Flow of shear-thinning fluids in geological media

As the primary conduits for water, oil, and geothermal resources, fractures and fracture flow are important in a wide range of applications, including water reservoir development, subsurface contamination, and petroleum and geothermal reservoir exploitation. Fracture flow estimations are subject to significant uncertainty and the role of rheology when the fluid is non-Newtonian makes the task considerably more difficult. In such a complex phenomenon, simple models allow us to qualitatively assess the effect of rheological and geometric characteristics on the flow. This study aims to investigate the effect of shear-thinning fluid rheology on fracture flow rate using smooth parallel plate to present the fracture. By using power-law, Ellis and Carreau rheology models, we can also compare the results of using different rheology models. To achieve the aforementioned goals, we first introduced some equations to relate the three aforementioned rheology models together and then we introduced equations to calculate the fracture flow rate for each of the models. Using MATLAB software to solve these for four different fluids with different flow behavior indices, several diagrams were drawn to show the relation between dimensionless flow rate and dimensionless reduced pressure gradient. By comparing the produced graphs, one can see that fluid rheology and the way it is modeled has an important influence on calculated fracture flows. The way we present the fluids' rheology is also important. For example in higher pressure gradients, the power-law model calculates the flow rate incorrectly in both large and small pressure gradients because of its incapablity to simulate both low and infinite-shear viscosity. There is an excellent match between all three rheology models in the middle range of pressure gradient, especially between Ellis and power-law models. Finally, it should be noted that the pressure gradient rules which model and equation can be used to calculate the flow rate