Laboratory Studies of Microscopic Dispersion Phenomena

This 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 bench-scale 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 1/24th 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. The use of dispersion coefficients in scaling laboratory models to represent solvent floods in oil reservoirs is discussed briefly. Introduction The physical processes involved in the displacement of one fluid from a porous medium by a second fluid which is miscible with the first are fundamentally important in many diverse fields. For example, chemical engineers have been particularly concerned with the relationship of such fundamental aspects of displacement processes as the distribution of heat and mass, and the effect of fluid mixing on reactor efficiency. The specific problem of fluid mixing in fixed bed reactors has been investigated by Bernard and Wilhelm and others. Because high reactor efficiencies often require turbulent motion of the fluids within the individual flow channels of the porous medium, the emphasis in most of these studies has centered on fluid mixing in the turbulent or almost turbulent flow regimes. The mixing between miscible fluids in the laminar flow regime at very low Reynold's numbers is of particular interest in the field of and in recovery of oil.