## 3 Results and Discussion
### Fitting Results  
The analysis of the experimental results related to toluene mineralization presented in Figure 6 indicates that nitrate concentrations decreased with the increasing amount of toluene degraded. The figure shows that toluene was reduced by 0.02 mmol/L on the first day, suggesting that after domestication, the microorganisms quickly adapted to the experimental environment. The adaptation period of microorganisms in this study was much shorter than that in other studies. Toluene decreased gradually with time. It was degraded by more than 80% on the fourth day of the experiment and was approximately fully degraded within eight days. The figure shows that the concentration of NO\({}_{3}\)\({}^{-}\) decreased gradually with time and was degraded by more than 80% on the fourth day of the experiment. The formation of NO\({}_{2}\)\({}^{-}\) was observed as a temporary phenomenon. According to [PERSON], [PERSON], a similar phenomenon was observed and was called a respiratory pattern [46]. The CO\({}_{2}\) resulting from the complete degradation of toluene reacts directly with CaCO\({}_{3}\) and water in the following reactions:  
\[\text{CaCO}_{3}+\text{CO}_{2}+\text{H}_{2}\text{O}=\text{Ca(HCO}_{3})_{2} \tag{23}\]  
Figure 5: Variation in ion concentration with the milligram equivalent of other ions. (**a**) Variation in H\({}^{+}\) with toluene concentration; (**b**) variation in HCO\({}_{3}\)\({}^{-}\) with toluene concentration; (**c**) variation in Ca\({}^{2+}\) with toluene concentration. If the above reaction occurs, the magnitude of the change in HCO\({}_{3}\)\({}^{-}\): Ca\({}^{2+}\) should be 2:1. A graph of the amount of change in the concentration of HCO\({}_{3}\)\({}^{-}\): Ca\({}^{2+}\) during the experiment is shown in Figure 7. The slope of the plot is 5.29, and the ratio of the change in the HCO\({}_{3}\)\({}^{-}\) concentration to the change in the Ca\({}^{2+}\) concentration is much greater than 2:1. This image also shows that mineralization promotes the increase in HCO\({}_{3}\)\({}^{-}\) concentration. To determine the degradation process of toluene and nitrate in the system, the theoretical and practical correspondence between toluene and nitrate was calculated using the following formula. The consumption of NO\({}_{3}\)\({}^{-}\) was equal to the concentration of the experimental group NO\({}_{3}\)\({}^{-}\) plus the reduction of the experimental group NO\({}_{3}\)\({}^{-}\). The consumption of NO\({}_{3}\)\({}^{-}\) and the residual amount of NO\({}_{3}\)\({}^{-}\) were measured, and the reduction of NO\({}_{3}\)\({}^{-}\) was calculated. Actual toluene consumption versus theoretical consumption is shown in Figure 8. The slope between the theoretical and actual consumption of toluene is  
Figure 6: Variations in toluene, nitrate, and nitrite concentrations with toluene degradation. Values represent mean values and the \(\pm\) range from three independent samples. Figure 7: Ca\({}^{2+}\) vs. HCO\({}_{3}\)\({}^{-}\) production for experiments in which calcite was the solid phase. 0.93, which indicates that the degradation roughly followed Equations (12) and (13), which would satisfy the presupposition of the model. Based on the results shown in Figures 6-8 and the physics models introduced earlier, it is necessary to fit the models' equations to the experimental data. The parameters of the model were set as follows:  
The ratio for both nitrate and nitrite at each monitoring time was calculated. Because the proportion of toluene consumed by microbial growth compared to total toluene content (f) has little influence, the median of 6.50% was substituted into the model calculation. According to the experimental design, V was 280 mL, Va was 250 mL, and T was 20 \({}^{\circ}\)C.  
The SSE, MSE, and RMS error of the Ca\({}^{2+}\) concentration of the theoretical model and the experimental model were calculated and were 3.15 \(\times\) 10\({}^{-9}\), 6.31 \(\times\) 10\({}^{-10}\), and 2.51 \(\times\) 10\({}^{-5}\), respectively.