NOTATION

NOTATION

2,

3

a

- specific surface of packing, m /m

a b

- mass transfer area in unit volume of equipment, m /m - mass fraction, dimensionless

C cΡ C

- molar concentration, kmol/m - heat capacity at constant pressure, J/(kg K) - molar heat capacity at constant pressure, J/(kmol K)

CF d

- capacity factor, m/s - diameter, m

D

- multicomponent diffusion coefficient, m /s

Λ D

- binary diffusion coefficient, m /s - generalized Stefan-Maxwell diffusion coefficient, m /s

2

3

p

2

2

2

D

D

D Ε Ε

- dispersion coefficient, m /s - binary thermal diffusion coefficient, m /s - enhancement factor, dimensionless - enhancement factor for instantaneous reaction, dimensionless

00

Ε Ε

- point efficiency, dimensionless - overall plate efficiency, dimensionless ο

Ε

- Murphree plate efficiency, dimensionless

M FP g g

- flow parameter, dimensionless - mass rate of gas, kg/s - acceleration of gravity, m/s

ζ

2

xii

NOTATION

G h H He H

-

molar rate of gas, kmol/s enthalpy per unit mass, J/kg enthalpy per unit kilomole, J/kmol, kJ/lmol Henry's law constant, Pa Henry's law constant, (Pa m) /kmol

Η' I k k

-

Henry's law constant, P a " mass transfer rate, kmol/s binary mass transfer coefficient, m/s binary liquid mass transfer coefficient, kmol/(m s)

k

X

y x k k

1

2

2

- binary gas mass transfer coefficient, kmol/(m s)

2

- binary liquid mass transfer coefficient, kmol/(m s) 2

R R

-

binary gas mass transfer coefficient, kmol/(m s) chemical reaction rate constant, different dimensions overall mass transfer coefficient, m/s liquid mass rate, kg/s liquid molar rate, kmol/s molarity, kmol/kg slope of equilibrium line, dimensionless molecular weight, kg/kmol reaction factor, dimensionless number of components in fluid mass flux with respect to stationary coordinates, kg/(m s) Avogadro's number, 1/kmol molar flux with respect to stationary coordinates, kmol/(m s) number of plates in plate column pressure, Pa heat flux, W/m mass transfer factor, dimensionless heat rate, W number of chemical reaction molar rate of chemical reaction, kmol/(m s) universal gas constant, J/(kmol K)

S t Τ u

-

cross-sectional area, m time, s temperature, Κ superficial fluid velocity in equipment, m/s

Y

k K 1 L m m M M η η Ν Ν Ρ Ρ q q Q Γ

V

V w

2

3

- volumetric flow rate, m /s 3

- molar volume, m /kmol - superficial mass fluid velocity, kg/(m s)

NOTATION

2

w X X. 1

- superficial molar fluid velocity, kmol/(m s) - rectangular coordinate, m - mole fraction of component i in liquid phase, dimensionless

y

- rectangular coordinate, m - mole fraction of component i in the gas phase, dimensionless

Ζ

Ζ

- rectangular coordinate, m - height of the equipment, m

a

- heat transfer coefficient, W/(m K)

oc

ß

- gas hold-up, m Im - volumetric fraction, dimensionless

ß

- liquid hold-up, m Im

Y δ ε

- solid volumetric fraction, m Im - film thickness, m - voidage of bed, dimensionless

ε

- energy flux, W/m - viscosity, kg/(m s) - conductivity, W/(mK)

2

3

3

3

3

3

3



2

η

λ

2

Ό Ό

- kinematic viscosity, m Is - stoichiometry coefficient, dimensionless

Ρ σ σ

- density, kg/m - surface tension, N/m - critical surface tension, N/m

3

c Η

- correction factor for the effect of high fluxes on heat transfer coefficient, dimensionless - dimensionless heat transfer factor, dimensionless

Subscripts A, Β, C - components in multicomponent systems av ­ average c ­ at critical point d ­ dynamic quantity G ­ gas phase i, j , k, 1 - components in multicomponent system ij - pair i-j in multicomponent system in - inert

ΧΜ

xiv

NOTATION

k 1 L m ρ r s t 0 1 2

-

column laboratory liquid phase logarithmic mean value bubble, element of packing reduced relative to critical value static quantity total mass (molar) flux reference state quantity evaluated at lower cross section of equipment quantity evaluated at upper cross section of equipment

Superscripts ef r * **

ο • Τ • δ

-

effective equilibrium value gas-liquid interface liquid-solid interface mean value partial value at infinite dilution for finite mass-transfer flux relative to the molar average velocity of fluid relative to the volumetric average velocity of fluid in the bulk of fluid

Vectors and Matrices vector of driving forces for diffusion, m"

1

vector of external force on

of

unit

mass

component i, N/m 2

vector of molar diffusion flux, kmol/(m s) vector of molar diffusion flux of component i 2

relative to velocity ω , kmol/(m s) vector of mass diffusion flux of compoent 2

i

relative to velocity ω , kg/(m s) matrix

of

multicomponent

mass

transfer

coefficients for "zero" mass transfer flux, m/s

NOTATION XV k

= ( k . ).

#

- matrix

#

i j i , j 2£ n - l

of

multicomponent

mass

transfer

coefficients for finite mass transfer flux, m/s Ν = [Ν ,,.,,Ν

n-l

1

Ν. = [Ν ι

]

Τ

2

- vector of molar flux, kmol/(m s)

, Ν. , Ν

ix

ly

lz

] - vector of molar flux of component i,

2

kmol/(m s)

2

η

= [η i

, η

, η

ix

1 - vector of mass flux of component i, kg/(m s)

îy

iz

Q = [<1 > Q > Q ] χ y ζ u = [u , u , u ] χ

y

- vector of heat flux, W/m - vector of mass average velocity, m/s

ζ

= [u^, u ^ , u ^ l χ

u

y

= [u , u , u

B

u

B

B

B

χ

y

ζ

= [u

, u

i

1

, u

ix

( ot)

- vector of molar average velocity, m/s

ζ

iy Cot)

- vector of volume average velocity, m/s 1 - vector of macroscopic velocity of component i,

iz

m/s

(a)

(oc)

wir ' = [ wi χr ' . wi ry ' . w irζ' l -

vector

of

mass

flow

velocity

of

gas

2

phase in absorber, kg/(m s)

= [w ^, (

i

i

w ^ ] - vector of mass flow (

x

i

y

i

z

velocity of

liquid

2

phase in absorber, kg/(m s) W °°= [W (

i

( a )

, W

( Û

ix

iy

°,W

( Û

°]-

vector

of

molar

flow

velocity

of

iz

gas 2

phase in absorber, kmol/(m s) W ^ = [ W ^ \ W ^ \ W ^ ] - vector of molar flow velocity of liquid (

}

(

i

(

ix 7

Γ

iy n-l

χ = [χ ,...,x y

=

J

]

[y 1>···>Υ' n - IΓ

Γ = (Γ

)

ij i,j ^

Φ = (Φ

)

ij i ,j ^

τ

τ

n-l

n-l

iz

2

phase in absorber, kmol/(m s) dimensionless - vector of mole fraction in liquid phase, - vector of mole fraction in gas phase, dimensionless - matrix of thermodynamic factors, dimensionless - matrix of mass transfer factor, dimensionless

NOTATION

XVI

Dimensionless Groups

*-ζ

Bo =

\ ρ a

De = — ι

^L

- Bond number - Deborah number

α

ρ

Ga = —

- Galillei number 3 Ü

L

u

Q

Fr =

R e

=

- Froude number

U

t

P

Sc = —^7=— ρ w k d Sh = — — —

~ y ° W s number R e

n

- Schmidt number - Sherwood number