Determination of oil reservoir permeability and porosity from resistivity measurement using an analytical model

In this paper we propose two new algorithms in order to determine the oil reservoir permeability and porosity starting from the experimental values of the radial resistivity variation. Starting from the experimental values of the resisitvity measured in the invaded zone we determine the water saturation values (and as a result the mud filtrate concentration values) in the invaded zone. For the analytical determination of the mud filtrate concentration in the invaded zone we use a mathematical model that describes two coupled phenomena that occur during the invasion: the mud cake formation and the mud filtrate diffusion process through the porous media. In this context we determine the reservoir porosity and permeability by minimizing a functional which establishes the difference between the measured values and the analytical values of the mod filtrate concentration in the invaded zone. In order to determine the minimum of this functional we use Rosen's algorithm, the bisection algorithm and a fixed point procedure. We check the algorithm's efficiency by testing it on four data sets corresponding to four wells. The numerical results obtained with our algorithms are in good agreement with the experimental values.