A new operator-splitting finite element scheme for reactive transport modeling in saturated porous media

The operator splitting approach has been widely accepted since it was introduced as a means to solve reactive transport problems. The conventional operator-splitting finite element scheme (Nodal-OS) handles speciation calculations on nodes, resulting in a mixing of heterogeneous reactions on opposing sides in multi-layer systems. Such mixing, however, is not physically accurate. In this context, we propose a new operator-splitting finite element scheme (IP-OS) for reactive transport modeling in saturated porous media. In contrast to the conventional scheme, speciation calculations are performed on integration points rather than on nodes in the new scheme. The implementation of the IP-OS scheme is verified through comparison with an analytical solution of a coupled diffusion-dissolution problem. On this basis, two representative benchmarks are used to examine the advantages and disadvantages of IP-OS. IP-OS is found to have the following advantages and disadvantages compared to Nodal-OS: (1) IP-OS is more accurate; (2) IP-OS is more straightforward to implement; (3) IP-OS is less sensitive to grid resolution and is numerically more stable with coarser grid spacing; and (4) IP-OS is computationally more expensive. In light of the above pros and cons, we recommend using Nodal-OS in cases where chemical reactions do not affect transport properties, and IP-OS in multi-layer heterogeneous cases where chemical reactions alter transport properties of porous media.

Automated summary

The IP-OS finite element scheme, compared to the traditional Nodal-OS, is more accurate and numerically stable, especially suitable for multi-layer heterogeneous systems. However, it is also more costly to implement.