The type curves developed by Fetkovich1 are widely used tools for decline curve analysis. Fetkovich combined the analytical constant pressure infinite (early transient period for finite systems) solutions with the "empirical" exponential, hyperbolic, and harmonic decline curve equations developed by Arps2 . There are software applications that have computerized this analysis technique; however, attempts to automate the matching process have been hindered by two problems: (1) a way to identify the transition from one flow period to the next, and (2) a way to minimize the adverse impact of oudiers, data considered to be bad observations. This paper presents methods to handle these issues.
Recognizing the point of transition between flow regimes is sometimes difficult, even when the matching process is done manually. If, however, the curves are regenerated using the proper derivatives of the production, the software can locate the transition simply by looking for a minimum. The process of estimating reservoir parameters is simplified as well.
To handle outliers, this paper proposes a robust algorithm consisting of a nonlinear parameter estimation using Least Absolute Value (LAV) as the criterion for minimization. One advantage of this approach is that it provides a smooth transition between full acceptance and total rejection of a given observation. Oudiers are systematically assigned less weight in the objection function. This method also avoids the computation of a second derivation of the model function. Most importandy, tests have shown that when outliers are introduced into the observations, the LAV algorithm still produces accurate parameter estimates.
The above techniques have been implemented in software that operates in the MS-Windows™ environment With its graphical user interface (GUI), this environment allows for clear visual displays of the matching process and the results. Moreover, it provides the user with many more options than the traditional, non-graphical operating systems. Because programming under MS-Windows is still relatively new to the industry, this paper also discusses some aspects of Windows programming, especially as it relates to petroleum applications.