Mass Balance | Skarstrom Docs

Overall Mass Balance

The overall mass balance ensures mass conservation throughout the packed bed.

\epsilon_t(\frac{1}{P}\frac{\partial P}{\partial t} - \frac{1}{T}\frac{\partial T}{\partial t}) + \frac{T}{P}\frac{\partial}{\partial z}(\frac{u P}{T}) + \frac{RT}{P}\rho_b\sum_{i=1}^{N}\frac{\partial{q_i}}{\partial{t}} = 0

Symbol	Description	Unit
$P$	Pressure	Pa
$T$	Temperature	K
$\epsilon_t$	Total void fraction	-
$u$	Superficial velocity	m s⁻¹
$q_i$	Component i mass source	mol kg⁻¹ s⁻¹
$t$	Time	s
$z$	Axial coordinate	m
$R$	Ideal gas constant	J mol⁻¹ K⁻¹

Component Mass Balance

The component mass balance accounts for axial dispersion, convection, and adsorption/desorption accordnig to the rate model selected. Axial dispersion can be constant or calculated from different empirical equations.

\epsilon_t (\frac{\partial y_i}{\partial t} + \frac{y_i}{P}\frac{\partial P}{\partial t} - \frac{y_i}{T}\frac{\partial T}{\partial t}) + \frac{T}{P} \frac{\partial}{\partial z}(\frac{u y_i P}{T}) - \epsilon_b \frac{T}{P}\frac{\partial}{\partial z}(\frac{D_{ax} P}{T} \frac{\partial y_i}{\partial z}) + \frac{RT}{P} \rho_b \frac{\partial q_i}{\partial t} = 0

Symbol	Description	Unit
$y_i$	Mole fraction of component $i$ in gas phase	-
$P$	Pressure	Pa
$T$	Temperature	K
$\epsilon_b$	Bed void fraction	-
$u$	Superficial velocity	m s⁻¹
$D_{ax}$	Axial disperion coefficient	m² s⁻¹
$q_i$	Component i mass source	mol kg⁻¹ s⁻¹
$t$	Time	s
$z$	Axial coordinate	m
$R$	Ideal gas constant	J mol⁻¹ K⁻¹