I want to know that does change the fluid's viscosity when it flows through the porous media and if the answer is yes, is there theoretical or empirical model or equation to find it?
Viscosity is intrinsic property of a fluid. It does not depend on the nature of media it is travelling through. However external factors such as temperature.
The pressures on the water are sufficiently small so that there is no compression and variations in its density. Changes in the composition of the soil solution does not lead to significant variations in viscosity except in specific situations of highly polluted soils with organic compounds such as hydrocarbons or solvents.
Newtonian fluids which are found in many processes do not have a viscosity change except for different temperatures and compositions mixed together. The Reynolds number will change for different equipment and media. Non Newtonian fluids can change viscosity from various mechanical forces and fluid sheer forces. Some products act like liquids in one place and plastics in another. Different products may be partially polymerized or depolymerized at different places. Sometimes the energy of a pumping operation goes into temporary or permanent chemical change of the liquid.