Comparison of optimization techniques for automatic history matching

Abstract

Reservoir parameters are estimated by adjusting simulation models to match field or laboratory data. Multivariate optimization techniques with physically realistic constraints on the parameters are used in order to obtain these estimates. Two examples are presented. The first example is the analysis of a drawndown test. Permeability and porosity are determined by minimizing an objective function which is the sum of the squares of the differences between theoretical and measured pressure-time distributions at the well. The minimization is performed by applying four different optimization techniques: Davidon-Fletcher-Powell (DFP), Fletcher-Reeves (FR), Quasi-Newton Approximation for the Least-Squares Problem (QNA) and Levenberg-Marquardt (LM). The second example is the simultaneous determination of capillary pressure and relative permeability curves of oil/water systems. It is based on the analysis of transient output data measured from a linear coreflood experiment. QNA and LM are used to match results from a numerical simulator to laboratory coreflood data. The special methods for the least-squares problem (LM, QNA) behave better than the two others (DFP, FR). LM and QNA arrive to the optimal point more frequently than DFP and FR. LM takes less computing time than QNA but is more affected by rounding errors. Therefore, QNA shows the best behavior when finding the optimum. The automatic algorithms are of particular use whenever the equations which govern the flow are too complex to be solved by the traditional analytical-graphical methods.