Influence of Fluid Rheology on Fluid Flow in a Natural Fracture Network

Abstract

Non-Newtonian rheology is widely acknowledged in subsurface fluids, yet its presence and effects are largely ignored in current fracture-flow studies. Here, we simulate fracture flow of non-Newtonian polymer solutions on a several metre-wide millimetre-aperture network of fractures, examining the complex interplay between fluid rheology, fracture geometry, and fluid inertia. Non-Newtonian fluid characteristics, including a yield stress and shear-thinning behaviour, are modelled using the Herschel-Bulkley-Papanastasiou approach. For the investigated flow rates, our Navier-Stokes simulations reveal significant viscosity variations, resulting in complex flow patterns at both aperture- and network scale. At low rates, non-yielded fluid forms rigid zones occupying up to ~65% of the network cross-sectional area, reducing fracture flow connectivity. At high rates, shear-thinning promotes inertia-dominated flow with circulations near fracture intersections. Regarding flow partitioning, yield stress confines flow to dominant pathways while shear-thinning promotes a broader fluid distribution as compared with a Newtonian fluid. Observed multimodal velocity distributions and nonlinear pressure drop-flow rate relationships underscore that fluid rheology must be considered during fracture-flow modelling.

Figures (23)

• Figure 1: Rheological curves of xanthan gum solutions modelled using the Herschel-Bulkley-Papanastasiou approach. At low shear rates ($\dot{\gamma_c} \leq 0.0001~\mathrm{s^{-1}}$), yield stress dominates rheological response, making the fluid unyielded. At high shear-rates, yielded fluid follows the power-law shear-dependence.
• Figure 2: Geometry of the one-inlet, two-outlet X-shaped intersection model. The fracture aperture is 2 $\mathrm{mm}$, with an intersecting angle of $60\degree$. For verification, fracture 2 is closed, reducing the model to a one-inlet, one-outlet channel.
• Figure 3: (a) Birds-eye view of the natural fracture network in the Devonian basin of Hornelen, western Norway odling1997. (b) $8 \times 8~\mathrm{m}$ subregion to which a dextral shear displacement of 5 mm was applied, opening fracture void spaces, creating flow conduits. (c) Interconnected fractures are highlighted in red. (d) Discrete fracture network model constructed from the interconnected fractures shown in (c). (e) Zoomed-in view of fracture intersections at positions 1-4 in (d).
• Figure 4: (a) Simulation setup for finite-volume (FV)-based flow simulations in the Hornelen network model. Inlet and outlet reservoirs are placed at the inflow and outflow surfaces to distribute fluid into and out of the network. (b) A closer view of the mesh at typical fracture intersections. The mesh consists of a total of 15M finite elements.
• Figure 5: X-model: Variations in flow pattern of fluid XG5000 with different meshes at $u_0 = 1~\mathrm{cm~s^{-1}}$ ($\mathrm{Re} \sim 0.11$ and $\mathrm{Od} \sim 1.59$). The low mesh resolution in (a) underestimates the extent of unyielded zones ($\tau \leq \tau_0$).