Pros and Cons of Applying Proxy-Models as a Substitute for Full Reservoir Simulations

Abstract

This paper presents a comparative study of proxy-modeling methodology (also known as surrogate modeling or metamodeling) as a computationally cheap alternative to full numerical simulation in assisted history matching, production optimization and forecasting. The study demonstrates the solution space complexity for different simulation models and the applicability of the proxy-models to mimic it. Focus is given to the practical aspects of model construction and to the limitations of which engineers should be aware. Results of stochastic optimization driven by full numerical simulation are compared to the proxy-model solutions in order to demonstrate strengths and weaknesses of each approach and determine desirable areas of application. Several simulation models of different complexity were used to demonstrate the impact of model structure, number of uncertainty parameters and type of problem on simulation model response and on efficiency of proxy-model application. The results are presented for different datasets, proxy-models and simulation model outputs to demonstrate the dependence of the approximation quality on these parameters. The dependence of the proxy-model prediction quality on sampling method, and on uncertainty domain complexity has been revealed. The efficiency of proxy-model application in history matching and production optimization was compared to stochastic optimization with full reservoir simulation. The results of this study have demonstrated that with increasing complexity of the solution space and number of uncertainties, the application of the proxy-modeling methodology is not recommended for history matching. In the history matching case, the use of full reservoir simulations, combined with stochastic search methods, is preferable and, above a certain level of complexity, the only acceptable solution. Nevertheless, proxy-modeling might be a good approach for certain production optimization projects and appropriate tool for forecasting of Hydrocarbons Initially In Place (HCIIP) and oil recovery (OR). This study suggests areas of application for proxy-models and full numerical simulation. It addresses pros and cons of both approaches in reservoir simulation and provides advice for their efficient application. Introduction Recent progress in computational hardware and software development has opened new frontiers in reservoir modeling. However, for many workflows in uncertainty quantification and optimization with application to reservoir simulation the availability of computing resources is still seen as a limiting factor. Therefore, engineers are still looking for a ways to reduce the computational load related to simulation studies, so application of computationally efficient proxy-models gains a lot of attention. In this paper we refer to a "proxy-model" as a mathematically or statistically defined function that replicates the simulation model output for selected input parameters. The terms "response surface model", "meta-model" and "surrogate model" are sometimes used as alternatives to "proxy-model". However, proxy-model seems to be more accepted in the petroleum industry and will be used in this paper. Proxy-models are widely applied in different areas of science for numeric modeling approximation. Typical application areas in reservoir simulation include:Sensitivity analysis of uncertainty variables;Probabilistic forecasting and risk analysis;Conditioning of a simulation model to historically observed data (history matching);Field development planning and production optimization.

Modelos proxy, alternativa para reducir los tiempos de cómputo durante la simulación numérica

“…Esto debido, a su facilidad de entendimiento, flexibilidad y eficiencia computacional (Zubarev, 2009). En general, para formular una regresión de tipo cuadrática se emplea la ecuación 1.…”

Joint stochastic constraint of a large data set from a salt dome

“…We develop and apply the approach to observed 3D joint seismic, MT, and gravity data sets obtained from a salt dome region, and we ultimately determine a model probability map for the profile. The method is akin to the response surface methodologies beginning to be used in the field of reservoir simulation (Zubarev, 2009). However in this case, we seek to fully model the uncertainty in the simulator-prediction system, and hence we aim to construct response clouds, rather than surfaces.…”

Real-time reservoir model updating in thermal recovery: Application of analytical proxies and Kalman filtering

“…Polynomial regression and artificial neural networks are two popular examples of these algorithms. Zubarev (2009) provides guidance on the advantages and disadvantages of using proxy modeling in reservoir engineering. He investigated different proxy-modeling techniques in history matching, production optimization and forecasting.…”