It is very difficult to forecast the production rate of oil wells as the output of a single well is sensitive to various uncertain factors, which implicitly or explicitly show the influence of the static, temporal and spatial properties on the oil well production. In this study, a novel machine learning model is constructed to fuse the static geological information, dynamic well production history, and spatial information of the adjacent water injection wells. There are 3 basic modules in this stacking model, which are regarded as the encoders to extract the features from different types of data. One is Multi-Layer Perceptron, which is to analyze the static geological properties of the reservoir that might influence the well production rate. The other two are both LSTMs, which have the input in the form of two matrices rather than vectors, standing for the temporal and the spatial information of the target well. The difference of the two modules is that in the spatial information processing module we take into consideration the time delay of water flooding response, from the injection well to the target well. In addition, we use Symbolic Transfer Entropy to prove the superiorities of the stacking model from the perspective of Causality Discovery. It is proved theoretically and practically that the presented model can make full use of the model structure to integrate the characteristics of the data and the experts' knowledge into the process of machine learning, greatly improving the accuracy and generalization ability of prediction.

翻译：油井产量受多种不确定因素影响，这些因素直接或间接地体现了静态、时变和空间属性对油井产出的作用，因此单井产量预测极具挑战性。本研究构建了一种新型机器学习模型，将静态地质信息、动态生产历史及邻近注水井的空间信息进行融合。该堆叠模型包含三个基础模块，作为编码器从不同类型数据中提取特征：第一个模块为多层感知器，用于分析可能影响油井产量的储层静态地质属性；另外两个模块均为长短期记忆网络，其输入形式为矩阵而非向量，分别表征目标井的时间序列信息与空间关联信息。两个模块的差异在于：空间信息处理模块特别考虑了水驱响应从注水井到目标井的时间延迟。此外，本研究采用符号传递熵从因果发现角度验证了该堆叠模型的优越性。理论证明与实际应用表明，该模型能充分利用其结构特性，将数据特征与专家知识融入机器学习过程，显著提升了预测的准确性与泛化能力。