Engineering Design of Neural Network Architectures for Estimation of Inter-Well Connectivity and Production Performance

Abstract

Summary Advances in machine learning and data science have given rise to a new set of tools and methods for developing efficient fit-for-purpose proxy models. Two major difficulties in adopting these methods are (i) the lack of physical constraints and domain insight in the design and construction of these models, and (ii) their limited interpretability, which can seriously impede their broader application to scientific domains, including reservoir engineering. In this paper, neural network architectures are designed based on simple reservoir engineering insights to characterize inter-well connectivity and well production performance under different operational conditions. Two different approaches are presented for construction of a neural network proxy model. The first approach takes a global view by representing all well connections in a fully connected neural network to allow any injector to be connected to a producer. The resulting network is a highly redundant description as many of the included connections are not plausible. To systematically eliminate unrealistic connections, l1-norm regularization is adopted to sparsify the network topology (connections) during the training stage. The resulting sparse structure characterizes the inter-well connectivity and defines a network topology that is supported by the training data. In the second approach, a local view is taken in building the proxy model. In this case, each producer is assumed to be supported by very few surrounding injection wells and likely to have weak connections with distant wells. However, inter-well connectivity in complex large-scale reservoirs is not just a function of distance and rather difficult to determine. Therefore, we use a series of randomly sized neighborhoods around each producer to include different number of injectors in the local networks. The variability in the neighborhood size reflects the prior uncertainty about the potential connectivity between wells at different distances. This approach results in many local neural networks (several local networks per each producer) that can be aggregated into a single large neural network model with pre-defined topological structure to represent possible connections. The training is then used to estimate the weights in the resulting architecture. The methods are applied to predict inter-well connectivity and oil production in a large-scale mature field that undergoes water flooding. Examination of the estimated connectivity parameters inside the neural network shows that the retrieved inter-well connectivity map is consistent with the existing geological features. The results suggest that even simple engineering insights can lead to noticeable improvement in the performance of neural networks.