## 5 Results
The injection concentrations are estimated as \(C_{\text{Ca}^{2+}\text{inj}}=10.64\) g/L and \(C_{\text{urea,inj}}=20.31\) g/L, which is, for calcium, only 80% of the prepared 0.33 M mineralization medium and, for urea, 101.5% of the nominal concentration of the 0.33 M injection solution (\(C_{\text{Ca}^{2+}\text{,prep}}=13.3\) g/L, \(C_{\text{urea,prep}}=20.0\) g/L). The reduction in the estimated calcium concentration is approximately the residual calcium concentration predicted in the model in the case where only the ad- and desorption rate coefficients were fitted; see Figures 2 and 3. Figure 3: Comparison of the results of the model calibration attempts to the concentration measurements at 40.64 cm from the inlet for column experiment #1 (0.33 M mineralization medium concentration). Figure 2: Comparison of the results of the model calibration attempts to the concentration measurements at 10.16 cm from the inlet for column experiment #1 (0.33 M mineralization medium concentration). For the case with the ureolytic activity \(c_{\text{u,0}}^{\text{e}}\) added to the set of fitting parameters, the adsorption rate coefficient increased by 8.2% to \(k_{\text{a}}=4.471\times 10^{-2}\)1/s and the desorption rate coefficient increased by orders of magnitude to \(k_{\text{d}}=4.534\times 10^{-10}\)1/s. The estimated ureolytic activity of the crude urease injected was with \(c_{\text{u,0}}^{\text{e}}=532.71\) m\({}^{3}\)/kg\(\,\)s, only 13% larger than the 462.74 m\({}^{3}\)/kg\(\,\)s determined in the kinetics batch experiments [23]. Including the multiplier \(f_{\text{pKa}}\) to the pKa value to the set of calibration parameters resulted in the adsorption rate coefficient increasing by 8.6% to \(k_{\text{a}}=4.360\times 10^{-2}\)1/s. The desorption rate coefficient increased by more than one order of magnitude to \(k_{\text{d}}=1.874\times 10^{-11}\)1/s. The multiplier was determined to be \(f_{\text{pKa}}=1.2\), the upper limit set in the calibration, implying that the combination of the relations by [51; 52] for the apparent pKa underestimates the pKa. \(f_{\text{pKa}}=1.2\) resulted in an increase of the dissociation constant Ka by 58%. The upper limit was chosen to allow for a significant change in Ka values. When comparing an extrapolation of the relation of [52] for zero salinity at 60 \({}^{\circ}\)C (pKa = 8.15) with the relation of [51] at 60 \({}^{\circ}\)C (pKa = 8.28), the difference in the predicted pKa was 0.13, resulting in a factor between both relations of 1.016. The limit set for the \(f_{\text{pKa}}=1.2\) thus allows for a more than an order of magnitude larger change of the pKa than the difference between the two relations as an estimate of the potential error. This model calibration suggests that the equilibrium between ammonium and ammonia is shifted by 0.2 pH units. As far as its impact on the conceptual model is concerned, this results in predicting that most ammonia produced by ureolysis will be converted to ammonium, consuming H\({}^{+}\) and creating calcium-carbonate precipitating conditions with less urea hydrolyzed, even at 60 \({}^{\circ}\)C. In a model calibration without setting an upper limit to \(f_{\text{pKa}}\) (not shown here) it was estimated to a completely unrealistic value of 1.86, increasing the Ka by six orders of magnitude. During none of the other model calibrations, a parameter reached the upper or lower bounds set; see Table 10 for the values set as bounds and the initial guesses of the parameter values. The fitted parameter values of all calibration attempts and the associated 95% confidence intervals estimated by the PEST protocol [58] are summarized in Table 1. For the adsorption rate coefficient, the 95% confidence intervals are narrow, around the estimated value \(\pm\)10%, for all sets of calibration parameters. Also, except for the base case with the sorption coefficients only fitted, the estimated \(k_{\text{a}}\) values are within the confidence intervals of the other calibration-parameter sets.