Unit Operations Of Chemical Engineering
Unit Operations Of Chemical Engineering
7th Edition
ISBN: 9789339213237
Author: MCCABE, WARREN
Publisher: Tata McGraw-Hill Education India
Question
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Chapter 7, Problem 7.15P

(a)

Interpretation Introduction

Interpretation:

The minimum fluidization velocity for the particle is to be determined.

Concept Introduction:

The velocity at which the drag force of the upward moving gas is equal to the apparent weight of the particle is known as the minimum fluidization velocity. In other words, it is the superficial velocity at which the bed of particle is just fluidized.

The minimum fluidization velocity is obtained at the incipient fluidization.

At incipient fluidization,

  ΔPL=g(1-εM)(ρp-ρ) ...... (1)

The notations used here are,

  ΔP = Pressure drop

L = Length of bed

g = Acceleration due to gravity

  ρ = Density of the fluid

  ρp = Density of the particle

  εM = Minimum bed porosity

The Ergun equation for the bed is given as,

  ΔPL=150V ¯0μ(1-ε)2ϕs2Dp2ε3+1.75V ¯02ρ(1-ε)ϕsDpε3 ...... (2)

The notations used here are,

  V ¯0 = Superficial velocity

Dp = Diameter of the particle

  ϕs = Sphericity of the particle

  ε = Bed porosity

  μ = Fluid viscosity

Combine equation (1) and (2),

  g(1-εM)(ρp-ρ)=150V ¯0Mμ(1-εM)2ϕs2Dp2εM3+1.75V ¯0M2ρ(1-εM)ϕsDpεM3 ...... (3)

  V ¯0M = Minimum fluidization velocity

The density of gas can be given as,

  ρ=PMRT.......(4)

In the equation (3), notations used are,

P is the pressure at which gas enters

M is the molecular weight of gas

R is the Universal Gas constant

T is the temperature at which gas enters

(b)

Interpretation Introduction

Interpretation:

For the given expansion of the bed the reason for the difficulty in prediction of the gas velocity is to be mentioned.

Concept Introduction:

The bed expansion is due to the space occupied by the gas bubbles.

In bubbling fluidization, the gas passes through the bed as bubbles or voids which is free from the solids.

The bed expansion can be given as,

  LLM=ub-V ¯0Mub-V ¯0 ...... (1)

The notations used here are,

L = Bed height

LM = Minimum bed height

  ub = Average bed velocity

  V ¯0 = Superficial velocity

  V ¯0M = Minimum fluidization velocity

The bubble velocity is given as,

  ub=0.7gDb ...... (2)

g = Acceleration due to gravity

  Db = Bubble diameter

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Do question 9 please! Question 7 Is just there for reference!!
7) You are tasked with separating two proteins by ion exchange chromatography on a 30 cm long column with an inner diameter of 2 cm. The resin has a diameter of 100 μm and a void fraction of 0.3, and your mobile phase flows through the column at a rate of Q = 5 cm³/min. The Van Deemter coefficients A, B, and C have been determined to be 0.0228 cm, 0.0036 cm²/min, and 0.00053 min, respectively, for both proteins. Protein A elutes from the column with an average retention time of 27 min and standard deviation of 0.8 min. Protein B elutes from the column. with an average retention time of 33.8 min and standard deviation of 1.0. a) How many theoretical plates does the column contain? b) What flow rate (Q) will give you the maximum resolution? c) What is the minimum height of a theoretical plate for the system?
4) A fixed bed adsorption unit contains rigid (incompressible) silica particles with a diameter of 120 um and porosity of 0.3. The resin bed is 200 cm long and has a diameter of 15 cm. A protein solution is pumped into the column at a rate of 50 L/min, and the mobile phase has a viscosity of 1.2 CP. a) What is the pressure drop for this system (in bar)? b) What would be the pressure drop if the particle diameter were decreased to 30 μm?
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