## 2 Analysis of the Potential for the Increase in Yeast Production and Results
\(S_{12}\), the \(S_{9}\) stream of process wastewater (directed to AF) diluted by \(S_{10}\) or \(S_{11}\) stream;  
\(S_{13}\), stream of pollutants from the ES (\(F_{p}\) fertilizer). The stream \(S_{9}\) [m\({}^{3}\)/yr] of process wastewater (Figure 1B) directed to the AF can be described as Equation (1)  
\[S_{9}=S_{1}+S_{4}+S_{5}+S_{7}-S_{8}. \tag{1}\]  
The \(S_{9}\) stream (Figure 1B) is averaged in the tanks of wastewater equalization. The nitrogen concentration (the analysis is based on nitrogen concentration) in the \(S_{9}\) stream can be described by Equation (1a):  
\[S_{9}C_{9}=S_{1}C_{1}+S_{4}C_{4}+S_{5}C_{5}+S_{7}C_{7}-S_{8}C_{8}, \tag{2}\]  
where \(C_{i}\) is the concentration of nitrogen in the stream \(S_{i}\) [kg/m\({}^{3}\)]. The stream (\(S_{8}\)) that is routed to WWTP is very small; however, it is needed for the adequate performance of micro-organisms in the WWTP. For this reason, it was neglected in the computations. Hence, the equation in 1a assumes the form  
\[S_{9}C_{9}=S_{1}C_{1}+S_{4}C_{4}+S_{5}C_{5}+S_{7}C_{7}. \tag{3}\]  
The concentration of pollutants in the \(S_{9}\) stream can be described as  
\[S_{9}=\frac{S_{1}C_{1}+S_{4}C_{4}+S_{5}C_{5}+S_{7}C_{7}}{C_{9}}, \tag{4}\]  
assuming that (taking into account that the \(S_{9}\) stream is omitted)  
\[S_{9}=S_{1}+S_{4}+S_{5}+S_{7}. \tag{5}\]  
The stream \(S_{12}\) is the stream \(S_{9}\) diluted by the \(S_{10}\) or \(S_{11}\) stream. Therefore, the amount of nitrogen in the \(S_{12}\) stream (directed to the AF) is equal to the amount of nitrogen in the \(S_{9}\) stream. The amount of nitrogen (deposited into the AF) is limited by the Regulation of the Minister of Environment of 16 November 2014 (on the conditions to be met when introducing wastewater into waters or into the ground, and on substances particularly harmful to the aquatic environment) and by the Directive 2010/75/EU of 24 November 2010 on the industrial emissions (integrated pollution prevention and control) [25; 26]. The analyzed yeast factory meets all Polish and EU standards for the amount of nitrogen deposited into the AF. Due to the high nitrogen pollution of the soils and the waters, an increase in yeast production is possible only if all the standards are met [24; 25; 26]. However, within these regulations, it is possible to control this parameter according to, for example, the kinds of plants grown on the AF. The \(D_{WW}\) dose (of the process wastewater) that can be utilized on the one hectare of AF (depending on the \(C_{N}\) nitrogen concentration) can be determined from Equation (6) [15; 16]  
\[D_{WW}=\frac{p_{N}\cdot k_{dN}}{C_{N}\cdot k_{uN}\cdot E_{N}}, \tag{6}\]  
where  
\(D_{WW}\) is the maximum dose of the process wastewater which can be directed to the AF [m\({}^{3}\)/ha\(\cdot\)yr]; \(p_{N}\) is the total nitrogen demand for the plants which are cultivated on the AF [kg/ha\(\cdot\)yr]; \(k_{dN}\) is the total nitrogen demand factor (if the AF are fertilized by only the process wastewater, \(f_{N}=1\));  
\(C_{N}\) is the total nitrogen concentration in the process wastewater directed to the AF [kg/m\({}^{3}\)];  
\(k_{uN}\) is the total nitrogen utilization factor (depending on the irrigation system); and  
\(E_{N}\) is the nitrogen fertilizer equivalent (for process wastewater from yeast production, \(E_{N}=1\)). The volume of nitrogen, \(m_{NAF}\), which can be deposited on the AF, can be defined as  
\[m_{NAF}=D_{WW}\cdot C_{9}, \tag{7}\]where  
\(m_{NAF}\) is the amount of nitrogen which can be deposited into the AF [kg/ha-yr], and  
\(C_{9}\) is the concentration of nitrogen in stream \(S_{9}\) [kg/m\({}^{3}\)]. The yeast production volume, \(Y_{p}\), is limited by the amount of nitrogen [Mg/yr]  
\[Y_{p}=\frac{A_{AF}\cdot m_{NAF}}{m_{NPY}}, \tag{8}\]  
where  
\(A_{AF}\) is the area of the AF [\(ha\)], and \(m_{NPY}\) is the amount of nitrogen in the process wastewater stream (directed to the AF) per 1 Mg of yeast production [kg/Mg].