Energy Balance

Skarstrom offers two thermal models, selected in Column Properties → Energy Balance via the Thermal equilibrium model drop-down.

Local Thermal Equilibrium (LTE)

This is the default. It assumes heat transfer between the gas and solid is fast enough that the two share a single temperature $T$ , so one lumped energy equation is solved per cell.

\left(\epsilon_b C_{p,g} \rho_g + C_{p,s} \rho_b\right) \frac{\partial T}{\partial t} - \lambda \frac{\partial^2 T}{\partial z^2} - \epsilon_b \frac{\partial P}{\partial t} + u C_{p,g} \rho_g \frac{\partial T}{\partial z} + \frac{4 h_i}{d_i} (T - T_w) - \frac{RT}{P}\rho_b\sum_{i=1}^{N}(-\Delta H_i)\frac{\partial{q_i}}{\partial{t}} = 0

Symbol	Description	Unit
$C_{p,g}$	Gas heat capacity	J kg⁻¹ K⁻¹
$C_{p,s}$	Adsorbent heat capacity	J kg⁻¹ K⁻¹
$T$	Gas/Adsorbent temperature	K
$T_w$	Wall temperature	K
$P$	Pressure	Pa
$u$	Superficial velocity	m s⁻¹
$\epsilon_b$	Bed porosity (gas phase only)	-
$\rho_g$	Gas density	kg m⁻³
$\rho_b$	Adsorbent bulk density	kg m⁻³
$\lambda$	Effective axial thermal conductivity	W m⁻¹ K⁻¹
$h_i$	Internal heat transfer coefficient (gas–wall)	W m⁻² K⁻¹
$d_i$	Wall internal diameter	m
$q_i$	Component i mass source	mol kg⁻¹ s⁻¹
$\Delta H_i$	Component i heat of adsorption	J mol⁻¹

The final term is the heat released (or absorbed) by adsorption, using the per-component isosteric heat of adsorption $\Delta H_i$ entered on the Adsorbent Material → Heat of Adsorption tab. The wall-coupling term $\tfrac{4 h_i}{d_i}(T - T_w)$ links this equation to the wall energy balance.

The effective axial thermal conductivity $\lambda$ and the internal coefficient $h_i$ are either constants or computed from the transport correlations.

Local Thermal Non-Equilibrium (LTNE)

When gas–solid heat transfer is not fast (for example large particles or fast cycles), select Local thermal non-equilibrium (LTNE). The solver then carries separate fluid and solid temperature equations coupled by a gas–particle heat transfer term. This requires a Particle heat transfer model and coefficient, described in the transport correlations. With LTNE, the solid temperature is available as its own plotted variable.

Adsorbed-phase heat capacity

The Adsorbed phase heat capacity selector (same tab) controls how the adsorbed molecules' heat capacity is treated:

Constant — enter a molar heat capacity per component.
Gas phase — the adsorbed-phase heat capacity is taken equal to the gas-phase value.

Energy source (heating / cooling)

Any step can apply a heat duty to a layer — the basis of temperature swing (TSA) operation. On the Step Data → Energy Sources tab, tick a layer and enter a Power [W]; positive values heat the layer, negative values cool it. The duty is distributed over the layer and added as a source term to the energy balance for the duration of that step.