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By Walter Rose, W. A. Bruce

Improved apparatus, methods, and experimental techniques for determining the capillary pressure-saturation relation are described in detail. In this connection a new multi-core procedure has been developed which simplifies the experimental work in the study of relatively homogeneous reservoirs. The basic theory concerning the Leverett capillary pressure function has been extended and has been given some practical application. Some discussion is presented to indicate the relationship of relative permeability to capillary pressure, and to provide a new description of capillary pressure phenomena by introducing the concept of the psi function. INTRODUCTION For the purposes of this paper the capillary character of a porous medium will be defined to express the basic properties of the system, which produce observed results of fluid behavior. These basic properties may be classified in the following manner, according to their relationship to: (a) The geometrical configuration of the interstitial spaces. This involves consideration of the packing of the particles, producing points of grain contact, and variations in pore size distribution. The packing itself is often modified by the secondary processes of mineralization which introduces factors of cementation, and of solution action which causes alteration of pore structure. (b) The physical and chemical nature of the interstitial surfaces. This involves consideration of the presence of interstitial clay coatings, the existence of non-uniform wetting surfaces; or, more generally, a consideration of the tendency towards variable interaction between the interstitial surfaces and the fluid phases saturating the interstitial spaces. (c) The physical and chemical properties of the fluid phases in contact with the interstitial surfaces. This involves consideration of the factors of surface, interfacial and adhesion tensions; contact angles; viscosity; density difference between immiscible fluid phases; and other fluid properties. Fine grained, granular, porous materials such as found in petroleum reser~oir rock possess characteristics which are expressible by (1) permeability, (2) porosity, and (3) the capillary pressure-saturation behavior of immiscible fluids in this medium. These three measurable macroscopic properties depend upon the microscopic properties enumerated above in a manner which defines the capillary character. Systems of capillary tubes or regularly packed spheres may be thought of as ideal and numerous references can be cited in which exact mathematical formulations are developed to show the relationships governing the static distribution and dynamic motion of fluids in their interstitial spaces. The capillary character of non-ideal porous systems such as reservoir rock also is basic in determining the behavior of fluids contained therein; although, in general, the connection is not mathematically derivable but must be approached through indirect experimental measurement. This paper gives consideration to the evaluation of petroleum reservoir rock capillary character. The methods employed may be applied to the solution of problems in other fields, and the conclusions reached should contribute to the basic capillary theory of any porous system containing fluid phases. In this paper, a modification of the core analysis method of capillary pressure is employed and it is intended to show that the capillary character of reservoir rock can be expressed in terms of experimental quantities. A very general method of interpretation correlating the capillary pressure tests with fundamental characteristics such as rock texture, surface areas, permeability, occasionally clay content and cementation is introduced. Eventually an attempt is made for establishing a method of deriving relative permeability to the wetting phase from capillary pressure data. The experimental evaluation of capillary character must be approached in a statistical manner if reservoir properties are to be inferred from data on small cores. This is implied by the heterogeneous character of most petroleum reservoirs, and suggests that considerable intelligence should be applied in core sampling. Finally, this paper supports the view that once the capillary character of a given type of reservoir rock has been established by core analysis, fluid behavior can then be inferred in other similar rock. Although no great progress has been made in establishing what variation can be tolerated without altering the basic fluid behavior properties, evidence will be presented to indicate that certain reservoir formations are sufficiently homogenous with respect to capillary character that the data obtained on one core will be useful in predicting the properties of other cores of similar origin. Tests have shown that cores under consideration can vary widely with respect to porosity and permeability and still be considered similar in capillary character. EXPERIMENTAL METHODS AND TECHNIQUES Various types of displacement cell apparatus for capillary pressure experiments have been described in the literature. Bruce and Welge; Thornton and Marshall; McCullough, Albaugh and Jones3; Hassler and Brunner; Lever-

Jan 1, 1949

By Walter Rose, W. A. Bruce

Improved apparatus, methods, and experimental techniques for determining the capillary pressure-saturation relation are described in detail. In this connection a new multi-core procedure has been developed which simplifies the experimental work in the study of relatively homogeneous reservoirs. The basic theory concerning the Leverett capillary pressure function has been extended and has been given some practical application. Some discussion is presented to indicate the relationship of relative permeability to capillary pressure, and to provide a new description of capillary pressure phenomena by introducing the concept of the psi function. INTRODUCTION For the purposes of this paper the capillary character of a porous medium will be defined to express the basic properties of the system, which produce observed results of fluid behavior. These basic properties may be classified in the following manner, according to their relationship to: (a) The geometrical configuration of the interstitial spaces. This involves consideration of the packing of the particles, producing points of grain contact, and variations in pore size distribution. The packing itself is often modified by the secondary processes of mineralization which introduces factors of cementation, and of solution action which causes alteration of pore structure. (b) The physical and chemical nature of the interstitial surfaces. This involves consideration of the presence of interstitial clay coatings, the existence of non-uniform wetting surfaces; or, more generally, a consideration of the tendency towards variable interaction between the interstitial surfaces and the fluid phases saturating the interstitial spaces. (c) The physical and chemical properties of the fluid phases in contact with the interstitial surfaces. This involves consideration of the factors of surface, interfacial and adhesion tensions; contact angles; viscosity; density difference between immiscible fluid phases; and other fluid properties. Fine grained, granular, porous materials such as found in petroleum reser~oir rock possess characteristics which are expressible by (1) permeability, (2) porosity, and (3) the capillary pressure-saturation behavior of immiscible fluids in this medium. These three measurable macroscopic properties depend upon the microscopic properties enumerated above in a manner which defines the capillary character. Systems of capillary tubes or regularly packed spheres may be thought of as ideal and numerous references can be cited in which exact mathematical formulations are developed to show the relationships governing the static distribution and dynamic motion of fluids in their interstitial spaces. The capillary character of non-ideal porous systems such as reservoir rock also is basic in determining the behavior of fluids contained therein; although, in general, the connection is not mathematically derivable but must be approached through indirect experimental measurement. This paper gives consideration to the evaluation of petroleum reservoir rock capillary character. The methods employed may be applied to the solution of problems in other fields, and the conclusions reached should contribute to the basic capillary theory of any porous system containing fluid phases. In this paper, a modification of the core analysis method of capillary pressure is employed and it is intended to show that the capillary character of reservoir rock can be expressed in terms of experimental quantities. A very general method of interpretation correlating the capillary pressure tests with fundamental characteristics such as rock texture, surface areas, permeability, occasionally clay content and cementation is introduced. Eventually an attempt is made for establishing a method of deriving relative permeability to the wetting phase from capillary pressure data. The experimental evaluation of capillary character must be approached in a statistical manner if reservoir properties are to be inferred from data on small cores. This is implied by the heterogeneous character of most petroleum reservoirs, and suggests that considerable intelligence should be applied in core sampling. Finally, this paper supports the view that once the capillary character of a given type of reservoir rock has been established by core analysis, fluid behavior can then be inferred in other similar rock. Although no great progress has been made in establishing what variation can be tolerated without altering the basic fluid behavior properties, evidence will be presented to indicate that certain reservoir formations are sufficiently homogenous with respect to capillary character that the data obtained on one core will be useful in predicting the properties of other cores of similar origin. Tests have shown that cores under consideration can vary widely with respect to porosity and permeability and still be considered similar in capillary character. EXPERIMENTAL METHODS AND TECHNIQUES Various types of displacement cell apparatus for capillary pressure experiments have been described in the literature. Bruce and Welge; Thornton and Marshall; McCullough, Albaugh and Jones3; Hassler and Brunner; Lever-

Jan 1, 1949

By John C. Calhoun, R. C. Newman

A report is made of experimental work performed on the capillary retention of water within porous solid systems, the displacement being accomplished with air and various organic liquids. A portion of the experiments were designed to measure the lowering of vapor pressure of water within a porous solid with subsequent conversion of such vapor pressure data to capillary pressure values. The form of the capillary pressure curve at high capillary pressures has been elucidated from this data. Certain theoretical approaches are presented to indicate the correlation between work done by previous investigators. The present work is correlated also with theory. Surface area values are calculated for the various core systems studied. INTRODUCTION Leverettl in 1941 presented a paper which gave the essential concepts of capillary behavior in porous solids. His presentation included both theoretical and experimental aspects of the problem. He defined the term "capillary pressure" and applied it to an ideal porous system. His work included the definition of a dimensionless quantity which was a function of fluid saturation and which could be correlated with porosity and permeability for clean, unconsolidated sands. His experimental work was performed by the drainage of water from packed columns of unconsolidated sands. Subsequently, other authors have presented experimental techniques which permit the determination of capillary pressure data on small core samples. Data have been presented on porous systems other than unconsolidated sand and with the use of liquids other than water. Notable among these are the works of Hassler, Brunner and Deahl,2 Bruce and Welge,³ Amyx and Yuster, and Purcell. Others have indicated the applicability of such data to field problems without regard to the theoretical aspects of the capillary pressure saturation function. Within the recent published literature there have also been reported studies of the correlations between capillary pressure data and other fundamental properties of porous solids. It was the intent of the present reported work to investigate the behavior noted by water and various other liquids within porous systems in an attempt to amplify existing correlations between capillary properties, surface properties, and other fundamental characteristics of porous systems. The experimental work described here was performed as two different investigations but due to its nature it is reported as separate phases of the same general topic. CAPILLARY PRESSURE AND VAPOR PRESSURE LOWERING It has long been recognized that the vapor pressure above the curved surface of a liquid is a function of the curvature of the liquid surface." The capillary pressure is also a function of the curvature of the liquid surface. Both capillary pressure values and vapor pressure lowering are, therefore, functions of the liquid saturation of a porous solid. A quantitative relationship between the vapor pressure lowering and the capillary pressure can be simply developed by considering a porous solid system containing water in equilibrium with its vapor. The capillary pressure at any height within the system is defined as Pc= Pv -P1.......(1) where PI is the pressure in the vapor phase and PI is the pressure in the liquid phase. Consider that both the water and its vapor are continuous phases within the system and that at any point the two phases are in equilibrium. The gradients in the liquid and vapor columns within the porous system are: PI = plgdh dPv = pvgdh By integrating these gradients from the point where h = 0 to the height h, values of PI and PI at the point h are found. Let the point where h = 0 be that where Pc = 0. At this point also Pv is equal to Pve, the equilibrium vapor pressure of the liquid above a flat surface. From the first of these integrations since p is independent of height: P = p1gh + P, From the second, by substituting pv = PvM/RT, where M is the molecular RT weight: Pv M Pvo- RT gh By combining the two last equations to eliminate h, one obtains: P1 RT Pv Substituting, values for Pv and Pi in equation (1) gives PyRT RT Pv which is approximately Pc=RT/Mp1 In Pvo/Pv .......(2) This equation relates the vapor pressure above a curved surface with the capillary pressure across the curved surface in terms of measurable quantities. The equivalent of this equation is given by Freundlich."

Jan 1, 1949

By John C. Calhoun, R. C. Newman

A report is made of experimental work performed on the capillary retention of water within porous solid systems, the displacement being accomplished with air and various organic liquids. A portion of the experiments were designed to measure the lowering of vapor pressure of water within a porous solid with subsequent conversion of such vapor pressure data to capillary pressure values. The form of the capillary pressure curve at high capillary pressures has been elucidated from this data. Certain theoretical approaches are presented to indicate the correlation between work done by previous investigators. The present work is correlated also with theory. Surface area values are calculated for the various core systems studied. INTRODUCTION Leverettl in 1941 presented a paper which gave the essential concepts of capillary behavior in porous solids. His presentation included both theoretical and experimental aspects of the problem. He defined the term "capillary pressure" and applied it to an ideal porous system. His work included the definition of a dimensionless quantity which was a function of fluid saturation and which could be correlated with porosity and permeability for clean, unconsolidated sands. His experimental work was performed by the drainage of water from packed columns of unconsolidated sands. Subsequently, other authors have presented experimental techniques which permit the determination of capillary pressure data on small core samples. Data have been presented on porous systems other than unconsolidated sand and with the use of liquids other than water. Notable among these are the works of Hassler, Brunner and Deahl,2 Bruce and Welge,³ Amyx and Yuster, and Purcell. Others have indicated the applicability of such data to field problems without regard to the theoretical aspects of the capillary pressure saturation function. Within the recent published literature there have also been reported studies of the correlations between capillary pressure data and other fundamental properties of porous solids. It was the intent of the present reported work to investigate the behavior noted by water and various other liquids within porous systems in an attempt to amplify existing correlations between capillary properties, surface properties, and other fundamental characteristics of porous systems. The experimental work described here was performed as two different investigations but due to its nature it is reported as separate phases of the same general topic. CAPILLARY PRESSURE AND VAPOR PRESSURE LOWERING It has long been recognized that the vapor pressure above the curved surface of a liquid is a function of the curvature of the liquid surface." The capillary pressure is also a function of the curvature of the liquid surface. Both capillary pressure values and vapor pressure lowering are, therefore, functions of the liquid saturation of a porous solid. A quantitative relationship between the vapor pressure lowering and the capillary pressure can be simply developed by considering a porous solid system containing water in equilibrium with its vapor. The capillary pressure at any height within the system is defined as Pc= Pv -P1.......(1) where PI is the pressure in the vapor phase and PI is the pressure in the liquid phase. Consider that both the water and its vapor are continuous phases within the system and that at any point the two phases are in equilibrium. The gradients in the liquid and vapor columns within the porous system are: PI = plgdh dPv = pvgdh By integrating these gradients from the point where h = 0 to the height h, values of PI and PI at the point h are found. Let the point where h = 0 be that where Pc = 0. At this point also Pv is equal to Pve, the equilibrium vapor pressure of the liquid above a flat surface. From the first of these integrations since p is independent of height: P = p1gh + P, From the second, by substituting pv = PvM/RT, where M is the molecular RT weight: Pv M Pvo- RT gh By combining the two last equations to eliminate h, one obtains: P1 RT Pv Substituting, values for Pv and Pi in equation (1) gives PyRT RT Pv which is approximately Pc=RT/Mp1 In Pvo/Pv .......(2) This equation relates the vapor pressure above a curved surface with the capillary pressure across the curved surface in terms of measurable quantities. The equivalent of this equation is given by Freundlich."

Jan 1, 1949

By C. C. Templeton, S. S. Rushing

Methods previously developed for the study of air-liquid displacements in microscopic capillaries (inner diameters of 3 to 40 microns) have been used to investigate oil-water displacements in capillaries initially filled with water. Displacement calculations assuming perfect displacement and no capillary pressure hysteresis yielded oil effective viscosities smaller than the macroscopic viscosities. For a given liquid pair, the oil effective viscosity decreased both with decreasing capillary size and with increasing oil-water viscosity ratio. This behavior can be explained by the existence of an annular water film (20 A to 260 A thick) on the capillary wall. When the capillary was first filled with oil, the ratio of the oil effective viscosity to the normal oil vircosity was highest for the first water displacement and decreased with subsequent displacements. Sometimes the oil effective viscosity ratio during the initial water displacement was greater than unity. INTRODUCTION In a previous paper1 a technique was described for studying air-liquid and liquid-liquid displacements in very small capillaries of uniform diameter, in the hope that such microscopic data would further the understanding of the nature of multiphase fluid flow through porous media. That paper contained comprehensive data for air-liquid displacements in Pyrex capillaries, with a few data for oil-water displacements in capillaries initially filled with water. The purpose of this paper is to present more complete results for oil-water displacements in capillaries initially filled with water, and to describe for the first time such observations in capillaries initially filled with oil. In this way the effect of the wetting history of the system upon the displacement process may be studied. METHODS The basic techniques employed were described in the previous paper.1 The measuring procedure and the working equations will be briefly summarized here and a few modilications will be pointed out. For the present study, temperature control within 0.l °C was obtained by placing the microscope and its immediate accessories in a thermostated air bath made of a steel frame covered with plexiglas. The water and oils used in this work were the same as in the previous paper,1 with the addition of "Medium Mineral Oil, U.S.P. supplied by the Harshaw Scientific Co. When the first liquid was introduced into the horizontal capillary, the air-liquid static capillary pressure Poc was measured along the observable length of the capillary. From the relation Poc = 4y cos 0/d, the capillary diameter d could be calculated from Poc if the "microscopic" air-liquid boundary tension, To = y cos On, was taken as equal to its known "macroscopic" value. This calculation involves assuming that cos 6 = 1 and that capillary size or the resulting high interfa-cial curvature has no effect on surface tension, or y cos 6, as was verified by our work, and also by that of Cohan and Meyers on air-liquid-solid systems. For several capillaries these calculated diameter values were compared with values measured visually with a filar micrometer eyepiece. For a given capillary the average values for the two methods agreed within 1 or 2 per cent, but the visual values were less reproducible than the calculated values. Further the calculated values were much less subject to personal bias and took into account any slight ellipticity that might be present. Hence diameters calculated from air-liquid Poc data were used throughout this paper. The second liquid was introduced in such a way that a single spherical interface separated the two liquids. Displacements were always made with a constant pressure, Pt, between the ends of the capillary. The times (t) at which the interface passed certain

Jan 1, 1957

By I. Fatt

This paper proposes the network of tubes as a model more closely representing real porous media than does the bundle of tubes. Capillary pressure curves are derived from network models and pore size distributions are calculated from these curves. In this way is shown the difference between the true and calculated pore size distributions when the capillary pressure curve is used to obtain pore size distribution for porous media. INTRODUCTION Despite the technological importance of the laws governing flow through porous media, many of these laws have not yet been clearly formulated. This is especially true of the laws governing multiphase flow. The static properties, such as the capillary pressure curve, are also not at present interpretable correctly in terms of the pore size distribution and other structural properties of porous media. In the absence of any well founded theoretical description of fluid flow through porous media, many empirical descriptions have been proposed. In addition to the strictly empirical flow equa- tions, some equations have been developed rigorously from simple geometrical models of the pore spaces. These equations are only as valid as is the model used in their development. The two models used in the past, the sphere pack and the bundle of tubes, have been too simple, and as a result, the equations derived from them have failed to predict the observed properties. Agreement between theory and observation has been achieved for these models by inserting parameters of doubtful physical significance. The work to be reported here was undertaken in the belief that the study of a model more closely resembling most real porous media than does the sphere pack or bundle of tubes would yield useful information concerning the structure of real porous media and the relation between structure and flow properties. There was no intention of developing any calculational procedures, as for example calculating relative permeability from capillary pressure data. The objective of the study was instead to develop a better qualitative understanding of the relation between the various measurable properties of porous media. The model chosen for study is the network of tubes in which each tube represents a pore space in the porous medium. Microscopic observations leave no doubt that sandstones and clastic carbonates are three-dimensional irregular networks of irregularly shaped pores. The irregularity of these structures makes any accurate theoretical study of their properties impossible. Results from an oversimplified model such as the bundle of tubes are worthless when applied to real systerns. The sphere pack model, on the other hand, not

Jan 1, 1957

By I. Fatt

Networks of resistors are used as analog computers to obtain relative permeability and resistivity index curves for networks of tubes. These curves have all of the characteristics of those obtained on porous media and, therefore demonstrate the validity of the network of tubes model. INTRODUCTION In paper I' of this series the network model was shown to give information on the structure of porous media that could not be obtained from the bundle of tubes model. The agreement between the capillary pressure characteristics of a network of tubes and those of typical porous media does not prove the validity of the network made. The bundle of tubes model, although it gives less information, also shows this agreement. In this paper the flow properties of a network of tubes are shown to be in agreement with flow properties of porous media. The flow properties of the bundle of tubes model are not in adequate agreement with those of porous media. The dynamic properties of porous media, such as fluid permeability and electrical conductivity, have been found experimentally to be more sensitive functions of structure and pore size distribution than are the static properties such as porosity and capillary pressure characteristics. The network model can, therefore, be best tested by comparing the dynamic properties of a network of tubes with the observed properties of porous media. All static and dynamic properties of a completely valid model must agree with the observed properties. The most commonly measured sensitive dynamic properties are the relative fluid permeability and the relative electrical resistivity. Experimental measurements of these dynamic properties on sandstone, sintered glass, sintered alumina, and soil are reported in the petroleum and soil science literature. These properties were chosen, therefore, for the test of the network model. In the network model, relative permeability is the permeability of the network when some of the tubes are not conducting fluid, relative to the permeability when all tubes are conducting fluid. Similarly, the relative resistivity is the electrical resistivity of the network of tubes when some of the tubes are filled with a nonconductor. relative to the resistivity when all tubes are filled with the electrical conducting fluid. Single Size Tube Network The simplest porous medium is one in which all pores are of the same size. Such media can be approached by packing beds or columns of uniform size particles of sand, glass, or metal. The model of such medium in this study is a network of single size tubes. The network form, the ß factor, is usually not known for real porous media. If the validity of the network model can be established, then the study of the flow properties

Jan 1, 1957

By I. Fatt

Relative permeability and relative electrical resistivity curves are obtained for networks of tubes with a tube radius distribution by means of a network of resistors used as an analog model. These curves are similar to those obtained from real porous media. The effects of pore size distribution and network structure on relative permeability and resistivity are demonstrated. INTRODUCTION Study of the dynamic properties of networks of single size tubes in paper IT' of this series has shown that the network model has flow properties similar to those observed on real porous media. The comparison of properties of single size tube networks with those of real porous media cannot be carried far because very few porous media have uniform size pores. The capillary pressure curve from most porous materials such as soil, sandstone, and sintered glass indicate that these materials have pore size distribution similar to those shown in Figs. 5-1, 9-1, and 10-I.† To properly test the network model, it is therefore necessary to compare the dynamic properties of real porous media with those of networks of tubes in which the tube radii are distributed accord- ing to the distributions in the aforementioned figures. A network in which the tube sizes are distributed cannot be treated in the same manner as a network of single size tubes. In the single size tube network, the relation between tube geometry, flow resistance, and tube volume did not have to be known if the assumption was made that whatever relation did exist was the same for all tubes in a particular network. In a network of distributed tube size, the relation between tube geometry and flow resistance must be known or assumed in order to replace the tubes by equivalent electrical resistors. Relation of Tube Geometry to Flow Resistance The interchangeability of tubes and electrical resistors in the network model is possible because of the analogy between Poiseuille's law and Ohm's law. Poiseuille's law for a cylinder is q= pr4/8µl ?P.........(1) where q is the volumetric rate of flow, µ is the viscosity, ?P is the pressure gradient, r is the tube radius, and 1 is the tube length. Ohm's law is I=1/R?E..........(2) where I is the flux and is equivalent to the volumetric rate in Poiseuille's law, R is the resistance, and ?E is the voltage gradient. Both laws give the flux as a function of the potential drop and the resistance of the medium. By analogy then, 1/R=pr4/8µl ?P...........(3)

Jan 1, 1957

By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy's law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy's law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By T. M. Geffen, J. L. Sanderlin, F. F. Craig, D. W. Moore

Scaled reservoir models have been used to study the effect of gravity on oil recovery performance in frontal-drive operations; namely, water, gas, or solvent flooding. The difference in density between the reservoir oil and the injected fluid causes their segregation, resulting in a non-uniform advance of the fluid front. In the laboratory flow tests, which simulated both five-spot and linear injection operations in flat reservoirs, the viscous, capillary, and gravity forces present in these operations were scaled. Dyed fluids were used so that the gross movement of the injected fluid could be observed. The studies covered a range of injection rates, formation thicknesses, and rock and fluid properties normally encountered in field operations. The results of the model tests indicate that the volume of the reservoir contacted by the injected fluid at its breakthrough into the producing well is less than that expected based on information which neglects gravity effects. This difference can often be as much as 80 per cent by gas or water injection in uniform sand bodies. Preliminary flow tests on a non-uniform sand body indicate that the uniformity of the flood fronts may in some situations be influenced to a much greater degree by permeability variations within the rock body than by gravity effects. The magnitude of fluid segregation due to gravity is controlled by the average injection rate, rather than day to day or week to week variations. INTRODUCTION One of the important factors controlling the oil recovery from a frontal-drive operation, such as water, gas, or solvent injection, is the volumetric sweep efficiency. This factor is a measure of the gross portion of the reservoir that is contacted by the displacing fluid. The volumetric sweep efficiency is influenced by gravity effects, well arrangements, and variations in rock permeability within the reservoir. The gravity effects are due to the displacing fluid being of different density than the reservoir oil. This causes the displacing fluid to move preferentially toward either the top or bottom of the formation. Non-uniform advance of the flood front can be caused by the relative positions of the injection and production wells. Variations in rock permeability also result in an uneven advance of the displacing fluid. Gas zones, representing paths of low resistance, may result in non-uniform movement of the injected fluid. The more uneven the advance of the displacing fluid, the lower is the volumetric sweep efficiency and thus the lower the oil recovery efficiency. The effects of well arrangement and permeability variations, upon the gross movement of the injected fluid have been the subjects of extensive investiga-ti0ns.1,2,3,4,5,6 Gravity effects have been recognized as being present in frontal-drive operations'.' but there has been little quantitative measure of their magnitude. Very likely the reason gravity effects have not been studied is that this problem does not lend itself to simple experimental or mathematical analysis. The development of reservoir modeling techniques has made possible a quantitative determination of the effect of gravity on fluid segregation and thus upon the oil recovery performance of frontal-drive operations. This paper presents a progress report on a laboratory investigation of gravity effects in fully liquid-saturated, horizontal, uniform as well as non-uniform systems. These results were obtained from scaled experiments on both linear and five-spot systems within the range of conditions normally encountered in secondary recovery operations. This study is concerned with the gross movement of the injected fluid to the time it first reaches the production wellbore. Therefore, it should be emphasized that the results of this paper can not be used to determine the effect of gravity segregation on oil recovery efficiency at abandonment conditions. MODEL SCALING The science of scaling models is relatively new as applied as petroleum production problems, Many of the scaling techniques have been adaptions of those used in basic studies of heat and fluid flow. There are

Jan 1, 1958

By John C. Calhoun, Frank T. Bethel

The application of a method for analyzing pressure build-up curves to determine the effective permeability in the Spraberry is presented. Sixteen upper Spraberry wells of the Driver area arc analyzed and show variations in the in-place effective permeability of 2 to 183 md. Since these value- are much larger than the .5 md. or less reported for the matrix rock. a large part of the vertical fractures noted in Spraberry cores- must be considered native to the formation. The effectiveness of the well fracture treatment in connecting the well bore to the native fracture system is analyzed by comparison of the effective permeability as determined from the PI test to that obtained from a pressure build-up curve. These results show that the fracture treatment is sufficiently effective in connecting tile well bore to the native fractrure system to yield a flow capacity within about 50 per cent of that dictated by the native fracture system About two-thirds of the wells show some degree of local blockage. INTRODUCTION Fractured reservoirs have been known in the past.' However, during the past two years the Spraberry formation has directed the attention of the petroleum industry to a study of the performance of a fractured reservoir. The large variation in the number of fractures noted in Spraberry cores rile large variation in the producing ability of offset well.. the dramatic effect of well treatment on well ,productivity. the unknown quantity of oil stored in the fractures and matrix rock. and the unknown oil to be recovered were part of the initial Spraberry puzzle. In this type reservoir where the well treatment is an important factor in determining the productivity. it i- particularly desirable to determine the in-place flow capacity of the drainage area at distance* far removed from the well bore. This value. when compared to the flow capacity obtained from a PI measurement, will show the effectiveness of the well treatment (completion. fracture treatment, acidization. etc. in establishing a flow capacity in the vicinity of the well bore equal to that in the more remote region. The object of this paper i.; to show the application of a method of pressure build-up analysis for this purpose in studying the Upper Spraberry formation in the Driver area. STATEMENT OF THEORY The theoretical basis for the application of a pressure buildup curve to show the effective permeability of the rock at distances far removed from the well bore has been presented in detail in earlier publications.', in the previous development it was shown that pressure build-up behavior of all wells could be reduced to the same dimensionless build-up curve of Fig. 1. This mean.; that the bottom hole pressure of a well after hut-in will rise in such a manner that a plot of pressure against the logaritllm of time yields a straight line. The slope of this linp can be rlzed to calculate the effective permeability as expressed by the following equation: where: effective oil permeability md oil production rate prior to shnt in. STB/I) In practice the flow which occurs into the well bore after shut in and the variation in flow capacity in the immediate vicinity of the well bore usually cause the early part of the build-up curve to be unsatisfactory in the determination of permeability. In general the effect of these factors on the straight line section will become negligible after a time when the of the following equation is equal to 0.1. and the preferred section Of the curve for use in defining the slope lie-

Jan 1, 1953

By John C. Calhoun, Frank T. Bethel

Glass beads have been surface treated with Dri-film to render them oil wet by n-octane to varying degrees, and capillary desaturation curves have been determined by the restored state method. The desaturation curves show a regularity of increasing displacement pressures as the oil wetness increases. This has been used to compute apparent contact angles between n-octane and water on glass. The family of desaturation curves also shows a regular crossover, such that the residual wetting liquid saturation values are in reverse order to the displacement pressures. A semi-logarithmic variation is shown between the apparent contact angle and the residual saturation. The desaturation data are interpreted to mean that the wetting liquid ceases to be a continuous phase within individual pores before the capillary pressure can be raised sufficiently to force out the wetting phase completely. The saturation of wetting liquid at which this break in liquid continuity occurs is higher as the oil wetness decreases. INTRODUCTION The petroleum industry has for some time been using measurements of capillary pressures on porous media for research correlations and engineering calculations. It has been generally recognized that the capillary desaturation curve reflects the character and arrangement of the pores within the media and the distribution of fluids within the pores. Methods have been proposed for computing pore size distributions, tortuosity factors. and relative permeabilities from capillary desaturation data.' There is little doubt that the interactions between porous rocks and their contained fluids resulting from surface forces play a dominant role in determining the magnitude and direction of capillary pressure measurements. There have been attempts to introduce as variables two quantities — inter-facial tension and contact angle — generally used to char- acterize surface forces, but in spile of the wide interest in these quantities as important variables, few definite conclusions have been drawn concerning their qualitative or quantitative significance. INTERFACIAL TENSION The interfacial tension appears in a capillary pressure function given by Leverett for correlating capillary desaturation type curves. Use of the interfacial tension in this function seems to be justified by other experiments reported. Apparently, interfacial tensions have little bearing on wetting phase residual by desaturation. CONTACT ANGLE The contact angle was utilized as a variable by Bartell and co-workers"." in tests on displacement pressures, later recognized as the initial point of capillary desaturation. Although Leverett did not include contact angle in his original formulation of the capillary pressure function, later workers suggested its addition. Few reports are available to show variation of residual liquid with contact angle as a result of capillary desaturation.' The problems attendant to measuring contact angle within a porous medium are great. As a consequence of the lack of a concrete approach to a measurement. the workers in this area of research have adopted the general expression of "wettability" to indicate the relative position of two liquids saturating a porous body. It has been shown that gross measurements on porous systems, including capillary desatura-tions, are sensitive to wettability. Attempts at giving a scale to wettability in terms of contact angle through capillary desaturation curves have been made and these apparently are steps in the right direction. In these attempts presence of many other variables precludes attainment of exactness. Also, as a result of other variables, it has been impossible to correlate changes in apparent contact angle with changes in other physical measurements of the systems in question. The present work is an attempt to eliminate as many variables as possible in measuring capillary desaturations resulting from changes in contact angle within a porous medium.

Jan 1, 1953

By N. T. Burdine

Formulas for calculating relative permeability from pore size distribution data are derived from basic laws of fluid flow ill porous media. The tortuosity factors that appear in the equation5 are described in. terms of the physical properties of tile medium and the saturations of the contained fluids. Procedures for calculating and methods for measuring the tortuosity factors are discussed. Values of relative permeability calculated by the formulas art: compared with results obtained by experimental measurements I INTRODUCTION Recently, several investigators have derived relative permeability equations from Darey's and Poisenille's Laws in which some, physical factor or factors describing the porous system appear. The factor that has caused the greatest amount of comment, and which is probably least understood, is the tortuosity of the fluid {lath ill the porous sample. Values of the tortuosity factors appearing in the equations range from a constant for all condition- of the fluid flow system to an inverse function of the pore radii. It is the purpose of this paper to compare wine experi~i~cntslly determined relative permeability curves with those calculated by a method which utilized capillary pressure infortmation. The capillary pressure data were obtained prefer.. ably from pore size distribution information as determined by mercury injection but. in some cases, in the absence of suitable mercury injection information. data were taken from measurements made by the porous semi-permeable diaphragm method. The physical significance of certain tortuosity concepts is inferred and the determinations of the tortuosity factors from pore size distribution data and by electrical measurements are discussed. THEORETICAL BACKGROUND In previously reported studies on pore size distribution in petroleum reservoir rocks. by the author and co-workers ail equation was derived relating specific permeability. k, to pore entry radii, R, porosity. . tortuosity factor. .,, and incremental pore volume. V. The equation is where being the "effective" length of the flow path in the porous sample. and L the length of the porous sample., The constant. 0.126. is a units conversion factor. (This definition of tortuosity factor X, = L L does not conform to all such definitions found in the literature. Fly similarity, in a two-phase system. the effective permeability of the wetting-phase.

Jan 1, 1953

By G. H. Lair, B. J. Langford, S. H. Rockwood

Volumetric reservoir analysis is dependent upon a firm relationship between porosity, connate water, and net pay. Capillary presswe data on core samples interrelate these three factors. It is shown that other reservoir problems may be resolved: (I) whether water production is indigenous or extraneous to the oil producing interval, (2) an oil-water contact is being approached, and (3) whether the oil-water contact is remotely situated. INTRODUCTION Volumetric analysis of carbonate reservoirs challenges the ingenuity of the reservoir engineer due to an absence of data on the minimum oil-bearing and oil-producing pores of a given reservoir rock. Many studies with this as the ultimate objective are available on the physical characteristics and fluid-flow behaviors of the carbonate reservoir. Some of these publications are: Hassler, Brunner and Deahl's1 study of the role of capillarity in oil production; Jan Law's' and A. C. Bulnes3 statistical treatment of core analysis data; Chalkley's method4,5 or estimating specific surface areas and porosity; Walter Rose's9 report on porosity, reserves, and recovery; Archie's78 tex-tural classification of carbonate rocks; Stewart and Spurlock's9 large core analysis; Purcell'sl0 mercury injection method in studying capillary pressure phenomena; Stewart, Craig, and Morse's" model multiple-phase flow test in investigating the relative permeability effect; and Fatt's12 illumi-nating network model of porous me-dia. The present study shows that the static reservoir parameters of porosity, connate water, and net productive thickness may be interrelated by utilizing a statistical arrangement of mercury capillary pressure data in addition to routine core analysis. This report summarizes the techniques that are followed to obtain these relations which are applicable to carbonate and sandstone reservoirs that do not contain clays. Capillary pressure statistical studies may be extended to include clay-bearing rocks by utilizing water capillary pressure data. POROSITY It is necessary that the laboratory determine the porosity value that includes the pores that are filled with hydrocarbons and water in the reservoir. This is the reservoir's total porosity. When true total porosity values are not available, correlations between porosity and capillary pressure characteristics lose their significance since they cannot be related through oil-base mud core data to the porosity and connate water values found in reservoirs. Methods used to obtain reliable porosity data will not be discussed; however, care should be exercised in selecting samples for measurement. In homogeneously porous formations, small core plugs sampled frequently will furnish adequate information. Where heterogeneity, particularly vugginess, is present, large-core porosity data may be required; in such reservoirs a suite of capillary pressure samples may be selected from small plugs. CAPILLARY PRESSURE Capillary pressure data provide a method for relating two carbonate reservoir parameters, porosity and connate water saturation, which in turn permit delineation of productive rock types necessary for selecting the third parameter, productive thickness. Specific applications of capillary pressure data to petroleum reservoirs were suggested by Archie8 and Pur-cell."' Their work demonstrated that in preferentially water-wet rock, porc

Jan 1, 1958

By W. O. Brown

A laboratory investigation was conducted to determine quantitatively the extent to which connate water was contacted and displaced by invading flood water. In these experiments the connate water in unconsoli-dated sand packed columns was completely displaced by injecting water. The nature of this displacement was similar to that previously described for single-phase miscible fluid displacement studies, and thus the presence of a non-wetting immiscible phase did not appreciably change the nature of the displacement. The effects of water injection rate, column length, and oil viscosity on connate water displacement were investi-gated. It is concluded that the connate water in a reservoir is the water which actually displaces oil from the pores of the rock during a water flood. During a water flood the connate water forms a zone which separates the invading flood water from the continuous oil phase. The size and shape of connate water bank is chiefly dependent oil the oil viscosity and the column length. INTRODUCTION Water flooding is one of the most widely used techniques for the secondary recovery of oil. Presently, however, it is still not possible to recover all the oil in a reservoir by water flooding. The research described in this paper was conducted as part of a study to determine the conditions under which 100 per cent oil recovery could be attained by water flooding. The particular objective of this work was to determine if any chemical agent, regardless of its nature, placed in the flood water could be effective in influencing the mechanism of displacement of the oil by water. It has been known for many years that water does not displace all the oil in a reservoir because a portion of the oil is "trapped" and held immobile by capillary forces. This oil is trapped within the pores of a water-wet rock when it becomes broken into discontinuous globules. Initially, when oil is present at high saturations within the pores of a water-wet rock, the connate water forms rings around the points of contact of the sand grains and may even completely fill small cavities between grains, whereas the oil occupies the larger void spaces between the grains.' Under these conditions, the oil in these spaces is in the form of irregular but continuous filaments, the diameters of which depend on the geometry of the sand pores. The filaments are formed by the oil contained in the small cells which are formed between the sand grains and are connected to their neighboring cells by channels or tunnels formed by pendular rings of water. At a high oil saturation, the oil filaments conform approximately to the shape and size of the cells and their connecting tunnels. Starting with this distribution, as the water saturation is increased the water layers in the small cavities and on the surface of the grains grow. As this occurs, the water rings grow and the diameters of the oil filaments decrease. When an oil filament is reduced to a critically small diameter, the filament breaks, and its tunnel fills completely with water. Any oil which remains within a cell after all its connecting tunnels have been water-filled is trapped as a discontinuous globule. Once the oil has become trapped, the capillary forces oppose distortion of the globules and may prevent their being squeezed through the water-filled tunnels. Only a very small pressure gradient is sufficient to keep oil moving as a continuous filament. On the other hand, once the filament has broken into discontinuous oil droplets a relatively large force is required to distort the surface of a drop and move it through a water-

Jan 1, 1958

By Charles C. Templeton

Any explanation of the nature of multiphase fluid flow through porous media must ultimately involve a knowledge of the mechanism of such flow through the individual pores of the medium. To provide quantitative information of the latter type, a study was made of gas-liquid and liquid-liquid displacements in single uniform Pyrex capillaries with diameters as small as 4 microns. Quantitative observation of air-liquid displacements with zero contact. angle indicates the adequacy of a model based on Poiseuille's Law and the independence of capillary pressure and interfacial velocity. Consequently, this work discounts previous claims that flow is abnormally retarded in very small capillaries. For the displacement of a very viscous oil by water in a capillary initially filled with water, flow is faster than predicted by the above model. This behavior is probably due to the existence of a thin annular film of water between the oil column and the capi1lary wall as postulated by Yuster. INTRODUCTION The need for experimental observation of the microscopic nature of multiphase fluid flow, to further the understanding of the results of macroscopic flow investigations, has been previously recognized. Chatenever and Calhoun1 in connection with the API Project 47B have extensively studied the flow of fluids through layers of glass or lucite spheres between glass or lucite plates. Lowman2 prepared an interesting film concerning flow in a single capillary, using an apparatus which made a moving interface appear stationary in the field of a microscope. The purpose of the present investigation was to deter- mine what contribution might be made to this field by comprehensive quantitative observation of gas-liquid and liquid-liquid displacements in single capillaries of uniform, very small diameter. The techniques used are similar to those of Lowman but incorporate improvements necessary for quantitative work. Quantitative observations must begin with fluids of simple chemical composition to provide a basis for analyzing the more complex behavior that may be expected with natural reservoir fluids. However, some qualitative observations on systems involving crude oils are presented. Experiments of this sort involve the observation of the velocity of the interface separating two fluids, and have been performed in horizontal or vertical capillaries by several investigators.3,4,5,6,7,8 The most general treatment of their mechanics, by Brittin,9 involves forces due to capillarity, viscous resistance, gravity, an "end-drag" effect, and the rate of change of momentum of the capillary contents. Since the range of pore diameters of interest in petroleum reservoirs is about 0.1 to 100 microns, it was desired to perform these experiments in the smallest capillaries possible, to ascertain whether capillary diameter had any effect on the existing theory based on data from larger capillaries.* It was also important to be able more systematically to vary the direction and rate of displacement than was done by previous investigators. Finally, to concentrate attention on viscous and capillary forces by eliminating gravity as a parameter, this study involves only horizontal capillaries. The work of Eley and Pepper' with a "large" (0.766-mm diameter) horizontal capillary is the previous investigation which is most similar to the present method of quantitative observation. Here capillaries with diameters as small as 4 microns will be studied.

Jan 1, 1955

By J. S. Osoba, J. G. Richardson, F. M. Perkins

Laboratory experiments have shown profound diffcrences in the behavior of so-called "fresh cores" from the East Texes field and of the same cores after ex~ractio~l with organic solvents. The residual oil satura/ion remaining after waterflooding fresh cores was appreciably lower than the corresponding saturations after flooding extracted cores. This behavior was also reflected in the water-oil relative permeability-saturatiorl relations, which were more favorable for high oil recovery from the fresh cores. These differences were evident not only in the amount of residual oil left after wafer flooding, but also in the saturation water remaining in the core after displacernent by oil. Residual water saturation after displacernetzt of water by oil was higher in the fresh cores than in the extracved core,. Capillary pressure-saturation relations were also different for the fresh crnd extracted cores. Imbibition experiments indicated that both fresh and extracted Bast Texas cores imbibed water spontarteOLISIY, but- the rate of imbibition of water was higher for samp1es after. extraction than it was for fresh core. material. INTRODUCTION Several years ago a series of waterflooding tests was made in the laboratory on a number of Woodbine core samples from the East Texas field. These samples had been stored in containers open to the air and were extracted with organic solvents before they were subjected to the laboratory tests. After water flooding, the residual saturation of kerosene, which was the oil used in the tests, was found to average about 30 per cent. This saturation was higher than expected. In investigating the circumstances which might have been responsible for such a high residual oil saturation, attention was given to possible changes in wetting properties of the rock brought about by the procedure employed in extracting the cores. Preliminary results indicated that the explanation for the high residual oil saturation lay in the wetting behavior of the cores, though what effect extraction had on this behavior was not clear. In consequence, the work described in this report was undertaken in an attempt to investigate the mechanism responsible, and to ascertain the actual residual oil saturation to be expected in the reservoir after water flooding. It was soon found that there were profound differcnces in the behavior of so-called "fresh cores" from the East Texas field and of the same cores after extraction with organic solvents. These differences were evident not only in the amount of residual oil left after water flooding, but also in the saturation of watet remaining in the core after displacement by oil. The complete explanation of this behavior is not yet apparent. The description of work and results described in following sections, therefore, must be considered as an interim report presenting facts which must await additional information before they can be fully interpreted.

Jan 1, 1956

By G. A. Croes, N. Schwarz

This paper reports the results of a series of model displacement experiments carried out for measuring the efficiency of the water-drive process. This series forms a continuation and extension of that described by Engel-herts and Klinkenberg. Detailed information has been obtained on the influence of the oil/water viscosity ratio. The results are represented in the form of a diagram from which both the oil recovery and the water/oil ratio can be easily read off as a function of the total production (oil plus water) for all values of the viscosity ratio M between I and 500. These resu1ts are viewed in the light of the two existing theories on water flooding, viz. that of Buckley and Leverett and that of Dietz. It is shown that if the Buckley-Leverett theory applies, the relation between the relative permeability ratio and saturation, which plays a major role in this theory, (.an be calculated with a high degree of accuracy from the results of the model experiments. Dietz's theory is found to be in agreement with the experimental results in a certain range of circumstances. A discussion of the physical background of the Buckley- Leverett and Dietz theories makes it clear why the latter fails to agree with some of the experimental results. INTRODUCTION For an economical exploitation of oil fields both a rational control of natural (primary) recovery processes and a proper application of artificial (secondary) recovery methods are essential. These require detailed information upon the dependence of the relevant flow processes on the variables by which they are governed. Three methods are available for obtaining this information: (1) (statistical) analysis of actual field data; (2) appropriately scaled model experiments; and (3) mathematical analysis of the physical problem. If sufficient data were available, the first method would, in principle, be the most reliable one, although it has the drawback that the basic relationships between the variables involved are to a large extent obscured by the natural inhomogeneities of most reservoirs. The most profitable procedure seems to be: (a) determining the fundamental relations for idealized reservoirs by methods (2) and (3); (b) checking the consistency of the results obtained by these two methods; and (c) establishing the range of applicability of these methods to actual reservoirs by comparison with the data accumulated under (1). In this paper items (a) and (b) are dealt with for the case of homogeneous loose sands initially saturated

Jan 1, 1956

By J. S. Levine

A series of four displacement experiments has been run in a large alundum core. Flow potential distribution in each liquid phase was measured continuously through oil-wet and water-wet capillary barriers, using a null-point pressure balance, and saturated distribution was determined from electrical resistivity measurements. A method has been devised for calculating the effective (and relative) permeability to each phase at any time and at any point in the flow system for the transient displacement process. Relative permeability points have been calculated and average curves drawn for oil displacing water and water displacing oil. The values of dynamic capillary pressure have also been determined. Data have been substituted into the generalized Buckley-Leverett fractional flow equation and a comparison between actual and theoretical breakthrough recoveries is shown. Displacement experiments have been performed in the laboratory for many years in an effort to determine the effect of a number of parameters on multiphase flow in porous materials. In the literature of petroleum technology, Wyckoff and Botset' were among the first to develop the relative permeability concept and to show experimentally that oil, gas, and water can flow simultaneously through a porous medium in a precise way governed by certain fluid properties, by the relative saturation of each fluid, and by characteristics of the medium itself. Somewhat later, Leverett2 and Hassler, Brunner, and Deahl11 developed some theoretical concepts of capillary behavior in porous materials. The work of Buckley and Leverett3 presented a theoretical analysis of immiscible liquid displacement based on the equation of continuity and the Darcy equation for viscous flow of each fluid. Subsequent investigators attempting to verify the Buckley-Leverett equation have, in general, deliberately neglected the capillary pressure term or have performed experiments in such a manner that it could be neglected. Terwilliger, et al4 in 1951, obtained agreement between theory and experiment for the constant rate displacement of water by gas in a long vertical sand column. Rapoport and Leas5 have investigated the

Jan 1, 1955