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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

By Howard B. Bradley, Charles F. Weinaug

The phase behavior of a naturally occurring hydrocarbon system whose critical temperature is near the reservoir temperature has been described. The same volume per cent liquid was observed for the firkt time at three different pressures for isotherms immediately below the critical temperature. The shapes of the isothermal equilibrium constant curves necessary to predict this phenomena are discussed and illustrated. INTRODUCTION The phase behavior of a number of hydrocarbon systems has been reported; however, very little data are available on natural occurring hydrocarbon systems whose critical temperature is near the reservoir temperature. This appeared to be the case for the fluid studied here; therefore the pressure-volume-temperature data for this system were determined for preqentation. METHOD The PVT data were obtained with equipment similar to hat described by Weinaug and Katz,1 consisting principally of a two-section, double-windowed gauge mounted in a conktant temperature air bath. The procedure followed was essentially that used by Katz and Kurata5 except that a cathetom-eter, reading direct to 0.01 cm, was used to determine the height of each extreme phase limit. The system studied was formed by recombining -.vapor and liquid samples from the first stage separator of the well. Portions of these samples were displaced with mercury into the cell which had previously been filled with mercury. A predetermined amount of the liquid sample was introduced, while an excess of vapor was admitted. The resulting mixture was brought to equilibrium at the condition of the separator during sampling. By adding mercury to maintain the pressure, enough vapor was displaced to give a gas/oil ratio within the cell equal to that produced by the separator at the time of sampling. The remaining material was then considered to be equivalent to the reservoir fluid. An analysis of material in the cell, computed from analysis of vapor and liquid samples and the separator gas/oil ratio. is given in Table I. Table I — Composition of Hydrocarbon System Component Mole Per Cent Carbon Dioxide 0.13 Nitrogen 0.76 Methane 53.91 Ethane 14.20 Propane 9.64 Iso Butane 1.25 Normal Butane 4.29 Iso Pentane 1.12 Normal Pentane 1.87 Hexane 2.72 Heptanes + 10.11 hloleculal. Weight of Heptanes + 178.50

Jan 1, 1951

By Howard B. Bradley, Charles F. Weinaug

The phase behavior of a naturally occurring hydrocarbon system whose critical temperature is near the reservoir temperature has been described. The same volume per cent liquid was observed for the firkt time at three different pressures for isotherms immediately below the critical temperature. The shapes of the isothermal equilibrium constant curves necessary to predict this phenomena are discussed and illustrated. INTRODUCTION The phase behavior of a number of hydrocarbon systems has been reported; however, very little data are available on natural occurring hydrocarbon systems whose critical temperature is near the reservoir temperature. This appeared to be the case for the fluid studied here; therefore the pressure-volume-temperature data for this system were determined for preqentation. METHOD The PVT data were obtained with equipment similar to hat described by Weinaug and Katz,1 consisting principally of a two-section, double-windowed gauge mounted in a conktant temperature air bath. The procedure followed was essentially that used by Katz and Kurata5 except that a cathetom-eter, reading direct to 0.01 cm, was used to determine the height of each extreme phase limit. The system studied was formed by recombining -.vapor and liquid samples from the first stage separator of the well. Portions of these samples were displaced with mercury into the cell which had previously been filled with mercury. A predetermined amount of the liquid sample was introduced, while an excess of vapor was admitted. The resulting mixture was brought to equilibrium at the condition of the separator during sampling. By adding mercury to maintain the pressure, enough vapor was displaced to give a gas/oil ratio within the cell equal to that produced by the separator at the time of sampling. The remaining material was then considered to be equivalent to the reservoir fluid. An analysis of material in the cell, computed from analysis of vapor and liquid samples and the separator gas/oil ratio. is given in Table I. Table I — Composition of Hydrocarbon System Component Mole Per Cent Carbon Dioxide 0.13 Nitrogen 0.76 Methane 53.91 Ethane 14.20 Propane 9.64 Iso Butane 1.25 Normal Butane 4.29 Iso Pentane 1.12 Normal Pentane 1.87 Hexane 2.72 Heptanes + 10.11 hloleculal. Weight of Heptanes + 178.50

Jan 1, 1951

By T. E. Ockershauser

The Southwest Antioch Oil Field located in T2&3N - R2&3W, Garvin County, Okla., was discovered in February, 1946, by The Globe Oil & Refining Co. and The Vickers Petroleum Co. at their Melinda Gibson No. 1. Oil production was encountered at a depth of 6,525 ft in 14 ft of lower Pennsyl-vanian sandstone. The producing sand, locally called the ."Gibson" or "Third Deese," is a sand bar deposit strung along the west flank of the Pauls Valley uplift in a northwest-southeast direction. The oil reservoir is defined to the east by the edge of sand deposition along the uplift and to the west by the gradation of sand into shale. Within the Antioch Unit, the sand dips from 150 to 400 ft per mile southwesterly and has a pay thickness varying from 10 to 55 ft and averaging 28 ft. Several areas of Gibson production have been developed, including the Katie pool on the south, the Elmore Area of the Southwest Antioch Gibson Sand pool. the Southwest Antioch Gibson Sand pool proper, the Southwest Maysville pool and the New Hope pool on the north. Production extends over a belt 22 miles long by about two miles wide and is continuous except into the Katie and New Hope pools. It appears that drilling will soon prove these intervening areas productive. To March 1, 1950, approximately 18,000 acres have been developed with 450 Gibson wells. It is likely this count will ultimately reach 32.000 acres with 800 wells. RESERVOIR The natural production of oil from the Gibson reservoir is primarily due to solution gas expansion though gravity also plays a part. There is no indication of water drive or evidence that an initial gas cap existed. Gibson oil has a stock tank gravity of 43" API and was saturated at the original reservoir pressure of 2.925 psi. It contained 1,3440 cu ft of gas per bbl in solution and had a high shrinkage of 70 per cent. Connate water amounts to 15 per cent. Reservoir temperature is 130°F. Porosity averages 15.5 per cent and permeability ranges from less than one md to over 1.000. Based on meacurement of 400 core plugs from 15 wells, 78 per cent of the permeabilities fell within the 10 to 1,000 md bracket and averaged l67. Primary oil recovery is estimated at 140 bbl per acre-ft or 22 million bbl for the present 137-tract unit. Due to unitization

Jan 1, 1951

By T. E. Ockershauser

The Southwest Antioch Oil Field located in T2&3N - R2&3W, Garvin County, Okla., was discovered in February, 1946, by The Globe Oil & Refining Co. and The Vickers Petroleum Co. at their Melinda Gibson No. 1. Oil production was encountered at a depth of 6,525 ft in 14 ft of lower Pennsyl-vanian sandstone. The producing sand, locally called the ."Gibson" or "Third Deese," is a sand bar deposit strung along the west flank of the Pauls Valley uplift in a northwest-southeast direction. The oil reservoir is defined to the east by the edge of sand deposition along the uplift and to the west by the gradation of sand into shale. Within the Antioch Unit, the sand dips from 150 to 400 ft per mile southwesterly and has a pay thickness varying from 10 to 55 ft and averaging 28 ft. Several areas of Gibson production have been developed, including the Katie pool on the south, the Elmore Area of the Southwest Antioch Gibson Sand pool. the Southwest Antioch Gibson Sand pool proper, the Southwest Maysville pool and the New Hope pool on the north. Production extends over a belt 22 miles long by about two miles wide and is continuous except into the Katie and New Hope pools. It appears that drilling will soon prove these intervening areas productive. To March 1, 1950, approximately 18,000 acres have been developed with 450 Gibson wells. It is likely this count will ultimately reach 32.000 acres with 800 wells. RESERVOIR The natural production of oil from the Gibson reservoir is primarily due to solution gas expansion though gravity also plays a part. There is no indication of water drive or evidence that an initial gas cap existed. Gibson oil has a stock tank gravity of 43" API and was saturated at the original reservoir pressure of 2.925 psi. It contained 1,3440 cu ft of gas per bbl in solution and had a high shrinkage of 70 per cent. Connate water amounts to 15 per cent. Reservoir temperature is 130°F. Porosity averages 15.5 per cent and permeability ranges from less than one md to over 1.000. Based on meacurement of 400 core plugs from 15 wells, 78 per cent of the permeabilities fell within the 10 to 1,000 md bracket and averaged l67. Primary oil recovery is estimated at 140 bbl per acre-ft or 22 million bbl for the present 137-tract unit. Due to unitization

Jan 1, 1951

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By Fred H. Poettmann

The vaporization characteristics of carbon dioxide in a League City natural gas - Billings crude oil system were studied at three temperatures, 38°. 120°, and 202°F and for pressures ranging from 600 to 8,500 psi. Variation of carbon dioxide concentration up to 12 mole per cent in the composite showed no effect on the equilibrium vaporization ratios (K values) of the hydrocarbon constituents or on the K value of carbon dioxide itself. It was shown that carbon dioxide is more soluble in crudes than in distillates which is contrary to the behavior of methane. A working chart of carbon dioxide K values is presented. INTRODUCTION The study of the equilibrium vaporization ratios of mixtures of paraffin hydrocarbons has been rather thorough.2,6,7,8,9 In the past few years considerable attention has been paid to the vaporization characteristics of the so-called noncondensable gases such as nitrogen, carbon dioxide, and hydrogen sulfide in mixtures of hydrocarbons. since they usually occur to some extent in most crude oils and natural gases.1,3,4,5 Knowledge of this behavior is useful to both the production and refining phases of the petroleum industry. This paper reports the equilibrium vaporization ratios (K's) of carbon dioxide in a mixture of League City natural gas and Billings crude oil, and compares them to those obtained in a natural gas-distillate system. The equilibrium vaporization ratios for the hydrocarbon components in this system had previously been studied by Roland.' In addition to the determination of the K values for carbon dioxide, the K values for methane and ethane were also determined in order to observe what effect, if any, the presence of carbon dioxide had on these K values. The concentration of carbon dioxide was also varied in order to observe the effect of this variable on the carbon dioxide K values. EXPERIMENTAL PROCEDURE The apparatus used in this study cotlsisted of a stainless steel equilibrium cell of about 2 liters capacity. The cell was mounted on trunions permitting rocking in a thermostatically controlled oil bath. Two high pressure valves fitted with steel tubing were mounted on the top of the cell. one was used for sampling the equilibrium gas phase and the other for sampling the equilibrium liquid phase by means of an induction tube within the cell. Stainless steel tubing from the bottom of the cell led to a mercury reservoir and manifold which was connected to a free-piston type pressure gauge manufac- lured by the American Instrunlent Ctr. and to a volumetric. putrip. The temperature of the oil bath was measured by means of a ralibrated mercury-in-glass thermometer. The recorded temperatures are believed to be accurate to ±0.5 °F. The pressures are correct to 22 psi. The crude oil used in this study was stock tank oil obtained from the Wilcox formation in the Billings Field, Noble County. Okla. The natural gas was obtained from the League City Field. Galveston County, Tex. The oil was treated with anhydrous calcium sulfate in order to remove the last traces of water. To insure a supply of constant composition gas at room temperature the cylinders of League City gas were cooled to about 30°F, inverted, and the condensed liquid was allowed to drain from the cylinders. The analysis of the gas and crude are tabulated in Table I. The carbon dioxide came from Pure Carbonic, Inc., and was .stated to have a purity of 99.5 per cent or better. The procedure used to obtain samples of the equilibrium liquid and vapor was similar to that employed by others making use of the rocking type equilibrium cell.6,7,8 The equilibrium cell was evacuated and calculated quantities of carbon dioxide, natural gas, and crude oil were charged to the cell to the desired pressure. In charging the equilibrium cell an attempt was made to maintain the ratio of the natural gas to crude oil as close as possible to that employed by Roland. After the cell was charged, samples of

Jan 1, 1951

By Fred H. Poettmann

The vaporization characteristics of carbon dioxide in a League City natural gas - Billings crude oil system were studied at three temperatures, 38°. 120°, and 202°F and for pressures ranging from 600 to 8,500 psi. Variation of carbon dioxide concentration up to 12 mole per cent in the composite showed no effect on the equilibrium vaporization ratios (K values) of the hydrocarbon constituents or on the K value of carbon dioxide itself. It was shown that carbon dioxide is more soluble in crudes than in distillates which is contrary to the behavior of methane. A working chart of carbon dioxide K values is presented. INTRODUCTION The study of the equilibrium vaporization ratios of mixtures of paraffin hydrocarbons has been rather thorough.2,6,7,8,9 In the past few years considerable attention has been paid to the vaporization characteristics of the so-called noncondensable gases such as nitrogen, carbon dioxide, and hydrogen sulfide in mixtures of hydrocarbons. since they usually occur to some extent in most crude oils and natural gases.1,3,4,5 Knowledge of this behavior is useful to both the production and refining phases of the petroleum industry. This paper reports the equilibrium vaporization ratios (K's) of carbon dioxide in a mixture of League City natural gas and Billings crude oil, and compares them to those obtained in a natural gas-distillate system. The equilibrium vaporization ratios for the hydrocarbon components in this system had previously been studied by Roland.' In addition to the determination of the K values for carbon dioxide, the K values for methane and ethane were also determined in order to observe what effect, if any, the presence of carbon dioxide had on these K values. The concentration of carbon dioxide was also varied in order to observe the effect of this variable on the carbon dioxide K values. EXPERIMENTAL PROCEDURE The apparatus used in this study cotlsisted of a stainless steel equilibrium cell of about 2 liters capacity. The cell was mounted on trunions permitting rocking in a thermostatically controlled oil bath. Two high pressure valves fitted with steel tubing were mounted on the top of the cell. one was used for sampling the equilibrium gas phase and the other for sampling the equilibrium liquid phase by means of an induction tube within the cell. Stainless steel tubing from the bottom of the cell led to a mercury reservoir and manifold which was connected to a free-piston type pressure gauge manufac- lured by the American Instrunlent Ctr. and to a volumetric. putrip. The temperature of the oil bath was measured by means of a ralibrated mercury-in-glass thermometer. The recorded temperatures are believed to be accurate to ±0.5 °F. The pressures are correct to 22 psi. The crude oil used in this study was stock tank oil obtained from the Wilcox formation in the Billings Field, Noble County. Okla. The natural gas was obtained from the League City Field. Galveston County, Tex. The oil was treated with anhydrous calcium sulfate in order to remove the last traces of water. To insure a supply of constant composition gas at room temperature the cylinders of League City gas were cooled to about 30°F, inverted, and the condensed liquid was allowed to drain from the cylinders. The analysis of the gas and crude are tabulated in Table I. The carbon dioxide came from Pure Carbonic, Inc., and was .stated to have a purity of 99.5 per cent or better. The procedure used to obtain samples of the equilibrium liquid and vapor was similar to that employed by others making use of the rocking type equilibrium cell.6,7,8 The equilibrium cell was evacuated and calculated quantities of carbon dioxide, natural gas, and crude oil were charged to the cell to the desired pressure. In charging the equilibrium cell an attempt was made to maintain the ratio of the natural gas to crude oil as close as possible to that employed by Roland. After the cell was charged, samples of

Jan 1, 1951

By Joseph Fry, Ralph H. Espach

In the spring of 1943, when it was evident that the Tensleep bandstone in the Elk Basin Field, Wyoming and Montana, held a large reserve of petroleum, Bureau of Mines engineers obtained samples of oil from the bottom of nine wells and analyzed them for such physical characteristics as the volumes. of gas in solution. saturation pressures or bubble points, shrinkage in volume caused by the release of gas from solution, expansion of the oil with decrease in pressure, and other related properties. The composition of the gas in solution in the oil was studied. The pressures and temperatures existing in the reservoir and the productivity characteristics of the oil wells were determined. The data obtained indicate that the oil in the Tensleep Reservoir of the Elk Basin Field has unusually varying physiral characteristics, such as a saturation pressure of 1,250 psia and 490 cu ft of gas in solultion in a barrel of oil at the crest of the structure and a saturation pressure of 530 psia and 134 cu ft of gas in solution in a barrel of oil low on the flanks. The hydrogen sulfide content of the gas in solution in the oil varies from 18 per cent for oil on the crest to 5 per cent for oil low on the flanks of the structure. Of even greater significance is the fact that these and other variable characteristics of the reservoir oil are related to the position of the oil in the structure. Many geologists and petroleum engineers have considered that all the oil in a petroleum reservoir has rather uniform physical characteristics and that equilibrium conditions prevailed in all underground accumulations of oil and gas; that such is not always so is borne out by the results of the study by the writers. INTRODUCTION The Rocky Mountain region is one in which may be found striking examples of the unusual in oil and gas accumulations, as is evident from the following: The high helium content (7.6 per cent) of the gas in the Ouray-Leadville limestone sequence in the Rattlesnake Field, New Mexico, and gases of similar helium content in other fields; 50" to 55' API gravity distillate in solution in carbon dioxide gas and recoverable through retrograde condensation, in the North McCallum Field, Colorado; the occurrence of gas, oil, or both in closely related structures contrary to the usual concepts of gravimetric segregation: the accumulation of gas and/or oil in structures closely related to other structures that apparently are more favorable but do not contain oil or gas accumulations; the high hydrogen sulfide content (as high as 42 per cent) of the gas associated with oil in some fields in the Big Horn Basin, Wyoming; and the wide range of fluid chararteristics found in the Elk Basin reservoir. Elk Basin, an interesting old oil field that has been producing oil from the Frontier formation since 1915, is situated in a highly eroded basin resulting from the erosion of the crest of an anticline and some of the underlying softer shales. The field came back into national prominence during 1943 when it became known that it was the largest single reserve of new oil discovered in the United States that year. The Tensleep sandstone was found to contain oil in November. 1942, when a well drilled to a depth of 4,538 ft (44 ft into the Tensleep sandstone) flowed oil at the rate of 2,500 B/D. By the end of 1949, 137 oil-producing wells and five dry holes had been drilled, and approximately 32 million bbl of oil had been produced. Approximately 6,000 acres may be considered productive of oil in the Tensleep Reservoir, and estimates of the oil that will be produced average 200 million bbl. The Tensleep Reservoir has further interest because it ha-greater closure than any oil field in the Rocky Mountain region; the closure of the Elk Basin anticline is variously estimated at 5.000 to 10,000 ft. of which the top 2.00 ft of the structure contained oil. SUBSURFACE OIL SAMPLING Fig. 1 is a structural map of the Elk Basin Tensleep Reservoir, on which the nine wells used in this study and the numbers correvponding to the well designations hereafter referred to are shown. Wells 1. 2, 3, 4, and 8 were tested and sampled during October and November. 1943. and Wells 5, 6. 7, and 9 during June and July, 1944. An electromagnetic type sampler developed by the Bureau of Mines and described by Grandone and Cook' was used in obtaining the subsurface oil samples. As the wells were tubed nearly to bottom, the sampler was run as far as possible in the tubing hut never below the top perforations. The following procedure was used in testing and sampling the wells: A well was shut in for at least three days, after

Jan 1, 1951

By Joseph Fry, Ralph H. Espach

In the spring of 1943, when it was evident that the Tensleep bandstone in the Elk Basin Field, Wyoming and Montana, held a large reserve of petroleum, Bureau of Mines engineers obtained samples of oil from the bottom of nine wells and analyzed them for such physical characteristics as the volumes. of gas in solution. saturation pressures or bubble points, shrinkage in volume caused by the release of gas from solution, expansion of the oil with decrease in pressure, and other related properties. The composition of the gas in solution in the oil was studied. The pressures and temperatures existing in the reservoir and the productivity characteristics of the oil wells were determined. The data obtained indicate that the oil in the Tensleep Reservoir of the Elk Basin Field has unusually varying physiral characteristics, such as a saturation pressure of 1,250 psia and 490 cu ft of gas in solultion in a barrel of oil at the crest of the structure and a saturation pressure of 530 psia and 134 cu ft of gas in solution in a barrel of oil low on the flanks. The hydrogen sulfide content of the gas in solution in the oil varies from 18 per cent for oil on the crest to 5 per cent for oil low on the flanks of the structure. Of even greater significance is the fact that these and other variable characteristics of the reservoir oil are related to the position of the oil in the structure. Many geologists and petroleum engineers have considered that all the oil in a petroleum reservoir has rather uniform physical characteristics and that equilibrium conditions prevailed in all underground accumulations of oil and gas; that such is not always so is borne out by the results of the study by the writers. INTRODUCTION The Rocky Mountain region is one in which may be found striking examples of the unusual in oil and gas accumulations, as is evident from the following: The high helium content (7.6 per cent) of the gas in the Ouray-Leadville limestone sequence in the Rattlesnake Field, New Mexico, and gases of similar helium content in other fields; 50" to 55' API gravity distillate in solution in carbon dioxide gas and recoverable through retrograde condensation, in the North McCallum Field, Colorado; the occurrence of gas, oil, or both in closely related structures contrary to the usual concepts of gravimetric segregation: the accumulation of gas and/or oil in structures closely related to other structures that apparently are more favorable but do not contain oil or gas accumulations; the high hydrogen sulfide content (as high as 42 per cent) of the gas associated with oil in some fields in the Big Horn Basin, Wyoming; and the wide range of fluid chararteristics found in the Elk Basin reservoir. Elk Basin, an interesting old oil field that has been producing oil from the Frontier formation since 1915, is situated in a highly eroded basin resulting from the erosion of the crest of an anticline and some of the underlying softer shales. The field came back into national prominence during 1943 when it became known that it was the largest single reserve of new oil discovered in the United States that year. The Tensleep sandstone was found to contain oil in November. 1942, when a well drilled to a depth of 4,538 ft (44 ft into the Tensleep sandstone) flowed oil at the rate of 2,500 B/D. By the end of 1949, 137 oil-producing wells and five dry holes had been drilled, and approximately 32 million bbl of oil had been produced. Approximately 6,000 acres may be considered productive of oil in the Tensleep Reservoir, and estimates of the oil that will be produced average 200 million bbl. The Tensleep Reservoir has further interest because it ha-greater closure than any oil field in the Rocky Mountain region; the closure of the Elk Basin anticline is variously estimated at 5.000 to 10,000 ft. of which the top 2.00 ft of the structure contained oil. SUBSURFACE OIL SAMPLING Fig. 1 is a structural map of the Elk Basin Tensleep Reservoir, on which the nine wells used in this study and the numbers correvponding to the well designations hereafter referred to are shown. Wells 1. 2, 3, 4, and 8 were tested and sampled during October and November. 1943. and Wells 5, 6. 7, and 9 during June and July, 1944. An electromagnetic type sampler developed by the Bureau of Mines and described by Grandone and Cook' was used in obtaining the subsurface oil samples. As the wells were tubed nearly to bottom, the sampler was run as far as possible in the tubing hut never below the top perforations. The following procedure was used in testing and sampling the wells: A well was shut in for at least three days, after

Jan 1, 1951

By C. Özgen Karacan

Degasification and methane control in underground coal mining is an important area augmenting conventional ventilation in order to prevent possible fires and explosions due to excessive methane emissions. Coal bed reservoir engineering has been applied for many years to coalbed methane production. In recent years, modeling the flow and draining methane, not only from coal bed itself but also from the overlying strata, have been recognized as important areas of expertise for supplementing underground ventilation. This paper demonstrates the applications of coal bed reservoir engineering and modeling techniques for optimizing and controlling methane emissions in longwall and continuous miner sections. Practical applications and some considerations are presented for reservoir modeling, borehole performances, and face emission predictions for various coal bed and borehole configurations. A section on field reservoir studies and well bore log analyses for methane control are also presented as a complementary way of controlling methane and optimizing ventilation.

Jan 1, 2009

By J. S. Aronofsky, A. S. Lee

Results and experimental procedures are presented covering a preliminary laboratory investigation of the compaction of reservoir rocks and its effect on porosity and permeability. "Egective" compressibility was measured by subjecting core material to an overburden load and reducing pore pressure. Preliminary results showed relatively high effective compressibilities which varied from 1.8 X 10-' pore volume/pore volume /lb / in.~ for limestones to 7.7 X 10-6 pore volume/pore volume/lb/in.' and even higher for sandstone reservoirs conmining large amounts of fine clay material. It appeared from the initiol results that the effective compressibility of the material could not be correlated directly with porosity and that other factors, such as the amount of clay material present might have to be taken into account. The work to date has indicated that effective compressibility factors will have to be measured for the particular reservoirs heing studied. Oil permeability of core materid was measured under various effective overburden loads from 0 to 8,000 psi. It has been found than reduction of permeability in clean sands was relatively small and the results agreed with published data. For sandstones containing large amounts of clay, preliminary tests indicated very large reductions in permeability with increasing effective overburden pressures. It is planned to continue laboratory work on this phase because of its importance in low-permeability reservoirs. INTRODUCTION During the past few years increasing interest has been shown in the differences obtained between conventional laboratory measurements on cores at atmospheric pressure and those when reservoir conditions are simulated. Since these data are used as the basis for calculations and the prediction of reservoir behavior, their evaluation under reservoir conditions is most important. The effect of the compressibility of the rock upon the reservoir behavior, as fluid pressure declines, is an important subject which has been insufficiently studied. The total pressure on any plane through a reservoir is the result of the grain-to-grain rock pressure due to the overburden and the pressure of the interstitial fluid on the plane. As reservoir fluid pressure declines, the net load on the rock phase must increase, and the result is the compaction of the rock structure which produces a decrease in pore volume. Simultaneously, the rock grains expand into the pore space as the fluid pressure declines. The result of these two effects is defined as the effective compressibility of the rock and is expressed in units of pore volume/original pore volume/psi. Work was started by Imperial in 1954 on the effects of pressure on the porosity of reservoir rock. These studies established effective compressibility factors for some limestones and dolomites. Since that time effective compressibilities have been obtained for other Canadian and some U. S. reservoir rocks. In conjunction with the study of porosity, an investigation has also been initiated to determine the effects of pressure on permeability. One outcrop and several reservoir sandstone cores have been tested to date. ROCK COMPRESSIBILITY Apparatus anD Procedure A diagram of the apparatus used in these studies is shown in Fig. 1. The equipment was constructed so that a uniform pressure, equivalent to the reservoir overburden, could be applied by the oil pump and transmitted on all sides of the core through the Lucite sheath. The sample was completely saturated by circulating brine through the mounted core. Pressure in

By B. G. Hurd

A liquid-Freon permeameter suitable for making routine permeability determinations on small plug samples is described. The instrument is characterized by simplicity of design and ease of operation, and can be assembled inexpensively from stock items of laboratory equipment. It combines the unique advantages of both liquid and gas permeam-eters while eliminating many undesirable features of both general classes of instruments. Precision and accuracy of the specific Freon permeability measurements compare favorably with results of conventional liquid and gas permeameters. INTRODUCTION The liquid-Freon permeameter described in this paper was designed and built for special investigations of the properties of petroleum reservoir rocks. However, its unique advantages over conventional gas and liquid permeameters make it eminently suitable for routine use in the core analysis of small plug samples. In general, gas permeameters are very popular because of their simplicity of design and ease of operation. However, apparent gas permeabilities are normally higher than true specific permeabilities unless special corrections for gas-slippage are applied. Since these corrections require two or more measurements at different internal gas pressures, much of the time advantage of the specific gas permeability measurements is lost. Liquid permeability measurements, on the other hand, require no slip correction, but liquid saturation of the sample is time-consuming and difficult to insure. Often, too, the saturating liquid must be extracted or dried from the plug before it can be used for another experiment. The liquid-Freon permeameter described herein retains the inherent accuracy of the liquid permeameter, while affording the speed and ease of operation of the gas permeameter. Freon-12 (dichlorodifluoromethane) is a haloge-nated hydrocarbon, immiscible in the liquid phase with water. It may be considered as an oil phase in laboratory fluid-flow studies. Like butane and propane, it is a gas at normal room temperatures and atmospheric pressure but can be liquefied at moderate pressures. Complete liquid saturation of a plug sample with any of these fluids can be easily achieved by condensing vapors in the sample and operating the permeameter at a pressure above the vapor pressure of the liquid. Freon-12 is superior to butane or propane for permeability measurements only in that it is relatively nontoxic and completely incombustible, and thus presents no fire or explosion hazard. Freon-12 is believed to be completely nonreactive with most petroleum-reservoir rock samples. It volatilizes immediately from a plug on depressurizing to leave a clean, dry sample suitable for subsequent experiments. Thus, the inherent risk of changing physical properties of rock samples by cleaning and drying operations between permeability measurement and subsequent experiments is eliminated. DESCRIPTION OF THE PERMEAMETER The design of the liquid Freon-permeameter is shown schematically in Fig. 1. Regulated nitrogen pressure caps are used both as a driving pressure

By J. W. Whalen

The design, operation and evaluation of an instrumental method for the determination of fluid saturation in porous materials during multiphase flow studies is described. The presence of a magnetic tracer comprising approximately 20 per cent by weight of the aqueous phase is necessary in the utilization of this method. The results of two-phase relative permeability studies on two samples of porous media are presented. The realizable accuracy of the magnetic susceptibility apparatus in fluid saturation determination is estimated to be 2 saturation per cent. The response characteristics of the instrument, together with its simplicity of operation and maintenance are sufficient to recommend its use in routine laboratory studies. INTRODUCTION The problem of fluid saturation determination in laboratory multiphase flow studies characterizing oil recovery processes is one which has been given exhaustive study. Briefly the requirements which are considered essential for a method sewing this purpose are: (1) that the measurement be made external to the porous rock sample under study with no interruption of the fluid flow pattern, (2) the saturation indication must be independent of fluid distribution in the volume scanned by the measuring device, (3) the sensing element should have a small field of definition enabling several independent measurements to be made along the length of a core sample, and (4) the properties of the fluid phases should not be too greatly influenced by required tracer substances. Several methods of saturation determination have found acceptance as meeting most of the above requirements. These include resistivity,1 X-Ray absorption,2,3,4 radiotracers,5,6,7 and neutron8 diffraction The merits of these techniques have been discussed elsewhere in detail and will not be considered here. It may, however. be pointed out that the elaborate instrumentation required by the methods mentioned above, with the exception of the resistivity method (which is undesirable from other standpoints) encourages the development of methods of saturation determination which, while meeting the requirements listed, are simple to operate and maintain. It is the purpose of this paper to describe the instrumentation and evaluation of a technique for the determination of fluid saturation which combines relative simplicity with an accuracy and applicability comparable with methods now in practice. DESCRIPTION OF THE METHOD If the magnetic susceptibility of one of the fluid phases contained within a porous material is sufficiently greater than that of the remaining phases, the fluid content of the material with respect to that phase may be determined by an induction measurement. This may be accomplished by measuring the induced voltage in the secondary of a transformer which contains the porous sample and its interstitial fluids as a portion of the magnetic flux path. Since the fluids used in multiphase flow studies involving petroleum reservoir samples possess uniformly low magnetic susceptibilities, the use of a magnetic tracer in one of the fluid phases is required. In view of the relatively high paramagnetic susceptibility of salts of the transition elements, together with their high water solubility. these compounds become logical choices as tracer materials. Cobaltous chloride, having a specific magnetic susceptibility of 17.5 x 106 cgs electromagnetic units, was used as the tracer material throughout this work, in a concentration of approximately 20 per cent by weight in the aqueous phase. MAGNETIC SUSCEPTIBILITY APPARATUS Basically, the magnetic susceptibility apparatus consists of a transformer serving as the detecting head, a

Jan 1, 1955

By C. H. Stewart, R. A. Fagin

A two-dimensional, three-phasereservoir simulator was programmed for a large memory digital computer. It was designed to provide a practical solution to describing the complex physical relation between the natural forces and the physical properties of a heterogeneous reservoir when subjected to a specific set of conditions. A reservoir study is briefly described to illustrate application of the model. A full volumetric account of three phases (oil, gas and water) is performed simultaneously throughout an integration net representing the reservoir. Absence of one or two of the phases is treated as a special case of the more general situation. Expansion (or contraction) of all phases, including rock expansion, is performed so that the pressure calculation is the general unsteady-state case. To account for the large variations of subsurface elevation encountered in some reseruoirs, and to allow for segregation of the various phases, a gravity head term is included in the basic drive potential. Appropriate fluid and rock properties are used in polynominal surface form (functions of pressure and/or depth) or they can be entered as space variables at each position of the integration net. An unsteady-state water influx calculation, based on the method of van Everdingen and Hurst, l was connected to the boundary of the matrix to simulate aquifers of various sizes. In addition to reservoir calculations, three-phase fluid flow from the producing depth to the wellhead, including provisions for gas lift, was incorporated in the simulator. A workover routine was also built which can automatically switch to a different set of production relations when a gas-oil ratio or water fraction reaches a limit; or it can shut-in the well if prescribed. INTRODUCTION This paper describes a reservoir engineering mathematical simulator used to represent the complex interaction of natural forces and physical properties of a reservoir during natural depletion or with various injection schemes. The simulator, which was programmed for a large memory digital computer, is a two-dimensional calculation which handles three mobile fluid phases simultaneously (oil, gas and water). Basic requisites for the method are individual well production and pressure data, hydrocarbon fluid properties, geological data (producing depth and net sand), capillary pressure data, relative permeability data and permeability and porosity information. Matching the past performance of a combination drive reservoir often has yielded information concerning continuity and the validity of basic data. Detailed predictions of future performance can be made for continuation of current depletion methods (natural depletion) as well as for various types of recovery by gas or water injection. Combination injection cases and pattern studies can also be performed. Workover programs, gas lift and different types of artificial lift programs have been investigated using a technique similar to that described by Kern and Nicholson2 except that conditions of pressure and saturation at the block within which the well is located are used rather than average reservoir conditions. Drilling additional wells to optimize profit was explored, both as to number and location, by placing wells at different spots within the reservoir matrix. Special depletion processes can be examined, such as upstructure drainage and lateral (or strike) waterfloods in thin oil columns. In one case the mathematics of the simulator were modified to calculate the displacement in the vertical plane rather than in the horizontal plane. In this manner specific reservoir problems can be studied, such as coning of gas and/or water around production points, fingering along permeable stringers or, more generally, frontal advances in a heterogeneous section.

Jan 1, 1967

By B. P. Nutter, M. Lebourg, J. A. McAlister

The Multi-Flow Evaluator (MFE) is a new system of tools providing an original approach in drill-stem testing. It improves control during the testing operation and gives a more accurate evaluation of the fluid recovered while providing additional pressure information for reservoir analysis. The tools are operated entirely by up and down motion of the drill stem. This up and down operation provides a positive means of control and offers easily observed surface indications of tool operating position. An unlimited number of shut-in and flow periods may be taken with this tool while in the hole. The key to the success of the MFE system of tools is the safety seal packer. Until this development, operation of the tools by up and down motion only had proven unreliable. The success ratio of the MFE now exceeds the ratio achieved by conventional tools. The equipment includes a 2,750-cc chamber in which a representative sample of the flowing formation fluid is trapped at the end of the last flow period and brought to the surface under pressure. The sample can be evaluated at the wellsite or transferred under pressure for laboratory analysis. The sampling feature of the tool allows a sample to be obtained from a reservoir which has suffered minimum influence from production. A representative sample can be obtained for laboratory or empirical analysis by employing a testing technique to minimize drawdown during flow periods. Interpretation methods to take advantage of this additional information are presented and supported by actual field examples. INTRODUCTlON The Multi-Flow Evaluator (MFE) represents the most recent technical advance in formation testing. Drill-stem testing techniques prior to the MFE have been limited in three areas—(1) operaiion, (2) recovery analysis, and (3) reservoir analysis. The tools in the MFE system allow maximum control during testing and provide test information superior to that obtainable with conventional tools. The system of tools and the operation procedures are described to illustrate the mechanical advantages over present tools. Methods of pressure build-up and fluid

Jan 1, 1966

By Mohamed Mortada

A practical analytical method is developed in this paper which provides the practicing reservoir engineer with a handy method for analyzing oilfield interference problems. The procedure employed entails the principle of superposition of individual eflects. A set of charts has been developed and can be used to evaluate the individual effects. The charts represent non-steady state pressure distribution in an extensive aquifer due to a constant rate of production from an oilfield which can be approximated by circular geometry; they are constructed from solutions to the diffusivity equation considering a circular sink as distinguished from a point sink. The solutions are obtained partially from mathenlatical considerations and partially from analog and digital computations. By virtue of the method of images, the charts can be used also to treat the case of production near a fault. In addition, provisions are made for treating oil fields, which are produced by partial water-drive. Treating an actual field case is deferred to a subyequent writing; however, illustrative example is presented to demonstrate the method of application. The pressure distribution in linear and limited radial aquifers is currently under study. INTRODUCTION With the increasing difficulty of discovering new oil reserves, attention is necessarily focused on the efficient development and production of existing reservoirs. Efficient production depends on the availability of reliable means for predicting the pressure-production behavior of oil fields. The prediction is usually performed by analytical methods or computers. Analytical methods are often limited to systems which can be approximated by simple geometry. However, analytical methods have the distinct advantage of being readily performed without special equipment. Analog and digital computers lend themselves to a variety of problems, but are not always locally available and consequently their use is limited. One particular situation in which analytical techniques are needed involves studies of multiple, water-drive oil fields sharing a common aquifer. Such oil fields are in hydrodynamic communication. Therefore, production from any of the oil fields is accompanied by a pressure decline which is transmitted through the aquifer to the other oil fields and manifested as pressure interference. The rate of propagation of the pressure decline is such that the pressure may be significantly reduced many miles away from a producing pool. An example of pressure interference is found in the Woodbine formation in East Texas. There. a dozen or more pools, including several of major size, draw on the Woodbine formation for water drive. The pressure in the water-bearing portion of the formation has been significantly reduced over an area of several thousand square miles. This reduction of pressure has been such that when the Hawkins pool was discovered in 1940, the pressure in it had already been reduced 280 psi below the initial value in the aquifer. This resulted from prior production from other Woodbine sand pools, including, in particular, the East Texas field some 20 miles to the east of Hawkins.' The above example indicates that the interference effect can be significant and should be taken into con-

Jan 1, 1956

By R. N. Hoffman

A new technique for determining capillary pressure curves has been developed and tested. The technique differs from previously reported centrifuge techniques in that the centrifuge is slowly accelerated from zero to the maximum desired speed rather than being held constant at particular, progressively higher speeds. An important advantage of this technique over other methods of determining capillary pressure curves is the short time required to obtain the desired amount of data over the chosen pressure range. For example, to obtain 30 data points between 1.2 and 104 psig with a 1.55-in. long, 3/4-in. diameter core using a brine-air system, 6.6 hours were required with this technique. An equally important development of this paper is an analytic method for the conversion of the data from the centrifuge experiment to capillary pressure curve data. Previously there has been only an approximate conversion available. Although the capillary pressure curves determined by this technique appear to be as accurate as those determined by other techniques, the accuracy could be improved if certain variables, not treated in this experiment, were investigated. Among these are the dynamic distortion of the centrifuge equipment and imperfect initial saturation of the cores. INTRODUCTION Pirson 1 defines capillary pressure in a porous medium as "the differential pressure that exists between two fluid phases at their interfaces when they are distributed under static equilibrium within a porous material". Capillary pressure in rocks is known to be a function of fluid saturation, among other things, and a capillary pressure curve is defined for the purposes of this paper as a plot of the capillary pressure-wetting phase saturation relationship for a particular rock sample. Several methods are used for determining capillary pressure curves for small rock cores. Prominent among these are the semi-permeable barrier, mercury injection, and, to a lesser extent, centrifuge methods. The semi-permeable barrier method is currently the most popular. It features simplicity in both execution and the mathematical conversion of the experimental data into a capillary pressure curve. The main disadvantages of the semi-permeable barrier method are the time required — as long as two months — to obtain several points for the curve, and a fairly low maximum pressure before breakthrough of the non-wetting phase into the barrier occurs, for example, about 32 psig for a brine-air system. It is for these reasons that other methods such as the centrifuge method have been introduced. High accelerations and the absence of a barrier result in quicker attainment of saturation equilibrium at a given pressure. However, the centrifuge method involves much more expensive equipment and more difficult procedures and calculations than does the barrier method. The purpose of this investigation has been to improve the equipment and procedures of the centrifuge method and to develop an analytic method for the conversion of the experimental data into a capillary pressure curve. Hassler and Brunner did the original work in the determination of capillary pressure using a centrifuge. In their work the centrifuge speed was increased in a step-wise manner, each speed being held constant until saturation equilibrium was reached in each core. Saturation equilibrium was indicated when the volume of liquid collected in the graduated pipette of the core holder remained constant. According to Hassler and Brunner, equilibrium was reached in "a few minutes to one-half hour or more". In the centrifuge method, as opposed to the barrier method, the fluid saturation of the core is not a constant throughout the length of the core, but varies with the radius of centrifugation. Also, the capillary pressure cannot be read directly but must be calculated from a knowledge of the centrifuge speed and other parameters. For these calculations, Hassler and Brunner derived the following equations: