Advances and Applications in Statistics
Volume 15, Issue 1, Pages 61 - 70
(March 2010)
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TIME VARYING AUTOREGRESSIONS FOR HYPERBOLIC DECLINE CURVE
Sri Wahyuningsih, Sutawanir Darwis, Agus Yodi Gunawan and Asep Kurnia Permadi
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Abstract: Most of the existing decline curve analysis techniques are based on the empirical Arps equation. The equation represents the relationship between production and time for oil wells during pseudosteady-state period. The three types of declines are exponential, hyperbolic and harmonic. It is difficult to foresee which equation the reservoir will follow. A wide variety of approaches to the problem of decline curve fitting has been presented in the petroleum literature. The hyperbolic type of decline, which occurs most frequently in applications, can be recognized by the fact that the loss ratios show an arithmetic series and that, therefore, the first differences of the loss ratios are constant or nearly constant. Stochastic approaches have increasingly been used to study the uncertainty in remaining reserves estimates. In this paper, we derive the hyperbolic decline model as time varying autoregressive (TVAR) process by means of the discretization of the flow rate equation. We find that the hyperbolic decline model leads to an AR(1) process with time varying parameter. This finding is a new approach in petroleum literature. We then apply the present model to simulate the performance data. The results can be used to forecast the production. |
Keywords and phrases: decline curve analysis, hyperbolic decline, time varying autoregressions. |
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