Experimental Hydromechanical Characterization and Numerical Modelling of a Fractured and Porous Sandstone

Abstract

The experimental device previously used to study the hydromechanical behaviour of individual fractures on a laboratory scale, was adapted to make it possible to measure flow through porous rock mass samples in addition to fracture flows. A first series of tests was performed to characterize the hydromechanical behaviour of the fracture individually as well as the porous matrix (sandstone) comprising the fracture walls. A third test in this series was used to validate the experimental approach. These tests showed non-linear evolution of the contact area on the fracture walls with respect to effective normal stress. Consequently, a non-linear relationship was noted between the hydraulic aperture on the one hand, and the effective normal stress and mechanical opening on the other hand. The results of the three tests were then analysed by numerical modelling. The VIPLEF/HYDREF numerical codes used take into account the dual-porosity of the sample (fracture + rock matrix) and can be used to reproduce hydromechanical loading accurately. The analyses show that the relationship between the hydraulic aperture of the fracture and the mechanical closure has a significant effect on fracture flow rate predictions. By taking simultaneous measurements of flow in both fracture and rock matrix, we were able to carry out a global evaluation of the conceptual approach used.

Appendix

$C_{ijkl}^{m}$ :

Drained compliance tensor (inverse of drained elastic constant tensor)

${\text{d}}\sigma_{ij}^{\text{e}} ;{\text{ d}}\sigma_{ij}$ :

Increment of effective and total stress tensor, respectively

${\text{d}}P$ :

Increment of pore pressure

b :

Biot’s coefficient (rock matrix)

${\text{d}}\varepsilon_{ij}^{\text{p}}$ :

Increment of non-elastic strain (plastic, viscoplastic …)

K ₀ :

Drained compressibility modulus (matrix)

du _n, du _s :

Increments of relative normal (closure is negative) and shear displacements, respectively

k _ni, V _m :

Initial normal stiffness and maximum fracture closure (>0), respectively

dτ :

Increment of shear stress

k _s :

Shear stiffness

${\text{d}}\sigma_{\text{n}}^{\text{e}} ;{\text{ d}}\sigma_{\text{n}}$ :

Increment of effective and total normal stress, respectively (positive in compression)

b _j :

Biot’s coefficient (fracture)

c _j , ϕ _j :

Fracture cohesion and friction angle

S :

Storage coefficient expressed as:

$$S = \left( {\frac{1}{M} + \frac{{b^{2} }}{{K_{0} }}} \right)\rho_{{f_{0} }} g$$

M :

Biot’s modulus (rock matrix)

g :

Gravity acceleration

k _ij :

Solid matrix permeability tensor

h :

Total hydraulic head

q _v, $q_{v}^{f}$ :

Source terms in porous medium and fracture, respectively

$\rho_{{f_{0} }}$ , μ ₀ :

Initial fluid density and dynamic viscosity

K _f :

Fluid compressibility modulus