Modelling of spatial contaminant probabilities of occurrence of chlorinated hydrocarbons in an urban aquifer

Abstract

In this study, a 3D urban groundwater model is presented which serves for calculation of multispecies contaminant transport in the subsurface on the regional scale. The total model consists of two submodels, the groundwater flow and reactive transport model, and is validated against field data. The model equations are solved applying finite element method. A sensitivity analysis is carried out to perform parameter identification of flow, transport and reaction processes. Coming from the latter, stochastic variation of flow, transport, and reaction input parameters and Monte Carlo simulation are used in calculating probabilities of pollutant occurrence in the domain. These probabilities could be part of determining future spots of contamination and their measure of damages. Application and validation is exemplarily shown for a contaminated site in Braunschweig (Germany), where a vast plume of chlorinated ethenes pollutes the groundwater. With respect to field application, the methods used for modelling reveal feasible and helpful tools to assess natural attenuation (MNA) and the risk that might be reduced by remediation actions.

Appendix

The following differential equation systems based on mass conservation principle are applied in this study:

For fluid phase f and species k:

$$ \frac{\partial }{{\partial t}}\left( {{s_{\text{f}}}{\varepsilon_{\text{f}}}{\Re_{\text{k}}}C_{\text{k}}^{\text{f}}} \right) - \nabla \cdot \left( {D_{\text{k}}^{\text{f}} \cdot \nabla C_{\text{k}}^{\text{f}}} \right) + \nabla \cdot \left( {{q^{\text{f}}}C_{\text{k}}^{\text{f}}} \right) - {s_{\text{f}}}{\varepsilon_{\text{f}}}Q_{\text{k}}^{\text{f}} = {R_{\text{k}}} $$

For solid phase s and species k:

$$ \frac{\partial }{{\partial t}}\left( {{\varepsilon_s}C_k^s} \right) - {\varepsilon_s}Q_k^s = {R_k} $$

with retardation factor: ${\Re_k} = 1 + \frac{{1 - \varepsilon }}{\varepsilon }{K_{{D,k}}}$ and hydrodynamic dispersion tensor: $D_{\text{k}}^{\text{f}} = \left( {{s_{\text{f}}}\varepsilon D_{{{\text{d,k}}}}^{\text{f}} + {\beta_{\text{T}}}{{\left\| q \right\|}^{\text{f}}}} \right)I + \left( {{\beta_{\text{L}}} - {\beta_{\text{T}}}} \right)\frac{{{q^{\text{f}}} \otimes {q^{\text{f}}}}}{{{{\left\| q \right\|}^{\text{f}}}}}$ and reaction term: ${R_k} = \sum\limits_{{m = 1}}^N {{\nu_{{k,r}}}{\kappa_m}{{\left( {C_m^{\alpha }} \right)}^{{{n_m}}}}}$

$C_k^{\alpha }$ :

= concentration of species k of α-phase

$D_k^{\alpha }$ :

= tensor of hydrodynamic dispersion of species k of α-phase

$D_d^{\alpha }$ :

= coefficient of molecular diffusion of species k of α-phase

α :

= phase indicator (f = fluid, s = solid)

k :

= species indicator

${\varepsilon_{\alpha }}$ :

= volume fraction of α-phase

$Q_k^{\alpha }$ :

= zero-order nonreactive production term of α-phase

R _k :

= bulk rate of chemical reaction of species k

${q^{\alpha }}$ :

= Darcy flux of α-phase

I :

= unit tensor

N :

= total number of chemical species

β _L, β _T :

= longitudinal and transverse dispersivity of porous medium

s _f :

= saturation of the fluid phase

ℜ _k :

= retardation factor of species k

κ _m :

= bulk rate constants

ν _kr :

= stoichiometric number of species k and reaction r

K _D,k :

= linear sorption coefficient (Henry coefficient) of species k

Flow regime is covered by the Darcy equation in the following form:

$$ q_i^f = - {K_{{ij}}}\frac{{\mu_0^f}}{{{\mu^f}}}\left( {\frac{{\partial h}}{{\partial {x_j}}} + \frac{{{\rho^f} - \rho_o^f}}{{{\rho^f}}}{e_j}} \right) $$

$q_i^f$ :

= Darcy velocity

K _ij :

= hydraulic conductivity

$\frac{{\partial h}}{{\partial {x_j}}}$ :

= gradient

ρ ^f :

= density of the fluid phase

$\rho_0^f$ :

= reference fluid density

e _j :

= gravitational unit vector

$\mu_0^f$ :

= reference viscosity

μ ^f :

= hydrodynamic viscosity

i, j :

= unit vectors in direction of main axis