An important use of simulation is to determine reservoir properties by interpreting transient well tests. In general, this determination is carriedout by systematically varying reservoir properties until the pressures computed by the simulator match pressures measured during the well test â?" a procedure known as history matching. Reservoir properties determined by history matching are subject to error. Here we present a method of estimating this error. As an example, we studied the problem of estimating porosity and permeability in both a homogeneous reservoir and one in which damage is present in the vicinity of the well. Results presented indicate that the accuracy of calculated reservoir parameters depends on (1) the type of parameter estimated, (2) the number of parameters estimated, (3) the true value of the parameters and (4) the design of the well test.
Research efforts in history-matching reservoir simulators have principally been directed toward improving and extending existing techniques with respect to decreasing computing time. Little attention has been paid, however, to the analysis of the accuracy of the parameter values from the history match. Without such an analysis, parameter estimates from history matching might be meaningless. The problem is to estimate errors in parameter values determined by history matching.
The theory that is presented in the Appendix is applicable in general to multiphase, two-dimensional simulators. However, as an illustration, we apply the theory to the well known radial form of the diffusion equation, describing the transient behavior of pressure in a radial, horizontal reservoir containing a single-phase fluid of small and constant compressibility. The equation allows for permeabilities to change with radial distance from a wellbore â?" a situation that might be encountered if damage is present. We assume that the reservoir is finite. Furthermore, we assume that the well produces at a constant rate for a certain time and then is shut in. Thus, both drawdown and buildup takes place. No wellbore storage effects are considered.
