essentially of utilizing a radial system flowing gas and oil in a succession of steady state calculations. The results of the calculations do not show any variation in the predicted behavior of the internal gas drive reservoir when either the drawdown or the spacing are changed. The prediction of performance on an internal gas drive reservoir has been presented by various authors. ',"' These predictions are in the form of a pressure decline and an instantaneous producing gas-oil ratio as a function of cumulative oil withdrawal. In making these predictions a basic assumption has been that the saturation of the reservoir is uniform throughout at any time, or that the pressure differential imposed on the reservoir system is zero. Because of these assumptions the validity of such predictions has been questioned. Their application to actual systems, where saturations are not uniform and where producing differentials exist, has been a hazardous procedure. The authors cited have used different methods of approach to the derivation of equations for making their predictions and for arriving at a solution of both equations, but basically the same relationships are utilized in each case. In all instances the instantaneous producing gas-oil ratio is calculated from the equation: In utilizing this equation an average reservoir pressure and an average reservoir saturation must be known, the former to define ß, v, s, and uo/ug and the latter to define kg/ko. Predictions can be made, therefore, only for the conditions of a uniform reservoir saturation and a uniform reservoir pressure. This restriction of requiring a uniform oil saturation can be resolved by applying two-phase steady state flow for the radial system to the reservoir's history. Radial steady state flow is defined when the ratio of phases flowing,

Jan 1, 1949

By John C. Calhoun, Raymond G. Loper

Theoretical calculations for the decline of pressure and the variation of instantaneous producing gas-oil ratio with increased cumulative production have been made for reservoir systems under various producing drawdown values and for various spacings. These variables have been included by a modification of previously Published techniques. This consists essentially of utilizing a radial system flowing gas and oil in a succession of steady state calculations. The results of the calculations do not show any variation in the predicted behavior of the internal gas drive reservoir when either the drawdown or the spacing are changed. The prediction of performance on an internal gas drive reservoir has been presented by various authors. ',"' These predictions are in the form of a pressure decline and an instantaneous producing gas-oil ratio as a function of cumulative oil withdrawal. In making these predictions a basic assumption has been that the saturation of the reservoir is uniform throughout at any time, or that the pressure differential imposed on the reservoir system is zero. Because of these assumptions the validity of such predictions has been questioned. Their application to actual systems, where saturations are not uniform and where producing differentials exist, has been a hazardous procedure. The authors cited have used different methods of approach to the derivation of equations for making their predictions and for arriving at a solution of both equations, but basically the same relationships are utilized in each case. In all instances the instantaneous producing gas-oil ratio is calculated from the equation: In utilizing this equation an average reservoir pressure and an average reservoir saturation must be known, the former to define ß, v, s, and uo/ug and the latter to define kg/ko. Predictions can be made, therefore, only for the conditions of a uniform reservoir saturation and a uniform reservoir pressure. This restriction of requiring a uniform oil saturation can be resolved by applying two-phase steady state flow for the radial system to the reservoir's history. Radial steady state flow is defined when the ratio of phases flowing,

Jan 1, 1949

By M. Muskat

Calculations are reported on the differential sensitivity of the updip invasion of oil strata of varving permeability to the driving pressure differential. It is assumed that the water-oil interfaces advance with sharp fronts, or that the microscopic displacement efficiency is independent of rate and capillary pressure effects. It is found that, under such conditions, limitations of withdrawal rates will not greatly inhibit the "fingering" and bypassing tendency through high permeability strata unless the differential fluid head across the original oil column is of the order of or exceeds about 80 per cent of the driving pressure differential. In practice, such restrictions will be feasible only for oil reservoirs and aquifers of high permeability and dip, but may develop automatically under combined gas injection and water drive operations. INTRODUCTION A commonly expressed view regarding the intrusion of edge-waters into oil producing formations is that the geometry of such advance is rate sensitive. Specifically, it has been suggested that high rates of advance, stimulated by rapid withdrawals, will lead to "fingering" and an irregular type of invasion, whereas at low withdrawal rates the water encroachment will be more uniform. Two factors tend to support this view. One is the resultant effect of capillary pressure and gravity gradients in the displacement processes' involved in water intrusion, which are magnified at low rates of flow so as to improve the recovery efficiency. The other is the direct retarding effect of the rising water head as it advances upslope into the producing area. Capillary pressure forces give rise to a rate sensitivity of the oil recovery by water displacement in uniform strata as well as differential effects in non-uniform formations. These are basically independent of the effect of gravity and would also occur in horizontal beds or when the oil and water have the same density. Unfortunately, however, the fundamental equation describing the displacement process under the action of capillary pressures can be solved only by numerical or graphical procedures, and moreover the solutions are sensitive to the character of the capillary pressure and relative permeability curves.* On the other hand, the direct effect of gravity can be given a formal analytical solution if the simplifying assumption is introduced that the water advances with sharp fronts in the individual uniform strata. It depends on the absolute permeabilities of the water invaded zones and hence results in a rate sensitivity of the differential invasion in stratified media. Although a tieatment of this factor alone will not give a complete evaluation of the effect of rate on water intrusion in non-uniform pays, it should provide at least a semiquantitative measure of the sensitivity of "fingering" to withdrawal rate. Such a treatment will be presented in the following sections. GENERAL THEORY The basic element of the theory is the history of water advance updip in a uniform stratum (Fig. 1). In contrast to the assumption of constant flow rate, generally made in the analysis of displacement processes, we shall assume here that

Jan 1, 1951

By M. Muskat

Calculations are reported on the differential sensitivity of the updip invasion of oil strata of varving permeability to the driving pressure differential. It is assumed that the water-oil interfaces advance with sharp fronts, or that the microscopic displacement efficiency is independent of rate and capillary pressure effects. It is found that, under such conditions, limitations of withdrawal rates will not greatly inhibit the "fingering" and bypassing tendency through high permeability strata unless the differential fluid head across the original oil column is of the order of or exceeds about 80 per cent of the driving pressure differential. In practice, such restrictions will be feasible only for oil reservoirs and aquifers of high permeability and dip, but may develop automatically under combined gas injection and water drive operations. INTRODUCTION A commonly expressed view regarding the intrusion of edge-waters into oil producing formations is that the geometry of such advance is rate sensitive. Specifically, it has been suggested that high rates of advance, stimulated by rapid withdrawals, will lead to "fingering" and an irregular type of invasion, whereas at low withdrawal rates the water encroachment will be more uniform. Two factors tend to support this view. One is the resultant effect of capillary pressure and gravity gradients in the displacement processes' involved in water intrusion, which are magnified at low rates of flow so as to improve the recovery efficiency. The other is the direct retarding effect of the rising water head as it advances upslope into the producing area. Capillary pressure forces give rise to a rate sensitivity of the oil recovery by water displacement in uniform strata as well as differential effects in non-uniform formations. These are basically independent of the effect of gravity and would also occur in horizontal beds or when the oil and water have the same density. Unfortunately, however, the fundamental equation describing the displacement process under the action of capillary pressures can be solved only by numerical or graphical procedures, and moreover the solutions are sensitive to the character of the capillary pressure and relative permeability curves.* On the other hand, the direct effect of gravity can be given a formal analytical solution if the simplifying assumption is introduced that the water advances with sharp fronts in the individual uniform strata. It depends on the absolute permeabilities of the water invaded zones and hence results in a rate sensitivity of the differential invasion in stratified media. Although a tieatment of this factor alone will not give a complete evaluation of the effect of rate on water intrusion in non-uniform pays, it should provide at least a semiquantitative measure of the sensitivity of "fingering" to withdrawal rate. Such a treatment will be presented in the following sections. GENERAL THEORY The basic element of the theory is the history of water advance updip in a uniform stratum (Fig. 1). In contrast to the assumption of constant flow rate, generally made in the analysis of displacement processes, we shall assume here that

Jan 1, 1951

By C. C. Miller, C. A. Hutchinson, A. B. Dyes

This paper presents a simple and practical method for the estimation of effective permeability and reservoir pressures from the rise in bottom hole pressure when a well is shut in. The equations on which the method is based consider a stabilized well producing from a uniform formation when flow is shut off at the sand face followed by the unsteady state flow of a compressible liquid from regions far from a well to points closer in during the build-up period. An approximation for extending the method for two-phase flow in the reservoir is also presented. In order to compare the effects of extremes in the conditions existing at the external boundary of the reservoir, two general equations defining the build-up characteristics of the reservoir are shown: first, for a reservoir with constant pressure maintained at the radius of drainage, and second, for a reservoir with no influx over the radius of drainage. These equations define the build-up characteristics for the shut-in well as functions of time, the permeability and porosity of the drainage area, the viscosity and compressibility of the fluid flowing, the production rate prior to shut-in, and the radius of drainage of the well. When a well is shut in at the surface, rather than at the sand face, flow will continue into the well bore after shut-in due to the compressibility of the fluids in the bore. The effect upon the build-up characteristics of this flow into the well after shut-in has been studied by means of the electrical analyzer. From the basic relationships and consideration of the limitations due to continued flow after shut-in, methods have been developed for the estimation of the effective permeability of an area from the plot of the build-up characteristics of the well producing that area. Likewise, equations are presented for the estimation of the reservoir pressure from an early portion of the build-up curve. By means of the electrical analyzer, studies have been made concerning the variations in the build-up characteristics resulting from damaged or improved permeability in the immediate vicinity of the well bore. These studies show that the permeability estimated from the build-up curves represents the average effective permeability of the majority of the drainage area and that the permeability in the immediate vicinity of the well does not affect this estimate. Since the major portion of the drawdown is in the immediate vicinity of the well, variations in the permeability of this area greatly affect the productivity of the well as expressed by the productivity index. From pressure build-up and productivity index tests the ratio of the permeability of some arbitrarily specified area immediately surrounding the well and the effective permeability in the majority of the drainage area can be computed. This ratio is a measure of any damage to the well incurred in drilling or reworking and likewise any benefits as a result of remedial measures. In build-up tests and many other tests that are made on a producing well it is at least desirable, if not absolutely necessary, that the well be stabilized prior to testing. A method is presented here for relating the time required to stabilize a well and the reservoir and fluid properties. An equation is also presented for approximation of the length of shut-in time required to obtain sufficient build-up data for the estimation of permeability and reservoir pressure.

Jan 1, 1950