Simulation of reactive transport in porous media using radial point collocation method

Abstract

In this paper, a meshfree Radial Point Collocation method (RPCM) for modelling of reactive transport involving first-order decay and adsorption is presented. Unlike conventional grid-based methods such as Finite Element (FEM) and Finite Difference Methods (FDM), it does not require nodal connectivity information for domain representation. The proposed method does not necessitate operator splitting for accommodating reactions as it is done in FEM and FDM. The model domain is divided into intersecting circular shaped local support domains. This technique solves the ill-conditioning problem associated with globally supported system and allows use of more number of nodes which increases the accuracy of models. The multi-quadrics radial basis function (MQ-RBF) is used for the approximation/interpolation of solute concentration values in the local support domain. 1D and 2D models are developed and verified against benchmark analytical solutions. Sensitivity analyses are performed for shape parameters of the MQ-RBF, support domain size and nodal density. Two case studies are presented with regular and irregular shaped domains and results are compared with FEM. The results demonstrate advantages of the proposed model over grid-based methods while handling adsorption and first-order decay reactions. This study shows that the proposed model is effective for simulating reactive transport problems in porous media.