# Study of the Dynamic Adaptive Calculation Method for River Water Environmental Capacity
## 3 Methodology
### Dynamic Adaptive Calculation Method for Water Environmental Capacity
#### 3.2.2 Calculation Model and Method  
1. Water environmental capacity calculation model
2. Section-beginning control model [(1)]  
The \"section\" in the section-beginning control refers to the river segment located between any two sewage outlet sections along the river, while the section-beginning refers to the first sewage outlet section located upstream of each section. It calculates the WEC, that is, based on the division of each section within a functional area (Figure 3), the water quality of the upstream section is controlled to meet the requirements of the functional area. Because the section-beginning control model ensures that the water quality of the entire river reaches the standard, it is suitable for areas with higher water quality requirements or lower pollution levels. At the beginning of the functional section, owing to the difference between the water quality standard of the functional area and the pollutant concentration of the incoming water, the dilution capacity of the incoming water is provided, as follows:  
\[W_{0}=Q_{0}(C_{s}-C_{0}) \tag{1}\]  
where \(W_{0}\) is the dilution capacity at the beginning of the functional segment, \(t/d\); \(C_{s}\) is the water quality standard for functional section, mg/L; \(Q_{0}\) is the incoming water flow, m\({}^{3}/s\); and \(C_{0}\) is the COD concentration of incoming water, mg/L. Since the water quality standard is controlled at the beginning of each section, after a period of degradation, the degradation amount at the end of a section is the WEC at the section. Then, the WEC at the \(i\) control section is as follows:  
\[W_{i}=(Q_{i}+q_{i})C_{s}-Q_{i}C_{s}f(x_{i}-x_{i-1}) \tag{2}\]  
where \(W_{i}\) is the WEC at the \(i\) section, \(t/d\); \(q_{i}\) is the sewage discharge at the \(i\) section, m\({}^{3}/s\); and \(Q_{i}\) is the main flow after mixing. Therefore,  
\[W=W_{0}+\sum_{i=1}^{n}W_{i} \tag{3}\]  
Organize the formula, as follows:  
\[W=Q_{0}(C_{s}-C_{0})+\sum_{i=1}^{n}C_{s}\bigg{[}Q_{i}\bigg{(}1-\exp\frac{K_{1 }x_{i}-K_{1}x_{i-1}}{u}\bigg{)}+q_{i}\bigg{]} \tag{4}\]  
2. Standard model  
The WEC was calculated according to the one-dimensional water quality model of a river given in the \"Water Environmental Capacity Calculation Regulations\" (GB/T 25173  
Figure 3: The division of each segment in the functional section. 2010) [43] promulgated by the People's Republic of China in 2010. The concentration of pollutants in a river section is as follows:  
\[C_{x}=C_{0}\exp\left(-K\frac{x}{u}\right) \tag{5}\]  
where \(C_{x}\) is the pollutant concentration after flowing through \(x\) distance, mg/L; \(x\) is the longitudinal distance along a river, m; \(u\) is the average velocity of the channel section under the design flow, m/s; \(K\) is the pollutant comprehensive attenuation coefficient, 1/s; and \(C_{0}\) is the concentration of pollutants in the initial section, mg/L. Its water environmental capacity is as follows:  
\[W=(C_{s}-C_{x})\big{(}Q+Q_{p}\big{)} \tag{6}\]  
where \(Q_{p}\) is the discharge flow of waste water, m\({}^{3}\)/s and \(Q\) is the inflow flow of the initial section, m\({}^{3}\)/s. (3) Section-end control model [42]  
The section-end control model is actually for the control of the water quality of the downstream section and the maximum discharge of the upstream pollution sources, but it is necessary to clarify each sewage outlet in advance. Figure 4 shows the model diagram. In the figure, \(C_{0}\) and \(Q_{0}\) are the concentration and discharge of water quality in the upper reaches of the river reach, respectively; \(C_{p}\) and \(Q_{p}\) are the concentration and discharge of sewage at the sewage outlet, respectively; \(C^{{}^{\prime}}\) is the concentration of pollutants after mixing; and \(C\) is the concentration of pollutants in the downstream section at the distance from the sewage outlet.