A non-iterative method of decline curve analysis

Decline curve analysis is one of the reserve estimation methods. It is widely used by companies and engineers. The oldest and most popular method is Arpʹs empirical equation. There is no theoretical basis for Arpʹs equations. Exponential equation almost always underestimates the flow rate and cumulative production and on the other hand harmonic decline overestimates. Also the parameters of hyperbolic equation cannot be calculated directly. In that case, using non-linear type curves or iteration is necessary. s article, first, two semi-theoretical rate–time equations were derived of which one is for oil reservoir and the other for gas reservoir. Flow equation in case of a boundary-dominated flow was modified to obtain an equation that consists of flow rate, time and some constants. In the second step, various approaches of calculating coefficients were discussed. In fact, an integrated study of the stated problem was done by evaluating a number of physical concepts and applying dimensional analysis. In this way, two correlations were proposed with which the coefficients were related to the inverse of time. Finally the proposed method, exponential, harmonic and hyperbolic equations were applied to actual field data and the results were analyzed and compared. In case of oil reservoir, the comparison between output of the proposed method and that of hyperbolic equation led to the same average error and in case of two gas wells, the proposed method was as reliable as the Arpʹs method. In the aspect of applicability, there is a significant distinction between the two methods. In the case of Arpʹs hyperbolic equation, iteration was used to find the best match; however, applying the new method does not need any iteration and it is enough to do a simple calculation to get the result.