APPENDIX B List of Variables

Thermodynamic Model

VARIABLE        DESCRIPTION                                                         UNITS

CpA                     Specific heat of vapor                                                 J/Kg K

CpAN             Specific heat of combined gas--funct. of T                 J/Kg K

CpL                     Specific heat of condensate                                         J/Kg K

CpN1             Specific heat of carrier gas in the tube                        J/Kg K

EnthN1             Sensible heat change for nitrogen gas T2 to T1`                 J/Kg

EnthN2             Sensible heat change for nitrogen gas T3 to T2                 J/Kg

EnthL             Sensible heat change of liquid condensate                 J/Kg

EnthA             Sensible heat change of vapor                                         J/Kg

EnthAN             Sensible heat change of vapor and                                  J/Kg

                            carrier gas T3 to T2

hA                     Latent heat of condensation for condensate                 J/Kg

hLN                     Latent heat of evaporation for carrier gas                 J/Kg

J5                     Reduced temperature of vapor                                 ------

m1dot           Mass flow rate of vapor and carrier gas at the                 Kg/s

    initial concentration

m2dot           Mass flow rate of vapor and carrier gas at the final            Kg/s

                           concentration

mLdot             Mass flow rate of condensate                                              Kg/s

mLNdot             Mass flow rate of carrier gas in the tube                              Kg/s

MWA             Molecular weight of vapor                                                   g/g-mol

MWN             Molecular weight of carrier gas                                           g/g-mol

MWT1                 Average molecular weight of combined gas at the initial  g/g-mol

                            concentration

MWT2        Average molecular weight of combined gas at the final        g/g-mol

                        concentration

P            Condenser operating pressure                                 Pa

Q1 Volumetric flow rate of combined gas at the final temperature m^3/s

Q2 Volumetric flow rate of combined gas at the final temperature m^3/s

R Ideal gas constant Nm/Kkgmol

rho1 Combined bulk gas density in the shell at the initial Kg/m³

temperature

rho2 Combined bulk gas density in the shell at the final Kg/m³

temperature

T1 Initial temperature of the refrigerant K

T2 Final temperature of refrigerant and vapor/carrier gas mixture K

T3 Initial temperature of the vapor and carrier gas mixture K

TaveA Average temperature of bulk gas in the element K

TaveN1 Average temperature of refrigerant K

TaveN2 Average temperature of carrier gas K

xA1 Mole fraction of vapor at the initial temperature ------

xA2 Mole fraction of vapor at the final temperature ------

xAave Average mole fraction of the vapor ------

xN1 Mole fraction of carrier gas at the initial temperature ------

xN2 Mole fraction of carrier gas at the final temperature ------

List of Variables: Mass Transfer Model

Variable Description Units

AAN Viscosity fitting parameter ------

Chapman-Enskog method--non-polar gas

Ak12 Combined gas conductivity fitting parameter ------

Lindsay-Bromley Modification

Ak21 Combined gas conductivity fitting parameter ------

Lindsay-Bromley Modification

Aouter12 Combined gas viscosity fitting parameter ------

Reichenberg Method w/ Brokaw Approximation

Aouter21 Combined gas viscosity fitting parameter ------

Reichenberg Method w/ Brokaw Approximation

area1 Heat transfer cylindrical surface area m²

area2 Outer tube cylindrical area m²

area3 Heat transfer cross-sectional area m²

area4 Inner tube cross-sectional area m²

area5 Inner tube cylindrical surface area m²

Astar Viscosity atomic bond parameter ------

Reichenberg Method

BBN Gas viscosity fitting parameter ------

Chapman-Enskog method--non-polar gas

CCN Gas viscosity fitting parameter ------

Chapman-Enskog method--non-polar gas

CpA Specific heat of vapor J/Kg K

CpAN Specific heat of combined gas--funct. of T J/Kg K

CpL Specific heat of condensate J/Kg K

CpN1 Specific heat of the refrigerant in the tube J/Kg K

CpN2 Specific heat of carrier gas in the shell J/Kg K

Cs Combined gas conductivity parameter ------

Cs = 0.73 for polar gas in mixture

Lindsay Bromley Modification

DDN Gas viscosity fitting parameter ------

Chapman-Enskog method--non-polar gas

De Heat transfer effective diameter m

4 H Flow area / wetted perimeter

deltaAce Viscosity Stockmayer parameter ------

based on dipole moment--delta>0.1 is

considered a polar gas

dHvb Condensate conductivity parameter--molal heat ------

of vaporization at the normal boiling point

Dii Diameter of inside tube m

Din Diameter of inside condensation area--i.e. outside m

tube

dipoleAce Dipole moment of acetone ------

Dout Diameter of outside condensation area--i.e. inside m

shell

dPlmAC Log-mean partial pressure difference between bulk Pa

vapor and the condensate film from i to i+1

dSstar Condensate conductivity--Entropy at normal ------

boiling point

dTlmAC Log-mean temperature difference between the bulk K

mixture and the condensate film from i to i+1.

dTlmALN Log mean temperature difference between the bulk K

mixture and the tube side refrigerant from i to i+1

dTlmAW Log mean temperature difference between the bulk K

mixture and the copper wall from i to i+1

dTlmNC Log mean temperature difference between the condensate K

film and the tube side refrigerant from i to i+1

dTlmNW Log-mean temperature difference between the wall K

and the tube side refrigerant from i to i+1

dx Element axial length from i to i+1 m

EEN Gas viscosity fitting parameter ------

Chapman-Enskog method--non-polar gas

Enth1 Latent and sensible heats of vaporization for W

refrigerant in the tube

Enth2 Latent heat of vapor condensation and sensible W

heats for vapor and gas mixture in shell

Enth3 Total heat determined from heat transfer W

resistance

Enth4 Heat transfer from tube side refrigerant to the W

condenser wall

Enth5 Heat transfer from bulk mixture to the condenser W

wall

Enth6 Heat transfer from the bulk mixture to the W/m²

condensate film

Enth7 Heat transfer from the tube side refrigerant to the W/m²

condensate film

EnthN1 Sensible heat change for nitrogen gas T2 to T1` J/Kg

EnthN2 Sensible heat change for nitrogen gas T3 to T2 J/Kg

EnthL Sensible heat change of liquid condensate J/Kg

EnthA Sensible heat change of vapor J/Kg

EnthAN Sensible heat change of vapor and carrier gas T3 to T2 J/Kg

epskA Potential energy constant / Boltzmann?s constant ------

for vapor gas--Viscosity determination--Brokaw

Approximation--determination of Vb

epskN Potential energy constant / Boltzmann?s constant ------

for gas--Viscosity determination--Brokaw

Approximation

FFN Gas viscosity fitting parameter ------

Chapman-Enskog method--non-polar gas

gamma Density of condensate fitting parameter based on ------

the reduced temperature

Gave Average mass flow rate of acetone from the bulk Kg/s m²

mixture into liquid form

GLA Mass flow rate of liquid refrigerant normalized to Kg/s m²

flow area

grav Acceleration due to gravity m/s²

h1 Convective heat transfer film coefficient of W/m² K

the gas film mixture

h2 Convective film coefficient of the condensate film W/m² K

h3 Convective film coefficient of the tube side refrigerant W/m² K

gas film

hA Latent heat of condensation for vapor J/Kg

HHkLA Refrigerant thermal conductivity parameter based

on functional groups method of Robbins and Kingrea

hLAP Latent heat of condensation for vapor modified by J/Kg

the Jakob Number

hLN Latent heat of evaporation for the refrigerant J/Kg

J7 Reduced temperature of vapor ------

JA Jakob Number ------

Jfactor Condensate viscosity parameter based on molecular bonds ------

Morris Method

kAce Thermal conductivity of vapor W/m K

kAceref Reference temperature for thermal conductivity W/m K

of the vapor

kAN Combined gas thermal conductivity W/m K

Wassiljewa Equation w/ Lindsay and Bromley mod.

kc Thermal conductivity of 99.9% pure copper W/m K

kd Molecular diffusivity m²/s

Gilliand Equation

Kg Mass transfer coefficient Kg g-mol

s m² Pa g

kLA Thermal conductivity of the condensate W/m K

Method of Robbins and Kingrea

kNG Thermal conductivity of refrigerant gas in tube W/m K

kNG2 Thermal conductivity of carrier gas in shell W/m K

kNGref Thermal conductivity reference for nitrogen gas W/m K

at 230 K

m1dot Mass flow rate of the vapor and carrier gas at the Kg/s

shell side outlet

m2dot Mass flow rate of the vapor and carrier gas at the Kg/s

shell side inlet

mLdot Mass flow rate of condensate Kg/s

mLNdot Mass flow rate of liquid refrigerant in the tube Kg/s

MWA Molecular weight of acetone g/g-mol

MWANave Average molecular weight of combined shell gas g/g-mol

MWN Molecular weight of nitrogen g/g-mol

MWTA1 Average molecular weight of combined gas at the g/g-mol

outlet of the shell

MWTA2 Average molecular weight of combined gas at the g/g-mol

inlet of the shell

mwx12 Combined gas viscosity molecular scaling parameter ------

Brokaw Approximation

MWy12 Combined gas viscosity molecular scaling parameter ------

Brokaw Approximation

NNkLA Condensate thermal conductivity parameter based ------

on functional groups

Method of Robbins and Kingrea

NuA Atomic volume of acetone for Gilliand Diffusivity Equation ------

NuN Atomic volume of nitrogen for Gilliand Diffusivity Equation ------

OMEGAvN1 Neufeld empirical equation for computation of Chapman ------

Enskog Non-polar gas viscosity in the tube

OMEGAvNO Neufeld empirical equation for computation of Chapman ------

Enskog Non-polar gas viscosity in the shell

OMEGAvNOc Neufeld empirical equation for computation of Chapman ------

Enskog Non-polar gas viscosity at the gas-condensate

interface

OMEGAvNw Neufeld empirical equation for computation of Chapman ------

Enskog Non-polar gas viscosity at the tube side wall

omrhoLA Accentric factor used in determining the density of liquid ------

acetone using the Gunn and Yamada equation

P Condenser operating pressure Pa

Pa1 Partial pressure of vapor at the outlet of the element Pa

Pa2 Partial pressure of vapor at the inlet of the element Pa

Pa2n Dummy variable to prevent Pa1 from exceeding Pa2 during Pa

computational solutions

Pc Partial pressure of vapor at the gas-condensate interface Pa

Pcn Dummy variable to prevent Pc from exceeding Pa1 during Pa

computational solutions

PHI12 Combined gas viscosity parameter for bulk flow in shell ------

Brokaw Approximation

PHI12c Combined gas viscosity parameter for bulk flow at condensate ------

film--Brokaw Approximation

PHI21 Combined gas viscosity parameter for bulk flow in shell ------

Brokaw Approximation

PHI21c Combined gas viscosity parameter for bulk flow at condensate ------

film--Brokaw Approximation

PNb Average bulk nitrogen partial pressure in the element Pa

PNc Average carrier gas partial pressure at the gas-condensate Pa

interface

Pngf Log-mean pressure difference of carrier gas between the bulk Pa

and gas-condensate interface

QAN1 Volumetric flow rate of combined gas at the element outlet m³/s

QAN2 Volumetric flow rate of combined gas at the element inlet m³/s

R Ideal gas constant Nm/Kkgmol

rhoAN1 Combined bulk gas density in the shell at the element outlet Kg/m³

rhoAN2 Combined bulk gas density in the shell at the element inlet Kg/m³

rhoANave Combined bulk gas density average in the shell Kg/m³

rhoLA Density of condensate Kg/m³

Sace Sutherland constant for determining combined gas ------

conductivity

Sacenit Sutherland constant for determining combined gas ------

conductivity

sigmaN Stockmeyer potential parameter for determination of carrier ------

gas viscosity

Snit Sutherland constant for determining combined gas ------

conductivity

Souter12 Combined gas viscosity parameter for polar--non-polar mixtures ------

Brokaw approximation

Souter12c Combined gas viscosity parameter for polar--non-polar mixtures ------

Brokaw approximation

Souter21 Combined gas viscosity parameter for polar--non-polar mixtures ------

Brokaw approximation

Souter21c Combined gas viscosity parameter for polar--non-polar mixtures ------

Brokaw approximation

TA1 Temperature of bulk gas in shell at the outlet K

TA1n Dummy variable to prevent TA1 from exceeding TA2 in K

computation

TA2 Temperature of bulk gas in shell at the inlet K

TaveA Average temperature of bulk gas in the element K

TaveN1 Average temperature of refrigerant in tube in the element K

TboilingA Normal boiling temperature of acetone K

TboilingN Normal boiling temperature of nitrogen K

Tc Temperature at the gas-condensate interface K

TN1 Temperature of refrigerant at the tube inlet K

TN2 Temperature of refrigerant at the tube outlet K

TrAc Reduced temperature of vapor at the gas-condensate ------

interface

TrAce Reduced temperature of vapor in the bulk shell flow ------

TrefA Reference temperature of acetone (373 K) K

TrefN1 Reference temperature of nitrogen (230 K) K

TrLA Reduced temperature of condensate ------

TrLAR Reduced temperature of reference liquid acetone temperature ------

TstarAc k T/ epsilon--parameter used in determination of vapor gas ------

viscosity at gas-condensate interface

TstarAce k T/ epsilon--parameter used in determination of vapor gas ------

viscosity in shell side

TstarN1 k T/ epsilon--parameter used in determination of carrier gas ------

viscosity in tube side

TstarNOc k T/ epsilon--parameter used in determination of carrier gas ------

viscosity at gas-condensate interface

TstarNO k T/ epsilon--parameter used in determination of carrier gas ------

viscosity in shell side

TstarNw k T/ epsilon--parameter used in determination of carrier gas ------

viscosity in tube side at wall

Tw Temperature of copper tube wall K

U1 Thermal resistance between bulk tube and bulk shell W/m² K

temperatures

U2 Thermal resistance between bulk tube and tube wall W/m² K

temperatures

U3 Thermal resistance between bulk shell and tube wall W/m² K

temperatures

U4 Thermal resistance between bulk tube and condensate W/m² K

temperatures

VboilingA Normal specific volume of acetone at the boiling point ------

VisAce Gas viscosity of acetone in the bulk shell side--used in ------

determination of combined gas viscosity

VisAcec Gas viscosity of acetone at the gas-condensate interface--used ------

in determination of combined gas viscosity at the interface

VisAN Combined gas viscosity in the shell N s/m²

VisANc Combined gas viscosity at the gas-condensate interface N s/m²

VisLA Condensate viscosity N s/m²

VisLAplus Reference parameter used in determining liquid acetone ------

viscosity--Morris Method

VisNG Viscosity of refrigerant in the tube N s/m²

VisNGO Gas viscosity of carrier gas in the shell used in determining ------

combined gas viscosity

VisNGOc Viscosity of carrier gas at the gas-condensate interface ------

VisNGw Viscosity of carrier gas at the tube side wall N s/m²

Vro Liquid acetone density parameter relating reduced ------

temperatures

VrrhoLA Liquid acetone density parameter relating reduced ------

temperatures

xA1 Mole fraction of vapor in the shell side gas outlet ------

xA2 Mole fraction of vapor in the shell side gas inlet ------

xAave Average mole fraction of vapor in the element ------

xAc Mole fraction of vapor at the gas-condensate interface ------

xN1 Mole fraction of carrier gas in the shell side gas outlet ------

xN2 Mole fraction of carrier gas in the shell side gas inlet ------

xNave Average mole fraction of carrier gas in the element ------

xNc Mole fraction of carrier gas at the gas-condensate interface ------