A comprehensive method for estimating relative permeability curves

Among the various properties important for simulating reservoir behavior, relative permeability curves may be the most poorly determined by present methods. The objective of this study is to develop a new methodology for improved estimation of relative permeability curves of petroleum reservoirs. Both reservoir production data and prior information of relative permeability, such as laboratory estimates, are used in the estimation. The estimates obtained with the new estimation methodology are consistent with the reservoir production data and yet conform to the prior estimates.;First, automatic history matching algorithms based on variable-metric optimization methods and the optimal control approach were developed. The algorithms were tested with hypothetical two-phase reservoir history matching problems, and the estimated parameters included porosity, permeability, and relative permeability. The new algorithms were found to be more efficient and accurate than algorithms which use the steepest descent and Nazareth's conjugate gradient methods. The variable-metric methods tested included the BFGS method and a self-scaling variable-metric (SSVM) method. When the number of unknown parameters is large, the SSVM method is more efficient than the BFGS method. As illustrated with the BFGS method, equality and inequality constraints can be incorporated efficiently in automatic history matching to increase the robustness of the algorithms.;The new estimation methodology uses a Bayesian type performance index for incorporating prior estimates of relative permeability curves, such as laboratory estimates, into an automatic history matching algorithm to complement reservoir production data. The relative weight given to the production data and prior estimates in the estimation is chosen such that the final estimates are the closest to the prior estimates without compromising the match of reservoir production data. The Bayesian methodology can be implemented more efficiently than the conventional automatic history matching which considers only reservoir production data. The Bayesian methodology was tested with the estimation of water/oil relative permeability curves for hypothetical waterfloods. It provided more reliable estimates than the conventional automatic history matching. Good history matches and improved predictions of reservoir behavior were also observed.