Radial Motion of a Surface Between Fluids Within a Porous Medium

Economic use of solvent flooding for secondary recovery of oil requires thelimitation of miscible solvent. In turn, solvent requirements depend onspreading from dispersion; reservoir heterogeneity, viscous fingering, and thetendency for low-density solvent to rise above oil, or to override. This paper considers miscible displacement outward from a central well in alarge cylindrical system. Under appropriate conditions, initial viscous fingersmay become damped out as they are spread in several directions by gravity anddispersion. Mathematically, displacement behaviour is represented by theradially outward motion of a free surface, representing the "interface" betweenfluids, from injection well toward producing wells. The equivalent linearproblem has been reported by several authors, but extrapolation to thecylindrical case is not justified. An approximate equation of motion for the free surface is deduced. Solutionsof the nonlinear equation are obtained by finite difference methods. For thelimiting case of a small density difference, just enough to cause fluidsegregation, a simple analytical solution describes the motion of the endpoints of the surface. Comparison with numerical results shows that the simplesolution provides a useful measure of the anticipated overrideforessentially all practical conditions. Introduction The injection of a miscible solvent to displace oil from a reservoir is apotentially valuable secondary recovery method. Field application has shownvarying degrees of success, however. Economic use of the process places a limiton the quantity of miscible solvent that may be used. In turn, the solventrequirement depends on the spreading initiated by viscous fingering (1), dispersion (2), pattern effects which cause incomplete sweepout, reservoirheterogeneity which leads to rapid breakthrough in portions of the reservoir,an d on the tendency for the solvent to override the oil. The latter is causedby a combination of density and viscosity differences.