## 2 Relevant Processes and Experimental Data  
Column experiment data are used for model calibration and validation using inverse modeling. The column studies were performed similar to those described for MICP in [21]. All columns were constructed from a polyvinyl chloride (PVC) pipe of 2.43 cm inner diameter and 61 cm length filled with 40 mesh quartz sand (0.5 mm effective filtration size, Unimin Corp., Emmet, ID, USA), packed under water, and vertically positioned. For the first column (#1), the mineralization medium included equimolar concentrations of urea and Ca\({}^{2+}\) at 0.33 M, which was doubled for the second column (#2, 0.66 M). The columns had initial pore volumes of 97.7 mL and 97.3 mL, respectively. Both columns were preheated to 60 \({}^{\circ}\)C by placing them in a temperature-controlled oven and kept in the oven for the course of the experiments. Sixty degrees Celsius was determined to be the temperature at which the optimal rate of ureolysis was achieved for the bacterial and plant-based sources of urease under conditions similar to those in the column experiment [22; 23]. This temperature is a compromise between a fast ureolysis rate and a relatively low urease inactivation rate, both rates increasing exponentially with temperature according to an Arrhenius-type relationship. A temperature of 60 \({}^{\circ}\)C thus maximizes the ureolytic activity in the experimental column. _S. pasteurii_ cells were used as the source of urease; the bacterial cells became thermally inactivated quickly at 60 \({}^{\circ}\)C and were not culturable on agar plates. This is in agreement with other reports of _S. pasteurii_ not being able to grow above 40 \({}^{\circ}\)C [24]. However, while plant-based and _S. pasteurii_ ureases are inactivated at 60 \({}^{\circ}\)C, the inactivation is slow enough to allow for significant ureolysis to occur [22; 23]. Thus, ureolysis in this experiment was catalyzed predominantly by the residual urease of the inactivated cells, while initially, to some extent, living-cell urea hydrolysis might have occurred although that was not measured. The injection strategy for column #1 consisted of a two-pore-volume injection of _S. pasteurii_ cell suspension with an optical density (OD) of 0.85 \(\pm\) 0.01 at 600 nm wavelength (OD 600 nm), measured in 96-well flat-bottom plates using 200 \(\mu\)L of culture volume (the background blank was OD 600 nm = 0.04). An OD 600 nm of 0.85 \(\pm\) 0.01 was found to be equivalent to biomass concentrations of 0.93 \(\pm\) 0.02 g/L cell dry weight, determined through filtration of a cell suspension in triplicate, rinsing with sterile water and drying to constant weight at 45 \({}^{\circ}\)C. The cell suspension of OD 600 nm = 0.85 hydrolyzed 90%of urea from the mineralization solution within 45 min at 60 \({}^{\circ}\)C for the urea concentrations used in the experiments, while at 30 \({}^{\circ}\)C, 240 min was required. Cell-suspension injection was followed by 10 mL of a spacer solution of 10 g/L NH\({}_{4}\)Cl and a two-pore-volume injection of mineralization medium with a 0.33 molar concentration of urea and calcium. For column #2, the injection strategy was similar to that of column #1 but _S. pasteurii_ cell suspension and spacer were injected only before every odd-numbered mineralization-medium injection for which the concentration was doubled to 0.66 M. The flow rate was for both columns 54.4 mL/min = 9.06667 \(\times 10^{-7}\) m\({}^{3}\)/s from bottom to top. Each sequence of media injection was followed by a two-hour batch period without injection, after which the injection sequence was repeated for a total of 13 times for column #1 and 12 times for column #2. For column #2, the full injection sequence of cell suspension, spacer, and mineralization medium was injected only during the odd-numbered injections. During the even-numbered injections, only the mineralization medium was injected into column #2.