a solution of organic colloids is to be concentrated from 15 to 50 percent solids in a vertical-tube evaporator. the solution has a negligible elevation in boiling point, and the specific heat of the feed is 0.93. saturated steam is available at 0.8 atm abs, and the pressure in the condenser is 100 mm hg abs. the feed enters at 15°c. the overall coefficient is 1,700 w/m 2 · °c. the evaporator must evaporate 25,000 kg of water per hour. how many square meters of surface are required, and what is the steam consumption in kilograms per hour?

Question

a solution of organic colloids is to be concentrated from 15 to 50 percent solids in a vertical-tube evaporator. the solution has a negligible elevation in boiling point, and the specific heat of the feed is 0.93. saturated steam is available at 0.8 atm abs, and the pressure in the condenser is 100 mm hg abs. the feed enters at 15°c. the overall coefficient is 1,700 w/m 2 · °c. the evaporator must evaporate 25,000 kg of water per hour. how many square meters of surface are required, and what is the steam consumption in kilograms per hour?

Answer 1

To determine the surface area required and the steam consumption in a vertical-tube evaporator, we can use the following steps:

Step 1: Calculate the heat duty (Q)
Q = Mass flow rate * Specific heat * Temperature difference

Given:
- Feed temperature (T1) = 15°C
- Concentration desired (% solids) = 50%
- Mass flow rate of water to be evaporated = 25,000 kg/h
- Specific heat of feed (Cp) = 0.93 kJ/kg°C

The temperature difference (ΔT) can be assumed as the temperature rise from the feed temperature to the boiling point.

Since the solution has a negligible elevation in boiling point, we can use the boiling point temperature to calculate ΔT. You need to consult a table or equation specific to the organic colloid solution to find the boiling point temperature at 0.8 atm abs.

Let's assume the boiling point temperature (Tb) as the value obtained from the table or equation.

ΔT = Tb - T1

Step 2: Calculate the heat duty in kilowatts (kW)
Q (kW) = Q (kJ/h) / 3600

Step 3: Calculate the required surface area (A)
A = Q / (Overall coefficient * ΔT)

Given: Overall coefficient (U) = 1,700 W/m2·°C.

Convert U to kW/m2·°C:
U (kW/m2·°C) = U (W/m2·°C) / 1,000

Step 4: Calculate the required surface area (A)
A = Q / (U * ΔT)

Step 5: Calculate steam consumption (S)
S = Q / (Latent heat of vaporization)

The latent heat of vaporization depends on the properties of water and will vary with pressure.

For saturated steam at 0.8 atm abs, we need to consult a steam table or calculator to find the corresponding latent heat of vaporization (Lv) at that pressure.

Step 6: Calculate steam consumption (S)
S = Q / Lv

Let's calculate the surface area and steam consumption using the given data:

Step 1: Calculate the temperature difference (ΔT)
Note: You need to find the boiling point temperature at 0.8 atm abs for the organic colloid solution.

Assuming ΔT = Tb - T1, calculate the temperature difference.

Step 2: Calculate the heat duty in kilowatts (kW)
Q (kW) = (Mass flow rate * Cp * ΔT) / 3600

Step 3: Calculate the required surface area (A)
A = Q / (1,000 * U * ΔT)

Step 4: Calculate the required surface area (A)

Step 5: Calculate steam consumption (S)
Note: You need to find the latent heat of vaporization (Lv) for saturated steam at 0.8 atm abs.

S = Q / Lv

The calculated surface area (A) will give you the required area in square meters, and the steam consumption (S) will provide the amount of steam needed in kilograms per hour.