Gas properties

Gas properties#

This property package provides the gas phase properties for the oxidation of a chemical looping combustion oxygen carrier. The components modeled are oxygen, nitrogen, carbon dioxide, and water.

Flow basis: Molar

Units: SI units

State Variables:

The state block supports the following state variables:

  • Component molar flowrate in mol/s,

  • Pressure in bar,

  • Component mole fraction in (dimensionless),

  • Temperature in K

Lists:

  • Component list - [O2, N2, CO2, H2O]

  • Shomate parameter list - [1 to 8]

  • Viscosity parameter list - [1 to 4]

  • Thermal conductivity parameter list - [1 to 4]

Parameters:

Parameter Name

Symbol

Description

Units

Reference

mw_comp

\(mw_{j}\)

Molecular weights of gas components indexed by component list

kg/mol

[1]

enth_mol_form_comp

\(H_{form,j}\)

Component molar heats of formation indexed by component list

J/mol

[1]

cp_param

\(CP_{j,i}\)

Heat capacity parameters indexed by component list and shomate list

[1]

visc_d_param

\(\mu_{param,j,i}\)

Viscosity parameters indexed by component list and viscosity list

[2]

therm_cond_param

\(k_{param,j,i}\)

Thermal conductivity parameters indexed by component list and thermal conductivity list

[2]

diff_vol_param

\(V_{param,j}\)

Diffusion volume parameters indexed by component list

[3]

gas_const

\(R\)

Gas constant

kJ/mol.K

Variables:

Variable Name

Symbol

Description

Units

flow_mol

\(F_{mass}\)

Component molar flowrate

mol/s

pressure

\(P\)

Pressure

bar

mole_frac_comp

\(y_{j}\)

Component mole fractions indexed by component list

None

temperature

\(T\)

Temperature

K

mw

\(mw\)

Molecular weight of gas mixture

kg/mol

dens_mol

\(C_{g}\)

Molar density/concentration

mol/m3

dens_mol_comp

\(C_{g,j}\)

Component molar concentration indexed by component list

mol/m3

dens_mass

\(\rho_{mass}\)

Mass density

kg/m3

visc_d

\(\mu_{vap}\)

Mixture dynamic viscosity

kg/m.s

diffusion_comp

\(D_{vap,j}\)

Component diffusion in a gas mixture indexed by component list

cm2/s

therm_cond

\(k_{vap}\)

Thermal conductivity of gas

kJ/m.K.s

cp_mol_comp

\(c_{p,mol,j}\)

Pure component molar heat capacities indexed by component list

J/mol.K

cp_mol

\(c_{p,mol}\)

Mixture heat capacity, mole-basis

J/mol.K

cp_mass

\(c_{p,mass}\)

Mixture heat capacity, mass-basis

J/kg.K

enth_mol_comp

\(H_{mol,j}\)

Pure component enthalpies indexed by component list

J/mol

enth_mol

\(H_{mol}\)

Molar enthalpy of gas mixture

J/mol

Methods:

Sum of component fractions:

\[1 = \sum_j{y_{j}}\]

Molecular weight of gas mixture:

\[mw = \sum_j{y_{j}mw_{j}}\]

Molar density:

\[C_{g} = 100 \frac{P}{RT}\]

Component molar density:

\[C_{g,j} = y_{j}C_{g}\]

Mass density:

\[\rho_{mass} = mwC_{g}\]

Mixture dynamic viscosity, see reference [2] for parameters:

\[\mu_{vap} = \sum_i{\frac{y_{i}\mu_{i}}{\sum_j{y_{j}{\left(\frac{mw_{j}}{mw_{i}}\right)}^{0.5}}}}\]
\[\mu_{i} = \frac{\mu_{param,j,1}T^{\mu_{param,j,2}}}{1 + \frac{\mu_{param,j,3}}{T} + \frac{\mu_{param,j,4}}{T^2}}\]

Thermal conductivity, see reference [2] for parameters:

\[k_{vap} = \sum_i{\frac{y_{i}k_{i}}{\sum_j{y_{j}A_{j,i}}}}\]
\[k_{i} = \frac{k_{param,j,1}T^{k_{param,j,2}}}{1 + \frac{k_{param,j,3}}{T} + \frac{k_{param,j,4}}{T^2}}\]
\[A_{j,i} = \frac{{\left(1 + {\left( \frac{k_{j}}{k_{i}} \right)}^{0.5} {\left( \frac{mw_{j}}{mw_{i}} \right)}^{0.25} \right)}^{2}} {{{8{\left(1 + {\left(\frac{mw_{j}}{mw_{i}}\right)} \right)}}}^{0.5}}\]

Diffusion of component in a multicomponent gas mixture, see reference [3] for parameters:

\[D_{vap,j} = \frac{1 - y_{j}} {\sum_{j,j ≠ i}{\frac{y_{i}}{D_{j,i}}}}\]
\[D_{j,i} = \frac{{0.00143} T^{1.75} {\left( \frac{1}{mw_{j}} + \frac{1}{mw_{i}} \right)}^{0.5} } {{P {\left( {V_{param,j}^{\frac{1}{3}}} {V_{param,i}^{\frac{1}{3}}}\right)} }^{2}}\]

Molar heat capacity of component, see reference [1]:

\[c_{p,mol,j} = CP_{j,1} + CP_{j,2}\bar{T} + CP_{j,3}\bar{T}^2 + CP_{j,4}\bar{T}^3 + \frac{CP_{j,5}}{\bar{T}^2}\]
\[\bar{T} = 10^{-3}T\]

Molar heat capacity of gas mixture:

\[c_{p,mol} = \sum_j{c_{p,mol,j}y_{j}}\]

Mass heat capacity of gas mixture:

\[c_{p,mass} = \frac{c_{p,mol}}{mw}\]

Molar enthalpy of component, see reference [1]:

\[H_{mol,j} = P_{j,1} + P_{j,2}\bar{T} + P_{j,3}\bar{T}^2 + P_{j,4}\bar{T}^3 + \frac{P_{j,5}}{\bar{T}^2}\]
\[\bar{T} = 10^{-3}T\]

Molar enthalpy of gas mixture:

\[H_{mole} = \sum_j{H_{mol,j}y_{j}}\]

References:

  1. National Institute of Standards and Technology, NIST Chemistry WebBook, (n.d.). (accessed March 10, 2018).

  2. R.H. Perry, D.W. Green, Perry’s Chemical Engineering Handbook, 1997, McGraw-Hill, n.d.

  3. Poling, B.E., Prausnitz, J.M. and O’connell, J.P., 2001. Properties of gases and liquids. McGraw-Hill Education.