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Rock physical and mechanical properties 57

where K nx and K ny are the fracture normal stiffnesses in the fractures
perpendicular to the x- and y-directions, respectively; Ds x , Ds y , and
Ds z are the effective stress increments in the x-, y-, and z-directions,
respectively, and the compressive stress is positive.
From Eq. (2.43), the permeability change is controlled by the stress
change, fracture aperture and spacing, and normal stiffness of the fracture. It
should be noted that shear stress effect is not considered in Eq. (2.43).
When shear stresses are large, their effect on permeability should be
considered. The permeabilityestress relationship also shows that the
effective stress change has a pronounced impact in permeability. This
effective stress-dependent permeability is significant for the fractured res-
ervoirs because a rapid increase in the effective stress can cause a quick
closure of natural fractures, which may cause a permanent loss of
permeability in the fractures. Therefore, slowing down the effective stress
change during production of a fractured reservoir can decelerate the
permeability reduction. For example, reducing reservoir drawdown can
decrease the fast increase in the effective stress, thus reduce the perme-
ability decrease.

2.4.5 Stress and proppant effects on permeability of
hydraulic fractures
Multistage hydraulic fracturing in the horizontal well and propping the
hydraulic fractures by proppants are the major completion method to
enhance permeability for oil and gas production in unconventional re-
sources. Experimental results from 88 Barnett shale samples show that the
conductivity of hydraulic fractures is dependent on the proppant size and
formation stresses (Zhang et al., 2014). The propped fracture conductivity
increases with larger proppant size and higher proppant concentration.
Longer-term laboratory fracture conductivity measurements also show that
within 20 h the fracture conductivity could be reduced by as much as 20%.
Laboratory results also demonstrate that higher proppant concentration
leads to higher fracture conductivity with the same-sized proppant
(Fig. 2.17A); larger proppant size consistently provides higher conductivity
than the smaller one (Fig. 2.17B). An interesting observation is the sig-
nificant conductivity increment with propped fractures (even those with a
very small proppant concentration) compared with unpropped fracture.
This is because the proppants support fracture surfaces to reduce the fracture
closure under stress. The fracture conductivity reduces as the stress increases,
but the reduction of the fracture conductivity in propped fractures is much