Unlocking Fast Reservoir Predictions via Non-Intrusive Reduced Order Models

Abstract

The present paper proposes a novel non-intrusive model reduction approach based on Proper Orthogonal Decomposition (POD), the Discrete Empirical Interpolation Method (DEIM) and Radial Basis Function (RBF) networks to efficiently predict production of oil and gas reservoirs. Provided a representative set of training reservoir scenarios, either POD or DEIM allows for effectively projecting input parameters (e.g., permeability, porosity), states (e.g., pressure, saturations) and outputs (e.g., well production curves) into a much lower dimension that retains the main features contained in the simulation system. In this work, these projections are applied across multiple levels to be able to collapse a large number of spatio-temporal correlations. It is observed that these projections can be effectively performed at a large extent regardless of the underlying geological complexity and operational constraints associated with the reservoir model. The RBF network provides a powerful means for developing learning functions from input-output relationships described by the reservoir dynamics entailed by multiple combinations of inputs and controls. In order to achieve a high degree of predictability from the resulting reduced model, the RBF network exploits locality by a means of Gaussian basis functions that are maximal at the sampled point and decrease monotonically with distance. Compared to multilayer perceptron networks (i.e., traditional artificial neural networks) RBF networks require less training and are less sensitive to the presence of noise in the data. In this regard, POD or DEIM acts as a data filter that additionally aids at designing a more compact RBF network representation suitable for targeting fast reservoir predictions. Numerical results show significant accelerations with respect to running the original simulation model on a set of field-motivated cases.

Non‐intrusive reduced‐order modelling of the Navier–Stokes equations based on RBF interpolation

“…This method is verified and validated by Burgers equation and convection–diffusion–reaction problems . Klie used a three‐layer RBF neural network combined with POD and DEIM to predict the production of oil and gas reservoirs .…”

“…This method is verified and validated by Burgers equation and convection-diffusion-reaction problems [38,39]. Klie used a three-layer RBF neural network combined with POD and DEIM to predict the production of oil and gas reservoirs [40].In this paper, we present a new non-intrusive reduced-order model (RBF/POD) for the Navier-Stokes equations. The novelty of this work lies in its application to construct the reduced-order model for the Navier-Stokes equations combined with POD.…”

Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods

“…The 'curse of dimensionality' is maybe less acute than some authors realize. However, as in all research, new useful insights may be discovered (Klie, 2013). It is not in doubt that, where possible, an optimization problem should reduce the dimensions, such as considering loop variables rather than node variables in network optimization.…”

Production Management Decision Analysis Using AI-Based Proxy Modeling of Reservoir Simulations – A Look-Back Case Study

“…Some recently published work have selected to use different flavors of the Principal Component Analysis such as Proper Orthogonal Decomposition (PDO) and Polynomial Chaos Expansion (PCE) in order to develop proxies of the numerical reservoir models (Cardoso 2010-Chen 2013-Klie 2013-He 2014. In the opinion of the authors 8 these new techniques will ultimately converge to the type of response surfaces that have been around for decades.…”