Full text loading...
-
Improved Estimation of the Stochastic Gradient with Quasi-Monte Carlo Methods
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery, Sep 2014, Volume 2014, p.1 - 25
Abstract
Summary
In practical reservoir management, although the intent is generally to maximize some key quantity (e.g., net present value or NPV, reserves, cumulative oil production etc.), the operating well parameters (e.g., rate and/or pressure) are seldom, if ever, determined using formal optimization techniques. The usual approach to do so is through a manual process or by simply reacting to key well events (e.g., water breakthrough, or water cut reaching a threshold values). These are either quite time consuming or very likely to provide suboptimal results. Existing optimization tools have not found much use for solving this problem, as they are not efficient enough for applications to large scale simulation models of real fields. Towards this end, both adjoint and ensemble based optimization techniques have recently received significant attention as viable means for practical control optimization of large scale simulation models.
Although adjoints are the most efficient approach for accurate gradient calculation, they are difficult to implement as they require significant changes to the simulator code. The stochastic gradient, although not as efficient, is much easier to implement as it is non-intrusive and treats the simulator as a black box. In this work, we propose the application of quasi-Monte Carlo methods for improving the efficiency and accuracy of calculation of the stochastic gradient compared to current methods. While the existing approaches rely on Monte Carlo sampling which has an error convergence rate proportional to the square root of the number of ensemble members, quasi-Monte Carlo sampling has a better convergence rate proportional directly to the number of ensemble members. In particular, we apply the Sobol sequence for sampling the ensemble members, which demonstrates better convergence compared to other quasi-Monte Carlo sampling techniques. The results are demonstrated on synthetic and real models and also compared to the true gradient obtained using adjoints. In general, more than 30% improvement was obtained in the accuracy of the stochastic gradient calculated with Sobol sampling over standard Monte Carlo sampling, resulting in faster convergence of the gradient based optimization algorithm used in this work (sequential quadratic programming).
© EAGE Publications BV