For improving CFD models of particle transport in wellbore flows, i.e. cuttings transport, we have extended the Lagrangian Discrete-Particle-Model model of the commercial code ANSYS Fluent 17.2 to describe the motion of a particle settling in an orthogonal shear flow of a shear-thinning, mildly viscoelastic fluid. Essentially, the fluid strain rate as the magnitude of the fluid deformation rate tensor is corrected by a particle-induced shear rate. This corrected strain rate is used to compute an apparent viscosity. The fluid is treated as a Generalized Newtonian Fluid using Cross and Carreau material functions. Different drag laws are investigated, including one which accounts for the fluids viscoelastic wake structure behavior via a correction term. We validate the model with eight different particle trajectories representing different combinations of particle diameters, fluid flow rates and rheological properties (water and polymeric solutions) provided by Khatibi et al. [1]. In general, the experimental trajectories are satisfactorily replicated by the CFD model. However, for small particles a trajectory mismatch is observed close to the lower channel wall. We find this mismatch to be a consequence of unexpectedly high particle x-velocities in the experimental data. Various possible causes are identified and discussed. More detailed experimental near-wall data of both particle and fluid velocities as well as more sophisticated modeling of the fluids rheology, including the rheology effect on the forces acting on the particles, may be required to minimize the mismatch. In addition, we further conclude that in case of the polymeric solutions particle drag is the dominant particle force, that the viscoelastic wake of the particle is not significantly affecting the trajectories, and that a Newtonian drag law may be used as long as the particle-induced shear rate is estimated with parallel to v(r)parallel to/d(p), and a material function accounting for the limiting zero-shear Newtonian viscosity is applied.