COMPUTATION OF SENSITIVITY COEFFICIENTS FOR CONDITIONING THE PERMEABILITY FIELD TO WELL-TEST PRESSURE DATA

Although simulated annealing has become an extremely popular simulatio n technique for generating reservoir descriptions, the computational c osts become immense if the objective function includes production data that must be generated at each iteration by solution of a forward pro blem using a reservoir simulator. Because dynamic production data are critical for reducing the uncertainty in reservoir description, we exp lore the application of inverse problem theory to incorporate well-tes t pressure data in stochastic simulation. Only the problem of generati ng heterogeneous, isotropic, two-dimensional permeability fields that honor ''known'' spatial statistics and multiwell pressure data is cons idered. Techniques for generating realizations conditioned to these da ta 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 pro blem is solved using: a reservoir simulator. In all cases considered, the Gauss-Newton procedure concierges in five to eight iterations. A m ethod is presented to efficiently generate sensitivity coefficients (d erivatives of pressure with respect to each gridblock permeability) as part of the simulation run. Two of the methods considered are based o n Bayes theorem and use the Gauss-Newton method to obtain the maximum a posteriori estimate. For these two methods, it is shown that multipl e realizations can be generated from an LU decomposition of the a post eriori covariance matrix. The third method uses the Gauss-Newton metho d to solve a regularized nonlinear least-squares problem.