Appendix F Model verification – analytical solution – Environmental Project No. 1295 2009 – Model assessment of reductive dechlorination as a remediation technology for contaminant sources in fractured clay: Modeling tool

Model assessment of reductive dechlorination as a remediation technology for contaminant sources in fractured clay: Modeling tool

Appendix F Model verification – analytical solution

The numerical model is verified by comparing results to an analytical solution for a system of parallel fractures [Sudicky and Frind, 1982]. This analytical solution is also used in SprækkeJAGG [SprakkeJAGG, 2008] and gives the exact solution for concentration in the fracture and matrix at steady-state with a constant concentration at the fracture inlet. In this model, the transport in the matrix is assumed to be one-dimensional in the direction perpendicular to the matrix. Furthermore the degradation rate is assumed to be a 1^st order. The parameters used in this verification are listed in Table F.1.

Table F.1 - Parameters used for the model verification

Parameters	Symbol	Value	Unit
Net recharge	I	0.1	m/year
Fracture spacing	2B	0.2	m
Fracture aperture	2b	0.001	m
Water velocity in fracture	vf	20	m/year
Matrix porosity	φ	0.33	-
Longitudinal dispersivity in fracture	α_L	0.1	m
Fracture dispersion coefficient	D_f	2	m²/year
Matrix diffusion coefficient	D_m	0.0066	m²/year
Degradation rate	λ	0.5	year^-1
Start concentration	C₀	1400	mg/L

$Figure F.1 – Contaminant concentration at different distances from the fracture for the numerical model (line) and analytical solution (symbol) for the parameters given in Table F.1$

Figure F.1 – Contaminant concentration at different distances from the fracture for the numerical model (line) and analytical solution (symbol) for the parameters given in Table F.1