Reverse Engineer a Subsurface Hybrid Model from an Analytical Model Using a Physics Based Neural Network

Abstract Reservoir simulation is widely regarded as the preferred method for production and reserve forecasting due to its capability to accurately capture the underlying physics of subsurface processes. However, developing a reliable model is a time-consuming and skill-intensive task, requiring significant effort. The time-consuming and complex nature of building reliable reservoir models often compels occupied reservoir engineers to switch to simpler analytical models. Often, the base case (or P50 model) is a history-matched, high-fidelity reservoir simulation model, however analytical methods such as decline curve analysis (DCA) are used to estimate low and high case scenarios. These approaches are useful when substantial historical data is available, such as predicting the terminal decline of old wells. However, they lack predictive power when it comes to new developments, like infill wells or the implementation of Improved Oil Recovery (IOR) techniques. In such cases, reservoir engineers often find themselves in need of more reliable forecasting tools than those provided by assumption-based analytical methods. This paper explores a method for quickly reverse-engineering a subsurface simulation model that not only captures the decline in line with analytical understanding for low /high cases but also improves forecasting accuracy for new developments. The approach begins by using the base case model and an analytical profile as inputs into a history matching and optimization tool. The design of experiments (DOE) is then developed, considering all relevant variables within the uncertainty space, such as petrophysical interpretations, fault transmissibility, and other key factors. This DOE is applied to the base simulation model. After the uncertainty model is set up, an objective function built on the simulation data set is run on a reservoir simulator to assess the entire uncertainty space and then the optimizer takes over to minimize the error. The cases which capture historical performance and desired decline are of interest. On the best fit runs, a neural network-based proxy model is built in and used for creating enough samples in defined uncertainty space. This neural network generated data provides sufficient samples to run a cumulative distribution function (CDF), that can be used to arrive at most likely "low case" or most likely "high case". In this study, a prototype reservoir model representing a real field is used, which incorporates 20 years of historical production data, as well as plans for infill drilling and waterflood implementation. The analytical profile is based on decline curve analysis, considering instantaneous potential (IP) and different b factors for both the depletion and waterflood phases. The outcome is an envelope of models that reflect the desired decline profiles and volumes. These models can either be used directly in a multi-model approach or, alternatively, the statistical distributions within the envelope can be used to derive a deterministic model that represents the desired (P10/P90) case scenario. In terms of results for the case considered, the production profile for matured wells and sectors using this subsurface twin model is in line with this DCA, however initial potentials for infill show considerable differences.