Fast modelling of gas reservoirs using non-intrusive reduced order modelling and machine learning

Abstract

This work focussed on developing approximate methods for rapidly estimating gas field production performance. Proper orthogonal decomposition (POD) - Radial basis function (RBF) and POD-Autoencoder (AE) Non Intrusive Reduced Order Models (NIROMs) were considered. The accuracy and speed of both NIROMs were evaluated for modelling different aspects of gas field modelling including reservoirs with time-varying and mixed production controls, reservoirs with and without aquifer pressure support, and for wells that were (or not ) shut-in during production lifecycle. These NIROMs were applied to predicting the performance of four gas reservoir models: a homogeneous synthetic model; a heterogeneous gas field with 3 wells and structures similar to the Norne Field; a water coning model in radian grid; and a sector model of a real gas field provided by Woodside Petroleum. The POD-RBF and POD-AE NIROMs were trained using the simulation solutions from a commercial reservoir simulator (ECLIPSE): grid distributions of pressure and saturations as well as time series production data such as production rates, cumulative productions and pressures. Different cases were run based on typical input parameters usually used in field performance studies. The simulation solutions were then standardised to zero mean and reduced into hyperspace using POD. In most cases, the optimum number of POD basis functions (99.9% energy criterion) of the solutions (training data) were used to reduce the training data into a lower-dimensional hyperspace space. The reduced training data and their corresponding parameter values were combined to form sample and response arrays based on a cause and effect pattern. RBF or AE was then used to interpolate the weighting coefficients that represented the dynamics of the gas reservoir as captured within the reduced training data. These weighting coefficients were used to propagate the prediction of new unseen simulation cases for the duration of predictions. The simulation results from either or both NIROMs was then compared against the simulation solution of the same cases in ECLIPSE. It was found that the POD-RBF is a better predictive tool for gas field modelling. It is faster, more accurate and consistent than the POD-AE, giving satisfactory predictions with up to 99% accuracy and 2 orders of magnitude speed-up. No single POD-AE is sufficient for predicting different production scenarios, besides, the process of arriving at a suitable POD-AE involves finetuning several hyper-parameters by trial and error, which may be more burdensome for practising petroleum engineers. The accuracy of NIROM’s prediction of production variable is generally improved by using more than the optimal number of POD-basis functions, while predictions of grid distributed properties are satisfactorily predicted with the optimal number of POD-basis functions. NIROM’s accuracy is dependent on whether the range of parameters of the prediction, their duration and specific production scenarios (such as having mixed production controls or aquifer pressure support) reflect those of the training cases. Overall, the number of training runs, the size of the reservoir model as well as the number of time intervals at which simulation output data is required all affect the speed of training both NIROMs for prediction. Other contributions of this work include showing that the linear RBF is the most suitable RBF for gas field modelling; developing a novel normalisation approach for time-varying parameters; and applying NIROMs to seasonally varying production scenarios with mixed production controls. This work is the first time that the POD-AE has been developed and evaluated for petroleum field development planning.