Some History Cases of Long-Term Linear Flow in Tight Gas Wells
Authors: Arevalo-Villagran J.A. , Wattenbarger R.A. , Samaniego-Verduzco F. 
Published: March 2010

Abstract
Many tight gas wells show transient linear flow that lasts for many years. Linear flow is normally associated with hydraulic fractures, but tight gas reservoirs may contain geometrical effects that lead to linear flow behaviour. In this study, long-term linear flow caused by the presence of natural parallel fractures is investigated and a systematic procedure to analyze linear flow in tight gas wells is described. Application of this methodology to production analysis of three tight gas wells, and validation of the results by using numerical simulation, is described.

Introduction
Linear flow is characterized by t behaviour during transient flow. This is sometimes associated with hydraulically fractured wells with linear flow perpendicular to the fracture. At the end of linear flow, the pressure response (for a constant rate solution) of these wells flatten as flow enters from outside the fracture tips(1,2). However, this paper refers to observed well behaviour in which the pressure response becomes steeper at the end of linear flow, indicating an outer boundary effect. For these wells, there appears to be only linear flow during transient and outer boundary dominated flow. Actual field data shows long-term linear flow for years in a large number of wells(3–12) because of the extremely low permeability.
A "half slope" (slope = 0.5) on a log-log plot of [m(pi) [m(pwf)]/ Qg vs. t for either constant gas rate production, qg, or constant bottomhole flowing pressure, Pwf, indicates linear flow.
Long-term linear behaviour has been reported in tight gas wells which have no or not particularly large fracture treatments(7, 9, 11). The reason for linear flow may not be known for a particular well. But several papers discuss physical scenarios which may cause linear flow(5, 7, 11, 13, 14), including the occurrence of natural fractures. Tectonic stresses determine the direction of natural fractures. These natural fractures may tend to be parallel to the hydraulic fracture plane and cause linear flow even if the hydraulic fracture length was limited. However, if the tectonic stresses have changed since the formation of the natural fracturing, the hydraulic fracture could have a different orientation from the natural fractures(15).
In this paper, we discuss how parallel natural fractures lead to permeability anisotropy and cause long-term linear flow. We show several field examples and outline a stepwise procedure for analyzing wells with long-term linear flow.

Linear Flow Due to Anisotropy
Parallel Natural Fracturing
Long-term linear flow in tight gas wells may develop because of large permeability anisotropy ratios. Anisotropic permeability in porous medium has been examined in several papers(15–25) and books(26–31). One of the most important reasons for anisotropic permeability is parallel natural fracturing.
Figure 1 shows a sketch of a well in a closed square with a parallel natural fracture system. In order to calculate the effect of the natural fractures on permeability, we assume that the natural fractures are continuous in the x direction and there is a regular spacing between fractures, dA, in the y direction.