1. Introduction
The strengthening of energy conservation and emission reduction in enterprises with high-energy-consumption has been raised to new heights due to the goal of achieving carbon peaking and carbon neutralization [
1]. The circulating cooling water system (CCWS) is an important auxiliary system in industrial production. Its energy consumption can reach 20–30% of the total energy consumption of the production process [
2], and the consumption of cooling water can account for 70–80% of total industrial water [
3,
4]. Many studies have been conducted to reduce the energy use in CCWS. However, frequent changes in ambient temperature and working medium flow increase the difficulty of CCWS management and control, and this situation seriously affects the long-term efficient operation of the system. Therefore, studying the impact of changes in ambient temperature and working medium flow on the operation cost of CCWS is crucial.
With regard to reducing energy use in CCWS, early researchers mainly optimized the design of the heat exchanger and water pump networks by using pinch point technology and the mathematical programming method. At the end of the 1970s, Professor Bodo Linnhoff and his colleagues at the University of Manchester in the UK proposed a comprehensive design technology for the heat exchange network, namely, pinch point technology [
5]. This technology divides a system into two subsystems separate from each other in terms of thermodynamics. The system above the pinch is regarded as a heat sink system, and the system below the pinch is considered a heat source system. The minimum utility consumption of the heat exchange network can be obtained through this method. However, optimal design of the heat exchange network structure guided by pinch point technology may increase the network pressure drop. Polley pointed out that a network layout with reduced system flow but increased pressure drop is likely to deviate from the optimal condition [
6]. Therefore, other scholars who applied pinch point technology began to consider network pressure drop in their design [
7,
8,
9]. However, due to the limitations in the dimension of the graphical method, pinch point technology still cannot deal with multi-parameter complex problems effectively.
In recent years, a network configuration with an auxiliary pump and turbine has been applied to CCWS. The auxiliary pump is installed on the branch of the high-level heat exchanger to reduce the head of the main pump [
10,
11,
12], and the turbine is installed on the return pipeline to recover the excess pressure energy of the system [
13,
14,
15]. Ma et al. [
13] showed that the structure with main and auxiliary pumps and turbines is the most energy-saving and cost-saving configuration. Solving the optimal network structure of the pump and turbine is a mixed-integer nonlinear problem [
16]. In a system with large fluctuation of the working medium flow, obtaining the global optimal solution based on the existing mathematical programming method is difficult.
Several scholars have considered the cooling tower when studying the overall modeling of a system. In 2003, Kim and Smith [
17] established an overall optimization model of CCWS on the basis of the superstructure method. The superstructure method for modeling can use network structure information as a variable of the system model, thus making the model easy to apply to other complex systems. Subsequently, the authors in [
18,
19,
20] proposed different CCWS overall optimization models on the basis of the methods of Kim and Smith. The authors in [
17,
18,
19,
20] considered the thermodynamic and hydraulic coupling of the cooling tower, pump, and heat exchanger units but did not describe the impact of ambient temperature and working medium flow changes on system operation.
With regard to the impact of ambient temperature change on CCWS, researchers have devoted much attention to the effect on the performance of the cooling tower unit. A wet cooling tower is often used in CCWS because its heat transfer efficiency is higher than that of a dry cooling tower [
21]. Muangnoi [
22] conducted an exergy analysis and showed that only at a specific inlet humidity and temperature can the wet countercurrent cooling tower achieve the best efficiency. Hajidavaloo [
23] studied the thermal performance of a wet cross-flow cooling tower under varying ambient wet bulb temperatures and found that increasing the wet bulb temperature while keeping the dry bulb temperature constant decreases the approach, range, and evaporation loss of the tower. Papaefthimiou [
24] investigated the effect of ambient air conditions on the thermal performance characteristics of a closed wet cooling tower. The results indicated that the thermal efficiency and operation cost of the closed wet cooling tower mainly depend on the air saturation at the inlet. Ricardo [
25] studied the impact of seasonal climate change on the operation efficiency of a cooling tower fan and installed an appropriate variable frequency drive (VFD) in the cooling tower fan to reduce the relaxation problem caused by the reduction in ambient temperature.
Thus far, only a few studies have comprehensively evaluated the impact of ambient temperature on the operation cost of the entire system from the perspective of the system, and no research has examined the impact caused by changes in working medium flow. Castro et al. [
26] pointed out that humidity is the main factor that affects the total system operation cost, but they did not consider the effect of the elevation of the heat exchanger on the operation cost of the water pump. In [
27], the impact of climate change on the operation cost of a cooling tower and chiller was analyzed. However, the developed model directly ignores the change in pump operation cost.
The current study analyzes the sensitivity of CCWS operation cost to ambient dry bulb temperature, ambient wet bulb temperature, and working medium flow. We consider the elevation of the heat exchanger when we calculate the operation cost of the water pump. In addition, this work aims to provide guidance for on-site operation optimization to deal with changes in ambient temperature or working medium flow. Therefore, we develop a CCWS operation cost analysis and optimization model on the basis of the superstructure method. The model uses the atmospheric environment dry bulb temperature, atmospheric environment wet bulb temperature, and load rate as random variables. Electricity fee, water fee, pipe network structure parameters, specification parameters of the water pump, the heat exchanger, and the cooling tower are adopted as fixed variables. Water supply temperature is used as the decision variable. With the minimum operation cost as the objective function, the optimal operation cost and corresponding operation parameters are calculated with the genetic algorithm. An optimal water supply temperature control equation is proposed to provide site guidance conveniently. Then, the operation of the case system is optimized in accordance with the actual ambient temperature and working medium flow.
2. CCWS Superstructure
CCWS is a typical heat and mass transfer system with water as a cooling medium (the water is recycled). It is mainly composed of a heat exchanger, cooling tower, water pump, and pipeline. The system operation comprises hydraulic and thermal cycles. The hydraulic cycle can be regarded as a closed cycle, and the thermal cycle is a semi-open cycle, as shown in
Figure 1.
The pool is usually regarded as the starting point of a cycle. The cooling water is pressurized by the water pump to a certain pressure energy and transmitted to the heat exchanger network. Then, the flow of each branch is redistributed by adjusting the valve opening. In the heat exchanger, the heat is transferred from the high-temperature working medium side to the cooling water through the tube wall. The heat transfer is affected by the flow mode of cold and hot fluids and the temperature entering the heat exchanger. After heat absorption, the cooling water enters the cooling tower under the action of the residual pressure of the return water of the system to exchange heat with the air again. The cooling water flows evenly from top to bottom after passing through the filler. The air is sucked into the cooling tower by the fan and flows out from bottom to top. The cooling water can be fully in contact with the air and cooled by contact heat transfer and surface evaporation heat transfer. After cooling by the cooling tower, the temperature of the cooling water is restored to the initial state, and the cooling water is stored in the pool for secondary circulation. During this period, the cooling water is lost due to evaporation, entrainment, purged water, leakage, and other reasons. Continuous supply of new water is necessary to keep the liquid level in the pool constant.
The CCWS superstructure is shown in
Figure 2. The cooling water enters the pipe network from position 0 and flows out from position 5. Positions 2 and 3 represent the diversion and confluence points of parallel branches, respectively. In the figure,
i is the index of parallel branches,
k is the index of parallel pumps, and
s is the index of parallel cooling towers. Additionally,
is the cooling water supply temperature,
is the return temperature of cooling water,
represents the working medium flow of heat exchanger
Ei,
is the cooling water flow of branch
i, and
is the total flow of the cooling water.
4. Sensitivity of Operation Cost to Ambient Temperature and Working Medium Flow
The developed program is an effective tool to study the impact of environmental temperature and load rate changes on the system operation cost. The data used in this section are from the numerical simulation results. The values of ambient dry bulb temperature, ambient wet bulb temperature, and load rate refer to the ambient temperature and production status of the research object.
The research object is a CCWS in Southern China, as shown in
Figure 4. The system is equipped with three mechanical ventilation countercurrent cooling towers, five water pumps, and five heat exchangers. The equipment specifications are shown in
Table 1. Each cooling tower fan in the system contains a VFD, and the operation of the fan is adjusted in accordance with the water pool temperature. One of the water pumps is also equipped with a VFD. The system controls the supply pressure and flow of cooling water by initializing and stopping the pump and variable frequency pump. The electricity price of the plant is 0.09
$/kWh, and the water price is 0.17
$/m
3. The motor efficiency is 95%, and the air pressure is the local atmospheric pressure of 104 kPa (although the atmospheric pressure changes in the entire process, the change is extremely small, and the atmospheric pressure can be regarded as a constant).
During the sensitivity analysis of ambient dry bulb temperature, its value changes between 20 °C and 30 °C. At this time, the ambient wet bulb temperature and load rate are 20 °C and 100%, respectively. The impact of ambient dry bulb temperature on the operation cost is shown in
Figure 5a. The water replenishment cost accounts for the smallest proportion in the total cost, contributing approximately 20–25% to the total cost. The operating cost of the fan is close to that of the water pump, but the operating cost of the water pump is slightly higher than that of the fan. When the ambient dry bulb temperature gradually increases from 20 °C to 30 °C, the operation cost of the fan increases slightly, whereas the operation cost of the water pump and the water replenishment cost do not change. That is, the change in ambient dry bulb temperature does not affect the best operation of the system.
During the sensitivity analysis of the environmental wet bulb temperature, its value changes between 20 °C and 30 °C. At this time, the environmental dry bulb temperature and load rate are 30 °C and 100%, respectively. The impact of ambient wet bulb temperature on the operation cost is shown in
Figure 5b. The ambient wet bulb temperature ranges from 20 °C to 30 °C. The operation costs of the system fan, water pump, and make-up water are significantly increased, and the change in the total system operation cost relative to ambient wet bulb temperature is significant. The reason is that the cooling water in the cooling tower is mainly dissipated by evaporation, and the power of evaporation and heat dissipation is the pressure difference between the saturated steam pressure of water and the water vapor in the air. The main factor that influences evaporative heat dissipation is ambient wet bulb temperature rather than ambient dry bulb temperature. Wet bulb temperature is the temperature limit at which the cooling tower can cool the cooling water. Given that the mass transfer and heat exchange efficiency at high wet bulb temperatures are higher than those at low wet bulb temperatures, the increase rate of fan operation cost decreases when the wet bulb temperature is high, as shown in
Figure 5b. When the wet bulb temperature is less than 28 °C, the increase rate of fan operation cost increases with the increase in wet bulb temperature. When the wet bulb temperature is greater than 28 °C, the increase rate of fan operation cost suddenly decreases.
In the load rate sensitivity analysis, the value changes between 80% and 120%. At this time, the ambient dry and wet bulb temperatures are 25 °C and 27 °C, respectively. As shown in
Figure 5c, with the increase in load rate, the operation cost of the system water pump, make-up water cost, and fan operation cost increase, and the sensitivity of water pump and fan operation costs to load rate are basically the same. The increase in load rate indicates that the heat transferred by the system increases. More cooling water or lower water supply temperature is required in the heat exchange process in the heat exchanger to enhance heat transfer, and more air volume is needed in the heat exchange process in the cooling tower to improve the gas–water ratio.