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Figure 2: Formation factor, $D/D^{f}$ , due to hydration (circles) and to leaching (squares) for w/c=0.35 (after [14]). The solid line represents the approximation used by 4SIGHT for the leaching formation factor.

THe relative change in permeability can be calculated using $\xi$ . The Katz-Thompson equation relates permeability to $\vartheta$ [15]:

k={\frac {d_{c}^{2}}{226}}\vartheta

(32)

where $d_{c}$ is the diameter of the largest sphere which can pass through the pore space of the sample. Also, given that $d_{c}\propto \vartheta$ [16], the relative change in permeability becomes

{\frac {k^{\prime }}{k_{o}}}=\left({\frac {\xi }{\vartheta _{o}}}\right)^{3}

(33)

The final dimensionless advection-diffusion equation is a combination of eqns. 14, 31, and 33:

{\frac {\partial c_{i}}{\partial T}}=\nabla \cdot {\frac {\xi _{i}}{\vartheta _{o}}}\nabla P+\left({\frac {\xi _{i}}{\vartheta _{o}}}\right)^{3}\mathbf {v} _{D}\cdot \nabla c_{i}

(34)

There is one such equation for chemical species $i$ .

11Program Outline

The flow of the program is summarized by the pseudo-code program shown in Figure 3. The program naturally divides itself into three parts: initialization, ion propagation, and final state output.

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