Decline analysis using Arp's equations is the primary empirical method used in the petroleum industry for estimating future reserve recovery and generating production forecasts. The development of tight gas and in particular shale gas reservoirs as important new sources of gas production has highlighted a concern with the hyperbolic form. That is, the expected ultimate reserve (EUR) is highly dependent on the choice of ‘b’ value.
Recent work by Ilk et al has proposed a new decline formulation called the "power law loss-ratio" that they claim is more general and robust than Arps. Essentially, the power law loss-ratio predicts that ‘b’ changes over a well's producing life and the ‘D’ and ‘b’ values can be replaced with more predictable parameters called ‘D∞’, ‘Di’, and ‘n’.
The purpose of this paper is to test the applicability of the power law loss-ratio method with readily available public data. Several wells were analyzed using Arps hyperbolic decline and the power law loss-ratio method. The results of each will be presented along with a comparison of the estimates of ultimate recoverable reserves.
Significant tight gas has been produced over the past few decades in Alberta. In 2005 it was estimated that tight gas accounted for 30% of the output from the WCSB(7). There is an estimated 575 Tcf of tight gas in Western Canadian reservoirs. Shale gas production is also gaining interest, with plays with a resource potential of 261 Tcf having already been discovered. With such valuable sources of gas available, it becomes important to be able to predict reserves using reliable methods. For many decades, the main tool used for analysis has been the Arps decline analysis method.
The purpose of this work is to demonstrate the practical application of a modified Arps method: the power law exponential method of decline analysis.
Decline analysis is a reservoir engineering technique that has been around for more than a century. The method has not significantly changed since the refined form proposed by J.J. Arps in 1945. Owing to its simplicity and reliability, it has been a popular method to forecast production and estimate reserves.
The purpose of decline analysis is to forecast the cumulative production of a well up to the point it reaches a defined abandonment criteria. The amount produced is known as its expected ultimate recovery (EUR).
There are two forms of the Arps equation that are commonly used to model rate decline. The exponential form is usually used for single phase liquid production or high pressure gas wells:
Equation (1) (Available in full paper)
The hyperbolic form is usually more appropriate for typical gas wells:
Equation (2) (Available in full paper)
Although Arps should be limited to the boundary-dominated flow portion of the production history where operating conditions (back-pressure) are relatively constant, practitioners regulary attempt to utilize Arps in the transient flow region. The transient period for a tight or shale gas well is often much longer than for a typical gas well.
