Reactive modelling of CO₂ intrusion into freshwater aquifers: current requirements, approaches and limitations to account for temperature and pressure effects

Abstract

The modelling of CO₂ intrusion into virtual freshwater aquifers after a leakage from CO₂ storage formations is a well-established approach for the identification of monitoring parameters and for the risk assessment. At presence, standard or close-to-standard conditions in terms of temperature (T), i.e. 25 °C and pressure (P), i.e. 1–5 bar, are assumed. This approach neglects the fact that temperature and pressure conditions change with the depth of the freshwater aquifer. This study tests the accuracy of T–P corrections of the geochemical constants in the system gaseous CO₂–water–mineral which are performed by the simulators PhreeqC (Parkhurst and Appelo in User’s guide to phreeqc (version 2)—a computer program for speciation, batch reaction, one-dimensional transport, and inverse geochemical calculations. Technical report, US Department of the Interior, 1999) and TOUGHREACT (Xu et al. in Toughreact user’s guide: a simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media. Technical report, Lawrence Berkeley National Laboratory, 2004). It further identifies the impact of T and P variations on the predicted concentrations of the monitoring parameters pH and total inorganic carbon (TIC) and on the predicted concentration of the trace metal lead (Pb) in 3D multiphase-multicomponent simulations of virtual aquifers. The results reveal a strong imprecision in the correction of kinetic rates of mineral dissolution and a lack of corrections of sorption equilibrium states. The predicted pH and concentrations of TIC and lead depend strongly on the assumed T and P conditions. It is concluded that a neglect of T and P effects results in inaccurate predictions of groundwater chemistry. The impact assessment and monitoring strategies based on currently available modelling results consequently require strong improvements.

Appendix

The following section gives a detailed description of the temperature (T) and pressure (P) correction of the single geochemical constants which are used by TOUGHREACT and PhreeqC. The presented information has been taken from the available software manuals, the reader is referred to Xu et al. (2004) for TOUGHREACT and Parkhurst and Appelo (1999) for PhreeqC. All following references of the software packages refer to these two sources.

CO₂ solubility

TOUGHREACT calculates the dissolution of CO₂ according to the mass-action-law (Eq. 2), where p (Pa) is the partial pressure of gaseous CO₂, f (−) is the fugacity coefficient, $K_{\rm H,CO_2}$ (mol Pa⁻¹ kgw⁻¹) is the Henry constant, c (mol kgw⁻¹) is the concentration of dissolved CO₂, and γ (−) is the activity coefficient.

$$ p*f*K_{\rm H,CO_2} = c*\gamma $$

(2)

The fugacity coefficient is adopted to P and T by fitting it to experimental data following Spycher and Reed (1988), thus accounting for non-ideal behaviour of the gas phase. The temperature correction of $K_{\rm H,CO_2}$ is performed by fitting to an analytical expression similar to the correction of all equilibrium constants in the database, which will be described in the following chapter.

The software PhreeqC also uses the mass-action-law, in contrast to TOUGHREACT it assumes ideal behaviour of the gas phase and consequently identifies fugacity with pressure, i.e. the fugacity coefficient is set to unity. To account for non-ideal gas behaviour, the user has to calculate fugacity externally and provide this as input to the software. The software corrects $K_{\rm H,CO_2}$ according to T conditions by fitting to an analytical regression. Here, non-ideal behaviour was accounted for by the external calculation of the fugacity coefficient according to a pure CO₂ thermodynamic model of Duan et al. (1992).

Equilibrium constants of mineral dissolution/precipitation and aqueous complex production

The software TOUGHREACT corrects log(K _eq,min) values for temperature changes using an analytical expression (Eq. 3), in which a to e depict regression coefficients and TK the temperature in Kelvin:

$$ \hbox{log}(K_{\rm eq,min})(TK) = a*\hbox{ln}(TK) + b + c*TK + \frac{d}{TK} + \frac{e}{TK^2} $$

(3)

This calculation uses regression coefficients derived from equilibrium experiments at different temperature conditions. PhreeqC uses preferentially an analytical expression of a similar form. In cases where regression coefficients are available in the thermodynamic database, PhreeqC calculates T dependence applying the van’t Hoff equation (Eq. 4), where $\Updelta H$ (J mol⁻¹) is the reaction enthalpy and R (8.314 J mol⁻¹K⁻¹) the gas constant.

$$ \frac{\hbox{d\,ln}k_{H}}{\hbox{d}TK} = \frac{\Updelta H}{R*TK^2} $$

(4)

Neither the analytical approaches nor the van’t Hoff equation take pressure effects into account.

Kinetic rates and kinetic rate constant

TOUGHREACT uses a general form of rate law according to Lasaga et al. (1994) (Eq. 5):

$$ R = K_{\rm kin,min}*\hbox{SA}*\left(1-\frac{Q}{K_{\rm eq,min}}\right) $$

(5)

Therein, R (mol s⁻¹) is the kinetic rate, K _kin,min (mol m⁻² s⁻¹) is the kinetic rate constant, SA (m² g⁻¹) is the reactive surface area, Q(−) is the reaction quotient, and K _eq,min (−) is the equilibrium constant of the mineral–water reaction. The kinetic rate constant is calculated as the sum of various mechanisms (Eq. 6).

$$ \begin{aligned} K_{\rm kin,min} &= K^{\rm nu}_{25}*\left[\frac{-E_{a}^{\rm nu}}{R}*\left(\frac{1}{T}-\frac{1}{298.15}\right)\right]\\ &\quad + \Upsigma K^{i}_{25}*\hbox{exp}\left[\frac{-E_{a}^{i}}{R}*\left(\frac{1}{T}-\frac{1}{298.15}\right)\right]*\Uppi c_{ij}^{nij} \end{aligned} $$

(6)

In this equation, the superscript nu indicates a neutral mechanism, the subscript or superscript i indicates additional mechanisms (e.g. H⁺-driven, CO₂-driven), R (8.314 J mol⁻¹ K⁻¹) is the gas constant, E _a (J mol⁻¹) is the activation energy of a mechanism, c (mol kgw⁻¹) the concentration of respective reaction partners, and n (−) represents the reaction order of the respective species. The input parameters are taken from compilations of experimental data. The most commonly used database has been compiled by Palandri and Kharaka (2004), which has also been used for the calculations in this study. Note that with regard to the rate law, the dissolution and precipitation rate is assumed to be of the same magnitude, but of opposite sign, for a given state of disequilibrium.

The software PhreeqC has no kinetic rate law incorporated, but allows for a manual incorporation.

Equilibrium constants of sorption on mineral surfaces

The ion exchange calculation of TOUGHREACT version 1.2, which has been used for the multiphase-multicomponent simulations in this study, does not incorporate a correction for T and P. Recently, a surface complexation model for TOUGHREACT version 2.0 has been developed (Xu et al. 2011), however, its mathematical equations for the calculation have not been published.

PhreeqC calculates the T dependency preferentially according to an analytical expression similar to Eq. 3. If no regression coefficients are available for specific surface complexes or ion exchanges in the database, it uses the van’t Hoff equation (Equation 4). Currently, the thermodynamic databases of the software lack regression coefficients and reactions enthalpies. Neither the analytical approaches nor the van’t Hoff equation take pressure effects into account.