Steam sparging heating rates?

Beware of the 'very simple' approach

It assumes 'lumped heat capacity' and a constant Cp water (or batch fluid).
This is probably good for heating small volumes over a small temperature
range, but not recommended for a 100 m3 tank as posed in the example.

Peter,
start with the first law of thermodynamics for a control volume (the tank)

dE/dt = (mh)in - (mh)out

where dE/dt is the rate of increase of energy (heating rate) in the tank, m
is a mass flow rate, h is an enthalpy, in is at the tank inlet, out is at the
tank outlet, inlet and exit potential and kinetic energy effects are
neglected, and any heat transfer through the tank wall is neglected.

The inlet and outlet enthalpies can be determined by going into a steam table
with the inlet and outlet temperatures and pressures.

dE/dt = dU/dt, with negligible potential and kinetic energies within the tank,
where U is the instantaneous internal energy of the batch.

dU/dt can be approximated as (m2u2 - m1u1)/(t2 - t1), where m2 is the final
mass in the batch (i.e., at time t2), u2 is the internal energy per unit mass
of the batch at t2, m1 is the initial mass in the batch (i.e., at time t1 =
0), u1 is the internal energy per unit mass of the batch at t1. u1 and u2
can be looked up in a steam table , or inversely, temperature data can be
determined from a computed u2

Also, (m2 - m1)/(t2 - t1) can be approximated by min - mout. Note that m1 and
m2 are masses, whereas min and mout are mass flow rates.

If there is no outlet, the problem is not too bad.

Tod


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Very simple:

Steam deltaH is about 2000 kJ/kg, cP(water) is 4.18 kJ/kg??C.

Heatup rate (??C/hr)=Steamflow (kg/h)*2000/Water mass (kg)/4.18. Ignore
superheat effect.

A 100 m3 water tank (100000 kg) with 1000 kg/h steam will thus heat up with
4.8??C/hr.

...

If you can find a mollier diagram you can use it to calculate enthalpy of the added steam per
lbm. After that it becomes a relatively simple math problem.

Pat


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I was wondering if anyone knows of any methods for calculating the
heat up rate of tank contents heated by direct steam injection to the
batch. Couldn't find anything in the standard references. I would
imagine the problem can become quite complicated, but there must be
some rules of thumb for design out there.

Thanks in advance,
Peter