  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.
