A rrew numerical method is proposed /or the solution of multidimensional miscible displacement pmldems. Besides the usual stationary grid associated with numerical procedures, the method uses moving points for which positions and concentra-; tions are computed each time step. Based on the method of characteristics~or treating combined trarxsport and dispersion, the method a~plies equally well to" any number o! dimensions and, in contrast with other riumerical procedures, properly takes into account the Qbysicd dispersion, no matter. bow small. Extensive tests show that accurate soktions of one-dimension al problems can be obtained over a wide range oj values of the dispersion coefficient, including zero. They also show" that the moving points do not need to be uniformly spaced, '&ad tbut increasing the number of moving' points beyond 2/grid interval does not significantly improve the accuracy 0/ the solution. Two-dimensional calculations using-the new method were carried out to simulate laboratory model displacements in which gravity caused or)erriding of solvent, Good agreeinent between observed and computed profites and measured and computed concentrations of produced fluid &as obtained for a viscosity ratio of L 89; at higher viscosity rat ios, fair agreement was obtained Computed results were found to be significantly af{ eeted by vertical" dispersion, and negligibly a{fected by dispersion in the direction o{ /low, in agreement with conclusions based on experimental observations.
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^
The results described demonstrate the conditions which the gas and oil relative permeabilities are independent of the connote (initial) water saturation. Summary Gas and oil relative permeabilities were measured on water-wet and mixed-wet Berea sandstone at various connate (initial) water saturation values, including zero, using the gas flood method. The centrifuge method was used to extend the measured oil relative permeability curves to lower total liquid saturations than could be permeability curves to lower total liquid saturations than could be achieved by gas flood. Composite cores were used in the gasfloods, whereas individual plugs were tested in the centrifuge. The results show that gas and oil relative permeabilities are independent of the connate water saturation in water-wet and mixed-wet Berea sandstone provided certain conditions are satisfied. Introduction Core preparations for flow tests can be difficult and time consuming. In fact, the preparation often requires more time than the actual now measurements. Among the different preparation considerations, achieving a specific value of initial water saturation in a core is especially difficult. The objective of this study is to quantify the effect that connate water saturation has on gas-oil relative permeabilities for both water-wet and mixed-wet Berea rock. A brief qualitative discussion of the effect that water saturation has on gas-oil relative Permeability measurements was presented by Owens et al. in 1956 . Permeability measurements was presented by Owens et al. in 1956 . Although no data were shown, the authors stated that the presence of water saturation has no effect if the water is immobile. In 1965, Knopp published his results of gasflood tests performed on extracted cores without connate water and with restored water saturations." He observed no effect on the gas-oil relative permeability ratio due to the presence of the water phase. In permeability ratio due to the presence of the water phase. In 1987, Delclaud et al. presented the results of a comparison on a single core sample. No difference in production was observed between the gasflood with low water saturation and the gasflood performed with no water saturation. performed with no water saturation. In this paper, we use the term "water wet" to describe the wettability condition of Berea sandstone as received from the quarry We visualize the water-wet state as one in which a continuous film of water is always present on the rock surface; this film prevents direct contact of the oil with the surface. We use the term "mixed wet" to describe the wettability state visualized by Salathiel, in which the smaller pores are water wet and the larger pores are oil wet. Water cannot come into direct contact with the rock surface in these larger oil-wet pores. Salathiel postulated that the oil-wet pores are connected over an appreciable distance, so that oil can continue to flow at low saturations. Procedures The porous rock used in this study was Berea sandstone. A number of 2- and 2.5-inch-long (5.08- and 6.35m) plugs were cut from a three-foot (0.9-m) length of Berea stock that was 1.5 inches (3.81 cm) in diameter. Test plugs were randomly selected from those obtained from a given three-foot length of stock. Several three-foot lengths were used during this work. Table 1 gives the routine porosity and permeability of the individual plugs. Relative permeabilities were measured by two methods: gasflood and centrifuge. In the gasflood (unsteady-state) method, injected gas displaced oil from the core. The production and differential pressure data were analyzed using the Johnson-Bossler-Naumann (JBN) pressure data were analyzed using the Johnson-Bossler-Naumann (JBN) method to obtain gas and oil relative permeabilities. In the centrifuge method, the core was enclosed in a sleeve and centrifuged in air at constant speed. The volume of oil produced was recorded versus time. The production data were analyzed using a method similar to the technique described by Hagoort to obtain oil relative permeabilities. Gas relative permeability cannot be calculated from centrifuge data because the analysis assumes that no pressure gradient exists in the gas phase.
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