It may be common for tight gas reservoirs (k< 0.1 md). to have pressure-dependent permeability. But it is not common to have this data available when analyzing well test or performance data. Consequently, engineers may not be aware of pressure-dependent permeability or may ignore this complication because the data are not available. This project attempts to evaluate the error made in ignoring pressuredependent permeability when, in fact, it should be included in analysis.
If pressure-dependent permeability data are available, it can be integrated into a modified real gas pseudo pressure, m(p), which would be expected to "linearize" the differential equation and provide correct values for permeability and skin factor. But if the customary real gas pseudo pressure, m(p) is used, then erroneous values for permeability and skin factor will be calculated.
This work was done by simulating pressure-dependent permeability using an exponential form for permeability vs. pressure drop. This is a convenient permeability model which just requires one parameter, Υ.
It is usually assumed that permeability is constant in well test analysis. That is, it does not change with reservoir (pore) pressure. However, pressure can have a dramatic effect on permeability in low permeability (tight) reservoirs. It has become common to use real gas pseudo-pressure for well test analysis. This was introduced in 1966 by Al- Hussainy et al.14 Their definition of real gas pseudo-pressure, m(p), is
Equation (1) (Available in full paper)
When this transformation variable is used in the derivation, it "linearizes" the flow terms in the partial differential equation. This allows well test analysis methods to be borrowed from the liquid case and adapted to gas flow. This works well for transient flow. But this assumed that permeability does not change with pressure. However, m(p) does not work properly if permeability changes with pressure. But if permeability does change with pressure and k(p) is a known function, then another transformation variable can be used which takes permeability variation into account.This variable is:
Equation (2) (available in full paper)
Several authors have investigated using transformations similar to Eq. 2. Samaniego et al.5 investigated the influences of pressure-dependent fluid properties and stress-sensitive rock properties on pressure transient analysis. They presented the results of an investigation of the application of the m(p) method to drawdown, buildup, and injection testing. Raghavan et al, 4 also worked on this problem and used a special transformation, again called pseudopressure, to linearize the problem. Results were obtained for five different sets of rock and fluid properties. They concluded that the m(p) function is an excellent 'linearizing' tool for constant massrate oil transient tests for all practical flow rates. Juris Vairogs et at.1 observed in the flow behavior of wells in tight gas reservoirs that measured flow rates are sometimes much lower than predicted by transient gas flow equations based on Darcy's law.