Reduced-Order Modelling for Production Optimisation

Abstract

Production optimisation of a reservoir simulation problem can be very computationally demanding as the reservoir model may contain many variables and nonlinearities, thus many iterations may be needed to obtain an optimal production schedule. Using Proper Orthogonal Decomposition and Trajectory Piecewise Linearization (POD-TPWL) developed in [1] and [2], simulations were performed on the Delft Egg model 100-200 times faster than the high-fidelity simulation with reasonable accuracy, depending on the distance from the trained solution. Production optimisation was performed using the gradient-based adjoint method. A reduced version of the adjoint equation was used by incorporating POD, as presented in [3] and by performing a first-order Taylor series expansion around a training point (similar to TPWL). This method allowed for time gains of 50-100 times when compared to the high-fidelity adjoint method. The results from the high-fidelity production optimisation compared with POD-TPWL showed a similar Net Present Value (NPV) for both optimisation methods, with an error of 0.1% between the two-values. However, the optimal injection schedules were not the same. When the high-fidelity model was run using the input schedules from POD-TPWL optimisation, the error in NPV was 4%. The speed-up observed for the optimisation loop using POD-TPWL was 6 times faster than the high-fidelity model. This is due to the number of snapshots that needed to be generated and the processing of the data from these snapshots. Robust optimisation was performed on the Egg model ensemble using a POD-TPWL model incorporating geological model parameters, states and well controls. Results showed a 0.7% deviation from the mean NPV value calculated in MoReS and a 4 million dollar increase in the standard deviation of the NPV. POD-TPWL was able to complete the robust optimisation 25 times faster than a high-fidelity simulation. POD-TPWL shows promise as a reduced-order modelling application for reservoir simulation and production optimisation. The accuracy needs to be improved in order to move to an operational application.