Well Test Interpretation of Vertically Fractured Gas Wells
Authors: Wattenbarger Robert A. , Ramey Henry J. 
Published: December 2007

In the analysis of field data it is important to bear in mind the proper relationship between the radial flow period and the linear proper relationship between the radial flow period and the linear flow period. The transition between these periods is quite long and can be misinterpreted as being the linear flow period. Another factor that can complicate analysis is turbulence.

Introduction
The trend in gas well testing has been to rely more on be early-time flow data of drawdown and buildup tests than on stabilized flow tests. The stabilized testing methods often are not adequate for complicated modem gas reservoirs because many of these reservoirs have extremely low permeabilities and the transient flow period of a well test can last for days or weeks.
It has become common to augment the flow capacity of gas wells by hydraulically fracturing their producing formations. In deep reservoirs the induced producing formations. In deep reservoirs the induced fractures are generally vertical and tend to follow a single plane of weakness. The presence of a vertical fracture at the wellbore complicates the transient flow behavior of a low permeability gas well. The flow is further complicated when turbulence occurs near the wellbore.
Russell and Truitt published transient drawdown solutions for vertically-fractured liquid wells. They developed methods of drawdown and buildup testing utilizing these solutions, which were based on numerical simulation. Clark applied the basic Russell-Truitt solutions to analyze fractured water injection wells by falloff tests. Field examples were given to substantiate the method of analysis.
The Russell-Truitt solutions and well testing methods can be extended to gas well flow. Millheim and Cichowicz presented the drawdown equations for ideal gas flow, including the effects of formation damage and turbulence. Two actual field cases were presented, both of which exhibited extensive fractures presented, both of which exhibited extensive fractures and turbulent flow. For the pressure range of these well tests, the use of ideal gas equations was acceptable. These field cases were significant in being the first published data showing the occurrence of turbulence in fractured gas wells. We, also, observed such cases in practice.
Our purpose here is to extend the theory of fractured gas well testing to the flow of real gases. To determine the effects of wellbore storage and turbulence on well test interpretation, we developed a finite-difference model to simulate well test conditions. Since gas wells usually are widely spaced and have high compressibility, the emphasis has been put on the early transient behavior before the effects of the outer boundary are noticeable at the wellbore.

The Mathematical Model
The geometry of our mathematical model is similar to that used by Prats. The well is centered in a circular uniform reservoir. A vertical fracture of infinite flow capacity penetrates the formation and passes through die wellbore. The wellbore itself is passes through die wellbore. The wellbore itself is not important. Fig. 1 shows a sketch of the problem. Fig. 2 shows the idealized model.
JPT
P. 625