Effective Elastic Moduli at Reservoir Scale: A Case Study of the Soultz-sous-Forêts Fractured Reservoir

The presence of discontinuities in fractured reservoirs, their mechanical and physical characteristics, and fluid flow through them are important factors influencing their effective large-scale properties. In this paper, the variation of elastic moduli in a block measuring 100 × 100 × 100 m³ that hosts a discrete fracture network (DFN) is evaluated using the discrete element method (DEM). Fractures are characterised by (1) constant, (2) interlocked, and (3) mismatched stiffness properties. First, three uniaxial verification tests were performed on a block (1 × 1 × 2 m³) containing a circular finite fracture (diameter = 0.5 m) to validate the developed numerical algorithm that implements the three fracture stiffnesses mentioned above. The validated algorithms were generalised to fractures in a DFN embedded in a 100 × 100 × 100 m³ rock block that reproduces in situ conditions at various depths (4.7 km, 2.3 km, and 0.5 km) of the Soultz-sous-Forêts geothermal site. The effective elastic moduli of this large-scale rock mass were then numerically evaluated through a triaxial loading scenario by comparing to the numerically evaluated stress field using the DFN, with the stress field computed using an effective homogeneous elastic block. Based on the results obtained, we evaluate the influence of fracture interaction and stress perturbation around fractures on the effective elastic moduli and subsequently on the large-scale P-wave velocity. The numerical results differ from the elastic moduli of the rock matrix at higher fracture densities, unlike the other methods. Additionally, the effect of nonlinear fracture stiffness is reduced by increasing the depth or stress level in both the numerical and semi-analytical methods.