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AN APPLICATION OF KALMAN FILTER MODEL TO RESERVOIR PRESSURE MAINTENANCE
Abstract
A problem of determining the effect of pressure maintenance system is considered. We want to estimate the influence of each of the water pumps to each of the extracting wells. We propose a stochastic model of the oil field?s liquid flow, which is based on the Kalman filter model. It is loosely based on the filtering theory, and is designed to simplify the computations. We also propose a method to estimate the parameters of the model, which is a variation of the EM-algorithm. It is proved that this procedure converges to some local optimum. One of the features of the proposed model is that it doesn?t depend on the geological characteristics of the reservoir and is estimated using the extraction and injection history of the oil field. But it is possible to expand the model to include other parameters, such as some of the geological data and borehole pressure data. It is shown how the model can be used to determine the water flow. We apply the model to the oil field with a rich extraction history and compute the flow directions. The results were in accordance with the tracer survey performed on that oil field.
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References3
Aanonsen, S. I., Nævdal, G., Oliver, D. S., Reynolds, A. C., Valès, B. The ensemble Kalman filter in reservoir engineering a review, SPE Journal., 2009, V. 14, No. 03, pp. 393 412.
Wen, X.-H., Chen, W.H. Real-Time Reservoir Model Updating Using Ensemble Kalman Filter With Confirming Option, SPE Journal, 2006, V. 11, No. 4, pp. 431 442.
McLachlan, G.J., Krishnan, T. The EM algorithm and extensions, Wiley: 1997, 287 pp.
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Number of times cited according to Crossref: 1
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