Analytical calculation of minimum miscibility pressure

Analysis of the problem of one-dimensional, dispersion-free displacement of a multicomponent oil by a gas such as CO2 or methane has shown that the behavior of the flow is controlled by a sequence of key tie lines: Those that extend through the original oil and injected gas compositions and nc − 3 tie lines known as crossover tie lines. The minimum miscibility pressure (MMP) is the lowest pressure at which any of the key tie lines is a critical tie line. We show how to identify the c − 3 crossover tie lines for oils that contain an arbitrary number of components as a sequence of tie lines whose extensions intersect. For displacement by a gas that contains only one component, that problem is equivalent to the problem of performing a flash calculation for single phase mixture with the composition of the intersection point. We transform the standard flash equation to a form that gives convergent solutions even for compositions well outside the phase diagram. We use the modified flash calculation to determine which of the key tie lines approaches the critical locus as the pressure is increased. Calculation of tie line lengths for a sequence of increasing pressures determines the MMP as the lowest pressure at which the length of one of the key tie lines becomes zero. Extension of the method to systems with two components in the injection gas is demonstrated for a four-component system, and further extension to multicomponent injection gases is discussed.