This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 134231, ’A Better Way To Forecast Production From Unconventional-Gas Wells,’ by Peter P. Valko, SPE, and W. John Lee, SPE, Texas A&M University, prepared for the 2010 SPE Annual Technical Conference and Exhibition, Florence, Italy, 19-22 September. The paper has not been peer reviewed.

The stretched-exponential-decline-curve model and data-intensive discovery provide a controlled production forecast for an individual tight gas well or shale-gas well on the basis of data gathered through parameter processing for a large group of wells. Group production for a large number of wells follows stretched-exponential-decline behavior of production rates. This approach moves production forecasts in tight and unconventional gas fields from individual and subjective curve matching to a group-data controlled-forecast methodology.   

Stretched-Exponential Decline

A natural interpretation of the stretched-exponential decay of a quantity is that it is generated by a sum (integral) of pure-exponential decays with a “fat-tailed” probability distribution of the time constants. Therefore, the stretched-exponential-production-decline (SEPD) model can be interpreted as the acknowledgement of the heterogeneity. The actual production decline is determined by many individually contributing volumes in exponential decay (i.e., in some kind of pseudosteady state), but with a specific distribution of characteristic time constants. The family of the background distribution of characteristic time constants is known analytically. The distribution is determined by a parameter pair: the exponent parameter n and the characteristic time parameter τ. Broadly, the τ parameter is the median of the characteristic time constants. The nearer parameter n is to zero, the larger is the tail of the distribution (i.e., more-elementary volumes have very large time constants).

One result of using the hyperbolic-decline approach in analytical models and reservoir simulators is that boundary-dominated flow is necessary for meaningful extrapolation. Because the traditional boundary-dominated state is questionable in tight and, especially, shale gas, little use can be made of the method. The stochastic interpretation, however, provides that the distribution of time constants is an intrinsic property of a continuous unconventional gas reservoir, and, hence, it determines the totality of the production-decline curve.

Data-Intensive Discovery

The desire of capturing the “individuality” of any well will remain. However, the probabilistic criterion for proved (P90) reserves does not require a good fit. Rather, it requires some kind of proof that a given estimate is met or surpassed by (future) reality in at least 90% of the cases. Strictly, such proof can be provided only if a sufficient number of wells have been abandoned, which is not the case for unconventional resources. Industry always will be interested in the performance of the newest technology in the newest plays. There are no long-duration data sets, and those of shorter duration are affected by the accelerated evolution of completion technology.

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