Flow and displacement of waxy crude oils in a homogenous porous medium: A numerical study

• By an increase in the breakdown-to-rebuild ratio in the Houska model, the time for water breakthrough and the sweep efficiency are increased.
• The variable yield-stress in the Houska model has an accelerating effect on the water breakthrough phenoemnon.
• The shear-thinning behavior of Houska fluids significantly overshadows it thixotropic behavior in the water-flooding operation.

In the present study, the displacement of waxy crude oils is numerically/theoretically investigated in the water-flooding operation. The oil was assumed to obey the Houska model―a robust thixotropic fluid model which is often realized to well describe the rheology of waxy oils in different parts of the world. Based on the concept of effective viscosity, a modified version of the Darcy's law was developed for this particular fluid model in order to describe its flow through a homogenous porous medium. Use was made of numerical and theoretical methods to study the displacement of Houska fluid by water in two benchmark problems: (i) the Buckley–Leverett problem, and (ii) the five-spot problem. It was found that the yield stress of the Houska fluid being variable (i.e., shear- and time-dependent) has a retarding effect on the water breakthrough phenomenon. The breakdown-to-rebuild ratio in the Houska model was shown to play a key role in the water breakthrough phenomenon provided that it is very large. At this extreme, however, the effect was attributed mostly to the shear-thinning behavior of the Houska fluid rather than its thixotropic behavior. In fact, at sufficiently low breakdown-to-rebuild ratios (i.e., when fluid's thixotropy becomes progressively more important) it had no significant effect on the water breakthrough phenomenon. Therefore, it is concluded that in competition with shear-thinning, the thixotropic behavior of Houska fluid plays a secondary role, if any, in the water-flooding operation.