History matching with iterative Latin hypercube samplings and parameterization of reservoir heterogeneity

• We formulate a history matching as a global minimization problem.
• A new population-based global optimization algorithm named iterative Latin hypercube samplings is proposed.
• The set of orthonormal basis functions is useful to reduce the number of parameters on reservoir heterogeneity.
• Numerical example would reveal that the suggested approach of history matching is efficient and of practical use.

History matching can be formulated as a global minimization of the difference between time-series observations and numerical results. Existence of a number of unknown parameters, however, makes the dimensionality of history matching intractably high. This study addresses two issues involved in solving history matching with a feasible number of simulation runs. One is the computational effort required for searching an optimal solution, the other the ill-posedness owing to reservoir heterogeneity. A new population-based search algorithm named iterative Latin hypercube samplings is proposed for the former and we would show the superior convergence of our proposed algorithm over those of other famous population-based search algorithms for a broad class of functions. As for the latter, parameterization of reservoir heterogeneity using orthonormal basis functions is considered, which can significantly reduce the number of unknown parameters to be optimized. Numerical example would reveal that our approach of history matching is efficient and of practical use.