Estimates packed bed pressure drop based on Ergun equation along with minimum fluidization and maximum superficial velocity.
Ergun Equation
\displaystyle \displaystyle \frac{\Delta P}{L} = 150\frac{\mu_f V \left( 1 - \varepsilon \right)^2 }{\phi_s^2 D_p^2 \varepsilon^3} + 1.75\frac{\rho_f V^2 \left( 1 - \varepsilon \right) }{\phi_s D_p \varepsilon^3}
Minimum Fluidization Velocity, Vmf
At minimum fluidization, pressure drop across bed is balanced by effective weight of the particle.
\displaystyle \displaystyle \left( \rho_p -\rho_f \right)g = 150\frac{\mu_f V_{mf} \left( 1 - \varepsilon_{mf} \right) }{\phi_s^2 D_p^2 \varepsilon_{mf}^3} + 1.75\frac{\rho_f V_{mf}^2}{\phi_s D_p \varepsilon_{mf}^3}
Maximum Velocity, Vmax
Beyond maximum superficial velocity, particles will be carried away by the gas and will leave at the bed exit.
\displaystyle \displaystyle V_{max} = \frac{g D_p^2 \left( \rho_p -\rho_f \right)}{18 \mu_f}
Plot for Pressure Drop, ΔP