00:00and when you put this value in your terminal velocity equation for the cd then this if your
00:07vapor phase is present and two liquid phases are present and low then it comes as a intermediate
00:14law by the drag or resistance of the object in the fluid so it is added to 1000 the micron
00:23hi friends welcome to our channel concept engineering flux focus on fundamentals we are
00:28in model 3 on separators we are discussing and this is the second lecture on separator introduction
00:34in today's session we will understand the three different laws of three different settling laws
00:39for the separation also the droplet size and other things we will discuss in today's session
00:47so just a quick recap on the lecture 1 introduction to the separators i request if you are not watched
00:54that earlier session or earlier video please go through it because without that this video will
00:59not be able to understand properly so in first session we have completed the method of separation
01:06separator zones what are the movement transfer and how how the three different ways of
01:12transfer or separation movement transfer gravity and the bulk transfer and then the terminal velocity and
01:20we have calculated the terminal velocity and we come to this equation of terminal velocity
01:26and in this equation we have not covered the cd which is the drag coefficient so drag coefficient so before
01:37to understand the drag coefficient we we have this equation of terminal velocity in this there are two
01:44unknown one is the diameter of the particle and the second is the drag coefficient so basically drag
01:50coefficient is the dimensionless quantity used to quantify the drag or resistance of the object in the fluid
01:58so it is it represents the basically the resistance in the fluid
02:07so drop the basically the drag coefficient is the function of shape and particle shape and the reynolds number
02:16so you know the reynolds number is nr is equal to dp rho u by mu this u you can
02:25define as the ut also
02:27which is your terminal velocity so at terminal velocity you will get the nre for that case but as a
02:34as we
02:35don't know the cd and cd is the function of shape and the reynolds number so to solve this terminal
02:43velocity
02:43equation we have to do some trial and error so instead of that uh there is a the drag coefficient
02:51presents the function of the product of drag coefficient and the reynolds number that eliminates if if you
02:59multiply the cd with nrv which is this function this function will because ut
03:08uh there are two unknowns like uh terminal velocity here also coming here also coming so when you
03:14multiply this the terminal velocity part will go and you can get a correlation so based on this
03:21correlation you can find the size uh or you can say cd or the drag coefficient for the different
03:27shapes of the particle like cylindrical spherical and other shapes and based on this equation
03:36the cd by cd by cd by reynolds number curve can be derived and this will be used for the
03:43uh finding out
03:45the drag coefficient for the various uh variation in reynolds number or the for the various uh number uh
03:55based on the reynolds number you can find out the uh cd
04:00in us unit or uh for the spherical particle this reynolds number is re comes as this and uh your
04:11cd into
04:11reynolds uh nre will be this so you will find out you have to just see the properly the uh
04:18unit of unit
04:19conversion this is for the us units and this is the mks or si units based on the equation of
04:26cd into
04:27reynolds square of reynolds number this equation or this graph has been plotted and this when uh we
04:35get the value of drag coefficient or cd from this graph based on the value of reynolds number
04:42and when you put this value in your terminal velocity equation for the cd then this
04:50graph will be separated into three sections which will be the three settling laws can be obtained
04:56for the based on the reynolds numbers the first settling law is the stroke's law so stroke's law
05:08follows when your reynolds number or nre will be less than two and based on this graph if you plot
05:17us
05:18take a slope the for the less than two nrv the slope comes out to be cd is equal to
05:2324 by nre
05:26so when nre is less than two that time the reynolds number and the terminal velocity equation
05:37you can find out based on the nre and the graph you know that the cd value is cd is
05:42equal to 24 by nre
05:44if you put this cd value into this equation of the terminal velocity then you will get the
05:50ut equal to rho p minus rho by g into dp square by 18 mu this will be the this
05:57is called as the stroke's law
06:00for the settling and if you use the us unit and for the spherical particle this terminal velocity
06:08for the stroke's law comes is 1488 g into dp square by rho 1 minus rho g upon u 18
06:15mu so this is
06:16basically based on the uh us equation us units and to find out this dp or you can say particle
06:27diameter
06:28gps gps has given some guideline or the formula which is dp is equal to kcr into
06:35mu square by g into rho g by rho 1 minus rho g to the power of 0.33 so
06:44if if for the nre less than 2
06:47if you put the kcr value as 0.25 then all these others are known to you so you can
06:55get the particle
06:56diameter as well so when this stroke's law is used this stroke's law is used when the vapor separation
07:03from continuous fluid flow is required or dispersed liquid separation from the continuous liquid phase
07:10so means vapor separation from continuous liquid phase means if you have a lot of liquid and
07:16the bubbles or vapors has to be separate then this stroke's law will be used
07:20or dispersed separation from the continuous liquid phase so if if one of the phase has to be go
07:25from the continuous liquid phase liquid continuous liquid phase we understood in earlier session as
07:30well drag coefficient versus reynolds number this graph when you when when we talk about the reynolds
07:38number between 2 to 500 then it comes as a intermediate law between the 2 to 500
07:50and if you take a slope of this line and if you take a slope of this line you will
07:53find that cd is
07:54equal to 18.5 by nre to the power 0.6 so this is the slope typical slopes comes on
08:02this section
08:03for nre or you can say reynolds number 2 to 500 so when nre is between the 2 to 500
08:11then for
08:12uh terminal velocity formula and from the the graph we can get the value of cd which is 18.5
08:21by nre to
08:22the power 0.6 when you replace this with drag coefficient value in the terminal velocity equation
08:27you will get the equation terminal velocity is equal to 0.15 g to the power 0.7 dp by
08:341.14
08:36uh it within the bracket rho p minus rho 1 to the power 0.71 uh to the rho to
08:42the power 0.9 divided by
08:43rho to the power 0.9 to the mu to the power 0.43 which is the intermediate law equation
08:49which is used for
08:50the uh finding out the terminal velocity when your reynolds number is between 2 to 500 this is this this
08:58expression is for the us unit for the feet and the um feet per second or for this uh that
09:06equation that
09:07units similarly to find out the particle diameter for this intermediate law uh the kcr can be replaced
09:15with 0.334 then you can get the particle diameter and this intermediate law is used generally when the
09:23liquid separation from the continuous vapor phase so it can be used mostly in the vertical section you
09:30can say where the vapor flow rate is more and the liquid has to be separated or separate out
09:36what law is the newton law newton law is always when uh the reynolds number is between the 500 to
09:45or more than 500 the this graph will be segregated into third part which is the last part which is
09:52the
09:52newton newton newton's law and if you see this the slope on this section you will find the cd is
10:00equal
10:00to 0.44 so for the uh reynolds number value of between find uh 500 above 500 and up to
10:10the 2 lakhs
10:11newton's law will be applicable and this is terminal velocity equation which from the first way we
10:18understood and from the graph we uh we find it out that cd is equal to 0.44 if you
10:24put this cd value into
10:26this terminal velocity equation then you will get ut equal to 0.175 gp by dp uh to the uh
10:35within the
10:36bracket rho p by rho divided by rho to the power 0.5 this is the basically the newton's law
10:43equation for
10:43uh newton's uh settling law equation which will be used for the finding out the terminal velocity
10:51this is in the us unit and to find out the particle size or dp of the particle when we
11:00replace the kcr value
11:02by 18.13 then you will get the dp for the for this particular conditions of rho mu and your
11:10inlet conditions
11:12so basically generally this newton's law is not used for the separators because if you see the
11:19particle size and the uh cd value it comes like a bigger particle size so which will not generally
11:27will be the use in the refinery separators it will be for some uh bulk chemical chemical plants it
11:35this will be used for the settlements where the particle size or crystallization or something can happen
11:40but not generally in the hydrocarbon if you see this droplet size uh distribution which is taken from the
11:50gpsa guideline again so in this if you see uh you have to see make little bit efforts to read
11:58this this
11:58is the stroke's law this is intermediate law and this is the newton's law if you draw a line like
12:04this
12:05so you will find the stroke's law will be applicable when the micron size or the particle size is between
12:10around 2 to less than 100 and intermediate law is between 100 to 1000 the micron i am talking about
12:20the micron particle size and if you see the newton's law newton's law is more than thousand microns or
12:27uh and then it increases like one centimeter or 10 000 micron or one like micron which is around
12:3410 centimeter here here is a one inch so particle size is bigger as i said in earlier section the
12:41earliest
12:44slide that this size is very big so it will not be used for the uh general use for the
12:49uh separators
12:50the hydrocarbon suppressor and if you see the particle size starts around the 0.001 micron which is on the
12:56molecular side so if you see this uh distribution you can find it out that which part like which this
13:04is foreground and this based on the sizes this is the uh law and even this to find out the
13:12droplet size
13:14or dp size the kcr factor is also mentioned in this here which is put it here to read it
13:21properly
13:23if you do not know the droplet size and you are not able to have the even enough information to
13:27calculate it then uh standardly there is liquid particle size used for the gravity separations are
13:37basically the liquid uh for a liquid from vapor separation then you can take as a 250 micron
13:44as a particle size if the vapor from liquid separation then it is 175 micron
13:51and if it is a dispersed liquid from the continuous liquid then it is a 125 micron you can take
13:57it as a
13:59general basic guidelines in some other uh guidelines it is based on the specific gravity of the material
14:06so if you have a light phase which is having the specific gravity less than 0.850 or which means
14:13which
14:13is basically hydrocarbon then you can go for the 121 micron size and if you have a
14:21light phase whose density or specific gravity is more than 0.850 then you can go for the 89 micron
14:28size
14:30this is a general guidelines given in some books also the settling velocity should not exceed the
14:390.005 meter per second for all these two cases any either cases or either phase
14:48this light phase this light phase specific gravity means the other phase is a heavy phase like such as
14:54water so here we are almost completed our theoretical part of separators and we are moving for the
15:03separator sizing so before the separator start the separator sizing we should uh understand what it is
15:11depending on what separator sizing is depending on basically a few factors like the effect on the
15:19downstream equipment effluent and overall economics so if what you are giving to the downstream equipment
15:26like pump or compressor is there then for filling the fulfilling the requirement that is your basis for
15:32the separator design considering difficulty and cost of separating smaller particles if you have a very
15:40fine particles and if you go if you want to how much percentage of removal you required based on that
15:46your size will be increased so that economics or cost versus removing the smaller particles is it has to be
15:53considered similarly the plot space required because if you go for the very long length of the horizontal
16:02separators then you need a more space of you go vertical then you need a vertical some empty space should
16:09be
16:10available separators should not be too tall or if you are shifting it from fabrication yard to your plant
16:20then it will be again a problem because it will incur you the more cost in transportation enough
16:28interfaces available between three phases or not means the density differences are there are not properly
16:33that also has to be checked density difference or they find they will they should form a uh emulsion
16:40emulsions and other things now the how much surface area is available for decreasing or separating the liquid
16:52surge volumes in liquid to be handled without large change in liquid levels
16:57because there will be a fluctuation into the uh in your vessel so you it should be handle your uh
17:04that
17:05surge or liquid such coming the liquid because of the some sudden high flow rate larger liquid retention
17:13retention is required or not because somebody will not ask you design your um separator with the level of
17:20maybe very high level so when you put a high level then uh vapor separation in the space will be
17:26less
17:26then you will increase the diameter so it will finally increase your cost and the dimensions everything so
17:33these few factors also you should understand before or you should take care before finalizing your separator
17:40sizing so before start the design of the vessel we should know vessel configuration whether we have to go for
17:47the
17:47vertical uh separator or the horizontal separator so how we will find it out if the flow rate is uh
17:55if the uh
17:56your fluid contain or your stream contains high vapor flow rate and the low liquid rate and it is only
18:02one
18:02liquid then you can go for the vertical type of configuration if a low vapor rate high liquid rate and
18:10one phase
18:11only then you can go for horizontal preferably but still you can go for the vertical as well the second
18:16option
18:18based on the space requirement and this parameter you can decide that whether you want to go for vertical
18:25no vapor phase and two liquid phases then you should go for horizontal if your vapor phase is present and
18:30two
18:31liquid phases are present and low heavy liquid phase rates are there heavy phase means the heaviest are
18:38lighter then you should go for the not lighter lower then you should go for the horizontal type of separator
18:45vapor phase is present also two liquid phases and low light liquid phase rate so that the liquid phase
18:54rate of the like water is more and there is a gases and there is a little amount of oil
19:01that is a low liquid
19:03phase rate then you should go for horizontal with a baffled outlet so it will be overflowed and
19:09uh the lower or lighter low light liquid will be overflow from the baffle so vapor if your vapor phase
19:18is
19:18present two liquid phases and the liquid phase is equal rates then you can go you can go for the
19:24horizontal
19:24with the two baffles outlet if the low light phase rate and the vapor phase is present then you can
19:32go
19:32horizontal with the horizontal with a calming vapor as well and the small droplet size and load density
19:38difference then you can go with the horizontal and the coalescer coalescer will give you more surface
19:44to coalesce and the get the settle because of the small droplet size or the load density differences
19:51so this way we have uh we can we can uh generalized or you can understood that the vessel configuration
19:58which vertical horizontal to be done and in next session we'll uh start the design of uh vertical
20:04and the horizontal uh separator so first we'll start with the horizontal separator design
20:10all the steps and the guidelines for the design of horizontal separation
20:16thank you very much if you have any question you can write to us or comment on the comment box
20:23or you can
20:23also reach on to us at conceptengineering2025gmail.com link of the sessions uh all the sessions we
20:32completed till date is module 1 pressure relief valve module 2 heat exchangers and model 3 separators
20:37are going on so links for all this uh available in description box you can go through it thank you
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