In Situ, Vol.19, No.2, 179-223, 1995
COMPUTATION OF SENSITIVITY COEFFICIENTS FOR CONDITIONING THE PERMEABILITY FIELD TO WELL-TEST PRESSURE DATA
Although simulated annealing has become an extremely popular simulation technique for generating reservoir descriptions, the computational costs become immense if the objective function includes production data that must be generated at each iteration by solution of a forward problem using a reservoir simulator. Because dynamic production data are critical for reducing the uncertainty in reservoir description, we explore the application of inverse problem theory to incorporate well-test pressure data in stochastic simulation. Only the problem of generating heterogeneous, isotropic, two-dimensional permeability fields that honor ＇＇known＇＇ spatial statistics and multiwell pressure data is considered. Techniques for generating realizations conditioned to these data are presented. In all methods, a description honoring the pressure data and prior information is obtained using a gradient method (Gauss-Newton). At each iteration of the Gauss-Newton method, the forward problem is solved using: a reservoir simulator. In all cases considered, the Gauss-Newton procedure concierges in five to eight iterations. A method is presented to efficiently generate sensitivity coefficients (derivatives of pressure with respect to each gridblock permeability) as part of the simulation run. Two of the methods considered are based on Bayes theorem and use the Gauss-Newton method to obtain the maximum a posteriori estimate. For these two methods, it is shown that multiple realizations can be generated from an LU decomposition of the a posteriori covariance matrix. The third method uses the Gauss-Newton method to solve a regularized nonlinear least-squares problem.