In this screencast, we're going to design a heat exchanger network based on information
we collected in a previous screencast with the transfer of energy between two hot streams
and two cold streams, and utilities that we designated also in the last screencast.
So a little background first on defining this pinch point, and how we would go about starting
to design our heat exchanger network.
So if we look at a heat exchanger between a hot stream and a cold stream, we've designated
our cold stream as C, so we have our inlet cold temperature, and our cold outlet, we
have our hot inlet, and our hot outlet.
We have some heat transfer, Q, and a temperature difference between the hot inlet and cold
outlet as delta T2, the same on the other side, we designate it delta T1, and then the
values Ch and Cc are the specific heat flow rates, and the units on this is given as an
energy per temperature.
So if we write out our equation for our heat transfer, it's just going to be for the hot
stream our Ch times the temperature difference between the outlet and the inlet, and we can
do the same for the other side.
So we can rearrange these equations to get the following.
Now hopefully what you see here is that if we subtract the two equations, these two groups
form our delta T2 and these two groups form our delta T1.
This means that we get the following result, where delta T2 minus delta T1 is equal to
the heat transfer, Q, times Cc minus Ch over Cc times Ch.
So what does this mean?
This means that when we're designing our two heat exchanger networks, one on the hot side
and one on the cold side of the pinch point, we're going to examine them in the following
manner.
First, we use this equation to say that if we're designing on the hot side, then delta
T1, this is for the hot side of the pinch, delta T1 is going to be our designated minimum
approach temperature.
This leaves us with a delta T2 equaling delta Tmin plus the value on the right side.
Now, to ensure that our delta T2 here is going to be greater than our approach temperature,
this value on the right side has to be positive.
Now Q is positive and our heat capacity flow rates are positive, so that means Cc has to
be greater than or equal to Ch.
Now the following is going to be true if we're looking at the cold side: We set delta T2
equal to delta Tmin, we rework this equation, this time there's going to be a negative sign.
Now for this to be true and to make our delta T1 is going to be greater than delta Tmin,
our Ch has to be greater than or equal to our Cc.
So we use these two guidelines when we're designing our heat exchanger networks to match
streams and determine whether or not it's a feasible match.
So let's practice this on our diagram here where we have our four streams, our pinch
point, our pinch temperature for both the hot and cold stream, and our source and target
temperatures.
So if we start with the hot side, which is arbitrary but something that's typically done
is to start with the hot side of the pinch, then we want to match two streams such that
Cc is greater than or equal to Ch.
So in that case, if we matched C2, we could match it with either H2 or we could match
it with H1, since in both cases, our value of 5 is greater than the values for the hot
streams.
However, if we match C2 with H2 and try to match C1 with H1, you would see that H1 has
a higher specific heat flow rate value than the cold stream, and that would mean that
the stream match is an infeasible match.
So we wouldn't want to do that.
That leaves us with let's start with C2 to H1, and then also draw C1 to H2.
So we want to do this to maximize the potential load on the heat exchanger, so we would calculate
what the heat transfer would be for that connection.
So if we look at this node right here, and we say that Q is equal to 3 times the difference
of 180 minus 90, then we would get 270 kilowatts.
We do the same thing for the other node, and we would see that 5 times 140 minus 80 is
equal to 300 kilowatts.
As you can see, at this node, we could decrease the temperature from 180 all the way to 90,
but we cannot increase the cold stream from 80 to 140.
So we can check mark that node knowing that we can go from 180 degrees and cool it to
90 degrees, but for the other node, we know that this load is 270 kilowatts, which means
that we could raise the temperature from 80 degrees, and we get that using the same calculation,
just showing that Q is equal to 270 times 5 and the temperature difference, which we
could say is x, some unknown temperature, minus 80.
We could calculate the load from our stream, our connection between H2 and C1, again you
can see with the hot stream we have a lower load than that with the cold stream.
So we can decrease from 150 to 90, but we cannot increase the cold stream 1 from 80
to 135.
So again we write the load under the connection, and we calculate what the new temperature
would be, which in this case would be a 30 degree difference and a maximum of 110 degrees.
So we've already reduced our hot streams from the inlet to our pinch temperature, so we
would need to add some kind of hot utility to raise it from their temperatures to their
final target temperatures, and we can write again what the duty on these utilities would
be.
So to go from 110 to 135, change of 25 degrees, times our capacity ratio of 2 would give us
50 kilowatts.
So our temperature difference of 6 degrees times our heat capacity flowrate gives us
a load of 30 kilowatts for this exchanger.
So as you can see, adding up the exchangers on the left side, we have 80 kilowatts, which
is what we had calculated before as our minimum energy target requirement for the hot side.
Now moving to the cold side, we do the same thing and we follow the rule that our hot
side loads have to be greater than our cold side.
So we don't have a C2, we just have the C1 to work with.
So let's match that, following the rule that it has to be higher, we'll match it with H1
and we'll calculate the Q associated with this.
If it were to go from 90 to 60, that would be a temperature change of 30 times 3, which
gives us 90 kilowatts.
On the bottom, to go from 30 to 80 gives us 100 kilowatts.
So again our limit is 90 kilowatts, so we'll put that under the exchange, calculate what
our temperature difference would be, so we can completely cool our hot stream 1 from
90 to 60, but we can only heat up our cold side stream from 80, and this is going to
be 35 degrees, and we calculate that again by 90 equaling 2 times 80 minus x, and you'll
see that x is equal to 35.
So now we need to cool our H2, and we could either do that trying to use our cold stream
or a cold utility.
Since we're at 30 degrees as our inlet and 35 as our outlet, we're not going to worry
about crossing over our minimum approach temperature.
So we could go ahead and try to match these up, and the load that we would have would
be the 5 degrees times 10, so it would be 10 kilowatts, so we can effectively cool down
H2 10 degrees to our 80 degrees Celsius.
However, our final temperature that we are looking for for our H2 stream is 30 degrees.
So at this point, we've completely heated our C1 stream, we've completely cooled our
H1 stream, and we have to further cool H2, so we have to add some kind of cold utility
that would take us from 80 to 30, and that would be equivalent to using 50 kilowatts
of cooling.
And if you recall, that's what we had determined in the previous screencast for our MER target
for the cold side of the pinch point.
So our redrawn final heat exchanger network would look like the following, making sure
we have appropriate connections between the streams.
We would label the duties under each connection, and then our utilities.
You can see we have our cold utility here, and our two hot utilities on the hot side.
So this is a network designed to minimize the energy requirements from our utilities.
Now, another possibility is to identify heat loops and minimize the amount of heat exchangers,
and that's something we'll discuss in further screencasts.
So hopefully this gives you a good idea on how to design a heat exchanger network using
the temperature interval method and stream matching at the pinch.