Estimation of absolute and relative permeabilities in petroleum reservoirs

The estimation of absolute and relative permeabilities for petroleum reservoirs on the basis of noisy data at wells is considered. The spatially varying absolute permeability is estimated by regularisation combined with a bi-cubic spline approximation. Relative permeability is represented by a given function of saturation with unknown coefficients. Numerical results provide an indication of the estimability of the two permeabilities in conventional petroleum production operations.