Use of a simple reservoir model to illustrate the effect of stress-dependence of permeability
As gas is drawn down during production the weight of the overlying column of rock squeezes shut the likely flow paths thereby decreasing permeability, i.e. permeability is a stress-dependent property.
To highlight this stress-dependency, finite difference numerical solutions for initial and boundary conditions can be obtained using program GASSIM (Lee and Wattenbarger, 1996; Figure 1).
Figures 1 and 2 are illustrative examples of Whitby mudstone data to show the effect of stress-dependent permeability. Flow through the sample was formation parallel through a single large hydraulic fracture.
Figure 1 shows how flow decreases more rapidly for models that take into account stress-dependent permeability than those that use stress-independent permeability. But failure to take into account the stress-dependence of permeability to gas at the well test stage will lead to an overestimation (by as much as a factor of 2) of likely gas yield over time over the entire lifetime of the well. The effect of stress-dependence of permeability is more apparent at smaller bottom hole pressure.
Figure 2 highlights the differences between stress-dependent and stress-independent inferences over the longer period. Initial cumulative production rates are not impacted significantly. However, over the lifetime of the well it is clear from this example that failure to take into account stress-dependence will have a significant impact upon expected production rates that will influence the economic viability of the well.
Lee, J., Wattenbarger, R. A., 1996. Gas reservoir engineering. Society of Petroleum Engineers Textbook Series v. 5, Richardson, Texas, 349pp
- Rutter, E.H., R. McKernan, J. Mecklenburgh, S.E. May. Permeability of stress-sensitive formations: its importance for shale gas reservoir simulation and evaluation. Petro-Industry News. 2013 September; 44-45. eScholarID:205885