Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation

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Mass Transfer 477

For binary mixtures of components 1 and 2, then

Yi -"

K l ( 1 - K 2 )

- K 2

(7-31)

and

Y2 = 1.0- Yl (7-32)

These two equations can be used to calculate the composition of a binary

vapor that will begin to condense at a given temperature and pressure.

EQUILIBRIUM FLASH COMPUTATIONS

Flash vaporization calculations involving multicomponent mixtures

are essential to the design and successful operation of many processes.

These calculations are often required to determine the condition of the

feed to a fractionating column or to determine the flow of vapor from a

reboiler or condenser.

Flash calculations often involve trial-and-error solutions that are time

consuming, tedious, and subject to error if performed manually. Coker

[6] has developed an improved iterative convergence method first sug-

gested by Oliver [7] and later modified by Kostecke [8], for isothermal

equilibrium flash computations. Multicomponent flash (isothermal and

adiabatic) computations are incorporated as part of overall process simu-

lation and equipment design. However, single-stage flash fractionation

processes are also employed to obtain a separation of the light compo-

nents in a feed and as a preliminary step before a multicomponent frac-

tionation column, such as crude oil distillation. Table 7-1 lists ways of

producing two-phase mixtures from a single phase at appropriate con-

ditions. The last process in the table typifies the well head separation

that takes place in an oil field. It is known as a flash process because the

Table 7-1

Ways to Produce Two-Phase Mixture

Initial

Gas

Liquid

Action to Produce Two-Phase Mixture

Cool, possibly after initial compression

Expand through a valve or an engine

Heat to achieve partial vaporization

Reduce pressure through a valve, if close to saturation

478

Fortran Programs for Chemical Process Design

vapor forms due to the rapid drop in the pressure.

Fundamentals

To carry out an appropriate flash calculation, the pressure, P, and the

temperature, T, must be known. If the values of P and T in the separat-

ing vessel are fixed, the value of P must not be so high that the two

phases cannot exist at any value of T. Nor must T lie outside the bubble

point and dew point range corresponding to R For a valid two-phase

equilibrium calculation, the following relationship must be satisfied:

Tbp <

< Tdp

(7-33)

where

Tbp --

the bubble point temperature

T~ = the specified temperature

Tap- the dew point temperature

The existence of a valid two-phase flash can be verified with the design

equations for the bubble point, dew point, and equilibrium data calcu-

lated at the specified pressure and temperature. The design equations

for the bubble and dew points are:

Bubble point

- ~

KiXi

(7-34)

i=l

Dew point

f2 - ~.,

Yi/Ki

(7-35)

i=l

Table 7-2 illustrates the phase condition using the liquid-vapor data

associated with the specified pressure and temperature.

From Table 7-2, the conditions for a valid two-phase equilibrium

flash are:

f~ -

,~ Kin i

> 1.0 (7-36)

i-I

and

f2 - ~_, n~/K

i--I

> 1.0 (7-37)

Table 7-2

Equilibrium Flash Criteria

Mass Transfer 479

f~ - s f2- s

i=1 i--1

Subcooled liquid <l > 1

Bubble point = 1 > 1

Two-phase condition > 1 > 1

Dew point > 1 = 1

Superheated vapor > 1 < 1

Feed analyses of component concentrations are normally not available

for complex hydrocarbon mixtures with a final boiling point of more

than about 38~ (e.g. n-pentane), unless such a feed is broken down

into pseudo-components (narrow boiling fractions). This enables the

mole fraction and equilibrium constant, K, to be estimated, and conse-

quently, flash calculation of the mixture can be carried out. A source of

K values for light hydrocarbon systems is the De-Priester [9] charts,

which are shown in Figures 7-2 and 7-3. These charts give the K values

over a wide range of temperature and pressure. Because the charts are

nomographs, a straight edge connecting the temperature and pressure

for which K values are required will intersect curves for each compound

at its K value. These K values have been obtained by calculating fugaci-

ties from an equation of state. Use of these charts for exact determina-

tion of K values requires trial-and-error calculations. Hadden and

Grayson [10] have presented correlations for hydrocarbon vapor-liquid

distribution ratios, and the charts from their work are shown in Figures

7-4 and 7-5. These charts can be readily used for determining the vapor-

liquid distribution coefficients. Figure 7-6 shows a continuous equilib-

rium flash fractionation process.

The Equations

The following equations are used for the multicomponent equilib-

rium flash calculations.

f~ - ~

niK i <

1 all liquid (7-38)

i=l

(text continued on page 484)

14.7

IS-~

20 -~

~. 9O

~ 9

150.2

2OO -:

300

400

500

700

800

:~ ,'.. ~ ~:~. _ " .

, 9 ol .~

~.~ ~ .;

M-

lJ o

ZlD o

, .~ " ,~

|.0 "!

.~"

,ID o

j;:

e., Q.

,,.,,

Figure 7-2. K-values for hydrocarbons, low temperature. Source: De-Priester [9].

480

],4.7.

15-

2O 2

70-

9 , 100

150 -

2OO

31111

400"

7O0

o ~

,jz, jj

Figure 7-3. K-values for hydrocarbons, high temperature. Source: De-Priester [9].

481

,,=r

A COMPARISON OF ABOUT 900 EXPERIMENTAL POINTS

WITH THE NOMOGRAM INDICATES THE FOLLOWING DEVIATIONS:

STANDARD DEVIATION 9 9A%

AVERAGE DEVIATION 9 6.8%

BIAS ,-20%

9

KNOMO" KEX~Px I00 E

DEVIATION

KEXP

, of.G. f

;=o

7OO

5OO

H L tN

-4)

NAPHTHA

iT ROO[N

O--t~

t,[NZ[N[

(:l).,t. H 1 IN

TOLU[N[

I Io~J~ ~oo

c~ mN '*o.J t"

D[NZ[N[7 /" WATKff,a~)

~00 (~ j~300 IN I)UTAN[

.......

cf,N C, TO C,z~,~ L

|OO.L.,,,.. ANo II. aAso..o.~'/-

,OCUCNE

:;:~/. -oo ..,RO,A.E

ZOO T ,,o ://- ..

CH& IN

L 9

---* I so L ..~ ~ '

L IQuI~

100

~4~ CYCLOHrXAN[ [ JCO s NAT. GAS-

70 ~ L 600 DISTILLATE

9 TER IN IN NAPHTHA

50 .".~ L ~ I,.- HEXANE 9 KEROSENE

=l~'W~ "G EL.O/ r" ACETYLENE

20 "~ ~'$0 ~- ETHAN[

9 S IN GAS OIL

PROPEN[

-5o

1.5

1.0

O.9

O.6

0.7

0~8 I~K) BUTANE-

0.5 I~I~BUTEN Ir

0.4

m -IMJTAN[.

0.3 WeH'ff"BUTIrN[ '

r N[

0.2

,0.15

-0.02

-30

-20

-10

~)~-,. M [.THYL

30 IdERCAPTAN IN

ABSORPTION

40 OiL. (195 H#)

,90

,100

9 II0

9 120

-13o ~

-14o ~

-t~ ~

-leo ~

170

190

1,000 --

800-

600

400

300

z00

150-

100-

80-

2o --='

15 "

-i

1.5-

0.8 "~

0.6 -;

0.4

0.3 ~

0.2-.:"

0.15

0.I_

0.08 -

0.06

0.04 -I

0.03

0.02 -.::

0.015

O.Ol

0.0O8

0.006 -

0.004

0.003

0.002

0.0015 "

O.OOI

k, ".~

(

t I I Cmrection(mul;iplier)for methaneK's//

1 3 --

in ethane ~ propane IF"

I I I I. I I

7 I

uB mmB Bnmn

80 40 0 -40-80-120-140-200-240

Temperature, "F

eCOz in It.

hydrocarbons

in It hydrocarbons

Methane in Methane

It. hydrocarbons,~/in ethane

,~ Metha

Methane,,, MW 30 %]~<~;,,

in COz ~ C! free lx~"~t) o'ro-at

liquid /# v v

Methane in C41

C? & in Nz8

natural gas

Nitrogen

9

in methane

Figure 7-5. Vapor-liquid equilibrium constants,-260 to +100~ Source" Hadden and

Grayson [10].

483

484

Fortran

Programs for Chemical Process

Design

Initial liquid flow rate,

F, moles/hr

Mole fraction, n.

Pressure

reducing

Heater to produce

nearly saturated

liquid

Vapor rate,V,

Moles/hr

Mole fraction

/// '~

, \\

Vapor

liquid

, /

\'~~iquid rate, L

Moles/hr

Mole fraction,x i

Figure 7-6. Continuous equilibrium flash fractionation.

(text continued from page 479)

f2 - ~ n~/K~ < 1 all vapor (7-39)

i=l

__ __

[M i (K~- 1)(R + 1)]

(K i + R)

(7-40)

where R- the liquid-vapor (L/V) ratio. The new L/V

ratio

for each

iterative calculation, R', is determined from:

R' = [FR- E(R + 1)]

[F+E(R+ 1)]

(7-41)

The constants E and F are determined by

E - ~_,

C i

(7-42)

i=l

Mass Transfer 485

F - ~

(C i )2/M~

(7-43)

i=l

The Algorithm

The computation then determines whether IEI < 0.001. If IEI is not

less than 0.001, R is set equal to R' and the calculations of Equations 7-40,

7-41, 7-42 and 7-43 are repeated until IEI < 0.001.

Once IEI < 0.001, the calculation proceeds to find the total moles of

component i in both the liquid and the vapor phases, that is, Li and V~.

These are given by

L i - MiR

(7-44)

(Ki + R)

and

V i - M i - L i (7-45)

The mole fractions of components in the feed, the liquid and vapor phases

are evaluated as follows"

Mi (7-46)

ni ,~M~

i=l

L i

X i - (7-47)

i=l

and

Yi --

where

~Vi

i=l

(7-48)

~n~-~X~-~Y~-1

i=l i=l i=!

(7-49)

486

Fortran Programs for Chemical Process Design

The method described here is based on the vapor-liquid equilibrium

relationships given in handbooks available from the Gas Processors

Suppliers Association. This technique will handle flash calculations with

feed streams containing up to 15 components. As an added feature, the

calculation will check the feed composition at flash conditions for dew

point or bubble point condition (i.e., whether the feed is either all vapor

or all liquid). These checks are done before the flash calculations are

started. If the feed is above the dew point or below the bubble point, an

appropriate message is displayed on the computer screen. A default value

for R (L/V) = 1.0 is used to start the iterative process.

Nomenclature

E,F = constants

K i =

equilibrium flash constant for each component in the feed stream

L~ = total moles of component i in the liquid phase

L = total moles of liquid at equilibrium conditions

M i = total moles of component i in the feed stream

n~ = mole fraction of component i in the feed stream

R = liquid-vapor (L/V) ratio

R'- new L/V ratio for each iteration calculation

V = total moles of vapor at equilibrium conditions

V i = total moles of component i in the vapor phase

X i = mole fraction of component i in the liquid phase

Y~ = mole fraction of component i in the vapor phase

TOWER SIZING FOR VALVE TRAYS

Introduction

Many types of trays are used in both fractionating and absorption

columns. In a fractionating column, the bubble caps with the weirs and

downcomers maintain a liquid level on the trays. The liquid flows across

the tray via the downcomer and across the next tray in the opposite

direction, and the vapor flows up through the caps and the slots, thus

mixing with the liquid. Figures 7-7 and 7-8 show a section of the col-

umn distributor and different types of packings. Figure 7-9 illustrates

the vapor flows through bubble cap, sieve, and valve trays. The riser in

the bubble cap can aid the design of the tray to prevent liquid from

"weeping" through the vapor passage. Sieve or valve trays control weep-

ing by vapor velocity. The bubble cap tray has the highest turn down