A nonlinear single phase mud-filtrate invasion model

In this paper we propose a nonlinear single-phase mud-filtrate invasion model in order to determine the mud-filtrate concentration in the invaded zone and the mudcake thickness. This nonlinear model describes two coupled phenomena that occur during the reservoir invasion: the mudcake formation and the mud-filtrate diffusion through the porous media. The nonlinear model proposed in this paper takes into account the modification of the reservoir permeability due to the invasion phenomenon. We propose a numerical algorithm (based on the successive approximation method) in order to obtain the numerical solution of this nonlinear model. The numerical results obtained with the nonlinear model proposed in this paper are in good agreement with the numerical results from the literature.