Assisted history matching is now widely used to constrain reservoir models. However, history matching is a complex inverse problem, and it is always a big challenge to history match large fields with a large number of parameters.In this paper, we present a new technique for the gradient-based optimization methods to improve history matching for large fields. This new technique is based on data partition for the gradient calculations. The objective function is first split into local components, and the dependence of each local component on principal parameters is then analyzed to minimize the number of influential parameters. The interaction between parameters and local components is allowed in the splitting. Based on this study, we can propose a perturbation design, which allows us to calculate all derivatives of the objective function with only a few perturbations. This method is particularly interesting for regional and well level history matching, and it is also suitable to match geostatistical models by introducing numerous local parameters. This new technique makes history matching with a large number of parameters (large field) tractable.
IntroductionAssisted history matching has been widely used in petroleum engineering to constrain reservoir and/or geological models by integrating well production data and/or 4D seismic data (see for example, Chavent et al. 1975;Bissell et al. 1994;Chu et al. 1995;Landa and Horne 1997;Roggero et al. 1998Roggero et al. , 2007Gosselin et al. 2000). History matching is a complex inverse problem for which the degree of difficulty and the computational effort (in terms of the number of reservoir simulations, which are very expensive in CPU time) increase with the increasing of the number of matching parameters. The general strategy of history matching is to start at the field level and work down to more detailed matching. A reasonable match is first at the field level, then at the regional level, followed by more rigorous individual well history matching. The number of parameters is generally increased when the history matching gets down to the regional or well levels. So, it is important to study optimization methodologies for a large number of parameters, and especially for large fields.Among the optimization methods for history matching, the gradient-based approaches are often used (see for example, Chavent et al. 1975;Gosselin et al. 2000; Olivier et al. 2008). However, the gradients of the objective function are generally calculated by numerical methods, which need the evaluation of the objective function through reservoir simulations, which, in turn, are very expensive in CPU time. If we want to optimize M parameters, we require at least M perturbations (M+1 simulations) to calculate all the gradients in order to obtain an optimized solution. When the number of parameters M is large, we may encounter serious problems in CPU time for optimizations in history matching.Adjoint method is an efficient technique to reduce the number of simulations for the gradient calculation (...