Using gradients to refine parameterization in field-case history-matching projects

Reservoir management is based on the prediction of reservoir performance by means of numerical-simulation models. Reliable predictions require that the numerical model mimic the production history. Therefore, the numerical model is modified to match the production data. This process is termed history matching (HM). Form a mathematical viewpoint, HM is an optimization problem, where the target is to minimize an objective function quantifying the misfit between observed and simulated production data. One of the main problems in HM is the choice of an effective parameterization-a set of reservoir properties that can be plausibly altered to get a history-matched model. This issue is known as a parameter-identification problem, and its solution usually represents a significant step in HM projects. In this paper, we propose a practical implementation of a multiscale approach aimed at identifying effective parameterizations in real-life HM problems. The approach requires the availability of gradient simulators capable of providing the user with derivatives of the objective function with respect to the parameters at hand. Objective-function derivatives can then be used in a multiscale setting to define a sequence of richer and richer parameterizations. At each step of the sequence, the matching of the production data is improved by means of a gradient-based optimization. The methodology was validated on a synthetic case and was applied to history match the simulation model of a North Sea oil reservoir. The proposed methodology can be considered a practical solution for parameter-identification problems in many real cases until sound methodologies (primarily adaptive multiscale estimation of parameters) become available in commercial software programs.