Historical Window-Enhanced Transfer Gaussian Process for Production Optimization

As a crucial step of reservoir management, production optimization aims to make the optimal scheme for maximal economic benefit measured by net present value (NPV) according to reservoir states. Despite the remarkable success, more advanced methods that can get higher NPV with less time consumed are still in urgent need. One main reason for limiting the optimization performance of existing methods is that historical data cannot be fully used. For a practical reservoir, production optimization is generally implemented in multiple stages, and substantial historical data are accumulated. These hard-won data obtained with lots of time encapsulate beneficial optimization experience and in-depth knowledge of the reservoir. However, when encountered with an unsolved optimization task in new stages, most methods discard these historical data, optimize from scratch, and gradually regain the knowledge of the reservoir with massive time for "trial and error" to find the right optimization direction, which is time-consuming and affects their practical application. Motivated by this, a novel method named historical window-enhanced transfer Gaussian process (HWTGP) for production optimization is proposed in this paper. Each optimization stage is regarded as a time window, and the data in historical windows are adopted as a part of training data to construct the transfer Gaussian process (TGP), which guides the whole optimization process. To solve the high-dimensional feature of practical problems, the prescreening framework based on a dimension-reduction method named Sammon mapping is introduced. The main innovation of HWTGP is that like experienced engineers, it can extract beneficial reservoir knowledge from historical data and transfer it to the target production-optimization problem, avoiding massive time for "trial and error" and getting superior performance. Besides, HWTGP has a self-Adaptive mechanism to avoid harmful and ineffective experience transfer when tasks in historical and current windows are unrelated. To verify the effectiveness of HWTGP, two reservoir models are tested 10 times independently and results are compared with those obtained by differential evolution (DE) and a surrogate-based method. Experimental results show that HWTGP can achieve the optimal well controls that can get the highest NPV, and has significantly enhanced convergence speed with excellent stability, proving the effectiveness of transferring historical data.