Description

The computation is based on the parameters provided by the technical report G7-04

Henry Contant: kh

The Henry constant is defined as shown in equation below. kh is expressed in MPa.

$$k_H = \lim_{x_2 \rightarrow 0} f_2/x_2$$

• $f_2$: liquid-phase fugacity
• $x_2$: mole fraction of the solute

The Henry’s constant kh is given as a function of temperature by:

$$\ln \left( \frac{k_H}{p_1^*} \right) = A/T_R + \frac{B \cdot \tau^{0.355}}{T_R} + C \cdot T_R^{-0.41} \cdot \exp \tau$$

• $\tau = 1-T_R$
• $T_R = T/T_{c1}$
• $T_{c1}$: critical temperature of the solvent as recommended by IAPWS.
• $p_1^{*}$ is the vapor pressure of the solvent at the temperature of interest and is calculated from the correlation of Wagner and Pruss for $H_2O$ and from the correlation of Harvey and Lemmon for $D_2O$.

Both equations have the form:

$$\ln \left( p_1^{*}/p_{c1} \right) = T_R^{-1} \sum_{i=1}^{n}a_i \tau^{b_i}$$

• $n$ is 6 for $H_2O$ and 5 for $D_2O$
• $p_{c1}$ is the critical pressure of the solvent recommended by the report R2-83

Vapor-Liquid Distribution Constant: kd

The liquid-vapor distribution constant kd is defined as shown in equation below. kd is adimensional.

$$k_D = \lim_{x_2 \rightarrow 0} y_2/x_2$$

• $x_2$: mole fraction of the solute
• $y_2$ is the vapor-phase solute mole fraction in equilibrium with the liquid

The vapor-liquid distribution constant kd is given as a function of temperature by:

$$\ln K_D =qF+ \frac{E}{T(K)}f(\tau)+(F+G\tau^{2/3} +H\tau) \exp \left( \frac{273.15 - T(K)}{100} \right)$$

• $q$ : -0.023767 for $H_2O$ and -0.024552 for $D_2O$.
• $f(\tau)$ Wagner et al. for $H_2O$ and fernandez-prini et al. for $D_2O$

In both cases, $f(\tau)$ has the following form:

$$f(\tau) = \sum _{i=1} ^{n} c_i \cdot \tau ^{d_i}$$

• $n$ is 6 for $H_2O$ and 4 for $D_2O$

Molar fractions

The molar fractions $x_2$ and $y_2$ as following:

$$x_2 = \frac{f_2}{k_H}$$ $$\frac{x_2}{f_2} = \frac{1}{k_H}$$ $$y_2 = \frac{k_D}{k_H} \cdot f_2$$ $$\frac{y_2}{f_2} = \frac{k_D}{k_H}$$

By fixing $f_2$ at 1.0 it comes that the molar fractions $x_2$ and $y_2$ are then expressed per unit of pressure as shown in the following equation .

$$x_2 = \frac{1}{k_H}$$ $$y_2 = \frac{k_D}{k_H}$$

The molar fractions can be converted to solubilties in ppm or cm3/kg by considering dilute solutions. $X$ is the considered gas and the solvent is either $H_2O$ or $D_2O$.

$$S_{X}[mg.kg^{-1}.bar^{-1}] = x_2[bar^{-1}] \cdot \frac{M_{X}[g.mol^{-1}]}{M_{solvent}[g.mol^{-1}]} \cdot 10^6$$
$$S_{X}[cm3.kg^{-1}.bar^{-1}] = \frac{S_{X}[mg.kg^{-1}.bar^{-1}]}{M_{X}[g.mol^{-1}]} \cdot V_m[mol.L^{-1}]$$

Available gases

kh and kd can be computed for the following gases:

• in water: He, Ne, Ar, Kr, Xe, H2, N2, O2, CO, CO2, H2S, CH4, C2H6, SF6
• in heavywater: He, Ne, Ar, Kr, Xe, D2, CH4

The available gases can be retrieved with

• gases which returns the available gases as a list.
• gases2 which return the available gases as a string.
• ngases which returns the number of available gases.

Plots