Analytical Studies for Processes at Vertical Equilibrium

Some new results are presented for systems in Vertical Equilibrium (VE) which extend our recent work on this subject (Yortsos, 1991). The linearized stability of a prototypical miscible displacement at VE is considered and shown to correspond to the short wavelength regime of previous studies in unbounded geometries. Concepts from VE are applied to model general displacement processes in various geometries. Under conditions of gravity-segregated flow we investigate and suggest simple methods for the construction of the solution. In particular, we extend our previous work to flows involving dip and show that the latter dominates the solution. Prepared for The 3rd European Conference on the Mathematics of Oil Recovery, 17-19 June 1992, Delft University of Technology, The Netherlands.