Network models for two-phase flow in porous media Part 2. Motion of oil ganglia

The behaviour of non-wetting ganglia undergoing immiscible displacement in a porous medium is studied with the help of a theoretical simulator. The porous medium is represented by a network of randomly sized unit cells of the constricted-tube type. The fluid of a non-wetting ganglion is in contact with the wetting fluid at menisci which are assumed to be spherical cups. The flow in every constricted unit cell occupied by a single fluid is modelled as flow in a sinusoidal tube. The flow in every unit cell that contains a meniscus and portions of both fluids is treated with a combination of a Washburn-type analysis and a lubrication-theory approximation. The flow problem is thus reduced to a system of linear equations the solution of which gives the instantaneous pressures on the nodes, the flowrates through the unit cells, and the velocities of the menisci. The motion of a ganglion is determined by assuming quasi-static flow, taking a small time increment, updating the positions of the menisci, and iterating. The behaviour of solitary ganglia is studied under conditions of quasi-static displacement (Ca slightly larger than critical), as well as dynamic displacement (Ca substantially larger than critical). Shape evolution, rate of flow, mode of break-up, and stranding are examined. The stranding and break-up coefficients are determined as functions of the capillary number and the ganglion size for a 100 × 200 sandpack. The dependence of the average ganglion velocity on ganglion size, capillary number, viscosity ratio and dynamic contact angle is examined for the simple case of motion between straight rows of spheres. It is found, among other things, that when μo < μw the velocity of ganglia can be substantially larger than that of the displacing fluid.