Abstract
Yield-stress is a problematic and controversial non-Newtonian flow phenomenon. In this article, we investigate the flow of yield-stress substances through porous media within the framework of pore-scale network modelling. We also investigate the validity of the Minimum Threshold Path (MTP) algorithms to predict the pressure yield point of a network depicting random or regular porous media. Percolation theory as a basis for predicting the yield point of a network is briefly presented and assessed. In the course of this study, a yield-stress flow simulation model alongside several numerical algorithms related to yield-stress in porous media were developed, implemented and assessed. The general conclusion is that modelling the flow of yield-stress fluids in porous media is too difficult and problematic. More fundamental modelling strategies are required to tackle this problem in the future.
Highlights
1 IntroductionYield-stress or viscoplastic fluids are characterized by their ability to sustain shear stresses, that is a certain amount of stress must be exceeded before the flow initiates
The accuracy of the predictions made using flow simulation models in conjunction with such experimental data is limited. Another difficulty is that while in the case of pipe flow the yield-stress value is a property of the fluid, in the case of flow in porous media it may depend on both the fluid and the porous medium itself [8, 9]
In the literature of yield-stress we can find two well-developed methods proposed for predicting the yield point of a morphologically-complex network that depicts a porous medium; these are the Minimum Threshold Path (MTP) and the percolation theory algorithms
Summary
Yield-stress or viscoplastic fluids are characterized by their ability to sustain shear stresses, that is a certain amount of stress must be exceeded before the flow initiates. Among the difficulties in working with yield-stress fluids and validating the experimental data is that yield-stress value is usually obtained by extrapolating a plot of shear stress to zero shear rate [2]. The vast majority of yield-stress data reported results from such extrapolations [5, 6], making most values in the literature instrument-dependent [2] Another method used to measure yield-stress is by lowering the shear rate until the shear stress approaches a constant. The accuracy of the predictions made using flow simulation models in conjunction with such experimental data is limited Another difficulty is that while in the case of pipe flow the yield-stress value is a property of the fluid, in the case of flow in porous media it may depend on both the fluid and the porous medium itself [8, 9]. These include Rossen and Mamun [17] and Chen et al [18, 19, 20]
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