Water-based muds invade oil formations during drilling. This immiscible cylindrical invading flow depends on relative permeability and capillary pressure. Although the invasion can be described in terms of reservoir engineering principles, unlike conventional reservoir flow models, a growing mudcake that is dynamically coupled to flow within the reservoir in part controls this invasion. This mudcake coupling is especially significant when formation permeabilities are low.
The formation tester described in the paper withdraws fluid from the cylindrical, invaded zone while invasion is taking place. However, the tester itself causes an ellipsoidal (anisotropic flow within the cylindrical flow. The resulting, combined flow is highly nonlinear and is solved with special boundary conditions involving pumping rate, skin, flow line storage, and transient mudcake growth.
This paper discusses a general immiscible formulation for flow in multi-layered heterogeneous media. The time-dependent, coupled pressure-saturation field is solved by numerical "IMPES" (implicit pressure - explicit saturation methods. The formulation does not assume constant density flow. Rather, the fluids involved are compressible and the formulation allows interpretation of pressure transients. The simulator forms the basis for a new series of interpretation methods in which heterogeneities and properties like relative permeability may be predicted from measurements.
Outputs are spatial ?snapshots? of pressure and oil saturation fields as they vary in time. A ?movie mode? option of the software shows changes in time. A very useful plot shows oil saturation obtained by the probe versus time. This plot discloses time needed to pump in order to obtain a good quality oil sample ? and the quality of that sample. A corresponding probe pressure versus time plot shows a different time scale that is partly dependent on fluid compressibility. This plot is useful in pressure transient permeability prediction. Calculations show, for example, the wait times needed for clean samples without filtrate are short for very low permeability mudcakes. For more permeable cakes, invasion is strong; and wait times are longer.
Modifications to the formulation are given which allow miscible flow simulation involving various combinations of fluids, e.g., fresh water vs brine, oil base mud invading formations containing oil. The mathematical models, numerical formulations and solution methods, and computed outputs and their practical application are described in detail for both immiscible and miscible job planning simulators."