Although it is possible to apply traditional optimization algorithms together with the randomized-maximum-likelihood (RML) method to generate multiple conditional realizations, the computation cost is high. This paper presents a novel method to enhance the global-search capability of the distributed-Gauss-Newton (DGN) optimization method and integrates it with the RML method to generate multiple realizations conditioned to production data synchronously.
RML generates samples from an approximate posterior by minimizing a large ensemble of perturbed objective functions in which the observed data and prior mean values of uncertain model parameters have been perturbed with Gaussian noise. Rather than performing these minimizations in isolation using large sets of simulations to evaluate the finite-difference approximations of the gradients used to optimize each perturbed realization, we use a concurrent implementation in which simulation results are shared among different minimization tasks whenever these results are helping to converge to the global minimum of a specific minimization task. To improve sharing of results, we relax the accuracy of the finite-difference approximations for the gradients with more widely spaced simulation results. To avoid trapping in local optima, a novel method to enhance the global-search capability of the DGN algorithm is developed and integrated seamlessly with the RML formulation. In this way, we can improve the quality of RML conditional realizations that sample the approximate posterior.
The proposed work flow is first validated with a toy problem and then applied to a real-field unconventional asset. Numerical results indicate that the new method is very efficient compared with traditional methods. Hundreds of data-conditioned realizations can be generated in parallel within 20 to 40 iterations. The computational cost (central-processing-unit usage) is reduced significantly compared with the traditional RML approach.
The real-field case studies involve a history-matching study to generate history-matched realizations with the proposed method and an uncertainty quantification of production forecasting using those conditioned models. All conditioned models generate production forecasts that are consistent with real-production data in both the history-matching period and the blind-test period. Therefore, the new approach can enhance the confidence level of the estimated-ultimate-recovery (EUR) assessment using production-forecasting results generated from all conditional realizations, resulting in significant business impact.