A level set method for simulating capillary-controlled displacements at the pore scale with nonzero contact angles

We present a level set method for simulating capillary-controlled displacements with nonzero contact angles in porous media. The main feature of the method is a level set evolution velocity which is different in the pore space and solid phase. This augments the standard level set equation with an extra term such that, at steady state, the contact angle is enforced in the solid phase, whereas capillary and interfacial forces are balanced in the pore space. We employ the method to simulate quasistatic drainage and imbibition processes for different contact angles in several pore geometries, and to compute capillary pressure and fluid/fluid specific interfacial area curves in each case. We validate the method by comparing stable fluid configurations computed in idealized two-dimensional geometries and three-dimensional (3-D) straight tubes with known analytical solutions. Simulations performed in a subset of a 3-D sandstone image show that the developed method accounts for well-known pore-scale mechanisms such as piston-like invasion, Haines jump, interface coalescence, and retraction, swelling of wetting films and snap-off. The contact angle is formed by an intersection of the fluid/fluid interface and the void/solid boundary. Therefore, the solid matrix surrounding the pore space is discretized with at least an equal number of grid points as the size of the numerical stencil used to approximate the level set derivatives.