Estimating Hyperbolic Decline Curves Parameters

Sri Wahyuningsih ( Statistics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Mulawarman)
Sutawanir Darwis ( Statistics Research Division, Faculty of Mathematics and Natural Sciences, ITB)
Agus Yodi Gunawan ( Industrial and Financial Mathematics Research Division,Faculty of Mathematics and Natural Sciences, ITB)
Kurni Permadi ( Reservoir Engineering Research Division, Faculty of Mining and Petroleum Engineering, ITB)

Jurnal Matematika & Sains
Vol 13, No 4 (2008)

The decline curve analysis refers to the estimation of some measure of well performance. The linearization of Arps hyperbolic decline curves leads to the estimation of initial value of decline exponent. This work proposes a graphical method to estimate the initial value of decline exponent and a binomial expansion to estimate the decline rate and the initial production value. The graphical approach is used to determine the initial value of the decline exponent for binomial expansion of hyperbolic Arps equations. Experimental study from some small data sets shows that our proposed method is capable in reducing the number of iterations needed in binomial linearization of hyperbolic decline curves. The main contribution of this work is a development of initial decline exponent estimation using graphical approach where the traditional approach is based on trial and error. Bias in estimating the initial values can produce large number of iterations in estimating the decline exponent. The proposed method is successfully reduce the number of iterations in estimating the decline exponent. Experimentally, this study indicates the existence of lower bound of decline exponent b* for each iteration using hyperbolic binomial expansion.