basics of reactor design mac2

Prof. A. B. PanditInstitute of Chemical Technology

University of Mumbai

Basics of Reactor Design & Selection

Mechanically Agitated Contactors

Design Variables

Independent Variables

1. Reactor Geometry : Diameter, Height

2. Impeller type

3. Impeller diameter

4. Impeller Position

5. Impeller rotational speed

Minor Variables

6. No. of baffles / baffle width

7. No. of nozzles / nozzle diameters

8. Other reactor internals : coil, sampling point, foam breaker etc

Function of Impeller

1. Mixing of liquid / liquids

2. Disperse gas / vapors

3. Suspend solid particles

4. Achieve certain heat transfer

Dependent Variables

Parameters defining them:

1) PowerImportant design variable; decides the operating cost

P = Power (watts) = NP N3 D5

NP – power number, function of impeller type and a weak function of geometry of vessel, strong function of Reynolds number, Re for Re< 104

– density of fluid, kg/m3 N – speed of rotation, rev/sec

D – diameter of impeller, m

PPower/unit volume =

2π T H4

• Good overall criteria for heat transfer, solid suspension and gas dispersion

• Not so good for mixing, except shear sensitive material

Dependent Variables

2) Torque

Useful for drive consideration / selection

3 5PNPowerTorque = τ = = ρN D

2 π N 2 π

• Also useful for selection of gear box, sizing of shaft

• Good criteria for flow velocity sensitive operations

Dimensionless Numbers

1) Power Number : P 3 5L

PN =

ρ N D

2) Reynolds Number :2ND ρ Inertial forces

Re =Viscous forces

– viscosity of fluid at operating conditions, kg/m s, mPas

1 cp = 1mPas = 0.001 kg/m s

Relation between NP & Re

P 3 5L

PN =

ρ N D

2ND ρRe =

Different impeller type

10 100 1041000 105

10

1

100

NP independent of

Re for Re 104


3) Froude No. : 2N D Acceleration due to impeller

Acceleration due to gravityg

Useful in mixing of different density liquids

4) Weber Number : 2 3N D inertial forces

surface tension forces

Useful in deciding gas dispersion or liquid emulsion

– surface / interfacial tension, N/m

5) Blend Number : NB = N

N – speed of agitation, rev/sec

– mixing time to achieve specific homogeneity


4) Pumping Number / coefficient : Q 3

QN =

ND

Useful in correlating pumping capacity of various impellers

Experimental observations : Q

DN

T

0.5

Q 3

DQ TNND

Q – pumping rate, m3/s

4) Richardson Number :

Concept of turnover

L2 2

L

Δρρ g HRi =

ρ N D

Certain Critical Impeller Speeds

1) Minimum impeller speed for gas dispersion :

3) Minimum impeller speed for solids suspension :

2) Minimum impeller speed for surface aeration :

2

1.25Cg

N DQ

T Constant as a function of type

0.450.1 0.2 0.11 -0.85

JS PgΔρN =Sυ d X Dρ

S – function of impeller type

0.191.98

1.11.34SN D g

T

Geometric Consideration

T

D

H

C

B

1) D/T ratio : 0.2 ≤D/T ≤0.5

Low D/T : low purchase price

low power

high shear/ low pumping

High D/T : Higher operating costs

Higher price

Low price / High pumping

2) H/T ratio : 0.5 ≤H/T ≤1.0

Multiple impellers for H/T ≥ 1.0

3) C/T ratio : 0.1 ≤C/T ≤0.3

Solid suspension, low C/T etc.

4) B = Baffles, 4 in No. diametrically opposite

B/T 1/10 to 1/12

Heat Transfer

Correlation for Reactor side HTC :

-0.14

0.59 0.33 -0.1wallRPr Fr

bulk

μh T=1.35 Re N N

k μ

…..For jacket heating / cooling

-0.14

0.64 0.33 -0.1wallRPr Fr

bulk

μh T= 0.87 Re N N

k μ

…..For coil

Overall heat transfer coefficient ‘U’ :

R m o

1 1 x 1= + +

U h k h x – metal thickness

Km – metal conductivity

ho – outside heat transfer coeff. (k.cal/hr m2 OC)

fluid

x

ho

hR

km

walllimpet

Typical Processes

Equal fluid Motion by far the most common actual mixing requirement: Adequate for heat transfer and solid suspension or

gas dispersion.

Equal fluid Motion

1. Most common mixing requirement

2. Constant torque per unit volume

3. Ensure motion throughout the tank

4. Solid suspension application

5. Blend time increases with increase in the reactor diameter

6. Flow velocity sensitivity operations e.g. heat transfer

Typical Processes

Solid Suspension

1. Scale-up rules can vary

2. P/V decreases with increase in tank diameter

3. T/V can be constant

Surface Effects

1. Vortex formulation

2. Dry solids drawdown

3. Foam breading / non-wetting nature

Dispersion

1. Constant P/V

2. Usually high shear , radial turbine

3. Gas dispersion

4. Emulsification

5. Shear sensitivity operations

High Viscosity Special Cases

Special Impellers : Close wall clearance

Anchors, Helical ribbons, screws / draft tubes

Range of applications :

Anchor : 10,000 cp – 1,50,000 cp

Ribbon : 30,000 cp – 1,50,000 cp

Power response can be calculated from

NP x Re = Constant

3 5constantP= ρN D

ReRe

NP

Blend time can be roughly estimated from

N = 50

Scale up techniques

Criteria for scale-up

N = constant. or constant tip velocity

Scale up criteria Validity of operation

1. Dimensionless Number (hT/K) Good for heat transfer

2. Impeller rotational speed (N) Good for mixing time

3. Power (P/V) Fluid motion, dispersion (but not solids suspension)

4. Torque Fluid motion (including suspension)

Impeller type & flow patterns

1) Radial flow : Turbine, paddles

Two loops with exchange at impeller plane


2) Axial flow : Propeller, Hydrofoil (fans)

Single loop : Low velocity


3) Mixed Flow :

Pitched blade turbines

4) Complex Flow :

Ribbons / screw

Two superimposed loops with greater

exchange

No loop : no mixing

Utility of the relations in design

Problem Statement : Dehydration and esterification of long / medium oil is to be carried out as per the recipe.

Process Conditions : Max temp. 260oC

Reactor charge : 3235 kgs of oil

Starting temp. of oil : 30oC

Solvent used : Xylene (100 kgs)

Other raw materials : Penta, pthalic in solid form

Neglecting reaction kinetics and assuming no heat effects associated with

the reaction.

The Reactor is expected to carry out the following physical operations

1. Mixing of solid / liquid raw material

2. Mixing of xylene for the removal of water of dehydration and or reaction

3. Supply of heat with thermic fluid to achieve temperature as per recipe.


Now let us assign some time frame to the above operations

Operation Alloted time (sec) Why this time

1. Heating oil to 150oC 1 hr Could be reduced

2. Heating to M. G. temp. 245oC

1 hr / 1 hr 15 min Thermic fluid as limiting temp

3. Cooling to 170oC 30 min Cooling media temp

4. Heating to 170oC 30 min Phthalic reactions(not too fast)

5. Esterification 6 to 7 hrs Reported O. K.


Total occupancy : 6o% of the geometric volume

Geometric volume = (3235+100)/0.6 = 5.56 K. L.

Let H/T 1.0 H = T = 1.92 m

Dished ends : Ease of drainage / discharging

Actual diameter to be selected in consultation with the fabricator :

Available plate size, no waste

Let T = 2.0 m, Hence rough geometry

2.0 m

2.0 m

4 in no. (0.2m)

A) Selection of Geometry :


B) Selection of heating surface /form/cooling :

1. Limpet coli 2. Jacket

Form of heating : steam or Thermic fluid

Max. temp. 260oC and hence hot fluid temp. 200oC very high steam pressure, increase in reactor wall thickness expensive

Thus : Thermic fluid : due to high viscosity it requires good velocities :

not possible in jacket due to large flow areas

and hence Limpet coils.

Cooling : Cooling oil or cold fluid through limpet coil.


C) Selection of Impeller :

Properties of fluid required for the same - viscosity at operating temperature or range of viscosities or max. 300

cp 3 poise 200oC

- density of fluid 900 kg/m3

Functions expected of impeller

Generate sufficient liquid motion : well directed to give

1) good mixing

2) good heat transfer

3) good solid suspension

4) good nitrogen dispersion (blanketing)

For the range of viscosities & densities encountered Anchor and / or ribbons are not required


Impeller type Its best usefulness

1. Radial flow Gas dispersion and heat transfer

2. Axial flow Good for mixing, good solid suspension

3. Mixed flow Multipurpose impeller

Better designs are available enhancing any of the above 4 functions

Radial flow : higher power consumptions

Axial flow : lower power but not good for dispersion

Thus MIXED FLOW IMPELLER IS SELECTED

Various designs are available : by varying pitch axial or radial component can be altered, by making it profiled, it could alter shear and flow levels etc.

Due to slightly higher viscosities D/T ratio used 0.5 and two impellers on the same shaft can be used

The final geometric design

2.0 m

2.0 m

0.75

1

0.75

Parameter selection

The only parameter remains to be selected is ‘ impeller speed’

We have number of choices

1. Impeller speed required for heat transfer

Largest heat duty : during esterification

Alloted time 6 hrs.

This time includes

1) 170 to dehydration temp

2) dehydration

3) esterification

The final design

Heat duty for each operation

1. m CpT = 3235 x 0.5 x (260-170) = 144575 kcal

2. Dehydration = water removed 80 kg

= 43200 kcal

3. Esterification = water removed 120 kg

= 64800 kcal

For 2 & 3 xylene is also evaporated

200 kgs of water is removed in 5 hrs. 40 kgs of water removed/ hr (if removed)

If less then accordingly : 100 kgs of xylene present

Based on the azeotropic concentration 1 kg of water is associated with 18kg of xylene

The final design

4. Heat duty required for xylene evaporation = 720 x 95 x 5 = 34200 kcal

Thus, total heat duty in 6 hrs is Q = 1 + 2 + 3 + 4 595000 kcal

1,00000 kcal/hrs

Total heat transfer area is 15.0 m2 of limpet coil

Average temp. gradient = o285-170 - 285-260

= ΔT =59 C115

ln25

Thermic fluid temp. is assumed to 285oC

Hence the required HTC Q 1,00000

= =A.ΔT 15.0×59

2o

kcalU =113

hrm C

The final design

Impeller speed required is calculated as follows

R m o

1 1 x 1= + +

U h k h R m

1 1 1 0.006= + +

113 h 800 k

R 2 o

kcalh 226

hr m C

2 3 0.241 32R w

o

h T μND ρ=0.485

k μ μCPk o 2o

kcalT=2.0m;k =0.163

hrm C

R 2o

kcalD=1.0m;h =226

hrm C

kg kg

=3 poise=0.3 1080ms m m

3P o

kcalC =0.5 ; 900kg m

kg C

N = 1.52 r/s 91 rpm (90 rpm)

Now check whether this impeller speed satisfies the other operational

requirements

The final design

Heating to 150oC in 1 hr.

Heat duty = m Cp T

= 3235 x 0.5 x (150-30) = 194000 kcal

Heat flux obtainable = U A T

= 113 x 15 x [(285-30)-(285-150)]/ln(255/135)

= 319816 kcal / hr.

Expected time of heating = 194000/319816 = 0.6 hrs 37 min.

Other parameters can also be checked

Cooling requirement also appear to be adequate if the thermic fluid is available at a temp. of 100oC or below

The final design

Mixing time calculations :

lengthofl ongest loopθ= ×5

Avg. circulation Velocity

4mt. 4×5= ×5= 21sec

0.1×2 ND 0.942

Final mixing depends upon the exchange between the two loops which is 35 %.

mix

21θ 60sec 1min

0.35

GOAL ACHIEVED

Process Reactor design is complete

Impeller drive selection

Parameter known : D = 1m, N = 1.5 rev/sec

Impeller type : Mixed flow, NP = 1.0 for Re > 104

22 1.5× 1 ×900ND ρReynoldsNumber= = =4500

μ 0.3

Thus, you can

• Expect NP to increase to about 1.1

• Actual power curve is necessary

Power, P = NP N3 D5 = 1.1 x 900 x (1.5)3 x (1)5 = 3341 watts

Now two such impellers

Total power = 1.9 x 3341 = 6348 watts = 8.5 HP

Thus with the knowledge of gear efficiency 10 HP motor should be adequate giving

3P=1.81Kw m

V{Normal Range is 1 to 5 kw/m3}

Thus quite satisfactory.

Additional Process Calculations

• Separator design

• Nozzle selection

• Nozzle location

3D ×RPMHP=

CC = 50, for only torsional

= 80, for torsional + bending

= 130 for

Mechanical design i.e. shaft diameter, critical speed

in consultation with the fabricator.

Selection and design of accessories

Basic Reactor Configuration:

B

C

AA – Reactor

B – Condenser for reflux

C – Separator for xylene return

& water removal

A – Reactor design has been complete

Condenser Design

B – Design of condenser :

Maximum heat duty of condenser = Maximum heat supplied to the reactor

= Q = 100000 kcal/hr

Cooling media = water at 30oC

Let the vapors be condensed and cooled at 30oC

Let it be a Shell and Tube Heat Exchanger

Vapors might be cooled due to atmospheric heat losses by the time they come to the condenser

Let the vapor temperature be 150oC ( as against 260oC)

Condenser Design150oC

37oC

30oC

80oC

o

150-37 - 80-30LMTD =

150-30ln

80-30

= 77 C

For water on shell side and vapors (condensing) on tube side, overall heat transfer coefficient (U) can be assumed to be 500 kcal / hr m2 oC

2

Q 100000Condenser Area, A =

U LMTD 500 77

2.58 3m

Due to pthalic evaporation, considerable fouling is observed,

Thus, Let A 10m2

Mounted Vertical : Washing of vapors and preheating of returned liquid

Fouling : Tube dia ≥ ¾”, periodic clearing

Cooling water requirement

Total heat removed = 1,00, 000 kcal/hr

(T)water = 37-30 = 7oC

Q = m CP T

1, 00, 00 = m x 1 x 7

m = 14285 kgs/hr 15 m2/hr

Pump required with of 50%

Power = h g Q = [30 x 1000 x 9.81 x (15/3600)]/0.5

= 3.3 HP 3.5 HP 3KW

Conclusions

Condenser type = Shell & Tube

Tube size 3/4”

Area 10 m2

Vertical Mounting

Cooling water : 15 m3/hr

at 3 kg/cm2 head

3 KW motor

Design of Separator

Options : Horizontal (larger space)

Vertical (less efficient)

Design information required

A. Time of separation of xylene / water

B. Reflux rate of xylene

A. 4 to 5 seconds : Lab experiments

B. 720 + 40 (xylene + water) : 760 kgs / hr

950 lits / hr 265 ccs/s

Mean residence time of mixture 10 times of separation

60 seconds or 1 min

Volume of the separator = 265 x 60 = 15900 cm3 16 lits

Design of Separator

Separation is taking place with continual agitation due to falling liquid

Net liquid velocity 10 mm/s

C/s area of separator = 265/1 (cm3/s)/(cm/s) = 265 cm2

Diameter of separator 20 cm

Height or length = 50 cm

Separator Arrangements

vap

liquidwater

xylene

AB

vapors

water

Xylene to reactor

vaporsC

Other Utilities

1) Thermic fluid boiler – 2, 00, 000 kcal/hr

Hytherm 600 – max. operating temp. 300oC

2) Cooling water

3) Electricity : Flame – proof connection

Design Problem

Problem Statement : To design a reactor for emulsion polymerization

Important Criteria

1) Size of the droplets

2) Heat of reaction to be removed

3) Controlling the molecular wt. distribution

Experimental work in the lab should provide the following information

1) Reaction kinetics : Rate of consumption of monomer as a function of reaction conditions, monomer concentration and the form (droplet surface area)

2) Heat effects associated with it

3) Effect of speed of agitation (shear) on the emulsion quality :

Droplet size distribution

Design Problem

Interpretation of lab results

Formulation of mathematical model

Material Balance : Reaction RA = k1 CAm

1 1i i i i 1 -k t

i i i

C k V t Ce

C -k V Co

- flow rate, m3/s

k1 – rate constant 1/s

C - initial conc. gmole/m3

Vi – initial volume, m3

Ci – molar conc. in inlet flow (gmoles/m3)

C1 – conc. at time, t1

Design Problem

Heat Balance : Including the heat of reaction

Enthalpy in – enthalpy out + enthalpy generated = Accumulation of enthalpy

m CP Ti – (Atm. losses + heat removal) + R . HR = CPR T d/dt (mR)

m – mass of monomer + water input, kgs/s

CPi – sp. Heat of entering mass, k.cal/kg oC

Ti - inlet temp. oC

R – rate of reaction, gm/s

HR – Heat of polymerisation, k.cal/gm

CPR – sp. Heat of reaction mass, k.cal/ kg oC

TR – temp. of reactor, oC

mR – reactor mass, kg

(1)

Design Problem

Neglect atmospheric losses

Over a period of specified time period

t t

Pi i L P R0 0

t

PR R i0

mC T dt - Q C Z ΔT×t+R H dt

=C T m +m dt

L PwhereQ C ΔT. t=totalheat removedby coolingwater

From equation (1) and (2) total kinetic information can be obtained

(2)

Design Problem

Process parameter selectionGeometrical consideration : Same as before

1) Mixing 2 ) Heat transfer 3) Effect of agitation on product quality

Factor 3 will affect the impeller selection in the following way

1) High shear impeller: low D/T, high speed, smaller drops, large shear gradients, poor heat transfer at wall but good at interface

2) Low shear impeller : High D/T, low speed, larger drops, lesser shear gradient (less wide drop size distribution) good heat transfer at wall but poor at interface

Thus, unless these effects on product quality are assessed in labs.

“Impeller selection is difficult”

Say we generate this information in labs, the design procedure is identical

Additional Impeller speed criteria

0.6

0.4 0.2

32 -0.1

c

d

σ

P V ρCd =a

μμ

Design Problem

We require, one impeller speed for good mixing

second for good heat transfer

Third for good dispersion (emulsion)

fourth for particular drop size distribution

Now, all these impeller speeds are function of the following additional parameters

1. Physical properties of system

2. Type and size of impeller

3. Required production rate (also dependent on temp. & catalyst conc.)

Thus number of combinations need to be tried for an optimum design

Again : parameter might be different for different recipes

Thus finding a compromise, suitable for all recipies

These are the general consideration in Reactor Design, many specific are related to individual processes

Mechanical Aspects

Material of Construction

Type of Services

• Continuous – Slow speed

• Otherwise – high speed

• Future changes / Experiments (built in flexibility)

• variable speed

Power for agitator

Absorbed for agitator

Add for baffles and fittings

Dip pipes (10%) and thermo wells (40%)

Transmission Losses

Worm wheel < 85%

Helical gears > 90%

Planetary gears > 96%

V belts 90 to 95 %

Gland Losses

Higher of ½ HP or 10%

Motor Aspects

Oversize for start up

oversize for settling solids

next higher standard size

Mechanical Aspects

Shaft diameter / size

• Slow speed : have design for (1.5 x full load motor torque)

• high speed : have design for (2.5 x full load motor torque)

Concerns

• Jamming

• Fatigue Failure

• Pitting / corrosion

• Deflection

Mechanical AspectsShaft diameter

dt

0.75 r

2r

L

S

Tm = 2.5 Tc ton.inc

3300×12×HPT =

2 n×2240

mm

TForce, F = ton

0.75r

Moment Mm = Fm x L ton.in

Shaft deflection

m

y 3

t

32 MStress, f =

d

0.75 r x

3m

4

F L448x= =

9 D E

Mechanical AspectCritical Speed

If ‘x’ is the critical speed we must not work at (0.7 x) RPM to (1.3 x) RPM

4s

EIx=k

W lRev / min.

E : Young’s Modulus

I : Moment of Intertia

Ws : Weight of shaft

K : from graph

k

= L/S

= length / distance from bearing

MixingTypes

• Liquid – Liquid (most common) a) density difference b) viscosity difference

• Solid – Liquid a) slurry b) suspension c) dissolution

• Gas – Liquid a) dispersion

• Liquid – Liquid (immiscible) a) emulsion / dispersion

Requirement

Energy to be supplied for moving the different phases

a) Supplied internally : e.g. Mechanically Agitated Contactors

b) Supplied externally : e.g. use of pumps, compressors, blowers

Devices Used

a) Stirred vessels

b) jet mixing

c) static mixing / mixers

Usually mixing is accompanied by other operations

Jet Mixing

a) liquid jet : low to medium viscosity liquids

Liquid velocity generated through the external pump

1 2L

4 61 6 1 6i o

Z TMixingtime = θ =

Re ν d g

Jet Mixing

b) gas jet : medium to high viscosity liquids

Use of external compressor : different fluid

Multipoint Single point

Static Mixers

Number of different designs are available

Simplest : baffle in heat exchanger shells

Job : divert the flow by putting an obstacle in its path

Energy associated with the moving fluid is used for mixing, i.e. if fluid is made to go everywhere in the reactor / vessel uniformity (mixing) will be achieved.

Common Examples

a) Kenics Twisted stripe

b) Sulzer SMXL / SMX

Inserted in pipes

Flow bifurcation takes place and the direction is changed

Energy for mixingStirred Vessel

P x mix = NP N3 D5 x mix joules

Typical = 0.2 to 0.4 %

Jet mixing

(Vg L g x volume) x mix

Typical = 0.03 to 0.8 % Due to pump or compressor

Static mixing

(P x volumetric flow rate) x (L/velocity)

Typical = 1 to 10 %

One of the most energy “Inefficient” operations

“Considerable Scope for improvement”

Problem Statement

1) To carry out blending of two liquids

2) To transfer O2 in the fermenter liquid by air sparging

3) To suspend the catalyst particle in a liquid – uniform suspension

4) To control the temperature of the reactor

5) Hydrogenation of fatty oils to saturated oils

a) Suspend Raney-Nickle catalyst

b) Sparge and distribute hydrogen

c) Control the hydrogenation temperature

Problem statement1) Blending of Two miscible liquids

e.g. Std. geometry, disk turbine

Estimation of ‘N’ (dimensionless mixing time)

AB

C D

E

Requirement

1) Length of loop, longest

2) Average velocity

3) No. of circulations

1) Length of the longest loop ‘ABCDE’

2) Average velocity Vrw = 0.53 (D/w) ND (D/T)7/6

3) No. of circulations 5 for 95% mixing

4 mix = 5 x circulation time

13/6aH+T T wNθ=9.43 D dT

Thus, loop length and average velocity

Problem Statement2) To transfer O2 in fermenter :

Requirement : 1) Good gas dispersion

2) Generate interfacial area

Rate of O2 transfer, gms/s = KLa x C* x V (1/s x gm/m3 x m3)

And

KL a = 0.025 (P/V)0.59 (VG)0.5

P/V – watts/m3, VG = superficial gas velocity, (m/s)

N

NPG/NP

QG/ND3

PG = NPG L N3 D5

Can be obtained by changing P/V or VG

Typical P/V – 1000 to 5000 watts / m3

VG 30 to 40 mm/s

P/V = g VG

Problem Statement3) To suspend catalyst particles

0.45

0.1 0.2 0.11 -0.85js p

gΔρN =S d x D

ρ

S – function of impeller type, location & geometry

jsG jsG 3N =Nb

GQxND

x – type of sparger / location and regime

b – extent of reduction in NPG

Thus knowing dp, , x & S. Select either Njs for a fixed D or select D for a

fixed Njs.

Now, Power N3 & D5. OPTIMISE / SCALE EFFECT

Problem Statement

-0.140.59 0.33 wallR

Prbulk

μh T=1.35 Re N

k μ

4) To control reactor temperature

Know heat flux Q = U A T

Know ‘A’ from reactor geometry

Know T from heat transfer medium conditions

Estimate U.

R m o

1 1 x 1Now, = + +

U h k h

Jacket

Coil

0.64 0.140.332R w

o

h T μND ρ=0.87

k μ μCPk

Optimise ‘ N & D’ in Re to get required ‘hR’

Problem Statement5) To control reactor temperature

a) Estimate Njs for the catalyst loading (Na)

typically, dp 5.0 x 10-6 m

x = 5 %

b) Estimate Required KL a (Nb)

i) Calculate NS = 1.25 QG 0.25 (T/D2)

ii) Estimate KL a or P/V (N) & VG to get the desired KL a

iii) Estimate H2 transfer rate

Estimate Njs again

c) Estimate N for the required heat transfer coefficient (Nc)

Select the higher of Na, Nb & Nc to satisfy all the requirement

Mixing time measurement methods

basics of reactor design mac2

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