Simulation of Counter-Current Spontaneous Imbibition Based on Momentum Equations with Viscous Coupling, Brinkman Terms and Compressible Fluids

A numerical model is investigated representing counter-current spontaneous imbibition of water to displace oil or gas from a core plug. The model is based on mass and momentum conservation equations in the framework of the theory of mixtures. We extend a previous imbibition model that included fluid–rock friction and fluid–fluid drag interaction (viscous coupling) by including fluid compressibility and Brinkman viscous terms. Gas compressibility accelerated recovery due to gas expansion from high initial non-wetting pressure to ambient pressure at typical lab conditions. Gas compressibility gave a recovery profile with two characteristic linear sections against square root of time which could match tight rock literature experiments. Brinkman terms decelerated recovery and delayed onset of imbibition. Experiments where this was prominent were successfully matched. Both compressibility and Brinkman terms caused recovery deviation from classical linearity with the square root of time. Scaling yielded dimensionless numbers when Brinkman term effects were significant.