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
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