油藏开发生产优化近似扰动梯度升级算法

Reservoir production optimization using an upgraded perturbation gradient approximation algorithm

油藏开发生产优化属于高维系统最优控制问题,求解其真实梯度异常困难。给出一种近似扰动梯度的一般式,证明此近似梯度恒为上山方向,且两种常用的无梯度算法SPSA与En Opt产生的近似梯度分别是该梯度的两种特殊形式;通过引入并优化三角阵进行近似扰动梯度升级,实现其对真实梯度的最优逼近。数值试验结果表明:该升级算法相比标准的SPSA算法优化效率提高了近1倍;在历史拟合基础上使用该算法进行了某实际油藏生产优化,所得注采控制方案降水增油预测效果显著、水驱波及效率明显改善,验证了该算法现场应用的可行性。

Reservoir production optimization is a high-dimensional optimal control problem, and it is very difficult to obtain a true gradient. In this paper, a general perturbation gradient approximation method was presented, and the gradient resolved was always in uphill direction. The commonly used SPSA and EnOpt algorithms, being derivative-free, can be considered as special cases of the general perturbation gradient approximation. The perturbation gradient approximation can be upgraded by introducing an optimized lower triangular matrix for approaching to the true gradient. The numerical simulation results show that, compared with the standard SPSA algorithm, the optimization efficiency of the upgraded algorithm can be increased nearly 100%. In a real case study, the reservoir production optimization was conducted using the new method on the basis of history matching. The field data have shown remarkable increase on oil production and decrease of water production, and the sweeping efficiency of water flooding is significantly improved, which validates the feasibility of the algorithm for practical ap-plications.