An efficient non‐newtonian fluid‐flow simulator for variable aperture fractures

Abstract

AbstractMany natural and industrial applications involve non‐Newtonian fluids w­ith high effective viscosity ratios flowing between surfaces with spatial variations in aperture. In particular, hydraulic fracturing operations often require pumping sequences of non‐Newtonian fluids with yield‐stress into a variable‐aperture fracture that initially contains water. Numerical methods for this class of problem must deal robustly with the high aspect ratio of the flow domain and large contrasts in effective viscosity while maintaining interfaces between immiscible phases. We avoid the computational burden of a fully three‐dimensional approach by introducing an aperture‐averaged analytic solution for flow of a Hershel‐Bulkley fluid between two plates. We discuss the incorporation of this analytic solution within a simulator of flow within a fracture with spatial variations in aperture. We minimize numerical diffusion through use of a hybrid Lagrangian‐Eulerian approach that naturally tracks the multiple fluid phases. We demonstrate effectiveness of the numerical method through comparison with analytic results and one‐dimensional finite difference numerical solutions. Benchmarking of the 2‐D model against a 3‐D model reveals both advantages and shortcomings of a through‐aperture averaged method. The two simulations agree on the bulk behaviour of the phases while the 2‐D model is two orders of magnitude more efficient. Comparison between predictions of the models after water injection behind the pad reveals that the 3‐D model predicts non‐uniformity across the fracture aperture. This suggests that while bulk behaviour may be well captured by the 2‐D model, improved accuracy could be obtained by introducing multiple fluid layers within each cell of the model.