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The performance of a two-horizon depletion-type reservoir produced through combination wells is analyzed. By introducing some simplifying approximations, it has been possible to obtain formulas which are easy to handle. Only ordinary differential equations are used, and the development of the analysis can be followed without difficulty by the non-specialist. A rigorous analysis has been made of this problem. It has been found that the approximations introduced in the simplified analysis are fully justified and that errors seldom will be more than 2 per cent. The report shows the effect of the rate of withdrawal upon the relative depletion of the two horizons. Numerical examples are given. INTRODUCTION In its simplest form an oil reservoir consists of a continuous, homogeneous body of porous and permeable rock, enclosed at the top and the bottom by impermeable material. The flow of fluid through such a reservoir has been the subject of numerous papers, and the mathematical analysis of well performance, pressure build-up, etc., has reached a high degree of refinement. One of the basic assump tions introduced into these analyses is the homogeneity of the reservoir. In non-homogeneous reservoirs, these computations still can be carried out satisfactorily, provided small irregularities in the physical properties of the rock are distributed in a random fashion. The flow equations are derived as solutions of the continuity equation, and their solutions are dependent upon the assumption of many constant factors in the reservoir: permeability to oil, compressibility of the reservoir fluid, viscosity saturation, etc. When these axe assumed to be constant, the continuity equation can be solved rigorously. When these assumptions do not hold and corrections are introduced, it becomes very difficult and often impossible to solve analytically. The present analysis is concerned with production from a two-layer depletion-type reservoir in which the layers have different permeabilities. Instead of using the continuity equation, results were derived from some simple physical ideas. In a single-layer reservoir in which the oil is at a pressure above the bubble point, the rate of production often has been assumed to be directly proportional to the pressure drawdown. In the simplified analysis it has also been assumed that the drop in average reservoir pressure is directly proportional with the cumulative withdrawal. These considerations in the past have been the basis of the analysis of reservoir performance and have been applied to a variety of problems, often with marked success. In the problem under investigation these relationships are shown to be compatible with the equation of continuity, but the approach has the advantage of leading to ordinary differential equations in which changes in constants can be introduced without making the analytical solution impossible. It has the additional advantage that it can be understood more readily by the large group of engineers who are not reservoir specialists. For that reason, detailed steps in the mathematical developments have been shown in full. SCOPE OF ANALYSIS The analysis in this paper has been applied to a two-layer depletion-type reservoir in which both horizons are produced simultaneously in the same well. Because of the difference in permeability, it is obvious that the depletion of the two zones will proceed at different rates. For various problems it may be of interest to know the degree of depletion of the two zones at any arbitrary time and to in-

By M. R. Tek, K. H. Coats, D. L. Katz

The nature and the limits of validity of Darcy's law US applied to the flow of natural gas through reservoirs has been considered in order to resolve some controversial aspects of the effect of turbulence on pressure drops. The equivalence between various concepts and viewpoints advanced in the past by several investigators to explain how and why a gas well does not necessarily perform according to Darcy's law is shown. Starting with generalized equations of flow of fluids through porous media, a partial differential equation has been derived which accurately represents the flow at all rates. This equation has been numerically solved using an IBM 704 digital computer. The results permit plots of unsteady radial pressure distribution curves from which specific isochronal backpressure curves may be constructed. These back-pressure curves show the effect of the ,8 factor on the slope of the back-pressure curve. The calculations further indicate that the drainage radius for a gas well in turbulent flow propagates at a rate dependent upon the rate of production at the wellbore. This is quite different from the case with liquid flow or natural-gas flow in laminar regime. Additionally, the effect of reservoir inhomogeneities and crossflow between layers of different permeability on the back-pressure performance of gas wells has been conridered. In light of the current numerical results the significance and linlitation of the rate of flow function Y proposed by Smith" has been discussed. INTRODUCTION The relationship between the pressure drop and flow rate in problems of fluid flow through porous media is known to be affected by the nature of flow through the porous matrix. It has been observed by many that, for a range of flow rates, the pressure drop remains proportional to the rate of flow. When some flow rate is reached, however, it is usually observed that the pressure drop gradually begins to increase more than proportionally to the flow rate. It is well known that this phenomenon was first observed by Osborne Reynolds in 1901 in experimenting with flow through pipes. In his classical experiments, Reynolds made visual observations on the condition of streamlines evidenced by injecting a dye into water flowing through glass tubes. In these experiments, the abrupt transition between steady, "streamline, laminar" flow and unsteady random turbulent flow was found to be a function of the dimensionless group (Dvp/u), now known as the Reynolds number. During these experiments, in addition to observations on the nature of flow regimes, the proportionality between flow rate and pressure drop in laminar flow was contrasted with the nonlinearity between these variables in turbulent flow. Fancher and Lewis' reported data on various consolidated and unconsolidated sands in 1933. Their conclusions were that ". . . the flow of fluids through these porous materials closely resembles that through pipes; that there is a condition of flow in porous systems which resembles viscous flow, another which corresponds to turbulent; that the change from one type to the other takes place at a definite and reproducible condition for each system". In 1947, Brownell and Katz published a method to predict the laminar and turbulent flow behavior from the particle size, bed porosity and the particle sphericity, employing the friction factor-Reynolds number charts for pipes. Several investigators have verified the work of Fancher, Lewis and Barnes and presented their data as friction factor-vs-Reynolds number plots.' The equation which would represent the pressure gradient over the whole range of velocity must have an added term over that represented by Darcy's law. Accordingly, the pressure gradient necessary to sustain flow at the velocity (v) through a porous medium may be represented by the following equation, suggested by Forscheimer." The nature and the range of validity of Darcy's law has been the subject of studies by many investigators over the past years. While everyone seemed to agree on the need for a quadratic correction term to Darcy's law to make it effective over the range of velocities, the concept of inception of turbulence and the use of the term "turbulent flow" remained controversial. Some fluid dynamicists define turbulence as a flow

By F. J. Fayers, J. W. Sheldon

A theoretical discussion is presented of the behavior of the interface between two fluids of different physical properties when displacement is occurring along a thin tilted bed. An approximate equation of motion is deduced for the motion of the interface, suitable boundary conditions are derived and the conditions necessary for the approximation to be valid are determined. Steady-state behavior and the circumstances under which a steady-state interface can develop are discussed. Finite-difference solutions of the equation of motion for two characteristic water-drive problems are presenled. The theory of displacement in a thin bed may be regarded as being the porous-medium-equivalent of the classical "shallow-water wave" theory of hydrodynamics. INTRODUCTION The solution of moving interface problems are important in predicting the behavior of oil reservoirs under various conditions of production. Kidder4,5 has obtained analytic solutions for the fingering problem and for another particular case of the motion of the interface between two immiscible fluids of unequal density in a porous medium. In the present analysis, we analyze the problem of the motion of an interface along a slightly dipping bed whose length is long compared with its thickness. The requirement of a thin bed is necessary in order to give a simple differential equation for the motion. The two fluids are of unequal density and mobility. In the derivation of the equation of motion, it is assumed that the lighter fluid is being injected at constant rate at the high end of the porous layer, while heavy fluid is produced at the low end of the layer. The analysis applies equally well, however, to the reverse procedure in which the heavier fluid is injected at the low end of the tilted layer. It will be shown that the behavior of the system is critically dependent on which fluid has the higher mobility and that the interface can in certain circumstances achieve a simple progressive steady-state shape. The fluids may be considered to be immiscible or miscible. It is assumed, however, that the thickness of the interface region is negligible in comparison with other dimensions of the system, and that the strength of the saturation or concentration discontinuity remains constant during the motion. In conjunction with Buckley-Leverett theory and areal sweep-out calculations, the tilted interface problem is one of the fundamental problems of reservoir engineering; it defines the very important underpassing and overpassing phenomena associated with water-drives, gas-drives and secondary recovery operations. The tilted interface problem has been dealt with previously by Dietz.2 In the present paper, we endeavor to derive the pertinent mathematical results more rigorously, and in doing so we obtain modifications in both the differential equation and boundary conditions for those given by Dietz. We also attempt to show the connection between these results and some of the recent work on the stability of interfaces. Finally, we attempt to demonstrate the practical importance of the thin bed theory by showing the difference in behavior of two characteristic waterflood problems. In the favorable mobility case recovery is improved by increasing production rate, while in the unfavorable case undercutting or overcutting is minimized by reducing the displacement rate. PROPERTIES OF THE EQUATION OF MOTION Fig. 1 illustrates a porous layer of constant thickness H and tilt 8 with Fluid 1 of mobility ?l and density pl below Fluid 2 of mobility ?2 and density p2. The fluids are incompressible and flowing with volumetric flux q along the layer. Both the slope a of the interface with respect to the bed and the curvature of the interface are assumed to be small. What is meant by "small" is indicated in the derivation given in Appendix A of an approximate equation of motion for the interface. Other symbols are defined in the "Nomen-

By R. E. Gilchrist, R. R. Harvey, M. R. Dean

A simple and rapid three-component analysis procedure has been developed for use in fluid-flow studies. The method is based on refractive index measurements, combined with refractive dispersion measured between the Ha and H wave lengths. The procedure requires. calibration curves for the three-fluid system. The only restriction on the fluids employed is that only one be an aromatzc or olefinic compound. Individual sample measurements require only a few minutes. Composition results within the limits of accuracy required for fluid-flow analog studies are obtained. INTRODUCTION The simultaneous analysis of three-component mixtures is a problem often encountered in fluid-flow analog systems. In petroleum production research, the problem is usually encountered in experiments on the displacement of fluid from a porous medium. In the case of immiscible displacement, simple volumetric measurements of the produced fluids are usually sufficient, the analog fluids often being the actual reservoir fluids themselves — oil, water and gas. However, modern secondary recovery of petroleum sometimes involves production under miscible conditions, in which the oil is displaced by liquefied petroleum gas which, in turn, is displaced by dry gas. Since this type of displacement is done under conditions of pressure and temperature that are not easily reproduced in the laboratory, studies are often performed with analog fluids at essentially atmospheric pressure. Since the number of samples taken during one of these experiments is usually quite large, the time required for analysis becomes an important factor. In the past, the difficulty of conventional analysis has been avoided by the addition of various tracers to one or more of the components, or by the use of a tracer fluid as one of the components. With these techniques, a relatively large amount of analytical time is still required. Moreover, in the case of added tracers, the tracer material may migrate in part to one of the other fluids, may be adsorbed on the solid surfaces of the model, or may introduce side effects not characteristic of the prototype fluid. The substitution of a tracer fluid for one of the components can severely limit the choice of analog fluids. Optical refractometry provides a rapid and economical method of analysis of two-fluid systems or of monitoring small changes in composition of an essentially one-component system. Refractometric methods are capable of high degrees of accuracy, require only very small samples and can easily be adapted to automatic methods. They are not generally applicable, however, where three or more fluids are present over wide ranges of concentration. The method of three-component analysis described here has three essential characteristics. 1. It is based on refractometric measurements and thus preserves all of these desirable properties. 2. It does not make any stringent demands on the choice of fluids that can be analyzed. 3. It is capable of accuracy sufficient for fluid-flow analog studies. THEORETICAL The difference in the refractive index of a substance at two different wave lengths of light is known as its dispersivity. When the difference is taken between the specific refractions at the two wave lengths, the quantity is referred to as the specific dispersivity. Specific refraction was defined empirically by Gladstone and Dale1 as r = n-1/d....[1] where n is the index of refraction and d is the density. The definition is given more correctly by the expression r =n2-1/n2+1 1/d..........(2) 1References given at end of paper. MICIFTV OF PETROLEUM ENGINEER JOURNAL.

By T. D. Mueller

Many investigators have used the response of the "dimensionless aquifer" to a unit pressure drop or a unit fluid-withdrawal volume to calculate the performance of an aquifer in supplying water influx to an oil reservoir. In the past, these response functions have been calculated with the aid of the Laplace transform. With the advent of ultra highspeed digital computers, it becomes practical to solve for the response functions with finite-difference techniques. The computer method also permits extension of the dimensionless-aquifer concept to include the nonhomogeneous aquifer wherein the permeability and other properties vary as a function of the space co-ordinates. This paper gives results of calculating the response functions for a series of nonhomogeneous aquifers. Response functions are presented for both linear and radial aquifers whose thickness, permeability-viscosity ratio and porosity-compressibility vary. These functions are new and should prove useful to the petroleum engineer in analyzing the behavior of nonbomogeneous aquifers. Results are presented in the form of charts that can be easily used by the field engineer. INTRODUCTION Aquifers which surround many oil and gas reservoirs have the ability to supply water influx to such reservoirs as oil and gas are withdrawn. This water influx, called natural water drive, provides one of the most effective driving mechanisms for the production of oil and gas. In producing a reservoir, therefore, it behooves one to make the maximum use of natural water drive. To achieve the maximum use, the reservoir engineer must be able to predict the performance of an aquifer under a variety of production schemes that may be proposed for the reservoir. Unfortunately, the physical properties which dictate aquifer behavior often are known only within limits. Seldom do wells penetrate the porous strata of the aquifer. Even when they do, quantitative information regarding porosity, permeability and water compressibility is seldom available. It is known, however, that the water efflux from most aquifer systems is governed by a single, relatively simple, linear, partial differential equation. Also, the general physical location of the aquifer boundaries often are known. A technique originall proposed by Hurst1 and van Everdingen and Hurst2 has been found useful in analyzing reservoirs in this situation. The idea was later expanded by van Everdingen, Timmerman and McMahan3 to include the mathematical technique of least-squares fitting. This latter method will be referred to as the VTM method. The basic assumptions of the VTM method include the following. 1. The location of the physical boundaries of the aquifer are known. 2. The flow conditions at these physical bound-daries are also known. 3. The aquifer is homogeneous; e.g., thickness, permeability, water compressibility and porosity are constant throughout. In the VTM method, a material balance is made on the fluids entering and leaving the reservoir. In the balance equations, the water-influx term is represented as the product of the water influx from an arbitrarily-selected, dimensionless aquifer system times an unknown conversion number. This balance can be formed as many times as there are data points in the history of the reservoir. Each time, the conversion number can be evaluated. If the reservoir engineer has picked the correct dimensionless aquifer to represent the real aquifer, the conversion number remains constant for all balances that have been made over the history period. If such a situation occurs, the reservoir engineer can then predict the performance of the reservoir for any type of production scheme by using the function associated with that particular dimensionless system and the derived conversion number. These functions will be referred to as the response function of the aquifer. If the aquifer is nonhomogeneous (e.g., if the porosity, permeability, thickness, porosity, or

By D. R. Parrish, K. W. Beaver, H. W. Wood, R. W. Rausch

A pilot test of forward combustion in the Shannon pool, Salt Creek field, Wyo., is described. The Shannon sand, 950-ft deep, contains a heavy (25" API), viscous (76 cp) oil. Natural reservoir energy is limited. Primary production, intermittent since 1889, recovered only about 2 per cent of the oil in place. The field is operated by Pan American Petroleum Corp. for the Midwest Oil Corp., the owner. The original pilot was a 1.32-acre five-spot. The expanded pilot has eight producing wells surrounding a roughly triangular area of about five acres with the injection well near the center. A control or comparison well was also recompleted in another part of the field. Operation of the pilot has been little different front an ordinary gas drive. Little special equipment was found to be absolutely necessary. Except for some use of a temperature-resistant cement, all wells were conventionally completed. In spite of poor oxygen consumption, the over-all performance of the pilot has been good. Total oil recovery to June 1, 1961, was 73,971 bbl. The wells of the original pilot alone had produced about 24,000 bbl, equivalent to 50 per cent of the oil in place, when fire breakthrough at the first well occurred. These wells have now produced oil equivalent to more than 74 per cent of the oil in place in the original pilot area and production is continuing. It appears that ultimate recovery will approach theoretical maximums before the wells must be abandoned. Performance of the pilot has been encouraging, and expansion to a fieldwide combustion operation is being investigated. INTRODUCTION The results of both laboratory investigations and field tests of underground combustion have been reported previously.' However, most of the field tests were primarily experimental. More information and experience are needed before forward-combustion operations can be engineered with confidence. The purpose of this paper is to present the results of a successful pilot test of forward combustion. These re- sults should increase confidence in forward combustion as a practical method for commercial oil recovery. HISTORY OF THE SHANNON POOL The Shannon pool is located on the north end of the Salt Creek field in Natrona County, Wyo. It is approximately 50-miles north of the city of Casper. The Shannon pool's3 discovery well was completed in 1889, making this one of the oldest oil fields in the Rocky Mountain region. Three more wells were drilled in 1890. First production was hauled in wooden barrels by horse and wagon to the railroad in Casper. In 1894 a small refinery, the first in Wyoming, was built in Casper to process the Shannon crude. In the following years the field changed hands several times. It appears that each new owner did some development drilling as several wells were completed in each of the years 1895, 1902, 1905 and 1912, with negligible development in the intervening years. Forty-eight wells were drilled in this period, but many were later abandoned. Discovery of the more prolific Salt Creek field proper ultimately forced suspension of operations at the Shannon pool. After 1915 there was only sporadic production, mostly to supply cheap boiler fuel to drilling rigs in the Salt Creek field. But even this was discontinued in 1931. Since then the pool had been dormant until the recent operations, which are the subject of this paper. The Shannon pool is now owned by the Midwest Oil Corp. Field operations are conducted for Midwest by Pan American Petroleum Corp. THE RESERVOIR Fig. 1 is a map showing subsurface contours of the Shannon pool. The reservoir is on a nose of the Salt Creek anticline dipping to the north at about 500 ft/mile. The trap is provided by a shallow fault on the updip side of the productive area. The downdip limits are bounded by water, but this water has not provided an effective source of reservoir energy. The Shannon sand outcrops at many places in the immediate vicinity, providing good surface indications of the Salt Creek anticline. At the Shannon pool the sand has been lowered by faulting and is overlain by about 900 ft of shale and other sands. The Shannon sand consists of two members. The upper, a water sand, is about 40-ft thick and is separated from the lower member by several feet of sandy shale. The oil pay occurs in the lower mem-

By O. R. Wagner, R. O. Leach, H. W. Wood, C. F. Harpke

PAN AMERICAN PETROLEUM CORP.TULSA, OKLA. CASPER, WYO A field test has been made in which additional oil recovery was obtained from a previously-waterflooded "oil-wet" sandstone reservoir. This recovery improvement was accomplished by adjusting the reservoir wettability through chemical treatment of the flood water. The test was made in the Muddy sand of the West Harrisburg Unit, Neb. The chemical used, sodium hydroxide, was injected as a slug of dilute caustic solution through a water-injection well. The natural wettability of the reservoir and the chemical requirements for reversing wettability were determined in the laboratory from contact-angle studies using field water and oil samples. Laboratory flood tests with a synthetic system had shown that reversing the wettability of an oil-wet consolidated core would lead to improved oil recovery. The field performance indicates that the mechanism by which increased oil retovery is obtained in the field is the same as that observed in the lahoratory. Laboratory studies indicate that higher ultimate recoveries and decreascd water-injection requirements result when the adjusting agent is added early in the life of the flood. However, a previously waterflooded area was intentiorzally chosen for the field test so that unambiguous conclusions could be made about the effects of chemical injection on wettability and the extent of oil-recovery improvernent afforded by wettability reversal. Forces existing at the fluid-solid and fluid-fluid interfaces in a porous medium have an important effect on oil recovery during a water flood. Modifying these interfacial forces in the reservoir to improve oil recovery has been the object of much research. Several papers' ' have discussed the use of surfactants to lower the water-oil interfacial tension. This paper describes work concerned with improving oil recovery by modifying the forces at the fluid-solid interfaces— that is, by changing the preferential wettability. An earlier paper: presented evidence to show that some reservoir systems could be changed from preferentially oil-wet to preferentially water-wet by the action of simple chemicals added to the water to increase waterflood oil recovery. The process was attractive for further study because it used only inexpensive chemicals and because it called for a gross "wettability reversal" rather than for a precise adjustment. The present paper is an extension of the earlier work. Laboratory flow tests were made using treated water and oil in a consolidated core to determine the amount of additional oil recovery and the producing performance which might be expected from reversing the wettability of an oil-wet reservoir during a flood. A contact-anglc study using water and oil from the Muddy "J" sand of the Harrisburg field, Banner County, Neb., indicated the reservoir to be preferentially oil-wet and susceptible to wettability reversal through chemical injection. Based on these studies, a field trial of wettability-reversal water flooding was initiated. in the Harrisburg field. The primary purpose of the trial was to determine if wettability-reversal flooding would improve oil recovery in an actual field situation. The field trial was also an important test of the laboratory tecnique used to determine the effect on oil recovery of certain wettability manipulation, as well as a test of the contract-angle method of determining reservoir wetra-bility. The paper is presented in two parts. The first part covers the laboratory experiments leading up to the field trial, and the second part covers the field trial. PART I—LABORATORY STUDY The laboratory experiments consisted of displacement tests using an idealized fluid system and of a contact-angle study with crude and water from the Muddy "J" sand of the West Harrisburg Unit, Banner County, Neb. The displacement tests were designed to determine the effects of a particular wettability manipulation, oil-wet to water-wet, on oil displacement in a water flood. The contact-angle measurements were made to determine the natural wettability of the reservoir and to determine if beneficial wetting changes could be brought about by a chemical addition to the flood water. PROCEDURE DISPLACEMENT TESTS The displacement tests were perfornled in a consolidated sandstone core using a refined oil and water. The wetting properties of this system could

By C. W. Carpenter, P. T. Bail, J. E. Bobek

This paper presents the results of model studies made to demonstrate the validity of applying the "basic" waterflooding scaling relationships of Rapoport1 to water-wet reservoirs composed of communicating strata of different permeability. Results demonstrate that these relationships can be validly applied, and also show the combined effect of variables on recovery. This demonstration was needed to confirm that the sizable effects of communicating strata on waterflood behavior, observed in model studies, were actually representative of field behavior. INTRODUCTION Rapoport1 Collins2 and others have presented scaling laws for modeling water-oil displacements. The validity of these laws has been experimentally demonstrated for homogeneous systems only. Recently, however, several investigators have presented the results of multilayer model studies made to determine the effects of viscous, capillary and gravitational forces on oil recovery in systems composed of communicating layers of different permeability. Dyes and Braun,3 using miscible displacements to simulate water flooding, showed that vertical communication adversely affects recovery at unfavorable viscosity ratios in the absence of capillarity. Ogandzhanyants and Egorova, 4 Gaucher and Lindley,5 and Richardson and Perkins6 modeled water-oil displacements in layered systems using immiscible fluids with capillary forces present. These investigators found more efficient behavior than in the miscible system of Dyes and Braun. However, since the scaling laws had not been verified for heterogeneous systems prior to or during these tests, it was necessary to assume that the results were representative of field behavior. This report presents the results of model studies made at Jersey Production Research Co. to find out if the waterflooding scaling relationships are valid when applied to water-oil displacements in heterogeneous reservoirs with vertical communication. Data obtained in the study show the combined effects of viscous, capillary and gravitational forces on oil-recovery behavior. The studies were performed in strongly water-wet systems where strong imbibition forces were present. For systems of different wettability, the effects of capillary imbibition would be somewhat different than those presented. APPROACH The scaling laws studied were those developed by Rapoport1 and designated by him as "basic" scaling laws. These relationships require that the model be scaled to the geometry of the prototype, and that the model and prototype be operated at the same viscosity ratio and have identical relative permeability curves, contact angles and boundary conditions. It is also necessary that the groups** be identical in the two systems, although any of the parameters making up the groups may be different. Finally, the capillary pressure of one system must be directly proportional to that of the second. Studies were conducted in two four-layer models, representing quadrants of five-spots, which were geometrically similar and which had the same glass-bead packing. The fluids used assured the same wettability in both models. Thus, the contact angles and relative permeabilities of comparative sand layers in the two models were identical and the capillary pressures were directly proportional. However, one model had a characteristic length three times that of the other. To make the scaling groups equal and to check the scaling laws, it was necessary to adjust the rate, water-viscosity level, interfacial tension and water-oil density difference to compensate for the difference in model sizes.

By M. H. Gaskell, D. C. Lindley

Small, steeply inclined reservoirs without natural water drives often are found associated with salt domes or other highly faulted structures. Frequently, only one well may be economically justified in these reservoirs, from which oil is produced by an expanding gas-cap drive or by a dissolved-gas drive. Although a large fraction of the oil upstructure from the well may be recovered during primary depletion, only a small fraction of the downdip oil can be produced because of gravity effects. This downdip oil has been defined as cellar oil991 in contradistinction to "attic oil" which is the oil above the structurally highest well in reservoirs where a natural water drive is present. In this study, two methods of producing cellar oil by water flooding a one-well reservoir were investigated by means of a laboratory model. This model was scaled to represent a prototype reservoir having an area of 30 acres, a permeability of 500 md, and a thickness and dip of 30 ft and 30°, respectively. One method considered, the simultaneous injection of water and production of oil from a single well, would require that the lower portion of the productive interval of a well be completed for water injection and the upper portion for oil production. The other method considered, intermittent injection, would involve alternate injection of water into and production of oil from a single well. Injection of water into the formation would repressure the reservoir, causing gas to go back into solution. Since some of the injected water would flow updip from the well, water injection usually would be followed by a waiting period during which the water could drain from above the wellbore. Production of oil by gravity drainage and gas-cap drive could be initiated when water drainage became sufficiently complete. The amount of water produced along with the oil would naturally depend on how soon after water injection ceased that production was started. This process could be repeated in cycles until oil could no longer be produced economically. Of these two methods, the intermittent injection technique would be simpler to put into operation since it does not require a dual completion. Also, it is probably more generally applicable than the simultaneous injection-production method. It is to be expected that in some reservoirs the rock and fluid properties would be such that practical oil-production rates could not be achieved by the simultaneous technique. However, in reservoirs where the simultaneous method will result in practical rates of oil production, it does have the advantage of permitting immediate, continuous oil production; whereas in the intermittent method, oil production is interrupted by periods of water injection and drainage. It was the objective of this study to determine whether these two methods of cellar oil production are practical for the representative prototype investigated and to evaluate their relative merits. DESIGN OF LABORATORY MODEL SCALING REQUIREMENTS The prototype reservoir and fluids were selected to have the dimensions and physical properties shown in Table 1. The laboratory model was then designed in accordance with well known scaling criteria, as discussed by Croes, et al,2 except for one modification. According to Croes, et al, one requirement of scaling a laboratory model to a reservoir prototype is that both the relative permeabilities and dimensionless capillary pressure be the same functions of water saturation for the model and the prototype. Since unconsolidated sand packs are used in the laboratory model to represent the consolidated porous media of the prototype, it is virtually impossible to satisfy this requirement. Much of the difficulty stems from the fact that unconsolidated sands usually exhibit lower residual oil and connate-water saturations than do reservoir rocks. To satisfy the scaling requirement as nearly as possible, Perkins and Collins' have suggested that the relative permeabilities be re-defined as

By F. E. Crane, J. Downie

The general application of Darcy's law to natural rocks has already been challenged in the literature.1 The evidence shows that the permeability as calculated from the Darcy equation can be a function of the pressure drop and the salt concentration of the water phase. Most explanations for aberrant behavior involve clays and their properties and have been qualitatively satisfactory.Recently, however, Odeh2 revived the theoretical views of Yuster.3 Since Yuster's concept implies a fundamental error in using Darcy's relationship for two-phase flow, and not merely that conditions may limit its use, Odeh's experimental support arouses considerable interest. However, Odeh's work as presented is thought to to be inadequate. He has omitted important information about his materials and procedures; therefore, acceptance of his conclusions should be withheld. Since a clay effect is possible, Odeh should have been allowed space to present a more detailed account of the rocks which he used and the precautions which he took to avoid confounding the effects of clay and fluid circulation. In addition, it follows from Odeh's discussion that the oil relative permeability should increase as the viscosity ratio increases. Odeh presents data corroborating this deduction. It also follows that the oil relative permeability should decrease as the viscosity ratio of oil to water decreases. However, our results show that a high relative permeability, when once attained by using a viscous oil, may be maintained when that oil is replaced by an oil of much lower viscosity. EXPERIMENTAL PROCEDURE The results are shown in Fig. 1 and were obtained as follows. Sandstone cores. 3-in. long X l-in, in diameter and which contained clays, were saturated with

By W. E. Brigham, P. W. Reed, J. N. Dew

By J. Downie, H. A. Kendall, G. H. F. Gardner

Some cases of the motion of two miscible fluids in uniform linear models are discussed. There is no bulk flow through the models, and the convection currents are caused solely by density gradients. Horizontal, vertical and inclined positions of the models are treated separately. Analytical formulas for the motion of a narrow transition zone between the fluids are obtained and compared with measurements, and the limitations are discussed. Observations of the ultimate stabilizing effect of diffusion on the motion me compared with the theory. It is shown that fluid motion in an inclined model with a constant rate of bulk flow can be directly deduced from the cases discussed, provided the viscosity ratio is small. INTRODUCTION In some reservoirs, convection currents caused by variations in the fluid densities may be significant. For practical purposes it may be desirable either to minimize the effect, particularly in miscible displacement, or to maximize the effect as in some schemes for the production of heavy crude oils by combustion. Experiments by Craig, et al,l have shown the effectiveness of gravity in reducing the efficiency of a miscible displacement when the mixed zone between the displacing and displaced fluids is narrow compared with the height of the system. The presence of a board transition zone from one fluid to the other has been shown by Perkins, et al,2 to nullify considerably the influence of a difference in density. Indeed, the theoretical discussion given by Perrine3 has shown that when the transition zone exceeds a certain critical length the efficiency approaches 100 per cent. Many additional results 495 have been published on miscible and immiscible displacements which show the importance of density difference and also mobility ratio. The aim of the present paper is to discuss some cases of gravity segregation of miscible fluids in linear models such as are often used in the laboratory to evaluate recovery processes, and to supply additional experimental evidence in support of the conclusions. An attempt is made to calculate simply the magnitude of the fluid motion caused by density pdients and mobility ratios, and to quantify the modifications in the fluid motion produced by the combined effect of molecular and convective dispersion. However, it should be pointed out that the uniform permeability of the models and the use of only a single pair of fluids (whereas several pairs of fluids may be employed in a recovery scheme) severely restricts direct conclusions about natural reservoirs. For conciseness, the motion generated by density gradients is emphasized for the case of no bulk flow through the models. This is not a drastic limitation because, as shown in Appendix A, a fluid motion with a constant bulk flow through any linear model is equivalent to a fluid motion with no bulk flow in the same model inclined at a different angle to the horizontal, provided only that the density is a linear function of the viscosity of the fluid mixture. HORIZONTAL MODEL In this case the model is assumed to have a rectangular cross-section with a horizontal breadth b, vertical height and a great length L. Throughout.the paper it will be assumed that x-axis points along the length, the y-axis along the width and the z-axis along the height. Thus, in the present case the x, y plane is horizontal. Initially, the transition zone between the fluids is assumed to be thin and parallel to the y, z plane. An example of this situation in a practical problem arises in a scheme for using air for cushion gas in the storage of fuel gas in aquifers. 6 With the passage of time the denser fluid sinks and spreads along the bottom of the model while the lighter fluid rises. The interface extends from the top plane of the model to the bottom. Experiments have shown that for practical purposes this interface may be treated as a plane surface at all times. The surface is significantly curved, however, for viscosity ratios greater than about 10. Other complications arise with large viscosity ratios because of the nonlinear dependence of the viscosity on the composition of the mixture, so that the simple results given here are restricted to fairly low viscosity ratios.

By J. H. Henderson, R. J. Wygal, J. Naar

Experimental work is reported which shows that consolidated rocks and unconsolidated porous media exhibit different imbibition flow behavior. At a given saturation the imbibition nonwetting permeabilities for a rock are smaller than the drainage permeabilities. The contrary happens for unconsolidated aggregates — imbibition nonwetting permeabilities are larger than drainage ones. A similar difference is observed for the wetting phase. Imbibition permeabilities are larger than drainage ones for a consolidated rock but smaller than drainage permeabilities for an unconsolidated medium. The results of these differences are examined for two cases. 1. Flooding Efficiency — Craig's1 scheme for the computation of production history of a five-spot water flood is shown to agree extremely well with experimental results obtained when using a system packed with glass spheres if imbibition relative permeability curves are used. 2. Alcohol-Slug Displacement — Published theory 2 on oil displacement by alcohol slugs has been questioned despite the apparent agreement between predicted and observed results. The present work suggests that, if imbibition relative permeability curves characteristic of the unconsolidated media used in the early experiments had been available to make the predictions, the inadequacy of the theory would have been immediately evident. The experimental work shows that poorly consolidated formations tend to behave like unconsolidated media. Finally, it is shown that the difference in imbibition behavior is directly related to pore-size distribution and cementation. PART 1 — THE FLOW BEHAVIOR OF UNCONSOLIDATED AGGREGATES Experiments on scaled models of field reservoirs are useful for studying new displacement processes which are incompletely understood. Even when a mathematical description is possible, the solution might be difficult and complex. An answer obtained from a scaled model is extremely valuable in such cases. A great amount of work$-5 therefore, has been devoted to the derivation of scaling laws. Similarity groups have been defined which assume (1) that the relative Permeability curves of the prototype and the model are the same whether the displacement is an imbibition or a drainage process and (2) that there is a linear relationship between the capillary pressure of the model and the prototype. For practical reasons (simplicity in the preparation of models, duration of the experiments, etc.), the porous media of laboratory models are usually unconsolidated packs of sand or glass particles. Hence, unless the capillary and flow characteristics of unconsolidated and consolidated systems are identical, the model data are applicable only to unconsolidated formations. The usefulness of scaled-model studies may then be seriouslyrestricted since most oil-bearing sands are consolidated. Perkins and Collins6 suggested the use of model and prototype curves normalized with respect to both relative permeability and saturation to improve compliance with scaling criteria. Even this technique does not give a satisfactory model-prototype match. This paper reports an observation of two-phase flow in unconsolidated sands which shows that, for most displacements, "scaling" in the strict sense of the word is not even qualitatively feasible with a sand model. It provides, however, a firm foundation for testing a theory by matching it with observed performance of laboratory-size models. EXPERIMENTAL AS a part of a basic study of packed aggregates, the relative permeability of glass-spheres and sand-grain packs was measured with capillary control. The fluids were oil and air' The spheres were packed in plastic cylinders 1-in. in diameter;

By J. J. Taber, I. S. K. Kamath, R. L. Reed

Alcohol floods of consolidated sandstone cores have shown the process to be strongly dependent on the phase behavior of the particular alcobol-oil-water system used. This means that in many cases the mechanism does not conform to the idea of a piston-like displacement. Instead, it is found that by changing the alcohol it is possible to change the relative velocities of the oil and water and, in fact, the entire mechanism of the process. The effects of rate, viscosity, initial saturation, distance travelled and hysteresis of relative permeability on the alcohol flooding mechanism are discussed. INTRODUCTION Reasons for interest in the use of alcohol to miscibly displace oil and water from a porous medium appear in the existing literature.l-7 The mechanism of the displacement has been considered and the apparent implications formulated into a theory which presumably would enable one to predict the essential features of the process.6 Unfortunately, most of the reported experiments have been performed with unconsolidated or artificially consolidated sands. With these systems some of the noteworthy facets of the process are obscured and resulting data appear uncertain. It is the purpose of this paper to show how the use of consolidated sandstones has led to revision of the mechanism and, hence, the theory of alcohol flooding. The practical result is increased pessimism toward the possibilities of commercial application of the simplest form of the alcohol-slug process. However, elucidation of the mechanism has made it possible to define the essential characteristics of a system of slugs which will behave in a nearly piston-like fashion and, thus, yield the best possible result. EQUILIBRIUM PHASE BEHAVIOR Fig. 1 is a diagram of the ternary system isopropyl alcohol (IPA)-Soltrol-calcium chloride brine. Brine was used to prevent plugging of the core and calcium chloride was used because sodium-chloride brine exhibits a solid phase with Soltrol and IPA. If alcohol is added in increments to the immiscible mixture of water and oil represented by Point A, the path followed by the successively equilibrated samples will be on the Line ABC and pass from the immiscible region to the miscible region by crossing the binodal curve at B. Consider the intersection D of this path with the tie Line EF. The quantity of oleic phase is proportional to the Segment ED and the quantity of the aqueous phase is proportional to DF. Compositions of the two phases are specified by Points E and F. It is clear that in the case shown the oleic phase is diminishing and entirely disappears when miscibility is achieved. Such will

By P. T. Bail, J. E. Bobek

In reservoirs containing soft shales interbedded with oil-producing sands, it is possible to have water movement from the shales into the sands during reservoir depletion. This paper presents the results of scaled flow-model tests performed to investigate the efficiency of oil displacement by this vertical influx of water into oil-producing sands. In these model tests, the effects of rate of influx and rock wettability were considered. Oil recoveries by shale-wafer influx and by water flooding were cornpared after 0.4 hydrocarbon volume of water entered the producing sand. This comparison was made for water-wet and oil-wet systems. In water-wet sand, shale-water influx produces slightly less oil than conventional water flooding; in oil-wet sand, shale-water influx produces about one-half as much oil as conventional water flooding. In another type of comparison, it was found that shale-water influx followed by water flooding recovers less oil than water flooding alone. This is true for both water-wet and oil-wet sands. A comparison of tests run at different rates of shale-water influx shows that oil recovery is insensitive to rate in water-wet sand; in oil-wet sand, oil recovery decreases with decreasing rate of influx. INTRODUCTION Localized subsidence of the earth's surface has accompanied the depletion of some oil reservoirs, particularly in California,1, 2 along the Texas Gulf Coast,3 4 and in the Bolivar Coastal fields of Venezuela. Subsidence occurs when fluid withdrawals reduce the pressure in the reservoir. The reasons for subsidence accompanying a reduction in reservoir pressure are not known with certainty.10° However, there is considerable evidence that compaction of soft shale beds adjacent to producing oil sands can be a major cause of this subsi-dence.3, 6, 10-12 When the shales compact, a limited amount of water moves from the shales into the producing sands. A schematic illustration of this oil-producing mechanism is shown in Fig. 1. As the pressure in the sand declines due to oil production, a predominantly vertical pressure gradient develops at the sand-shale boundary. This causes water to move from the shale into the sand as indicated by the solid arrows. This paper reports the results of scaled flow-model tests to investigate the efficiency of oil displacement by the vertical influx of shale water into producing sands. The model tests were not performed with the aim of duplicating the recovery behavior of any specific reservoir. The primary purpose of the tests was to obtain a better understanding of oil displacement by shale-water influx. A knowledge of the oil- and water-production characteristics of even a simplified reservoir system should be of value to engineers estimating the performance of reservoirs where shale-water influx is occurring in conjunction with other production mechanisms. The following limitations and assumptions apply to the model work. 1. The sand of the prototype reservoir is homogeneous and horizontal. 2. The shale-water influx is uniformly distributed along the top and bottom of the sand member being studied. 3. No effects of edge-water drive or dissolved-gas drive that might accompany shale-water influx are considered. PROTOTYPE RESERVOIRS Scaled-model tests were performed to study oil displacement from three prototype reservoir sections. The reservoir sections modeled consist of single sand layers out of a sequence of -sand and -shale layers, as illustrated in Fig. 1. Each prototype represents a homogeneous, high-permeability, unconsolidated sand layer. In the field, the prototype is oriented in such a manner that one end is at the radius of drainage of a producing well and the other end is pointed toward the producing well (Fig. 2). The sand and fluid properties and the dimensions of the three prototypes are given in Table 1. The capillary pressure relationships for the three prototypes are presented in Figs. 3, 4 and 5. The oil-water per-

By J. F. Wilson

Steady-state flow theory, previously applied to displacements with two mobile phases, is extended to cover down-structure flow involving three mobile phases: oil, gas and water. When used with normal reservoir fluid properties, the theory predicts the existence of four distinct flow regimes and the conditions under which each regime exists. The predicted behavior is verified by a parallel-plate model study. INTRODUCTION Special problems exist when a water flood is contemplated in a dipping reservoir having a substantial gas cap. Normally, the gas-cap region is one of very low oil saturation. If oil is moved into the gas cap during the flood, a loss in recovery results. Efficient recovery of the oil underlying the gas is therefore difficult. In two reported field water floods, injection into the gas cap has been used to solve these problems. At the West Norfolk Garr Sand Unit, injection into the upstructure region of the reservoir was made for the stated purpose of filling up the gas cap with water.' The purpose in the Sholem Alechem Fault Block "A" Sims Sand Unit was to form a continuous water barrier between the gas cap and oil band.' A laboratory model study preceded this flood and was described in the same publication. Both of these gas-cap water injections gave satisfactory results, but the published data are insufficient to allow generalizing to other field conditions. The present investigation was also undertaken to obtain results for a specific field problem. However, these results will be shown to be in agreement with an extension of the Dietz3-5 mathematical model to three-phase flowing systems. The agreement between the theory and the model studies indicates that the mathematical model can be used to describe completely the flowing system under some conditions, and to indicate the general type of flow to be expected under all conditions. FLOW THEORY The Dietz equations for two-phase flow are derived "' for the case of constant-velocity linear flow in a homog- eneous porous medium. The transition zone between the fluids is assumed to be of negligible extent so that the displaced and displacing fluids are separated by a sharply defined interface, as illustrated in Fig. 1. The density and mobility of the displacing fluid are constant over the region behind the interface, and the same properties of the displaced fluid are constant over the region ahead of the interface. To extend the Dietz equations to three-phase systems, we postulate the flowing system shown in Fig. 2 and determine the conditions under which it can exist. The

By Wayne E. Glenn

The San Miguelito Field of Ventura County, California, lies along the coast approximately five miles northwest of the city of Ventura. The structure is one of several in the Ventura anticline, a series of anticlinal folds trending northwest-southeast through the San Miguelito Field. The Ventura Avenue Field lies to the southeast along the anticline, and Padre Canyon and Rin-con Fields lie to the northwest; the series then extends beneath the Pacific Ocean. Production is obtained from the Lower Pico and Repetto formations of Pliocene age, and oil accumulation is controlled by faulting, lithology and structure. The first well in the First Grubb Pool was completed in November, 1931, and to date 48 producing wells have been drilled on the 276 productive acres. Approximately 685 ft of net pay are contained in the eight sand bodies grossing 1,220 ft of section. Production of oil to date has been 15,-600,000 bbl. A gas injection project was instigated in April, 1940, but was discontinued in September, 1949. This paper is confined to a discussion of the development and performance history of the First Grubb Pool of the San Miguelito Field. LOCATION AND GEOLOGY The San Miguelito Oil Field is located in Ventura County about five miles northwest of the city of Ventura along the coastal highway to Santa Barbara. It is located within sections 23, 24, 25, and 30 of Township 3 North, Range 24 West, San Bernardino Base and Meridian. Surface elevation in the field ranges from sea level to plus 1,200 ft, and the terrain is extremely rugged. The structure is well defined on the surface and on the wall of the Amphitheatre Canyon where appears a so-called "text book" anticlinal section. The San Miguelito structure is an asymmetrical, elongated anticline about two miles long and three-fourths of a mile wide. The trend of the axis of the anticline is northwest-southeast. Fig. 9 illustrates the contours and major faults of this structure. Dips on the southwesterly flank average about 40 degrees, whereas the northeasterly flank ranges from 60 to 75 degrees. There are several faults striking generally east and west. These faults do not appear to affect materially the area of accumulation or performance behavior. It is believed that accumulation was affected by steeply dipping beds and extremely low permeability of the northeast flank of the structure. As shown by the typical log, Fig. 1. the San Miguelito Field is divided into two stratigraphic producing intervals. The First Grubb Pool comprises the interval from the "G" to "L" markers; the Second Grubb Pool from the "L" to "M" markers. The First Grubb Pool, ranging in thickness from 1,105 to 1,680 ft, with an average of 1,220 ft, includes approximately 685 ft of oil-bearing sands. The First Grubb zone consists of eight sand intervals separated by shales. The shale bodies separating the eight sand intervals within the First Grubb Pool are continuous throughout the major part of the structure and serve as an effective barrier. Many of the thin, irregular shale or siltstone streaks within these sand bodies are discontinuous and do not affect well performance appreciably. The productive horizons in the First Grubb Pool are siltstones and sandstones of the Lower Pico and Repetto formations of Pliocene age. It is apparent from inspection of the typical log that the "G" to "L" interval might have been separated into at least six producing zones and selectively pro. duced. Unfortunately the electric log and some of our modern tools were not available or were in their infancy dur. ing the period 1931 through 1937. Not until 1937 when eight wells had been completed were there sufficient geological data to permit definition of the sand bodies. Then the problem of reservoir control in this multiple-sand field, where all sands are open to a common

Jan 1, 1950

By E. P. Burtchaell

A method is presented for evaluating the effect of gravity drive upon the reservoir performance of a high relief pool. Conventional forms of reservoir analysis do not consider the alterations in the basic material balance data caused by gravity segregation of reservoir fluids. A procedure is outlined for structurally weighting physical and chemical data for use in the material balance equation. It is demonstrated how actual pool performance data can be utilized to evaluate the future reservoir performance of a gravity drive pool. INTRODUCTION Conventional reservoir engineering. procedure is inadequate for the analysis of an oil pool which has considerable structural relief, steep dips, and good permeability development. In, pools of this type, gravity drainage has an important part in the movement of oil to the wells and the effects of gravity on the overall pool performance should be included in any analysis of reservoir behavior. Many engineers have the opinion that the force of gravity in the movement of oil is not important until the later life of a pool.' Probably the basis for this belief is that gravitational effects may not be readily discernible until a pool is nearing depletion. This would be especially true for pools not having a high degree of structural relief and permeability development. Actually the effects of gravitational forces are at a maximum when the pool pressure is high, for during this period the hydrostatic head of the oil column is at a maximum and the viscosity of the oil is at a minimum. Oil recoveries from pools having favorable gravity drive characteristics may equal or even exceed recoveries which might be expected from water displacement. Field evidence indicates that in some reservoirs gravity drive has resulted in recoveries greater than that which could have been expected from gas expansion or water drive.'.3 Unfortunately, the possible effects of gravity drive on pool performance have been underestimated and other reasons have been sought to explain the high recoveries obtained. There are unquestionably many reservoirs to which the principles of gravity drainage can be effectively applied. It is the purpose of this paper to illustrate one method whereby gravity drive is included in the reservoir analysis of an oil pool. A hypothetical pool, typical of many California reservoirs, is used as an example. As used in this paper, "gravity drive" is defined as the overall effect of gravitational influences on the recovery of petroleum from the reservoir; "gravitational segregation" as the gravity separation of oil and gas within the reservoir; and "gravity drainage" as the downward movement of oil as caused by the force of gravity. SAND VOLUME DATA Fig. 1 presents a structural contour map of the pool under study. Maximum closure is 1950 feet with dips on the south flank approaching 45". The original gas-oil interface was set at -5200 feet. Average thickness of the producing sand was 200 feet. For use in subsequent calculations ill this paper, the pool was subdivided into 100-foot vertical increments and the sand-volume content of each increment was obtained. If the gross sand thickness is small, under 100 feet, the sand-volume content can be obtained by superimposing an isopachous map upon a structural contour map and planimetering the average thickness of each 100-foot increment. For sand thicknesses over 100 feet, one approacli would be to construct a sufficient number of cross-sections of the pool from which the weighted sand-volume of each 100-foot increment could be obtained. Variations in the sand body with depth, as determined by core data, can also be included in the above process. Table I presents a summary of sand-volume calculations, core data, and the original distribution of reservoir hydrocarbons in the pool. Fig. 2 illustrates the structural distribution of the sand-volume content. A total of 171,398 acre-feet is contained within the productive limits of the pool. Assuming an average porosity of 25% and an interstitial water content of 20%, the original hydrocarbon content was computed to be 227,075,000 barrels. DEPTH-PRESSURE DATA The determination of the initial vertical pressure arrangement in the pool is necessary for PVT and material balance calculations. Whenever sufficient data are available, a plot of pressure versus subsea depth of measurement should be made. From this plot a representative fluid pressure gradient can be established. Lacking sufficient initial pressure data, an initial pressure gradient may he estimated or calculated from avail-

Jan 1, 1949

By E. P. Burtchaell

A method is presented for evaluating the effect of gravity drive upon the reservoir performance of a high relief pool. Conventional forms of reservoir analysis do not consider the alterations in the basic material balance data caused by gravity segregation of reservoir fluids. A procedure is outlined for structurally weighting physical and chemical data for use in the material balance equation. It is demonstrated how actual pool performance data can be utilized to evaluate the future reservoir performance of a gravity drive pool. INTRODUCTION Conventional reservoir engineering. procedure is inadequate for the analysis of an oil pool which has considerable structural relief, steep dips, and good permeability development. In, pools of this type, gravity drainage has an important part in the movement of oil to the wells and the effects of gravity on the overall pool performance should be included in any analysis of reservoir behavior. Many engineers have the opinion that the force of gravity in the movement of oil is not important until the later life of a pool.' Probably the basis for this belief is that gravitational effects may not be readily discernible until a pool is nearing depletion. This would be especially true for pools not having a high degree of structural relief and permeability development. Actually the effects of gravitational forces are at a maximum when the pool pressure is high, for during this period the hydrostatic head of the oil column is at a maximum and the viscosity of the oil is at a minimum. Oil recoveries from pools having favorable gravity drive characteristics may equal or even exceed recoveries which might be expected from water displacement. Field evidence indicates that in some reservoirs gravity drive has resulted in recoveries greater than that which could have been expected from gas expansion or water drive.'.3 Unfortunately, the possible effects of gravity drive on pool performance have been underestimated and other reasons have been sought to explain the high recoveries obtained. There are unquestionably many reservoirs to which the principles of gravity drainage can be effectively applied. It is the purpose of this paper to illustrate one method whereby gravity drive is included in the reservoir analysis of an oil pool. A hypothetical pool, typical of many California reservoirs, is used as an example. As used in this paper, "gravity drive" is defined as the overall effect of gravitational influences on the recovery of petroleum from the reservoir; "gravitational segregation" as the gravity separation of oil and gas within the reservoir; and "gravity drainage" as the downward movement of oil as caused by the force of gravity. SAND VOLUME DATA Fig. 1 presents a structural contour map of the pool under study. Maximum closure is 1950 feet with dips on the south flank approaching 45". The original gas-oil interface was set at -5200 feet. Average thickness of the producing sand was 200 feet. For use in subsequent calculations ill this paper, the pool was subdivided into 100-foot vertical increments and the sand-volume content of each increment was obtained. If the gross sand thickness is small, under 100 feet, the sand-volume content can be obtained by superimposing an isopachous map upon a structural contour map and planimetering the average thickness of each 100-foot increment. For sand thicknesses over 100 feet, one approacli would be to construct a sufficient number of cross-sections of the pool from which the weighted sand-volume of each 100-foot increment could be obtained. Variations in the sand body with depth, as determined by core data, can also be included in the above process. Table I presents a summary of sand-volume calculations, core data, and the original distribution of reservoir hydrocarbons in the pool. Fig. 2 illustrates the structural distribution of the sand-volume content. A total of 171,398 acre-feet is contained within the productive limits of the pool. Assuming an average porosity of 25% and an interstitial water content of 20%, the original hydrocarbon content was computed to be 227,075,000 barrels. DEPTH-PRESSURE DATA The determination of the initial vertical pressure arrangement in the pool is necessary for PVT and material balance calculations. Whenever sufficient data are available, a plot of pressure versus subsea depth of measurement should be made. From this plot a representative fluid pressure gradient can be established. Lacking sufficient initial pressure data, an initial pressure gradient may he estimated or calculated from avail-

Jan 1, 1949

By D. R. McCord

Data of a known statistical quality has been successfully used in a system of conventional fluid mechanics equations essentially free of empirical "conformance factors to prediet early detailed field 03 in a reservoir where gravity drainage is important and oil and rock properties vary con. siderably. The system is useful where comparative recovery predictions for one or more cases of natural depletion and gas cap pressure maintenance are needed and the reservoir is not too heterogeneous. INTRODUCTION Many authors, have examined various facet* of the gravity drainage-gas cap pressure maintenance problem over the last several years. Two of them. Burtchaell and Elkins, have published practical studies. In the case described in the present paper the best development and operating plan for one of the important reservoirs of the Bolivar Coastal Field in Western Venezuela was urgently needed. It was requested that sound comparative economics be presented along with an engineering evaluation of no additional drilling, maximum drilling. several cases of gas pressure maintenance, of water flooding and combination cases. A rapid analysis of the effect on recovery of the range of crude and rock properties indicated that none of the published methods using average properties would yield adequate comparative predictions. This paper covers the predictive system developed to deal with natural depletion and gas cap pressure maintenance. The large amount of data available for this field permitted statistically reliable correlations to be made of most rock and oil properties, and the evident smooth areal variations of these properties encouraged the construction of a lineal mathematical model of material balance and fluid flow equations, which could be manipulated by a modified iterative procedure. The manipulation is much more adaptable to computing machines than manually operated calculators and subsequent studies have been prepared for the IBM Card Program Calculator. A matrix as opposed to linear model has been tentatively worked out by other members of our group to deal with more heterogeneous reservoirs. It is more adaptable to computers such as IBM-701 or the Remington-Rand Univac. In 1950, when the system reported below was developed, no rapid computing machines were available to the author. Their existence and promise encouraged an initial approach by hand. Some details of oil and rock Property correlation are included because there are a surprisingly large number of medium-sized reservoirs in the world that show systematic property variations which are significant for a rigorous analycon. All large reservoirs (over half a billion barrels recovery) with which the author is familiar contain at minimum a significant temperature variation. Using the rock and oil property correlations, past pressure and production, the gas-oil ratio history of the reservoir was computed and found to be in close agreement with field measurements. The future performance under cases of natural depletion, gas injection of 100 MMcf/day, and of 130 MMcf/day, was then computed; a 70 MMcf/day case was also carried far enough to provide data for comparative economics. The 130 MMcf/day case proved to be the most attractive. A 50,000 horsepower gas turbine driven centrifugal compressor plant to take this quantity of adjacent field gas from 30 to 1,950 psia and inject it into the reservoir is under construction. The total cost of the project will exceed 20 million dollars.

Jan 1, 1953