Introduction Mathematical reservoir simulation models are widely used to predict field behavior. Their use requires that permeability and porosity be specified at numerous points throughout the reservoir. The usual procedure is to first estimate these parameters, compute the past field history and then compare the computed results with the observed performance. If the comparison is not satisfactory, the estimates are repeatedly modified until an acceptable match is obtained. It is then assumed that the rock properties are adequately specified for future predictions. This trial and error procedure can consume considerable computer time and money. In view of this, some people have investigated iterative adjustment and regression techniques linear and nonlinear programming methods and energy dissipation analysis in an effort to automate the procedure. These methods are essentially similar insofar as they are ex post facto techniques; i.e., after one or more computer runs have been executed, then the known performance history is used in some fashion to performance history is used in some fashion to deduce an acceptable set of rock parameters. This approach is tantamount to using a differential equation solver for treating an inverse problem, and is not the most efficient. In this work, we present a direct method for treating the inverse reservoir simulation problem. The technique enables one to compute problem. The technique enables one to compute reservoir permeabilities and porosities in a single computer run utilizing appropriate data from several periods of the performance history. It is applicable to multiphase, compressible flow in heterogeneous reservoirs. A procedure is described that recognizes, during the course of the computation, whether or not a unique solution can be obtained. The method is capable of handling inconsistent data and constructing the best set of non-unique properties within realistic limits when unique solutions do not exist. Results of studies on several hypothetical reservoir problems are presented. Finally, examples which show the effect of non-unique history matches on future predictions are also cited.