Numerical simulation of three-phase mud invasion using an epidermal effect model and adaptive time-stepping

The numerical simulation of reservoir mud invasion is widely used for studying the dynamic invasion process. To investigate the saturation changes of the three phases (water, oil, and mud filtrate) during mud infiltration into intact formations, this study presents a mathematical model for three-phase invasion in cylindrical coordinates. The principle of mud intrusion into the reservoir allows the derivation of the basic equation of three-phase mud seepage from Darcy's law and the law of mass conservation. This is followed by the derivation of the differential equations of pressure and three-phase saturation during mud intrusion. A numerical simulation program for the three-phase seepage flow of mud intrusion is written using the finite-difference method. An adaptive time-step algorithm is developed to address the inadaptability of the intrusion algorithm in the case of mud surges. Additionally, an epithermal effect algorithm is developed to address the problem of mud particles entering the stratum and affecting the absolute permeability. The results show that, as the porosity increases, the radial depth of intrusion decreases, along with a reduction in the invaded annulus range. It can be demonstrated that, when the reservoir pressure is maintained at a constant level, the size of the borehole pressure leads to an increase in the depth of radial intrusion and the extent of the intrusion annulus, under different differential pressure conditions.