## 2 Relevant Processes and Experimental Data
Thus, column #1 received 13 cell-suspension and mineralization-medium injections, while column #2 received 6 cell-suspension and 12 mineralization-medium injections. There were additional 15.52 h overnight resting periods after injections 4 and 8. The mineralization medium, together with the spacer solution, was stored inside the oven at 60 \({}^{\circ}\)C to minimize non-isothermal effects. The _S. pasteurii_ cell suspension was stored at room temperature, to minimize inactivation of cells and urease through prolonged exposure to high temperatures. Cell suspensions were injected without preheating into the tubing leading to the column. The tubing volume of the cell-suspension injection line was 54 mL, half of which was inside the oven, allowing some heating before the cell suspension entered the column. The minimum temperature measured with a thermocouple (OM-EL-USB-TC-LCD, OMEGA, Norwalk, CT, USA, with the probe THS-113-373-T-L, ThermoWorks, American Fork, UT, USA) at the column was 58 \({}^{\circ}\)C during the cell-suspension injection. The columns were constructed with two sampling ports at 10.16 cm and at 40.64 cm. Samples were taken during each batch period at 1, 15, 30, 60, and 120 min after each previous mineralization medium injection for column #1 (0.33 M) and at 1, 15, 30, 45, 60, 90, and 120 min for column #2 (0.66 M). Approximately 1 mL of sample was extracted using a syringe and needle and filtered through a 0.2 \(\upmu\)m filter. Sixty microliters (60 \(\upmu\)L) of each sample were transferred immediately into a centrifuge tube containing 540 \(\upmu\)L of 0.56 M H\({}_{2}\)SO\({}_{4}\) and stored at 4 \({}^{\circ}\)C to stop any ureolytic activity until analysis. All samples were analyzed for their urea and Ca\({}^{2+}\) concentrations using the colorimetric assays by [25; 26], for urea and calcium, respectively, modified as described in [27; 28]. At the end of the experiment, the column was destructively sampled by cutting it into twelve 2-inch sections. Triplicate samples of approximately 1 g of each section were digested with 10% trace-metal-grade nitric acid (Fisher, Fair Lawn, NJ, USA). The resulting Ca\({}^{2+}\) concentration of the solution was measured using the colorimetric assay [26], modified as described by [28]. The remaining solids after acid digestion were rinsed and dried to determine the mass of sand from which Ca\({}^{2+}\) had been dissolved. The experimental results are shown in Tables 1 and 2 and are available at [[https://darus.uni-stuttgart.de/dataverse/sfb1313_eicp_model_calibration](https://darus.uni-stuttgart.de/dataverse/sfb1313_eicp_model_calibration)]([https://darus.uni-stuttgart.de/dataverse/sfb1313_eicp_model_calibration](https://darus.uni-stuttgart.de/dataverse/sfb1313_eicp_model_calibration)). Enzymatic ureolysis is the driving force of EICP hydrolyzing urea. At typical environmental pH conditions, ureolysis produces bicarbonate (HCO\({}_{3}\)-) and ammonium (NH\({}_{4}\)+):  
\[(\mathrm{NH_{2}})_{2}\mathrm{CO}+3\,\mathrm{H_{2}O}\xrightarrow{\mathrm{ urease}}\mathrm{NH_{4}}^{+}+\mathrm{H_{2}NCOO}^{-}+2\,\mathrm{H_{2}O}\longrightarrow 2\, \mathrm{NH_{4}}^{+}+\mathrm{HCO_{3}}^{-}+\mathrm{OH}^{-} \tag{2}\]  
Due to the production of hydroxide (OH\({}^{-}\)), ureolysis leads to an alkalinization of the solution, as long as NH\({}_{4}\)+ is the dominant form in the Bronsted-Lowry acid-base pair with ammonia (NH\({}_{3}\)). \[\mathrm{NH_{3}}+\mathrm{H^{+}}\rightleftharpoons\mathrm{NH_{4}}^{+} \tag{3}\]  
Alkalinization increases the amount of carbonate (CO\({}_{3}\)2-) in the solution:  
\[\mathrm{H_{2}CO_{3}}\rightleftharpoons\mathrm{H^{+}}+\mathrm{HCO_{3}}^{-} \rightleftharpoons\mathrm{2\,H^{+}}+\mathrm{CO_{3}}^{2-} \tag{4}\]In the presence of Ca\({}^{2+}\), this increase in CO\({}_{3}\)\({}^{2-}\) leads to a supersaturation of calcium carbonate, promoting precipitation. Thus, when modeling EICP, the key issue is predicting the distribution of ureolytic activity within the porous medium, since urease is the main agent and the prerequisite for EICP.