Determining the distribution of optimal injection and production wells along with their operating conditions is a complex problem. The objective of this study is to compare the effectiveness of an experimental based approach (central composite design, CCD) with a machine learning method (xGBoost) in a well-placement optimization application.
In this study, the well-placement problem consists of the joint optimization of drainage radius, well-operating conditions, and the number of injection and production wells. Our objective function is the net-present-value (NPV) for a specified operational life of the reservoir under study. Both algorithms (CCD and xGBoost) are applied to three different optimization scenarios, i.e., production from (I) homogeneous reservoir, (II) heterogeneous reservoir, and (III) waterflooding into a heterogeneous reservoir. Like all machine-learning algorithms, our methods need a training dataset. The fast predictor module (i.e., trained model) is obtained by running several numerical simulations by a commercial simulator internally called in an own developed Python code. Moreover, R-squared is chosen as the statistical quality measure in this study.
In the first scenario, both algorithms show satisfying predictions (R-squared of 0.943 and 0.999 for CCD and xGBoost, respectively). In scenario II, the CCD and xGBoost show a similar response again (0.948 and 0.997, respectively). As a sub-result, the optimum distance between the two producers was found approximately five simulation blocks in the first case, and three blocks in the second one. The CCD method reveals unreliable results (0.840) in scenario III, while the NPV predictions of the xGBoost algorithm are still acceptable (0.986). Moreover, unlike CCD, xGBoost could find the optimum solution. In other words, the CCD method does not always converge to an optimum solution. However, the number of required simulation runs for CCD is equal to that for the xGBoost model.
In this study, a machine learning approach and an experimental design method were compared together in detail. Their efficiency in predicting the NPV of a well-placement problem through multiple homogeneous and heterogeneous reservoir scenarios differ significantly.