Most experimental results demonstrate that the first normal stress difference of viscoelastic polymer solution is higher than the second normal stress difference. Therefore, the Upper-Convected Maxwell (UCM) equation is adapted to describe this property. The steady flow mathematical model of UCM fluids is established. The simulation results of the Finite Volume Method are given. The Finite Volume Method can effectively ensure the convergence together with improvement in the calculation accuracy. The Weissenberg number (We) of the Finite Volume Method can be calculated to 3.2, which is higher than by the Finite Differential Method to simulate the flow characteristics of polymer solutions. When using the Finite Differential Method, the Weissenberg number can only be less than 0.4, otherwise it cannot converge.
The contours of stream function and velocity of polymer solution with different Weissenberg number (We) or Reynolds number (Re) are drawn in three simplified micro-pore structures, expansion channel, contraction channel and expansion-contraction channel, respectively. The influence of Weissenberg number (We) and Reynolds number (Re) on microscopic sweep efficiency is studied. Numerical results show that the viscoelasticy of polymer is the main property that increases the sweep efficiency. With the increase in elasticity, the solution velocity of micro-pores at the corner of where the diameter suddenly changes is bigger; the flow region is enlarged, which is favorable for the residual oil becoming moveable, thereby increasing the micro-scale sweep efficiency. The higher the Reynolds number (Re) is, the larger the micro-scale sweep efficiency will be. But in reservoir condition, Reynolds number (Re) has little influence on improving the micro-scale sweep efficiency.
The above results are important to further understand the mechanism of driving fluid viscoelasticity increasing the Displacement Efficiency of porous medium.