WEBVTT
Kind: captions
Language: en
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So, welcome back yesterday whatever we were
discussing is about the diameter of the bubble,
00:00:28.070 --> 00:00:32.610
that how the diameter of bubble is being calculated
and, what we have done we have said that there
00:00:32.610 --> 00:00:37.350
is different forces which are critical and
those forces was buoyancy force, momentum
00:00:37.350 --> 00:00:43.219
flux of the gas, the surface tension force
drag force and inertial force. And we said
00:00:43.219 --> 00:00:47.819
that if we do the combined balance, we will
get a diameter equation that.
00:00:47.819 --> 00:00:51.870
What will be the diameter of the bubble which
will be formed and, it will be detached from
00:00:51.870 --> 00:00:56.719
the surface ok. And we have taken a simple
C plate holes where the small holes were there
00:00:56.719 --> 00:01:01.170
and, that is going to be the function of the
hole velocity, the flow rate, Weber number,
00:01:01.170 --> 00:01:05.740
and surface tension and all.
So, all this this we have done we have also
00:01:05.740 --> 00:01:09.980
derived the formula for the simpler case where
the buoyancy and surface tension is already
00:01:09.980 --> 00:01:13.920
playing a role, and the surface and this bubble
size generated because of that. So, if you
00:01:13.920 --> 00:01:18.380
see this formula whatever we have developed
if you see the such a first term Weber number
00:01:18.380 --> 00:01:22.380
term, only the first term of this which will
be multiplied by 1. So, it will be the first
00:01:22.380 --> 00:01:27.270
term that will be the only formula for the
diameter of the bubble once only buoyancy
00:01:27.270 --> 00:01:31.009
and surface tension is playing a role. If
all other forces are also playing the role,
00:01:31.009 --> 00:01:34.920
then you will have a different formula and
which you can use to calculate the bubble
00:01:34.920 --> 00:01:39.499
diameter ok. And if you see this this is the
function of Weber number, and Weber number
00:01:39.499 --> 00:01:44.429
is defined as the ratio of inertial force
to the surface tension force ok.
00:01:44.429 --> 00:01:49.110
And which is critical to determine the bubble
diameter. Now several researcher have put
00:01:49.110 --> 00:01:53.640
their own correlation or different correlation
to calculate the bubble diameter depending
00:01:53.640 --> 00:01:58.360
upon the different cases the properties of
the system, or different type of the systems.
00:01:58.360 --> 00:02:03.409
So, I am not going to discuss all those correlations,
but what I am going to see what I have
00:02:03.409 --> 00:02:07.450
discussed already is about the basics how
these correlations are derived. Now you can
00:02:07.450 --> 00:02:12.080
say that for certain system some forces are
important, some forces are not important and,
00:02:12.080 --> 00:02:16.730
you can modify the equations or the diameter
of the bubble, but the basics remains same.
00:02:16.730 --> 00:02:21.370
The next question in the bubble column design,
if you go for bubble column design or if you
00:02:21.370 --> 00:02:26.319
want to understand the bubble column is, what
is the shape of the bubble? So, what we have
00:02:26.319 --> 00:02:30.670
done we have found that what will be the diameter
of the bubble, as I said that I am interested
00:02:30.670 --> 00:02:34.430
in the mass transfer, I am interested in the
heat transfer, I want to do the reaction.
00:02:34.430 --> 00:02:38.890
So, I have to first see that what will be
the shape of the bubble depending on my flow
00:02:38.890 --> 00:02:42.959
rate. Again I am quoting that I am not taking
coalescence into that account if the coalescence
00:02:42.959 --> 00:02:47.900
will take place a bubble break, will take
place this story may be little bit different
00:02:47.900 --> 00:02:52.260
and you have to model the bubble size distribution
and all that can be done with the advanced
00:02:52.260 --> 00:02:56.790
model, I will give the glimpse of that, but
if you have interest we can go and discuss,
00:02:56.790 --> 00:02:59.390
we can discuss it further you can write it
to me.
00:02:59.390 --> 00:03:03.269
This is the next problem is the bubble shape
that what will be the shape of the bubble
00:03:03.269 --> 00:03:06.750
once it will be formed.
So, generally the bubble 4 type of bubble
00:03:06.750 --> 00:03:11.349
shape is being reported in the literature
and, the first shape is if the bubble is very
00:03:11.349 --> 00:03:19.819
small in diameter it will be cynical in nature.
So, you will see a very pretty much spherical
00:03:19.819 --> 00:03:26.400
bubble. So, if the bubble is small you will
see the spherical size bubble, but if you
00:03:26.400 --> 00:03:30.890
put more gas then what will happen before
detachment bubble size will increase. Now
00:03:30.890 --> 00:03:35.800
once the bubble size will increase it will
go to elliptical bubble when you see a ellipse
00:03:35.800 --> 00:03:50.689
nature. So, this is elliptical bubble, now
if you further increase the velocity or the
00:03:50.689 --> 00:03:54.599
bubble size it means the bubble size what
will happen, you will see the bubble which
00:03:54.599 --> 00:03:59.849
will be kind of elliptical, but the upper
surface will be more towards this silicon
00:03:59.849 --> 00:04:02.810
and the bottom surface you will see some (Refer
Time: 04:02) elliptical portion ok.
00:04:02.810 --> 00:04:08.150
But it will not be perfectly ellipse the upper
top surface will start swelling up and it
00:04:08.150 --> 00:04:12.819
will be going towards the spherical shape.
And if you further increase the velocity then
00:04:12.819 --> 00:04:17.190
you will get that a spherical cap bubble,
it means this bottom will get flattened up
00:04:17.190 --> 00:04:21.220
the bottom will go up, it, will be flatten
up and the top will becomes more and more
00:04:21.220 --> 00:04:26.750
spherical you will see this kind of a shape.
Now this bubbles will start bubbling ok well
00:04:26.750 --> 00:04:30.850
if you keep on increasing it you will get
the spherical cap bubble. So, this is called
00:04:30.850 --> 00:04:46.390
a spherical cap bubble spherical cap ok. So,
this kind of 4 type of bubble is being formed
00:04:46.390 --> 00:04:51.850
depending on that velocity and the orphans
diameter which you use for the bubble gas
00:04:51.850 --> 00:04:55.221
injection. .
Now, we know that if suppose the spherical
00:04:55.221 --> 00:04:59.030
bubble is forming you can calculate the diameter
of the bubble very simply that it will be
00:04:59.030 --> 00:05:02.981
what it will be the volume of the bubble you
can calculate and that will be pi by 6 D p
00:05:02.981 --> 00:05:07.460
cube and, if you know the volume of the
bubble you can calculate the diameter of the
00:05:07.460 --> 00:05:13.450
bubble. Now if suppose this is not a spherical,
then the problem comes that how you will define
00:05:13.450 --> 00:05:17.350
the size of the bubble because, suppose is
a elliptical then what you are going to do
00:05:17.350 --> 00:05:22.110
how you are going to decide the size of the
bubble. Now to bubble size or bubble shape
00:05:22.110 --> 00:05:26.790
are actually going to be different and what
we will decide, we will decide based on the
00:05:26.790 --> 00:05:31.910
equivalent diameter ok. Now equivalent diameter
how you will say that for elliptical thing,
00:05:31.910 --> 00:05:35.380
then we have to find the equivalent diameter
based on the that elliptical volume.
00:05:35.380 --> 00:05:39.880
So, we will take the volume of the ellip elliptical
bubble and we will say that this would be
00:05:39.880 --> 00:05:44.020
equivalent to whatever the volume of the spherical
bubble. So, this volume will be fitted in
00:05:44.020 --> 00:05:48.800
which diameter of a spherical bubble which
have the same volume as the of the elliptical
00:05:48.800 --> 00:05:53.690
bubble. So, you have to do the volume balance
and based on that you can find it out the
00:05:53.690 --> 00:05:58.630
de correlation that what will be the equivalent
diameter equivalent to c a diameter for the
00:05:58.630 --> 00:06:00.650
different shaped bubble. So, we define it
that way.
00:06:00.650 --> 00:06:07.620
So, say for elliptical bubble if this is the
a if the major axis is say a, and I am using
00:06:07.620 --> 00:06:12.150
a notation which you might have used widely
in the mathematics classes. So, this is say
00:06:12.150 --> 00:06:20.380
a and if this is b, or let us make it the
mathematic little bit simpler let us say it
00:06:20.380 --> 00:06:26.060
it is 2 a and this is 2 b. So, that from the
axis it is a one side, and from the axis the
00:06:26.060 --> 00:06:31.160
height is b. So, if it is 2 a and 2 b and
I want to find it out for this elliptical
00:06:31.160 --> 00:06:37.030
bubble which major axis is 2 a the minor 1
is 2 b, then what will be the diameter of
00:06:37.030 --> 00:06:40.940
the spherical bubble which will have a equivalent
volume as of the this elliptical bubble.
00:06:40.940 --> 00:06:45.650
So, to do that there is a very simple mathematics
we know that volume of the bubble for the
00:06:45.650 --> 00:06:53.580
spherical bubble that will be pi by 6 say
D p cube I will write it D p e cube, or say
00:06:53.580 --> 00:07:00.500
let us write it d b e let us give a notation
which is d b e, it means the bubble volume
00:07:00.500 --> 00:07:05.300
diameter which is equivalent bubble diameter
in terms of the spherical if this volume is
00:07:05.300 --> 00:07:10.160
equal to the spherical bubble volume. So,
I will write it d b e, and that will be equal
00:07:10.160 --> 00:07:17.280
to that what will be the volume it of this.
Now this volume will be pi by 4 3 and then
00:07:17.280 --> 00:07:24.850
b into a square. So, that will be the volume
of the ellipse and that is equivalent to this
00:07:24.850 --> 00:07:30.190
volume. So, you can find it out what is d
b e. So, d b e if you calculate from this
00:07:30.190 --> 00:07:37.020
place that will be what d b e will be equal
to this pi pi will be cancelled out this 6
00:07:37.020 --> 00:07:44.230
so, you will get 8 into b a square whole raised
to the power 1 by 3.
00:07:44.230 --> 00:07:49.660
So, you will get this will be what will be
the d b e for the elliptical bubble. Now this
00:07:49.660 --> 00:07:54.380
d b e can be used further to do the calculation
because, we know the calculation whatever
00:07:54.380 --> 00:07:58.950
the we did the calculation till now in the
multi phase flow, we did it for the spherical
00:07:58.950 --> 00:08:04.220
particles. So, now you can use this d b e
2 and use your equations whatever we have
00:08:04.220 --> 00:08:09.340
discussed the momentum equation the continuity
equations and, then you can solve these problem
00:08:09.340 --> 00:08:13.850
by using d b e to get that does you can solve
the momentum equation.
00:08:13.850 --> 00:08:19.090
So, that will make your life little bit easier
and that is why for all the bubbles we define
00:08:19.090 --> 00:08:23.850
it it it in this way the diameter we define
for this way ok in this way. Now how it will
00:08:23.850 --> 00:08:27.190
be generated what will be the diameter that
you will be generate whatever I have said
00:08:27.190 --> 00:08:31.250
in the previous, but if suppose the bubble
shape has generated that diameter will be
00:08:31.250 --> 00:08:36.529
further modified and, you have to use this
kind of a d b e this d b e can be used in
00:08:36.529 --> 00:08:41.259
your momentum equation in your continuity
equation if needed or any other equation which
00:08:41.259 --> 00:08:45.110
we have discussed till now. So, you can use
this to do the calculation ok.
00:08:45.110 --> 00:08:49.300
Similarly, you can do it for the other shape
also what you need to do you have to just
00:08:49.300 --> 00:08:53.620
find the volume of that shape and that should
be equivalent to the volume of equivalent
00:08:53.620 --> 00:08:58.490
volume of the sphere which represent the same
volume. So, that is the way you calculate
00:08:58.490 --> 00:09:04.339
the d b e in this way. Now for wobbling bubble,
or a elliptical bubble, different people have
00:09:04.339 --> 00:09:09.930
given different kind of a correlation to calculate
that what will be the d e what will be the
00:09:09.930 --> 00:09:15.160
d b e why because, it is difficult to measure
the 2 a and 2 b how you will measure that.
00:09:15.160 --> 00:09:18.819
So, what you need to do if you want to measure
the 2 a and 2 b, then you have to depend on
00:09:18.819 --> 00:09:22.660
measurement techniques you have to take a
high speed camera, you have to take the photograph
00:09:22.660 --> 00:09:26.040
of the bubble send off.
So, what people have done people have tried
00:09:26.040 --> 00:09:31.020
to correlate it with the for the different
condition different system and many people
00:09:31.020 --> 00:09:36.399
many researcher has given different correlation
to predict that what will be the d b e ok,
00:09:36.399 --> 00:09:42.300
and d b e instead of d b e they have defined
it in a parameter, in another parameter, for
00:09:42.300 --> 00:09:47.709
say elliptical bubble they have parameter
the parameter they have defined is small e
00:09:47.709 --> 00:09:54.130
and, that is small is nothing, but it is equal
to b upon a. So, they have defined a parameter
00:09:54.130 --> 00:09:59.060
e which is b upon a what is the smaller
to the maximum angle. So, e value is going
00:09:59.060 --> 00:10:04.140
to be less than 1 so, this way they have defined
that whatever the e value, they have tried
00:10:04.140 --> 00:10:08.259
to correlate this e value with the different
correlation.
00:10:08.259 --> 00:10:13.209
Now, once you have this e value what you can
do you can convert this in terms of the e,
00:10:13.209 --> 00:10:17.149
you can say that in terms of the e and you
can get the d b e correlation that what will
00:10:17.149 --> 00:10:21.560
be the d b e correlation. So, suppose if you
want to calculate in terms of the e what you
00:10:21.560 --> 00:10:26.750
can do you can replace say b with the e, if
you do that then b will be equal to e into
00:10:26.750 --> 00:10:35.660
a. So, if I replace it here it will be d b
e will be equal to 8 into a and cube, this
00:10:35.660 --> 00:10:40.880
will be a cube and that will be multiplied
by e 1 by 3. Now sorry whole raise to the
00:10:40.880 --> 00:10:48.560
power 1 by 3, now if I do that then it will
be d b e upon a will be equal to 2 e raised
00:10:48.560 --> 00:10:54.399
to the power 1 by 3. So, I can develop this
correlation.
00:10:54.399 --> 00:11:00.329
So, now if I know this d b e upon a if I know
this e value. So, people have what they have
00:11:00.329 --> 00:11:03.839
done they have calculated this e value given
the different correlation in terms of the
00:11:03.839 --> 00:11:08.749
e, for the different flow rates ok for the
different surface tension to the gravity to
00:11:08.749 --> 00:11:13.410
the surface tension ratio based on that, and
they have for depending upon the different
00:11:13.410 --> 00:11:18.050
flow rate, different fluid property and all
this e value will keep on changing and the
00:11:18.050 --> 00:11:23.850
correlation has been developed, in which you
can see that how the e will be correlated
00:11:23.850 --> 00:11:27.329
for the different system.
So, several such correlation is available,
00:11:27.329 --> 00:11:33.720
but most of those correlation again is being
available in the form of e say if I want to
00:11:33.720 --> 00:11:42.120
find this e e is equal to 1 upon c 1 plus
eotvos number raised to the power c 2.
00:11:42.120 --> 00:11:48.959
So, most of this correlation is in this form
e is equal to 1 upon c 1 plus E naught E o
00:11:48.959 --> 00:12:01.800
raised to the power c 2. now this E o is what
it is eotvos number. So, this E o is a eotvos
00:12:01.800 --> 00:12:09.529
number
and which says the ratio of gravitational
00:12:09.529 --> 00:12:18.029
to the surface tension force. So, this eotvos
number is actually gives the ratio of gravitational
00:12:18.029 --> 00:12:30.470
force to surface tension force ok, that is
going to determine that what will be the shape
00:12:30.470 --> 00:12:35.779
of the bubble. So, this is this correlation
is there now many researcher have used most
00:12:35.779 --> 00:12:40.589
of this correlation has formed at it in this
way, the value of the constant c 1 and c 2
00:12:40.589 --> 00:12:45.110
are the constant depends on your semi specific.
And if you change your system, you change
00:12:45.110 --> 00:12:49.540
your property, you change your conditions
this value of c 1 and c 2 will change.
00:12:49.540 --> 00:12:55.029
But most of this correlation of the e is validated
in this way for elliptical and wobbling bubbles
00:12:55.029 --> 00:13:00.410
ok. Now what is the eotvos number actually
you correlate in terms of the eotvos number
00:13:00.410 --> 00:13:07.339
and if you write the eotvos number for this
case it will be g d cube and it will be rho
00:13:07.339 --> 00:13:14.730
of liquid minus rho of gas upon sigma. So,
this is the way eotvos number is being defined.
00:13:14.730 --> 00:13:18.810
So, you can say that this is going to be the
gravitational forces what is the gravitational
00:13:18.810 --> 00:13:24.079
forces there and what is going to be the your
surface tension force ok. So, this is the
00:13:24.079 --> 00:13:28.350
ratio of this most of this correlation is
being developed it it in this way. So, you
00:13:28.350 --> 00:13:32.100
can find that what will be the shape of the
bubble and, if you find the shape you can
00:13:32.100 --> 00:13:37.759
also find the e value if you know the e value
you can find in the d b e value ok. So, all
00:13:37.759 --> 00:13:40.850
these correlation all these things you can
find it out ok.
00:13:40.850 --> 00:13:44.980
Now, this d b e can be used in the momentum
equation, or any other equation which you
00:13:44.980 --> 00:13:50.100
want to understand the flow. So, that is the
way we discuss about the shape and definitely
00:13:50.100 --> 00:13:53.869
there is mainly 4 type of shape is available
as I said it is spherical, if the velocity
00:13:53.869 --> 00:13:58.579
is very less, bubble diameter is very less,
most of the bubbles are spherical in nature
00:13:58.579 --> 00:14:03.470
if the diameter is very less. So, if the diameter
is less it will be spherical bubble if you
00:14:03.470 --> 00:14:09.300
increase the diameter further it will be elliptical,
if you further increase the diameter flow
00:14:09.300 --> 00:14:13.779
rate from which the diameter is increasing
the bottom portion will start shrinking, the
00:14:13.779 --> 00:14:18.280
top portion will be becomes like a sphere.
And then further increase velocity you will
00:14:18.280 --> 00:14:23.279
see that a spherical cap bubble where the
bottom will be flat and the top will be the
00:14:23.279 --> 00:14:27.040
spherical shape a spherical cap kind of a
behaviour. So, this kind of a force shape
00:14:27.040 --> 00:14:31.050
of the bubble is being formed.
Now, next is what will be the bubble velocity
00:14:31.050 --> 00:14:35.260
how to calculate the bubble velocity. Now
if I know the velocity, I know the diameter,
00:14:35.260 --> 00:14:39.360
I know the shape, I can calculate about the
mass transfer provided, if I know the volume
00:14:39.360 --> 00:14:43.079
fraction ok.
So, for volume fraction again several correlations
00:14:43.079 --> 00:14:46.920
are available most are those correlation are
empirically fitted correlation based on the
00:14:46.920 --> 00:14:51.699
experimental data. Again I am not interested
to do all those things here because, that
00:14:51.699 --> 00:14:55.740
will be a dedicated work on the bubble column
reactor, what we are trying to see is that
00:14:55.740 --> 00:15:02.009
how the basics force balance equations can
be used to understand or to solve the these
00:15:02.009 --> 00:15:05.459
kind of a reactor problem.
So, in the bubble column again if you want
00:15:05.459 --> 00:15:11.200
to find the velocity, then we know that how
the velocity if the bubble will move upward,
00:15:11.200 --> 00:15:15.759
once it will achieve its terminal velocity
then what will happen, that the forces acting
00:15:15.759 --> 00:15:21.119
on it will be equal. Now what will be the
forces acting on it it will be buoyancy force,
00:15:21.119 --> 00:15:24.990
it will be gravity force and it will be the
drag force, they are going to be equal. Once
00:15:24.990 --> 00:15:29.529
they are going to be equal the bubble will
achieve its terminal velocity and it will
00:15:29.529 --> 00:15:32.490
rise with its terminal velocity.
And that is going to happen because, when
00:15:32.490 --> 00:15:37.629
the bubble will start then after certain time
it will achieve its terminal velocity, it
00:15:37.629 --> 00:15:41.779
will achieve where all the forces will be
balanced, and then it will be achieving its
00:15:41.779 --> 00:15:46.179
terminal velocity. So, if you want to calculate
that what will be the bubble terminal velocity,
00:15:46.179 --> 00:15:50.550
then what we can do again we can use the force
balance equation which we have done. We can
00:15:50.550 --> 00:15:57.149
say that drag will be equal to whatever the
drag will be equal to the buoyancy minus the
00:15:57.149 --> 00:16:03.680
gravity ok because, this bubble will be lifting
upward. So, what will happening that gravity
00:16:03.680 --> 00:16:07.660
will be going to be balanced with the drag
and this ok.
00:16:07.660 --> 00:16:12.759
So, drag and the buoyancy so, in that case
if I write the equation I will say that the
00:16:12.759 --> 00:16:22.509
drag force is going to be equal and we calculated
the drag force. So, drag and buoyancy will
00:16:22.509 --> 00:16:27.059
be equal and once I say buoyancy the interact
will be equal I am taking the gravity in part
00:16:27.059 --> 00:16:32.050
of the buoyancy. So, if you do that you can
write it as a C D the drag force equation
00:16:32.050 --> 00:16:39.930
is C D into area into rho into V square upon
2. So, that will be the bubble this and, then
00:16:39.930 --> 00:16:50.670
buoyancy will be pi by 6 or you can say pi
by 6 d bubble cube and that will be rho l
00:16:50.670 --> 00:16:56.470
minus rho g into g. So, that will be your
overall the buoyancy force which will be acting
00:16:56.470 --> 00:17:01.240
buoyancy of the this because of that it will
be this kind of forcing it.
00:17:01.240 --> 00:17:05.650
So, drag and buoyancy is going to be equal
the buoyancy will be pulling it upward drag
00:17:05.650 --> 00:17:11.110
will be pulling it downward ok. So, in that
thing if you do it then what will happen that
00:17:11.110 --> 00:17:15.480
your this forces will be equal so, if you
do that you can write it in in terms of C
00:17:15.480 --> 00:17:20.270
D, if you know that area what will be the
area if I am taking again a spherical bubble
00:17:20.270 --> 00:17:26.300
the area projected area will be pi by 4 d
b square, this will be the row of fluid or
00:17:26.300 --> 00:17:30.750
it means it will be if I am taking liquid,
this will be flow of liquid into velocity
00:17:30.750 --> 00:17:34.220
of the bubble.
Now say if velocity of the bubble, we are
00:17:34.220 --> 00:17:38.910
getting it the terminal velocity to I will
state V T b square terminal velocity of the
00:17:38.910 --> 00:17:47.530
bubble divide by 2 it will be pi by 6 d b
cube into rho l minus rho g into g. So, you
00:17:47.530 --> 00:17:51.881
can simplify it further we can write it in
terms of the Reynold number. So, if we try
00:17:51.881 --> 00:17:55.280
to write it it in terms of their internal
number. So, that we can easily do it we can
00:17:55.280 --> 00:18:01.030
write it in the non dimensional form I can
say that C D will be equal to I will writing
00:18:01.030 --> 00:18:03.600
in I am trying to write it it in terms of
the Reynolds number.
00:18:03.600 --> 00:18:11.300
So, this pi and this pi will be cancelled
out it will be this 4 D p and this D p will
00:18:11.300 --> 00:18:18.111
be cancelled out. So, you will get d b ok,
then you will say rho l minus rho g you will
00:18:18.111 --> 00:18:25.230
see g and then it will be once you will divide
it you will see that pi by 6 naught d. So,
00:18:25.230 --> 00:18:29.480
this will be 6 and this will be rho into l
rho l.
00:18:29.480 --> 00:18:34.890
So, you will get something like this now what
we need to find, there will be this V T b
00:18:34.890 --> 00:18:40.810
square also V T b square. Now this 2 will
be also multiplied so, this will be the 2.
00:18:40.810 --> 00:18:44.680
So, you will get this kind of equation for
the C D which we have already developed. So,
00:18:44.680 --> 00:18:50.050
if you see that C D will be equal to this
2 pi pi will be cancelled out d b cube if
00:18:50.050 --> 00:18:56.320
you go out so it will be only d b. So, this
will be 4 into 2 8, then it will be d b rho
00:18:56.320 --> 00:19:00.020
l minus rho g into g upon rho l into V T b
square.
00:19:00.020 --> 00:19:03.900
Now we can write it in terms of the Reynolds
number, if you want to write it in terms of
00:19:03.900 --> 00:19:07.800
the Reynolds number what we have to do, we
know that what is Reynold number I have to
00:19:07.800 --> 00:19:12.400
multiply it here by it is V square. So, I
want to write it it in terms of the Reynold
00:19:12.400 --> 00:19:16.400
number a square function so, that my velocity
will be accommodated. So, what I am going
00:19:16.400 --> 00:19:21.030
to do if I want to write it it in this way,
I will write it d b square, I will multiply
00:19:21.030 --> 00:19:27.010
up d b square down, I will multiply 1 rho
l up I am multiplying with 1 rho l up and
00:19:27.010 --> 00:19:32.290
1 rho l up 1 rho l down.
So, what will happen now this equation will
00:19:32.290 --> 00:19:47.340
be 8 into d b cube rho l minus rho g into
g into rho l upon 6 rho l square so, rho l
00:19:47.340 --> 00:19:55.480
square into V T b square into d b square.
Now what we need we need mu square up and,
00:19:55.480 --> 00:20:00.680
then 1 mu square will be multiplied with the
down. Now if you see this this is what this
00:20:00.680 --> 00:20:06.740
is nothing, but Reynold number.
So, I can write this equation as C D will
00:20:06.740 --> 00:20:24.010
be equal to 8 upon 6 8 d b cube rho l minus
rho g into rho l into g upon you say mu square
00:20:24.010 --> 00:20:31.880
6 into mu square and, then this value you
can write it as mu square upon rho l square
00:20:31.880 --> 00:20:40.560
into d b square into V T b square. Now this
function is nothing, but 1 upon Reynold number
00:20:40.560 --> 00:20:50.270
square. So, I can write it as 8 upon 6 this
will be 8 upon 6 d b cube rho l minus rho
00:20:50.270 --> 00:20:59.040
g into rho l into g upon mu square, and this
will be 1 upon Reynold number square, so,
00:20:59.040 --> 00:21:02.841
we find that Reynold number and because this
is based on that. So, I will say Reynold number
00:21:02.841 --> 00:21:10.230
of the bubble, so bubble Reynold number square.
So, this is bubble Reynold number.
00:21:10.230 --> 00:21:20.250
Now, this function whatever we are saying
that this is nothing, but are called Archimedes
00:21:20.250 --> 00:21:25.490
number. So, this function is called as Archimedes
number and this will be if you write it here
00:21:25.490 --> 00:21:33.260
then it is 8 by 6 or you write 4 by 3 better.
So, you will write 4 by 3 Archimedes number
00:21:33.260 --> 00:21:39.400
upon Reynold number square Reynold number
of bubble square that will be the C D value
00:21:39.400 --> 00:21:42.400
.
Now, Archimedes number this is nothing, but
00:21:42.400 --> 00:21:53.730
Archimede number
and which defined the motion of the fluid
00:21:53.730 --> 00:21:59.240
basically due to the density difference. So,
this is the Archimede number defines the motion
00:21:59.240 --> 00:22:20.470
of the fluid of the fluid due to density difference.
So, why the bubble is rising bubble is rising
00:22:20.470 --> 00:22:27.940
mainly because, of buoyancy and the buoyancy
is being generated mainly because of the density
00:22:27.940 --> 00:22:34.060
difference. So, Archimedes numbers shows that
the motion of the fluid of motion of the bubble,
00:22:34.060 --> 00:22:38.560
because of the density difference it is being
characterized by the Archimedes number, and
00:22:38.560 --> 00:22:43.560
the Archimedes number is being defined by
this value which is d b cube rho l minus rho
00:22:43.560 --> 00:22:48.880
g into rho l g upon mu square.
So, that is nothing, but the Archimedes number;
00:22:48.880 --> 00:22:52.940
and Archimedes number actually characterize,
the motion of the fluid due to density difference.
00:22:52.940 --> 00:22:58.640
So, if I do the force balance again I will
get the correlation between C D and A r e.
00:22:58.640 --> 00:23:03.230
Now what if you want to find the bubble terminal
velocity you have the formula available, that
00:23:03.230 --> 00:23:06.680
what will be the bubble terminal velocity.
Now the only question is what will be the
00:23:06.680 --> 00:23:09.650
value of C D.
Now again we have discussed several correlation
00:23:09.650 --> 00:23:14.260
while discussing the drag force, you can use
depending upon the system, depending upon
00:23:14.260 --> 00:23:18.511
what is your Reynolds number as we discussed
that several correlation is there we are valid
00:23:18.511 --> 00:23:23.950
for a particular range, you can find the C
D value. Now most important or most oftenly
00:23:23.950 --> 00:23:29.020
used or widely used correlation for the C
D for the bubble column is Sciller Nauman
00:23:29.020 --> 00:23:38.000
which is 1 upon sixteen upon R e into 0.15
into R e raised to the power 0.687 this is
00:23:38.000 --> 00:23:50.900
nothing, but the Sciller Nauman equation.
So, Sciller Nauman equation is being used
00:23:50.900 --> 00:23:54.630
widely to do this C D.
Now, if you have the C D you can correlate,
00:23:54.630 --> 00:23:59.760
it you can find it out the bubble velocity,
it will be also the function of Reynold number,
00:23:59.760 --> 00:24:04.420
you can get the bubble velocity. So, Archimedes
number if you if you see the Archimedes number,
00:24:04.420 --> 00:24:08.730
if you know the bubble diameter, if you know
the system, you know the system viscosity,
00:24:08.730 --> 00:24:12.760
you know the density of the liquid. you know
the density of the gas and if you can calculate
00:24:12.760 --> 00:24:16.010
that what will be the d b what will be a bubble
diameter.
00:24:16.010 --> 00:24:20.170
Then what will happen Archimedes number will
be calculated, now bubble diameter will be
00:24:20.170 --> 00:24:24.630
fixed the moment you fix you distribute your
plate, your gas velocity, we have already
00:24:24.630 --> 00:24:28.210
discussed that how to calculate the bubble
diameter. We have already discussed that how
00:24:28.210 --> 00:24:32.210
D p will be modified if the bubble diameter
is of different shape, you can do that you
00:24:32.210 --> 00:24:37.100
can calculate the d b, if you know the d b
you can calculate the Archimedes number, if
00:24:37.100 --> 00:24:40.900
you know the Archimedes number ideally speaking,
you can calculate the terminal velocity of
00:24:40.900 --> 00:24:45.190
the bubble. So, we will also get that what
will be the bubble terminal velocity. .
00:24:45.190 --> 00:24:49.990
And if you get all this phenomenon you can
actually model all the things you can understand
00:24:49.990 --> 00:24:53.450
that how the velocity of the bubble is there,
what will be the velocity of the bubble you
00:24:53.450 --> 00:24:58.500
can develop the correlation, for the mass
transfer for the heat transfer and all and
00:24:58.500 --> 00:25:02.900
you can analyze the system. So, this is the
basic force balance we are doing, again we
00:25:02.900 --> 00:25:07.030
have neglected many of the part like we have
not included the shear that which will be
00:25:07.030 --> 00:25:10.010
caused and, which may change the bubble shape,
bubble size.
00:25:10.010 --> 00:25:14.280
We have neglected that if the bubbles are
having coalescence or their changing the shape
00:25:14.280 --> 00:25:19.780
over the time, or if they are having the coalescence
they are forming a bigger bubble they or they
00:25:19.780 --> 00:25:24.550
again they break into the smaller bubble,
we have not taken in to the account any distribution
00:25:24.550 --> 00:25:30.050
the bubble death, or bubble generation, or
any shear migration, or any because of
00:25:30.050 --> 00:25:33.990
the shear or any other forces the breakage
of the bubble, all those things we have not
00:25:33.990 --> 00:25:37.410
generated, we have not done.
Because if you do that then you cannot solve
00:25:37.410 --> 00:25:41.910
it the analytical solution and, I said in
the beginning itself that the motivation of
00:25:41.910 --> 00:25:47.510
all this course is to have a analytical solution
a simpler solution to analyze the flow, if
00:25:47.510 --> 00:25:51.560
you want to have a kind of a detailed solution
whatever I said, then we have to go for the
00:25:51.560 --> 00:25:55.060
numerical modelling approach which we have
already discussed in the previous cases.
00:25:55.060 --> 00:26:00.510
So, this is all about the bubble column force
balances, now as I said that different type
00:26:00.510 --> 00:26:05.170
shape of the bubble is being formed different
regimes is being there, and because of
00:26:05.170 --> 00:26:10.000
the bubble coalescence bubble death and all.
The typical flow structure there are several
00:26:10.000 --> 00:26:15.070
flow structures has been found in the bubble
column, but different flow structures depend
00:26:15.070 --> 00:26:20.560
again on the column geometry, column dimensions,
your velocities properties of the fluids all
00:26:20.560 --> 00:26:25.330
these actually play a role in determining
these structures. Now these are the 2 graphs
00:26:25.330 --> 00:26:30.730
where the Diaz et al in 2006 and 2008 and
followed by some of my own work which we have
00:26:30.730 --> 00:26:35.410
published in as a thesis, and some chemical
engineering science paper, we have observed
00:26:35.410 --> 00:26:39.560
that there is different regimes you can get
different kind of flow structures, you can
00:26:39.560 --> 00:26:46.010
get and that flow structure in 2 D column
this is for the 2 D column and I will not
00:26:46.010 --> 00:26:51.200
say 2 D column I will say it a rectangular
column.
00:26:51.200 --> 00:26:56.090
So, in the rectangular column these are the
flow regimes is being observed, that if your
00:26:56.090 --> 00:27:00.490
velocity if you are increasing on this side
what will happen, if your now velocity is
00:27:00.490 --> 00:27:05.850
their low H by W ratio H by W ratio means
height to width ratio of the liquid say this
00:27:05.850 --> 00:27:10.340
is the width and, this is the height of the
liquid inside. So, if the height to width
00:27:10.340 --> 00:27:15.330
ratio is lower say around 1 you get that what
happen if you inject the plume, you will see
00:27:15.330 --> 00:27:20.870
a single plume which moves towards 1 wall,
if you have higher velocity for H by d ratio
00:27:20.870 --> 00:27:25.840
1 H by W ratio less, than 1 then you will
see what will happen that whatever the gas
00:27:25.840 --> 00:27:30.780
you will inject it will form like a jet and
it will move outside. If you have even higher
00:27:30.780 --> 00:27:35.020
height, then what will happen you see the
unstructured behaviour and you observe certain
00:27:35.020 --> 00:27:39.410
plume. So, if suppose the height of the liquid
is there, and you inject the bubble. So, I
00:27:39.410 --> 00:27:44.190
inject the gas it form certain plume you will
see this sneak kind of a plume behaviour is
00:27:44.190 --> 00:27:46.570
there.
So, these works are being done again these
00:27:46.570 --> 00:27:52.010
are the detailed analysis of the bubble column,
but I am just trying to show you that the
00:27:52.010 --> 00:27:55.610
regimes are there in the bubble column even,
if you operate the bubble column there are
00:27:55.610 --> 00:28:01.100
different regimes and that regimes again,
if you see these things it is going in the
00:28:01.100 --> 00:28:05.380
rectangular column, it is going to be the
function of the dimensions of the column,
00:28:05.380 --> 00:28:09.721
or the liquid height inside the column, it
is going to be the function of the velocity
00:28:09.721 --> 00:28:14.100
at which you are operating the column ok.
And if you make it inclined or something it
00:28:14.100 --> 00:28:19.740
would be also the function of inclination.
Similarly, Chen et al and Lin et al as in
00:28:19.740 --> 00:28:24.080
1994 and 1996 has given the dynamic macroscopic
structure, and they said that their different
00:28:24.080 --> 00:28:28.780
structures are being formed. And if you want
to analyze those structures, you cannot use
00:28:28.780 --> 00:28:33.481
the single model which can predict all the
structural which can cover all the structure
00:28:33.481 --> 00:28:38.390
and the multi scale nature of the bubble column
has been showed, it means you have to use
00:28:38.390 --> 00:28:43.630
the different scale model or you have to use
the model which can be used at the different
00:28:43.630 --> 00:28:48.720
length scales, which can predict at different
length scale, or which is accurate or equally
00:28:48.720 --> 00:28:52.820
valid at different length of scale, then only
you can found all the structures inside.
00:28:52.820 --> 00:28:58.730
So, this is about the glimpse of the bubble
column whatever is available industry, you
00:28:58.730 --> 00:29:03.070
can do the simple calculations, if you want
to find that what will be the shape of the
00:29:03.070 --> 00:29:06.870
bubble, what will be the velocity terminal
velocity of the bubble, what will be the diameter
00:29:06.870 --> 00:29:11.660
of the bubble, or you can have a numerical
methods again you can have a detailed analysis.
00:29:11.660 --> 00:29:16.100
So, you can do the simple force balance and
you will get a clear cut idea, or not even
00:29:16.100 --> 00:29:20.060
the very clear cut idea, but at least you
will get a fair idea that how your system
00:29:20.060 --> 00:29:24.760
is going to behave, what will be the bubble
size. At least the bubble size you will calculate
00:29:24.760 --> 00:29:29.020
definitely to be very close to the mean bubble
size, which you will be found in your system.
00:29:29.020 --> 00:29:33.370
So, what will be the bubble size what would
be the diameter of the bubble, or what will
00:29:33.370 --> 00:29:37.430
be the bubble size, what type of shape you
will get if you are getting this shape how
00:29:37.430 --> 00:29:40.940
the bubble diameter will change, what will
be the velocity of the bubble which you will
00:29:40.940 --> 00:29:44.990
through which it will be moving upward.
So, different correlations is also being developed
00:29:44.990 --> 00:29:49.900
again I saying that while telling the velocities
this you can find the velocity here, different
00:29:49.900 --> 00:29:54.520
researcher have, different given different
correlation lot of correlation is there one
00:29:54.520 --> 00:30:01.080
of the important correlation which I missed
here is actually given by the Clift Clift
00:30:01.080 --> 00:30:07.360
and grace. To find that what will be the bubble
rise velocity and, they said that bubble rise
00:30:07.360 --> 00:30:22.140
velocity U b r which is the bubble rise velocity
it will be equal to 0.711 under root of g
00:30:22.140 --> 00:30:33.610
into d b, where d b is the bubble diameter,
and g is the gravitational fault. So, this
00:30:33.610 --> 00:30:36.450
will be there.
So, similarly lot of people have done different
00:30:36.450 --> 00:30:40.690
correlation has been developed, you can calculate
the bubble rise velocity, you can find the
00:30:40.690 --> 00:30:44.400
if you know the bubble rise velocity, you
can find that what will be the residence time
00:30:44.400 --> 00:30:48.760
inside, that will be be kind of you can be
discuss, you can if you know the bubble this
00:30:48.760 --> 00:30:52.910
now, you can calculate the Reynolds number
you can use your mass transfer equations,
00:30:52.910 --> 00:30:57.320
to calculate that mass transfer whatever it
is happening. You can use the film theory,
00:30:57.320 --> 00:31:00.950
you can use the penetration theory, you can
use the surface renewal theory, all those
00:31:00.950 --> 00:31:06.050
theories whatever you feel is valid or is
valid for your case, you can do that you can
00:31:06.050 --> 00:31:09.890
do the analysis of the bubble column, you
can see that how much reaction is going to
00:31:09.890 --> 00:31:13.810
happen what will be the conversion, what will
be the residence time. So, all those studies
00:31:13.810 --> 00:31:16.620
can be done.
Similarly, the another class of the bubble
00:31:16.620 --> 00:31:21.990
column you can say is air lift rector. Now
this is again a gas liquid system what we
00:31:21.990 --> 00:31:28.260
do we give the guided path to the gas. So,
what we put we put some 1 riser and downer
00:31:28.260 --> 00:31:33.010
this. So, we put some draft tube these
are the draft tubes ok sorry, this is the
00:31:33.010 --> 00:31:37.960
draft tube and this is the draft tube and
what we happen we inject the bubbles, or we
00:31:37.960 --> 00:31:42.340
inject the air only and that the riser section,
why we call it riser because here the bubble
00:31:42.340 --> 00:31:45.330
is moving upward, and with the bubble liquid
will also move upward.
00:31:45.330 --> 00:31:49.820
Now what will happen on the disengagement
section, the bubble will go outside of the
00:31:49.820 --> 00:31:53.910
system while the liquid, which is coming here
because most of the bubble is coming from
00:31:53.910 --> 00:31:58.260
this place on this place. The liquid will
have only 1 path to go down from this place
00:31:58.260 --> 00:32:02.620
which is called downer, and again it will
come back and do the riser. So, you get a
00:32:02.620 --> 00:32:07.320
directed flow this kind of a system is widely
used, there are different geometries possible
00:32:07.320 --> 00:32:12.190
the riser can be centered, of the column the
riser can be near the wall, or it can be on
00:32:12.190 --> 00:32:14.850
the one side it can be riser, other side can
be downer.
00:32:14.850 --> 00:32:19.800
So, different type of structures are available,
these kind of flow reactors are widely used
00:32:19.800 --> 00:32:24.060
for the biological application, rest water
treatment or any (Refer Time: 32:23) kind
00:32:24.060 --> 00:32:27.790
of a generation of biological application
this kind of air lift reactors are widely
00:32:27.790 --> 00:32:32.170
used, all the principles are going to remain
same, the force balances are going to remain
00:32:32.170 --> 00:32:36.820
same, as we have discussed earlier ok. The
only thing will be the structure will be different
00:32:36.820 --> 00:32:41.200
and if you want to solve the 3 dimensional
simulations, the way we did the modelling
00:32:41.200 --> 00:32:45.700
then the models will be little bit different
the flow profiles will be different, but the
00:32:45.700 --> 00:32:51.100
basic force balance for the bubble size, for
the bubble velocity for the shape, this these
00:32:51.100 --> 00:32:54.150
are going to be the same as whatever we have
discussed till now.
00:32:54.150 --> 00:32:59.120
So, with this gas liquids column or gas liquid
systems, we have covered which is the main
00:32:59.120 --> 00:33:04.060
class is the bubble column and air lift reactor
ok. So, I am not going to discuss air lift
00:33:04.060 --> 00:33:08.120
reactor in detail, if you have any problem
or if you have certain interest please write
00:33:08.120 --> 00:33:12.730
to me on forum and, we will try to discuss
it further ok, but that will be the offline
00:33:12.730 --> 00:33:16.080
discussion.
So, with this what we will move now towards
00:33:16.080 --> 00:33:21.480
the gas solid reactors. So, gas liquid reactor
we have already covered, the next class of
00:33:21.480 --> 00:33:25.970
the reaction, or next class of the reactor
is gas solid reactor.
00:33:25.970 --> 00:33:31.220
Now in the gas solid reactor actually there
are different type of reactor available, now
00:33:31.220 --> 00:33:39.660
those are packed bed reactor is 1 of them,
then fluidized bed reactor actually before
00:33:39.660 --> 00:33:44.510
fluidized bed there will be 1 more thing will
come which is called tricle bed, but that
00:33:44.510 --> 00:33:51.630
is mostly tricle bed are gas liquid solid,
most of the time it is being operated as a
00:33:51.630 --> 00:33:56.080
gas liquid solid not most of the time the
tricle bed reactors are gas liquid solid reactor,
00:33:56.080 --> 00:34:00.550
then fluidized bed reactor, then fluidized
bed has a certain class, now it can be bubbling
00:34:00.550 --> 00:34:22.349
fluidized bed ok, it can be turbulent fluidized
bed, fluidize or it can be circulating fluidized
00:34:22.349 --> 00:34:34.919
bed. There are several other class, we will
discuss about the regimes, but mainly this
00:34:34.919 --> 00:34:39.220
is divided in this 3 part bubbling, turbulent
and the circulating fluidized bed.
00:34:39.220 --> 00:34:44.089
So, what we are going to do now, we are going
to discuss briefly about all these beds we
00:34:44.089 --> 00:34:48.210
will discuss mainly about the packed bed tricle
bed is approximately same again all the force
00:34:48.210 --> 00:34:51.200
balance will be going to be the same, only
the liquid part will be increased,then we
00:34:51.200 --> 00:34:55.440
will discuss about the fluidized bed and in
the fluidized bed we will try to discuss mainly
00:34:55.440 --> 00:35:00.500
about the bubbling bed and briefly about the
circulating fluidized bed, again we will try
00:35:00.500 --> 00:35:04.090
to see some force balances here.
So, let us start with the packed bed I will
00:35:04.090 --> 00:35:08.509
briefly cover it most of you might have done
it thoroughly, but I just want to show that
00:35:08.509 --> 00:35:13.740
how the force balances which we have learnt
can be used to do the force balance in the
00:35:13.740 --> 00:35:18.270
packed bed and to derive the some of the equations,
which is widely used in the packed bed reactor.
00:35:18.270 --> 00:35:22.710
So, now what is packed bed or fixed bed, it
is also referred to as a fixed plate what
00:35:22.710 --> 00:35:27.920
we do we dump the solids inside the column,
inside the reactor say this is my reactor
00:35:27.920 --> 00:35:32.200
vessel, we dump the solid though I sold a
very systematic bed, but generally the bed
00:35:32.200 --> 00:35:37.480
is not being. So, that was symmetric. You
dump the solids and it forms a certain shape
00:35:37.480 --> 00:35:42.779
inside. The only thing is you operate it at
a velocity that the bed will not move it is
00:35:42.779 --> 00:35:46.910
lower than the fluidization velocity, or minimum
fluidization velocity, the solid will be in
00:35:46.910 --> 00:35:52.920
the packed form ok, and it means what it will
be packed and they will not move in the time
00:35:52.920 --> 00:35:56.200
frame of reference.
If you talk about the with the time the particle
00:35:56.200 --> 00:36:01.099
movement will be 0 they will not be moving.
So, that this kind of a bed where the particle
00:36:01.099 --> 00:36:07.140
is being dumped, or catalysts are being dumped
and, they held at a certain place and their
00:36:07.140 --> 00:36:12.589
place or their position does not change with
the time it is called as a packed bed. So,
00:36:12.589 --> 00:36:18.569
the position of the solid they move certain
things, but not much position of the solid
00:36:18.569 --> 00:36:27.790
they can vibrate, but they cannot move solid
change with the time.
00:36:27.790 --> 00:36:34.089
So, such frame of reference is called packed
bed reactors, now this is 1 of the simplest
00:36:34.089 --> 00:36:50.569
gas solid reactor ok, very simple the advantage
is low maintenance, low cost, because there
00:36:50.569 --> 00:36:56.089
is nothing available here ok. So, this is
all is there the only problem is the heat
00:36:56.089 --> 00:37:14.329
management, the problem is temperature management
or heat management slash control. So, this
00:37:14.329 --> 00:37:19.970
is the only problem neither generally this
reactors are very calm, very simple what you
00:37:19.970 --> 00:37:25.400
need to do very simple to operate also and,
there is no maintenance cost almost only the
00:37:25.400 --> 00:37:29.660
cost of the catalyst you need to change, but
the column wise the reactor wise there will
00:37:29.660 --> 00:37:33.819
be no maintenance it will be available. So,
it is and it is very low cost because you
00:37:33.819 --> 00:37:38.289
just have to dump the solid inside.
You take a vessel you dump the solid inside,
00:37:38.289 --> 00:37:42.730
you pass the gas or the liquid you can pass
the gas or liquid, and you have to maintain
00:37:42.730 --> 00:37:48.180
it in such a way that the particle does not
fluidize ok. So, you have to maintain a velocity
00:37:48.180 --> 00:37:53.180
which is lower than the minimum fluidization
velocity. The only drawback of this column
00:37:53.180 --> 00:37:58.099
is you have a very high pressure drop, the
pressure drop will increase and if you keep
00:37:58.099 --> 00:38:02.730
on increasing the bed length of bed height
the pressure drop will be very high. So, what
00:38:02.730 --> 00:38:08.559
is the basic question which you have to encounter
and once you are designing a packed bed reactor
00:38:08.559 --> 00:38:17.099
is that what will be the pressure drop, or
what will be the pump specification of blower
00:38:17.099 --> 00:38:23.130
specification, or compressor specification,
you need to pass the flow or pass the gas
00:38:23.130 --> 00:38:26.420
from this packed bed.
So, you have to give that much delta P that
00:38:26.420 --> 00:38:31.390
that should be operated at that delta P or
that pressure then only the gas will pass
00:38:31.390 --> 00:38:36.160
through this bed. So, that is the only question
is being asked or you should understand that
00:38:36.160 --> 00:38:40.920
this much is the pressure requirement is there.
So, the delta P calculation in the packed
00:38:40.920 --> 00:38:45.970
bed is the major critical parameter ok, the
bed has certain several advantages I discuss
00:38:45.970 --> 00:38:53.009
very simple geometry, low cost, low maintenance,
ok it performs well only for very highly exothermic
00:38:53.009 --> 00:38:56.779
reaction, or endothermic reaction.
Whether the heat evolved from the system,
00:38:56.779 --> 00:39:01.480
or you supply the heat from outside of the
system you are supplying the energy from the
00:39:01.480 --> 00:39:05.609
outside, what happened if the diameter of
the column is very big, then you will not
00:39:05.609 --> 00:39:09.650
see they will proper temperature balance.
So, you will see the temperature gradient
00:39:09.650 --> 00:39:14.680
across the radial and across the axis also
if you are supplying the temperature, or hot
00:39:14.680 --> 00:39:19.069
air or something hot fluid. So, you will see
the temperature gradient the temperature maintenance
00:39:19.069 --> 00:39:23.829
or temperature management of the bed is not
that good, temperature control of the bed
00:39:23.829 --> 00:39:29.410
is not that good, and in case of very fast
reaction a very highly exothermic reaction,
00:39:29.410 --> 00:39:33.720
you see some hot spot formation and it may
also cause a runaway reaction.
00:39:33.720 --> 00:39:39.269
So, these are the basic drawback of the packed
bed reactors, but the major advantage is it
00:39:39.269 --> 00:39:44.079
is a simple you have to just dump the solid
and then forget about it your job will be
00:39:44.079 --> 00:39:49.319
done. So, it is very easy to operate very
easy to handle, very easy to maintenance,
00:39:49.319 --> 00:39:54.960
and it is low cost and that is why that given
a choice, if I have a choice I would never
00:39:54.960 --> 00:39:59.720
like to operate a fluidized bed, I will always
try to go with the packed bed the fluidized
00:39:59.720 --> 00:40:02.349
bed we operate and we will discuss about the
fluidized bed.
00:40:02.349 --> 00:40:07.990
Once the conditions are such that we cannot
live with a packed bed reactor ok, in the
00:40:07.990 --> 00:40:13.089
packed bed the calculations are very simple
you just need to have 1 question in your mind
00:40:13.089 --> 00:40:18.009
that what will be the pressure drop needed,
to force the fluid through the bed and based
00:40:18.009 --> 00:40:22.180
on that pressure drop calculation, you can
calculate that what will be the pump specification,
00:40:22.180 --> 00:40:27.369
or compressor is specification, or blower
specification, you require. So, what we are
00:40:27.369 --> 00:40:29.819
going to do we are going to see that what
will be the force balance.
00:40:29.819 --> 00:40:38.299
So, suppose this is a bed and certain solids
are dumped inside of the bed as you eat, there
00:40:38.299 --> 00:40:43.359
is some you are seeing some force. So, the
solids are being dumped, they are being kept
00:40:43.359 --> 00:40:49.640
inside. Now let us assume that the height
of the bed is say L b this is the length of
00:40:49.640 --> 00:40:55.589
the bed and the area is a capital A is the
area of this, or you can say the diameter
00:40:55.589 --> 00:40:59.009
I am writing in terms of the area, because
the area will be cancelled out all the time.
00:40:59.009 --> 00:41:03.710
And this is the superficial velocity which
is say U naught, which will be the superficial
00:41:03.710 --> 00:41:09.599
velocity of the gas, which is going inside
the reactor. So, what we need to do we need
00:41:09.599 --> 00:41:13.519
to calculate that what will be the delta P.
Now, let us assume that we have already done
00:41:13.519 --> 00:41:17.880
that delta P calculation in the beginning
of this multi phase flow courses. And I will
00:41:17.880 --> 00:41:21.710
take you a little bit back and we have also
discussed it in this course that for single
00:41:21.710 --> 00:41:25.539
phase flow how you will calculate what will
be the delta P equation, we have already done
00:41:25.539 --> 00:41:29.759
that ok we have seen that you can solve
the Navier stoke equation or Bernoulli equation
00:41:29.759 --> 00:41:34.489
and, you can derive the delta P. So, the delta
P equation for the single phase flow where
00:41:34.489 --> 00:41:39.039
the flow is taking place in a pipe is being
kind of derived and that equation, if you
00:41:39.039 --> 00:41:47.210
remember this delta P will be equal to 4 delta
P upon rho will be equal to 4 f, they should
00:41:47.210 --> 00:41:54.390
be friction factor L V square upon 2 this
will be divided by D.
00:41:54.390 --> 00:41:59.069
So, this is the delta P equation where f is
the fanning friction factor. So, you will
00:41:59.069 --> 00:42:04.289
get this equation now this equation again
can be modified actually you can see that
00:42:04.289 --> 00:42:08.680
how to calculate so, you know the delta P
in a pipeline. So, this is the equation only
00:42:08.680 --> 00:42:13.539
if the single pipe line is there 1 pipe line
is there empty pipe line, where the fluid
00:42:13.539 --> 00:42:18.589
is passing. So, what will be the delta P of
the fluid you can calculate it with this equation.
00:42:18.589 --> 00:42:22.359
I do not want to derive this equation we have
done out already in the earlier class you
00:42:22.359 --> 00:42:27.970
can do it ok. So, this will be the equation
we use for the delta P ok, delta P upon rho.
00:42:27.970 --> 00:42:34.549
So, I can write the equation for delta P.
So, delta P equal to 4 f into rho, now rho
00:42:34.549 --> 00:42:39.450
of fluid or I said that say I will write it
in terms of the fluid, why because it can
00:42:39.450 --> 00:42:45.099
be gas, or it can be liquid the basic force
balance equation remains same. It will be
00:42:45.099 --> 00:42:50.810
L upon D into V square ok.
Now, that is what is the pressure drop in
00:42:50.810 --> 00:42:56.109
a pipeline, where there is no solid present.
Now if there is a solid present what will
00:42:56.109 --> 00:43:00.579
happen your what the pressure drop equation
will be modified. Why the pressure drop equation
00:43:00.579 --> 00:43:06.160
will be modified? Because now the gases or
the liquid whatever you will flow across it
00:43:06.160 --> 00:43:11.349
or whatever you will pump or push through
this bed, with go through the path available
00:43:11.349 --> 00:43:13.819
or the fractured path available between the
solids.
00:43:13.819 --> 00:43:17.760
So, suppose this is the path available it
will go through this, it will never go through
00:43:17.760 --> 00:43:22.400
the solids ok till the solids are not porous,
assume that solids are non porous, they it
00:43:22.400 --> 00:43:27.460
will not pass through the solids. So, it will
go through the path which is available after
00:43:27.460 --> 00:43:31.720
the packing of the solids. So, which is the
torturous path is there or the wide fraction
00:43:31.720 --> 00:43:35.980
which is present within the solid. So, it
will go through that and because of that what
00:43:35.980 --> 00:43:40.549
will happen, your equation will get modified
now how the equation will get modified will
00:43:40.549 --> 00:43:43.720
try to see that.
So, coming back to this equation what we are
00:43:43.720 --> 00:43:47.940
going to do we are going to take the delta
P in empty column and, then will pack it with
00:43:47.940 --> 00:43:52.380
the solids and we will see that how this equation
will be modified. Now we know that this equation
00:43:52.380 --> 00:43:56.759
actually the friction factor is a major problem
that what will be the friction factor and,
00:43:56.759 --> 00:43:59.260
this friction factor is a function of Reynold
number.
00:43:59.260 --> 00:44:04.680
And we know that if the f Reynolds number
is laminar or this flow is laminar, I will
00:44:04.680 --> 00:44:09.589
say not I will not write the Reynolds numbers
number because, that is valid only for spherical
00:44:09.589 --> 00:44:20.970
pipe, I said that if flow is laminar, then
f is equal to 16 upon R e Reynold number and
00:44:20.970 --> 00:44:28.299
R e is nothing, but 16 upon V into rho of
the fluid into D upon mu of the fluid ok.
00:44:28.299 --> 00:44:33.930
And this is the diameter of the pipe. So,
I can modify this equation and this equation
00:44:33.930 --> 00:44:46.549
will be 32 into mu into mu of fluid into V
into L upon D square ok into rho of fluid
00:44:46.549 --> 00:44:52.170
ok. So, that will be it would be modified
now rho of fluid rho fluid will be cancelled
00:44:52.170 --> 00:44:57.260
out, actually of fluid is here also. So, this
rho of fluid rho of fluid will be cancelled
00:44:57.260 --> 00:45:03.039
out, so, you can say that this will be the
delta P equation ok this will be the delta
00:45:03.039 --> 00:45:06.430
P equation.
Now, what we need we need to know that what
00:45:06.430 --> 00:45:10.930
is the diameter, what is the diameter now
the diameter will not be the diameter of the
00:45:10.930 --> 00:45:16.329
system because you are going to have a void
ok. So, the exact diameter is not the diameter
00:45:16.329 --> 00:45:21.140
of the system, exact diameter will be the
fraction where the voids are present wherever
00:45:21.140 --> 00:45:25.349
the void is there. So, you need to find this
D value and you need to see that what will
00:45:25.349 --> 00:45:29.750
be this V value, earlier we can take a superficial
velocity because the column was empty ok.
00:45:29.750 --> 00:45:35.070
So, we work on the superficial velocity ok,
but now what will be the value of V what will
00:45:35.070 --> 00:45:39.859
be the value of D that is the major question,
if you understand that we can calculate that
00:45:39.859 --> 00:45:43.829
what will be the pressure drop through the
packed bed for laminar flow condition.
00:45:43.829 --> 00:45:48.289
Now, we know that we have already derived
it that what will be the correlation between
00:45:48.289 --> 00:45:53.369
the velocity inside and superficial velocity.
So, we have already developed that correlation
00:45:53.369 --> 00:45:58.869
we have discussed it. So, inside velocity
say u will be equal to u naught upon epsilon
00:45:58.869 --> 00:46:07.829
where epsilon is the void fraction. So, what
you can do how you have derived it you can
00:46:07.829 --> 00:46:12.660
do it with the continuity. So, continuity
says that mass in is going to be the mass
00:46:12.660 --> 00:46:15.400
or whatever the mass is going to be balanced
at 2 different layer.
00:46:15.400 --> 00:46:20.190
So, if you take at any place inside this what
will be happening that u naught whatever the
00:46:20.190 --> 00:46:27.609
mass going is is rho of fluid into u naught
into area, and that will be equal to rho of
00:46:27.609 --> 00:46:32.770
fluid that is into u into your area and area
will be now multiplied with the volume fraction.
00:46:32.770 --> 00:46:37.049
So, that you know that whatever the flow area
is available. So, if you do that area area
00:46:37.049 --> 00:46:40.559
will be cancelled out rho rho will be cancelled
out you will get this value it means, if I
00:46:40.559 --> 00:46:48.289
write it I will say this will be u into void
fraction into area into rho of fluid that
00:46:48.289 --> 00:46:53.170
will be equal to rho of fluid into u naught
into area.
00:46:53.170 --> 00:46:58.660
Now, you know that rho f and rho f is cancelled
out overall area is same. So, you will get
00:46:58.660 --> 00:47:03.059
u will be equal to u naught upon epsilon,
we have already done that just to revise it
00:47:03.059 --> 00:47:06.859
again. So, you will get this u value. So,
we already know the u value now. Now what
00:47:06.859 --> 00:47:11.890
is about the D p what is about the diameter
of the column. So this V will be modified
00:47:11.890 --> 00:47:15.880
with this value. So what will happen your
equation will be changed I will just put it
00:47:15.880 --> 00:47:22.390
here so, it will be 32 mu of fluid it will
be u naught into length now length will be
00:47:22.390 --> 00:47:27.210
the length of the bed.
So, I will replace it with the L b upon D
00:47:27.210 --> 00:47:32.630
square into rho of fluid. So, this will be
into rho of fluid, so, that is the way it
00:47:32.630 --> 00:47:38.380
will be modified this equation will be
modified, now what we are going to do we are
00:47:38.380 --> 00:47:42.539
going to put it here that how this things
will be modified, I think rho will not be
00:47:42.539 --> 00:47:47.140
there I just forget to cut the rho because,
this will be rho delta P will be equal
00:47:47.140 --> 00:47:51.640
to rho f, and if you write it it in terms
of the Reynolds number this will be 16 upon
00:47:51.640 --> 00:47:54.299
v rho and f and this rho rho will be cancelled
out actually.
00:47:54.299 --> 00:48:00.019
So, it will be only d I just did it. So, please
do it is you will find it out this will 4
00:48:00.019 --> 00:48:06.470
f rho f L D upon V square, if you will write
it 16 upon V rho D upon mu f if you do it
00:48:06.470 --> 00:48:11.170
here, then what will happen this 2 and this
2 will be cancelled out this will be V square
00:48:11.170 --> 00:48:24.910
upon 2 also. So, this 2 and this this will
be cancelled out this will be 2, now if you
00:48:24.910 --> 00:48:30.680
put it here right let me do it actually so
delta P will be equal to 32 this will be mu
00:48:30.680 --> 00:48:38.349
f into rho f into L V square upon D. Now reynold
number I am writing it in in terms of the
00:48:38.349 --> 00:48:45.920
V rho of f into D. So, v rho of f into D into
mu this rho f rho f will be cancelled out
00:48:45.920 --> 00:48:50.720
V this will be cancelled out this will be
D square. So, what you will get thirty 2 mu
00:48:50.720 --> 00:48:55.210
f into V into L upon D square. So, that is
what you will get.
00:48:55.210 --> 00:48:59.599
So, now you will get this equation and this
will be divided by epsilon. So, this will
00:48:59.599 --> 00:49:04.099
be the delta P equation. Now what you need
you need that what will be the diameter because
00:49:04.099 --> 00:49:10.170
diameter is not going to change. So, we know
that in case the diameter is not regular
00:49:10.170 --> 00:49:14.530
what we need to do we define a term which
is called equivalent diameter.
00:49:14.530 --> 00:49:18.960
Now equivalent diameter is being defined or
hydraulic diameter, or equivalent diameter
00:49:18.960 --> 00:49:25.680
or hydraulic radius it is being defined as
D h since the hydraulic radius or hydraulic
00:49:25.680 --> 00:49:46.569
diameter is 4 times of the cross sectional
area by wetted parameter ok. So, 4 times cross
00:49:46.569 --> 00:49:53.400
sectional area by wetted perimeter. Now if
I am talking about the cylindrical column
00:49:53.400 --> 00:49:57.890
what we need to do, we need to find it it
in terms of the volume. So, I will multiply
00:49:57.890 --> 00:50:02.549
by the length top and bottom, if I just multiply
with the length which is going to be the same.
00:50:02.549 --> 00:50:07.559
So, that is the length if I multiply it it
will be say L b L b if I am multiplying this
00:50:07.559 --> 00:50:19.319
will be 4 into volume of reactor or volume
of flow, of flow volume available divided
00:50:19.319 --> 00:50:31.259
by wetted surface area. So, volume of flow
into 4 divided by weighted surface area. Now
00:50:31.259 --> 00:50:34.799
what you need to do we know that what we need
to find it out that what will be the volume
00:50:34.799 --> 00:50:39.609
of the flow. So, volume of the flow will be
what we know that what is the volume of this
00:50:39.609 --> 00:50:46.170
reactor that is if suppose this is their.
So, volume of this reactor will be area 4
00:50:46.170 --> 00:50:51.970
cross area into length say L b that will be
the volume, but volume available for the flow
00:50:51.970 --> 00:50:55.980
will be only the void portions. So, we will
multiply with the epsilon which will say that
00:50:55.980 --> 00:51:00.489
what is the void fraction available. So, volume
of flow or volume available for the flow I
00:51:00.489 --> 00:51:10.540
will write it it in this way for more clarity,
you can say volume available for flow a flow
00:51:10.540 --> 00:51:15.270
or fluid. So, this will be this now area will
be what that will be the wetted area.
00:51:15.270 --> 00:51:20.250
Now, that wetted area will be what that will
be across the particle fraction, that what
00:51:20.250 --> 00:51:24.410
will be the surface to volume ratio of the
particle. So, that area will be defined as
00:51:24.410 --> 00:51:29.920
your length we have already multiplied up
and down. So, that will be 1 minus epsilon
00:51:29.920 --> 00:51:35.950
and this area will be defined as area surface
to area of this whatever the surface to particle
00:51:35.950 --> 00:51:39.760
volume ratio.
So, that will be the a small a I am defining
00:51:39.760 --> 00:51:43.700
it as the surface to volume ratio of the particle
and because, you are multiplying with the
00:51:43.700 --> 00:51:48.009
volume of the particle you have to multiply
with the volume it will be multiplied by capital
00:51:48.009 --> 00:52:01.619
A into L b. Where a is surface to volume ratio
of the particle ratio of particle. So, what
00:52:01.619 --> 00:52:05.499
we are doing, we have to find the wetted area
that what will be the wetted area. So, wetted
00:52:05.499 --> 00:52:10.420
area will be the area which will be wetted
so this particle is there between these 2
00:52:10.420 --> 00:52:14.339
particles say this is the flow. So, fluid
will pass through say this line. Now a fluid
00:52:14.339 --> 00:52:18.760
will pass through this line what will happen
that this areas are the wetted area.
00:52:18.760 --> 00:52:22.729
So, for that what you need to find that what
is the surface to volume ratio of the particle
00:52:22.729 --> 00:52:27.460
and, then that will be multiplied with the
volume of the reactor whatever is available
00:52:27.460 --> 00:52:32.269
into 1 minus epsilon, why 1 minus epsilon
because, 1 minus epsilon is the solid fraction.
00:52:32.269 --> 00:52:36.229
So, that will give you that what will be the
wetted perimeter or what will be the wetted
00:52:36.229 --> 00:52:40.640
area that will be all the solids which will
be wetted not only the walls, but the solids
00:52:40.640 --> 00:52:42.799
will be also be wetted that will be the wetted
area.
00:52:42.799 --> 00:52:47.989
So, in that way we write it it in this way
now this is small a is surface to volume ratio
00:52:47.989 --> 00:52:52.369
of the particle. Now surface to volume ratio
for say if the particle is a spherical the
00:52:52.369 --> 00:53:00.999
surface area of the particle is 4 pi into
D square. So, 4 pi R square you can say and
00:53:00.999 --> 00:53:09.029
the diameter this ways particle is 4 upon
3 pi R cube where R is the diameter of the
00:53:09.029 --> 00:53:13.769
solid. So, if you do that what will happen
this 4 pi 4 pi will be cancelled out, it will
00:53:13.769 --> 00:53:22.130
be what it will be 3 upon R or you can write
it 3 upon diameter of the particle.
00:53:22.130 --> 00:53:33.489
So, I am writing D p which is the dia of the
particle, and it will not be 3 because you
00:53:33.489 --> 00:53:39.890
are converting R to D p it will be 6. So,
the a will be 6 upon D p. Now what will happen
00:53:39.890 --> 00:53:44.849
you can replace this a value here, and you
can calculate the D h. So, now the D h will
00:53:44.849 --> 00:53:49.630
be I will just modify the D h here again,
so if the D h I will say A and L b A and L
00:53:49.630 --> 00:53:53.970
b will be cancelled out, it will be 4 epsilon
upon 1 minus epsilon into A.
00:53:53.970 --> 00:54:03.799
So, this will be 4 into epsilon upon 1 minus
epsilon into a, and a is what it is 6 upon
00:54:03.799 --> 00:54:12.550
D p. So, this will be 6 upon D p so, it means
you can write it as 4 upon 6 epsilon upon
00:54:12.550 --> 00:54:17.230
1 minus epsilon into D p that will be the
D h value.
00:54:17.230 --> 00:54:22.900
So, now again I can do this D h value put
I can put it here and here, D is will be what
00:54:22.900 --> 00:54:27.579
it will be D h because, I will take the hydraulic
diameter, instead of the pipe diameter, this
00:54:27.579 --> 00:54:35.990
will be again modified delta P will be equal
to 32 it will be mu of fluid it will be the
00:54:35.990 --> 00:54:45.799
length of u naught L b u naught into L b upon
D h square into epsilon. Now this D h square
00:54:45.799 --> 00:54:50.969
will be replaced here you will write it out
D h square. So, this will be 32, now you can
00:54:50.969 --> 00:54:58.140
cancelled it out it will be 2 upon 3 again,
you can write here mu f into u naught into
00:54:58.140 --> 00:55:02.239
L b upon epsilon this epsilon we can say right
here.
00:55:02.239 --> 00:55:07.079
Now I am doing D h square on the separate
side, if you do that it will be epsilon square
00:55:07.079 --> 00:55:18.400
4 it will be into 9 and then this will be
4 into 9 upon 1 minus epsilon square into
00:55:18.400 --> 00:55:25.019
D p square into D p square. So, you will get
this value. Now if you solve this then this
00:55:25.019 --> 00:55:30.589
will be again further solved this will be
8. So, this will be 9 72. So, you will get
00:55:30.589 --> 00:55:44.549
72 mu f u naught into L b upon D p square
into 1 minus epsilon square upon epsilon cube,
00:55:44.549 --> 00:55:53.299
this will be the delta P ok, this will be
the delta P value which will be mu f u naught
00:55:53.299 --> 00:55:58.380
and L b which is the length of the bed D p
square 1 minus epsilon square upon epsilon
00:55:58.380 --> 00:56:03.219
cube that will be this. So, this is the delta
P in the packed bed for the laminar flow.
00:56:03.219 --> 00:56:07.589
Now, experimentally it has been observed that
this equation actually the constant is not
00:56:07.589 --> 00:56:14.270
72, but it is 150 that is the experimental
observation why it is the more because, we
00:56:14.270 --> 00:56:18.670
are taking the straight path we have not taken
the torturous nature, actually if you see
00:56:18.670 --> 00:56:23.130
this bubble column the path is not straight
there is a torturous nature of this path and,
00:56:23.130 --> 00:56:26.769
we simplified that while doing our this force
balance calculation.
00:56:26.769 --> 00:56:31.289
And because of that the constant value get
modified and instead of 72 we found that more
00:56:31.289 --> 00:56:35.410
resistance is there and that is why delta
P will be higher, because of the torturous
00:56:35.410 --> 00:56:40.600
path. So, this 72 is being replaced with 150
and that has been found experimentally so,
00:56:40.600 --> 00:56:45.150
this is 150, and again I am telling why it
is 150 do not worried all the force balance
00:56:45.150 --> 00:56:48.869
is correct we have not taken the torturous
path into the account and that is why it is
00:56:48.869 --> 00:56:51.770
coming 150.
So, this is there and that is the class of
00:56:51.770 --> 00:56:57.269
the equation which is being used to calculate
the delta P in a packed bed for the laminar
00:56:57.269 --> 00:57:02.989
flow. So, this is for the laminar flow. Now
we know that the laminar flow concept for
00:57:02.989 --> 00:57:08.410
the particle flow when the particle is there,
this is equation has been found to be experimentally
00:57:08.410 --> 00:57:13.719
valid till the R e p Reynolds number of the
particle is less than 10. And the equation
00:57:13.719 --> 00:57:22.710
is very famous equation and it is known as
Kozeny Carman equation Kozney Carman equation,
00:57:22.710 --> 00:57:26.930
which is valid for laminar flow of the packed
bed reactor.
00:57:26.930 --> 00:57:30.589
Similarly what we can do, we can derive the
equation for the turbulent flow. Now if I
00:57:30.589 --> 00:57:34.170
divide the equation for the turbulent flow,
we can do it very quickly you can also do
00:57:34.170 --> 00:57:39.039
it.
So, that will be again delta P upon rho is
00:57:39.039 --> 00:57:47.089
what will be equal to 4 f rho of fluid into
L upon D into V square upon 2. Now V we have
00:57:47.089 --> 00:57:54.219
already defined that is u naught upon epsilon.
So, we can say that this will be 4 into f
00:57:54.219 --> 00:58:01.579
L upon D into u naught square upon epsilon
square into 2. And D will be equal to what
00:58:01.579 --> 00:58:06.279
D h. So, you can replace this D h value from
there whatever the way we have defined and
00:58:06.279 --> 00:58:13.440
D h is what D h will be equal to 2 upon 3
epsilon upon 1 minus epsilon into D p.
00:58:13.440 --> 00:58:19.859
So, you can use this so this will be D h will
be replaced this will be 4 f L u naught square
00:58:19.859 --> 00:58:28.140
upon say 2 into epsilon square. Now D h I
am again replacing with this it will be 2
00:58:28.140 --> 00:58:36.499
into 3 this will be multiplied by say 3 into
2, then into it will be epsilon to 1 minus
00:58:36.499 --> 00:58:44.579
epsilon upon D p. If you simplify it then
this 4 4 will be cancelled out you will get
00:58:44.579 --> 00:58:55.950
3 f L u naught square into upon D p into 1
minus epsilon upon epsilon raised to the power
00:58:55.950 --> 00:59:00.359
3, that will be delta P upon rho. Now if you
want delta P you can also multiply it with
00:59:00.359 --> 00:59:04.940
the rho of fluid.
So, you will get this value and this is for
00:59:04.940 --> 00:59:11.701
the turbulent flow and that is valid for R
e p greater than 1000. So, this is for the
00:59:11.701 --> 00:59:16.130
turbulent flow you can say and what you need
to find you need to find the value of f. Now
00:59:16.130 --> 00:59:21.019
depending on the value of f it has been found
that for Reynolds number f this value is 3
00:59:21.019 --> 00:59:29.400
into f is being replaced with 1.75 rho into
u naught square into L of bed, this will be
00:59:29.400 --> 00:59:37.960
the L of bed everywhere L of bed upon D p
into 1 minus epsilon upon epsilon cube that
00:59:37.960 --> 00:59:44.130
is delta P. And that is again the experimental
observation 3 f is being replaced with 1.75
00:59:44.130 --> 00:59:48.450
and this is valid for the turbulent flow Reynolds
number of particle is more than 1000, and
00:59:48.450 --> 00:59:56.160
again this is a class of equation which is
called Burke Plummer equation Plummer equation,
00:59:56.160 --> 01:00:07.019
which says that delta P in the turbulent flow.
Then there is another class which is being
01:00:07.019 --> 01:00:11.460
there. So, this equations if you will see
is valid for the 2 different zone due to different
01:00:11.460 --> 01:00:16.589
region, 1 is for Reynolds number less than
10 for Reynolds number greater than 1000.
01:00:16.589 --> 01:00:21.210
So, Ergun equation is there a scientist Ergun
what he did he added both the equation together
01:00:21.210 --> 01:00:25.329
and say that.
If you have to calculate the delta P in a
01:00:25.329 --> 01:00:30.539
packed bed, that will be the combination of
Kozney Carmen and Burke Plummer equation.
01:00:30.539 --> 01:00:40.119
So, it will be what it will be 150 into mu
into u naught into L b 1 minus epsilon upon
01:00:40.119 --> 01:00:49.869
D p square into epsilon cube plus 1.75 into
rho into u naught square into L b into 1 minus
01:00:49.869 --> 01:01:02.150
epsilon upon D p into epsilon cube, and this
is called Ergun equation
01:01:02.150 --> 01:01:06.719
which is used to calculate the delta P in
a packed bed. And it has been derived from
01:01:06.719 --> 01:01:09.650
the basic force balance equation the way we
have done.
01:01:09.650 --> 01:01:14.150
So, if you know this delta P what you can
do, you can calculate that now you know that
01:01:14.150 --> 01:01:18.019
what is the delta P is there. Now you can
calculate that delta P you can use the Bernoulli
01:01:18.019 --> 01:01:22.210
equation, you can calculate that what will
be the power required for the pump. So, you
01:01:22.210 --> 01:01:25.539
can find it out the pump power, you can find
it throughout the compressor power, or blower
01:01:25.539 --> 01:01:30.609
power whatever you are using in the flow.
So, this is the basic force balance we do
01:01:30.609 --> 01:01:36.400
in the packed bed reactor, again this reactors
is widely used for many application the only
01:01:36.400 --> 01:01:40.869
drawback of this reactor is the temperature
management and higher delta P.
01:01:40.869 --> 01:01:50.809
So, next time what we are going to do we will
discuss about the fluidized bed reactor.
01:01:50.809 --> 01:02:04.169
Thank you.