Monte Carlo simulation of permeability fields and reservoir performance predictions with SVD parameterization in RML compared with EnKF

Abstract

In a previous paper, we developed a theoretical basis for parameterization of reservoir model parameters based on truncated singular value decomposition (SVD) of the dimensionless sensitivity matrix. Two gradient-based algorithms based on truncated SVD were developed for history matching. In general, the best of these "SVD" algorithms requires on the order of 1/2 the number of equivalent reservoir simulation runs that are required by the limited memory BroydenFletcher-Goldfarb-Shanno (LBFGS) algorithm. In this work, we show that when combining SVD parameterization with the randomized maximum likelihood method, we can achieve significant additional computational savings by history matching all models simultaneously using a SVD parameterization based on a particular sensitivity matrix at each iteration. We present two new algorithms based on this idea, one which relies only on updating the SVD parameterization at each iteration and one which combines an inner iteration based on an adjoint gradient where during the inner iteration the truncated SVD parameterization does not vary. Results generated with our algorithms are compared with results obtained from the ensemble Kalman filter (EnKF). Finally, we show that by combining EnKF with the SVD-algorithm, we can improve the reliability of EnKF estimates.

Model Design and Strategy for Integrated Management and Control of Enterprise Risk

“…Risk analysis can be carried out by using simple approaches to depict multifarious risks, such as probability and impact matrices, or more sophisticated probabilistic methods, such as threepoint estimates or probability functions and Monte Carlo simulations [4][5][6].…”

Truncated Conjugate Gradient Method for History Matching in Reservoir Simulation

“…Various schemes have been designed to solve the HM problem, such as L-BFGS [3,13] and TSVD [1,10,12]. Most recently, we have proposed the Truncated Conjugate Gradient 2 (TCG) algorithm for HM [2].…”

“…In TSVD, the summation in this linear combination is truncated in an appropriate way, see [1,10,12] for further details.…”

Data assimilation and uncertainty assessment for complex geological models using a new PCA-based parameterization

“…A number of these methods were described in [45]. General approaches include PCA-based procedures [9,29,36,40], kernel PCA approaches [25,39], discrete wavelet transforms [2,24,38], discrete cosine transforms [14,15], level-set methods [7], and SVD [42,44] and K-SVD techniques [18]. The O-PCA approach offers advantages relative to some of these procedures, as it is piecewise differentiable and captures the connectivity structure of the geostatistical realizations used in its construction.…”

“…EnKF is a Monte Carlo type method that assimilates data sequentially and generates an ensemble of realizations. It does, however, assume that the prior model is Gaussian, and it can be subject to ensemble collapse if an insufficient number of models is used [44]. In comparisons between EnKF and RML procedures, EnKF was found to perform similar to or better than the RML method for realistic reservoir problems [30], though EnKF was shown to incorrectly sample the posterior distribution in a simple idealized nonlinear problem, while the RML method provided almost perfect sampling [46].…”