Reserves Estimation Using a PC Decline Analysis Program
Authors: Hsieh F.S. , Vega C. , Vega L. 
Published: July 2010

Abstract
Arps equations and type curve matching are the two major decline analysis techniques for reserves estimation. Both techniques extensively depend on a trial-and-error approach to define the decline exponents, particularly, for the case of hyperbolic decline. This paper presents a PC-based decline analysis program developed based on the method released in recent papers. This program can be applied to analyse a wide range of decline types, including the most complicated hyperbolic decline. It improves the accuracy of the analysis, and it can be conveniently executed from a PC with an Excel spreadsheet.

Introduction
Decline analysis is frequently conducted to predict future well rates by extrapolating a curve based on an equation that best fits the historical rate-time performance of that well. Two commonly used approaches are the least-squares method and the type-curve match method. Both methods are aimed at identifying the parameters that would best fit one of the three empirical decline types: the exponential, the hyperbolic and the harmonic declines developed by Arps(1).
To apply the least-squares a method to Arps' equations, one must assume the type of decline based on the historical performance before the mathematical curve fitting technique can be performed. The process of assuming a decline type is inconvenient, difficult and time-consuming. The type-curve matching method also has some disadvantages, mainly due to the non-uniqueness problem in determining the correct type-curve to use. This paper presents an easy to apply technique based on the rate-time decline equation presented by Hsieh et al.(2, 3). The simplicity of this method is assured because of the use of a universal decline equation instead of the three presented by Arps. The adequacy of the new formulation and the readiness for applying a spreadsheet approach to the new formulation is illustrated with a field example.

Review of Proposed Equation
This section briefly reviews the rate-time decline equation that will be programmed using VBA (visual basic application) of Microsoft Excel. The details on the development of the equation can be found in the SPE (Society of Petroleum Engineers) papers presented by Hsieh et al.(2, 3)
The rate-time decline equation proposed by Hsieh et al. contains a time-dependent exponent as,
Equation (1) q = k t − ( n + m t )
Equation (1) contains two exponents, n and m. During the production period (pressure decline or pressure change) a well may experience hysteresis effects such as the formation of free gas, encroachment of aquifer water, and reduction of permeability, etc. Changing physical conditions with pressure or time usually accelerates the decline rate, and acceleration of the decline rate gives the rate-time curve an ever-changing, time-dependent slope. Hsieh et al. use the time-dependent exponent "m" to model this effect. In Equation (1), k is the initial flow capacity from which the current decline cycle (the decline cycle being analysed) began, rather than the average rate during the initial (first) time interval. Rate-time decline is usually a hyperbolic function as reported by Cutler(4). The reason that time decline is usually in a hyperbolic function has also been discussed in the same paper by Hsieh et al.(2)