Ensemble methods are remarkably powerful for quantifying geological uncertainty. However, the use of the ensemble of reservoir models for robust optimization (RO) can be computationally demanding. The straightforward computation of the expected net present value (NPV) requires many expensive simulations. To reduce the computational burden without sacrificing accuracy, we present a fast and effective approach that requires only simulation of the mean reservoir model with a bias correction factor. Information from distinct controls and model realizations can be used to estimate bias for different controls. The effectiveness of various bias-correction methods and a linear or quadratic approximation is illustrated by two applications: flow optimization in a one-dimensional model and the drilling-order problem in a synthetic field model. The results show that the approximation of the expected NPV from the mean model is significantly improved by estimating the bias correction factor, and that RO with mean model bias correction is superior to both RO performed using a Taylor series representation of uncertainty and deterministic optimization from a single realization. Use of the bias-corrected mean model to account for model uncertainty allows the application of fairly general optimization methods. In this paper, we apply a nonparametric online learning methodology (learned heuristic search) for efficiently computing an optimal or near-optimal robust drilling sequence on the REEK Field example. This methodology can be used either to optimize a complete drilling sequence or to optimize only the first few wells at a reduced cost by limiting the search depths.

集成方法对于量化地质不确定性非常有用。但是，在计算上需要使用储层模型的集合进行鲁棒优化（RO）。期望净现值（NPV）的直接计算需要许多昂贵的模拟。为了在不牺牲精度的情况下减少计算负担，我们提出了一种快速有效的方法，该方法仅需要模拟带有偏差校正因子的平均油藏模型。来自不同控件和模型实现的信息可用于估计不同控件的偏差。两种应用说明了各种偏差校正方法和线性或二次逼近的有效性：一维模型中的流量优化和合成场模型中的钻探问题。结果表明，通过估计偏差校正因子，可以显着改善均值模型的预期NPV近似值，并且采用均值模型偏差校正的RO优于使用不确定性的泰勒级数表示和确定性优化的RO。单一实现。使用偏差校正后的均值模型来解决模型不确定性，可以应用相当通用的优化方法。在本文中，我们将非参数在线学习方法（学习型启发式搜索）应用于REEK Field示例中，以有效地计算出最佳或接近最优的稳健钻探序列。通过限制搜索深度，该方法可用于优化完整的钻井程序或仅以降低的成本优化前几口井。