Previous workers have developed differential equations to describe oil displacement by water imbibition, but have not explicitly defined the relationship between recovery behavior for a single reservoir matrix block and its size. In the present work, imbibition theory is extended to show that the time required to recover a given fraction of the oil from a matrix block is proportional to the square of the distance between fractures. Using this relationship, recovery behavior for a large reservoir matrix block is predicted from an imbibition test on a small reservoir core sample. The prediction is then extended to analyze recovery behavior for fractured - matrix, water - drive reservoirs in which imbibition is the dominant oil-producing mechanism. Experimental data are presented to support the basic imbibition theory relating matrix block size, fluid viscosity level and permeability to recovery behavior. Introduction Imbibition has long been recognized as an important factor in recovering oil from water - wet, fractured-matrix reservoirs subjected to water flood or water drive. Recently, two approaches have been published which might be used to predict imbibition oil-recovery behavior for reservoir - sized matrix blocks. Graham and Richardson used a synthetic model to scale a single element of a fractured-matrix reservoir. Blair, on the other hand, used numerical techniques to solve the differential equations describing imbibition in linear and radial systems. This latter method requires auxiliary experimental data in the form of capillary pressure and relative permeability functions. These two approaches, i.e., synthetic models and numerical techniques, have been used to study a variety of reservoir fluid-flow problems. One purpose of this work is to present, with experimental verification, a third method for predicting imbibition oil recovery for large reservoir matrix blocks. This method uses scaled imbibition tests on small reservoir core samples to predict field performance. The imbibition tests are easier to perform than the capillary pressure and relative permeability tests required to apply the numerical method. Furthermore, when suitably preserved reservoir-rock samples are used, the properties of the laboratory system are the same as those of the field. This offers an important advantage over the use of synthetic models because there is usually some question as to how accurately reservoir-rock properties can be duplicated in such models. Based on the recovery behavior for a unit matrix block, an analysis is presented to predict oil recovery for a fractured, water-drive reservoir made up of many such unit blocks. In the analysis, it is assumed that the flow resistance and the volume of the reservoir fracture system are negligible compared with that of the porous matrix. These assumptions are generally consistent with observed characteristics of many fractured-matrix reservoirs, and have been employed in previous studies. It is further assumed that the effect of gravity on flow in the matrix blocks is negligible. On first thought, the latter assumption might appear to seriously limit application of the method. However, in a fractured reservoir, the effect of gravity on flow in a matrix block will be restricted by the height of the block. Furthermore, matrix permeabilities are often very low (10 md or less) in such reservoirs. This means that capillary or imbibition forces will be large, thus tending to minimize the relative importance of gravity. For these reasons, imbibition should be the dominant oil-recovery mechanism in many fractured-matrix, water-drive reservoirs. The predictive method presented in this report is applicable to such reservoirs. SPEJ P. 177^

This paper presents an improved procedure for calculating dynamic pseudo junctions that may be used in two-dimensional, areal reservoir simulations to approximate three-dimensional reservoir behavior. Comparison of one-dimensional areal and two-dimensional vertical cross-sectional results for two example problems shows that the new pseudos accurately transfer problems shows that the new pseudos accurately transfer the effects of vertical variations in reservoir properties, fluid pressures, and saturations from the properties, fluid pressures, and saturations from the cross-sectional model to the areal model. The procedure for calculating dynamic pseudo-relative permeability accounts for differences in computing block lengths between the areal and cross-sectional models. Dynamic pseudo-capillary pressure transfers the effects of pseudo-capillary pressure transfers the effects of different pressure gradients in different layers of the cross-sectional model to the areal model. Introduction Jacks et al. have published procedures for calculating dynamic pseudo-relative permeabilities fro m vertical cross-section model runs. Their procedures for calculating pseudo functions are procedures for calculating pseudo functions are more widely applicable than other published approaches. They demonstrated that, in some cases, the derived pseudo functions could be used to simulate three-dimensional reservoir behavior using two-dimensional areal simulators. For our purposes, an areal simulator is characterized by purposes, an areal simulator is characterized by having only one computing block in the vertical dimension. The objectives of this paper are to present an improved procedure for calculating dynamic pseudo functions, including a dynamic pseudo-capillary pressure, and to demonstrate that the new procedure pressure, and to demonstrate that the new procedure generally is more applicable than any of the previously published approaches. The new pseudos previously published approaches. The new pseudos are similar to those derived by jacks et al. in that they are calculated from two-dimensional, vertical cross-section runs. They differ because (1) they account for differences in computing block lengths between the cross-sectional and areal models, and (2) they transfer the effects of different flow potentials in different layers of the cross-sectional potentials in different layers of the cross-sectional model to the areal model. Differences between cross-sectional and areal model block lengths are sometimes desirable to reduce data handling and computing costs for two-dimensional, areal model runs. For very large reservoirs, even when vertical calculations are eliminated by using pseudo functions, as many as 50,000 computing blocks might be required in the two-dimensional areal model to minimize important errors caused by numerical dispersion. The new pseudos, of course, cannot control numerical pseudos, of course, cannot control numerical dispersion in the cross-sectional runs. This is done by using a sufficiently large number of computing blocks along die length of the cross-section. The new pseudos then insure that no additional dispersion will occur in the areal model, regardless of the areal computing block lengths. Using this approach, the number of computing blocks in the two-dimensional areal model is reduced by a factor equal to the square of the ratio of the block lengths for the cross-sectional and areal models. The new pseudos do not prevent some loss in areal flow-pattern definition when the number of computing blocks in the two-dimensional areal model is reduced. A study of this problem and associated errors is beyond the scope of this paper. Our experience suggests that, for very large reservoirs with flank water injection, 1,000 or 2,000 blocks provide satisfactory definition. Many more blocks provide satisfactory definition. Many more blocks might be required for large reservoirs with much more intricate areal flow patterns. The next section presents comparative results for cross-sectional and one-dimensional areal models. These results demonstrate the reliability of the new pseudo functions and illustrate their advantages pseudo functions and illustrate their advantages over previously derived pseudos for certain situations. The relationship between two-dimensional, vertical cross-sectional and one-dimensional areal reservoir simulators has been published previously and will not be repeated here in any detail. Ideally, the pseudo functions should reproduce two-dimensional, vertical cross-sectional results when they are used in the corresponding one-dimensional areal model. SPEJ P. 269

Introduction Theory indicates that linear waterfloods should exhibit scaling and stabilization properties in both oil-wet and water-wet porous media. Experimental verification of these properties in oil-wet media was obtained some time ago, and more recently, Perkins employing a high permeability unconsolidated sand and a low oil-to-water viscosity ratio, has obtained flooding data in a water-wet medium which follow the pattern of scaling and stabilization. Also, Root and Calhoun have found similar trends in the displacement of gas by liquids from unconsolidated sands. In general, however, the experimental evidence appears still somewhat conflicting since scaling and stabilization of water floods in water-wet media has not been observed in most of the studies to date. The purpose of this paper is to provide a more comprehensive picture of waterflood behavior in water wet media and to corroborate the validity of the scaling and stabilization concepts. The need for differentiating between the intrinsic nature of water-oil displacements inside a porous medium and perturbating secondary end effects is discussed, pertinent experimental procedures are outlined and the results of flooding tests conducted at low and at high oil-to-water viscosity ratios on consolidated, water-wet Alundum cores are analyzed.

Published in Petroleum Transactions, AIME, Volume 207, 1956, pages 215–221. Abstract Experimental studies covering a wide range of core materials and fluid properties have been conducted to determine the mechanism of oil displacement by water in a partially gas-saturated porous medium. In all instances, the presence of a gas phase was found to have a beneficial effect in reducing residual oil saturations. The practical significance of this benefit is discussed, and a simplified procedure is outlined for evaluating the effects of free gas on water flooding by means of short core tests. Introduction In addition to oil and water, reservoirs subjected to water flooding frequently contain, also, a gas phase. Common engineering procedures account for the presence of this "free gas" only from the viewpoint of volumetric balance, implying that the only role of the gas consists of providing "fill up" space. It is usually visualized that during the initial stages of the water invasion, the oil, moving ahead of the water, displaces part of the gas and that subsequently the remaining portion of the gas phase is totally compressed and dissolved in the advancing oil bank. Thus, consideration of a two-phase, water-oil flooding mechanism supplies an adequate basis for predictions of oil recovery if the pressure build-up caused by the flood is sufficiently great, so as to reduce the free gas saturation to a negligible value in any portion of the reservoir by the time that portion is reached by the advancing flood water. In many in stances, however, waterflooding operations are carried out when the reservoir pressure is still relatively high so that the pressure build-up associated with the water flood may not result in complete dissipation of the gas phase. Under such circumstances it is necessary to ascertain whether or not the presence of free gas has an effect on waterflood behavior and, if so, to account for any such effect in the evaluation of field operations.

Previous laboratory investigations to predict recovery from matrix blocks in a fractured reservoir have been primarily concerned with the imbibition oil recovery process. Gravity segregation can sometimes be more important than imbibition as a mechanism for oil recovery from matrix blocks. This paper describes a new method to predict oil recovery behavior for matrix blocks in a fractured-matrix reservoir. Centrifuge tests are performed with preserved reservoir core samples to scale the effects of both gravity and capillarity. The tests are easy to perform. Yet, The results should be more reliable than results obtained by other available methods for predicting matrix-block recoveries. Centrifuge tests were performed on different-sized reservoir rock samples to confirm the scaling theory. These tests were performed to simulate a water-oil displacement in a weakly water-wet reservoir. The method is equally applicable to other reservoir wettabilities and gas-oil displacements. In the weakly water-wet system, oil recovered by imbibition was found to be almost negligible as compared with the amount of oil recovered by gravity segregation. Introduction In many fractured-matrix reservoirs, most of the oil is contained in matrix blocks that are surrounded by a high-permeability fracture system. The flowing pressure gradient in the fractures is small, and pressure gradient in the fractures is small, and local capillary and gravity forces will dominate the recovery process for each matrix block. The unit matrix-block behavior then becomes an important factor in predicting reservoir oil recovery and assessing secondary or tertiary recovery prospects. Other investigators have used synthetic models and reservoir core samples to study the imbibition oil recovery process in fractured-matrix reservoirs. The methods they used to predict matrix-block recoveries are applicable when the reservoir rock is strongly wet by water and imbibition is the dominant mechanism for oil recovery. Wettability studies show that some reservoir rocks are not strongly wet by water in the presence of crude oil so that imbibition oil recovery will be low. Under these circumstances, gravity segregation can be an important mechanism for oil recovery, and its influence should be included in predicting matrix-block recovery. Marx has previously used scaling principles to show that the gas-oil gravity drainage characteristics of long, linear columns can be predicted from centrifuge tests on reconstituted core samples. In the current work, application of the scaling theory is extended to include three-dimensional systems and water-oil displacements. In addition, procedures are suggested to either duplicate or scale reservoir wettability and interfacial tension. The objectives of the present work are to present a centrifuge method that can be used to predict the effects of both gravity and capillarity on matrix-block oil recovery and to demonstrate the importance of gravity in recovering oil from matrix blocks in fractured reservoirs. In this paper, discussion of the centrifuge method will be limited, for the most part, to water-oil displacements. Application of the method to gas-oil displacements is discussed briefly near the end of the paper. PROCEDURE FOR PREDICTING PROCEDURE FOR PREDICTING MATRIX-BLOCK RECOVERY The laboratory procedure developed for predicting matric-block recovery consists of the predicting matric-block recovery consists of the following.Select a preserved core believed to have the same wettability, porosity and permeability as the prototype reservoir matrix block. prototype reservoir matrix block. A preserved core is defined as one cut and stored under conditions designed to preserve the original reservoir wettability.Cut a sample (or model) from the core so that it will simulate the reservoir matrix-block geometry in the centrifuge tests. SPEJ P. 164