Model-reduced gradient-based history matching
By M. Kaleta, R. Hanea, Arnold W. Heemink, Jan Dirk Jansen. 2011
56 citations recorded by the source corpus.
Gradient-based history matching algorithms can be used to adapt the uncertain parameters in a reservoir model using production data. They require, however, the implementation of an adjoint model to compute the gradients, which is usually an enormous programming effort. We propose a new approach to gradient-based history matching which is based on model reduction, where the original (nonlinear and high-order) forward model is replaced by a linear reduced-order forward model and, consequently, the adjoint of the tangent linear approximation of the original forward model is replaced by the adjoint of a linear reduced-order forward model. The reduced-order model is constructed with the aid of the proper orthogonal decomposition method. Due to the linear character of the reduced model, the corresponding adjoint model is easily obtained. The gradient of the objective function is approximated, and the minimization problem is solved in the reduced space; the procedure is iterated with the updated estimate of the parameters if necessary. The proposed approach is adjoint-free and can be used with any reservoir simulator. The method was evaluated for a waterflood reservoir with channelized permeability field. A comparison with an adjoint-based history matching procedure shows that the model-reduced approach gives a comparable quality of history matches and predictions. The computational efficiency of the model-reduced approach is lower than of an adjoint-based approach, but higher than of an approach where the gradients are obtained with simple finite differences.
Subfields: Environmental Engineering, Mechanical Engineering, Ocean Engineering
View Paper: https://www.semanticscholar.org/paper/b7f81cd81f8f89290c082ebb2c20bc04552c240e
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Citations in the corpus
- Use of reduced-order models in well control optimization (2017, methodology): “A different way to use POD in gradient-based well control optimization was suggested by Kaleta et al. (2011). In this approach an approximate adjoint is obtained by using the transpose of the reduced-order Jacobian matrix.”