Testing and Analyzing Low-Permeability Fractured Gas Wells
Authors: Millheim Keith K. 
Published: December 2007

Abstract
The constant-rate drawdown test performance for a low-permeability, vertically fractured gas well was investigated. A series of gas wells were tested by flowing each well at a constant rate until the data could be analyzed using conventional radial flow theory. Each well was then shut in to build up. After a sufficient buildup was obtained, another flow test commenced but at a higher flow rate than the first test. Again, the well was shut in when radial flow was obtained. This procedure was repeated for three to four different flow rates. Two wells in the San Juan basin were tested using this procedure. Both wells were fractured after completion, cleaned up and then shut in until flow testing commenced. Test designs of both wells permitted investigation of the most realistic values of effective permeability, wellbore radius and turbulence factor. Also, being able to determine the effective fracture flow area and vertical fracture efficiency was inherent with this testing approach.
It was observed that fractures in both wells influenced the pressure behavior for approximately 18 to 40 hours (depending on the flow rate) before radial flow was evident. After this time, drawdown data were analyzed using radial flow theory. When a low-permeability gas well has vertically oriented, induced fractures, the early flow geometry is essentially linear. It will be shown how to determine when a flow test has been conducted long enough so that the most representative values of effective permeability, wellbore radius and turbulence factor can be calculated. From the linear pressure data, valuable information about the fracture treatment, such as the effective flow area and vertical fracture efficiency, can be determined for vertically fractured wells.

Introduction
During tests on gas wells in the San Juan basin, initial transient behavior lasted for many days because of the low permeability of some porous media. As a result, stabilized flow performance could not be obtained. If these wells received some type of stimulation treatment, early pressure behavior deviated from conventional theoretical radial flow. When conventional radial flow theory was used to analyze these low-permeability fractured gas wells, larger values of flow capacity and absolute open flow potentials (AOF) sometimes resulted. Wells were assigned open flow potentials that proved to be 3 to 10 times higher than the well would sustain over a longer period of production. In some cases where the wells had flowed for longer periods of time during a constant-rate drawdown test, it was noticed that the effective flow capacity appeared to be decreasing with time until a certain value was reached.
The early nonradial pressure behavior can be explained if linear flow is assumed. Russell and Truitt mathematically investigated the vertically fractured well in a bounded area. They showed that early flow behavior was essentially linear and, for x(f)/x(e) approximately less than 0.10 radial flow was obtained after short periods of time. Then realistic values of effective permeability and skin could be determined. Scott experimentally studied the vertically fractured well with a heat flow analog. He showed that early flow was linear. Both studies indicate that, for small values of x(f)/x(e), linear flow approaches radial flow if the well is tested long enough.
To help prove this concept of early linear flow caused by induced vertical fractures, two low-permeability gas wells were tested. Both wells received large fracture treatments prior to testing. A vertical fracture was indicated from the analysis of fracture treatments.
As anticipated, tests of both wells indicated early linear flow that was later followed by a period of radial flow. Data collected from each well were analyzed. From the well tests, plus other information on each well, the effective permeability, wellbore radius and turbulence factor were calculated. Effective fracture flow areas calculated from test analyses for each well proved to be approximately one-fourth the created area calculated from classic hydraulic fracturing theory. Other fractured wells that were tested but not presented in this paper also indicated that the effective fracture flow area was one-fourth to one-third the created area predicted from hydraulic fracturing theory. The vertical fracturing efficiency was estimated from the calculated values of effective wellbore radius and fracture flow area. For the two wells tested, calculated fracture lengths x(f) were 112 and 105 ft, and the vertical fracturing efficiencies E(f) were 122 and 183 percent.

Development of Flow Model
Agnew showed that most induced fractures below 1,500 ft are vertical. Anderson and Stahl indicated that most of the fractures they studied were vertical. The model proposed for early flow in most vertically fractured gas wells is shown by Fig. 1.