In this work, a comprehensive study of the influence on shear viscosity of polyelectrolyte concentration, persistence length, salt concentration and solvent quality is reported, using numerical simulations of confined solutions under stationary Poiseuille flow. Various scaling regimes for the viscosity are reproduced, both under good solvent and theta solvent conditions. The key role played by the electrostatic interactions in the viscosity is borne out when the ionic strength is varied. It is argued that these results are helpful for the understanding of viscosity scaling in entangled polyelectrolyte solutions for both rigid and flexible polyelectrolytes in different solvents, which is needed to perform intelligent design of new polyelectrolytes capable of fine tuning the viscosity in complex fluids.