10 replies to this topic

[chemE610]

I am wanting to calculate the duty of a heat exchanger that has an inlet temperature of 45 C and an exit temperature of 150 C.  So it is going in as a liquid and coming out as a vapor.  The mass flow rate is 100 kg/s.  I want to use the equation Q=mCp(delta(T)), the main issue I am having is trying to decide how to calculate the Cp, since there is a phase change. I was looking back through some old text books and couldn't find exactly what I was looking for.  The inlet stream is all water.  Any hints or help would be great.  Thank you. 

[Francisco Angel]

Dear chemE610:

Remember that if a phase change is present, you must account for it using the enthalpy of vaporization value:

 

dH=m*Cp_l(T_b-T_in)+m*L+mCp_v*(T_out-T_

 

So, the total energy transferred is equal to the energy in going from the inlet temperature to the boiling temperature, plus the energy required to go from liquid to gas, plus the energy in going (as a gas) from the boiling temperature to the outlet temperature.

Best regards.

[chemE610]

what is m*L?

[breizh]

mass flow * latent heat !

 

Breizh

[chemE610]

Sorry for another question but Tb is the temperature that water boils at right, and latent heat is m*lambda ?

[chemE610]

I got Tb = 100 C, m=100kg/s, Tin=45 C, Tout =150 C, Lvap=2264.76 kJ/kg, Cpl=4.187 kJ/kg K, Cpv=1.996 kJ/kg K

dH= (100)(4.187)(100-45) + (100)(2264.76) + (100)(1.996)(150-100) = 259485 kJ/s

[Padmakar Katre]

I am wanting to calculate the duty of a heat exchanger that has an inlet temperature of 45 C and an exit temperature of 150 C.  So it is going in as a liquid and coming out as a vapor.  The mass flow rate is 100 kg/s.  I want to use the equation Q=mCp(delta(T)), the main issue I am having is trying to decide how to calculate the Cp, since there is a phase change. I was looking back through some old text books and couldn't find exactly what I was looking for.  The inlet stream is all water.  Any hints or help would be great.  Thank you. 

 

Hi,

If there is phase change; you have to account both heat effects i.e. sensible and latent. You forgot to mention the pressure of the system, you can use steam table and P, T conditions at inlet and outlet to get the enthalpies and just substract the enthalpies (outlet minus inlet) and multiply this with mass flow you should get the duty.

Simple calculations...all the best

Edited by Padmakar Katre, 12 April 2016 - 11:19 PM.

[shantanuk100]

Hi chemE610,

 

Once the concept is grasped completely, the calculations automatically become much easier.

The calculations you have written are absolutely correct.

Also, let's try to understand the concept as we go along through an example.

 

1. Basically the Duty you need for the exchanger is nothing but the amount of heat exchanged per unit time.

Depending on what process is occuring in the exchanger, you calculate the respective heat being exchanged, whether it is condensation, evaporation, etc or any other process.

 

2. In your case, you have a certain phase change occuring in the heat exchanger. For example take an evaporation phse change.

In evaporation what occurs is :

a. There is certain rise in temperature of the water being heated. (Sensible heat change)

b. Once water reaches boiling point, there is phase change (Latent heat change)

c. There is a little further rise in temperature of the new phase (Vapor or steam) once water completes boiling. So now, there is a new phase that is heated (another sensible heat change with different Cp)

 

3. So your total heat change will be :

 

a. H = Heat Taken by water to reach boiling point + Phase change Heat (Latent) + Heat taken by vapor for further temp. increase

 

b. Temperature change of Water is (B.P of Water - Inlet Water Temp)

while Temperature change of Vapor is (Final Steam Outlet Temp - BP of Water). 

There is no change in temperature at the phase change point. This is what we called latent heat, because it is hidden.

 

c. This will give

    H/sec = mass flow rate of water X Cp of Water X (BP of water - Water Inlet Temp) 
              + mass flow rate of water X (Latent Heat of Vaporisation of Water L or Lambda)

              + mass flow rate of water X Cp of Steam X (Final Steam Outlet Temp. - BP of Water)

 

d. Now in your case you have 100 kg/s flow  and inlet going as water at 45 C and outlet coming as steam at 150 C

 

So your duty is calculated as :

 

H = 100 kg/s X Cp water X (100-45) DegC    +     100 Kg/s X 2258 KJ/kg      +     100 Kg/s  X Cp Steam X (150-100)

   = 100 Kg/s X 4.187 KJ/Kg.C X 55 DegC        +     225800  KW     +      100 Kg/s X 1.996 KJ/Kg.C X 50 DegC

   = 23028.5 KW  +   225800  KW  +  9980 KW

 

So, the Heat Exchanged = 258808.5 KW

                                       = 258.8085 MW

 

 

Regards,

Shantanu

Edited by shantanuk100, 13 April 2016 - 12:13 AM.

[breizh]

Yes ........kj/s =Kw

[samayaraj]

Hi ChemE610,

 

Find attached the excel used to calculate the heat load. Step wise calculation is made for your easy understanding. This excel sheet has inbuilt steam data, so enable macros before using this. 

 

Hope this will help you. Revert back if you have further query.

Attached Files

•  Heat duty calc.xls   630KB   50 downloads

Edited by samayaraj, 13 April 2016 - 01:38 AM.

[samayaraj]

In simple, you can calculate by subtracting outlet heat content and inlet heat content.

 

Inlet water at 45 Deg C and its enthalpy is 188.4 kJ/kg

 

Outlet superheated steam enthalpy (at 1.014 Bar a & 150 Deg. C) is 2776.5 kJ/kg

 

Heat added = 100 kg/s x (2776.5 - 188.4) kJ/kg = 258810 kJ/s = 258810 kW = 258.81 MW