Multilevel Grid Method for History Matching Multi-dimensional Multi-phase Reservoir Models

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Applied Numerical Mathematics


The multilevel grid method (different from the multigrid method commonly used for accelerating the iterative solution process of linear algebraic equations) is used here to develop an efficient numerical algorithm for history matching multi-phase multi-dimensional reservoir models. The purpose of history matching is to identify the unknown oil reservoir structural parameters by matching the computed pressure values with measured pressure values at observation wells. One of the major problems in history matching is that the identified parameter distribution is very sensitive to the initial guess used to start the history matching process. The problem becomes worse as the number of grid points increases. With the multilevel grid, the history matching process starts on a coarse grid; the parameter distribution identified on the coarse grid is then interpolated onto a finer grid and used as a better initial guess to start the history matching on the finer grid. Although the history matching process becomes more sensitive to the initial guess as the number of grid points increases, the better initial guess obtained from the solution on the coarse grid offsets the increased sensitivity and improves the quality of the identified parameter distribution on the finer grid. The grid can be refined repeatedly until the desired resolution has been achieved. Numerical examples for two- and three-dimensional reservoir models are given in the paper, which demonstrate that the algorithm presented here is able to identify the reservoir absolute permeability distributions varying over the field by an order of magnitude with a constant initial guess deviating from the true distribution by two orders of magnitude. The use of the multilevel grid also reduces the computational complexity of the algorithm and speeds up the computations.

Original Citation

Zhu, J., , & Ming Chen, Y. (1992). Multilevel grid method for history matching multi-dimensional multi-phase reservoir models. Applied Numerical Mathematics, 10(2), 159-174. doi:10.1016/0168-9274(92)90038-F