1. Adsorption Zone Mass Balance & Sieve Inventory
In a dynamic fixed bed, the total required molecular sieve mass per active dehydrating tower balances the equilibrium zone capacity (\(q_e\)) and the mass transfer zone (\(MTZ\)):
\[ M_{bed} = \frac{W_{cycle}}{q_{design}} \cdot f_{MTZ} \]
Where \(W_{cycle} = \dot{m}_{H_2O} \cdot t_{ads}\) is total water adsorbed per cycle, \(q_{design}\) is the design desiccant loading (typically 9 to 13 wt% for Type 4A after aging), and \(f_{MTZ}\) is the mass transfer zone correction factor (typically 1.15 to 1.30).
2. Superficial Velocity & Bed Anti-Fluidization Limit
To avoid crushing the fragile extruded zeolite pellets or spherical beads, upward gas superficial velocity must remain below the Ledoux fluidization threshold:
\[ v_s = \frac{Q_{actual}}{A_{bed}} \qquad v_{max} = C_f \sqrt{\frac{\rho_b \cdot d_p}{\rho_g}} \]
In downward-flow dehydration service, bed diameter is selected to maintain superficial velocity between 0.12 and 0.35 m/s (24 to 70 ft/min).
3. Packed Bed Pressure Drop: The Ergun Equation
The frictional pressure gradient across the packed bed of desiccant is governed by the Ergun equation combining viscous and inertial drag:
\[ \frac{\Delta P}{L} = 150 \frac{(1 - \epsilon)^2}{\epsilon^3} \frac{\mu v_s}{d_p^2} + 1.75 \frac{1 - \epsilon}{\epsilon^3} \frac{\rho_g v_s^2}{d_p} \]
4. Regeneration Thermal Duty
Thermal regeneration heating duty requires heating desiccant, steel shell, and adsorbed water, plus water desorption enthalpy (\(\approx 4,180\text{ kJ/kg}\)):
\[ Q_{reg} = 1.15 \left[ M_{sieve} C_{ps} \Delta T + M_{steel} C_{pm} \Delta T + W_{cycle} \left( \Delta H_{des} + C_{pw} \Delta T \right) \right] \]