## 5 Results
Even in the sorption-coefficients-only case, \(k_{\text{a}}=3.993\times 10^{-2}\)1/s is only slightly lower than the lower limit of the confidence intervals of the calibrations set, adding either the injected concentrations or the \(f_{\text{pKa}}\) to the calibration parameters. Figure 4: Predicted volume fractions of final calcite for the model calibration attempts compared to the experimental data for column experiment #1 (0.33 M mineralization medium concentration) for the four parameter sets fitted: The error bars represent the standard deviation calculated from triplicate measurements. Note that the calcite volume fraction was not used for calibration. In contrast, \(k_{\text{d}}\) is not a reliably estimated parameter. It changes orders of magnitudes from one set of calibration parameters to another, being estimated to being as low as \(k_{\text{d}}=8.230\times 10^{-13}\)1/s for the sorption-coefficients-only case or as high as \(4.534\times 10^{-10}\)1/s for the case with the sorption coefficients and the urease activity fitted. Additionally, in all sets of calibration parameters, its confidence intervals are one or more orders of magnitude larger than the estimated value itself, resulting also in unrealistic, negative lower limits of the confidence intervals. The confidence intervals of the concentration estimates are also quite narrow with the estimated value \(\pm 4.1\%\) for the urea and \(\pm 5.2\%\) for the calcium injection concentration, making them relatively confidently estimated parameters. The estimated ureolytic activity coefficient \(c_{\text{u,0}}^{\text{e}}=532.71\) m\({}^{3}\)/kg\({}_{\text{s}}\) appears less reliable than the concentration estimates with the 95% confidence limits of 467.77 m\({}^{3}\)/kg\({}_{\text{s}}\) and 597.64 m\({}^{3}\)/kg\({}_{\text{s}}\) being at \(\pm 12\%\). The ureolytic activity coefficient estimated from batch experiments is with 462.74 only slightly lower than the lower 95% confidence limit. The multiplier to the apparent pKa, \(f_{\text{PKa}}\), is not very reliably estimated, as the the 95% confidence limits span from 0.851494 to 1.54851. Considering the logarithmic scale, the estimated multipliers for those limits to the actual apparent dissociation constant of ammonium and ammonia span from 0.71 to 3.54, resulting in a decrease of Ka by 29% or an increase by 254%, respectively. Table 2 provides for all parameter calibration attempts the correlations of the estimated parameters as given by the PEST protocol [58]. The ad- and desorption rate coefficients \(k_{\text{a}}\) and \(k_{\text{d}}\) are not strongly correlated for any of the sets of fitted parameters. Some correlation between the ad- and desorption rate coefficients might be expected as they both determine the amount of adsorbed urease which, by its ureolytic activity, is the main driver of the overall induced CaCO\({}_{3}\) precipitation reaction. Thus, a high adsorption rate coefficient might be offset by a correspondingly high desorption rate coefficient. When adding calibration parameters other than the ad- and desorption rate coefficients, \(k_{\text{d}}\) correlates less with the other parameters than \(k_{\text{a}}\), but even \(k_{\text{a}}\) reaches a maximum at a correlation of 0.743 to the ureolytic activity, when the ureolysis activity coefficient \(c_{\text{u,0}}^{\text{e}}\) is added to the set of fitting parameters. All other parameter correlations are less than 0.5, with the second strongest parameter correlation being 0.424 for the correlation between \(C_{\text{Ca}^{2+},\text{inj}}\) and \(C_{\text{urea,inj}}\) in the parameter set with the injection concentrations being added into the set of calibration parameters. This indicates that our model calibration is not overparameterized and that the chosen calibration parameters are independent of each other.