History Matching of Field Production using Design of Experiments

Abstract

An important aspect of reserves estimates is to quantify the contribution of uncertainties in underlying parameters such as structure, Sand extent, Fault Seal, Aquifer support, etc. If field production history is available, it can be incorporated to generate reliable measures of uncertainties for these parameters and identify the most likely field models. History Matching (HM) can be solved successfully using the Design of Experiment (DOE) method to define modeled scenarios. In the past decade DOE methodology has been used to compute estimated reserves while minimizing the simulation effort. This paper describes its extension to History Matching.The process of HM using DOE is a four stage process. The first step is to identify an uncertainty frame-work listing the uncertain parameters (X) and history matching parameters (Y). The second stage is to generate a design (the specified model combinations of the reservoir parameters) capable of estimating the effect and interactions of all parameters. Thirdly, the specified models are made and simulated and the response surface y(x) calculated, relating reservoir simulator input x and each output y. The last step is to predict the history matching parameter values for all possible model scenarios and measure goodness of history match for each model.The History Match can be quantified by the D-Score, a measure of the difference between the realized and predicted value of the history matching parameter standardized across modeling error. The D-score based probabilistic measures are flexible and allow the user to incorporate prior information.The above methodology for History Match will be presented for a field, which has over 11 years of oil production and 7 years of water-cut. We will demonstrate that History Matching using DOE is reliable, fast, efficient, and can quantify the probability of scenario occurrence.

Development of proxy models for petroleum reservoir simulation: a systematic literature review and state-of-the-art

“…The authors [31] made the comparison of SRM with least square support vector machine. Use of experimental design to develop response surface [32][33][34][35][36][37][38][39][40][41], integrated with Monte Carlo simulations to characterise the response surface and to estimate the uncertainty [42,43]. Application of Bayesian multi-stage MCMC approach, based on an approximation with a linear expansion to reduce high computational costs [44], more accurately obtained model uncertainty and also assists in productionforecast business decisions [45], with Bayesian workflow based on two-step MCMC inversion [46].…”

“…ED is used to avoid the time-consuming process to captured all changes with the minimum number of simulator runs [31,38]. The authors [34,38,41) show many studies in petroleum engineering which applied the ED methodology.…”

Assisted history matching using pattern recognition technology

“…Response surface models have been frequently used in petroleum engineering. There are number of articles available in uncertainty analysis of reservoir behavior (Damsleth, Hage and Volden 1992, Friedmann, Chawathe and Larue 2003, Cheong and Gupta 2005, well optimization (Zabalza, et al 2000, Landa and Güyagüler 2003, Valladao, et al 2013, and history matching (Eide, et al 1994, White and Royer 2003, Alessio, Bourdon and Coca 2005, Gupta, et al 2008, Cheng, Dehghani and Billiter 2008, Arwini and Stephen 2011).…”

“…For example, response surface proxy models which use regression have a fixed structure with different components and coefficients. These coefficients then are adjusted during the training process; however, the structure of function (for example polynomial function) is fixed (Eide, et al 1994, White and Royer 2003, Alessio, Bourdon and Coca 2005, Gupta, et al 2008, Cheng, Dehghani and Billiter 2008, Arwini and Stephen 2011. In order to match these functional forms, hundreds of runs are needed.…”