Application of Differential Evolution as a New Method for Automatic History Matching

Abstract

This paper presents a novel approach in automatic history matching using a differential evolution algorithm. Differential evolution is becoming a popular global optimization method and has been widely applied in many challenging engineering problems outside the oil industry. Some advantages of differential evolution are its simplicity in structure which leads to ease of coding and straightforward parallelisation, and its few control parameters making it easy to use in an operational context. These advantages make it important to evaluate differential evolution for use in automatic history matching frameworks where reservoir engineers require a powerful, yet easy to work tool with little effort to find optimum algorithm parameters. We have applied differential evolution approach to obtain history matched models of a reservoir simulation case in Gulf of Mexico. The effect of different tuning parameters on the performance of differential evolution has been studied and the algorithms sensitivity to initial starting conditions investigated. Results confirm that differential evolution is a good optimization tool in obtaining multiple good history matched models. We have also compared the match quality of models obtained using differential evolution with the Neighbourhood Algorithm (NA). This comparison shows that differential evolution obtains comparable or better models in terms of matching misfit. Finally, we studied the effect of the number of observation data points used in history matching with differential evolution algorithm. We show how additional information helps the algorithm in finding the promising regions of the search space and narrowing down the uncertainty intervals of the predictions. Introduction For the past 50 years finding models that can reproduce the history of the reservoir is one of the topics where researchers within petroleum engineering community have focused. From the very first attempts [Kruger, 1960][Jacquard and Jain, 1965] the goal in history matching was to automatically and quickly adjust the parameters of the reservoir simulation model in a way that it can reproduce the past production or pressure profile of the reservoir. This is essentially an inverse problem, where no unique answer exists and many combinations of the reservoir model can result in a good match. Finding these alternate models for history matching later became the main target. With this change in the research focus, we were no longer looking for a single set of parameters which can yield a good match; instead we are now searching for many other realizations of the reservoir simulation model with different geological and petrophysical properties that can reproduce history of reservoir. This ensemble of multiple history matched models enables us to realistically quantify uncertainty for future performance of reservoir. On the other hand, in real life problems, single reservoir simulation may take hours or even days to complete. This indeed makes another challenge when we are looking at automatic history matching algorithms. We need to obtain diverse history matching solutions in minimum possible iterations.

Evaluation of Reservoir Quality and Forecasted Production Variability along a Multi-Fractured Horizontal Well. Part 2: Selected Stage Forecasting

“…The history-matching task was completed using the Differential Evolution module (DE) of CMG CMOST TM with scaling factor, crossover rate, and population size values of 0.5, 0.8, and 35, respectively. Differential Evolution is a population-based metaheuristic optimization technique [35] which can be applied to high-dimensional oil and gas engineering problems [36][37][38][39][40][41]. A detailed discussion of DE algorithm can be found in Price et al [42].…”

Gaussian Process for Uncertainty Quantification of Reservoir Models

“…These include gradient-based algorithms (Slater and Durrer (1970), Watson and Lee (1986)), populationbased approaches (genetic algorithm (Romero et al, 2000), evolution strategy (Schulze-Riegert et al, 2001), differential evolution (Hajizadeh et al, 2009), estimation of distribution algorithms (Abdollahzadeh et al, 2011)) and particle filter methods (Naevdal et al, 2003). The majority of assisted history matching packages adopted by the industry are powered by stochastic population-based sampling algorithms.…”

Reservoir Model History Matching With Particle Swarms

“…Stochastic techniques have been used in the petroleum engineering including Genetic algorithms (Carter and Ballester, 2004;Erbas and Christie, 2007;Romero et al, 2000), Population-Based Incremental Learning (Petrovska and Carter, 2006), Hamiltonian Monte Carlo (Mohamed et al, 2009), Evolutionary Strategies (Schulze-Riegert et al, 2001;Schulze-Riegert and Ghedan, 2007), Ant Colony Optimisation Jalali-Farahani, 2008a, 2008b;Hajizadeh et al,2009a), Differential Evolution (Jahangiri, 2007;Hajizadeh et al, 2009b), and Neighbourhood Algorithm (Christie et al, 2002;Subbey et al, 2004;Rotondi et al, 2006). Currently some innovative global optimisation approaches have gained popularity in research among oil companies for tackling history matching problems like evolutionary algorithms, swarm intelligence techniques and others.…”