By

MOHAMMAD SIRAJ ALAM

SIMULATION OF PACKED TRAY COLUMN

A DISSERTATION Submitted in partial fulfilment of the

requirements for the award of the degree of

MASTER OF -TECHNOLOGY in

CHEMICAL ENGINEERING (With Specialization in Computer Aided Process Plant Design)

DEPARTMENT OF CHEMICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY ROORKEE

ROORKEE-247 667 (INDIA)

FEBRUARY, 2003

CANDIDATE'S DECLARATION

I hereby certify that the work which is being presented in the dissertation

entitled "SIMULATION OF PACKED TRAY COLUMN", in the partial

fulfillment of the requirements for the award of the degree of Master of Technology in

Chemical Engineering with specialization in "Computer Aided Process Plant

Design", submitted in the department of CHEMICAL ENGINEERING, INDIAN

INSTITUTE OF TECHNOLOGY, ROORKEE is an authentic record of my own

work carried out for the period from July 2002 to February 2003 under the

supervision of Dr. V.K. Agarwal.

The matter embodied in this dissertation has not been submitted by me for the

award of any other degree.

Place: Roorkee

Date: Feb21 , 200; (MOHAMMAD SIRAJ ALAM)

CERTIFICATE

This is certified that above statement made by the candidate is correct to the

best of my knowledge.

Date: Febag 200;

(Dr. V.K. AGARWAL)

Assistant Professor

Dept. of Chemical Engineering

Indian Institute of Technology, Roorkee

Roorkee-247667

ACKNOWLEDGEMENTS

These few lines of acknowledgement can never substitute the deep

appreciation that I have for all those without whose help, support and inspiration this

dissertation would not have taken its present shape.

I am deeply indebted to my guide Dr. V.K. Agarwal, Assistant Professor,

Department of Chemical Engineering, IIT Roorkee, without whom this concept of

working in the area of the simulation of catalytic distillation column would not have

taken birth in my mind. I would like to sincerely acknowledge his valuable guidance,

relentless support, discerning thoughts and loads of inspiration that led me forward to

delve deeper into the issue.

I am highly thankful to Dr. B. Mohanty, Head, Department of Chemical

Engineering, IIT Roorkee, for his constant invigoration at each stage which enthused

my work spirits.

I do not have words to thank Dr. S.C. Gupta, Chairman D.R.0 for his

valuable guidance and kind cooperation to make this work a success.

I express my deep sense of gratitude to staffs of CAD Lab., and Process

Integration Centre, Deptt. of Chemical Engineering, for their instant help in all kinds

of computer work.

I do not have words to thank Mr. Vinod, Surendra, Manoj, Pramod, Ambuj,

and above all my pathfinder to this project, Anil and all my colleagues who showed

their full cooperation with me.

Above all, I would like to acknowledge that the greatest role has been of my

parents who have helped me to cultivate the system of values and instincts that shall

always enlighten my path all these living years.

(MOHAMMAD SIRAJ ALAM)

ii

ABSTRACT

The present investigation pertains to a theoretical study of the effects of

installing thin layer mesh packing on the performance of sieve trays under distillation

conditions. Since the installation of mesh packing can be easily carried out at a low

cost, this could provide the best method to revamp existing sieve tray columns. This

type of arrangement is termed as packed tray. The methanol water system is chosen

for the study so that the results could be applied to aqueous as well as organic

systems.

The present study includes the objective of theoretical study of simulation of

packed tray column under distillation condition and then developing a computer

program that can be used to predict, design and to determine the influence of such

packing on the hydraulic and mass transfer performance of sieve trays; This study also

deals with the development of a steady state, equilibrium model for a multicomponent

system. It also includes the solution technique for solution of model.

Using the basic principle of conservation of mass, energy, and phase

equilibrium a mathematical model of a distillation column under steady state

condition has been developed. These balance equations includes component material

balance, enthalpy balance, phase equilibrium, and summation equation. These balance

equations are linear in nature and can be easily transformed into a tridiagonal system.

The resulting system of linear algebraic equations is solved by using the Thomas

algorithm to get the component composition on each tray.

iii

CONTENTS

Title Page No.

CANDIDATE'S DECLARATION

ACKNOWLEDGEMENT ii

ABSTRACT iii

CONTENTS iv

LIST OF TABLES vii

LIST OF FIGURES viii

NOTATIONS ix

Chapter 1 : INTRODUCTION 1

1.1 OBJECTIVES OF THE PRESENT STUDY 3

1.2 ORGANIZATION OF THESIS 3

Chapter 2 : LITERATURE REVIEW 4

2.1 SIEVE TRAY 4

2.2 PACKED TRAY AND PACKED COLUMN 7

Chapter 3 : DESIGN OF PACKED —TRAY COLUMN 16

3.1 PLATE SPACING 16

3.2 COLUMN DIAMETER 16

3.3 TRAY AREAS 17

3.4 FLOODING VELOCITY 17

3.5 HOLE PITCH 18

3.6 WEIR DIMENSIONS 19

3.7 WEIR LENGTH TO TRAY DIAMETER RATIO 19

3.8 PHASE INVERSION 19

3.9 TRAY TO TRAY ENTRAINMENT 19

3.10 ROTH HEIGHT, LIQUID HOLDUP, EFFECTIVE FROTH 20

DENSITY

3.11 WEEPING POINT VELOCITY 21

iv

3.12 PRESSURE DROP THROUGH PACKED TRAY 23

3.13 DOWN COMER DESIGN 26

3.13 A DOWN COMER BACK UP 26

3.13B RESIDENCE TIME IN DOWNCOMERS 27

3.13C DOWNCOMER VELOCITY 28

3.14 MASS TRANSFER COEFFICIENTS 28

3.15 PACKING HEIGHT 31

3.16 INTERFACIAL AREA 32

Chapter— 4 : SEPARATION OF MULTICOPONENT MIXTURE 33

4.1 FENSKE-EQUATION 33

4.2 UNDERWOOD'S METHOD FOR MINIMUM REFLUX RATIO 34

4.3 ACTUAL REFLUX RATIO AND THEORETICAL STAGES 34

4.4 FEED-POINT LOCATION 35

4.5 MATHEMATICAL MODEL 37

4.5.1 Assumptions 37

4.5.2 Model Formulation 37

4.5.3 Solution of the Model 39

Chapter 5 : RESULTS AND DISCUSSION 42

5.1. PACKED TRAY DESIGN 42

5.1.1 Total Tray Pressure Drop 43

5.1.2 Tray-to-Tray Entrainment 44

5.1.3 Froth Height 44

5.1.4 Weeping 44

5.1.5 Packing Height and Eddy Diffusivity 44

5.1.6 Tray Efficiency 45

5.2 SEPARATION OF MULTICOMPONENT MIXTURE 45

Chapter 6 : CONCLUSION AND RECOMMENDATIONS 58

6.1 CONCLUSION 58

6.2 RECOMMENDATIONS 58

REFERENCES 60

APPENDIX-A PROGRAM LISTING 63

APPENDIX-B PHYSICAL PROPERTIES 77

APPENDIX-C FLOODING VELOCITY 78

APPENDIX-D RELATIONSHIP BETWEEN DOWNCOMER AREA 79 AND WEIR LENGTH

APPENDIX-E DISCHARGE COEFFICIENT 80

APPENDIX-F DATA FOR RESULTS 81

APPENDIX-G SCHEMATIC DIAGRAM FOR DISTILLATION 85

COLUMN FOR COMPONENT MATERIAL

BALANCE

vi

LIST OF TABLES

Table No. Title Page No.

Table 3.1 Recommended residence time in downcomer 27

Table 5.1 Specification of the system 42

Table 5.2 Provisional Design of Tray 43

Table 5.3 Distribution of components in distillate and bottoms 46

Table B-1 Antoine Coefficients 77

Table B-2 Enthalpy Coefficients 77

Table F.1 Data for Tray Pressure Drop (Fig. 5.1) 81

Table F.2 Data for Aerated Liquid Pressure drop (Fig. 5.2) 81

Table F.3 Data for Pressure Drop Vs Vapour Velocity for different 82

Hole Sizes (Fig. 5.3)

Table F.4 Data for Entrainment (Fig. 5.4) 82

Table F.5 Data for Effective Froth Height (Fig. 5.5) 83

Table F.6 Data for Froude Number as a function of F-Factor (Fig. 5.6) 83

Table F.7 Liquid Mole Fraction for Packed Tray (Fig. 5.9) 84

Table F.8 Liquid Mole Fraction for Sieve Tray and Packed Tray (Fig. 5.10) 84

vii

LIST OF FIGURES

Figure No. Title Page No.

Fig. 4.1

Fig. 4.2

Fig. 4.3

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10

Figure C-1

Algorithm for multicomponent distillation by empirical method

36

Equilibrium stage j

38

Algorithm for solution of multicomponent distillation system

40

Variation of total column pressure as a function of

48

F-factor (kg1/2M-1/2S-1/2).

Variation of aerated liquid pr. drop as a function of 49

F-factor (Kg1/2m-1/2s-1/2).

Packed tray Total pressure drop as function of vapor velocity. 50

Variation of entrainment as a function of F-factor (kg1/2m1/2s1/2) 51

Variation of Effective froth height at function of

52

F-factor (kg1/2n11/2s-1/2).

Variation of Fruode Number as a function of

53

F-factor (kg1/2m-1/2s-12/).

Variation of eddy diffusivity as a function of vapor velocity. 54

Variation of Murphree Tray Efficiency as a Function of 55

F-Factor (Kg1/2m.1/2s-1/2)

Variation of liquid mole fraction on different plates 56

Plate to plate calculation of liquid mole fraction. 57

Flooding velocity 78

Figure D-1

Relationship between downcomer area and weir length

79

Discharge coefficient

Figure E-1

Discharge coefficient 80

viii

NOTATIONS

Aa Active tray area, m2

Aap Clearance area under the downcomer, m2

A8, Ab Bubbling area, m2

Au Area of calming zone, m2

Ad Downcomer area, m2

AH Perforation area, m2

Ak Perforated tray hole area of stage k, m2

Am Either the downcomer area Ad or the clearance area under the downcomer Aar, Which is smaller, m2

Ao Total area of perforation zone, m2

Ap Area of perforation zone, m2

At Total tray area, m2

Awe Area of wall clearance, rn2

a Interfacial area per unit bubbling area

B Channel base dimension, mm or m; Bottom flow rate

c Total number of components

Co Discharge (orifice) coefficient, dimensionless

Cw Width of wall clearance, mm

Distillate rate

T, Column diameter, m

T Tray diameter, m

DH do,dl, Hole diameter, mm

DE Eddy diffusivity, m2/s

deq Equivalent diameter, mm

F Tray to tray entrainment, kg/100kg of gas

Emv,Emv Murphree plate efficiency

Ear Point efficiency

F Feed rate, and F-factor (va pg / 2 ), Kg1/2S-1M-I/2

FLV Liquid vapor flow factor Fr Froude number

Point of inversion

ix

f

H,h

Hp

hAL

hap

hb

hc1

hb,

hd

hFe

hf

hi,

hig

hL

how

hr

Ht,hT

hw

h2(1)

vs

K

L

LW

Lwd

N

Nv

NL

Nov

PT

Pe

Po

Fractional degree of approach of flooding

Enthalpies of vapor and liquid respectively

Height of packing, m

Aerated liquid pressure drop, m of liquid

Height of the bottom edge of the apron above the plate, mm

Downcomer back-up, measured for plate surface, mm

Clear liquid height, m

Clear liquid back-up, m

Head loss in the downcomer, mm

Dry tray pressure drop, mm of liquid

Effective froth height, mm

Froth height, mm

Operating hole pressure dorp, m of liquid

Liquid gradient pressure drop height, m

Liquid hold up on trays, m

Crest of liquid over the weir, m

Residual pressure loss, m of liquid

Total tray pressure drop, m of liquid

Weir height, m

Over all height of froth

Density corrected vapor velocity over the bubbling area, m/s

K- value of component

Liquid flow rate, Kg/s

(q/W)liquid flow rate over weir, m3/s m

Liquid flow rate in downcomer, Kg/s

Weir length, m

Number of stages

Gas phase transfer units

Liquid phase transfer units

Overall transfer units

Packed Tray

Peclet number

Hole pitch

Q

Volumetric flow rate of vapor, m3/s

Qc Condenser duty, KJ/hr

QL Volumetric flow rate of liquid per length of weir, m3/s.m

QR Reboiler duty, KJ/hr

q Volumetric flow rate of liquid, m3/s

rd Ratio of downcomer are a to tray area

co Ratio of total perforation area to tray area

S Channel side, mm

ST Sieve Tray

s Tray spacing, m

TPD Elevation where the liquid volume fraction in the gas reaches 0.02

t Tray spacing, m

tr Residence time, s

Va Gas velocity based on active area of tray, m/s

vd Liquid downcomer velocity, m/s

vg,uG Superficial velocity of gas, m/s

vo Velocity though hole area, m/s

vw Weep point velocity, m/s

V Vapor mass flow rates, Kg/s

Ejection velocity of the droplet form the top of liquid continuous region

vb Bubbling velocity, m/s

of Flooding velocity, m/s

vs Superficial velocity of vapor, m/s

Vw Weeping velocity, m/s

z Liquid flow rate, m3/s m of width of flow path on the plate

Z Height of packing, m

Greek Symbols

Liquid density, Kg/m3

pv Vapor density, Kg/m3

13 Aeration factor

xi

is

Effective froth density

Average froth density

Liquid flow based on perimeter Kg/s m

Viscosity of liquid, m Pa.s

Void fraction of packing

Average froth density

Dry pressure drop per unit packed height

Pressure drop per unit packed height

Surface tension, N/m

Chapter 1 INTRODUCTION

Distillation is a method of separating component of a solution, which depends

upon the distribution of the substances between a gas and a liquid phases applied to

cases where all components are present in both phases. Distillation is a dominant

process for separating large multicomponent streams into high purity products. So the

chemical process industries ongoing quest to improve energy, utilization reduce

capital costs, and boost operating flexibility is required increasing attention to

distillation column optimization during design. A distillation column can use either

trays or packing. Their mechanism of mass transfer differ, but the key for both is a

good approach to equilibrium through the generation of large amount of interfacial

area. This interfacial area results from the phases of vapor through the perforation of

trays, or the spreading of liquid on the surface of packing.

Sieve trays have been widely used in mass and heat transfer applications

because of their design and reliability and low cost. However a major drawback is

their relatively low efficiency among distillation column internals. To achieve high

capacity and efficiency, numerous tray design modification have been proposed, have

failed to gain wide acceptance. High efficiency, large capacity, low pressure drop and

high turndown ratios are the desirable tray performance characteristics and these are

affected by tray operating regime, vapor and liquid load system properties and tray

geometry. There is a littler flexibility in changing system properties, although sieve

tray efficiency is not very sensitive to tray geometry. It has been found that trays with

small holes are expensive to manufacture, most industrial installation use a hole

diameter larger than 6 mm.

Both trays and packings are used to provide intimate contact between the

ascending vapors and descending liquid without a great reduction in throughput or

capacity of fractionating column. The main difference between trays and packing is

the percentage opening of each phase contacting device. A tray has an opening of 8-

15% of the tower cross-section area while the projected opening of a typical packing

design is usually more than 50% of tower cross-section. Also with packing contact is

1

readily achieved between the vapor and the liquid phase through the column rather

than at specific points, as with trays. The following further illustrates the advantages

of using packed towers over trays towers:

1. High capacity with high liquid rates or high viscosity: Trayed columns

employ the energy of the vapor to create mass transfer surface area by

bubbling through the liquid. Packed towers with aid of gravity create mass

transfer surface by the action of liquid falling over the packing. Thus there

are no downcomer in the packed tower, and 100 percent of the tower cross-

section combinations: is utilized for mass transfer.

2. High capacity/efficiency: Because the capacity of a packed tower is greater

than a comparable sized trayed tower, smaller more efficient packing can be

used to handle the same capacity.

3. High capacity in foaming system: Trayed columns use the continuous liquid

phase to create a froth that is difficult to separate. Packed towers make the

vapor phase continuous and the liquid phase discontinuous.

4. Packed tower have a low-pressure drop per theoretical stage or transfer unit.

Despite the above-mentioned advantages packed towers are also not without

problem. The problems generally encountered with packings are:

Difficulty in cleaning

• Clogging of void space with presence of solids

o Not suitable for the distillation with chemical reactions

o High cost.

Thus packed columns also need to improve as sieve tray columns. It appeared

that there was a little scope to improve tray design until Spagnolo and

Chuang(19)reported the performance of sieve trays combined with knitted mesh

packing. They found that tray efficiency increased due to the installation of mesh

packing on the sieve tray. Salem and Aalsay(18)reported that the efficiency of a 75

mm diameter test column was enhanced with the installation of various kind of

random packing on sieve trays. They concluded that the improved tray efficiency

might be due to the large surface introduced by packing on the reflux liquid and the

vapor rising in the tower. Other researchers also studied the hydraulic and mass

transfer performance of a sieve tray with the bed of different mesh packing heights

and also reported increase in Murphree tray efficiency.

2

With greatly increasing demand for olefins and petrochemicals, to upgrade the

efficiency of high capacity trays, placing wire mesh packing on the decks of screen

trays gives rise to the following phenomenon that incipient bubble formation is

inhabited thus the bubbles of vapor becomes very finely dispersed and also forth

height becomes more uniform which cause reduction in back mixing to the point

where the true plug flow regime is approached. Both these effect enhanced mass

transfer efficiency while maintaining high capacity. The following effects were

observed on addition of mesh packing on sieve tray. The clear liquid height on the

tray increases significantly. However the froth height did not increase proportionally.

Therefore the aerated function for the packed sieve trays must be smaller than for

sieve trays. At high gas velocities froth turbulence or spray jets are damped. Packed

tray did not show any froth oscillation or non-uniform spray jets. As a result packed

sieve tray had much less entrainment than sieve tray.

1.1 OBJECTIVES OF THE PRESENT STUDY

e To study the influence of the installation of a thin layer of mesh packing

on the performance of sieve trays under distillation conditions.

e To compare the performance sieve trays column without packing, and with

mesh packing under distillation conditions.

• To develop and simulate a mathematical model for separation of

multicoponent mixture using results of the performance of sieve tray with

installation of a thin layer of mesh packing.

1.2 ORGANIZATION OF THESIS

The thesis has been organized in six chapters. Chapter second describes the

different correlation available in literature for design of both sieve tray and packed

tray, and reviews the literature on the packed tray column available in research

papers. Chapter third presents design of packed tray column. Fourth Chapter presents

the development of steady state mathematical model and also solution of the model.

Results and discussion of design and mathematical model have been given in chapter

five. Finally, chapter sixth highlights the main conclusions of the thesis and provides

the recommendation for future work.

3

Chapter 2 LITERATURE REVIEW

Sieve trays have been widely used in mass and heat transfer applications

because of their reliability and low cost. However a major drawback is their relatively

low efficiency among distillation column internals. The rising cost of energy in recent

years has resulted in the use of high efficiency packing instead of sieve tray as the

choice for the new application. In addition, it is justifiable to replace an existing sieve

tray column with packed tray column, since the cost of revamping can be recovered

quickly through lower operating expenses. However this practice is not without

problem; the design procedure of a packed column is less reliable and on a few

occasion, the packing did not perform as expected and sieve tray had to be reinstalled.

Therefore, it is desirable to develop a method to obtain high tray efficiency at

minimum risk. So a lot of work are started to improve the performance of sieve tray.

The woks in the field of hydraulic and mass transfer performance of sieve and packed

tray are being reviewed below.

2.1 SIEVE TRAY

Lockett and Banik (14) discussed the influence on the weeping rate of

individual perimeter such as hole gas velocity, liquid rate, weir height, hole diameter

and functional perforation area and given a correlation:

WF = 0.02F,-1 — 0.03 (2.1)

This correlation can be used to predict weeping rate and hence weeping

fractions, when used in combination with in the Calwell's correlation for the clear

liquid height IT should not be used when the predicted weep fraction is greater

than 0.5.

Chen and Chuang (8) explained various alternates of increasing capacity and

efficiency of distillation tower by using high capacity tray or tray/packing

combination. When a designer wants to size a new distillation column, he normally

must calculate four parameters, capacity, pressure drop, mass transfer, and hold of the

4

contacting device he intends to use. For preliminary design or evaluation of a given

fluid contacting device, one may estimate pressure drop, (AP „) at a given percent of

flood, when pressure drop ( APb ) at a different percent of flood is know, by the

following rule of thumb which is accurate ± 5% up to 75% of flood.

APb

where PF=

For

= APo (PFb

percentage

capacity, author

Pv . —0.5

/PF, )17'

flood.

used

C2 vL

Wallis expression

Pv —0.5

(2.2)

of the following from:

(2.3) _(Pv — PL ,_(Pv — PL)_

where C2 and C3 are related to the hydraulic of corrugated sheet metal or metallic

gauze packing by the following relationships:

C2 = 0.914 118 (2.4)

C3 = 0.914" (2.5)

where dH is hydraulic diameter.

At column loads up to 70% of flood, the specific liquid hold up can be

calculated by: ,N1/3

Fr Re L

where Fr and ReL are the Froude and Reynold number for the liquid phase and C5 is a

constant that depends on the load and feature of the packing.

Bennett et al. (1) developed a phenomenological based model for froth height

using the assumption of both vapor and liquid - continuous zones within the total froth

height. The model demonstrates the importance of the liquid and vapor rates and

determines that the Weber number has little effect on froth height. They gave

entrainment correlation for the froth regime and entrainment correction for the spray

regime for non-air-water system. \ 2.77 ( \1.81 ( .0 .19

V gh, PI, E fi.0 ,„ 0.742 2 \.gOet i Vs Pv

= C5 (2.6)

(2.7)

2 v..56 V ghL 1

, + 2.48 .!;0et) s

(A0 /4)

r

—0.614 V" d,

\ hi,

( N1.08

PL

Pv

(2.8)

F ,'pray = 8.0 x10-18

1+8.27 020

5

( \ -1 10 X 0, 5 Pc

Y2q1 Pv

E = 0.0035 h20

(2.10)

The author given an overall correction for the spray or froth regime that based

on their reported data.

1.04 r .,0 5 t - ' PL E = 0.04 oi 2/3 (2.9) h20 \ PI , ,

Bennett et al. (2) given new correlation for sieve tray point efficiency (Eon , 1 ,

entrainment (E) and section efficiency (SECT , SECT )• The entrainment was calculated from

the following correlation:

The value of the entrainment was used to calculate the Entrainment corrected

(2.11)

(2.12)

where

E„,„= En,„(E)

Bennett et al. (3) gave the optimization rules for tray-column and packed

column. They suggested following points to maximize the number of theoretical

stages for a given section height.

For sieve trays:

• Keep the fraction open area low, e.g, in the range of 5%.

• Use smallest practical perforation diameter.

• If practical, select a tray spacing that yields high entrainment — a tray

spacing corresponding to an entrained - liquid- to vapor flow ratio of about 0.2 is reasonable.

• Consider parallel flow trays, if the cost increase is justified.

For structured packing:

• Use packing with a high specific area, and run the column near the upper

range of stable operation.

Murphree efficiency En,„(E).

En,(E) V =1-0.8E0„/V m3 E E„,„(E = 0) L

The section efficiency is now calculated from:

ln + E„,, (A-1)) r 1 SECT = In

6

e Use packing with a corrugation angle of 45°.

e Be consented about the need for redistribution, which is related more to

theoretical tray count in a section than section height.

o To minimize the pressure drop per theoretical stage using structured

packing with a 30° corrugation angle can given a modest improvement in

pressure drop per theoretical stage, but also will result in a higher HETP.

2.2 PACKED TRAY AND PACKED COLUMN

Strigle et al (20) During the development of Intalox metal packing many

experiments for evaluation of packing performance was carried out including Strigle

et al. tests. It was that any particular packing shape could be made in many different

sizes. However for any shape, it was found that with the increase in size, vapor flow

per unit area increased and pressure drop at constant vapor flow was reduced.

Simultaneously, with increase in the size the number of theoretical plates develops per

unit of height was also reduced. They found that one packing shape might be

compared to another only if capacity and efficiency are considered together.

Therefore they concluded that the above comparison required the consideration of

size. The efforts to develop high efficiency, low pressure drop, Intalox metal packing

has led to a greater understanding of high efficiency packing performance and a

refinement of the design methods for using them in distillation. The results of that

development program may be summarized as follows:

o Low-pressure drop, high efficiency packing must be designed on the basis

of maximum operational capacity rather than on the basis of allowable

pressure drop.

o Maximum operation capacity is a more consistent basis for the design of

atmospheric and high-pressure distillation towers than in flooding or

pressure drop regardless of the packing being used.

o The use of Intalox metal tower packing reduced the overall capacity and

operating costs of new distillation tower because it permits smaller tower

with lower pressure drop.

7

Existing towers revamped with Intalox metal packing was able to achieve

the same throughput for the less energy input or greater throughput for the

same energy input.

Spagnolo and Chuang (19) studied the effect of adding a shallow led of

knitted mesh packing on the trays and found that with packing, tray pressure drop

increased, tray to tray entrainment decreased, and mass transfer tray efficiency

increased by 3% to 20%. The great efficiency gain occurred in low gas flow range

where the tray operated in bubble regime. They also developed relationship between

liquid holdup and aerated liquid pressure drop (ham.,) by a mean gas momentum change

term:

hL = 0 .102h A P v vL + 998.4 ---(vo PL. g

And defined average froth density (a)

a = hL TDP

) (2.13)

Bravo et al. (4) represent a design model for a very special verification of

structured packing, on that is fabricated from metal gauge (woven wire cloth) as

corrugated sheets. They defined resulting equivalent decimeter i.e. an arithmetic

average of triangle and square hydraulic radii.

d eq = B h -1

25)

+ —1

B 2S (2.14)

The effective vapor velocity through the channels is determined for the

following relationships

= v,,, /6 sin 9 (2.15)

The effective liquid velocity is based on the following film relationship for

laminar flow:

VLe, =

( 2 \ "33 PL g

2p 3,u r \ L

(2.16)

Salem and Alsaygh (18) reported that adding packing to a sieve tray tower is

an economical way to improve its efficiency. This study explored ways to increase

product purity. The feed was methane-water blends. The data of their report shows

8

that packing height of 10 cm may be assumed to be the optimum at which the best

purity and Spartan efficiency can be obtained in the fractionating tower. More

packing height would not improve the separation. Tower performance with or without

packing was evaluated using the Murphree plate efficiency E„,v calculation suggested

by Fair.

E„,,, = (.1"' — 1)/(A — 1) (2.17)

where X = m (V/L)

And E'I N = - N Oleo, actual (2.18)

Chen et al. (6) reported about the hydraulic and mass transfer performance of

a combined metal packing and sieve tray for the distillation of methane —water

mixtures. It was found that by adding a shallow bed of packing, the Murphree tray

efficiency increased by 40 - 50% over a wide range of concentration and flow rates.

This increase in tray efficiency can be attributed to much smaller and were uniform

bubble formation on the packed tray. Hydraulic measurements have shown that the

packed tray has lower weeping and entrainment, as well slightly higher froth heights

and pressure drops.

Fair et al. (10) compared two models in terms of flooding capacity; mass

transfer and pressure drop in case of structural packing.

Bravo-Rocha-Fair Model: This model applies in the reify below the loading

point because it does not include the effects of gas velocity on liquid hold up.

where

AP =

Reg =

V =

0.171+

P '

(92.7 „2 y ■ e ∎ 1 5

(2.19)

(2.20)

(2.21)

(2.23)

Re S 1— C0 Fr°. ns

Vv

FrL _

E sin 6)

g

Simichlumair-Bravo-Fair model: This model is used for both random and

structural packing for wide range of following and pressure drop.

9

And

AP =

AP =

h, =

Fr , L.

Reg

C =

=

M{1-1— E [1—ho iE (+ 20[AP/09,0]2 41— e))12+c)/3 (2.24)

d p =6(1—e)la p

0.75f,

0.555Fri,'

+

1— hje

E

(1+ 20[AP/(ZpLa r

(2.25)

(2.26)

(2.27)

(2.28)

(2.29)

(2.30)

46S PVIIv2/dP E •

=

Reg Reg"

6 (1— G)

+

Pl a P - - 'iv

C2

Reg 2Res'i2

fU

First equation is implicit in pressure drop and requires a numerical solution.

Coker (9): had given guidance for the design of packed column. Packed

towers are finding increasing use in wide variety of application in chemical process

industries because of high capacity/high efficiency combination and capacity in

foaming system, low pressure drop, low residence time and higher capacity with high

liquid rates or viscosity. Packed column design is depend upon four principles

characteristics, namely pressure drop ( AP ), flooding characteristics, and operating

conditions and of course, the specific packing system. Author given following

formula for pressure drop:

AP = a *10fil. (G 2 /pv ) (2.31)

where a and # are the packing constants in given in paper, L and G are liquid and

vapor mass velocity respectively in lb/ft3. Packed towers are typically operated at a

gas velocity that corresponds to about 50- 80% of flooding condition. This usually

results in a pressure drop of 0.5-1,0 in H20/ft of packing.

Kister and David (11): - modified the existing Sherwood-Leva-Eckert (SLE)

chart for the prediction of pressure drop and flood point. Sherwood, Leva and Eckert

gradually developed SLE data chart. Eckert produced a later version of the SLE

10

correlation chart than that given in the Perry's handbook. The later version omitted the

flood curve. Strigle changed the scales of Eckert's later version of the SLE correlation

from log-log to semilog to make interpolation between adjacent pressures drop curves

easier. Strigle also update packing factors based on Eckert's later version. They used

the Strigle's semi log plot of Eckert's later version. For the prediction of the improved

pressure drop, converted the SLE correlation into an interpolation tool. Pressure drop

calculated by interpolating the plotted pressure drop data, while the correlation curves

were used to guide this interpolation. The conversion of the SLE correlation into an

interpolation chart overcomes all of the limitation of SLE correlation. But for the

prediction of the flood- point and Maximum Operating Capacity (MOC), it was

practically impossible to use interpolation. Therefore, they developed a new

correlation for the calculation of flood point pressure drop on the basis of plot

between flood point pressure drop data and packing factor:

APfi,„„1 = 0.115Fp°7 (2.32)

This equation used for the estimation of the flood pressure drops for all

random packing. Flood velocity or flood point was estimated by back-calculation

using the SLE chart, after the calculation of the flood pressure drop using above

correlation. Plot between flood pressure drop and packing factor, which was used to

develop above equation, shown some scatter of data and thus introduced some

inaccuracy.. Inaccuracies in packing factor also adversely affect the calculations. Both

of these factors lowered the accuracy of the estimates for flood pressure drop (About

20%). However, it was found that the error in calculation of the flood velocity was

about 4-8%, which is reasonable. While the procedure they have introduced

overcomes the limitations of SLE correlation. It did not surmount the limitations

inherent in the flood point and pressure drop data. Finally they strongly recommended

that SLE data chart only be used once the user is familiar with the data limitations and

can reasonably evaluated their impact on chart prediction.

Chen et al. (5) explained mass transfer and hydraulics of packed sieve trays.

Performance characteristics of packed tray have been obtained with system that

covers a wide range of properties. It was found that the mass transfer efficiency of

packed tray is 40-50 % higher than that of trays without packing for the distillation of

the acetic acid - water mixtures. This increase in efficiency is mainly due the large

11

interfacial area and small bubble diameter resulting from the mesh packing. The total

pressure drop of packed tray is about 15% higher than that of trays without packing.

Correlations for pressure drop and entrainment of packed trays were determined from

data obtained in a 600mm diameter, air-water column.

(mm of water). 4.16 + 17.51v2 + 0.55L + 2 . 11do (2.33)

where L is liquid load (m3 m-I hd).

Xu et al. (26) examined the liquid mixing on a packed sieve tray in a 300mm

diameter air-water column. The degree of mixing was measured in terms of

longitudinal eddy diffusivity (DE) and peclet number (Pe). It was found that by adding

25.4mm thick mesh packing on a sieve tray, the eddy diffusivity decreased

significantly. The effects of packing height on liquid mixing were also investigated

and it was found that the eddy diffusivity decreased further with greater packing

heights. The experimentally measured De values were correlated. The results

indicated that eddy diffusivity was influenced by liquid rate, gas superficial velocity

and packing height. They also gave following empirical correlation for representation

of liquid diffusivity.

DE = 0.0275 + 0.0206L + 0.00378v0 171 — 0.321H°p 835 (2.34)

Leva (13) developed a new method for the prediction of the pressure drop in

packed columns. The method proposed was the modified version of the Generalized

Pressure Drop Correlation (GPDC) that method offered a number of advantages over

alternative approaches:

• That was largely self -contained, and permitted the evaluation of the dry-

bed packing factor for a single dry -packing pressure drop reading.

• That provides a means for modifying the packing factor of dry packing so

that pressure drop estimates for two phase counter current gas/liquid flow

can be made based on liquid densities and liquid viscosities.

• Results form the proposed GPDC showed no discernible bias due to

influence of the particular physical properties of the system.

Since the original GPDC was found not suitable for evaluating non-irrigated

packed tower pressure drop and less satisfactory for prediction of pressure drop for

the systems in which the irrigated liquids are substantially heavier than water. In

12

response to above limitations an auxiliary, empirical two-term equation for pressure

drop prediction was developed:

AP = cr(G 2 pv )x (2.35)

where a and # are the empirical constants for the packing involved. This equation

consists of two parts. The first part a(G 2 p,), permits estimation of pressure drop

through the non-irrigated (dry) packing, while the second part, 104 is a pressure drop

correction factor due to simultaneous liquid flow concomitant liquid holdup.

An improved correlation proposed by author as with the original form of the

GPDC, relates the flow capacity factor given in the form:

Y = 0.0160[F 2Of (PL )]/g, (2.36)

To the relative flow factor

X---(LIVXpr, 1 P LY' (2.37)

Rocha et al. (16) developed a comprehensive model for predicting the liquid

holdup, pressure drop, and flood capacity for column containing structured packings

of the corrugated metal type. The model was consistent in that the same parameters

were used for each of the prediction approaches. It was taken in to account the

texturing of the packings surface as well as the wettability of the surface material,

when in contact with various types of liquids. The model was validated for air/water

as well as organic distillation systems, and operating pressures ranging from 0.02 to

4.14 bars.

They also gave the following equations:

For liquid holdup:

where

ht = (4/S) Fs Ostat (4/S) FO Sop (2.38)

Fs — correction factor that accounts for the entire surface not being wet

when only static holdup occurs.

Fo - represents the corresponding correction when liquid flow is present.

And gstio = 1— cosy

-05

(2.39) 2p •\ ■

g PI' sin 0 \ \PL _

13

0.5

LS 3/1z,

p, (613)( 1 sin —

pLehs 1— pi. AZ PLg

(2.40) 6 = op

For pressure drop:

AP,, 0.177 2 88.772,u, AZ Se 2 (sin 9)2

vvS + S2esin 9 vs

(2.41)

Rocha et al. (17) This paper was the second part of a two-part paper dealing

with the hydraulic and mass transfer in structured packings for distillation column

services. The second part of this series covered the generation of effective interfacial

area and provided a general correlation for predicting the mass transfer efficiency as a

function of surface type, packing geometry, phase flow conditions, and fluid

properties. The mass transfer model was tested against a variety of commercial

structured packings, for distillation pressure ranging from 0.33 to 20.4 bars.

They also gave the correlation for overall transfer rate on the basis of

conventional definitions of the transfer units:

where

Hot, =

—

kr = 0.054

k L = 2

ae Fsr ae

H v + All I.

vs A LS +

0.8

Y115

Pv \0.33

(2.42)

(2.43)

(2.44)

k La

( D LC

e k LCie

(1, + Le )i),

E v Le \0.5

/Iv

eL rL

\D„ p,

r."9

7rS

29 120 • (2.45) 0.26 0.6 0— 0.93 cosyXsin Or3 ReL

The term X is the ratio of slopes of equilibrium line to operating line. For a

point in the column where both of these lines may be considered straight, a value of

HETP may be calculated:

HETP =H In A (2.46)

A —1

14

Lacks (12) published a paper which addressed the under lying physical

relationship between plate and packed column, which leads to a definition of transfer

units for packed columns that is consistent with the useful definition of transfer units

for packed column and given a relationship between transfer units and equivalent

theoretical plates:

N plate.col. ov low

ETP 110

(2.47)

To obtained the result of packed columns, the ratio q„„, ph, is evaluated in the

limit that 77„„, approaches zero, the following result is obtained for packed columns:

ln( L = mV

N ET p 1 m V L

(2,48)

15

Chapter 3

DESIGN OF PACKED -TRAY COLUMN

Sieve trays continue to be the standard equipment used for distillation column.

Properly design sieve trays are efficient, of low cost and of higher turn down ratio. To

achieve high capacity and efficiency, numerous tray design modifications have been

proposed, one is sieve tray packed with mesh packing. On each packed tray gas

emerging from the opening in the plate penetrates into the liquid and thus, generates a

two-phase mixture with a large interfacial area. An approximate estimate of the

overall column size can be once the number of real stages required for the separation

is known. The design of packed tray column will be discussed in this section.

3.1 PLATE SPACING

The overall height of the column will column will depend on the plate spacing.

Plate spacing from 0.15 m to 1.0 are normally used. The spacing chosen will depend

on the column diameter and operating conditions. For column above 1.0 m diameter,

plate spacing of 0.3 to 0.6 m will normally be taken as initial estimate.

3.2 COLUMN DIAMETER

The diameter of the tower must be chosen to accommodate the flow rates. The

principal factor that determines the column diameter is the vapor flow rate. The vapor

velocity must be bellow that which would cause excessive liquid entrainment or a

high-pressure drop. Brown equation can be used to estimated the maximum allowable superficial velocity, and hence the column area and diameter.

1/2

V5 = (-0.171.t 2 + 0.27/ — 0.047) (PL — Pv) Pv

(3.1)

where, v, = maximum allowable vapor velocity, based on the total column cross-

sectional area, m/s.

The column diameter, T, can then be calculated:

16

T, (3.2)

where, V, is the maximum vapor rate, kg/s.

3.3

(i)

TRAY

Following

Total

A, =

AREAS

column

( Vir

area terms are used in the packed column design.

cross-sectional area:

(3.3)

where vapor velocity v, is calculated from the flooding vapor velocity.

v f s (3.4)

(ii) Total tray area:

Ac A, — (3.5)

1— (Ad /At )

where,

Ad /A, is downcomer ratio.

(iii) Downcomer area:

Ad = (A:

A, (3.6) \ A,

(iv) Active tray area:

Aa = - 2Ad (3.7)

(v) Tray diameter,

(4A '"s (3.8)

3.4 FLOODING VELOCITY

The limiting vapor or flooding velocity, vf can be calculated from the equation.

v = K1 1

05 PL — PA'

P (3.9)

where Ki is the Souders — Brown coefficient. In this equation of is based on the total

area of the column minus the area of one downcomer. K1 can be obtained form the

7r 2

17

chart presented by Coulson, Richardson and Sinnott. the chart data is correlated by the

following equation.

K1 = 0.0129 + 0.1674 s + (0.0063 – 0.2686 s).FLy + (-0.008 + 0.1448 s)FLv2

(3.10)

(3.11)

The flooding condition fixes the upper limit of vapor velocity. A high vapor

velocity is needed for high tray efficiencies, and the velocity will normally be

between 70 to 90 percent of that which would cause flooding. For design, a value of

80 to 85 percent of the velocity should be used.

3.5 HOLE PITCH

The hole pitch range:

2.5d0 < po < 4.0do

The hole pitch p0 should not be less than 2.0 hole diameters and the normal

range will be 2.5 to 4.0 of hole diameter. The hole pitch p0 can be calculated from the

following equations:

where

po = 1.0529d0

Ao = ro A a

= A,

A„, = fir = - 2a

a= sin -I

–

2 2

csti

( \ -0.04458 A0

( , *10-3

}

sin a cosa

(3.12)

(3.13)

(3.14)

(3A5)

(3.16)

(3.17)

(3.18)

W D, —cosa

A P I

– AC:

2–C„,

N21, _ *10'

2

r L„„

) 2

L, – ---) L ( p, 0.5

where F – PL

18

3.6 WEIR DIMENSIONS

The height of the weir determines the volume of the liquid on the plate and is

an important factor in determining the plate efficiency. A high weir will increase the

plate efficiency but at the expanse of higher plate pressure drop. For column operating

above atmospheric pressure the weir height will normally be between 40mm to

90mm.

With segmental downcomer the length of the weir fixes the area of the

downcomer. The chord length will normally be between 0,6 to 0.85 of the column

diameter. A good initial value to use is 0.77, equivalent to downcomer area of 12%.

3.7 WEIR LENGTH TO TRAY DIAMETER RATIO

A graphical correlation from which the ratio of weir to tray diameter can be

predicted has been presented by Coulsen,Richardson and Sinnott. The correlation has

been fitted with following equation:

W=T ( \ 0 5

1.1687 Ad +0.35 A, (3.19)

3.8 PHASE INVERSION

Normally the two-phase mixture on the plate is in the form of a bubbly or

aerated liquid. This liquid continuous mixture is called froth. Under high rates and

low liquid rates, however, the regime can invert to a gas continuous spray comprising

a magnitude of liquid droplets of varying diameter. It appears that a spray is favored

bye high superficial gas velocity, low hole areas (high hole velocity), low liquid rates,

and large hole sizes. The correlation for the phase inversion is given by the following

equations:

= 0.0567p1.O 692 Cr 06 (A() //1„ ) j 25 (q11,,,,r5 c1-' 1° (3.20)

This equation is given for a weir height of 50 mm. For other heights, multiply

Fga° by 0.92 for 25mm weir height and by 1.12 for 100mm weir height.

3.9 TRAY TO TRAY ENTRAINMENT

Tray to tray entrainment is a measure of liquid water carried out by the upward

flowing gas to the tray above.

19

moles of liquid entrained 1(area)(time) Fractional Entrainment —

L + moles of liquid entrained l(area)(tinte)

The tray entrainment correlation for the packed tray is given by the following

equation:

E = 5.325 * 10'3 F2 (3.21)

where the tray-to-tray entrainment is in Kg/100Kg of gas, and F is active area F-

Factor defined as:

F = va * pv1/2 (3.22)

The range of the correlation is for 1.0-4.0 F-Factor and average resultant error is

± 10%. For sieve tray entrainment can be estimated from the following equations.

E = 0.00335 ( \ -1.10 r \ 0.5

P Ail 20

2.0 P' (3.23)

1h \ —0.15

# = 0.5 1— tanh (3.24)

From the above equation for the entrainment of size plate, the correlation for

the packed tray can be check by reducing the value of E by 30% for low flows

(F-Factor=1.2) and by 85% for high flow (F-Factor = 4.0).

3.10 ROTH HEIGHT, LIQUID HOLDUP, EFFECTIVE FROTH DENSITY

To predict the height of aerated liquid on the plate, and the height of the froth

in the downcomer, estimation of the froth density is required. The density of the

aerated liquid will normally be between 0.4 to 0.7 times that of the clear liquid height.

The packing caused the froth height to increase due to mainly smaller size of bubbles

generated on the packed tray. This is because of the fact that smaller bubbles are more

stable, and this results in a greater number of bubbles accumulated on the packed tray.

The correlations available in literature for estimation of above parameters are given

below.

The correlation for the estimation of total liquid holdup:

k = (3.25)

where h j: is effective froth height and (I), is effective froth density. Correlations for the

estimation of these two parameters are as follows:

20

( \2/3

hw. +C, q (3.26) e

0 = exp(— 12.55.v,' 1 )

where C, = 0.501+ 0.439.exp(-137.8* h1 ,.)

And vs is the density corrected vapor velocity (m/s) defines as:

(3.27)

(3.28)

= \..PL —

)1/2

(3.29)

The correlation for the average froth density:

02m — h (3.30)

where h20 is average froth height, which is estimated from the following equation:

h2 = hp,

where F,,, is vapor

Frt.,

froude

+ 6.9

number.

( \ -1.85

(3.31)

(3.32)

(3.33)

2

g.h,

And v = 3.v (A,, I A„)0,

3.11 WEEPING POINT VELOCITY

The lower limit of the operating range occurs when liquid leakage becomes

excessive through the holes. This is the weeping point, and vapor velocity at weeping

point is the minimum value for stable operation. An analysis of the correlation

proposed for predicting the weeping point indicated that the most important parameter

is the Froude number based on hole gas velocity.

Froude Number defined as:

Fr =1, Pv \ ghLpi,

(3.34)

The dry plate pressure drop is defined as:

21

( hd = 50.8

\ 2 Pv VO

PL ACo (3.35)

(3.36) ( 05

From this the significance of the Froude number in determining the weeping

can be understood. It represents the ratio between dry tray pressure drop, which tends

to prevent weeping and the clear liquid height, which tend to cause weeping. Based on

this simple analysis, Lockett and Banik (1986) have attemped to correlate their

weeping data by plotting the weep flux vs Fr* The weep flux (WF) is defined as:

WFweeping rate(m3 Is) =

hole area(m2 )

WF = — 0.030 (3.37)

This equation cab be used to estimate the weeping point (WF= 0) which occurs when

Fr = 0.67.

The clear liquid height is estimated from

hL = APT — APd (3.38)

where APT is the measured total pressure drop and APd the measured tray dry pressure

drop at the same velocity.

There is one more method available in literature given by Coulson,Richardson

& Sinnett, which is simple in presentation and results the weeping velocity as function

of hole diameter and vapor density.

K 1 , — 0.90(25.40 — do )-

PV"

VIV = (3.39)

where

= 1.661n(hw + how )+23,48 (3.40)

where height of the liquid crest over the weir can be calculated from the Francis

formula as:

how = 0.664.Fw .(q/W)2/3 (3.41)

22

3.12 PRESSURE DROP THROUGH PACKED TRAY

Packing has shown to have beneficial effects on tray efficiency and capacity.

The only drawback is the higher-pressure drop associated with the installation of

packing. It is important to estimate the extra pressure drop caused by the packing. The

total pressure drop is the head required to drive gas through the perforation (hi) and

through the aerated liquid and packing on the tray.

h, = h„ +17,41 (3.42)

The pressure drop experienced by the vapor flowing through a tray is assumed

to be the some of the contribution by the holes and by the head of the two-phase

mixture.

h„ = hd + h, (3.43)

where ha is the dry tray liquid height and h1 is the liquid height. The pressure drop

through holes that is dry pressure drop is estimated using the simplified orifice

equation.

// \ 2

hri = 0.0508 Pr .L \PL. /. C0

l = hc, +h

r 2 +

h-A

(3.44)

(3.45)

Total liquid holdup, hL, for packed tray

hL= + ht (3.46)

The clear liquid height, hd, is calculated from the following correlation:

hc) = ahw + how (3.47)

where the liquid fraction of the froth, a, is computed with Barker and Self(1962)

correlation:

0.37hw +0, 012F., +1.78(q10+ 0.024 a= (3.48) 1.06hw + 0.035Fa + 4.82(8/0+ 0.035

The choice of correlation for the liquid fraction turns out to be impartent as

certain correlations are dynamically unstable. The height of liquid over the weir, how,

is computed by the various correlation for different types of tray weirs and weir factor

(Fw) correction is employed. For segmental weir:

23

)2/3

how = 0.664F0, ( pir-/-/

14/ w = —

w 2

(3.49)

(3.50) =

1 — F,w(1.68q

2/3 2 r1 — w2

w2.5 " •

The residual height, hr, is only taken into account for sieve trays. Bennett's

method for calculation of residual height is: N 213 \( \213(

NI/3 6 ' a- ' PL—PV

0.27PL)g) \ do )

The froth density is computed from:

h = —EL (3.52) a

The liquid gradient, his, is estimated from a method given by Fair:

R, = z.h

(3.53) z +211 J.

U f = (3.54) hc ,

R,U Ref (3.55)

f = 7 x104 h,, Re f106 (3.56)

Zft1.;. h,g =

(3.57) gR,

where z, is average flow path width for liquid flow, and Z the flow path length.

For the calculation of aerated liquid pressure drop (hAl), Bernard & Sergent

(1966), equation, which relates the liquid holdup and aerated pressure drop by a mean

gas momentum charge term, is generally used

( Pv va(vo v „) h,, = 9.804 hz. (3.58) 1-.) g

hr = (3.51)

24

For pressure drop of structured packing, Stichlmair et al, (1989) semi-

empirical method from an analogy of the friction of a bed of particle is used. It

contained a correction for the actual void fraction corrected for holdup, that is depend

on the pressure drop. The pressure drop is:

AP I — 6 -, 1

= 0.75 P 4.65 Pv u (3.59) Az

P al P

where ep = h,

This relationship differs from the Ergun equation in the friction factor C and in

the porosity term. Here, C denotes the friction factor of the single particle and not of

the whole bed. The friction factor is correlated by the following equation:

Cl = +

C2 +C,

e e (3.60)

R RIl2

where C1 , C2 and C3 are constants that depend on the type of the packing. For

structured wire mesh packing value of Cl, C2 and C3 are 18, 4, 0.20 respectively.

The Reynolds number is given by:

rwd p,, Re = (3.61)

Pv

In structured packing it is necessary to define the equivalent diameter of a

channel, which is used in the above equation.

d 1, = 6(1— c (3.62)

Above correlation can be used for calculation of dry pressure drop assuming

e p = e . Liquid holdup is computed with the liquid Froude Number:

1.1 L a

ge 4.65 (3 63)

h, = 0.555Fr" (3.64)

The pressure drop of irrigated packing is related to the pressure drop of dry

packing by the following equation:

A/3w, 1— e(1— hi 6.)` (2" )13 (1— h , I e)-4 65 (3.65)

APd 1—e

The exponent in the above equation is given as:

25

( 1 CI C2 c (3.66)

Re 2Re" 2

This pressure drop of irrigated packing term is added to aerated liquid pressure

drop for packed tray.

Chen et al. (1992) gave the following correlation for wire mesh packing

through a computerized regression analysis:

hr (mm of liquid) = 4.16 +17.511,02 + 0.55/, + 2.11d,, (3.67)

The above correlation is valid for the operations in the ranges:

vs = 1.2 to 2.5 m/s,

d = 7.0 to 12.5 mm,

L = 10 to 30 m3/(m.h)

hw = 0.05 m.

3.13 DOWN COMER DESIGN

Downcomers are conduits having circular, segmental or rectangular cross-

sections that convey liquid from and upper tray to a lower tray in distillation columns.

At the design stage checks are carried out to ensure that:

• The downcomer provides sufficient residence time for vapor

disengagement,

• Downcomer velocity is not excessive and

• Liquid thrown over the weir is not too large.

3.13 A DOWN COMER BACK UP

The downcomer area and plate spacing must be such that the level of liquid

and froth in the downcomer is well below the top of the outlet weir on the plate above.

If the level rises above the outlet weir, the column will be flood. The back up of the

liquid in the downcomer is caused by pressure drop over the plate and resistance to

flow in the downcomer itself. In terms of clear liquid height the downcomer backup is

given by:

hb = (111v + how) + 11T + hdC (3.68)

26

where hb is downcomer backup, measured from plate surface (in mm) and hde is the

head loss in the downcomer (in mm).

The main resistance to flow will be caused by the constriction at the

downcomer outlet, and the head loss in the downcomer can be estimated using the

equation given by Cicalese et al. (1947):

= 0.166 Lvt ,d

PL A nr

(3.69)

where Lwa is liquid flow rate in downcomer (kg/s) and A. (m2) is the area minimum

of Ad and Area under downcomer apron Aap.

where Aap = hap * W

where hap is height of the bottom edge of apron above the plate and W is the weir

length. The height hap is normally set at 5 to 10 mm below the outlet weir height.

hap =h,„ - (5 - Onnn)

3.13B RESIDENCE TIME IN DOWNCOMERS

Sufficient residence time must be provided in the downcomer to allow total

disengagement of vapor from the descended liquid, so that the liquid is vapor free by

the time it enters the tray below. Failure to totally remove the vapor from the liquid

will cause premature flooding in downcomer. Recommended downcomer are in the

range of 3 to 7 s, depending on the foaming tendency of the system. A recommended

set of design values is given in Table (2). The downcomer residence time is given by

the following correlation:

q (3.70)

Table 3.1: Recommended residence time in downcomer

Foaming Tendency Example Residence time Low Low molecular weight

Hydrocarbons, and alcohols 3

Medium Medium molecular weight Hydrocarbons

4

High Mineral oil absorbers 5

Very high Amines and glycols 7

27

3.13C DOWNCOMER VELOCITY

Downcomer residence time is to provide a low enough liquid velocity to

achieve satisfactory vapor disengagement from the downcomer liquid. Values

recommended ranges from 0.1 to 0.4 ft/s depending on the foaming tendency of the

system. In some cases velocity as high as 0.7 ft/s .have been recommended for low

foaming systems. Downcomer area is usually fixed by specifying the superficial

velocity of the liquid in the downcomer on a vapor free basis, vd. A convenient

equation due to Glitsch, Inc. (1974) is:

va = 0.0081(t(pL — pi, r. 5 (3.71)

3.14 MASS TRANSFER COEFFICIENTS

Mass transfer coefficients can be computed from the Number of Transfer

Units (NTU's) by:

ki . = N lt,,a

k,=N L It La

(3.72)

The correlations used for calculation of Number of Transfer units are:

O. 776 + 0.00457k, — 0.238Fa + 104 .8(q / W) N (3.73)

N L =19700.D0 5 (0.40P, + 0.17)tL (3.74)

where Fa, active area F-factor, Scy, Schmidt Number for vapor and, tL, residence time

can be computed from the following correlations:

= l'„ \Tv (3.75)

Sc = PLD,

Individual mass transfer coefficient, kG and kL can also be calculated by

equations obtained by Zuiderweg:

0.13 0.065 (3.77)

Pg Pg -

k L = 0.024D: 25

(3.78)

where Di., is liquid diffusivity (m2/s).

(3.76)

28

On the basis of two films model for mass transfer, and relating all efficiency to

gas phase concentration, point efficiency can be expressed in terms of transfer units:

1\1"v

(3.79)

where Nov, is Overall Transfer Units calculated from the following equation:

N „ ' 1 (3.80)

1/Ni . +A/N1

where

A = ,L

It is necessary in most of the instances to convert point efficiency Eov to

Murphree plate efficiency E,„v. This is because of incomplete mixing, only in small

laboratory or pilot plant column, under special conditions, the assumption Eov = Emv

likely to be valid. For a cross flow plate with no mixing there is a plug flow of liquid.

For this condition of liquid flow, Lewis analyzed effects of gas mixing on efficiency.

He considers three cases:

1. Gas enters plate at uniform composition (gas completely mixed

between plates).

2. Gas unmixed, liquid flow in the same direction on the successive

plates.

3. Gas unmixed, liquid flow in alternative direction on successive plates.

Case 1 has found the widest application in practice and is represented by the

following relationship:

E„,„ = [exp(AE,,, )— 1.0] (3.81)

Above equation assumes the following in addition to the base condition:

1. L/V is constant.

2. Slope of equilibrium curve m is constant.

3. Point efficiency is constant across the tray.

Most plate column operates under condition such that gas is completely mixed

as it flows between the plates, but few operate with pure plug flow of liquid.

Gautreaux and O'Connell have studied departure from plug flow of liquid by

29

assuming that liquid mixing can be represented as occurring in a series of completely

mixed liquid. For this model,

(1+ A E"11 )" —1.0 (3.82)

where n is number of stages occurring on the tray.

An approximation of number of stages can be obtained from figure, given in

index using the following criteria:

1. Increased liquid rate favors plug flow.

2. Sieve plates have less back mixing than bubble-cap plates because of

less obstruction to flow.

3. Increased gas rate increases turbulence and the degree of back mixing

of liquid

An alternative approach is presented in the' AIChE Bubble-tray Design

Manual and is based on an eddy-diffusion model. According to this model,

L5 111 6' 1_e-(1)+P) C l ) -1 (3.83)

( 1;:()I (11 + Pe)1+111Pe- ii 1+ 11

) + Pe )

where

e 1 42, E'v 1.0 17=12 (3.84) 2 Pe

Z 2 Pe= (3.85)

DEtL

where, Pe is peclet number, Z length of travel and A, stripping factor.

The term DE is an eddy-diffusion coefficient (m2/s). For Sieve tray, Barker and Self

obtained the following correlation:

DE = 6.675 x 10-3 l'„ + 0.922 x 10-4 - 0.00562 (3.86)

If mesh packing is added on the sieve tray the characteristics of liquid mixing

change dramatically. Any existing correlations for predicting eddy diffusivity for

sieve trays are no longer valid for packed trays .Xu,Afacan and Chuang measured

values of eddy diffusivity for packed trays which were correlated in terms of liquid

30

rate, L (m3/hr), superficial gas velocity based on active area, Va (m/S), and the

packing height, Hp (m),as follows:

D = 0.0275 + 0.0206L + 0.00378v; 11 0.3211-1,"3' (3.87)

The average absolute relative error between the measured DE and those

calculated using equation (3.61) is 14.7%.

— log

Colburn equation for the effect of entrainment on efficiency:

Ea = 1

E Inv 1+ In [V j + Vi )]

where Ea = Murphree vapor efficiency, corrected for recycle effect of liquid

entrainment. The ordinate value, 11/ is defined as follow:

E = + L

where E is absolute entrainment of liquid and, L liquid down flow rate without

entrainment.

3.15 PACKING HEIGHT It was that the eddy diffusivity increases with increasing gas and liquid load

for sieve and packed trays. It was also found that the measured eddy diffusivity

decreases with increasing height of mesh packing. Most often, Peclet number is also

used to characterize the degree of mixing and predicting tray efficiency from point

efficiency. A high Pe is larger than 10, the enhancement of packing height on the tray

efficiency is not significant. From the consideration of Peclet number and pressure

drop, packing height can be optimize.

Overall Column Efficiency:

Calculated values of E„,v must be corrected for entrainment, if any by the

Colburn equation. The resulting corrected efficiency Ea is then converted to column

efficiency by the relationship of Lewis:

log[1+ Ea (t— 1)] (3.88)

(3.89)

31

3.16 INTERFACIAL AREA

The interfacial area of the tray with or without packing can be estimated by the

following equation:

1 = —

1 47 NOG (3.90)

k k \ G L

Assuming that the liquid on the tray is completely mixed in column and vapor

distribution approaches plug flow, then

NOG = —In(1—E00)=—In(1—En„) (3.91)

Individual mass transfer coefficient, kG and kr, can be calculated by equations

obtained by Zuiderweg:

kG = 0

'13 0.065

Ps Ps -

k L

= 0.024DL ° 25

where DL is liquid diffusivity (m2/s).

32

Chapter— 4

SEPARATION OF MULTICOPONENT MIXTURE

The general objective of distillation is the separation of substances that have

different vapor pressures at any given temperature. Rigorous design procedure for

separation of multi component mixture requires number of trays, feed location, reflux

ratio and physical properties

4.1 FEN SKE-EQUATION

Minimum number of trays is required for a given separation at total reflux and

Fenske- equation can be applied to the key components of a multi component system

to determine the minimum number of theoretical stages needed to effect a specified

separation:

log ( X IkD ( XhkB

\XhkD )\XIkB Nm +1 = ;n log a,k

(4.1)

log{( D.XIAD \i B,xlikB N}

D)Chk1) B.X1k13 N111111 + = (4.2)

logaik

where N1111, is number of theoretical plates (stages) required, 1 is added to include the

reboiler stage.

• = mole fraction of light key in the distillate.

• = mole fraction of heavy key in the distillate.

x„.8 = mole fraction of light key in the bottom.

• = mole fraction of heavy key in the distillate.

cra. = average value of relative volatility of light key w.r.t. heavy key.

D = distillate flow rate.

B = bottom flow rate.

33

The relative volatility c is taken as the geometric mean of the value at the

fractionator's top and bottom temperatures.

4.2 UNDERWOOD'S METHOD FOR MINIMUM REFLUX RATIO

A.J.V. Underwood developed the following two equations to determine the

minimum reflux ratio, Ruin of a multi component mixture:

..x1F a1 .x2F Cz3.X3E

al —0 a2 —0 a3 —0 =1—q' (4.3)

ai.xiD a2.x2D a3 .x3D al —9 a2 -19 a3 —0

Rmin + 1 (4.4)

where,

a 1, a 2, a 3... correspond to relative volatilities of components 1,2,3... w.r.t. the

heaviest component in the mixture.

x1F ,x2F,x3p, ...Correspond to mole fraction of components 1,2,3 ...in the feed

stream.

X1D,X2D,X3D ...Correspond to mole fraction of component 1,2,3...in the distillate.

The root of the equation (4.2) is 0. The required value of 0 must satisfy the relation:

az < 0 < al

where 1 is light key and 2 is heavy key in the mixture.

Underwood's equation presupposes that relative volatilities remain constant

throughout the column.

4.3 ACTUAL REFLUX RATIO AND THEORETICAL STAGES

To achieve a specified separation between two key components, the reflux

ratio and the number of theoretical stages must be greater than their minimum values.

In practical, super fractionators requiring a large number of stages are frequently

designed for a value of RI Rm,„ of approximately 1.10, while separations requiring a

small number of stages are designed for a value of RI R. of approximately 1.50. For

intermediate cases, a commonly used rule of thumb is R R,„,„ equal to 1.30.

34

Gilliland developed the most successful and simplest empirical correlation

for multi components mixture. The data points cover the following ranges of

conditions,

1. Number of components: 2 to 11

2. q.: 0.28 to 1.42

3. Pressure: vacuum to 600 psig.

4. a: 1.11 to 4.05.

5. Rmin: 0.53 to 9.09

6. Nmin: 3.4 to 60.3

The line drawn through the data represents the equation by Molokanov is:

N —N n,in Y =

N +1 =1 exp..'" 1+54.4X \( X —11

... 11+117.2X)\ X°5 (4.5)

where X =R — R

mi."

R+1

4.4 FEED-POINT LOCATION

An estimate can be made by using the Fenske equation to calculate the number

of stages in the rectifying and stripping section separately, but this requires an

estimate of feed-point temperature. An alternative approach is to use the empirical

equation given by Kirkbride:

\2 B

- 0.206

X hkF X IkB

(XIA.F )\ X. up ) D )

where,

NR = Number of stages above the feed, including any partial condenser

N s = Number of stages below the feed, including the reboiler

xhh.F = Mole fraction of heavy key in the feed

x„,,. = Mole fraction of light key in the feed

NR N s

(4.6)

35

START

Specify feed condition

Specify splits of two components, specify column Pressure and type of condenser

Calculate minimum theoretical stages (Fenske Equation)

Calculate minimum reflux ratio (Underwood Equation)

Calculate actual theoretical stages for specified reflux ratio > minimum value (Gilliland correlation)

Calculate feed stage location (Kirkbride Equation)

V EXIT

Fig. 4.1 : Algorithm for multicomponent distillation by empirical method

36

4.5 MATHEMATICAL MODEL

This section describes the formulation of mathematical model for a Distillation

Column. Based on principle of conservation of Mass and Enthalpy a model for a

conventional Distillation Column is developed in present Section. This section also

describes the solution of developed model.

4.5.1 Assumptions

Mathematical Modeling of column is based on the following assumptions:

1. Vapor and liquid on any particular theoretical stage are in phase

equilibrium.

2 No chemical reaction occurs.

3. Condenser is a total condenser.

4. Steady state operation.

4.5.2 Model Formulation

Associated with general theoretical stages are the following index equations

expressed in terms of the variable set in Fig. 4.2. The equations are often referred as

MESH equations. The set of equation required to represent such a system is as

follows:

Material Balance:

Fx j.., + + —Viy—L1x1. 1 = 0 (4.7)

where j = 1,2,3...N and i = 1,2,3...c

Equilibrium Relation ship:

Phase equilibrium: - y11 — K = 0 (4.8)

Summation Equations: -

E —1.0 = 0 (4.9)

xfi —1.0 = 0 (4.10)

Energy Balance:

L j_, .h j_, + V j.÷1 H Vi , .H = 1 h ~_~ +D.hD 0„ (4.11)

Total balance

L = V)+I +F — (4.12)

37

In general, = yJ), = Hj (Ti, Pi, yj) and hi = Pi, xi). If

these relations are not counted as equations and these three properties not counted as

variables, each equilibrium stage is defined only by the 2c + 3 MESH equations. A

counter current cascade of N such stages is represented by N(2c+3) such equations in

[N(3c+10)+1] variables. If N, F, xr, Tr, P-1 and all Pi are specified, the model

represented by N(2c+3) simulataneous algebraic equations in N(2c+3) unknown

variables comprising all xii, yji, Lj, Vi and Tj.

Liquid from Stage above

Vi 1-Ii Tj Pi YIJ

Feed

Heat Tramfer

Stage j

(+) if from stage (-) if to stage

Li.] hi_,

Pi_ i xi J-1

Fj, xFi, hFi, PFJ

Vj+1 Hi+i Ti+i Pin xi j+ i

LJ hi Tj Pi

j

Vapor from Stage below

Figure 4.2 Equilibrium Stage j

38

4.5.3 Solution of the Model

This section presents a method to solve the model equations described in the

previous section. The algorithm for the solution of model is as given in the figure 4.1.

A computer program in C++ has been given in the appendix. Problem specifications

consist of conditions and stage locations of all feeds, total flow rates of all side

streams, heat transfer to or from all stages, total number of stages and distillate flow

rate. To initiate the calculations, values for tear variables Ti and Vi are assumed. An

initial set of V.; values has been obtained on the assumption of constant molar

interstage flows. An initial set of Ti values has been obtained by computing both the

bubble-point temperature of an estimated bottom product and the dew-point

temperature of an assumed distillate product and then determining the other stage

temperatures by assuming a linear variation of temperature with stage location.

Solution of Material Balance equations:

Solving material balance equation given in previous section:

(V, + —V —(1/ j+,+ F —V j +V J K,,)x i , j +V

(4.13)

This equation can be written in the following form:

A.x.. +B x. +C x.10 =1) 1-1 ‘ ,1 1

where,

Al =(t1 + F —V 1_1 )

B1 = 41+ , + F —V 1 +V

C1 = (v j+Ilc1+1 )

(4.14)

D at feed plate

= 0 I else where

Step by step calculation of variables, such as 1(0, x,o, To and total flow rates are

done according to algorithm given in Fig. 4.2.. Variable Kii is calculated by the help

of Antoine equation. Further this equation is used to calculate temperature of stages

after the calculation of liquid mole fraction by Thomas algorithm. Total flow rate Vi

and Li is calculated by the enthalpy balance equations.

39

Check error in N

Calculation of K

Solution of component balances by Thomas algorithm to

calculate x values

Calculation of stage temperatures

Evaluation of molar flow rates from enthalpy balances

INLET DATA

Guess of initial T, L, V, x values

Print of results

Fig. 4.3 : Algorithm for Solution of multicomponent distillation system

40

Matrix form of equations (4.14) can be written as: 13,

A,

CI

B,

0 0

C. 0

.0

0

x1

xi , D,

0 A3 B3 C3 0 xi .3 D3

0 .0 AN BN _, Civ _, 0 X i , N -2

0 .0 0 AN .BN C AT Xi,N-1

0 0 0 0 AN BN xi., DN

(4.15)

The above matrix can be solved using Thomas algorithm. The Thomas

algorithm for solving the linearized equation set is a Gaussian elimination procedure

that involves forward elimination starting from stage 1 and working toward stage N to

finally isolate xi,N . Other values of xii are then obtained starting with xi,N.1 by

backward substitution.

Enthalpy Calculation

If the vapour and liquid streams from ideal solution, the enthalpy per mole of

vapour and the enthalpy per mole of liquid leaving plate j are given by the following

equation C

i =1

C

I hi; xis

where the enthalpies of each pure component `i' in the vapour and liquid streams

leaving plate j are represented by Hi; and hi; respectively. These are evaluated at the

temperature and pressure of plate j.

41

Chapter 5

RESULTS AND DISCUSSION

This chapter discussed the results obtained by designing of packed tray using

the design equation presented in Chapter-3. In this chapter, effect of installation of

knitted mesh packing on sieve tray hydraulic and mass transfer variables namely

pressure drop, aerated pressure drop, entrainment, weeping velocity, froth height, and

Murphree tray efficiency are analyzed. This Chapter also discussed the results

obtained by solving the model developed in Chapter-4 by using the algorithms as

explained in the same Chapter for a multicomponent system.

5.1 PACKED TRAY DESIGN

CASE 1: Methanol is to be removed from methanol-water blend. The feed

contains 10%(w/w) methanol. The specifications of the system are given in Table 5.1.

Table 5.1: Specification of the system.

System Methanol and water solution

Temperature 951 C

Pressure 1 atm Feed Rate 0.00424 kmol/s

Feed mole fraction 0.059 (10% w/w of feed)

Distillate mole fraction 0.95

Bottom mole fraction 2.81x 10.5 (50 ppm)

Slope of operating line 5.0

Number of theoretical stages 10

As the liquid flow rates and composition vary up the column, the plate design

should be based on above and below the feed point. Here, only the bottom plate

design is considered. The column provisional design is given in the table (5.2) and the

C++ program for designing of sieve and packed tray is given in the Appendix.

42

Table (5.2): Provisional Design of Tray

Column diameter 0.153 m

Total column cross-sectional area 0.0184 m2

Active area 0.014 m

Downcomer area 0.0022 m2

0.00086 m2 Open hole area

Hole diameter 0.00476 m

Tray thickness 0.0025 m

Outlet weir height 0.063 m

Weir length 0.1104 m

Tray spacing 0.318 m

5.1.1 Total Tray Pressure Drop

Packing has shown to have beneficial effects on tray efficiency and capacity.

The only drawback is higher-pressure drop associated with the installation of packing.

Figures (5.1) and (5.2) represent the effect of packing on total tray pressure drop and

aerated pressure drops respectively as a function of gas flow rate in terms of active

area F-factor. With packing total and aerated pressure drop are higher because of

additional pressure drop due to the packing. For methanol-water distillation system, it

is found that total and aerated pressure drop of column increased by 15-25%. The

smaller increase in pressure drop, due to the packing, is because of its high void

fraction. Therefore, the packing contributes little additional resistance to the vapor

flow. Since packing has no effect on dry tray pressure drop. Thus the higher total

pressure drop is due to increased liquid holdup and higher residual pressure drop, and

the higher residual pressure drop might result from the extra energy consumed by

packing to breakup the bubbles. If the total pressure drop needs to be controlled, the

extra pressure can be compensated for slightly increasing the hole area, or lesser trays

can be used to give similar total pressure drop because the increase in efficiency for

the packed tray is greater than that in pressure drop.

Figure (5.3) represents the variation of packed tray pressure drop as function

of gas vapor flow rates for different tray hole diameter. It is found that the effect of

tray hole size on packed tray pressure drop is similar to that of sieve trays.

43

5.1.2 Tray-to-Tray Entrainment

Figure (5.4) depicts the effect of packing on tray-to-tray entrainment, in which

tray to tray entrainment is function of active area F-factor. It is observed that Packing

reduced entrainment by 30% at low flow rates that is for lower values of F-factor and

about 80% at high flow rates that is for higher values of F-factor as compared with the

same tray without packing. Thus, the beneficial effect of packing on entrainment

becomes more significant with increasing vapor velocity. The packing appeared to

dissipate energy causing smaller bubbles to form which on bursting at froth surface

produced droplets having lower kinetic energy. For unpacked tray, the dependency of

entrainment on the gas flow is higher while with the packing this dependency is

lower. The lower entrainment rates associated with the packed trays should result in

higher tray capacity.

5.1.3 Froth Height

Figure (5.5) depicts the effect the variation of effective froth height as a

function of active area factor both with packing and without packing on sieve tray.

The packing caused the froth height to increase by about 10-20%. This happens

because of smaller size of bubbles, which are more stable, and this results in a greater

number of bubbles accumulated on the packed tray.

5.1.4 Weeping

For checking weeping, the concept of Froude number based on hole gas

velocity is used. Figure (5.6) represents the variation of Froude number as a function

of F-factor. To avoid weeping Froude number should be greater than 0.67, according

to a correlation given in the design part. Packing causes reduction in Froude number,

which is the ratio of dry tray pressure drop, which tends to prevent weeping and the

clear liquid height, which tends to cause weeping. The reduction in Froude number is

because of increase in clear liquid height in case of packed tray column, while

packing has no effect on dry plate pressure drop.

5.1.5 Packing Height and Eddy Diffusivity

Figure (5.7) depicts the variation of eddy diffusivity as a function of active

area F-factor with different heights of packing. It can be seen from Figure (5.7) that

44

eddy diffusivity decreases with increasing in height of the mesh packing. With 25mm

packing on sieve tray there is still a layer of froth on the top of the packed bed. With

packing height of 50mm, which is almost height of outlet weir, the froth height on the

top of the packed bed is lower than that of with 25mm packing. A froth gradient is

appeared between the inlet and outlet weir. This indicates that packing height up to

50mm greatly decrease the eddy diffusivity. With increase in packing height, Peclet

number also increases. A high Pe indicates a close approach to plug flow. When the

Pe is larger than 10, the enhancement of packing height on the tray is not significant.

5.1.6 Tray Efficiency

Figure (5.8) represents the influence of knitted mesh packing on Murphree gas

phase tray efficiency for both sieve tray and packed tray as a function of active area

F-factor. The efficiency of sieve tray improved by 30-35% for lower values of active

area F-Factor. The influence of packing decreased with increasing gas flow rate that is

for higher value of F-Factor increase in tray efficiency is about 20%. Figure (5.8) also

describes that with increase in vapor velocity that is active area F-factor, efficiency of

both packed tray and sieve tray decreases. This can be explained by the fact that with

increase of vapor velocity tray-to-tray entrainment also increases, and at high flow

rates entrainment is very high, which adversely affects the capacity and efficiency of

the tray. The packing appeared to cause the breakup of larger bubbles in to uniform

smaller size of bubbles. The surface area of smaller size bubbles is higher than larger

size bubbles, which increase the interfacial area and, thus enhanced the tray

efficiency.

5.2 SEPARATION OF MULTICOMPONENT MIXTURE

CASE 2: For separation of multicomponent mixture following case is taken

into consideration.

The feed to a butane-pentane splitter of the following composition is to be

fractioned into a distillate product containing 95% of the n-butane contained in the

feed and a bottom product containing 95% of iso-pentane in the feed. The reflux ratio

of the fractionation will be 1.3 times the minimum reflux ratio, and the column

45

pressure will be 6.895 bar at the top plate. The reflux and feed are at their bubble

point temperatures. The conditions estimated for the column are:

Distillate and reflux bubble point temperature at 6.895 bar = 63° C

Bottoms bubble point temperature at 7.033 bar = 102° C

Feed plate pressure drop = 6.964 bar (assumption AP/plate = 0.00552 N/m2)

Estimated Bubble point feed temperature = 87° C

On the basis of above information estimated distribution of components in

distillate and bottoms are given in Table 5.3 and estimated values of minimum

number plates, minimum reflux ratio, minimum number of theoretical stages, and

Feed plate location are given below.

Minimum number of plates (Fenske' Method) = 8.26

Minimum reflux ratio (Underwood's Method) = 2.805

Actual reflux ratio = 1.3(Minimum reflux ratio) = 3.65

Number of theoretical stages (Gilliland's Method) = 12.5

Feed plate location (Kirkbride's Method) = 6th or 7th

Table 5.3: Distribution of components in distillate and bottoms

Component Feed Distillate Bottoms

Moles Xf Moles xd Moles xb

i-C4 0.06 0.06 0.0595 0.2450 0.00048 0.0006

n-C4 0.17 0.17 0.1615 0.6650 0.00850 0.0112

i-05 0.32 0.32 0.016 0.0659 0.30400 0.4022

n-05 0.45 0.45 0.0059 0.0242 0.44411 0.586

From the above study it was found that the efficiency of distillation column

increased by more than 30% in case of tray with packing, therefore the separation will

be higher in case of packed trays than the same number of sieve trays. In other words,

the same degree of separation, number of packed trays will be lesser than the number

of sieve trays. The fact is used for the solution of multicomponemt mixture. Using the

algorithm of Figure (4.1), for present case required number of theoretical plates for

packed tray is approximately 10, while in case of sieve tray, that is approximately 13.

46

After that algorithm of Figure (4,3) is used for the solution of multicoponent mixture

given in Case 2. The results obtained are discussed below and calculated data are

given in appendix.

Figure (5.9) describes the variation of mole fraction of various components at

different plates in packed tray column. Here it is observed that the required separation

is achieved by using 10 trays in case of packed tray column, but for sieve tray 13 trays

are needed for the required separation. Figure (5.10) depicts the variation of mole

fraction of component at different plates for both sieve tray and packed. Since

Figure (5.10) is plotted for the same number of trays 13, for both sieve trays and

packed trays, thus it provides direct comparison of the composition of liquid at

different stages. From here it is observed better trend of liquid composition for packed

tray than that of for sieve tray at each stage. Thus it can be concluded that results are

in good agreement with the previous results.

47

0 0.4 0.8 1.2 1.6. 2 2.4 2.8 3.2 3.6 4 4.4 4.8

F-Factor

Figure 5.1: Variation of total column pressure as a function of

F-factor (kg1/2M

-1/2S

-1/2).

48

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8

F-Factor

Figure 5.2: Variation of aerated liquid pr. drop as a function of

F-factor (Kg1/2M-112S-1/2).

49

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6

Vapor velocity (m/s)

Figure 5.3: Packed tray Total pressure drop as function AL 0344 of vapor velocity.

II w o11.14

(c No

ICJ 50

1

.--e-SieyeTray -a-Packed Tray

0.001

- r

0 0.4 0.8 1.2 1,6 2 2.4 2.8 3.2 3.6 4 4.4 4.8

F-Factor Figure 5.4: Variation of entrainment as a function of

F-factor (kg1/2 n11/2s-1/2)

51

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4

F-Factor

Figure 5.5: Variation of Effective froth height at function of

F-factor (kern-Ins-in).

52

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2

F-Factor

Figure 5.6: Variation of Fruode Number as a function of

F-factor (kg1/2m"1ns-12).

53

Del

l 00

00 m

2/s

100

90

80 -

70 -

60 -

50 -

40 -

30 -

20 -

10 -

—0— Sievs-Tray+ 75mm packing

—4— Sieve-Tray + 50mm packing

—5— Sieve-Tray + 25mm packing

—0— Sieve-Tray

0.5 1 1.5 2 2.5 3 3.5 4

Vapor Velocity (m/s)

Figure 5.7: Variation of eddy diffusivity as a function of vapor velocity.

0 0

54

120

100 -

2_. 80

C.) a)

0 60 - a)

0.

2 L'zs 40 -I-

20 -

-4—Sieve Tray Packed Tray

r T -1 1 r T i

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 F-Factor

Figure 5.8: Variation of Murphree tray efficiency as a function of

F-factor (,ginni_ine2)

55

Pla

te N

um

ber

- iso-butane - n-butane --A— iso-pentane - n-pentane

0 0.1 0.2 0.3 0.4 0.5

0.6 0.7

Mole Fraction

Figure 5.9: Variation of liquid mole fraction on different plates

56

butane(ST)

—NI— n-butane(ST)

—A-- i-pentane(ST)

--0— n-pentane(ST)

—0— i-butane(PT)

n-butane(PT)

i-pentane(PT)

—0— n-pentane(PT)

a O

E 2

E .0

c+

a. 9 ft

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Liquid mole fraction

Figure 5.10: Plate to plate calculation of liquid mole fraction.

57

Chapter 6

CONCLUSION AND RECOMMENDATIONS

6.1 CONCLUSION

The investigations of influence on performance of sieve tray installed with

mesh packing help us to draw the following conclusions:

• Mass transfer efficiency of the packed tray is observed 30-35% higher than

that of trays without packing for the distillation of methanol water mixture.

Packing on sieve tray significantly improves mass transfer by generating

small size of bubbles, which provides large interfacial area.

• A reduction in tray entrainment is observed in case of packed tray, thus we

can expect higher tray capacity.

o Pressure drop in packed tray is higher than sieve tray, and this extra

pressure drop caused by the packing because when larger bubbles break up

into smaller ones, the extra surface energy should be absorbed by the extra

interface. This energy is transferred from the vapor kinetic energy and

result in a pressure drop.

• The packed tray is simple, economical and Instillation of mesh packing

can be easily carried out at a low cost, which provides the best method to

revamp existing sieve tray column.

6.2 RECOMMENDATIONS

Although in this study an effort was made to study the performance of sieve

tray with mesh packing, but this field is still new and needs more comparison with

trays, henceforth being recommended here for further investigation.

• Since increased pressure drop is the major draw back of packed column, so

a detailed study is proposed for reduction of pressure drop. For vacuum

services, larger hole area may be use to compensate pressure drop.

e In case of reactive distillation use of packed tray may yield better result.

Hence, further it is recommended to study the effect of packed tray with

reactive distillation.

58

• Combined with other high capacity trays, such configuration may yield

better results, for example, combined with screen tray, it may reduce

column height.

• A comparison with other trays can also be investigated to check the

suitability of packed tray.

REFERENCES

1. Bennett,D.L., A.S.Kao, and L.W.Wong, "A mechanistic analysis of sieve tray

froth height and entrainment."A/ChEJ, Vol.41,No. 9,p2067(1995).

2. Bennett,D.L., and K.W.Kovak, "Optimize distillation columns", Chem. Engg.

Progress, p 19, May (2000).

3. Bennett,D.L.,D.N.Watson, and M.A.Wiescinski, "New correlation for sieve

tray point efficiency, entrainment & section efficiency", AlChE

J,Vol.43,No.6, PI611(1997).

Bravo,J.L., J.A.Rocha, and J.R. Fair, "Mass Transfer in Gauge

Packings."

5. Chattopadhyay, P., " Unit operation of chemical engineering", V-2, Khanna

Publication, 1st edition (1998).

6. Chen,G.X., K.T.Chuang, C.Chien, and Y.Ye, "Mass transfer and hydraulic of

packed sieve trays", Gas Separation & Purification , Vol. 6, No. 4, p

207,(1990).

7. Chen,G.X., A.Afacan, C.Xu, and K.T.Chuang, "Performance of combined

mesh packing and sieve tray in distillation", Can. J. Chem. Engg., 68, p.382,

(1990).

8. Chen,G.X., and J.J.Jhon, "Comments of clear liquid height and froth density

on sieve trays in distillation", Can. J. Chem.Engg.,68, p.382(1990).

9. Chen,G.X., and K.T.Chuang, "Recent Development in Distillation",

Hydrocarbon processing, p.37,(1989).

10. Coker,A.K., "Understand the basics of packed-column design",Chem.Engg.

Progress, p.93,(1991).

60

11. Fair, J.R., and J.L.Bravo, "Distillation columns containing structured

packing", Chem. Engg. Progress, p.19„Ian(1990).

12. Henley,E.J., and J.D.Seader, " Equilibrium-stage separation operation in

chemical engineering", John Wiley & sons (1998).

13. Holland,C.D., " Fundamental of multicomponent distillation", McGraw-Hill

publication (1981). Hydrocorban processing,p.91(1985).

• 14. Kister,H.Z., and D.R.Gill, " Predict flood point and pressure drop for modern

random packings", Chem. Engg. Progress, p.32, Feb(1991).

15. Lackett,M.J., "Distillation tray fundamentals", Cambidge University press,

Cambidge (1986).

16. Lacks,D.J., "Teaching pakced-column design from a plate- column

perspective", Chem. Engg. Education, p.302 (1998).

17. Leva,M., "Reconsider packed-tower pressure-drop Correlations", Chem. Engg.

Progress, p.65„lan(1992).

18. Lockett,M.J., and Banik, "Weeping from sieve trays", Ind.EngChem.Process

Des. De v. , 25, p.56I,(1986).

19. Robbins L.A., "Improved pressure- drop prediction with a new correlation",

Chem. Engg. Progress, p.87 May(1991).

20. Rocha ,J.A., J.L.Bravo, and J.R.Fair, "Distillation columns containing

structured Packings: a comprehensive model for their performance. 1.

Hydraulic Models", Ind. Engg. Chem. Res., 32, p.641, (1993).

21. Rocha ,J.A., J.L.Bravo, and J.R.Fair, "Distillation columns containing

structured Packings: a comprehensive model for their performance. 2. Mass-

Transfer Model", hid. Engg. Chem. Res., 35, p.I660, (1996).

22. Schweitzer,P A., " Handbook of separation techniques for chemical

engineers", McGraw-Hill, 2nd ed. (1988).

61

23. Spagnolo,D.A., and T.Chuang , " Improving sieve tray performance with

knitted mesh packing", Ind Engg. Chem.Process Des. Dcv., 23, p.561 (1984).

24. Stichmair,J.G., and J.R.Fair, " Distillation principle and practices", Wiley-

VCH (1998).

25. Strigle,R.F., and F.Rukovena, " Packed distillation column design", Chem.

Engg. Progress, p.86, March (1979).

26. Treybal,R.E., "Mass transfer operations", 3rd edition, McGraw-Hill,

International edition (1981).

27. Winkle,M.V., "Distillation", McGraw-Hill, international edition (1981).

28. Xu,Z.P., A. Afacan, K.T. Chuang, "Liquid mixing on packed sieve tray",

TrawslChemE, V73, Part A,(1995).

62

APPENDIX-A

PROGRAM LISTING

//* PROGRAM: DESIGN OF PACKED TRAY *//

/*Header Files*/ #include<iostream.h> #include<math.h> #include<conio.h>

void main() {

/* VARIABLE DECLARATION */

float F,V,L,D,B,xf,xd,xb,MF,M1,M2,MD,MB,Rd,R1,R2,R3,R4,R5,Dw,n,dv,d 1,P,Tt,s,d0,p,pt,A0,Aa,An,Ad,At,W,T,t,Fp,a,b,Cf,q,Q,vf,v,Wf,r 1,r2,r3,r6,r5,h1,h11,h12,Z,Z1,R12,V1,L1,V12,L12,P1,dvl,d11,P1 2,dv12,d112,s12,Fpl,q1,Q1,R31,Cfl,s11,vfl,v1,Anl,R41,T1,At1,-F p12,Q12,q12,T12,R32,Cf12,v12,An12,R42,At12,vf12,Ttl,Tt12,v0,v a,CO3 s1,Rg,f,hD,h2,h3,h4,hL,hW,hR,hG,Acl,Ap,1,Z2,Z3,Z4,vw,E, Zc,Scg,Ntg,tL,Ntl,Ntog,Eog,Pe,r4,n1,Emg,Emge,m,De,y1,y2,Fv, Lp,Dl,Dv,Fa,Ep; int N,Nr,Re; clrscr();

/* READ INPUT DATA */ cout<<"Enter Feed Rate(F in Kmol/s)and mole fraction of feed(xf)"<<endl; cin>>F>>xf; cout<<"Enter molefraction of Distillate (xd) "<<endl; cin>>xd; cout<<"Enter Mole Fraction of Bottom(xb) "<<endl; cin>>xb; cout<<"Enter Moleculer weights of components 1 and 2 "; cin>>M1>>M2; cout<<"Enter Reflux Ratio Rd "; cin>>Rd; cout<<"Enter No. of Stages "; cin>>N; cout<<"Enter slope of top operating line (L1/V1=R1 ratio)= "; cin>>R1; cout<<"Enter slope of bottom operating line(L12/V12=R12 Ratio)= "; cin>>R12; cout<<"Enter temperature(Ttl in K) and pressure (in bar)of top plate "; cin>>Ttl>>P1; cout<<"Enter vapor density(dv)and liquid density(dl)in Kg/m3 II •

63

cin>>dvl>>d11; cout<<"Enter surface tension(s11) in N/m "; cin>>s11; cout<<"Enter temperature (T12 in K) and pressure (in bar)of top plate "; cin>>Tt12>>P12; cout<<"Enter vapor density(dv12)and liquid density(d112)in Kg/m3 "; cin>>dv12>>d112; cout<<"Enter surface tension(s12) in N/m "; cin>>s12; cout<<"Select column efficiency ";

.cin>>n; cout<<"Select Hole Diameter(d0 in m) and Hole pitch(p in m)

cin>>d0>>p; cout<<"Select Tray Spacing(t range 0.5-1.0 m) "; cin>>t; cout<<"Selecting actual velocity as 80% of flooding velocity "<<endl; cout<<"select Downspout or Downcomer Ratio(Ad/At) "; cin>>R4; //* Ad/At = R4 *// cout<<"select weir length to tower dia(W/T) Ratio "; cin>>R5; cout<<"Enter initial value of liquid creast over the Weir(h1)

cin>>h1; cout<<"Enter value Zi for calculation of length on tray from Table(6.1-4) "; cin>>Z1; cout<<"Enter The thickness of the Plate "; cin>>1; cout<<"Enter constanat CO for Calculation of hD "; cin>>C0; cout<<"Enter viscosity(s1) of vapor at Ti and P "; cin>>s1; cout<<"Enter Weir Height (hW in m) "; cin>>hW; cout<<"Enter liquid diffusivity of the system(D1) "; cin>>D1; cout<<"Enter vapor diffusivity of the system(Dv) "; cin>>Dv; cout<<"Enter Distribution coefficient (m) "; cin>>m;

//* CALCULATION OF FLOW RATES *//

//Calculation of Molecular Weight MF=M1*xf+(1-xf) *M2; MD=M1*xd+(1-xd)*M2; MB=M1*xb4-(1-xb)*M2; D=(F*(xf-xb))/(xd-xb);

64

/* Calculation of Distillate and Bottom Rates */ B=F-D; cout<<"D= "<<D<<"\t"<<"B= "<<B<<"\t";

/* Calculation of No, of Real Stages */ Nr=(N-1)/n; cout<<"Nr = "<<Nr<<"\t";

/* Calculation of Plate thichness(pt) and (A0/Aa=R2) ratio */

pt=0.43*d0; R2=0.907*(pow((dO/p),2));

/* Calculation of constanat a,b */ a=0.0744*t+0.01173; b=0.0304*t+0.015;

/* CALCULATION FOR TOP PLATE */

V1=D*(Rd+1); L1=R1*V1; cout<<"V1= "<<V1<<"Ll= "<<L1<<"\t"; Fp1=(Ll/V1)*(pow((dvl/d11),0.5)); if(Fpl<0.1)

{ Fp1=0.1; }

q1=(L1*MD)/d11; Q1=22.41*V1*((Tt1+273)/273); R31=(gl/Q1)*(pow((d11/dv1),0.5)); if(R31<0.1)

{ R31=0.1; }

Cf1=(a*(log10(1/R31))+b)*(pow((s11/.02),0.2)); vf1=Cf1*(pow(((d11-dv1)/dv1),0.5)); v1=0.80*vfl; An1=Q1/v1; At1=An1/(1-R4); T1=pow(((4*At1)/3.14),0.5); cout<<"Tl(top conditions)= "<<T1<<"\t";

/* CALCULATION FOR BOTTOM *

V12=B/(R12-1); L12=R12*V12; Fp12=(L12/V12)*(pow((dv12/d112),0.5)); if(Fp12<0.1)

{ Fp12=0.1;

65

q12=(L12*M8)/d112; Q12=22.41*V12*((Tt12+273)/273); R32=(q12/Q12)*(pow((d112/dv12),0.5)); if(R32<0.1)

{ R32=0.1; }

Cf12=(a*(log10(1/R32))+b)*(pow((s12/.02),0.2)); vfl2=Cf12*(pow(((d112-dv12)/dv12),0.5)); v12=0.80*vf12; An12=Q12/v12; At12=An12/(1-R4); T12=pow(((4*At12)/3.14),0.5); cout<<"T12 (bottom condition)- "<<T12<<endl;

/*CONSIDERATION OF ACTUAL DESIGN VARIABLE*/

if(T12>T1) { T=T12; v=v12; vf=vf12; An=An12; At=At12; q=q12; Q=Q12;

dl=d112; dv=dv12;s=s12; Cf=Cf12;

R3=R32;Fp=Fp12;L=L12;V=V12;P=P12;Tt=Ttl;

} else

{ T=T1; v=v1; vf=vfl; An=An1; At=Atl; q=q1; Q=Q1; dl=d11;

dv=dvl; s=s11; Cf=Cf1; R3=R31;Fp=Fpl;L=L1;V=V1;Tt=Tt12;P=P1; }

/*CALCULATION OF PROVISIONAL PLATE DESIGN VARIABLE*/ W=R5*T; Ad=R4*At; Aa=At-2*Ad-0.18*At; AO=R2*Aa; v0=Q/A0; va=Q/Aa; Dw=0.5*T-0.5* (pow ( ( (T*T) - (WW) ) , 0 . 5) ) ;

/*Calculation of liquid creast over the weir and effective weir height*/ al:r1=T/W;

r2=pow(((rl*r1)-1),0.5); r3=r2+(2*(hl/W)); r6=(rl*r1)-(r3*r3); Wf=W*(pow(r6,0.5)); r5=q/Wf; h11=0.666*(pow(r5,0.6667));

if(h1<h11) { h12=h11-h1;

}

66

else { h12=h1-h11; }

if(h12<0.0001) { hl=h11; }

else { hl=h11; goto al; }

// Calculation of length of travel on tray Z=2*(Z1*T);

//Calculation of F-factor Fa= va*pow(dv,0.5);

/*PROVISIONAL• DESIGN OF PLATE*/

cout<<"T= "<<T<<"\t"<<"V= "<<V<<"\t"<<"L= "<<L<<"\t"; cout<<"q= "<<q<<"\t"<<"Q= "<<Q<<"\t"; cout<<"An= "<<An<<"\t"<<"At= "<<At<<"\t"<<"Aa= "<<Aa<<"\t";

cout<<"Ad= "<<Ad<<"\t"<<"A0= "<<A0<<"\t"<<"W= "<<W<<"\t"; cout<<"hW= "<<hW<<"\t"<<"d0= "<<d0<<"\t"<<"1= "<<1<<"\t"; cout<<"v0= "<<v0<<"\t"<<"va= "<<va<<"\t"<<"t= "<<t<<"\t"; cout<<"h1= "<<h1<<"\t"<<"Z= "<<Z<<"\t"<<"Fa= "<<Fa<<"\t";

/*CONDITIONS CHECKING*/

if(q/T<0.015) { cout<<"Condition satisfied for (q/T) "<<"\t"; }

else { cout<<"Condition does not for(q/T) satisfies "<<"\t"; }

if(q/W<0.032) { cout<<"Condition satisfies for(q/W) "<<"\t"; }

else { cout<<"Condition does not satisfies(q/T) "<<"\t"; }

/* PRESSURE DROP CALCULATION START FROM HERE */

//Dry plate pr. drop calculation. hD=0.051*(vO/C0)*(vO/C0)*(dv/d1);

67

cout<<"hD= "<<hD<<"\t";

//Hydraulic pr. drop calculation hL=(hW+hl); cout<<"hL= "<<hL<<"\t";

//Residual pr. drop calculation hR=12.5/d1; cout<<"hR= "<<hR<<"\t"; //Total pr. drop calculation hG=hD+hL+hR; cout<<"hG) "<<hG<<"\t";

//Area under apron calculation. Ac1=(hW-.025)*W; if(Ad<Acl)

Ap=Ad;

else

Ap=Acl; }

cout<<"Ap= "<<Ap<<"\t";

//Pressure drop condition checking. h2=(1.5/9.81)*(q/Ap); h3=hG+h2; //cout<<"Downcomer Backup= "<<h3<<"\t"; h4=hW+hl+h3; if(h4<(0.5*t))

cout<<"condition satisfies"<<endl; }

else 1 cout<<"Condition Does not satisfies "<<endi; 1

/* WEEPING VELOCITY CALCULATION */

Z2=(sl*sl*d1)/(s*dO*dv*dv); Z3=(1.155*Aa*d0)/(p*p*p); Z4=2.8/(pow((Z/d0),0.724)); vw=((0.0229*s)/s1)*(pow(Z2,0.379))*(pow((l/d0),0.293))*(pow(Z

3,z4)); cout<<"Weeping Velocity (vw) = "<<vw<<"\t"; if (vO>vw)

{ cout<<"Weeping condition satisfies"<<endl; }

else {

68

cout<<"Weeping condition does not satisfies"<<endl; 1

/*ENTRAINMENT CACULATION */

float vs,C1,fe,He,H1,ve,Frv,Hf,fa,e1,e;

//Calculation of density corrected vapor velocity vs=va*(pow((dv/(dl-dv)),0.5)); cout<<"Density corrected vapor velocity(vs)= "<<vs<<endl;

//Calculation of constant C1=0.501+0.439*(exp(-137.8*hW)); cout<<"Cl= "<<C1<<endl;

//Calculation of Effective froth density fe=exp(-12.55*(pow(vs,0.91))); cout<<"fe= "<<fe<<"\t";

//Calculation of froth height He=hW+(C1*(pow((q/fe),0.666667))); cout<<"He= "<<He<<"\t";

//Calculation of Total Liquid Holdup on the tray H1=He*fe; cout<<"Hl= "<<H1<<"\t";

//Calculation of ve ve=(3.94822*vs)/(pow(((A0/Aa)*fe),0.5)); cout<<"ve= "<<ve<<endl;

//Calculation of froude no. Frv=(ve*ve)/(9.81*He); cout<<"Frv= "<<Frv<<"\t";

//Calculation of Total froth height Hf=He*(1+(1+6.9*(pow((Hl/d0),-1.85)))*0.5*Frv); cout<<"Hf= "<<Hf<<"\t";

//Calculation of average froth density fa=H1/Hf; cout<<"Average Froth density (fa) = "<<fa<<endl;

//Calculation of ENTRAINMENT e1=(1.3*log(Hl/d0))-0.15; e=0.5*(1.0-(tanh(e1)));

// FOR SIEVE TRAY E=0.00335*(pow((t/Hf),-1.10))*(pow((dl/dv),0.5))*(pow(fa,e)); cout<<"Entrainment(E)= "<<E<<"\t";

69

//FOR PACKED TRAY Ep=0.005325*Fa*Fa; cout<<"Ep= "<<Ep<<"\t";

/* EFFICIENCY CALCULATION START FROM HERE */

Fv=va*(pow(dv,0.5)); Lp=q/(Aa/Z);

//Liquid hold up calculation. Zc=0.006+(0.00073*hW)-(0.00024)*Fv*hW+1.22*Lp; cout<<"Zc= "<<Zc<<"\t";

//Eddy diffusivity calculation. De=pow((.0038+(0.017*va)+(3.86*Lp)+(0.00018*hW)),2); cout<<"De= "<<De<<"\t"; tL=(Zc*Z)/Lp;

//Peclet No. Calculation. Pe=(Z*Z)/(De*tL); cout<<"Pe= "<<Pe<<"\t";

//Schmit No. calculation. Scg=s1/(Dv*dv); cout<<"Scg= "<<Scg<<"\t";

//Calculation of Gas phase transfer Unit. Ntg=(0.776+(4.57*hW)-(0.24*Fv)+(105*Lp))/(pow(Scg,0.5)); cout<<"Ntg= "<<Ntg<<"\t";

//Calculation of liquid phase transfer unit. Nt1=(pow((413000000*D1),0.5))*((0.21*Fv)+0.15)*tL; cout<<"Ntl= "<<Ntl<<"\t";

//Calculation of overall Transfer unit. Ntog=(L*Ntg*Nt1)/((L*Nt1)+(m*V*Ntg)); cout<<"Ntog= "<<Ntog<<"\t";

//Calculation of gas phase tray point Efficiency. Eog=1-exp(-Ntog); cout<<"Eog= "<<Eog<<"\t";

//Calculation of Murphree Efficiency. r4=1+((4*m*V*Eog)/(L*Pe)); n1=(Pe/2)*((pow(r4,0.5))-1); cout<<"n1= "<<n1<<"\t"; yl=n1+Pe; y2=y1/n1; Emg=Eog*(((1-(exp(-y1)))/(y1+(yl*y2)))+(((exp(n1))- 1)/(n1+(nl/y2)))); cout<<"Emg= "<<Emg<<"\t";

70

//Calculation of Entrainment corrected Murphree Efficiency. Emge=Emg/(1+((Emg*E)/(1-E))); cout<<"Emge= "<<Emge<<"\t";

getch(); }

71

/**********PROGRAM FOR SOLUTION OF MODEL EQUATIONS**********/

#include<iostream.h> #include<stdio.h> #include<conio.h> #include<math.h>

void main() {

/* Variable Declaration */ int i,j,N,c,Nf; float A[5],H[5],C[5],Pt,F,xf[5],D,bet,Tn,Tnl,T1,fn,fnl,f1,f2,a1,b1, a2,b2,q1,Qcr; float T[20],L[20],V[20],x[5][20],xn[5][20],P[5][20],K[5][20],a[5][2 0]

b[5][20],d[5][20],xn1[5][20],gam[20],H[5][20],h[5][20],c1[5][ 20] ,u[5] [20]

,hf[5],p[5][20],q[5][20],h1[5],h2[5],h3[5],Lat[5],Sx,Sy,Hd;

/* Read Input */ clrscr(); cout<<"Enter Feed Rate (F) "; cin>>F; cout<<"Enter Distillate Rate(D) "; cin>>D; cout<<"Enter Distillate Enthalpy "; cin>>Hd; cout<<"Enter Operating Total pr. of the column(in mmHg) "; cin>>Pt; cout<<"Enter no. of trays "; cin>>N; cout<<"Enter Feed Plate "; cin>>Nf; cout<<"Enter the no. of components "; cin>>c; for(i=1;i<=c;i++) { cout<<"Enter feed mole fraction of component "<<i; cin>>xf[i]; } cout<<"Enter Condenser Duty "; cin>>Qcr; for(j=1;j<=N;i++) { cout<<"Enter the value of Temperature "<<j<<" "; cin>>T[j]; } for(j=1;j<=N;j++)

72

cout<<"Enter Liquid flow rate "<<j<<" "; cin>>L[j];

for(j=1;j<=N;j+t) { cout<<"Enter Vapor flow rate "<<j<<" "; cin>>V[j]; } for(i=1;i<=c;i++) { for(j=1;j<=N;j44)

cout<<"Enter mole fraction of component "<<i<<" at plate"<<j<<" "; cin>>xn[i][j]; }

//* Calculation of K values *// for(i=1;i<=c;i++)

cout<<"Enter the the value of Antony Constants A,B,C, for component "<<i<<" "; cin>>A[i]>>B[i]>>C[i];

for(i=1;i<=c;i++)

cout<<"Enter enthalpy constants hl,h2,h3 /t"<<i<<" "; cin>>hl[i]>>h2[i]>>h3[i]; } for(i=1;i<=c;i++) { cout<<"Enter latent heat "<<i<<" "; cin>>Lat[i]; } all:for(i=1;i<=c;i++)

for(j=1;j<=N;j++) { Pri) [j]=exp(A[i]-(B[i]/(T[j]+C[i]))); K[i][j]=P[i][j]/Pt; cout<<K[i][j]; } 1 cout<<endl; for(i=1;i<=c;i++) { b[i][1]=-(L[1]+V[1]*K[i][1]); cl[i][1]=V[2]*K[i][2]; d[i][1]=0; for(j=2;j<=N;j++)

a[i][j]=L[j-1];

73

b[i][j]=-{L[j]+v[j]*K[i][j]); cl[i][j]=V[j+1]*K[i][j+1]; if (j==Nf) { d[i] [j]=-F*xf[i]; } else { d[i] [j]=0; 1

cout<<endl; //* Thomas Algorithm for calculation of Liquid phase composition *// for(i=1;i<=c;i++) { p[i][1]=ci[i][1]/b[i][1]; q[i] [1]=d[i] [1]/b[i] [1]; for(j=2;j<=N;j++) { P[i][jl=c1[i][j]/(b[i][j]-(a[i][j]*P[i][j-1]));

for(j=2;j<=N;j++)

q[i][j]=(d[i][j]-(a[i][j]*q[i][j-1]))/(b[i][j]- (a[i] [j]*p[i] [j-1])); 1 x[i][N]=q[i][N]; for(j=(N-1);2=1;j--)

x[i][j]=q[i][j]-(p[i][j]*x[i][j+1]);

//* Temperature Calculation *// for(j=1;j<=N;j++) { al:Tn=T[j]; fn=0; fn1=0; for(i=1;i<=c;i++)

fl=((exp(A[i]-(B[i]/(Tn+C[i]))))/Pt)*x[i][j]; fn=fn+f1; f2=(B[i]/(Pt*(Tn+C[i])*(Tn+C[i])))*(exp(A[i]- (B[i]/(Tn+C[i])/))*x[i][i]; fnl=fnl+f2;

Tn1=Tn-((fn-1)/fnl); if(abs(Tnl-Tn)<1.0f) { T[j]=Tnl; }

74

else

T[j]=Tn1; goto al;

//*Flow rate calculations for(i=1;i<=c;i++) { for(j=1;j<=N;j++) { h[i][j]=hl[i]*T[j]+(h2[i]*T[j}*T[j])/2+(h3[i]*T[j]*T[j]*T[j]) /3; H[i] [j]=h[i] [j]+Lat[i];

Sx=0; Sy=O; for(i=1;i<=c;i++)

for(j=1;j<=N;j++)

SX=Sx+(x[i][j]*h[i][j]); SY=STF{K{i}[j]*x{i}[j]*H[i][j]}; }

for(j=1;j<=N;j++)

L[j]=(D*(Hd-Sy)-Qcr)/(Sy-Sx); Y[j]=1,[j]+0;

for(i=1;i<=c;i++)

for(j=1;j<=N;j++) { if(xnl[i][j]>xn[i][j])

u[i][j]=xnl[i][j]-xn[i][j];

else

u[i][j]=xn[i][j]-xnl[i][j];

}

q1=0; for(i=1;i<=c;i++)

for(j=1;j<=N;j++)

if(q1<u[i][j])

ql=u[i][j];

75

} if(ql>0.01)

for(i=1;i<=c;i++)

for(j=1;j<=N;j++)

xn[i][j]=xnl[i][j];

goto all;

else { x[i][j]=xnl[i][j];

for(i=1;i<=c;i++)

for(j=1;j<=N;j++)

cout<<flx[x<i<<“][n«j«, ]= "«x[i] ji<<n\tu;

for(j=1;j<=N;j++) { cout<<"L["<<i<<"]= "<<L[j]<<"\t";

for(j=1;j<=N;j++) { cout<<"V["<<j<<"]= "<<V[j]<<"\t";

for(j=1;j<=N;j++)

cout<<"T["<<j<<"]= "<<T[j]<<"\t";

getch();

APPENDIX-B

PHYSICAL PROPERTIES

Properties of Methanol, at 95° C and 1 atm

Vapor density p, = 0.781 kg/m3

Liquid density PL = 691 kg/m3

Surface tension a = 0.047 N/m

K- value of components:

Ki=1),

P,. = exp A,T +Ci

where P = vapor pressure, mm Hg

T = temperature, K

A, B, C = Antoine Coefficients

Table B-1: Antoine Coefficients

Component A, Bi Ci i-C4 15.6782 2154.90 -34.42 n-C4 15.5381 2073.73 -33.15 i-05 15.833 2477.07 -39.94 n-05 15.6338 2348.67 -40.05

Enthalpy Calculation:

H = a+bT +c-f 2

and a, b, c = constants

H= enthalpy of vapor, kJ/kg

T= temperature, K (Range —20 K to 1200 K)

Table B-2: Enthalpy Coefficients

Component a b cx103 Butane 17,283134 0.412696 2.028601 Pentane 63.201677 -0.011701 3.316498

B.

77

APPENDIX-C FLOODING VELOCITY

-...---

111:11:1111:11111111111111

ginitiMil

IMININIMIN= il 1111==

MOM

ill

n — •

1 lirrilliellimmillill I 01111001=111

MEN ztelammmommnii=mnon

IMM111111111111.11111111.11iiiii

• bitiribtomm 2.1162.624

5

II mow

iiim—ww,4„_

L 1111111

misommommosmommestaam,— 111111111Migenieraii

91 _Ai utiMISIM

1111 .... Plotesiweli

. 6

IIi••Buu ant

filli

—g:,c30

-•0

"3

.44,14., .... kcp.si %•• \

N. \

.

001 0; S0 fe y

Figure C-1: Flooding velocity

The following restrictions apply to the use of Figure C-1:

1. Hole size less than 7 mm.

2. Weir height less than 15% of the plate spacing. 3. Non-foaming systems.

4. The hole area and active area should be greater than 0.10, for other

ratios apply the following corrections:

5. Llquld surface tensions 0.02 N/m, for other surface tensions multiply

the value of K1 by {a- /0.02r .

A0/A„ 0.10 0.08 0.06 Multiply K1 by 1.00 0.90 . 0.80

78

(AdiA

j x 1

00

10

20

15

r:

5

APPENDIX-D

RELATIONSHIP BETWEEN DOWNCOMER AREA

AND WEIR LENGTH

0.6 0,7

0.8

0.9 l w /Dc

Figure D-1: Relationship between downcomer area and weir length

Discharge coefficient

79

0 /

1.0

(446■6

7 /

)

44:06

/1,2

../

1.0

0.8

D.8

0.2

10 15

0.

0,9

0.8

0.70

0.65 0

APPENDIX-E

DISCHARGE COEFFICIENT

Per cent perIotated area, Ai, / Art x 100

Figure E-1: Discharge coefficient

80

APPENDIX-F

DATA FOR RESULTS

Table F.1 : Data for Tray Pressure Drop (Fig. 5.1)

F-Factor (kg1/2.m-1/2 s'I/2) Tray Pressure Drop (ST) (m of water)

Tray Pressure Drop (PT) (m of water)

0.4 0.0553 0.0659

0.8 0.0628 0.0744

1.2 0.0709 0.0842

1.6 0.0783 0.0933

2 0.0862 0.1037

2.4 0.0953 0.1167

2.8 0.1048 0.1312

3.2 0.1142 0.1466

3.6 0.1264 0.1641

4 0.1403 0.1856

Table F.2 : Data for Aerated Liquid Pressure drop (Fig. 5.2)

F-Factor (kg1/2.rill/2 s-1/2) Aerated Liquid Pressure

Drop (ST) (m of water)

Aerated Liquid Pressure Drop (ST)

(m of water)

0.4 0.0678 0.0553

0.8 0.0587 0.0472

1.2 0.0509 0.0399

1.6 0.0438 0.0335

2 0.0377 0.0279

2.4 0.0322 0.0231

2.8 0.0272 0.0192

3.2 0.0236 0.0157

3.6 0.0208 0.0131

4 0.0189 0.0113

81

Table F.3 : Data for Pressure Drop Vs Vapour Velocity for different Hole Sizes

(Fig. 5.3)

Vapour Velocity

(ms-')

Pressure Drop

(do = 5mm) m of liquid

Pressure Drop

(do = 12.5mm)

m of liquid

0.4 0.02901 0.03584

0.8 0.03742 0.04724

1.2 0.04842 0.06245

1.6 0.06505 0.08286

2 0.08513 0.11208

2.4 0.11107 0.14589

2.8 0.14449 0.18331

3.2 0.18351 0.22734

Table F.4 : Data for Entrainment (Fig. 5.4)

F-Factor

( cg1/2.m-1/2 s-12)

Entrainment (ST)

(kg/100 kg of gas)

Entrainment (ST)

(kg/100 kg of gas)

0.4 0.0031 0.0014

0.8 0.0077 0.0033

1.2 0.0166 0.0071

1.6 0.0317 0.0132

2 0.0531 0.0217

2.4 0.0811 0.0312

2.8 0.1201 0.0423

3.2 0.1702 0.0551

3.6 0.2331 0.0677

4 0.3111 0.0847

82

Table F.5 : Data for Effective Froth Height (Fig. 5.5)

F-Factor (cgin.m-in s'2)

Effective Froth Height (ST)

(m)

Effective Froth Height (PT)

(m)

0.4 0.0342 0.0541

0.8 0.0411 0.0613

1.2 0.0487 0.0679

1.6 0.0561 0.0747

2 0.0632 0.0814

2.4 0.0697 0.0882

2.8 0.0761 0.0949

3.2 0.0815 0.1016

3.6 0.0866 0.1083

4 0.0911 0.1151

Table F.6 : Data for Froude Number as a function of F-Factor (Fig. 5.6)

F-Factor (kgit2.m-1/2 s-12)

Froude Number

(Packed Tray)

Froude Number

(Sieve Tray)

0.4 0.221 0,291

0.8 0.311 0.392

1.2 0.429 0.518

1.6 0.578 0.679

2 0.745 0.883

2.4 0.928 1.119

2.8 1.122 1.421

3.2 1.311 1.803

3.6 1.495 2.253

4 1.715 2.811

83

Table F.7 : Liquid Mole Fraction for Packed Tray (Fig. 5.9)

Plate number From top xt- c, xn-c., x,-C, xn-C3

1 0.1732 0.6276 0.1279 0.0679

2 0.0843 0.5315 0.2457 0.1852

3 0.0492 0.3197 0.3427 0.2652

4 0.0317 0.2361 0.3461 0.3439

5 0.0266 0.1784 0.3617 0.3937

6 0.0173 0.1421 0.3997 0.4406

7 0.0079 0.1214 0.4226 0.4668

8 0.0053 0.1053 0.4384 0.4899

9 0.0034 0.0921 0.4372 0.5235

10 0.0021 0.0823 0.4354 0.5437

Table F.8 : Liquid Mole Fraction for Sieve Tray and Packed Tray (Fig. 5.10)

Plate number

x, -C4 x,,-c, x-I-05 x„-c, ,x,_c., x„-c.4 x,-c, xn_c.,

From top (ST) (ST) (ST) (ST) (PT) (PT) (PT) (PT)

1 0.1739 0.6158 0.1354 0.0742 0.1766 0.6276 0.1279 0.068

2 0.1206 0.5165 0.2197 0.1437 0.1232 0.5315 0.2111 0.1341

3 0.0845 0.4008 0.2909 0.225 0.0858 0.4133 0.2857 0.2152

4 0.0627 0.3036 0.3322 0.3017 0.0492 0.2369 0.3500 0.3639

5 0.0508 0.2376 0.3462 0.3670 0.0317 0.1784 0.3590 0.4309

6 0.0444 0.1974 0.3464 0.419 0.0166 0.1421 0.3863 0.455

7 0.0335 0.1846 0.3519 0.4306 0.0079 0.1014 0.4119 0.4787

8 0.0255 0.1733 0.3633 0.4405 0.0053 0.0822 0.4226 0.4899

9 0.019 0.1588 0.3746 0.4497 0.0034 0.0648 0.4310 0.5007

10 0.0138 0.1415 0.3866 0.4598 0.0022 0.0496 0.4366 0.5116

11 0.0098 0.1219 0.3979 0.4654 0.0014 0.0376 0.4348 0.5235

12 0.0068 0.1038 0.4108 0.4812 0.0008 0.0260 0.4352 0.5380

13 0.0046 0.0852 0.4212 0.4915 0.0005 0.0174 _ 0.4327 _0.5476

84

Accumulator j = 0

Lo, xoi

APPENDIX-G SCHEMATIC DIAGRAM FOR

COMPONENT MATERIAL BALANCE

j - 1

J + 1

► Feed plate Feed

F, x1

j = N

+1

Reboiler = N+1

J

1

Bottoms

B, xBi

85