Heat Balance

Does this make sense (for a heat exchanger with one stream undergoing phase change):

MCpD(Theta) = M*(dh vap) + M*Cp(T(boiling) - T(inlet))

Where left hand terms (shell side):
M: mass flow rate of hot process fluid (kg/s)
Cp: Specific heat capacity of hot process fluid kJ/kg K
Delta(Theta): Change in temperature between process fluid inlet and outlet (K)

Where right hand terms (Tube side):
M: mass flow rate of cooling fluid (kg/s)
dh vap: kj/kg
M: mass flow rate of cooling fluid(kg/s)
Cp: Specific heat capacity of cooling fluid (kJ/kg K)
T(boiling): Temperature at which cooling fluid boils (at prescribed pressure) (K)
T(Inlet): Temperature at which cooling fluid enters heat exchanger.


I am away from university and unfortunately haven't got any of my reference material with me. I would be greatfull of any help offered, thank you for your time.

So you are saying the sensible duty performed on the shell side (LHS of eqn) = the sensible duty required to heat the tube side fluid to its boiling point, plus the total duty required to boil it?

That looks fine if you make the following assumptions:

1) No heat transferred with surroundings
2) No superheating of the tube-side vapour.
3) Tube side fluid is pure (i.e. it boils at constant temperature).

If the tube side fluid is a mixture you will need to construct a heat curve between the bubble point temperature and the dew point temperature, and replace the term M*(dh vap) with M*SUM(dH1, dH2, dH3,.........dHx), where dH is the enthalpy change between 2 points on the boiling curve (i.e. you divide the boiling point curve up into increments). Note that dH here is a lumped term representing sensible and latent duties.

If the vapour is superheated you will need to add another M*Cp*dT term for the vapour to the right hand side of the equation.

Thank you greatly for your reply Building upon it; would I be able to obtain a seperate value for U (heat transfer coefficient ) for the first term on the right hand side(duty required to boil it) and the second term (duty required to bring to boiling point) and if so.. how?

I'm Guessing:

1) Duty required to bring to boiling point = UA*(Dt) ?
2) Total duty required to boil it = UA*(Dt)

Rearranging for U, assuming I know A (Area of tubes, and their respective temperature difference) ??

Thanks once again!!

Adding to above, would my maximum heat duty acheivable be given by this equation: MCp(min) * (Th1 - Tc1) + M*Dhv

where:
MCpmin (minimum heat capacity * flow rate value) (kJ/s K)
Th1-Tc1 (Temperature of hot inlet minus temperature of cold inlet) (K)
M (mass flow rate of cold fluid) (kg/s)
Dhv (Heat of vaporisation of cold fluid) kJ/kg

I would say yes, you can get an estimate for the mean heat transfer coefficient in a zone by back-calculating from Q = UA*(MTD).

A second approach would be to sum the reciprocals of the individual resistances and invert:

(1/U) = (1/h-o) + (r-o) + (1/h-i) + (r-i)

where h is the heat transfer coefficient for the stream (which I like to think of as the film coefficient), r is the fouling resistance, -o refers to outside the tubes, -i refers to inside the tubes.

If I had the means available, I would prefer to 'rate' the heat exchanger design by dividing the heat transfer area into increments. The heat transfer coefficient can be calculated for each increment, and increments can be averaged over an area of interest.

If I were designing the heat exchanger, I would calculate the single-phase heat transfer coefficient separately to the 2-phase coefficients (which vary with vapour quality).

Please tell me more about calculating the two phase coefficients, how does the calculation differ from that of one phase coefficients taking into account vapour quality?

Thanks
Chrisp