# Integrating Process Re-Engineering Models in Cement Production to Improve Energy Efficiency
## 2 Materials and Methods
### Model Formulation  
Modelling of Kiln System  
The kiln system was modelled using MATLAB 2024a and Simulink 10.7. The primary objective was to maintain the kiln temperature at 1450 \({}^{\circ}\)C, which is the optimal level for clinker production. The model incorporated a feedback loop that continuously monitored the actual temperature from the plant and accounted for heat loss dynamics, ensuring stable kiln operation. As shown in Equation (1), the model was built on the basis of using a proportional-integral-derivative (PID) controller to control the kiln. The PID controller is composed of proportional, integral, and derivative components. The equation describes the ability of the PID controller to adjust the heat input of the kiln based on the real-time error, therefore managing temperature fluctuations, responding quickly to disturbances and enhancing both process stability and energy efficiency [35; 36; 37]. \[u(t)=K_{p}e(t)+K_{i}\int_{0}^{t}e(\tau)dt+K_{d}\frac{de(t)}{dt} \tag{1}\]  
where \(K_{p}\) is the proportional gain, \(K_{i}\) is the integral gain, \(K_{d}\) is the derivative gain, and \(e(t)\) is the error at time \(t\). Transfer functions were used to simulate the dynamic responses of the burner and kiln, while heat loss to the environment was included as a major factor affecting energy \begin{table}
\begin{tabular}{l c c} \hline \hline
**Parameters and Issues Associated with Energy Loss** & **Plant A** & **Plant B** \\  & **(MJ/t)** & **(MJ/t)** \\ \hline Flue gas temperature leaving the Kiln (FgTK) & 700 & - \\ Clinker discharge temperature (CDT) & 460 & - \\ Flue gas Temperature at the recovery point (FgTR) & 350 & 331.4 \\ Overload flue gas Temperature (OFgT) & 305.5 & 305.5 \\ Leakage in the kiln shell (LR) & 66.2 & - \\ Thermal conductivity of kiln shell insulation (TcKs) & 4.87 & - \\ Excess air ratio (EuR) & 2.5 & - \\ Tertiary air duct dumper temperature (TaDT) & - & 803 \\ Cooler air exhaust temperature (CaET) & - & 326.4 \\ Discharge temperature from the cooler (DPC) & - & 66.2 \\ Leakage rate false air (LFa) & - & 4.87 \\ Others & - & 2.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Factors contributing to energy losses in clinker production. efficiency. As shown in Figure 1, the model includes a total heat detector to monitor both generated and lost heat and a controlled heat detector to track heat regulated by the PID controller. Operating in a closed-loop mode, the PID controller continuously adjusts to minimise error and maintain the desired kiln temperature [37]. Several assumptions were made to simplify the analysis and calculations for the modelling of the kiln system. The specific heat of the reaction was assumed to be constant and independent of temperature along the axial direction. Similarly, shift and diffusion coefficients were considered independent of temperature. The damper was considered constant, as only the valve controls flow. The thermal conductivity of the refractory lining of the kilns was assumed to be 0.74 \(\mathrm{W/m/^{\circ}C}\), the metallic wall's conductivity was assumed to match that of alloyed carbon steel at 45 \(\mathrm{W/m/^{\circ}C}\), and the thermal capacitance of the kiln was assumed to be 26.17 \(\mathrm{kWh/^{\circ}C}\). The heating zone for kilns in both Plants A and B was assumed to be at 1450 \(\mathrm{\SIUnitSymbolC}\), with the clinker density at this temperature being 1415 \(\mathrm{kg/m^{3}}\). The kiln length from Plant A is 70 m and 62.5 m for Plant B. _i._ _Convetion Heat Transfer for the burner_  
The heat transfer between the burner and the metal surface of the kiln was calculated using the principle of energy conservation shown in Equation (2). \[q_{in}-q_{out}=\frac{d\theta}{dt}\rho Vc \tag{2}\]  
where \(q_{in}\) is the inlet temperature, \(q_{out}\) is the outlet temperature, \(\rho\) is the density of air, \(V\) is the volume, and \(c\) is the specific heat capacity.