Deep-CRM: A New Deep Learning Approach for Capacitance Resistive Models

Abstract

Summary Classical reservoir engineering studies require building geological models and solving complex fluid flow transport equations that require high-quality data, numerous computational resources, time and workflows. For large and mature fields data-driven models can be used to get faster answer and to perform production analysis more efficiently. Capacitance Resistive Models (CRM) are a class of methods based on material balance that can be used to estimate production wells liquid rates as a function of injected water and Bottom Hole Pressure (BHP) variations. CRM methods quantify the connectivity between producers and injectors using only dynamic data. An important drawback of CRM is that they can suffer from parameter identification problems. Moreover, the analytical solution can be only obtained in specific conditions: linear variations of BHP and fixed injection rate between two consecutive time steps. In this work we present a new approach combining CRM material balance equations with neural networks in order to obtain more robust and reliable estimation of the CRM parameters (i.e. well connectivity, productivity indices and time constants). This proposal is also interesting since it is not based on any assumption on BHP and injection rates. To this end, we use a recent approach called Physics Informed Neural Networks (PINNs). In this approach neural networks are trained on observed data with additional physics constraints traduced in appropriate loss functions. The parameters of this physical equation are evaluated at the same time as the neural network weights. The introduction of PINNs in our approach raised after testing classical machine learning (ML) models (SVMs, Random Forests …) and deep learning models (MLP, LSTM, RNNs…). Indeed, such models can perform well in some specific cases but usually struggle to produce robust results (i.e. forecasting) in the long term. Unfortunately, such systems do not natively integrate physics constraints. Our aim is to impose physic constraints in neural networks. Thus, we may obtain more stable and reliable results. On the same time, we should be able to account for more behaviors that are not explained by simplified physic equations such as material balance. We performed a full comparison between our approach using PINNs, other standard ML and DL approaches and a given framework of CRMs on two data-sets: a simple but realistic model build using a commercial reservoir simulator, and a real data set. We show that our approach gives more robust results (in terms of MSE) while not suffering from parameter identification issue.