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Abstract
The history match procedure in an oil reservoir is of paramount importance because good estimates of the reservoir parameters may lead to a better forecast of the production. The reservoir is said to be ‘matched’ when the discrepancies between the model predictions and the observations of the real reservoir are below a certain tolerance. The determination of the model parameters via history matching requires the minimisation of an objective function in a parameter space that may be populated by many local minima. In other words, more than one set of reservoir model parameters fits the observation. Moreover, even a solution associated to a given minimum may be unstable. In order to reduce the ambiguity, it is necessary to incorporate constraints in the reservoir parameters to be estimated. Here, we use the smoothness constraint to regularise this inverse problem using as an example a modified version of the PUNQ model. The PUNQ model is suitable for applying this constraint because the sediments were deposited in a deltaic costal plain environment where good lateral continuity of the sediments is expected. We show that it is possible to recover all important features of the spatial distribution of the permo-porosity fields in all layers of the PUNQ model. In particular, the directions and widths of the sand channels were recovered.
Acknowledgements
The authors wish to thank ‘Rede Cooperativa de Pesquisa–Caracterização Geológica e Geofísica de Campus Maduros’ (FINEP/CTPETRO/PETROBRAS) for financial support. FLS thanks CNPq for his MSc scholarship. AFdN and WEM thank CNPq for their research grants. All the fluid flow simulations were done using IMEX® from CMG Ltd. Finally, we thank the Associated Editor, Prof. Anatoly G. Yagola and three anonymous reviewers for improving the original manuscript.