Analysis of Herschel–Bulkley fluids flow through rough-walled rock fractures

Cement grouts are typical non-Newtonian fluids, the flow behavior of which through fractured strata is governed by rheological properties of the grouts (e.g., yield stress and viscosity) and geometrical characteristics of rock fractures (e.g., surface roughness and variable aperture structures). Particularly, the complex void structure of rock fractures renders the flow field complex and heterogeneous, significantly increasing the difficulty of theoretically predicting the pressure gradient – flow rate relation that is essential for rock grouting in engineering practice. In this study, we aim to analyze the effect of aperture structure on flow behavior of Herschel-Bulkely (H–B) grout flow in rough-walled rock fractures. Here, H–B fluids were prepared using Sodium Polyacrylate solutions and flow experiments were conducted on 3D-printed rough-walled fracture and smooth parallel-plate models. Grout flow through these models were numerically simulated based on the regularized Herschel–Bulkely–Papanastasiou (H–B–P) rheological model. Well-matched results were obtained between experimental and numerical results that validated the numerical method. The fracture surface was then decomposed into three levels using a wavelet analysis subject to different normal stresses to create a series of aperture structures for numerical simulations of the flow process. A regressively fitted function based on numerical results was developed that can reflect the deviation of grout flow through a rough-walled model from a parallel-plate model. This modified theoretical model was validated by applying it to predict the pressure gradient-flow rate relation of another rough-walled fracture independently. The high-resolution experimental and numerical results revealed the response of H–B fluid flow to the applied normal stress and roughness; the modified theoretical model can readily be used to predict H–B fluids flow through rough-walled rock fractures, which is useful for rock grouting analysis in engineering practice.