Determination of oil reservoir permeability from resistivity measurement: A parabolic identification problem

In this paper we propose a new method in order to determine the oil reservoir permeability starting from the experimental values of the radial resistivity variation caused by mud filtrate invasion process. This process consists of two coupled phenomena: the filter cake formation (modeled by a Cauchy problem for an ordinary differential equation of first order) and the mud filtrate diffusion process through the porous media (modeled by a mixed problem for diffusion equation). The oil reservoir permeability is determined by the identification method for a parabolic problem. In this context we obtain two algorithms for the numerical calculus of oil reservoir permeability. These algorithms use as the main tool the derivative of the objective functional with respect to the reservoir permeability. The method for the reservoir permeability determination presented in this paper was numerically tested using four sets of data (which correspond to four wells). The oil reservoir permeability values obtained with our algorithms are in good agreement with the experimental data.