Efficient reservoir history matching using subspace vectors

In this paper, we describe a method of history matching in which changes to the reservoir model are constructed from a limited set of basis vectors. T he purpose of this reparameterization is to reduce the cost of a Newton ite ration, without altering the final estimate of model parameters and without substantially slowing the rate of convergence. The utility of a subspace m ethod depends on several factors, including the choice and number of the su bspace vectors to be used. Computational gains in efficiency result partly from a reduction in the size of the matrix system that must be solved in a Newton iteration. More important contributions, however, result from a redu ction in the number of sensitivity coefficients that must be computed, redu ction in the dimensions of the matrices that must be multiplied, and elimin ation of matrix products involving the inverse of the prior model covarianc e matrix. These factors affect the efficiency of each Newton iteration. Alt hough computation of the optimal set of subspace vectors may be expensive, we show that the rate of convergence and the final results are somewhat ins ensitive to the choice of subspace vectors. We also show that it is desirab le to start with a small number of subspace vectors and gradually increase the number at each Newton iteration until an acceptable level of data misma tch is obtained.