## 3 Results and Discussion
### Mathematical Model
2.1 The Effect of the Proportion of Nitrate Consumed by the Complete Reduction of Nitrogen to the Total Amount Consumed (d)  
It has been reported that microbial growth can consume from 5% to 8% of toluene, so it is assumed that the consumption of microbial growth is 6.5% in this section [45]. The temperature is assumed to be 20 \({}^{\circ}\mathrm{C}\), which combines the average groundwater temperature with the culture temperature of the bacteria used in this paper. If d is 0, there is no nitrite in the solution, and the nitrate entirely transforms into nitrogen (Equation (2)). As shown in Figure 2, carbon dioxide produced by toluene mineralization reacts with water, increasing the amount of hydrogen ions and producing a large amount of bicarbonate. The precipitation rate of calcium carbonate resulting from reaching the SI value is greater than the dissolution rate of calcium carbonate caused by increased hydrogen ions. This result is consistent with the study of [PERSON] et al. [10]. When d equals 0.5, half of the nitrate in the solution is reduced to nitrogen, while the remaining half is reduced to nitrite. The concentration of H\({}^{+}\) in the solution increases due to the production of carbon dioxide (Equations (12) and (13)) and the consumption of OH\({}^{-}\) (Equation (13)). Carbon dioxide produced by toluene mineralization reacts with water to increase the concentration of bicarbonate, which is the same as when d = 0. However, the precipitation rate of calcium carbonate in this state is higher than the formation rate, and the concentration of Ca\({}^{2+}\) increases. When d is 1, all the nitrate in the solution is converted to nitrite. The reduction of nitrate to nitrite neither consumes nor produces hydrogen ions. However, the carbon dioxide produced by the reaction increases the concentration of H\({}^{+}\) in the solution. Increased bicarbonate in solution makes the SI always greater than the solubility rate, and the Ca\({}^{2+}\) concentration decreases. It can be seen from the figure that when the reaction does not occur, the amount of each element in the solution is the same in the three cases. The mineralization of toluene increases the concentration of hydrogen ions to varying degrees, and the formation of carbon dioxide increases the concentration of bicarbonate. Depending on the reaction mechanism in the solution, the concentration of Ca\({}^{2+}\) varies with the proportion of nitrate consumed in the two-step reaction. Under natural practical conditions, the nitrite concentration in the solution is small, the reaction is less likely, and d = 0 occurs more often. 2.2 The Effect of the Proportion of Toluene Consumed by Microbial Growth on the Total Toluene Content (_f_)  
Mathematical models were created to illustrate the impact of microbial growth on CaCO\({}_{3}\), with diagrams presented in Figure 3 for levels of 0%, 4%, and 8%. Under natural practical conditions, nitrate is completely reduced to nitrogen, and it is assumed that d is 0 and the temperature is 20 \({}^{\circ}\)C.  
It can be seen that f has little effect on concentration, the consumption of toluene increases, and the concentrations of H\({}^{+}\), Ca\({}^{2+}\), and HCO\({}_{3}\)\({}^{-}\) decrease (Figure 3). The influence of microbial growth on calcium carbonate is mainly reflected in the fact that the more significant the consumption of microorganisms is, the smaller the amount of toluene used for the reaction. Figure 2: Variations in ion concentrations with the proportion of nitrate consumed by the complete reduction of nitrogen to the total amount consumed. (**a**) Variation in H\({}^{+}\) with toluene concentration; (**b**) variation in HCO\({}_{3}\)\({}^{-}\) with toluene concentration; (**c**) variation in Ca\({}^{2+}\) with toluene concentration.