| a | interfacial area per volume, ft2/ft3 or m2/m3 |
 | interfacial area for heat transfer on stage j, m2 |
| aflow, aheat, amass | eddy diffusion parameters, Eqs. (15-48) |
| ap | surface area/volume, m2/m3 |
| ap1, ap2, ap3, aT1, aT2, aT6 | constants in Eq. (2-30) and Table 2-3 |
| A | area, m2 |
| A,B,C | constants in Antoine Eq. (2-34) |
| A,B,C,D,E | constants in Eq. (2-60) |
| A,B,C,D | constants in matrix form of mass balances, Eqs. (6-13) and (12-58) |
| AE, BE, CE, DE | constants in matrix form of energy balances, Eq. (6-34) |
| Aactive | active area of tray, ft2 or m2 |
| Ac | cross-sectional area of column, ft2 or m2 |
| Ad | downcomer area, ft2 or m2 |
| Adu | flow area under downcomer apron, Eq. (10-28), ft2 |
| Af | area for flow, m2 |
| Ahole | area of holes in column, ft2 |
| AI | interfacial area between two phases, ft2 or m2 |
| Amixer | cross-sectional area of mixer, m2 |
| Anet | net area, Eq. (10-13), ft2 or m2 |
| b | empirical constant, Eq. (13-63b) |
| b | equilibrium constant for linear equilibrium, y = mx + b |
| bflow, bheat, bmass | eddy diffusion parameters, Eqs. (15-48) |
| B | bottoms flow rate, kmol/h or lbmol/h |
| C | number of components |
| CBM | bare module cost, Chapter 11 |
| CC | concentration of solute in continuous phase, kmol/m3 continuous phase |
 | concentration of solute in continuous phase in equilibrium with CD, kmol/m3 |
| CD | concentration of solute in dispersed phase, kmol/m3 dispersed phase |
| CfL | vapor load coefficient, Eq. (15-38) |
| CA, CB, Cm | molar concentrations, of A, B, and mixture, mol/m3 |
| Co | orifice coefficient, Eq. (10-25) |
| Cp | heat capacity, Btu/lb°F or Btu/lbmol°F or cal/g°C or cal/mol°C, etc. |
| Cp | base purchase cost, Chapter 11 |
| Cp,size | packing size factor, Table 10-5 |
| CpW | water heat capacity |
| Cs | capacity factor at flood, Eq. (10-48) |
| Csb | capacity factor, Eq. (10-8) |
| d | dampening factor, Eq. (2-57) |
| D | diffusivity, Fickan m2/s or ft2/h |
| D | distillate flow rate, kmol/h or kg/h |
| D, Dia | diameter of column, ft or m |
| D’col | column diameter, see Table 16-1, ft |
| dhydraulic | hydraulic diameter of drop, Eq. (13-62), m |
| di | impeller diameter, m |
| dp, dd | drop diameter, m |
 | characteristic drop diameter, Eq. (16-97b), m |
| dtube | tube diameter, m |
| dsettler, Ds | diameter of horizontal settler, m |
| Dlarge, Dpilot | diameters of Karr columns for scale-up, Eq. (13-66), m |
| D° | infinite dilution Fickian diffusivity, m2/s |
| D | Maxwell-Stefan diffusivity, m2/s |
| Deddy | eddy diffusivity, Eq. (16-111a, b), m/s |
| Dtotal | total amount of distillate (Chapter 9), moles or kg |
| e | absolute entrainment, mol/h |
| e | plate fractional free area in Karr column |
| erf | error function, Eq. (18-70) |
| E | extract flow rate (Chapters 13 and 14), kg/h |
| Ê | mass extract, kg |
 | energy transfer rate on stage j from bulk liquid to bulk vapor, J/s |
| Ek | value of energy function for trial k, Eq. (2-51) |
| EML, EMV | Murphree liquid and vapor efficiencies, Eqs. (4-58) and (4-59) |
| E0 | activation energy, Kcal/mol |
| Eo | Overall efficiency, Eq. (4-56) |
| Ept | point efficiency, Eq. (10-5) or (15-76a) |
| Êt | holdup extract phase in tank plus settler, kg |
| f | friction factor |
| fAB | friction coefficient between molecules A and B |
| f = V/F | fraction vaporized |
| f | fractional approach to flooding |
| f | frequency of reciprocation of Karr column, strokes/s |
| f(x) | equilibrium function, Chapter 9 |
| fk(V/F) | Rachford-Rice function for trial K, Eq. (2-43) |
| F | packing factor, Tables 10-3 and 10-4 |
| F | degrees of freedom, Eq. (2-4) |
| F | charge to still pot (Chapter 9), moles or kg |
| F | mass of feed in batch extraction, kg |
| F | feed flow rate, kmol/h or lbmol/h or kg/h etc. |
| FD | diluent flow rate (Chapter 13), kg/h |
| Flv, FP |  , flow parameter |
| Fm | material factor for cost, Table 11-2 |
| Fp | pressure factor for cost, Eqs. (11-5) and (11-6) |
| Fq | quantity factor for cost, Eq. (11-7) |
| Fs,Fsolv | flow rate solvent (Chapter 13), kg/h |
| Fsolid | solids flow rate in leaching, kg insoluble solid/h |
| Fweir | weir modification factor, Eq. (10-26) and Figure 10-22 |
| gap | gap from downcomer apron to tray, Eq. (10-28), ft |
| g | acceleration due to gravity, 32.2 ft/s2, 9.81 m/s2 |
| gc | conversion factor in English units, 32.2 ft·lbm/(lbf·s2) |
| G | flow rate carrier gas, kmol/h or kg/h |
| G′ | gas flux, lb/s ft2 |
| h | pressure drop in head of clear liquid, inches liquid |
| h | height of liquid on stage (Chapter 16), ft |
| h | height, m or ft |
| h | height of liquid in mixer, m |
| h | liquid enthalpy, kcal/kg, Btu/lbmol, etc. |
| h | step size in Euler’s method = Δt, Eq. (8-29) |
 | pure component enthalpy |
| hf | enthalpy of liquid leaving feed stage |
| hF | feed enthalpy (liquid, vapor or two-phase) |
| hheat transfer | heat transfer coefficient |
| hL | clear liquid height on stage, m or cm |
| ho | hole diameter, inches |
| hp | packing height, ft or m |
| htotal | height of flash drum, ft or m |
| hw | height of weir, m or cm |
| H | Henry’s law constant, Eqs. (8-9), (8-10), and (12-1) |
| H | molar holdup of liquid on tray, Eqs. (8-27) and (8-28) |
| H | stage height in Karr column, m |
| H | vapor enthalpy, kcal/kg, Btu/lbmol, etc. |
 | partial molar enthalpy of component i in vapor on stage j, J/kmol |
 | height of tank, m |
| Ht,OD | overall height of a transfer unit for mass transfer driving force in concentration units, Eq. (16-83a analog), m |
| HG | height of gas phase transfer unit, ft or m |
| HL | height of liquid phase transfer unit, ft or m |
| HOG | height of overall gas phase transfer unit, ft or m |
| HOL | height of overall liquid phase transfer unit, ft or m |
| HETP | height equivalent to a theoretical plate, ft or m |
| HTU | height of a transfer unit, ft or m |
| jD, jH | j-functions, Eqs. (15-50) |
| JA | flux with respect to molar average velocity of fluid |
| k1, k2 | empirical constants, Eq. (13-63b) |
| kB | Botzmann’s constant, J/k |
| kconduction | thermal conductivity, J/(ms K) |
 | individual mass transfer coefficients in liquid and vapor phases, see Table 15-4 |
| kc | mass transfer coefficient with concentration driving force, m/s, Eq. (15-25b) |
| k’y | mass transfer coefficient in concentrated solutions, Eq. (15-32f) |
| kx, ky | individual mass transfer coefficient in molar units |
| kx,c, kxD | individual mass transfer coefficients in continuous and dispersed phases, kg/(s·m3) or kmol/(s·m3) |
| kLD, kLC | individual mass transfer coefficients in continuous and dispersed phases with driving force in concentration units, m/s |
| kL, kV | individual liquid and vapor mass transfer coefficients in distillation, Eq. (16-108), m/s |
| k | mass transfer coefficient in Maxwell-Stefan analysis, Đ/Δz, m/s |
| Kd | y/x, distribution coefficient for dilute extraction |
| K, Ki | yi/xi, equilibrium vapor-liquid ratio |
| Kdrum | parameter to calculate uperm for flash drums, Eq. (2-64) |
| Kx, Ky | overall mass transfer coefficient in liquid or vapor, lbmol/ft2 h, or kmol/h·m2 |
| KLD | overall mass transfer coefficient in extraction based on dispersed phase in concentration units, Eq. (16-80b analog), m/s |
| KO-ED | overall mass transfer coefficient in extraction based on dispersed phase, Eq. (16-80a), kg/(s·m3) or kmol/(s·m3) |
| lw | weir length, ft |
| L | length, m |
| L | liquid flow rate, kmol/h or lbmol/h |
 | mass liquid flow rate, lb/h (Chapter 15) |
| L′ | liquid flux, lb/(s)(ft2) |
| Lg | liquid flow rate in gal/min, Chapter 10 |
| m | linear equilibrium constant, y = mx + b |
| m | local slope of equilibrium curve, Eq. (15-30b) |
| M | ratio HETPpractical/HETPpacking Eq. (10-46) |
| mCD | slope of equilibrium curve of continuous versus dispersed phase mass or mole fractions, Eq. (16-80c) |
| mCD,conc_units | slope of equilibrium curve of continuous versus dispersed phase in concentration units, Eq. (16-80c analog) |
| M | flow rate of mixed stream (Chapter 13), kg/h |
| M | multiplier times (L/D)min (Chapter 7) |
| MW | molecular weight |
 | average molecular weight |
| n | moles |
| n | number of drops |
| n1, n2 | empirical constants, Eq. (13-65) |
| nG | number of gas phase transfer units |
| nL | number of liquid phase transfer units |
| nO-ED, nO-EC | number of overall extraction transfer units in dispersed and continuous phases, Eq. (16-81) |
| nOG | number of overall gas phase transfer units |
| nOL | number of overall liquid phase transfer units |
| norg | moles organic in vapor in steam distillation |
| nw | moles water in vapor in steam distillation |
| N | impeller revolutions per second |
| N | number of stages |
| NA | flux of A, lbmol/(h)(ft2) or kmol/(h)(m2) |
| Nf,Nfeed | feed stage |
 | transfer to liquid from vapor on stage j, mol component i/s |
 | transfer to vapor from liquid on stage j, mol component i/s |
| Nmin | number of stages at total reflux |
| Nfeed,min | estimated feed stage location at total reflux |
| NPo | power number, Eq. (13-52) |
| NtOD | number of overall extraction transfer units for mass transfer driving force in concentration units, Eq. (16-81a analog) |
| Nu | Nusselt number, Eq. (15-33g) |
| NTU | number of transfer units |
| O | total overflow rate in washing, kg/h |
| p | pitch of sieve plate holes, m |
| p, ptot | pressure, atm, kPa, psi, bar etc. |
 , pB | partial pressure |
| P | Number of phases |
| P | power, W |
| Pe | dimensionless Peclet number in terms of molecular diffusivity, Eq. (15-33c) |
| Pe | dimensionless Peclet number in terms of eddy diffusivity, Eq. (16-111a) |
| Perf | flow perimeter, Figure 13-33B, m |
| Pr | dimensionless Prandt number, Eq. (15-33f) |
| q | LF/F = (L – L)/F, feed quality |
| q | volumetric flow rate/plate width, m2/s |
| Q | amount of energy transferred, Btu/h, kcal/h, etc. |
| Qc | condenser heat load |
| Qc, QC | volumetric flow rate continuous phase, m3/s |
| Qd, QD | volumetric flow rate dispersed phase, m3/s |
| Qflash | heat loss from flash drum |
| QL | volumetric flow rate of liquid, m3/s |
| QR | reboiler heat load |
| Qz | heat flux in z direction, J/s |
| r | radius of column, ft or m |
| R | gas constant, 1.9859 cal/(mol·K) or 8.314 m3Pa/(mol·K) |
| R | raffinate flow rate (Chapter. 13), kg/h |
| RA | solute radius, m |
 | mass raffinate, kg |
 | Holdup raffinate phase in tank plus settler, kg |
| Re | dimensionless Reynolds number, Eq. (15-33b) |
| Resettler | Reynold’s number for settler, Eq. (13-60a) |
| S | solvent flow rate kmol/h or lbmol/h |
| S | tray spacing, inches, Eq. (10-47) |
| S | moles second solvent in constant-level batch distillation |
| Ŝ | mass of solvent, kg |
| S | solvent flow rate, kg/h |
| ScL | Schmidt number for liquid = μ/(ρD) |
| Scv | Schmidt number for vapor = μ/(ρD) |
| Shc, Shx, Shy | dimensionless Sherwood numbers, Eq. (15-33a) |
| Stc, Stx, Sty | dimensionless Stanton numbers, Eq. (15-33d) |
| t | time, s, min, or h |
| tbatch | period for batch distillation, Eq. (9-28) |
| tdown | down time in batch distillation |
| (tf,95 – t0) | residence time in extractor for 95% extraction, Eq. (16-105), s |
| tL, tV | average residence time per pass for liquid and vapor, s |
 ,residence | liquid residence time, Eq. (16-111c), s |
| tresidence,dispersed | residence time of dispersed phase in settler, s |
| toperating | operating time in batch distillation |
| tres | residence time in downcomer, Eq. (10-30), s, or on plate, Eq. (16-35e) |
| ttray | tray thickness, inches |
| T | temperature, °C, °F, K, or °R |
 | liquid and vapor temperatures on stage j at the interface, K |
| Tref | reference temperature |
| u | vapor velocity, cm/s or ft/s |
| uflood | flooding velocity, Eq. (10-8) |
| uop | operating velocity, Eq. (10-11) |
| uperm | permissible vapor velocity, Eq. (2-64) |
| ut,hindered | hindered settling velocity, Eq. (13-58) |
| ut, ut,Stokes | Stokes’ law terminal velocity, Eq. (13-57), m/s |
| U | underflow liquid rate, (Chapter 14), kg/h |
| Ua | superficial vapor velocity in active area of tray, m/s |
| v | superficial vapor velocity, ft/s |
| vcharacteristic | characteristic velocity of Karr column, Eq. (13-68), m/s |
| vc,flood, vd,flood | continuous and dispersed phase flooding velocities, m/s |
| vo | vapor velocity through holes, Eq. (10-29), ft/s |
| vo,bal | velocity where valve is balanced, Eq. (10-36) |
| VA, VB | component transfer velocities, Eqs, (15-15e, f) |
| vref | reference or basis velocity, Eqs. (15-15c, d) |
| vy | vertical velocity |
| V | vapor flow rate, kmol/h or lbmol/h |
| Vi | molal volume Eq. (13-1) |
| VA | molar volume solute at normal boiling point, m3/kmol |
| Vliq,tank | volume of liquid in tank, m3 |
| Vmax | maximum vapor flow rate |
| Vmixer | volume of liquid in mixing tank, m3 |
| Vsettler | volume settler, m3 |
| Vtank | volume tank, m3 |
| Vsurge | surge volume in flash drum, Eq. (2-68), ft3 |
| VP | vapor pressure, same units as p |
| w | plate width, m |
| WL | liquid flow rate, kg/h or lb/h |
| WL | liquid mass flux, lb/s ft2 or lb/h ft2, (Chapter 16) |
| WV | vapor flow rate, kg/h or lb/h |
| x | weight or mole fraction in liquid |
| x | [L/D – (L/D)min]/(L/D + 1) in Eqs. (7-42) |
| x* | equilibrium mole fraction in liquid |
| xA,ref, xB,ref | fractions to calculate velocity of center of total flux, Eq. (15-17) |
| xi,k, xi,k+1 | trials for integration, Eq. (8-29) |
| xI | interfacial mole fraction in liquid |
| x*out | liquid mole fraction in equilibrium with inlet gas, Eq. (16-35b) |
| X | weight or mole ratio in liquid |
| y | weight or mole fraction in vapor |
| yvol | volume fraction in vapor |
| y* | equilibrium mole fraction in vapor |
| y*out | vapor mole fraction in equilibrium with inlet liquid in countercurrent system, Eq. (16-35a) or in equilibrium with outlet liquid in cocurrent contactor, Eq. (16-71) |
| ylm | log mean difference, Eq. (15-32d) |
| yI | interfacial mole fraction in vapor |
 | mass fraction in vapor |
| Y | weight or mole ratio in vapor |
| z | weight or mole fraction in feed |
| z | axial distance in bed (Chapters 15 and 16) |
| zl | distance from downcomer exit to weir, m |
| a, aj | term in quadratic equations for well-mixed membrane systems, Eqs. (17-10b), (17-74a), and  |
| â | constant in expression to calculate osmotic pressure, kPa/mole fraction, Eq. (17-15a) |
| a′ | constant in expression to calculate osmotic pressure, kPa/weight fraction, Eq. (17-15b) |
| ai | activities, Eq. (17-51) |
| A | membrane area available for mass transfer, cm2 or m2 |
| b, bj | term in quadratic equations for well-mixed membrane systems, Eqs. (17-10c), (17-74b), and  |
| c, cj | term in quadratic equations for well-mixed membrane systems, Eqs. (17-10d), (17-74c) and  |
| c | concentration, g solute/L solution |
| cout | outlet concentration of solute, g/L |
| cp | permeate concentration of solute, g/L |
| cw | concentration of solute at wall, g/L |
| c′ | water concentration in permeate in Figure 17-17 |
| CPL,p | liquid heat capacity of permeate, kJ/(kg °C) |
| CPV,p | vapor heat capacity of permeate, kJ/(kg °C) |
| dt | diameter of tube, cm |
| dtank | tank diameter, cm |
| D | diffusivity in solution, cm2/s |
| Dm | diffusivity in the membrane, cm2/s |
| Fp | volumetric flow rate of permeate, cm3/s |
| Fout | volumetric flow rate of exiting retentate, cm3/s |
| Fsolv | volumetric flow rate of solvent in RO, cm3/s |
 | molar flow rate, mol/s, mol/min, etc. |
| F′ | mass flow rate, g/s, g/min, kg/min, etc. |
| h | ½ distance between parallel plates, cm |
| hin | enthalpy of inlet liquid stream in pervaporation, kJ/kg |
| hout | enthalpy of outlet liquid retentate stream in pervaporation, kJ/kg |
| HA | solubility parameter, cc(STP)/[cm3 (cm Hg)] |
| Hp | enthalpy of vapor permeate stream in pervaporation, kJ/kg |
| k | mass transfer coefficient, typically cm/s, Eq. (17-33) |
| K′solv | permeability of the solvent through membrane, L/(atm m2 day) or similar units |
| j | counter for stage location in staged models in Figure 17-19 |
| J | volumetric flux, cm3/(s cm2) or m3/(m2 day), Eq. (17-1b) |
| J′ | mass flux, g/(s cm2)or g/(m2 day), Eq. (17-1c) |
| Ĵ | mole flux, mol/(s cm2) or kmol/(day m2), Eq. (17-1d) |
| K′A | solute permeability, g/(m s wt frac) |
| Km,i | rate transfer term for multicomponent gas permeation, dimensionless, Eq. (17-11d) |
| L | tube length, cm |
| M | concentration polarization modulus in wt fraction units, dimensionless, Eq. (17-17) |
| Mc | concentration polarization modulus in concentration units, dimensionless, Eq. (17-48) |
| MW | molecular weight, g/mol or kg/kmol |
| N | number of well-mixed stages in models in Figure 17-19 |
| p | pressure, Pa, kPa, atm, mm Hg, etc. |
| pA | partial pressure of species A, Pa, atm, mm Hg, etc. |
| pp | total pressure on the permeate (low pressure) side, Pa, kPa, atm, mm Hg, etc. |
| pr | total pressure on the retentate (high pressure) side, Pa, kPa, atm, mm Hg, etc. |
| PA | permeability of species A in the membrane, cc(STP) cm/[cm2 s cm Hg] |
| R | rejection coefficient in wt frac units, dimensionless, Eq. (17-24a) |
| R° | inherent rejection coefficient (M = 1), dimensionless |
| Rc | rejection coefficient in conc. units, dimensionless, Eq. (17-48) |
| R | tube radius, cm |
| Re | Reynolds number, dimensionless, Eq. (17-35b) |
| Sc | Schmidt number, dimensionless, Eq. (17-35c) |
| Sh | Sherwood number, dimensionless, Eq. (17-35a) |
| tms | thickness of membrane skin doing separation, μm, mm, cm, or m |
| T | temperature, °C |
| Tref | reference temperature, °C |
| ub | bulk velocity in tube, cm/s |
| vsolvent | partial molar volume of the solvent, cm3/gmole |
| x | wt frac of retentate in pervaporation. In binary system refers to more permeable species. |
| xg | wt frac at which solute gels in UF |
| xp | wt frac solute in liquid permeate in RO and UF |
| xr | wt frac solute in retentate in RO and UF |
| y | wt frac of permeate in pervaporation. In binary system refers to more permeable species. |
| yp | mole fraction solute in gas permeate for gas permeation |
| yr | mole fraction solute in gas retentate for gas permeation |
| yr,w | mole fraction solute in gas retentate at membrane wall |
| yt,A | mole fraction solute A in gas that transfers through the membrane |
| a | constant in Langmuir isotherm, same units as q/c, Eq. (18-6c) |
| a | argument for error function, dimensionless, Eq. (18-70), Table 18-7 |
| ap | surface area of the particles per volume, m–1 |
| Ac | cross-sectional area of column, m2 |
| Aw | wall surface area per volume of column for heat transfer, m–1 |
| b | constant in Langmuir isotherm, (concentration)–1, Eq. (18-6c) |
| cA | concentration of species A, kg/m3, kmol/m3, g/L, etc. |
| ci | concentration of species i, kg/m3, kmol/m3, g/L, etc., or |
| ci | concentration of ion i in solution, typically equivalents/m3 |
 | concentration of species i that would be in equilibrium with  , same units as ci |
 | average concentration of solute in pore, same units as ci |
| cpore | fluid concentration at surface of adsorbent pores, same units as ci |
| ci,surface | fluid concentration at surface of particles, εp = 0, same units as ci |
| cRi | concentration of ion i on the resin, typically equivalents/m3 |
| cRT | total concentration of ions on the resin, typically equivalents/m3 |
| cT | total concentration of ions in solution, typically equivalents/m3 |
| Ci | constant relating solute velocity to interstitial velocity, dimensionless, Eq. (18-15e) |
| CP,f | heat capacity of the fluid, cal/(g °C), cal/(mol °C), J/(g K), etc. |
| CP,p | heat capacity of particle including pore fluid, same units CP,f |
| CP,s | heat capacity of the solid, same units as CP,f |
| CP,w | heat capacity of the wall, same units as CP,f |
| dp | particle diameter, cm or m |
| D | desorbent rate in SMB, same units as F |
| D/F | desorbent to feed ratio in SMB, dimensionless |
| Dcol | column diameter, m or cm |
| D | diffusivity including both molecular and Knudsen diffusivities, m2/s or cm2/s |
| Deffective | effective diffusivity, m2/s or cm2/s, Eq. (18-4) |
| DK | Knudsen diffusivity, m2/s or cm2/s, Eq. (18-51) |
| Dmolecular | molecular diffusivity in free solution, m2/s or cm2/s |
| Ds | surface diffusivity, m2/s or cm2/s, Eq. (18-53) |
| erf | error function, Eq. (18-70) and Table 18-7 |
| ED | axial dispersion coefficient due to both eddy and molecular effects, m2/s or cm2/s |
| EDT | thermal axial dispersion coefficient, m2/s or cm2/s |
| Eeff | effective axial dispersion coefficient, same units ED, Eq. (18-68) |
| F | volumetric feed rate, e.g., m3/h, cm3/min, liter/h |
| hp | particle heat transfer coefficient, J/(K s m2) or similar units |
| hw | wall heat transfer coefficient, J/(K s m2) or similar units |
| HETP | height of equilibrium plate, cm/plate, Eq. (18-78b) |
| kf | film mass transfer coefficient, m/s or cm/s |
| km,c | lumped parameter mass transfer coefficient with concentration driving force, m/s or cm/s, Eqs. (18-56a) and (18-57a) |
| km,q | lumped parameter mass transfer coefficient with amount adsorbed driving force, m/s or cm/s, Eqs. (18-56b) and (18-57b) |
| KAB | mass action equilibrium constant for monovalent-monovalent ion exchange, dimensionless, Eq. (18-40a) |
| KA,c | adsorption equilibrium constant in terms of concentration, units are (concentration)-1 |
| K′i,c | linearized adsorption equilibrium constant in terms of concentration, units are units of q/c, Eq. (18-6b) |
| KAo | pre-exponential factor in Arrhenius Eq, (18-7a), same units as KA |
| KA,p | adsorption equilibrium constant in terms of partial pressure, units are (pressure)-1 |
| K′A,p | linearized adsorption equilibrium constant in terms of partial pressure, units are units of qA/pA, Eq. (18-5b) |
| Kd | size exclusion parameter, dimensionless |
| KDB | mass action equilibrium constant for divalent-monovalent ion exchange, same units as cT/cRT, Eq. (18-41) |
| KDE | Donnan exclusion factor, dimensionless, following Eq. (18-44) |
| L | length of packing in column, m or cm |
| LMTZ | length of mass transfer zone, Figure 18-23, m or cm |
| M | molecular weight of solute, g/mol or kg/kmol |
| Mi | multipliers in Eqs. (18-29), dimensionless |
| N | equivalent number of plates in chromatography, Eq. (18-78) |
| NPe | Peclet number, dimensionless, Eq. (18-62) |
| pA | partial pressure of species A, mm Hg, kPa, or other pressure units |
| ph | high pressure, mm Hg, kPa, or other pressure units |
| pL | low pressure, mm Hg, kPa, or other pressure units |
| PeL | Peclet number based on length, dimensionless, Eq. (18-78a) |
| qA | amount of species A adsorbed, kg/kg adsorbent, mol/kg adsorbent, or kg/L |
| qA,max | maximum amount of species A that can adsorb, kg/kg adsorbent, mol/kg adsorbent, or kg/L |
| qF | amount adsorbed in equilibrium with feed concentration, same units as qA |
 | average amount of species i adsorbed, kg/kg adsorbent, mol/kg adsorbent, or kg/L |
 | amount adsorbed that would be in equilibrium with fluid of concentration ci, same units as qA |
| Q | volumetric flow rate, m3/s, L/min, etc. |
| rp | pore radius, m or cm |
| R | resolution, dimensionless, Eq. (18-82) |
| R | gas constant (e.g.,  ) |
| Re | Reynolds number, dimensionless, Eq. (18-60) |
| Sc | Schmidt number, dimensionless, Eq. (18-60) |
| Sh | Sherwood number, dimensionless, Eq. (18-60) |
| t | time, s, min, or h |
| tbr | breakthrough time, s, min, or h |
| tcenter | time center of pattern exits column, s, min, or h, Eq. (18-85b) |
| telution | elution time, s, min, or h |
| tF, tfeed | feed time, s, min, or h |
| tMTZ | time of mass transfer zone, Figure 18-23, s, min, or h |
| tR | retention time, s, min, or h |
| tsw | switching time in SMB, s, min, or h |
| T | temperature, °C or K |
| Tamb | ambient temperature, °C or K |
| Ts | solid temperature, °C or K |
| uion,i | velocity of ion i, m/s or cm/s |
| us | average solute velocity, m/s or cm/s |
 | average of solute velocities for A and B, cm/s, Eq. (18-83) |
| us,ion,i | diffuse wave velocity of ion i, m/s or cm/s |
| ush | shock wave velocity, m/s or cm/s |
| ush,ion,i | shock wave velocity of ion i, m/s or cm/s |
| uth | thermal wave velocity, m/s or cm/s |
| utotal_ion | velocity of total ion wave, m/s or cm/s |
| vA,product | interstitial velocity of A Product if it was in the column, m/s or cm/s = (A Product)/(εe Ac) |
| vB,product | interstitial velocity of B Product if it was in the column, m/s or cm/s = (B Product)/(εe Ac) |
| vD | interstitial velocity of desorbent if it was in the column, m/s or cm/s = D/(εe Ac) |
| vFeed | interstitial velocity of feed if it was in the column, m/s or cm/s = F/(εe Ac) |
| vinter | interstitial velocity, m/s or cm/s, Eq. (18-2b) |
| vsuper | superficial velocity, m/s or cm/s, Eq. (18-2a) |
| Vavailable | volume available to molecule, m3, Eq. (18-1c) |
| Vcolumn | column volume, m3 |
| Vfeed | volume feed gas, m3 |
| Vfluid | volume available to fluid, m3, Eq. (18-1a) |
| Vpurge | volume purge gas, m3 |
| wA, wB | width of chromatographic peak, s, min or hours |
| W | weight of the column per length, kg/m |
| x | deviation from the location of the peak maximum, dimensionless Eq. (18-79) |
| xl | deviation from peak maximum in length units, Eq. (18-80b) |
| xt | deviation from peak maximum in time units, Eq. (18-80a) |
| x | weight or mole fraction solute in liquid, kg solute/kg liquid or kmol solute/kmol liquid, dimensionless |
| xi | = ci/cT equivalent fraction of ion in solution, dimensionless |
| Xbreakthrough (z,t) | general solution for column breakthrough for linear isotherms, same units as c, Eq. (18-72) |
| y | weight or mole fraction solute in gas, kg solute/kg gas, or kmol solute/kmol gas, dimensionless |
| yi | = cRi/cRT equivalent fraction of ion on resin, dimensionless |
| z | axial distance in column, m or cm.
(Measured from closed end for PSA pressure change calculations) |
