## 2 Materials and Methods
### Model Validation  
#### 2.2.1 The Validation Experiment  
1. Toluene biodegradation enrichment cultures  
The enrichment culture microorganisms originated from groundwater in a Chinese cooking plant.  
Microcosms were set up using 280 mL air-tight bottles. Each microcosm contained 225 mL of sterilized basic culture medium, 25 mL of bacterial solution, and 0.0175 g of CaCO\({}_{3}\) to simulate the carbonate environment. The bacterial culture medium was modified from a recipe developed by [PERSON] [38]. The basic culture medium was prepared according to the following compositions (per liter): KNO\({}_{3}\), 80 mg; KH\({}_{2}\)PO\({}_{4}\), 0.50 mg; K\({}_{2}\)HPO\({}_{4}\) 3H\({}_{2}\)O, 1.00 mg; MgSO\({}_{4}\), 1.00 mg; mineral solution, 0.10 mL; and vitamin solution, 0.20 mL. The components of the vitamin and mineral solutions are shown in Tables 1 and 2. Then, the bottles were autoclaved at 121 \({}^{\circ}\)C for 30 min to prevent biological activity. The medium was purged with nitrogen to remove oxygen, and the air-tight bottles were sealed with a halogenated butyl rubber stopper to ensure their air tightness. Furthermore, toluene was added to each bottle to form 0.1 mmol/L toluene solution. Three parallel controls were established for the blank and experimental groups. In the sterile controls, the bacterial solution was replaced with purified water. All of the microcosms were stored in a biochemical incubator at 20 \({}^{\circ}\)C. On days 1, 2, 4, and 8, water samples were collected from each microcosm for analysis. Sampling procedures were accomplished under strictly anaerobic conditions. As CaCO\({}_{3}\) is an insoluble impurity in water, it was difficult to observe, and there were no other calcium inputs in the system, so the concentration of Ca\({}^{2+}\) was used to characterize the dissolution and precipitation of calcium carbonate. To evaluate the carbonate dissolution/precipitation via biodegradation, the consumption of Ca\({}^{2+}\), HCO\({}_{3}\)\({}^{-}\), NO\({}_{3}\)\({}^{-}\), and NO\({}_{2}\)\({}^{-}\) was continuously measured during the entire experimental period.  
2. Physical and chemical parameter analyses The toluene samples were analyzed by headspace-based gas chromatography (Nexis GC-2030, Shimadzu, Japan) carried out on an automated headspace sampler (HS-10, Shimadzu, Japan). Headspace operating conditions were as follows: low shaking of the tested sample solution at 35 \({}^{\circ}\)C for 2 min, GC cycle time of 25 min, and vial pressurization time of 0.1 min. The gas chromatograph was equipped with a capillary column (HP-5, Shimadzu, Japan) and a flame ionization detector (FID). The injector, detector, and column temperatures were held at 150, 200, and 100 \({}^{\circ}\)C, respectively. Air and hydrogen served as fuel gases for the FID. Nitrogen served as a carrier gas, and the flow rate was 40.1 mL/min. The pH value was measured with a portable pH meter (portable pH meter pH30, CLEAN, Sherman Oaks, CA, USA), and the Ca\({}^{2+}\) and HCO\({}_{3}\)\({}^{-}\) concentrations were measured via titration. The NO\({}_{2}\)\({}^{-}\) and NO\({}_{3}\)\({}^{-}\) concentrations were analyzed according to the International Organization for Standardization ISO 10304-1 [39] with an ultraviolet spectrophotometer (UV-2550, Shimazu, Japan).