Taking the outlet temperature of cooling water in the cooler and the heating steam temperature in 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 outlet temperature of cooling water in 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 outlet temperature of cooling water directly affects the size of the cooler and the consumption of cooling water. A higher outlet temperature of cooling water can save 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 temperature of heating steam directly affects the size of the heater and the cost of heating steam. A higher heating steam temperature can reduce 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 outlet temperature of cooling water and the temperature of heating steam, 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, 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 outlet temperature of cooling water and the temperature of heating steam 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.
When the cooling water outlet temperature is 48 degrees Celsius, the total cost of the cooler is minimized. However, considering that high 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 price is higher, 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 effectively reduces the heat transfer area, thereby decreasing the equipment cost;
(4) When the heat load increases, both equipment cost and operating cost increase, i.e., the total cost increases accordingly.
