Abstract
The flow dynamics of non-Newtonian fluid in porous media is much different from the Newtonian fluid. In this work, we establish a lattice Boltzmann model for polymer flooding taking into both the power law fluid properties and viscoelastic fluid properties. Using this model, we investigate the viscosity distribution in porous media, the local apparent permeability in porous media, and the effect of elastic force on the remaining oil in dead ends.
Firstly, we build a single phase lattice Boltzmann model to evolve the fluid velocity field. Then the viscosity and shear rate in each lattice can be calculated based on the relaxation time and velocity field. We further make the fluid viscosity change with the shear rate according to the power-law fluid constitutive equation, consequently establish the lattice Boltzmann model for power law fluid. Moreover, we derive the Maxwell viscoelastic fluid model in integral form using Boltzmann superposition principle, and the elastic force is calculated from the divergence of the stress tensor. We then couple the elastic force into the lattice Boltzmann model by Newton's second law, and finally establish the lattice Boltzmann model of the viscoelastic fluid. Both the models are validated against analytical solutions.
The simulation results show that when the power-law index is smaller than 1, the fluid viscosity shows a distribution of that viscosity is higher in pore center and lower near the wall; while when the index is larger than 1, the fluid viscosity shows a opposite distribution. This is because the pore center has a high velocity but a low shear rate, while the boundary has a low velocity but a high shear rate. Moreover, the local apparent permeability decreases with the power law index, and the number of hyper-permeable bands also decreases. In addition, the local permeability shows pressure gradient dependence. Considering the viscoelasticity effects, the displacement fluid has a clear tendency to sweep deeply into the dead end, which improves the oil washing efficiency of the dead end.
The model provides a pore scale simulation tool for polymer flooding and help understand the flow mechanisms and enhanced oil recovery mechanisms during polymer flooding.
Enhanced computational performance of the lattice Boltzmann model for simulating micron- and submicron-size particle flows and non-Newtonian fluid flows
