4SIGHT Manual: A Computer Program for Modelling Degradation of Underground Low Level Waste Concrete Vaults/Chemical Equilibrium

by Kenneth A. Snyder and James R. Clifton

8Chemical Equilibrium

After each time step, each computational element is brought to chemical equilibrium by satisfying two conditions:

1. If a salt exists as solid, the constituent ion concentration product equals the solubility product.
2. The sum of the free charges from all available ions equals zero, insuring local charge neutrality.

Given the salt $A_{\beta }C_{\alpha }$, composed of anion $A^{\alpha -}$ and cation $C^{\beta +}$, condition 1 above implies that if $A_{\beta }C_{\alpha }$ exists as a solid then

$\left[A^{\alpha -}\right]^{\beta }\left[C^{\beta +}\right]^{\alpha }=K_{sp}$

(23)

where $K_{sp}$ is the ion solubility product. Condition 2 implies that with $m$ anions and $n$ cations present in the pore solution:

$\sum _{i=1}^{m}\alpha A_{i}^{\alpha -}=\sum _{j=1}^{n}\beta C_{j}^{\beta +}$

(24)

4SIGHT satisfies eqns. 23 and 24 using an iterative process. Each iteration is composed of two steps:

1. Determine how many moles of salt should be precipitated or dissolved to satisfy eqn. 23.
2. Given $K_{sp}$ for water what concentration of hydroxyl ions ($OH^{-}$) is needed to satisfy eqn. 24

These two steps are repeated, as necessary, until both equations are satisfied.