Chapter 7, Problem 7.11P

Interpretation Introduction

Interpretation: The diameter of the vessel which just fluidize the catalyst at the given conditions is to be calculated.

Concept introduction: The condition at which particles just fluidize is called minimum fluidized condition and the expression for same is,

  $\frac{\text{ΔP}}{\text{L}}\text{=}{\text{g(1-ε}}_{\text{M}}{\text{)(ρ}}_{\text{p}}\text{-ρ)}\mathrm{.......}\text{(1)}$

In the above formula, the notations used are,

  $\begin{array}{l}\text{ΔP}\text{=}\text{Pressure}\text{drop}\text{through}\text{vessel}\\ \text{L}\text{=}\text{Length}\text{of}\text{the}\text{vessel}\\ {\text{ε}}_{\text{M}}\text{=}\text{Minimum}\text{Bed}\text{porosity}\\ {\text{ρ}}_{\text{p}}\text{=}\text{Density}\text{of}\text{particles}\\ \text{ρ}\text{=}\text{Density}\text{of}\text{air}\\ \text{g}\text{=}\text{Acceleration}\text{due}\text{to}\text{gravity}\end{array}$

The Ergun equation for the particles is given as,

  $\frac{\text{ΔP}}{\text{L}}\text{=}\frac{{\text{150<mover accent="true"><mo>V</mo><mo>¯</mo></mover>}}_{\text{0}}{\text{μ(1-ε)}}^{\text{2}}}{{\varphi }_{\text{s}}{}^{\text{2}}{\text{D}}_{\text{p}}{}^{\text{2}}{\text{ε}}^{\text{3}}}+\frac{\text{1}{\text{.75<mover accent="true"><mo>V</mo><mo>¯</mo></mover>}}_{\text{0}}{}^{\text{2}}\text{ρ(1-ε)}}{{\varphi }_{\text{s}}{\text{D}}_{\text{p}}{\text{ε}}^{\text{3}}}$ ……. (2)

  $\begin{array}{l}\text{ΔP}\text{=}\text{Pressure}\text{drop}\text{through}\text{vessel}\\ \text{L}\text{=}\text{Length}\text{of}\text{vessel}\\ {\text{<mover accent="true"><mo>V</mo><mo>¯</mo></mover>}}_{\text{0}}\text{=}\text{Superficial}\text{velocity}\\ \text{μ}\text{=}\text{Viscosity}\text{of}\text{fluid}\\ \text{ε}\text{=}\text{Bed}\text{porosity}\\ {\text{D}}_{\text{p}}\text{=}\text{Pellet}\text{diameter}\\ {\varphi }_{\text{s}}\text{=}\text{Sphericity}\text{of}\text{particles}\end{array}$

  $\text{ρ=}\text{Density}\text{of}\text{air}$

The density of air can be given as,

  $\text{ρ}\text{=}\frac{\text{PM}}{\text{RT}}\mathrm{.......}(3)$

In the equation (3), notations used are,

P is the pressure at which air enters

M is the molecular weight of air

R is the Universal Gas constant

T is the temperature at which air enters