Ingeniero petrolero

The Use of Genetic Algorithms to Improve Reservoir Characterisation
Pedro J. Ballester
Abstract In Petroleum Engineering, reservoir management aims to maximise the profit from a hydrocarbon reservoir. Numerical models, which describe the internal structure of hydrocarbon reservoirs, are used to make reservoir management decisions. These models are aimed at providing accurate predictions of thereservoir behaviour under different scenarios. The latter requires calibrating the model parameters to reproduce all available data. However, given the impossibility of directly measuring these parameters, one has to resort to infer them from indirect measurements, such as the oil production rate at a given reservoir well. This is known as the inverse problem. My research focuses on the developmentof new techniques to improve the resolution of nonlinear inverse problems. These techniques are tested on inverse problems arising in the Petroleum Industry.

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Current Research and Scope of Dissertation

Reservoir management aims to maximise the profit from a hydrocarbon reservoir. The ability to make correct reservoir management decisions relies mainly on being able to predict theirconsequences. The latter in turn depends on the accuracy in the description of the internal structure of the reservoir. Reservoir characterisation is the process of describing a hydrocarbon reservoir, in terms of the parameters of a numerical model, so that its performance can be predicted. Reservoir characterisation requires numerical models. Such models represent a highly nonlinear mapping betweenmodel parameters and the simulation of indirect measurements (ie. the model output), for which an analytical expression is not available. Also, the location of petroleum reservoirs (thousands of metres below ground) and their extension (typically several kilometres) make direct measurements of the model parameters mostly impossible. Only few of these parameters can be estimated from measurements

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at wells drilled into the reservoir. In this context, indirect measurements usually take the form of fluid production data and thus the inversion is known as history matching. This can be posed as a search and optimisation problem by defining an objective function quantifying the mismatch between the model output and the measured productiondata. There are a number of challenges in history matching, which are also common to many other nonlinear inverse problems. First, the inferred model may differ from the true internal structure of the reservoir (henceforth referred to as the truth model). This occurs as a consequence of two situations that in practice appear superposed. The first is that the truth model may not be associated with aglobal optimum because of errors distorting the objective function landscape. These errors are originated by the measurement process and the model inaccuracy. The second situation is better analysed from a non-error perspective. In the absence of errors, the truth model has, by definition, a global optimum associated with it. The function landscape may be multimodal and therefore challenging formany search algorithms. Therefore, the applied algorithm may find a suboptimal solution and hence obtain a wrong model of the studied system. Furthermore, inverse problems may be non-unique in the sense that there are several models that explain the data equally well, each of them represented by a different global optimum. In this case, even if all global optima could be identified, there would beuncertainty in which optimum represents the truth. Within the relevant research community, it is widely believed (eg. [1]) that nonlinear inverse problems are inherently non-unique. It is also accepted that current search methods cannot determine the size or shape of optimal objective function regions. In addition, it is unknown whether these optimal regions are simply connected or whether there are...