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The interplay between fracture roughness, topology, and permeability is of major interest in hydrogeology, and models that account for the roughness and tortuosity of fractures to upscale hydraulic apertures that represent the microscale aperture distribution have been the focus of many studies in the past decades (He et al., 2021). However, these models often overlook the tensorial aspects of hydraulic aperture, focusing instead on scalar aperture models (Smith & Freeze, 1979; Neuzil & Tracy, 1981; Schrauf & Evans, 1986; Nick & Bisdom, 2018), which do not fully capture the anisotropy that may be observed in the fluid flow in fractures (Nick & Bisdom, 2018). To address this gap, our study introduces a method for upscaling microscale aperture distributions into equivalent hydraulic aperture tensors.
Constraints in experimental designs limit hydraulic aperture measurements in fractured media to a single direction (Xing et al., 2021; Phillips et al., 2021), preventing the direct verification of hydraulic aperture tensors in the lab. To overcome this challenge, we test our method through numerical experiments. Our approach involves creating synthetic fracture walls using fractional Brownian motion (Mandelbrot & Van Ness, 1968) with varying joint roughness coefficients (Barton et al., 1985). We then use fluid flow simulations to explore the effects impacts of compressive and shear stresses, translated into contact area and shear displacement, on the hydraulic aperture tensors.
Our findings indicate that highly anisotropic fluid flow patterns might emerge due to changes in the contact area between fracture walls, which scalar aperture models cannot capture. In addition, no clear correlation between the JRC values and the anisotropy change with contact area was observed, meaning that more information is necessary for characterizing the flow properties of rough fractures. The flow model used in this research has been previously verified through laboratory tests (Konzuk & Kueper, 2004) and numerical experiments (Rybak & Metzger, 2020), and the upscaling methodology has been validated using analytical solutions (Ferreira et al., 2022). This supports the reliability of the present study, thus suggesting the necessity of a tensorial representation for hydraulic apertures. This work provides a basis for developing a rigorous upscaling methodology utilizing a tensorial representation for the hydraulic aperture.
| References | Barton, N., Bandis, S., Bakhtar, K., 1985. Strength, deformation and conductivity coupling of rock joints. International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 22, 121–140. Ferreira, C.A.S., Kadeethum, T., Bouklas, N., Nick, H.M., 2022. A framework for upscaling and modelling fluid flow for discrete fractures using conditional generative adversarial networks. Advances in Water Resources 166, 104264. He, X., Sinan, M., Kwak, H., Hoteit, H., 2021. A corrected cubic law for single-phase laminar flow through rough-walled fractures. Advances in Water Resources 154, 103984. Konzuk, J.S., Kueper, B.H., 2004. Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture. Water Resources Research 40. Mandelbrot, B.B., Van Ness, J.W., 1968. Fractional brownian motions, fractional noises and applications. SIAM review 10, 422–437. Neuzil, C.E., Tracy, J.V., 1981. Flow through fractures. Water Resources Research 17, 191–199. Nick, H.M., Bisdom, K., 2018. Fracture aperture in flow models: to average, or not to average?, in: Third EAGE Workshop on Naturally Fractured Reservoirs, European Association of Geoscientists & Engineers. pp. 1–4. Phillips, T., Bultreys, T., Bisdom, K., Kampman, N., Van Offenwert, S., Mascini, A., Cnudde, V., Busch, A., 2021. A systematic investigation into the control of roughness on the flow properties of 3D-printed fractures. Water Resources Research 57, ewrcr.25233. Rybak, I., Metzger, S., 2020. A dimensionally reduced Stokes–Darcy model for fluid flow in fractured porous media. Applied Mathematics and Computation 384, 125260. Schrauf, T.W., Evans, D.D., 1986. Laboratory studies of gas flow through a single natural fracture. Water Resources Research 22, 1038–1050. Smith, L., Freeze, R.A., 1979. Stochastic analysis of steady state groundwater flow in a bounded domain: 2. Two-dimensional simulations. Water Resources Research 15, 1543–1559. Xing, K., Qian, J., Zhao, W., Ma, H., Ma, L., 2021. Experimental and numerical study for the inertial dependence of non-Darcy coefficient in rough single fractures. Journal of Hydrology 603, 127148. |
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| Country | Denmark |
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