Pressure Transient Tests in Formations Having Stress-Sensitive Permeability
Authors: Vairogs Juris , Rhoades Vaughan W. 
Published: December 2007

In this study of the conventional analysis of gas well tests in stress-sensitive formations it was found that kh and wellbore condition determined from drawdown tests can be significantly in error when permeability is stress-dependent. A similarity in test results suggests permeability is stress-dependent. A similarity in test results suggests that stress sensitivity of the formation and turbulence of gas flow may affect test data in the same manner simultaneously.

Introduction
Conventional methods of analysis of drawdown and buildup test data are not strictly applicable to gas reservoirs because of the highly variable gas compressibility. However, they have been used with success for that purpose for some time, Conditions for applicability of the pressure, pressure squared, and real-gas potential plots' have been studied and discussed by a number of investigators and further elucidated by Wattenbarger and Ramey. Data taken under conditions of turbulent flow were also analyzed by the same authors and reported in Ref. 8. They concluded that reservoir conductivity determined from drawdown tests run under such conditions is not representative but conductivity determined from buildup tests is nearly correct. A different kind of flow-reducing mechanism has been studied experimentally by a number of investigators, most recently by Thomas and Ward . This mechanism is the reduction in permeability caused by an increase in effective frame stress. In the reservoir an increase in effective frame stress is caused by fluid withdrawal and the accompanying decrease in pore pressure. Since the overburden force on the reservoir pressure. Since the overburden force on the reservoir rock remains the same, the decreasing pore pressure results in an increased effective frame stress. Because low-permeability formations are more affected by stress changes, this effect can be expected to be more significant in deep gas reservoirs. The detrimental effect of stress on rock permeability and gas production has been demonstrated by Vairogs et al. production has been demonstrated by Vairogs et al. This paper presents the results of a theoretical investigation of the use of conventional pressure transient analysis methods in stress-sensitive formations. The great similarity between results from tests under turbulent flow and under stress-sensitive conditions is emphasized.

Method of Investigation
The numerical model used in the simulation was described in an earlier paper. Briefly, it is a radial gas flow model that uses real gas properties and allows radial variation of permeability and porosity. The latter feature permits the simulation of wellbore damage or stimulation. The model has the additional capability to calculate radial variations in rock frame stress that result from changes in pore pressure near a borehole in an initially stressed pressure near a borehole in an initially stressed medium. Changes in formation permeability at various distances from the wellbore are then calculated from experimentally determined stress/permeability relationships. These relationships are determined in the manner described in Ref. 7. An example of such a relationship is shown in Fig. 1. The initial permeabilities - i.e., permeabilities at a net confining permeabilities - i.e., permeabilities at a net confining stress of 500 psi - are 0.14 md for Sand A and 0.32 md for Sand B. Sand A is twice as sensitive to stress as Sand B, but both exhibit the same proportional permeability reduction. permeability reduction.
JPT
P. 965