R. J. BLACKWELLMEMBER AIME T his paper presents the results of a laboratory investigation of the process by which one fluid is displaced from a porous medium by a second fluid which is miscible with the first. The study included investigations of the microscopic mixing processes and of the gross displacement behavior. The results of this study are useful in scaling small benchscale models or reactors to represent larger systems such as oil reservoirs or large, fixed bed reactors.Mixing in both the direction of flow and perpendicular to the direction of flow was measured in sand-packed columns. Dispersion coefficients were calculated from data obtained over a range of rates for various fluid pairs and sand-grain sizes. The data are presented by plotting the ratios of the dispersion coefficients divided by the molecular diffusivity vs a dimensionless parameter relating the forward transport by convection to lateral transport by diffusion. It was found that both longitudinal and lateral mixing are governed by molecular diffusion at low rates and by convection at high rates. At high rates, however, the lateral dispersion coefficients are about 1I24th those in the longitudinal direction. The ratio of lateral to longitudinal dispersion coefficients is compared with that predicted by various mathematical models of the pore system in a packed bed.T he use of dispersion coefficients in scaling laboratory models to represent solvent floods in oil reservoirs is discussed briefly.

Published in Petroleum Transactions, AIME, Volume 217, 1959, pages 1–8. Abstract This paper presents results of an experimental investigation of factors that control the efficiency with which oil is displaced from porous media by a miscible fluid. The study was made to elucidate the relevant processes both on microscopic level (within individual or between neighboring pore spaces) and on macroscopic level (within a large sand body). Mixing of miscible fluids on the microscopic level was studied in sand-packed tubes. It was found that molecular diffusion is the dominant dispersion mechanism for reservoir conditions of rate, length and pore sizes. Macroscopic channeling was studied for various mobility ratios in reservoir models-scaled to relate viscous gravitational, and diffusional forces. The formation of channels was due to viscous fingering, gravity segregation and variations in permeability. With adverse mobility ratios, it was found for reservoirs of realistic widths that diffusion will not be effective in preventing the formation and growth of fingers, even in homogeneous sands. At sufficiently low rates channeling was eliminated by gravity segregation in tilted reservoirs. The dependence of recovery on mobility ratio, length-to-width ratio, flow rate and angle of dip is presented. Introduction Oil recovery by solvent flooding is finding increasing application in the field. while the process promises high recoveries from the region swept by solvent, under adverse conditions only a small fraction of the reservoir volume may be swept at the time solvent breaks through to the producing well. Further, the high cost of the solvent encourages its use only as a bank whose size must be kept at a minimum. Thus, two important questions arise:what fraction of the reservoir can be swept, practically, by solvent? andwhat is the minimum size solvent bank that can be used to carry out the displacement? The answers to these questions require knowledge of both macroscopic channeling processes and microscopic mixing processes. The studies described here were carried out to gain this knowledge. Microscopic mechanisms which cause mixing will be discussed first, because an understanding of these mechanisms is necessary for proper interpretation of the experimental work on channeling described later.

Scaled laboratory-model studies provide a powerful method for evaluation of a proposed oil-recovery process. In recent years, models have been used extensively to evaluate processes in which solvents displace oil, both for general cases and for specific reservoir conditions. Since the performance of a miscible flood in a horizontal reservoir can be significantly affected by transverse mixing between solvent and oil, this displacement mechanism must be accurately simulated in the scaled model studies. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long times for experiments.If scaling requirements for miscible displacements could be relaxed while accurate simulation of essential displacement mechanisms is maintained, the utility of model studies would be greatly enhanced. The purpose of the work reported herein was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascertain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. These studies were performed with completely miscible systems in linear, horizontal models packed with unconsolidated media.From the experimental results, a set of relaxed scaling criteria was formulated which allows the requirements of geometric similarity and equality of the ratio of viscous to gravity forces to be omitted for specified conditions. The relaxed criteria are valid whether transverse mixing is by molecular diffusion or by convective dispersion.Correlations which permit prediction of vertical sweep efficiencies in linear, horizontal reservoirs were developed from the experimental data when transverse mixing is by molecular diffusion, These same correlations may be used when transverse mixing is by convective dispersion if an empirically defined, effective, transverse dispersion coefficient is used in the description of the mixing process. The effective transverse dispersion coefficient correlation essentially duplicates the dispersion coefficient correlation for equal-viscosity, equal-density fluid systems. Experimental values for the effective transverse dispersion coefficient can be measured readily. Introduction One of the most effective methods for evaluation of miscible-displacement oil-recovery processes is that of displacements in laboratory models scaled to simulate reservoir conditions. For these laboratory studies to be meaningful, however, the essential displacement mechanisms affecting reservoir performance must be accurately simulated.Since the performance of a miscible flood in horizontal reservoirs, or in dipping reservoirs at high rates, can be significantly affected by transverse mixing of solvent and oil, this mechanism must be considered in the design of laboratory experiments. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impracticality large laboratory models and long experiment times. This difficulty seriously limits the utility of laboratory model studies.Craig, et al, demonstrated that geometric similarity is not required when mixing is unimportant. Their experimental data indicate, for the cases studied, that the displacement is sufficiently characterized by scaling the ratio of viscous-to-gravitational forces. This work suggests that relaxation of the requirement of geometric similarity and, possibly, other criteria might also be permissible when mixing is important, provided suitable groups describing the mixing process are scaled.The purpose of the work reported here was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascertain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. SPEJ P. 28^

Here is an approach for solving reservoir flow problems where behavior is dominated by a rate-limiting step. Simple models are developed for gravity drainage where vertical flow occurs, for water underrunning of viscous oils, for gravity segregation of water banks in gas caps, and for control of coning by injection of oil. Introduction Forecasting the behavior of a reservoir is one of the more important but complicated tasks of engineers in the oil industry. Knowledge of reserves remaining in a reservoir is vital to planning optimum depletion of a field. Unfortunately, the engineer assigned the task of predicting reserves often faces a difficult choice. For the most accurate answer, he can use a computer program that takes into account all of the pertinent factors, but this approach is usually pertinent factors, but this approach is usually expensive and time consuming, and requires a detailed knowledge of the reservoir. On the other hand, he can use conventional one-dimensional displacement calculations that are easily applied but that in some cases do not adequately describe the reservoir flow system. The purpose of this paper is to describe a middle-ground approach that in special situations has many of the advantages of the above methods with out their more serious drawbacks. This approach uses mathematical models that describe the principal flow mechanisms and can be quickly applied by hand calculations. The technology of predicting reservoir behavior has grown steadily since the pioneering work of Muskat and of Buckleys and Leverett. Muskat's tank-type or zero-dimensional method of predicting behavior in dissolved gas drive reservoirs has been invaluable to the industry. Another milestone was reached with the Buckley-Leverett method of predicting linear displacement of oil by water or gas when flow was principally along the bedding plane. The classic work of Hurst, Muskat, and van Everdingen and Hursts laid a firm foundation for problems involving unsteady-state flow of fluids. Later, progress was made by Welge in solving one-dimensional progress was made by Welge in solving one-dimensional displacement equations more easily. The advent of digital computers led to the development of methods of solving problems of greater and greater complexity. Indicating the progress being made with computers, Douglas et al. in one paper, included the effect of capillary pressure in one-dimensional flow, and in another paper dealt with the flow of two phases in two dimensions. The utility of computers in predicting reservoir behavior has continued to grow as programs have become more user-oriented and as computers have become faster and more economical to employ. But even today, the time, effort, and money required to use computers to solve reservoir problems cannot always be justified. Thus, other tools are needed. An excellent example of another approach is given in a paper by Joslin. In analyzing a gas injection project in a large Venezuelan reservoir, Joslin realized project in a large Venezuelan reservoir, Joslin realized that gas had overridden the entire oil sand because production was above the critical rate. However, the production was above the critical rate. However, the presence of pancake-like shale members penetrated presence of pancake-like shale members penetrated by the wells prevented coning of gas into perforations located below the shale near the base of the sand. Oil recovery was predicted by assuming that gas displaced oil vertically downward throughout the producing area. Another paper demonstrating the practical use of simple mathematical models is that of Matthews and Lefkovits for predicting producing rates for wells in depletion-type reservoirs. JPT P. 1145

A steady-state technique for measuring oil-water relative permeability curves is presented. The technique allows measurements to be made on preserved core samples at reservoir temperature and pressure, using reservoir fluids. Live oil and brine are circulated simultaneously through the core in a closed system, and relative permeability data are taken when conditions in the core have stabilized. A series of five to ten flow rate ratios is normally used, providing data at saturations ranging from irreducible water to residual oil. Saturations are determined by monitoring the oil content of a high-pressure oil-water separator in the system. The technique is particularly useful for heterogeneous cores and cores with mixed wettability, where dynamic displacement tests can give inaccurate relative permeability data. The use of reservoir conditions and live fluids is preferred because the true wettability of reservoir rocks may not be preserved in tests performed with dead crude or at room temperature. Data is presented which demonstrates the application of this steady-state technique to the study of relative permeability hysteresis.