Multiple Realizations of the Permeability Field From Well Test Data

Although it is possible to generate smooth radially-symmetric permeability distributions that honor a given set of pressure data, the assumption of radial symmetry is unrealistic for most heterogeneous reservoirs. The alternative for generating two-dimensional permeability fields that honor the pressure data and a variogram, without the radial symmetry of the deterministic methods, has usually been to resort to Monte Carlo methods. In this paper I show that it is possible, using models which are linearized about the maximum likelihood point, to generate multiple realizations of the permeability field that are conditioned to well test data, point measurements of permeability, and the variogram. The proposed procedure is far more efficient than current simulated annealing or genetic algorithms and the resulting conditional simulations have no radial artifacts.