How can we calculate the solids content of the final product in a single effect evaporator?
Calculating Solids Content in Single Effect Evaporator
To determine the solids content of the final product in the single effect evaporator, we need to calculate the mass flow rate of the final product and the mass flow rate of the solids.
1. Calculate the mass flow rate of the water evaporated:
- Mass flow rate of water = Mass flow rate of steam * (1 - Quality of steam)
- Mass flow rate of water = 125 kg/hr * (1 - 0.9) = 12.5 kg/hr
2. Calculate the mass flow rate of the feed entering the evaporator:
- Mass flow rate of feed = Mass flow rate of water evaporated + Mass flow rate of final product
- Mass flow rate of feed = 12.5 kg/hr + 90 kg/hr = 102.5 kg/hr
3. Calculate the mass flow rate of the solids in the feed:
- Mass flow rate of solids = Mass flow rate of feed * Solids content
- Mass flow rate of solids = 102.5 kg/hr * 0.25 = 25.625 kg/hr
4. Calculate the heat transfer required to evaporate the water:
- Heat transfer = Mass flow rate of water evaporated * Specific heat of water * Temperature difference
- Heat transfer = 12.5 kg/hr * 4000 J/kg K * (70 °C - 10 °C) = 20,000,000 J/hr
5. Calculate the heat transfer provided by the steam:
- Heat transfer = Mass flow rate of steam * Specific heat of steam * Temperature difference
- Heat transfer = 125 kg/hr * 4000 J/kg K * (90 °C - 70 °C) = 10,000,000 J/hr
6. The heat transfer required to evaporate the water should be equal to the heat transfer provided by the steam. If it's not, the calculations need to be adjusted.
7. Determine the solids content of the final product:
- Solids content of final product = Mass flow rate of solids / Mass flow rate of final product
- Solids content of final product = 25.625 kg/hr / 90 kg/hr = 0.2847 or 28.47%
Therefore, the solids content of the final product in the single effect evaporator is approximately 28.47%.