Nanoparticle dispersion in porous media in viscoelastic polymer solutions

•We report on the effects of fluid rheology on macroscopic flow and transport properties in porous media.•Fluid viscoelasticity increases the shear rate and changes the local flow to be more elongational.•FENE-P fluid in porous media behaves like a Newtonian, shear-thinning and thickening fluid by increasing the Deborah number.•Above a critical Deborah number, flow does not reach a steady-state and the pressure gradient fluctuates. These fluctuations increase with the Deborah number.•The long-time particle dispersion in a random porous media cannot be modulated by fluid rheology.