Model-reduced Variational Data Assimilation for Reservoir Model Updating

Variational data assimilation techniques (automatic history matching) can be used to adapt a prior permeability field in a reservoir model using production data. Classical variational data assimilation requires, however, the implementation of an adjoint model, which is an enormous programming effort. Moreover, it requires the results of one complete simulation of forward and adjoint models to be stored, which is a serious problem in real-life applications. Therefore, we propose a new approach to variational data assimilation that is based on model reduction, where the adjoint of the tangent linear approximation of the original model is replaced by the adjoint of a linear reduced model. The Proper Orthogonal Decomposition approach is used to determine a reduced model. Using the reduced adjoint the gradient of the objective function is approximated and the minimization problem is solved in the reduced space. If necessary, the procedure is iterated with the updated estimate of the parameters. We evaluated the model-reduced method for a simple 2D reservoir model. We compared the method with variational data assimilation where the gradient is approximated by finite differences and we found that the reduced-order method is about 50 % more efficient. We foresee that the computational efficiency will significantly increase for larger model size and our current research is focused on quantifying this computational benefit.