Reservoir model parameters generally have very large uncertainty ranges, and need to be calibrated by history matching (HM) available production data. Properly assessing the uncertainty of production forecasts (e.g., with an ensemble of calibrated models that are conditioned to production data) has a direct impact on business decision making. It requires performing numerous reservoir simulations on a distributed computing environment. Because of the current low-oil-price environment, it is demanding to reduce the computational cost of generating multiple realizations of history-matched models without compromising forecasting quality. To solve this challenge, a novel and more efficient optimization method (referred to as SVR-DGN) is proposed in this paper, by replacing the less accurate linear proxy of the distributed Gauss-Newton (DGN) optimization method (referred to as L-DGN) with a more accurate response-surface model of support vector regression (SVR).
Resembling L-DGN, the proposed SVR-DGN optimization method can be applied to find multiple local minima of the objective function in parallel. In each iteration, SVR-DGN proposes an ensemble of search points or reservoir-simulation models, and the flow responses of these reservoir models are simulated on high-performance-computing (HPC) clusters concurrently. All successfully simulated cases are recorded in a training data set. Then, an SVR proxy is constructed for each simulated response using all training data points available in the training data set. Finally, the sensitivity matrix at any point can be calculated analytically by differentiating the SVR models. SVR-DGN computes more-accurate sensitivity matrices, proposes better search points, and converges faster than L-DGN.
The quality of the SVR proxy is validated with a toy problem. The proposed method is applied to a real field HM example of a Permian liquid-rich shale reservoir. The uncertain parameters include reservoir static properties, hydraulic-fracture properties, and parameters defining relative permeability curves. The performance of the proposed SVR-DGN optimization method is compared with the L-DGN optimizer and the hybrid Gauss-Newton with a direct-pattern-search (GN-DPS) optimizer, using the same real field example. Our numerical tests indicate that the SVR-DGN optimizer can find better solutions with smaller values of the objective function and with a less computational cost (approximately one-third of L-DGN and 1/30 of GN-DPS). Finally, the proposed method is applied to generate multiple conditional realizations for the uncertainty quantification of production forecasts.