Analytical model for solute transport in discrete fracture networks: 2D spatiotemporal solution with matrix diffusion

A computationally efficient analytical network (AN) model simulating solute transport in discrete fracture networks (DFNs) is developed. The model simulates two-dimensional spatial and temporal distribution of a solute considering advection and hydrodynamic dispersion within the fractures, matrix diffusion, sorption onto the fracture walls and in the matrix, and first order decay for one constituent. The AN model is based on previously developed analytical solutions for a single fracture, and the convolution method is applied to extend these solutions to a DFN. Mass sharing at fracture intersections is calculated using the complete mixing and stream-tube methods. The AN model was verified against numerical models based on the time domain random walk and random walk particle tracking methods using two different fracture networks with a range of properties. In all cases, the AN model solutions showed excellent agreement with the numerical model solutions. The sensitivity of the mass sharing methods to the dominant transport mechanism (i.e., advection or diffusion) was investigated for Peclet numbers ranging from P e  = 3 × 10−6 - 380. Both mass sharing methods give the same results when the transport processes are advection-dominated and matrix diffusion is considered; however, attention must be paid to the mass sharing method employed under other conditions, particularly when the fracture density is small. The AN model was at least 97% more efficient than the numerical models used in this work, and this efficiency will increase with network complexity. The AN model provides a useful reference tool for the verification of numerical dual-porosity fracture network simulations.