Question

Saturated steam at a gauge pressure of 0.50 bar is to be used to heat a stream of ethane.

The ethane enters a heat exchanger at 16°C and 1.5 bar gauge pressure at a rate of 795 m³/min and is heated at constant pressure to 93°C.

The steam condenses and leaves the exchanger as a liquid at 20.0°C.

The specific enthalpy of ethane at the given pressure is 941 kJ/kg at 16°C and 1073 kJ/kg at 93°C.

You may take the compressibility factor for ethane to be 0.970 at the inlet conditions.

a) How much power must be transferred to the ethane to heat it from 16°C to 93°C? (kW)
b) At what rate must steam be supplied to the heat exchanger if all the energy transferred from the steam goes to heat the ethane?? (m^3/s)

For part A, I calculated 5490 kW but the answer was incorrect and it gave me this hint ---> "You can calculate the specific enthalpy change by subtraction. Use ideal-gas behavior to calculate the mass of ethane. Carry sufficient significant figures throughout calculation." I used those steps to redo the problem but I continue to get my original answer. Any help would be appreciated.

Answer 1

Given:

saturated steam at 0.50 bar (50kPa) temp from steam table is (81.35^oC)

steam condenses & leaves heat exchanger as liquid at 20^oC.

a)

Ethane heated from 16 to 93^oC at 1.5 bar at rate of 795m³/min.(13.25m³/sec)

ethalpy of ethane at 16^oC is 941 kJ/kg & 1073 kJ/kg at 93^oC

Q=m

for ethane compressibility factor = 0.970

Z=PV/RT

0.970=150*13.25/(n*8.314*289.15)

n=0.8523kmol

m (mass of ethane)=nM=no. of moles *molar mass

m=0.8523*30

m=25.569 kg/s

Q=25.569 (1073-941)

Q=3375.108kJ/s = 3375.108 kW   ans.

b)

from part a we get to know that rate of heat supply should be 3375.108 kJ/s

this much heat should be given by steam

so required rate of steam supply can be calculated as

Q=mCp.dT+m

as steam given latent heat plus sensible heat

3375.108 = m (Cp.dT+)

3375.108 = m (1.9654(81.35-20)+2305.42)

3375.108=m*2425.99

m=1.3912kg

n=m/M = 1.3912/18 =0.07728kmol

converting to volumetric flow rate

PV=nRT

50*V=0.07728*8.314*(273.15+81.35)

V=4.5553m³/s