Taking the cooling water outlet temperature of the cooler and the heating steam temperature of the heater as decision variables, and the total cost as the objective function, a mathematical model is proposed to determine the optimal steam temperature of the heater and the optimal cooling water outlet temperature of the cooler, i.e., the optimal heat transfer temperature difference. The calculation method is illustrated with an example.
Cooling water is a cheap coolant, and steam is a cheap heat carrier. Therefore, water coolers and steam heaters are among the most commonly used heat exchange equipment in chemical plants. When designing a water cooler, it is necessary to select an appropriate cooling water outlet temperature, i.e., the average heat transfer temperature difference. The cooling water outlet temperature directly affects the size of the cooler and the consumption of cooling water; a higher cooling water outlet temperature saves cooling water consumption but increases the cooling area of the cooler, and vice versa. Similarly, when designing a steam heater, it is necessary to select an appropriate heating steam temperature, i.e., the heat transfer temperature difference. The heating steam temperature directly affects the size of the heater and the cost of heating steam; a higher heating steam temperature reduces the heat transfer area of the heater but increases the cost of heating steam, and vice versa. Therefore, there must be an optimal economic value for the cooling water outlet temperature and the heating steam temperature, i.e., the heat transfer temperature difference of the cooler and heater. Operating under this condition minimizes the sum of equipment cost and operating cost of the cooler and heater, i.e., the total cost. Hence, studying the optimization design of heaters and coolers is of certain significance.
For coolers and heaters, the optimization calculation takes the cooling water outlet temperature and the heating steam temperature as decision variables, the total cost of the cooler and heater as the objective function, and the minimization of the total cost of the cooler and heater as the optimization goal.
The total cost of the cooler is minimized when the cooling water outlet temperature is 48 degrees Celsius. However, considering that higher water temperature may cause scale deposition, affecting heat transfer and increasing flow resistance, the cooling water outlet temperature should not be too high.
It can be seen that the factors affecting the total cost of coolers and heaters include:
(1) Related to the price of the heat exchanger: when the heat exchanger is more expensive, the equipment cost increases;
(2) Related to the prices of cooling water and heating steam: when the prices of cooling water and heating steam increase, the operating cost increases;
(3) When the overall heat transfer coefficient of the cooler and heater is larger, it is equivalent to reducing the heat transfer area, thus reducing the equipment cost;
(4) When the heat load increases, both equipment cost and operating cost increase, i.e., the total cost increases accordingly.
