Numerical Investigation of Static and Dynamic Mud Filtration Considering Compressibility of Mud Cake: Comparison of Darcian and Non-Darcian Flow Conditions

One of the main reasons of formation damage is invasion of drilling mud into the formation during drilling operations. Therefore, modeling and numerical simulation of this process in oil industry is very important. However, the effect of flow regime on filtrate invasion into formation is not well considered especially when compressible cake is assumed. In this study, invasion of a water based drilling mud in the linear system at static as well as dynamic conditions for Darcy and non-Darcy flow regimes have been investigated through numerical simulation. In addition, the model includes presence of compressible mud cake, penetration of solid particles into the formation, and erosion of the cake particles from the cake surface due to shear stress caused by drilling fluid. The saturation distribution of the invaded mud filtrate into the formation is obtained by simultaneous solution of coupled equations of convection-diffusion, momentum, and mass balance in porous media. The equations have been improved by considering compressible mud cake. It is found out that by considering compressible mud cake, the depth of invaded filtrate in the formation is increased and the thickness of the cake decreases from 0.015 mm to about 0.013 mm. The results also showed that the depth of filtrate invasion in Darcian flow regime in the dynamic filtration is about 1.27 cm more than the filtrate invasion depth in static filtration condition. In Non-Darcian flow conditions, entire sample was invaded by mud filtrate within 30 minutes dynamic mud filtration. Finally, the results of this study can help to better understand the drilling fluid invasion and mud cake growth in non-Darcy flow condition when erosion due to shear stress induced by drilling mud on cake surface occurs.