distillation column design (methanol-water)

Distillation Column Design

Methanol-Water separation

Welahetti W.P.K

080533H

Distillation Column Design 2012

Table of Contents1 Introduction......................................................................................................................4

2 Theory.............................................................................................................................. 4

2.1 Operating Line equation for Top Operating Line (TOP)..............................................4

2.2 Operating Line equation for Bottom operating Line (BOP)........................................6

2.3 Equation of q – factor................................................................................................7

3 Calculation........................................................................................................................7

3.1 Data........................................................................................................................... 7

3.2 Calculation of amount of distillate and bottom product............................................8

3.3 Equilibrium data of methanol and water mixture......................................................9

3.4 Calculation of Minimum Reflux Ratio.......................................................................10

3.4.1 Drawing q line...................................................................................................10

3.4.2 Drawing Top Operating Line (TOP) at minimum reflux.....................................10

3.5 Calculation of Operating Reflux Ratio......................................................................11

3.6 Calculation of Actual number of stages required.....................................................12

3.7 Calculation of liquid and vapuor amounts in both sections.....................................14

3.8 Liquid and Vapour Density calculation.....................................................................15

3.8.1 Rectifying section densities..............................................................................16

3.8.2 Stripping section densities................................................................................16

3.9 Calculation of column diameter...............................................................................17

3.9.1 Diameter of rectifying section..........................................................................17

3.9.2 Calculation of diameter of stripping section.....................................................20

3.10 Calculation of hole diameter and area.................................................................21

3.11 Number of Holes in a tray at rectifying section....................................................21

3.12 Number of Holes in a tray at stripping section.....................................................22

3.13 Flow pattern identification and down comer selection........................................22

3.13.1 Flow pattern of rectifying section.....................................................................23

3.13.2 Flow pattern of stripping section......................................................................24

3.14 Column efficiency calculation...............................................................................24

3.15 Calculation of actual number of stages required.................................................27

Prasanna Welahetti


3.16 Calculation of height of the column.....................................................................27

3.17 Calculation of feed tray location..........................................................................28

4 References......................................................................................................................29

5 Summary........................................................................................................................ 30

Table of Figure

2.1 TOP Line............................................................................................................................. 52.2 Bottom Operating Line.......................................................................................................73.1 Data....................................................................................................................................83.2 Mass balance......................................................................................................................93.3 Methanol Water Equilibrium Data...................................................................................103.4 Temperature Composition Diagram of methanol/water..................................................103.5 R min Figure........................................................................................................................113.6 Vapour Liquid Equilibrium Curve......................................................................................133.7 Column 1.......................................................................................................................... 143.8 Feeding Section................................................................................................................153.9 Recommended general conditions and dimensions for tray tower..................................203.10 selection of Liquid-flow arrangement............................................................................233.11 Reverse Flow Down Comer............................................................................................233.12 Cross flow down comer..................................................................................................243.13 Van Winkle’s correlation................................................................................................25

Content of Table

3.1 Density data..................................................................................................................... 153.2 Density of Mixture............................................................................................................165.1 Summary.......................................................................................................................... 30

Prasanna Welahetti


1 Introduction This is continuous distillation with reflux. There are two sections in fractionation column. The upper section is called the rectification section and lower section is called stripping section. Rectifying section enriches with more volatile components and stripping section enriches with less volatile components.

2 Theory

Here we can use the Mc-Cabe-Thiele method,

Assumptions;

Constant molar overflow There is no any chemical reaction There are no any mass generation, mass accumulation and mass generation

2.1 Operating Line equation for Top Operating Line (TOP)

2.1 TOP Line

Prasanna Welahetti


Material balance around the envelope shown:

Overall Balance;

Vn+1=ln+D

Material Balance for More Volatile component (MVC);

V n+1Y n+1=Ln X n+D X D

Thus we have,

(Ln+D)Y n+1=Ln X n+D XD

Under constant molar overflow assumption:

L1=L2=.......... ln−1=ln=ln+1=L=constant

V 1=V 2=..........Vn−1=Vn=Vn+1=V=constant

The subscripts can be dropped. Thus, the equation simplifies to:

(L+D)Y n+1=L Xn+D XD

Re-arranging in the form y = f(x), and Introducing Reflux Ratio R = L / D,

Equation 2.1

This is the Operating Line Equation for the rectifying section (Top Operating Line) or TOL in short.

Characteristics: Straight Line Equation

Slope R/ (R+1)Intercept(1/R+1)XD,

Prasanna Welahetti


2.2 Operating Line equation for Bottom operating Line (BOP)

2.2 Bottom Operating Line

Material balance around the envelope shown: Under constant molar overflow assumption:

Overall Balance;L ’=V ’+W

Material Balance for More Volatile component (MVC);

L ’ X N=V ’Y N+1+W XW

Thus we have,

Equation 2.2

Prasanna Welahetti


Y N+1= L’L’−W

X N− WL’−W

XW

2.3 Equation of q – factor

Yq= qq−1

Xq− 1(q−1 )

Xf

q=heat required ¿ vapourise1molof feed ¿Molarlatent heat of the feed

3 Calculation

3.1 Data

3.3 Data

3.2 Calculation of amount of distillate and bottom productThese two values can calculate using simple material equations.

Assumptions

Prasanna Welahetti


At steady state there are no any material losses, material accumulation and material generation.

There is no any chemical reaction inside the column

3.4 Mass balance

Overall Material balance around the envelope shown:

F=D+W

250=D+W

Material balance for MVC around the envelope shown:

F X F=D X D+W XW

250×0.35=D×0.96+W ×0.02

Solving above two equations;

D=87.77kmolhr

W=162.23kmolhr

Prasanna Welahetti


3.3 Equilibrium data of methanol and water mixture

X 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Y 0 0.42 0.58 0.66 0.73 0.78 0.82 0.87 0.91 0.96 1T( C̊) 100 87.7 81.7 78 75.3 73.1 71.2 69.3 67.6 66 64.5

3.5 Methanol Water Equilibrium Data

3.6 Temperature Composition Diagram of methanol/water

3.4 Calculation of Minimum Reflux Ratio

3.4.1 Drawing q line

Feed is at saturated liquid condition; therefore according to q line equation q value should be 1.

Therefore,

q=1

Prasanna Welahetti


3.4.2 Drawing Top Operating Line (TOP) at minimum reflux

At the minimum reflux ratio; maximum numbers of theoretical stages are given. Therefore TOP line should be pass through interception of equilibrium curve and q-line.

3.7 R min Figure

Gradient of TOL ¿ 0.96−0.70.96−0.35

¿0.426

RminRmin+1

=0.426

Rmin=0.742

Prasanna Welahetti


3.5 Calculation of Operating Reflux Ratio

No hard and fast rules can be given for the selection of the design reflux ratio, but for many systems the optimum will lie between 1.2 to 1.5 times the minimum reflux ratios. Assume operating reflux ratio is 1.25 of minimum reflux ratio. Therefore operating Reflux ratio (R);

R=1.25× Rmin

R=1.25×0.742

R=0.9275

3.6 Calculation of Actual number of stages required

Slop of the TOL ¿ RR+1

¿ 0.92750.9275+1

¿0.481

Therefore TOL equation;

y=0.481x+0.498

BOL can easily draw with starting (Xw,Xw) to ending intersection of q line and TOL.

Prasanna Welahetti


3.8 Vapour Liquid Equilibrium Curve

Prasanna Welahetti


According to figure 3.6 vapour- liquid equilibrium curve it can count number of theoretical plates.

Total number of stages ¿14

There are total condenser and partial reboiler. Total condenser is not act as equilibrium stage, but partial reboiler is act as equilibrium stage. So, reboiler stage need reduce from total theoretical stages.

Number of theoretical stages required ¿14−1

¿13

3.7 Calculation of liquid and vapuor amounts in both sections

3.9 Column 1

Rectifying section

0.9275=L0 /87.77

L0=81.41kmol /hr

According to constant molar overflow;

Ln=L0=81.41kmol/hr

Material balance for above envelop

Vn=Lo+D

Prasanna Welahetti


Vn=81.41+87.77

Vn=169.18kmol /hr

Stripping Section

3.10 Feeding Section

According to given data, feed is at saturated liquid condition therefore all feeding liquids join with stripping section liquid.

Lm=F+ ln

Lm=250+81.41

Lm=331.41kmol /hr

Vm=Vn

Vm=169.18kmol /hr

3.8 Liquid and Vapour Density calculationInside temperature of the distillation column is varying point to point. Therefore average temperature was considered for a section.

Position

Compositions of Methanol Liquid

Compositions of Methanol Vapour Temperature

Density of Water(kg/m3)

Density of Methanol(kg/m3)

Liquid Vapour Liquid VapourFeed 0.35 0.68 77˚C 973 0.27 742 2.01Distillate 0.96 0.99 65˚C 980 0.165 752 1.12Residue 0.02 0.04 100˚C 958 0.59 714 4.33

3.1 Density data

Prasanna Welahetti


Density of liquid at 77˚C ¿973×0.65+742×0.35

=892.15kg/m3

Similarly;

Temperature Density of liquid mixture kg/m3 Density of vapour mixture kg/m3

77˚C 892.15 1.4565˚C 761.12 1.11100˚C 953.12 0.74

3.2 Density of Mixture

3.8.1 Rectifying section densities

Rectifying section is operating in between 65˚C -77˚C. Therefore at the average temperature density values can calculate.

Liquid density of rectifying section L = (761.12+892.15)/2

L =826.6 kg/m3

Vapour density of rectifying section v = (1.11+1.45 ) /2

v =1.28 kg/m3

3.8.2 Stripping section densities

Stripping section is operating in between 100˚C -77˚C. Therefore at the average temperature density values can calculate.

Similarly;

Liquid density of rectifying section L’ =922.64 kg/m3

Vapour density of rectifying section v’ =1.095 kg/m3

Prasanna Welahetti


3.9 Calculation of column diameter

3.3 Flooding velocity, sieve plates

3.9.1 Diameter of rectifying section

3.4 Liquid Vapour factor

F LV= 81.41169.18 √ 1.28

826.6

F LV=0.01 89

Assume tray spacing = 0.45 m

According to figure 3.1;

K 1=0.084

The flooding velocity can be estimated from the correlation given by Fair

Prasanna Welahetti


Uf=0.084 √ 826.6−1.281.28

Uf=2.13m /s

Dc- Column diameter

Ac- Column cross sectional area

Ad-Down comer area

Aa – Active area

Ah-Holes area

An- Net area

Ua-Actual vapour velocity required through the column

An=Ac−Ad

Assume Ad=12% of Ac.

An=Ac−0.12 Ac

An=0.88 Ac

Assume 80% flooding condition;Ua=0.8Uf

Ua=0. 8×2.13m / s

Ua=1.70m /s

Average molecular weight of the mixture assuming 50% methanol

¿32×0.5+18×0.5

¿25kg /kmol

(When it calculate the average molar weight, feed methanol composition is 35%,

assume inside the distillation column 50% methanol in mixture)

Prasanna Welahetti


An=1.1751.704

An=0.69m2

Therefore according to above derived equations;

An=0.88 Ac

0.69=0.88× Ac

Ac=0.784m 2

Ac=π Dc2

4

0.784=π Dc2

4

Dc=0.999m

Therefore the column diameter of rectifying section is 0.999m

3.9.1.1 Rechecking the assume tray space value

Here we have assumed tray spacing for the column. According to the “Recommended general conditions and dimensions for tray tower” table, it can check.

Tower diameter Tray spacing0.15

1 or less 0.51 to 3 0.63 to 4 0.754 to 8 0.9

3.11 Recommended general conditions and dimensions for tray tower

According to above “Recommended general conditions and dimensions for tray tower”

table, diameter of the column is correct. Because assume tray space was 0.45m and

received column diameter is 0.999m. Therefore assumed column space is correct(It is in

range).

Prasanna Welahetti


3.9.2 Calculation of diameter of stripping section

This is similar to rectifying section.

F LV=331.41169.18 √ 1.095

922.64

F LV=0.06 75

Assume tray spacing = 0.45 m

According to figure 3.1;

K 1=0.08

Uf=0.08√ (922.64−1.095 )1 .095

Uf=2.32m /s

Assume 80% flooding condition;

Ua=0.8×2.3 2m /s

Ua=1.86m / s

There is no vapour amount changes in stripping section with compare to rectifying section. Therefore,

An=1.1751.86

An=0.63m2

Therefore according to above derived equations;

An=0.88 Ac

Ac=0.55m2

Prasanna Welahetti


Dc=0.837m

Therefore stripping section column diameter is 0.837m

3.10 Calculation of hole diameter and area

Hole size less than 6.5 mm. Entrainment may be greater with larger hole sizes. (Page No. 568 Coulson & Richardson 6th volume 4th edition).

Therefore hole diameter is considered as 6mm.

3.11 Number of Holes in a tray at rectifying section

For a plate there is one down comer on the plate and top down comer also affected to bottom plate. Therefore two down comer areas need to reduce from active area. So,

Aa=Ac−2 Ad

Aa=Ac− (0.12×2 Ac )

Substituting to above equation;

Aa=0.596m 2

Assume holes area is 10% of active area;

Ah=0.1 Aa

Total holes area in a tray Ah=0.1×0.596

¿0.0596m 2

Area of a hole ¿ π× 0.0062

4

¿2.83×10−5m 2

Number of hole in a plate ¿ 0.0596

2.83×10−5

¿2106

3.12 Number of Holes in a tray at stripping section

All equations are similar to rectifying section calculation;

Prasanna Welahetti


Aa=0.418m 2

Assume holes area is 10% of active area;

Ah=0.1 Aa

Ah=0.0418m 2

Number of hole in a plate ¿ 0.0418

2.83×10−5

¿1478

3.13 Flow pattern identification and down comer selection The most common flow pattern is cross flow pattern. It can identify using below graph (figure 3.10 selection of liquid flow pattern).

3.12 selection of Liquid-flow arrangement

3.13.1 Flow pattern of rectifying section

Liquid flow rate of rectifying section ¿( 81.413600

kmols

×25kgkmol

)/( 826.6kgm 3

)

Prasanna Welahetti


¿6.83×10−4 kg /s

Column Diameter ¿0.999m

Therefore the flow pattern is “Reverse flow”(According to figure 3.10)

3.13 Reverse Flow Down Comer

3.13.2 Flow pattern of stripping section

Liquid flow rate of stripping section ¿( 331.413600

kmols

×25kgkmol

)/( 922.64 kgm 3

)

¿2.09×10−3kg /s

Column Diameter ¿0.837m

Therefore the flow pattern is “Cross flow”. (According to figure 3.10)

3.14 Cross flow down comer

3.14 Column efficiency calculation

Here we can use “Van Winkle’s correlation” for calculate to efficiency of column.

Prasanna Welahetti


3.15 Van Winkle’s correlation

Maximum and minimum temperatures of inside the column are respectively 100C˚ and 65C˚. Assume liquid temperature is average temperature of column. Assume properties of liquid mixture are equal to water properties.

Average temperature of column ¿ 100+652

¿82.5C˚

Surface tension of liquid at 82.5C˚ is calculated according to their molar basis of feed.

σL=0.109N /m

As the Uv ; I have taken maximum Ua value from both sections.

Uv=Ua

Uv=1.86m /s

μL=355×10−6Ns /m2

As vapour and liquid densities; average densities were taken,

v=1.19 kg/m3

Prasanna Welahetti


L=874.62kg /m3

D LK=5×10−9m2/s

Weir height for 1 atm column is 40-90mm. Therefore here I’m assuming weir height of the column is 45mm.

hw=45mm

Fractional area calculation;

FA=Fractional Area= area of holestotal columncross sectional area

FA=0.04180.625

FA=0.067

Surface tension number calculation;

Dg= σLμL×Uv

Dg= 0.109

355×10−6×1.86

Dg=126.07

Liquid Schmidt number calculation;

Sc= μLL×D LK

Sc= 355×10−6

874.62×5×10−9

Sc=81

Reynolds number calculation;

ℜ=hw×Uv× ρvμL×FA

ℜ=0.045×1.86×1 .19

355×10−6×0.067

Prasanna Welahetti


ℜ=4187 .93

Therefore;

Emv=0.07×126.070.14×8 10.25×4187 .930.08

Emv=0.79

¿79 %

Therefore efficiency of column ¿79 %

3.15 Calculation of actual number of stages required

I have already calculated required number of theoretical plates.

Number of theoretical stages required ¿13

In other way below equation can use for efficiency calculation;

Emv= numberof ideal stagesnumber of actual stages

0.79= 13number of actual stages

number of actual stages=16.46

Therefore number of actual stages required =17

3.16 Calculation of height of the column

Height of columnH c= (N act−1 )H s+∆H+ plates thickness

No. of plates Nact=17

Tray spacing Hs = 0.45 m

∆H= 0.5 meter each for liquid hold up and vapor disengagement

∆H=1 m

Prasanna Welahetti


Assume thickness of a plate is 5mm.

Total thickness of trays ¿0.005×17

= 0.085m

Height of column = (17−1)×0.45+1+0.034

¿8.234 m

Therefore the height of the column is 8.234m.

3.17 Calculation of feed tray location

Assume here plate numbers are count from top to bottom.

According to figure 3.6 vapour-liquid equilibrium curve; it can find the feed tray location.

Feed composition of methanol is 0.35. This value is at 10 th plate (theoretical) of the column. To calculate the actual feed tray location this value need to divide with column efficiency.

Therefore feed tray location ¿ 100.79

¿12.66

¿13 th plate

4 References Separation Process En gineering,2nd Edition, Phillip C.Wankat

Prasanna Welahetti


Chemical Engineering volume 6, 4th Edition, Coulson & Richardson’s Mass-transfer Operations,3rd Edition, Robert E.Treybal http://pubs.acs.org/doi/abs/10.1021/je00019a016 http://www.engineeringtoolbox.com/water-dynamic-kinematic-viscosity-d_596.html http://www.engineeringtoolbox.com/methanol-properties-d_1209.html

5 Summary

Name Sign Result

Prasanna Welahetti


Distillate flow rate D 87.77 kmol/hrWaste flow rate W 162.23 kmol/hr

q value q 1

Minimum Reflux ratio Rmin 0.742

Operating Reflux ratio R 0.9275

Number of theoretical plates 13

Liquid flow rate of rectifying section L0,Ln 81.41 kmol/hr

Vapour flow rate of rectifying section Vn 169.18kmol /hr

Flooding velocity of rectifying section Uf 2.65m /s

Column Diameter of rectifying Section Dc 0.999m

Flooding velocity of Stripping section Uf 2.53m /s

Column Diameter of Stripping Section Dc 0.837m

Tray Space of both sections lt 0.45m

Hole diameter Dh 6mm

Number of hole in a plate at rectifying Section 2106

Number of hole in a plate at Stripping Section 1478Down comer type of rectifying section Reverse flow down comer

Down comer type of Stripping section Cross flow down comer

Column efficiency Emv 79%

Number of actual plates 17

Height of the column 8.234 m

Feed tray location 13th plate

5.3 Summary

Prasanna Welahetti

distillation column design (methanol-water)

Documents