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Temperature Interval Method for Heat Exchanger Networks

WEBVTT
Kind: captions
Language: en

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In this video we're going to focus on a specific
design approach for creating a heat exchanger
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network, and we're just going to work through
an example problem that's shown here, where
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we have four streams that are going through
a process, and they have certain inlet temperatures
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and outlet temperatures, and just to clarify
the inlet temperature of 30 degrees exits
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at an outlet temperature of 135, which means
that the inlet temperature of 180 exits at
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60, so looking at these temperatures you can
see that we have two hot streams and two cold
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streams.
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So I am going to go through an approach step-by-step
using a temperature interval method to figure
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out what our minimum energy requirements,
MER, are going to be in this process.
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So we're going to specifically focus on trying
to minimize the utility loads that come in
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from both the hot side and a cold side of
a process that we would need to off balance
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any energy that we would have to provide or
take away from these four streams.
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So the first step is to create a table for
our streams.
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So T(s) stands for our source temperature,
so that's really our inlet, and T(t) stands
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for our target temperature.
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C is our heat capacity flow rate, and that's
just something you've seen before as the flow
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rate times a specific heat, and you could
see that the units on this are an energy per
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temperature, so that accounts for our mass
flow rates for each stream.
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So I'll start filling in the temperatures
here, so we were given the heat capacity flow
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rate values in the problem statement, so that's
something I am going to write in here, and
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I have this assumption that these heat capacity
flow rates are going to stay constant as a
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function of temperature, or in other words
we would write that C is not a function of
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temperature, and you know that if we had a
phase change for any of these streams we would
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definitely have to account for the energy
associated with that, or a reaction that might
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be occurring, and for many species the heat
capacity won't be constant over a large range
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in temperatures, and that's something that
you may have to use in breaking up the streams
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into those specific intervals.
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So the first thing we could do is just calculate
a heat transfer for each of the streams where
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we know that the heat transfer rate is going
to be mC delta T, and we've already been given
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this mC as our heat capacity ratio, so it's
just a matter of multiplying the heat capacity
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flow rate by this temperature difference,
and I'll fill that in.
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So you could see that our cold load here on
the cold side adds up to 510, and our hot
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load adds up to 480.
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So we know in this case that our difference
between the two streams is 30 kW, and we'll
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have to determine later on how to account
for these 30 kW.
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Now just a note this is not the minimum energy
requirement that we're looking for, because
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we haven't designated a minimum approach temperature
for our heat exchangers.
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So the first step in using the temperature
interval method is to designate this minimum
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approach temperature for our design of our
heat exchangers, and a good starting point
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is going to be 10 degrees Celsius, and to
account for this in our energy balances we're
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going to take the hot streams, and we're going
to subtract this approach temperature from
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the temperatures from the hot streams, so
this becomes 170 and 50, 140 and 20.
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Now we maintain the temperatures for the cold
streams, and we take these temperatures, these
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adjusted temperatures, as the temperatures
that we're going to use to create our intervals.
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So a good place just to show where the streams
are is to draw a diagram of this where we
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label our temperatures that we saw from our
adjusted temperatures in order from coldest
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to hottest, and then we could draw arrows
to designate which stream overlaps these temperature
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intervals.
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So if we look at our cold stream, for C(1),
that goes from 30 to 135, we could draw an
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arrow that shows that shows that, and we could
do the same thing for our second cold stream
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that goes from 80 to 140.
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Now if we do this for our hot streams we have
one that goes from 140 to 30, and our other
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one that goes from 170 to 50, and I'll show
you why this is going to be important as we
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move further into this approach.
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Our next step is to draw a basic flow chart
that shows the transfer of energy in between
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each of these temperature intervals.
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So we start with the lowest temperature at
the bottom, and in between each of these boxes
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we'll write what the temperatures of those
intervals are.
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So the next step after this is to determine
the enthalpies of each interval, and to do
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that our equation for our change in enthalpy
is just going to be our heat capacity flow
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rate times our temperature difference.
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However, we have to account for all of the
streams, so I'll put a summation on here.
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This is where the chart comes in handy, if
we go back and look at our chart and we could
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fill in our information for the heat capacity
rate we could see for the interval of 140
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to 170 we have one stream that's involved,
so our delta H for the first process is just
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going to be 3 times the change in temperature,
which gives us 90 kW.
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Now for this second process we go back and
look at our chart, and we notice that we have
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three streams that are involved with this
interval, so we take the hot streams and we
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add up the heat capacities, that gives us
4, and we're going to subtract out the heat
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capacities of the cold streams.
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4-5 will give us negative 1.
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So I'll have negative 1 as our summation times
our interval, 5 degrees Celsius, and this
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gives us negative 5 kW.
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Now I'll do this for the rest of the temperature
intervals, and you could see the resulting
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enthalpies of those calculations.
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The next step is to calculate the residual
enthalpy, which is going to be a cumulative
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addition of all the intervals, so our residual
enthalpy starts with our 90 kW and then as
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we add the negative 5 we drop down to 85,
and so forth.
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So this gives us an idea of where the pinch
point of this process is going to be.
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Now this pinch point is defined such that
no energy is transferred across the pinch,
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and that's in order to maintain our approach
to minimize our utility loads.
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So at this point we're going to choose the
most negative enthlapy value, which is shown
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here, and we're going to take that as our
hot utility load and add it to the beginning
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of this block diagram.
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So we do a final pass through our temperature
intervals, where now we're going to start
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with 80 kW, we're going to add the enthalpies
from each temperature interval such that at
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a pinch point we have 0 as our value.
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What this does is tell us our eventual residual
enthalpy that's associated with our cold utility.
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So our hot utility was what we added to the
system to start, and now our cold utility
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is the bottom, and these values are our MER
targets.
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We've identified our pinch point to be 80
degrees for our cold stream, and because our
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minimum approach temperature was 10 degrees
our hot side is going to be 90.
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So the last part of this process is to do
what's known as a pinch decomposition of our
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hot and cold streams just to show what our
networks going to look like from start to
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finish before we put in any of the heat exchangers.
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So I've filled in the specific heat flow rates
on the right of each stream, and designated
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the hot streams going left to right, and the
cold stream's right to left.
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So we plug in our values for our pinch temperatures,
so on the cold side it's going to be 80 degrees,
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and on our hot side it's going to be 90 for
our pinch temperature, we'll fill in our source
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and target temperatures for each stream.
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So we use the actual values given in the problem
statement, so our hot stream starts at 180
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and finishes at 60.
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Our second hot stream starts at 150, finishes
at 30 degrees Celsius, our cold stream starts
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at 30 and finishes at 135.
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The other one starts at 80, and finishes at
140.
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Now what you can notice is that we have a
pinch temperature of 80, and our start temperature
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of 80.
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So this means that we can actually get rid
of this side altogether, and we have the second
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cold stream, C(2) only on the hot side of
the pinch, and we've designated this as our
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hot side, and this as our cold side.
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So we would at this point would move on to
designing our two heat exchanger networks,
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one for the hot side of the pinch, and one
for the cold side, and we'll do that in a
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subsequent screencast.

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