## 6 Discussion  
We used heat-inactivated cells as a urease source in this study. Since it is not yet completely clear whether the urease stays within the heat-inactivated cells or is released over time, its transport behavior cannot be exactly modeled and might be influenced by reversible and irreversible sorption. We are modeling EICP on scales larger than the molecular scale; thus, the exact state of urease within cells attached to cell residues, suspended, or absorbed is not of as much relevance for the model as the amount of urease within each control volume. Additionally, several processes could lead to changing apparent bulk ureolytic activity; e.g., sorbed urease might exhibit different activities or, when urease is released from cells, the apparent bulk ureolytic activity might rise as the limiation due to transport of urea across the cell membrane is removed. As the distribution of urease is not known for the EICP experiments, direct validation of the urease transport modeling is not possible. However, the in situ measurements of urea and Ca\({}^{2+}\) in the column experiments allow an indirect evaluation of the model's capabilities in predicting the urease distribution by comparing predicted and measured concentrations resulting from the ureolytic activity. Once more is known about the actual state and distribution of urease in porous media, the use of more complex and more specific sorption kinetics might be justified, e.g., as in [38, 39], and might lead to better model predictions. All model calibration attempts result in a crude urease adsorption rate coefficient of \(k_{\text{a}}\approx 4.3\times 10^{-2}\,\
icefrac{{1}}{{s}}\) and a crude urease desorption rate coefficient of \(k_{\text{d}}<4.534\times 10^{-10}\,\
icefrac{{1}}{{s}}\), indicating that the crude urease adsorbs mainly irreversibly to the solid surfaces. Furthermore, \(k_{\text{d}}\) has wide confidence intervals, indicating a low model sensitivity to this parameter. Thus, for all investigated sets of calibration parameters, the desorption of crude urease is likely not significant, at least for the conditions and on the spatial scale of the column experiment used to fit the model. For conditions close to clogging, mechanical detachment of urease might remain a relevant process. The remaining residuals for the concentration data of column #1 (see Figures 2 and 3) can to some extend be reduced by increasing the number of fitting parameters (see Table 3). This reduction is mainly due to a reduction in the residuals for the calcium concentrations. The residuals of the urea concentrations remain more or less unchanged, no matter which of the parameter sets is being fitted. Some of these residuals might be caused by the rapid ureolysis rates occurring at 60 \({}^{\circ}\)C. An experiment was conducted. Due to the high reaction rates, small deviations in sampling time might have led to significant differences in measured concentrations. Contrary to the findings in [21, 59] for MICP and EICP, respectively, adding the urease activity to the calibrated parameters resulted in a ureolytic activity approximately equal to the activity determined in batch experiments [22, 23]. This is interesting information supporting the use of kinetic rate equations determined in batch experiments for modeling reactive transport in porous media. The amount of precipitated CaCO\({}_{3}\) in the model seems plausible between 61% and 69% of the amount that could theoretically be precipitated based on the injected calcium. In the experiment however, only 34% of the injected calcium could be detected as CaCO\({}_{3}\). It might be that some of the CaCO\({}_{3}\) precipitated in the experiment was only loosely attached to the solid matrix or suspended long enough to be flushed out of the columns by the following injections or partly redissolved during the urease- and spacer-solution injections. In the model, it is assumed that all precipitated calcite is immobile. Potential transport of suspended precipitates is not included in the model.