A Study On The Lattice Boltzmann Models For Predicting Effective Permeability Of Non-newtonian Fluid In Porous Media

Pore-scale simulation of non-Newtonian fluid flows provides a unique new medium for oil exploitation and aneurysm in biomedicology,which has important theoretical significance and potential practical value.Since non-Newtonian fluids usually have more complex constitutive equations,the viscosity is related to shear rate or velocity gradient,which brings great challenges to the traditional numerical methods.As a new mesoscopic numerical calculation method,the lattice Boltzmann(LB)method is widely used in the study of non-Newtonian fluid flows.It is easy to deal with complex boundaries,has high computational efficiency and is easy to parallelize,showing great advantages in the simulation of complex fluid flows.In this thesis,we present a multiple-relaxation-time lattice Boltzmann model for nonNewtonian fluid flows at the pore scale,and predict the permeability of non-Newtonian fluid in porous media.Firstly,the MRT model is used to simulate the flow of non-Newtonian fluid in two-dimensional channel,such as power law fluid and Bingham fluid.MRT model is more stable than traditional LBGK model,with second-order precision.Secondly,the microstructure of porous media is idealized as circular,square and triangular cylindrical arrangement.The change of the cylindrical size produces porous media with different porosity and permeability.For the same porosity,the square arrangement has lower permeability than the circular arrangement,and the triangular arrangement is the lowest.Influenced by the inertia effect,the permeability under the pore varies with different Reynolds Numbers,and its change trend is related to the properties of the non-Newtonian fluid.Finally,the complex microstructure of realistic porous materials is reconstructed using the Quartet Structure Generation Set(QSGS)method.Simulating fluid flows in random porous media,the equivalent viscosity is calculated based on the shear rate in the pores,and the influence of viscosity on fluid flows is given qualitatively.Compared with the ideal porous media,the permeability of non-Newtonian fluid in the real porous media is smaller at the same low porosity.Similarly,the properties of non-Newtonian fluids have a great influence on the flow in real porous media.