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