At the same vacuum level, with a 5 °C temperature difference in the feedstock, the calculation logic for the difference in annual energy consumption for low-temperature evaporation

First, let us clarify the premise: maintaining the same vacuum means that the saturated evaporation temperature on the evaporation side remains constant; there is a sensible heat temperature difference between the feedstock and the saturated temperature of the evaporation chamber, this portion of heat represents the energy consumed in raising the temperature of the feed solution to the evaporation temperature; it does not include the latent heat of phase change. The latent heat of phase change is solely related to the evaporation rate; for a given evaporation rate, the latent heat component remains constant, and the difference in energy consumption stems solely from the sensible heat required to raise the temperature of the feed solution.

The basic formula for the heat required to raise the temperature of a liquid:

Sensible heat load Q = m × c × Δt

m: annual feedstock processing volume, kg/year; c: specific heat capacity of the feedstock, kJ/(kg·°C); Δt = 5 °C

In the vast majority of low-temperature evaporation wastewater systems, where salt content is not high, the specific heat capacity is approximately that of water and may be taken as 4.18 kJ/(kg·°C); for high-salt mother liquors, this value decreases and may be replaced with measured values.

Substituting Δt = 5 °C, the additional heat generated by the temperature difference per unit mass is:

q = 4.18 × 5 = 20.9 kJ/kg of feed solution.

It is important to distinguish between two types of energy carriers: the conversion calculations differ between heat pump-based low-temperature evaporation and steam-heated evaporation. System thermal efficiency must also be taken into account; heat cannot be directly equated with electrical energy.

In the case of heat pump-based low-temperature evaporation—that is, the heat pump low-temperature evaporation unit used in the complete set of equipment described earlier—

the heat pump has a Coefficient of Performance (COP), and the additional electrical energy required is W = Q / COP.

Under long-term operating conditions at the site, the actual operating COP of heat pump low-temperature evaporation generally ranges from 2.5 to 3.5, which is not the ideal value stated on the nameplate.

Taking COP = 3 as an example, for every 5 °C increase in the temperature of 1 kg of feedstock, the additional electricity consumption is: 20.9 ÷ 3 ≈ 6.97 kJ/kg. Converted to kWh by dividing by 3,600, this is approximately 0.00194 kWh per kg of feedstock.

In other words, for every 1 metric tonne of feedstock processed, a 5°C reduction in feed temperature results in an additional annual electricity consumption of approximately 1.94 kWh; if the COP drops to 2.5, the additional electricity consumption per metric tonne of feedstock is approximately 2.32 kWh.

In the case of steam-heated low-temperature evaporation, the steam consumption is calculated as follows: assuming a latent heat of vapour of 2,260 kJ/kg, the additional steam consumption per metric tonne of feed solution is ≈20.9/2,260 ≈ 0.00925 kg of steam per kg of feed solution, i.e. an additional 9.25 kg of steam per metric tonne of feed solution.

Correction factors for long-term operation, which are also the site-specific deviations most likely to distort this calculation

Firstly, variations in the additional energy consumption required to maintain vacuum. If the feed temperature is 5 °C lower, the system must maintain the original vacuum; as the evaporation driving force decreases, the evaporation rate will naturally decline. To ensure the rated throughput, the automatic control system will increase the heat pump’s heating load or extend the operating time; if the equipment is not operating continuously at full load, additional energy losses will arise from intermittent start-up and shutdown, which constitute an additional increment not included in the basic sensible heat formula.

Secondly, the offsetting effect of the heat recovery system. If the equipment is fitted with a heat exchanger for condensate or mother liquor heat recovery, high-temperature feed will transfer heat to the low-temperature effluent; the energy consumption difference resulting from a 5°C temperature differential will be reduced by the heat recovery ratio. For example, with a heat recovery rate of 60 per cent, the actual additional energy consumption is calculated based on only 40 per cent of the difference.

Thirdly, correction for the specific heat capacity of the feed solution. High-salinity wastewater, wastewater containing colloids or organic solvents has a specific heat capacity lower than that of pure water. For example, in the case of a mother liquor with a very high salt content, c ≈ 3.5 kJ/(kg・℃); in this instance, the sensible heat difference per metric tonne of feed solution decreases to 17.5 kJ/kg, and the energy consumption difference is reduced accordingly.

Fourthly, the coupling of heat dissipation losses. At lower feed temperatures, the temperature difference between the equipment casing, pipework and the ambient environment decreases, resulting in a slight reduction in heat dissipation from the equipment surface. This partially offsets the energy consumption required for heating; whilst this can be disregarded for small-scale systems in engineering estimates, it is recommended to include it in verification calculations for large-scale continuous evaporation lines.

Complete example of annual energy consumption difference calculation

Assumptions: Annual feedstock processing volume 80,000 tonnes; specific heat capacity of wastewater 4.18 kJ/(kg·°C); heat pump COP = 3; no waste heat recovery; continuous operation at full load; stable vacuum.

Annual additional heat load = 80,000 × 1,000 kg × 4.18 × 5 = 1,672,000,000 kJ

Annual additional electricity consumption = 1,672,000,000 ÷ 3 ÷ 3,600 ≈ 154,815 kWh, which equates to an additional annual electricity consumption of approximately 154,815 kWh.