[HOW TO]Calculate the Volume Occupied by Torispherical Dish

Got a query asking How to Calculate the volume occupied by torispherical dish of a batch reactor,
this query will definitely have a solution, but usually many engineers will keep following some of the thumb rules those are applicable here, and some of the others will apply whatever thumb they remember, so its better to use thumb rule practically, but before that its very recommend to know the reason behind deriving the thumb.




So before going into calculation directly, first of all we should know some basic concepts involved in the design of torispherical dish [doom/disc].,

** Crown Radius: A torispherical dish is the surface obtained from the intersection of a spherical cap with a tangent torus, as Shown in above pic. The radius of the sphere R is called the "crown radius,"

** Knuckle Radius: The Radius of the circle's those are formed at the transition phase from spherical surface to flat surface is called Knuckle Radius, Usually the sphere's / circle's those were formed at those transition phases were called Torus, and in plural form mentioned as Torii, so having torii is the reason behind deriving the name as torispherical dishes, And 

generally the knucle radius of a torispherical dish will be 0.6 times the diameter of the vessel.

Usually these torispherical dishes were designed for the sake of pressure vessels and storage vessels, to avoid the breathing losses in such vessels these dishes were designed.

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** Critical Radius: The Radius where the transition occurs from Spherical to Torus is called as Critical Radius.,



   
So, if you are clear with the above basic definitions we can enter into calculation part,

Let  be the distance from the center of the torus to the center of the torus tube, let 'c' be the radius of the torus tube, and let 'h' be the height from the base of the dome to the top. Then the radius of the base is given by a + c < R. In addition, by elementary geometry, a torispherical dome satisfies 

The transition from sphere to torus occurs at the critical radius 

So from the basic Dome equation from 3d Co-ordinate geometry, we are having two equations based on different cases

Where,

The Torispherical Dome has Volume

So, these are the theoretical Myth that our thumb is basing , and now i'm gonna tell you the thumb for calculating the Torispherical end volume,




Volume occupied by torispherical dish, V= (Pi/24)* Di*Di*Di.,

And some people want to have some clarity even through Thumb, so for them practice this,

Volume, V= [0.0847*Di*Di*Di]+ [ (pi*Di*Di*S.F)/4].

Thats it......Cheers,




Comments are appreciated......!!!!!

Some of the Readers wont have much time to read and digest all the above theory and may need instant results, for them i have developed an excel sheet, use that sheet for calculation,

DOWNLOAD EXCEL SHEET HERE

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About The Author

---

Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
Follow Me on Twitter AjaySpectator & Computer Innovations

[HOW TO] Select Required Vacuum Pump Capacity

Today i wanna Demonstrate HOW TO SELECT VACUUM PUMP CAPACITY for a operation in pharma operations, especially pharma because the use of vacuum can make tremendous change in field of Pharma, one right selection of Vacuum pump can reduce huge efforts in specific operations like crystallisation, drying, saturation, Separations etc.
So the its the main target of a process engineer or project engineer to provide with the right vacuum pump to manufacturing team for achieving high yields in small span of time, but before going to discuss about vacuum pump selection, i want all to know about the vacuum some more briefly,

What is Vacuum? Vacuum is simply a pressure below atmosphere. To create vacuum in a system, a pump is required to remove mass (gas/vapor) from the system. The more mass is removed, lower is the pressure that exists inside the system. Various vacuum levels are defined depending upon the ultimate vacuum as:

                           Range                                Absolute pressure range ‰
                           Coarse Vacuum                          10 – 760 Torr ‰
                           Medium Vacuum                        0.001 – 10 Torr ‰
                           Fine Vacuum                              10^-3 – 10 ^-7 Torr ‰
                           Ultra High Vacuum                     < 10^-7

Pumping speed: It is the volumetric rate of exhausting, generally expressed in Lts/min., m3 /hr or cfm. It is the rate at which the inlet of the pump actually removes the gas / vapor load. It should not be confused with Displacement of the pump. Displacement of a pump is the geometric volume swept by the pump per unit time at rated operating speed. For most of the pumps, pumping speed is close to displacement value at no load conditions (FAD-Free air delivery) and changes with inlet pressure, reaching to zero where the pressure attained is said be pumps ultimate pressure.







The below data gives an approximate idea of how booster combination can yield lower pressures while maintaining high pumping speeds.
                               Vacuum Pump              Pressure Range   Pressure Range with Booster

                            Single Stage Ejector             150 Torr                  15 – 30 Torr
                           Water Ejector                         100 Torr                  10 – 20 Torr
                           Water Ring Pump                  40 – 60 Torr             5 – 10 Torr
                           Liquid Ring Pump                 20 – 30 Torr             2 – 5 Torr
                          Piston Pumps                          20 – 30 Torr             2 – 5 Torr
                          Rotary Piston Pumps             0.1 Torr                     0.01 Torr
                         Rotary Vane Oil Pump          0.01 – 0.001 Torr       0.001 – 0.0001 Torr.
Vacuum Booster being a very versatile vacuum machine is used in a wide range of processes, some of them being;
Coarse vacuum applications
• Vacuum Drying Application.                                • Tray dryer
• Rotary vacuum dryers                                           • Flash Drying
• Vacuum Distillation processes.                             • Solvent recovery.
• Vacuum Filtration                                                  • Replacement of Steam Ejectors.
• Enhancing the performance of Water Ring Pumps /Water ejectors
• Vacuum Flash cooling / Evaporative Cooling        • Vacuum Crystallization
Medium Vacuum applications
• Efficient backup for Diffusion Pump Systems.     • Thin Film Deposition /Coating
• Short path/ Molecular distillation.                         • Solvent Recovery.
• Vacuum Heat Treatment and Degassing / Vacuum Furnaces
• Freeze Drying                                                        • Vacuum Impregnation
• De-humidification                                                 • De-gassing




And Now i think you gained some brief knowledge regarding vacuum, and now i'll get into point directly of selecting a pump capacity,

Also Read:

Batch Failure Analysis by Fault Tree Analysis 

How to Handle an Out Of Specification[OOS] 

Practical Way to Determine Order of Reaction

For an installed system air leakage load can be estimated by “Drop Test / Pressure rise test” method. Based on the fact that air leaks into the system at a constant rate as long as the pressures in the system is below 400 Torr because of critical flow conditions, the above test is effectively used to determine the leak rate of assembled system.
The system is evacuated to pressures between 10-100 Torr and isolated. The pressure is allowed to rise, but not exceeding about 300 Torr and the time lapsed is noted.




* The Leak Rate “QL” is calculated as, 

QL = ∆PxVs/ t

where QL leak tare in Torr Ltrs/sec 

∆P pressure rise in Torr

VS system volume in Litres 

t is elapsed time in seconds 

* For the known leak rate, the capacity of vacuum pumping system can be evaluated by the expression, 

Savg = 3.6xQL / P

Where Savg = Average pump speed in m3/hr 

QL = Leak rate Torr ltr/sec

P = System Pressure in Torr 

[ You might get a doubt that, how the formula for pump capacity is derived, but there is nothing but just a unit conversion by incorporating the required end vacuum(i.e., ultimate pressure).

Let's get into units now, air leakage rate holds units of Torr. Lt/Sec.

Ultimate pressure holds units of Torr.

So, (Torr. Lt/Sec) / Torr = Lt/Sec, which can be derived by dividing Air leakage rate with Ultimate pressure.

by doing so, we'll get in Lt/Sec, now simply convert it into m3/hr, 

for that we need to multiply with 3600/1000 = 3.6,

Now i think you got an idea, how i used that 3.6 in the main formula.]

* As a thumb rule for pressures in the range of 10-100 Torr pipeline “D” may be selected as

D = 2.4 (Q)^0.5

where D= diameter of pipe in mm

Q= Pumping speed in M3/hr .

Case Study was requested by Mr. Srikanth, 

Pl find below case:

Let's suppose, i need to select a vacuum pump for a 10 KL distillation system, where i need to attain 750 mmHg of vacuum atleast.

So, lets start the show,

I've taken a vacuum leak test for the system, 

applied vacuum, attained 756 mmHg of vacuum.

Hold the vacuum for 10 mins, so my evacuation time is 10 mins,

Observed vacuum leak is 30 torr. Let's suppose the air load is 3 Kg/hr at that particular area.

Now using above formulas,

Air leakage rate = 500 Torr.Lt/Sec,

Pump capacity required = 180 Cu.m / hr,

Considering safety i'll prefer 30% excess, i.e., 234 Cu.m / hr ~ 250 Cu.m /hr.

Line size from pump to system required is 1.27" ~ 2".

That's it

That's it Cheers, comments are appreciated,

Many of the readers found this somewhat difficult to calculate, and for them i've simulated these in an excel sheet, and download this excel sheet below.

DOWNLOAD HERE

Also Read:

How to Design a Condenser?  

How to Select a Pump , Motor, Line Sizings ? 

How To Select a Condenser? 

Determine the Power Required for an Operation?  

Industrial Distillation Column Design Steps

About The Author

---

Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
Follow Me on Twitter AjaySpectator & Computer Innovations

Theoretical Way to determine the time required for Distillation in Batch Reactor

Hello everyone, Based on requests received asking how to determine the theoretical distillation time cycle in a batch reactor, and today i'm gonna demonstrate you a simple way to determine outta many critical ways to do that,

Today this determination of Time required to carry out distillation is Based upon the Reactor Heat transfer area.








So Please read

How to find heat transfer area before proceeding to determination of distillation time

So, initially we need some of the data regarding

* The reactor mechanical design which includes some parameters like shell thickness, inner dia, length of reactor,

* The batch input details like how much amount of volume we need to handle, how much amount we need to distill out,

* The properties of the material we need to handle like density, specific heat, composition etc, and on the other end we need some properties like thermal conductivity of materials which out heat transfer area is composed off.




Properties of Materials:
Usually for make of Heat Transfer surface we will be usually going for SS316 Grade and for other purposes like for preparing the limpet jacketed coil and the insulation coating, we will be using SS304, and occasionally we will use GLR for Ph sensitive distillation, so below are the thermal conductivities of these materials

Material                Thermal Conductivity,K [W/m.K]
SS304                         10-13
SS316                         13-17
MSGLR                     1.2-1.5





So, after Collecting the required data, we need to calculate the amount of heat needed to perform the distillation operation, 
For the calculation of
* sensible heat we need to take total mass in reactor,
Sh = M * Cp * dT,
M - mass flowrate = Volume * Density
Cp - Specific heat[ usually cp will vary based on temp., so we need to take Cp at distillation temp.]
dT - Distillation temp. - RT temp.
* Latent heat calculation,
Lh = M * Lambda
M - Mass flowrate = volume of distillate * Density
Lambda - latent heat of vapour solvent

After getting the total heat load, we need to calculate the amount of heat that can be transferred through the heat transfer area per sec.
* Amount of heat transferred through the HT area per sec = K * A * dT * ( 1 / X )
K - thermal Conductivity 
A - Heat Transfer Area,
dT - Temp. Difference= Distillation temp. -RT temp.
X - thickness[usually considered as 10mm]

After Getting the heat that can be transferred through out HT area, we need to divide the Overall heat load with the Heat Transfer volume that can be transferred through one Sec,

T= ( ( M * Cp * dT ) + ( M * Lambda ) ) / ( K * A * dT ), Sec





Lemme explain this with a sample calculation,

Need to distill out 1 KL of methanol in a batch reactor GLR of capacity 5 KL, reaction mass volume is 4 KL(i.e., 80% occupancy), now i need to calculate the time for distillation.

Heat transfer area of a 5 KL batch reactor is 12.41 Sq.m, ( Calculate Heat Transfer Area )
Available heat transfer area = ( 4 / 5 ) * 12.41 = 9.93 Sq.m,
Thermal conductivity of a MSGL surface is 1.2 w/m.k = 0.029 KCal/m.Sec.K.

Methanol properties: 



Specific heat = 0.45 KCal/Kg.K, 
Latent Heat = 264 KCal/Kg,
Density = 790 Kg/Cu.m,
Boiling point = 64 degC.

Sensible heat load = M x Cp x dT = 4 x 790 x 0.45 x ( 64 - 25 ) = 56880 KCal,
Latent heat load = M x Lambda = 1 x 790 x 264 = 208560 KCal.

Total Heat load = 265440 KCal.

Amount of heat transfer that a MSGL surface can transfer = K x A x dT = 0.029 x 9.93 x (64-25)

i.e., 11.52 KCal

Time required for distilling out 1 KL methanol is 265440 / 11.52 = 23279 Sec = 388 mins.

i.e., 6.47 hrs. I think this will match with our practical cases.



Thats it, cheers.....


Is any queries, feel free to send me a message or comment here.

Comments are most appreciated.

An automated excel sheet specially designed for our readers/visitors.

DOWNLOAD HERE

About The Author

---

Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
Follow Me on Twitter AjaySpectator & Computer Innovations

[How to] find Reactor Heat Transfer Area Theoretically

Gotta request from a reader asking how to Determine Reactor Heat Transfer area theoretically,

Getting into point, A reactor usually used for carrying out reactions, extractions, distillations, pH treatments, etc, that means a common equipment for multiple operations, and to avoid some problems, reactors comes in different Materials of Construction, out of those many MOC's most commonly used were SSR- Stainless Steel Reactors, GLR- Glass Lined Reactors, MSGLR- Mild Steel Glass Lined Reactors, PPR- Poly Propylene Reactors etc.
Usually SSR can be made with two high proportional Steel grades, those were SS316, SS304,

they both vary in Molybdenum content

Both SS304 and SS316 are austenitic stainless steels.

         CHEMICAL COMPOSITION OF SS304 AND SS316               

              C       Mn       P         S        Si           Cr              Ni             Mo

        

SS304  0.08    2.0    0.045   0.03    1.0    18.0-20.0     8.0-10.0        -

SS316  0.08    2.0    0.045   0.03    1.0    16.0-18.0    10.0-14.0    2.0-3.0 

* From the above chemical composition chart we can see the main difference between SS304 and SS316 is that SS316 contains 2%-3% molybdenum and SS304 has no molybdenum.Now the question arises that we are paying double money for SS316 only for that 2.5% 'Moly'.The answer is yes, because this  "molybdenum" is added to improve the corrosion resistance to chlorides (like sea water).That is why in coastal area plants SS316 is used.

Lets start the Calculation of Heat transfer area of Reactor,

So usually one thumb rule is used for calculation,
* Length to Dia ratio is considered in between 1.2 to 1.6,
L/D=1.3 (i make it 1.3)

and the data i needed is the Batch Reactor Volume, and i take it 200L (0.2KL),

so my reactor volumes compromises of one cylindrical middle part and a torispherical bottom(ASME head),



so Volume of Reactor(0.2)=(Cylindrical Volume+Torispherical Dish volume)
                                          =((Pi*r*r*l)+((Pi/24)*D*D*D))    *here D is Internal dia
                                          =((Pi*(D/2)*(D/2)*(1.3D))+((Pi/24)*D*D*D)))
                                          =(1.022+0.1311)*D*D*D
                                    0.2 =1.153*D*D*D
so now i got the value of D=0.5576 m=0.56 m, L=0.728 m=0.73 m,

So now coming to the Calculation of Heat transfer Area, if you cut off the reactor cylindrical surface and spread it parallel to the ground it will take the shape of a Rectangle, so the area of a rectangle is Length * Breadth, and in this case the length becomes perimeter of cylinder and Breadth becomes length of cylinder,





so Heat Transfer area of cylinder= Perimeter of the Rectangle * Length of Cylinder
                                                    = (2*Pi*r) * (L)
                                                    = (2*3.147*(0.56/2)) * (0.73)
                                                    = 1.2864 Sq.m= 1.29 Sq.m
And now we got the Heat transfer Area of Cylinder, and we still need to calculate the Heat transfer surface of the Torispherical Dish, 

Area of a torispherical dish = (𝝅 / 4) x ((1.147 x D)^2) = (3.141/4) x ((1.147 x 0.5576)^2)
                                                = 0.785 x 0.409 = 0.32 Sq.m

Total heat transfer area of the reactor = Area of cylinder + Area of torispherical dish 
                                                                   = 1.29 + 0.32 = 1.61 Sq.m




That's it, Cheers.

Below is the quick demo on estimating the reactor heat transfer area:

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Specially for my Visitors or Readers, we have simulated the Calculation of heat transfer area calculation, Download this

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About The Author

---

Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
Follow Me on Twitter AjaySpectator & Computer Innovations