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.

Figure 1: Example of a comparative production rate decay with time for stress-independent (γ = 0 MPa-1) and stress-dependent (γ = 0.00024 MPa-1) reservoirs at constant bottom hole pressures (Pwf) of 28 MPa (4000 psi) and 62 MPa (9000 psi). for an overburden of 67 MPa (10000 psi). From Rutter et al. (2013).
Figure 2: Example of the effect of stress-dependent permeability (γ = 0.00024 MPa-1) on cumulative production (millions standard cu. ft. at 16 oC) after 225 and 2000 days for a range of constant bottom hole pressures, compared to stress-insensitive permeability (γ = 0 MPa-1). Overburden pressure is 69 MPa (10000 psi), initial gas pressure is 67.6 MPa (9800 psi). From Rutter et al. (2013).
References
  • 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

Academic Staff: Prof Ernest Rutter, Dr Julian Mecklenburgh | Research Staff: Dr Rochelle Taylor | PhD: Rosanne Mckernan

 

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