Designing a Heat Exchanger Network

WEBVTT
Kind: captions
Language: en

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