Model-reduced gradient-based history matching |
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| Authors: | Ma?gorzata P Kaleta Remus G Hanea Arnold W Heemink Jan-Dirk Jansen |
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| Institution: | 1.Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics,Delft University of Technology,Delft,The Netherlands;2.TNO Built Environment and Geosciences, Business Unit Geo Energy and Geo Information,TNO,Utrecht,The Netherlands;3.Faculty of Civil Engineering and Geosciences, Department of Geotechnology,Delft University of Technology,Delft,The Netherlands |
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| Abstract: | 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. |
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