A Theory of the Optimal Policy of Oil Recovery by Secondary Displacement Processes

We consider the stability of the displacement of a viscous fluid in a porous medium by a less viscous fluid containing a solute. For the case in which the total amount of injected solute is fixed, we formulate a theory for the optimal injection policy, i.e., the policy which minimizes the growth constant of the Saffman–Taylor–Chouke instability. The result is a nonlinear constrained eigenvalue problem with the viscosity ratio, α, of the two fluids and the total solute, N, as parameters. We develop perturbation solutions for large and small N and numerical solutions for all N. Several features of the optimal policy which have been noted or demonstrated empirically by previous workers are proven, and new features of the solution are discussed.