Numerical modeling of non-Newtonian fluid flow in fractures and porous media

Abstract

Non-Newtonian fluids having Bingham or power-law rheology are common in many applications within drilling and reservoir engineering. Examples of such fluids are drilling muds, foams, heavy oil, hydraulicfracturing and other stimulation fluids, and cement slurries. Despite the importance of non-Newtonian rheology, it is rarely used in reservoir simulators and fracture flow simulations. We study two types of non-Newtonian rheology: the truncated power-law (Ostwald-de Waele) fluid and the Bingham fluid.For either of the two types of non-Newtonian rheology, we construct relationships between the superficial fluid velocity and the pressure gradient in fractures and porous media. The Bingham fluid is regularized by means of Papanastasiou-type regularization for porous media and by means of a simple hyperbolic function for fracture flow. Approximation by Taylor expansion is used to evaluate the fluid velocity for small pressure gradients to reduce rounding errors. We report simulations of flow in rough-walled fractures for different rheologies and study the effect of fluid parameters on the flow channelization in rough-walled fractures. This effect is known from previous studies. We demonstrate how rheologies on different domains can be included in a fully-unstructured reservoir simulation that incorporates discrete fracture modeling (DFM).

On the application of simplified rheological models of fluid in the hydraulic fracture problems

“…As the shear-thinning rheology improves suspending properties of the fluid, many fracturing fluids are intentionally made shear-thinning (e.g. by adding polymers (Bao et al, 2017)).…”

A Review of Rheological Modeling of Cement Slurry in Oil Well Applications

“…This modified Herschel-Bulkley model was used to study the flow between parallel plates and flow in the screw extruder in cement 3D printing. Bao et al [288] used the Bingham and the power-law fluid models in porous media to study the flow between parallel plates with discrete fracture modeling (DFM) by applying the open-source MATLAB Reservoir Simulation Toolbox (MRST). Tardy and Bittleston [289,290] solved the flow in 2D and 3D axial-azimuthal-radial space and annular displacement of wellbore completion by considering Newtonian fluids with CAFFA and ANSYS FLUENT CFD software.…”

Flow of non‐Newtonian fluids in fractured porous media: Isogeometric vs standard finite element discretisation

“…Herein, p is the pressure inside the fracture, equal to the pressure of the fluid at the boundary of the surrounding porous medium, and v is the tangential velocity inside the fracture. Integrating Equation 19 and assuming the velocity at the walls to be equal to the velocity v f inside the porous medium (no slip assumption) results in an expression for the fluid velocity profile inside the fracture:…”

“…Yet the potential impact of including non‐Newtonian fluid flow on the propagation speed and direction of fractures has been demonstrated . Further simulations of non‐Newtonian fluids in porous media with pre‐existing cracks, albeit restricted to nondeformable porous media, have shown the influence of these cracks on the pressure gradient, which in turn influences the behaviour of the fluid inside the porous medium …”

“…18 Further simulations of non-Newtonian fluids in porous media with pre-existing cracks, albeit restricted to nondeformable porous media, have shown the influence of these cracks on the pressure gradient, which in turn influences the behaviour of the fluid inside the porous medium. 19 While many applications involve non-Newtonian fluids and the effects can be important, no formulations exist for a deformable, poroelastic medium, including the effect of the fluid transport inside fractures. The aim of this paper is to present a formulation that encompasses these effects.…”