A constant vacuum level means that the saturated evaporation temperature in the evaporation chamber remains fixed. Given a 5°C difference in the initial temperature of the feed solution, the energy consumption difference consists of two parts: the sensible heat required to raise the feed temperature to the evaporation temperature, and the additional losses resulting from the process. There will be discrepancies between theoretical thermal calculations and actual on-site operation; therefore, low-temperature heat pump evaporation cannot be calculated based solely on the latent heat of phase change. First, let’s consider the basic physics: the sensible heat required to raise the temperature of one kilogram of raw liquid by 5°C. Since the specific heat of wastewater is approximately equal to that of water, the sensible heat per unit mass equals the specific heat multiplied by the temperature difference. The specific heat capacity of water is 4.2 kJ/(kg·°C); raising the temperature of one liter of wastewater by 5°C requires absorbing 21 kJ of heat. When converting this to an electrical energy equivalent, the heat pump’s COP (Coefficient of Performance) must be considered—heat cannot be directly converted to kilowatt-hours. The heat output and input power of a heat pump are determined by the COP. Using an engineering-based reasoning approach, assume the unit’s annual evaporation treatment capacity is M metric tons of wastewater, with an inlet temperature difference ΔT = 5°C and a specific heat capacity of water c = 4.2 kJ/(kg·°C). The total annual sensible heat difference Q = M × 1000 × c × ΔT. This represents the total additional heat required throughout the year.

Under heat pump operating conditions, the electrical energy input W = Q ÷ COP. Here, COP refers to the actual average operating COP during low-temperature evaporation, not the ideal COP listed on the equipment nameplate. Due to on-site factors such as scaling, cooling water conditions, and load factors, the actual COP is often significantly lower than the catalog value. For example, for the annual evaporation of 10,000 metric tons of wastewater with an inlet temperature difference of 5°C,

the total sensible heat difference Q = 10,000 × 1,000 × 4.2 × 5 = 210,000,000 kJ.

Since 1 kWh equals 3,600 kJ, the thermal equivalent is 58,333 kWh of heat.

If the average COP of the on-site heat pump is 3—meaning that for every 1 kWh of electricity consumed, 3 units of heat are produced—the additional electricity consumption would be approximately 58,333 ÷ 3 ≈ 19,444 kWh per year.

If operating conditions deteriorate and the COP drops to 2, the difference would increase to nearly 29,166 kWh per year. This is merely the theoretical difference in sensible heat. However, the actual annual energy consumption gap on-site will deviate from the theoretical calculation above, primarily due to additional losses—an aspect that is often overlooked in low-temperature evaporation applications. First, cold feedstock disrupts the thermal equilibrium of the evaporation chamber. The continuous inflow of low-temperature raw liquid into the evaporation chamber does not merely absorb sensible heat; it also causes an instantaneous decrease in the evaporation rate within the chamber. The heat pump system automatically increases the compressor load to continuously supply additional heat. When the feed temperature is low, localized subcooling occurs inside the chamber, leading to the release of non-condensable gases in certain areas. This causes slight fluctuations in system vacuum, which in turn alters the workload of the vacuum pump, resulting in additional power consumption by the vacuum pump. Second, energy efficiency degrades due to fluctuations in the heat load. When the feed temperature is low, the unit operates for extended periods in a higher output load range, causing the heat pump to deviate from its optimal operating point, and the actual COP will decline further. While the unit can operate stably at medium load when the feed temperature is high, it frequently runs at full load when the feed temperature is low. This increases the compression ratio and raises the electricity consumption per unit of heating capacity. This portion of the loss is not reflected in simple sensible heat formulas, resulting in an actual energy consumption difference greater than the theoretical calculation. Third, it is essential to determine whether feed preheating is configured. If condensate waste heat recovery is used to preheat the feed, the energy consumption difference resulting from a 5°C temperature difference will be significantly offset by the waste heat recovery; in this case, the formula above cannot be directly applied. Many sites utilize high-temperature condensate to preheat the raw solution, thereby smoothing out feed temperature fluctuations and reducing electricity consumption in this area. If there is no waste heat recovery and all heat is supplied by the heat pump, the theoretical estimate holds greater reference value. Fourth, adjustments for intermittent operation. If the unit does not operate continuously for 24 hours but instead undergoes frequent starts and stops—where cold feed causes the chamber temperature to drop, requiring the feed liquid to be reheated to the evaporation temperature each time the unit is started—the repeated heating cycles will amplify the annual energy consumption difference. For units operating in a continuous, steady-state condition, the discrepancy between theoretical and actual values is relatively smaller. Another key point to understand is that a 5°C difference in feed temperature only affects the sensible heat required to heat the feed to the evaporation temperature; the latent heat of phase change remains constant. Regardless of the feed temperature, the latent heat required for water vaporization under the same vacuum conditions is a fixed value, so this portion of energy consumption will not vary. Many people make calculation errors by including the latent heat of evaporation in the differences attributed to temperature variations. In actual project applications, it is not recommended to rely solely on formula-based calculations on paper; theory should only serve as a reference for preliminary estimates. The best approach is to collect two sets of operational data on-site. Assuming that the vacuum, concentration ratio, and composition of the feedstock are essentially the same, record the electricity consumption per unit of evaporation for feed temperatures that are 5°C higher and 5°C lower, respectively. After collecting data over a sufficient number of cycles, extrapolate the results to the annual processing volume; the resulting annual energy consumption difference will more accurately reflect actual on-site conditions. At the same time, it is important to consider the boundaries; if