List of Nomenclature

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List of Nomenclature

Symbol	Definition	SI Units
a	Stoichiometric Coefficient
a	Interfacial, Mass Transfer Area	m²
a	Mean Ionic Diameter of an Electrolyte	m
a′	Interface Area per Unit Volume	m²/m³
A	Equipment Cost Attribute
A	Area, Heat Transfer Surface Area	m²
A	Absorption Factor
A	Annuity Value	$/time
A	Constant in Antoine’s Equation
A/F, i, n	Sinking Fund Factor
A/P, i, n	Capital Recovery Factor
A_b	Bubbling Area	m²
A_c	Cross-Sectional Area	m²
A_t	Total Cross-Sectional Area of Packed Bed	m²
b	Fin Spacing	m
B	Constant in Antoine’s Equation	°C
BC	Baffle Cut (% of Shell Diameter)
B_o	Boiling Number
BV	Book Value	$
C	Constant in Antoine’s Equation	°C
C	Molar Density	mol/m³
C	Equipment Cost	$
C or c	Molar Concentration	kmol/m³
C_sb,f	Parameter in Flooding Calculation	m/s
CA	Corrosion Allowance	m
CBM	Bare Module Cost	$
C_D	Drag Coefficient
C_f	Material Constant for Surfaces Used in Boiling Heat Transfer
COM	Cost of Manufacture	$/time
cop	Coefficient of Performance
C_p, C_v	Heat Capacities (Constant Pressure, Constant Volume)	kJ/kg°C or kJ/kmol°C
CCP	Cumulative Cash Position	$
CCR	Cumulative Cash Ratio
D, D_AB	Diffusivity, Diffusion Coefficient of Solute A in Solution B	m²/s
d, D	Diameter	m
D*	Dimensionless Diameter
D	Amount Allowed for Depreciation	$
D	Distillate Product Flowrate	kmol/time
d	Yearly Depreciation Allowance	$/yr
DCFROR	Discounted Cash Flow Rate of Return
DMC	Direct Manufacturing Cost	$/time
DPBP	Discounted Payback Period	years
$\bar{D}$ $\bar{D}$	Average Diffusivity	m²/s
D₀	Diffusivity at Infinite Dilution	m²/s
D_p, D_S	Particle Diameter, Sphere Diameter	m
d	Vector of Disturbance Inputs
d_s	Average Solvent Density	kg/m³
e	Elementary Charge	Columb
e	Pipe Roughness Factor	m
e_f	Energy Dissipated by Friction	J/kg
E	Money Earned	$
E	Weld Efficiency
E(t)	Residence Time Distribution in Reactor	s^-1
E_act or E	Activation Energy	kJ/kmol
E_o	Overall Column Efficiency
EAOC	Equivalent Annual Operating Cost	$/yr
ECC	Equivalent Capitalized Cost	$
_f	Fraction of Stream
_f,	Friction Factor
_f	Rate of Inflation
_f	Factor Used in Convective Boiling Correlation
f_q	Quantity Factors for Trays
F	Faraday’s Constant	Columb/kmol
F	Future Value	$
F	Molar Flowrate	kmol/s, kmol/h
F	Equipment Module Cost Factor
F	Correction for Multipass Heat Exchangers
F	Force	N
F	Packing Factor in Packed Beds
F_lv	Parameter in Flooding Calculation
F_d, F_g, F_p	Drag, Gravitational, and Pressure Force	N/m² or kPa
F_x, F_y	Mass Transfer Coefficients for Liquid (x) or Vapor (y) Phase	m/s
F/A, i, n	Uniform Series Compound Amount Factor
FCI	Fixed Capital Investment	$
F/P, i, n	Single Payment Compound Amount Factor
FMC	Fixed Manufacturing Costs	$/time
F_Lang	Lang Factor
f_i	Fugacity of Pure Component i	bar or kPa
${\hat{f}}_{i}$ ${\hat{f}}_{i}$	Fugacity of Component i in Mixture	bar or kPa
f	System of Equations (vector)
g	Acceleration Due to Gravity	m/s²
g_c	Unit Conversion of 32.2 ft lb/lb_f/sec²	ft lb/lb_f/sec²
G, G′	Superficial Mass Velocity	kg/m²/s
G	Gibbs Free Energy	kJ
G	Gas Flowrate	kg/s, kmol/s
GE	General Expenses	$/time
h	Individual Heat Transfer Coefficient	W/m²/K
H, H_A	Henry’s Law Constant	bar or kPa in Equation (13.5), but can be different elsewhere
H, h	Enthalpy, Specific Enthalpy	kJ or kJ/kg
H or h	Height or Head	m
H, HTU	Height of Transfer Unit	m
HETP	Height Equivalent of a Theoretical Plate	m
h_f	Height of Froth on a Tray	m
h_mf	Bed Height at Minimum Fluidization	m
I	Identity Matrix
I	Ionic Concentration	kmol/m³
I_x	Ionic Strength on a Mole Fraction Basis
I	Cost Index
i	Compound Interest
i′	Effective Interest Rate Including Inflation
INPV	Incremental Net Present Value	$
IPBP	Incremental Payback Period	years
J	Jacobian Matrix
k	Thermal Conductivity	W/m K
k	Ratio of Specific Heat Capacities of a Gas
k_o, K	Preexponential Factor for Reaction Rate Constant	Depends on molecularity of reaction
K	Loss Coefficient for Elbows, Fittings, etc.
K_p	Equilibrium Constant	Depends on reaction stoichiometry
k_B	Boltzmann Constant	kJ/K
${\bar{k}}_{m}$ ${\bar{k}}_{m}$	Average Mass Transfer Coefficient	m/s
k_reac or k_i	Reaction Rate Constant	Depends on molecularity of reaction
k_SB	Souders-Brown Constant	m/s
K	Geometric Factor for Elliptical Heads
K_c	Proportional Gain
K_cu	Ultimate Controller Gain
K_eq	Equilibrium Constant of a Chemical Reaction
K_i	Vapor-Liquid Equilibrium Ratio of Species i
K_x, K_y	Mass Transfer Coefficient (x is Liquid Phase, y is Vapor Phase)	kmol/m²/s
L	Lean Stream Flowrate	kg/s
L	Length (also Baffle Spacing), Characteristic Length of a Catalyst Particle	m
L_eq	Equivalent Length of Pipe	m
L, $\bar{L}$ $\bar{L}$	Liquid Flowrate (Over Bar signifies Below Feed in Distillation Column)	kg/s or kmol/s
$\dot{m}$ $\dot{m}$	Mass Flowrate	kg/s
m	Equilibrium/Partition Coefficient (y/x)
m	Molality	kmol/kg
m	Parameter Used in Fin Effectiveness, m = (2h / δk)^1/2 for Rectangular Fins, etc.
m, M	Ratio of Tube Side and Shell Side Flows in Performance Problems
M, mw	Molecular Weight	kg/kmol
M	Mass	kg
M	Stress Intensity Factor for Dished Heads
M_T	Thiele Modulus
n	Life of Equipment	years
n	Years of Investment	years
n	Number of Batches
n_c	Number of Campaigns
N	Number of Streams, Trays, Stages, Transfer Units, Shells, etc.
N_u	Nusselt Number
N	Molar Flowrate or Molar Flux	kmol/s or kmol/m²/s
NPSH_A NPSH_R	Net Positive Suction Head (Available, Required)	m of liquid (or Pa)
NPV	Net Present Value	$
N_toG	Number of Transfer Units
N	Molar Holdup	kmol
OBJ, OF	Objective Function	usually $ or $/time
p	Tube Pitch (Distance between Centers of Adjacent Tubes)	m
p	Price	$
p_i	Partial Pressure	Pa
P	Dimensionless Temperature Approach Used in Log-Mean Temperature Correction Factor
P, p	Pressure and Partial Pressure	bar or kPa
P	Present Value	$
P*	Vapor Pressure	bar or kPa
P_i	Membrane Permeability of Component i	m³/m²/s/kPa
P/A, i, n	Uniform Series Present Worth Factor
PBP	Payback Period	year
PC	Project Cost	$
P/F, i, n	Single Payment Present Worth Factor
PVR	Present Value Ratio
P(x)	Probability Density Function of x
Pr	Prandtl Number
P_u	Ultimate Period of Oscillation	s
Q or q	Rate of Heat Transfer or Heat Duty	W or MJ/h
q	Fraction of Liquid in Distillation Column Feed
$\dot{Q}$ $\dot{Q}$	Heat Transfer Rate	W or MJ/h
r	Radius	m
r	Reaction Rate	kmol/m³ or kmol/kg cat s
r	Rate of Production	kg/h
r_k	Knuckle Radius for Dished Heads	m
R	Gas Constant	kJ/kmol K
R	Ratio of Heat Capacities Used in Log-Mean Temperature Correction Factor
R	Residual Funds Needed	$
R	Reflux Ratio
R	Heat Transfer Resistance	m²K/W
R	Restoring Force to Keep Elbow (pipe fitting) Stationary	N
Re	Reynolds Number
Re_emf	Reynolds Number at Minimum Fluidization
Re_t	Reynolds Number at Terminal Velocity
R	Rich Stream Flowrate	kg/s
Rand	Random Number
ROROI	Rate of Return on Investment	% p.a.
ROROII	Rate of Return on Incremental Investment	% p.a.
s	Suppression Factor Used in Convective Boiling Correlation
S	Entropy	kJ/K
S	Salvage Value	$
S	Maximum Allowable Working Pressure	bar
S	Salt Concentration Factor
S	Sensitivity
S	Interfacial Surface Area	m²
S	Stripping Factor
SF	Stream Factor
t	Thickness of Wall	m
t	Time	s, min, h, yr
$\bar{t}$ $\bar{t}$	Average Time Spent in Reactor	s
t_m	Membrane Thickness	m
T_m	Melting Temperature	K
T	Total Time for a Batch	s, min, h, yr
T	Temperature	K, R, °C, or °F
U	Internal Energy	kJ
u	Vector of Manipulated Inputs
u	Flow Velocity	m/s
$u_{t}^{}$ $u_{t}^{}$	Dimensionless Terminal Velocity
u_s	Superficial Velocity in Packed or Fluidized Bed	m/s
u_t	Terminal Velocity of a Particle	m/s
U	Overall Heat Transfer Coefficient	W/m²K
U	Internal Energy	J
v	Molar Volume	m³/mol
V	Volume	m³
V, $\bar{V}$ $\bar{V}$	Vapor Flow Rate (Over Bar is Below Feed in Distillation Column)	kmol/h
v_react	Specific Volume of Reactor	m³/kg of product
v_p	Velocity	m/s
$\dot{v}$ $\dot{v}$	Volumetric Flowrate	m³/s
W	Weight	kg
W	Total Moles of a Component	kmol
W	Width of Heat Transfer Fin	m
W or W_S	Work or Shaft Work	kJ/kg
${\dot{W}}_{s}$ ${\dot{W}}_{s}$	Shaft Power	W
WC	Working Capital	$
X	Matrix of Independent Variables
x	Vector of Variables
x	Mole or Mass Fraction
x	Wall or Film Thickness	m
x	Mole Faction in Liquid Phase
X	Conversion
X	Base-Case Ratio
X_tp	Martinelli’s Two-Phase Flow Parameter
y	Mole or Mass Fraction (in Vapor Phase)
Y	Yield
YOC	Yearly Operating Cost	$/yr
YS	Yearly Cash Flow (Savings)	$/yr
z	Valence of Ions
z	Solids Mole Fraction, Mole Fraction in Feed Stream
z	Distance or level	m
z	Coordinate in Direction Opposite Gravity	M

Greek Symbols

α	Multiplication Cost Factor
α_AB	Relative Volatility or Relative Permeability (between Species A and B)
α	NRTL Nonrandomness Factor
α	Parameter in Calculating Pressure Drop in Packed Bed
β	Parameter in Calculating Pressure Drop in Packed Bed
β	Orifice Diameter/Pipe Diameter
δ	Thickness of the Ion-Free Layer below
δ	(Condensing) Film Thickness or Fin Thickness	m
ε	Void Fraction
ε	Pump Efficiency
ε	Tolerance, Error
ε	Emissivity
ε	Effectiveness (for fins)
ε_ij	Lennard-Jones Energy Parameter between Species i and j	kJ/kmol
ε_r	Relative Permittivity of the Solvent
$ε_{r}^{'}$ $ε_{r}^{'}$	Relative Permittivity of the Vapor Phase
ε_s	Permittivity of the Solvent	Columb²/kJ m
φ	Fugacity Coefficient
$\hat{ϕ}$ $\hat{ϕ}$	Fugacity Coefficient in Mixture
φ*	Fugacity Coefficient of Saturated Vapor
γ	Activity Coefficient
γ	Ratio of Heat Capacities = C_p/C_v
γ^∞	Activity Coefficient in the Mixture at Infinite Dilution
γ_±	Mean Ionic Activity Coefficient
κ	Inverse of Debye-Hückel Length	m^–1
η	Catalyst Effectiveness Factor
η	Selectivity
η, η_c, η_f, η_p, η_t	Efficiency for Compressor, Separator, Pump, Turbine
λ	Heat of Vaporization	kJ/kg
λ	Eigenvalue
λ	Heat of Vaporization/Condensation	kJ/kg
λ	Lagrangian Multiplier Vector
λ₀	Thermal Conductivity of Pure Solvent	W/m K
μ	Viscosity	kg/m s
μ_c	Chemical Potential	kJ
μ₀	Viscosity of Pure Solvent	kg/m s
ν	Stoichiometric Coefficient
θ	Parameter Vector
θ	Ratio of Species Concentration to That of Limiting Reactant
θ	Angle	° or rad
θ	Stage Cut in Gas Permeation Membrane
σ	Statistical Variance
σ	Collision Diameter	m
σ	Surface Tension	N/m (dyne/cm²)
σ	Stefan-Boltzmann Constant	W/m²/K⁴
ξ	Selectivity
ρ,ρ_s	Density, Solid (Particle) Density	kg/m³
Θ	Stoichiometric Parameter
Θ	Cycle Time	s
τ	Space Time	s
τ	NRTL Binary Interaction Energy Parameter
τ_D	Derivative Time Constant	s
τ_I	Integral Time Constant	s
ψ	Density of Water/Density of Liquid in Packed Bed
Ψ	Sphericity
Ψ	Inertial Separation Parameter
Ω	Overall Catalyst Effectiveness (Including Internal and External Resistances)
Ω	Collision Integral

Subscripts

1	Base Time, Base Case, or Inlet Condition
2	Desired Time, New Case, or Outlet Condition
a	Required Attribute
air-leak	Air Leak Due to Vacuum Conditions
A, B, R, S	Designating Components A, B, R, S
ACT, actual	Actual
Active	Refers to Active Column Area
Aux	Auxiliary Buildings
a, a′	Anion
b	Base Attribute, Baffle
b	Bulk or Bubble Phase
bare	Bare Fin
base	Fin Base
B	Bottoms of Distillation Column
BM	Bare Module
c, c′	Cation
c	Cold, Corrected, Critical, Coolant
cb	Convective Boiling
cat	Catalyst
clean	Cleaning
cocurrent	Designating a Cocurrent Arrangement for an S-T Heat Exchanger
countercurrent	Designating a Countercurrent Arrangement for an S-T Heat Exchanger
Cont	Contingency
C	Refers to Condenser
cv	Control Volume
cw	Cooling Water
cycle	Cycle
d	Without Depreciation
dished	Dished Vessel Head
elliptical	Elliptical Vessel Head
D, d	Demand
D	Distillate
E	Emulsion Phase
E	Contractor Engineering Expenses
eff	Effective
eq	Equivalent
el	Electrolyte(s)
eq	Metal in the Equipment
f	Flooding Conditions
fb	Film Boiling
fin	Fin
film	Film
F,f	Feed
Fee	Contractor Fee
FTT	Transportation, etc.
g	Gas
GR	Grass Roots
h	Hot
H	Hydraulic
i	Species
i	Index, Inside, or Interface
in	Inlet or Inner
int	Internal
k	Year
lm	Log-Mean
l-h	Liquid Holdup
l, L	Liquid
L	Installation Labor
L	Lean Streams
L	Without Land Cost
LF	Long-Range Force
m	Molality Scale
m	Mass Transfer
m	Molecular Species
m	Heating/Cooling Medium or Membrane
m	Number of Years
M	Materials for Installation
M	Material Cost Factor
max	Maximum
MC	Matching Costs
mesh	Mesh
min	Minimum
n	Index for Time Instant
nom	Nominal Interest
o	Outside
out	Outlet
O or OH	Construction Overhead
Off	Offsites and Utilities
OL	Operating Labor
OL, OV, ov	Overall Liquid and Overall Vapor Transfer Units or Height of Transfer Unit, Respectively
opt	Optimum
p	Production
p	Process Stream or Permeate Stream
pb	Pool Boiling
P	Equipment at Manufacturer’s Site (Purchased), Pressure Cost Factor, Process or Particle
P&I	Piping and Instrumentation
rev	Reversible
rxn, r	Reaction
r	Reduced (Pressure)
r	Retenate Stream
rad	Radiation
R	Rich Stream, Reboiler, Reference
RM	Raw Materials
s	All Nonwater Solvents, Simple Interest, Surface, or Stream
sat	Saturated
s, shell	Shell (Side) of Heat Exchanger
S	Supply
SB	Souders-Brown
Site	Site Development
SF	Short-Range Force
sph	Spherical or Equivalent Spherical
t, tube	Tube (Side) of Heat Exchanger
t	Terminal
tp	Tube Passes
TM	Total Module
UT	Utilities
V, v	Vapor
vap	Vaporization
ves	Vessel
wire	Wire
WT	Waste Treatment
w	Water or Wall
y	Designation for Type in Effectiveness Factor for Heat Exchangers, y = 1-2, 2-4, 3-6, etc.
z	Distance Along Reactor or Tube
+	Cation
–	Anion

Superscripts

α, β	Powers of Coefficients in Langmuir-Hinshelwood Kinetics
a, b	Powers in Simple Rate Laws
DB	Double Declining Balance Depreciation
E or ex	Excess Property
L	Lower Limit
L, l	Liquid
*	Equilibrium Value
o	Cost for Ambient Pressure Using Carbon Steel
s	Solid
SL	Straight Line Depreciation
SOYD	Sum of the Years Depreciation
U	Upper Limit
v	Vapor
∞	Aqueous Infinite Dilution
′	Includes Effect of Inflation on Interest
′′′	Signifies Reaction Rate Per Unit Mass of Catalyst

Additional Nomenclature

Table 1.2	Convention for Specifying Process Equipment
Table 1.3	Convention for Specifying Process Streams
Table 1.7	Abbreviations for Equipment and Materials of Construction
Table 1.10	Convention for Specifying Instrumentation and Control Systems

Note: In this book, matrices are denoted by boldface, uppercase, italicized letters and vectors are denoted by boldface, lowercase, italicized letters.

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List of Nomenclature

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List of Nomenclature