Numerical simulations of solute transport in highly heterogeneous formations: A comparison of alternative numerical schemes

We compare the accuracy of five numerical schemes in modeling transport of nonreactive and reactive solutes in porous formations with heterogeneity increasing from low (σY2=0.2) to very high (σY2=10). Two schemes, the Total Variation Diminishing (TVD) and the Eulerian–Lagrangian Method of Characteristics (MOC), are available in widely used packages. The other three schemes are the Random Walk Particle Tracking (RWPT), the Smoothed Particle Hydrodynamics (SPH) and a Streamline-Based (SB-FV) method, which we modified to improve its accuracy. The advective nature of the transport problem renders the numerical solution very challenging with the solutions provided by classic Eulerian methods that are plagued by numerical diffusion and spurious oscillations. Our analysis shows that TVD is severely affected by numerical diffusion, while the modified SB-FV method shows the tendency to underestimate dilution to an extent that increases with σY2. In addition, we show that MOC is not mass-conservative, SPH is computationally demanding and cannot handle anisotropic dispersion, while RWPT develops spurious concentration fluctuations, which can be attenuated by increasing the number of particles at the expenses of an increase of the CPU time. Moreover, we investigate the effect of uniform and non-uniform local dispersion models on the overall plume dilution. These results help to consciously choose the numerical scheme according to investigation’s objectives and heterogeneity degree.

► Five numerical schemes to solve transport in highly heterogeneous porous media.
► Lagrangian and hybrid methods show negligible numerical diffusion.
► Classic TVD Eulerian methods are adversely affected by numerical diffusion.
► Streamline based methods may underestimate dilution.