This numerical model solves a 1-D transport problem, representative of a column experiment. The compound is subject to advection, dispersion, sorption and reaction.
The model employes a fully implicit Crank-Nicholson scheme to compute reactive and dispersive processes:
With s = \( \mathrm{\frac{D * dt}{dx^2}} \) and r = \( \lambda *\mathrm{dt} \), dispersion coefficient D, first-order rate constant \( \lambda \), time step dt, distance between cells dx, number of cells N, index of cell i and timestep k
Top Cell: \( (-s) c_{2}^{k+1} + (1 +s + r) c_{1}^{k+1} = c_{1}^{k} \)
Internal Cells: \( (-s) c_{i-1}^{k+1} + (1 +s + r) c_{i}^{k+1} + (-s) c_{i+1}^{k} = c_{i}^{k} \)
Bottom Cell: \( (-s) c_{N-1}^{k+1} + (1 +s + r) c_{N}^{k+1} = c_{N}^{k} \)
Internal Cells: \( (-s) c_{i-1}^{k+1} + (1 +s + r) c_{i}^{k+1} + (-s) c_{i+1}^{k} = c_{i}^{k} \)
Bottom Cell: \( (-s) c_{N-1}^{k+1} + (1 +s + r) c_{N}^{k+1} = c_{N}^{k} \)