Applying Linear-Flow Analysis to Shale-Gas Wells - Field Cases
Authors: Denney Dennis 
Published: February 2015

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 130370, ’Application of Linear-Flow Analysis to Shale-Gas Wells - Field Cases,’ by Hasan A. Al-Ahmadi, SPE, Anas M. Almarzooq, SPE, and R.A. Wattenbarger, SPE, Texas A&M University, prepared for the 2010 SPE Unconventional Gas Conference, Pittsburgh, Pennsylvania, 23-25 February. The paper has not been peer reviewed.
Tight gas wells behave as if controlled by transient linear flow. The “half-slope” on a type curve indicates this behavior, which enables determining certain reservoir parameters. Linear-flow behavior has been observed in shale-gas wells also, but these wells tend to exhibit a significant “skin effect” that is less common in tight gas wells. This skin effect can mask early linear behavior but may be accounted for with a modified equation.
Introduction
Shale-gas reservoirs are being developed with horizontal wells and multistage fracturing. These wells produce in a transient-linear-flow manner, and, in some cases, this flow regime could last for years and might be the only flow regime available for analysis. A half-slope on the log-log graph of gas rate vs. time or a straight line on the square-root-of-time graph characterizes this behavior. Fig. 1 shows an example of a shale-gas well in transient linear flow for more than 2 years.
The approach used in this study was to assume that linear-transient-flow drainage out of matrix blocks controls production. However, unlike tight gas wells, shale-gas wells tend to exhibit a significant skin effect, which masks the early linear behavior and which must be accounted for with a modified equation. Gas adsorption is not accounted for in this model because most of the data are in the transient-flow regime in which gas-desorption effects are negligible.
Occurrence of Linear Flow
Fig. 1 shows a log-log graph and a square-root-of-time graph for daily production from Well 114. Transient linear flow is shown as a half-slope on the log-log graph and as a straight line on the square-root-of-time graph. However, the early part of these curves, before 200 days, does not seem to represent transient linear flow. In earlier work, it was thought that the early departures from a half-slope might represent bilinear flow in a dual-porosity reservoir. A more-plausible explanation and analysis were determined with this study.
Dual-Porosity Linear-Flow Model
An ideal shale-gas well would produce from a rectangular dual-porosity reservoir—a system of fractures with matrix blocks flowing into the fractures, with the reservoir not extending beyond the fracture system. Thus, this system is a linear dual-porosity system, and solutions have been presented as Laplace-domain solutions.
Two conceptual models are shown in Fig. 2. They are equivalent in the sense that they both represent dual-porosity linear systems. Model 1 is a linear, dual-porosity “transient-slab model.” The dominant fracture system in Model 1 is hydraulic fractures emanating from equally spaced perforation clusters in the wellbore. The matrix blocks in Model 1 are treated as homogeneous, although they may contain natural fractures. The main calculation advantage of Model 1 is knowledge of fracture spacing, L1, because it depends on the perforation-cluster spacing.