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Real Reactors. Fixed Bed Reactor – 1 . (1) The catalyst are held in place and do not move, (2) Material and energy balance must be conducted for fluid in (a) the interstices of particles (inter-particle space) and (b) within the particle (intra-particle space),

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slide1

Real Reactors

Fixed Bed Reactor – 1

(1) The catalyst are held in place and do not move,

(2) Material and energy balance must be conducted for fluid in (a) the interstices of

particles (inter-particle space) and (b) within the particle (intra-particle space),

(3) Reaction occurs only within the catalyst particles,

(4) Reaction in bulk fluid is approximately zero.

slide2

Real Reactors

Fixed Bed Reactor – 2

(5) Catalytic Reaction Steps

(a) transport of reactants and energy from bulk liquid to the catalyst pellet

surface,

(b) transport of reactants and energy from pellet surface to pellet interior,

(c) adsorption of reactants, chemical reaction and desorption of products at

catalytic sites,

(d) transport of products from the pellet interior to the surface,

(e) transport of products into the bulk fluid.

- usually one or at most two of the five steps are rate limiting and dictate,

- most often it is the intra-particle transport step

slide3

Fixed Bed Reactors

Catalyst Bed

  • Single pellet model is established by averaging the microscopic processes that occur within the intra-particle environment,
  • An effective diffusion coefficient is used to
  • represent the information about the
  • physical diffusion process
  • and pore structure,
  • A viable commercial catalyst must have sufficient
  • active sites to maintain a product formation rate
  • in the order of 1 mol/L h,
  • Catalyst pellets usually takes the shape of spheres
  • (0.3-0.7 cm), cylinders (0.3-1.3 cm O.D. and
  • L/O.D. = 3-4) and rings (ca. 2.5 cm)
slide4

Fixed Bed Reactors

General Balances

Catalyst Particle

  • Material Balance
  • where
slide5

Fixed Bed Reactors

General Balances

Catalyst Particle

  • Energy Balance
  • where
slide6

Fixed Bed Reactors

Catalyst

  • Catalyst (usually metal sometimes also metal oxides) is often dispersed onto large surface area support material,
  • The support is often a refractor, metal oxide such as alumina. Silica, clay, zeolite, carbonaceous (e.g., activated carbon and graphite) are also popular support material.
  • The support often have surface areas between 0.05-100 m2/g.
slide7

Fixed Bed Reactors

Catalyst Pellets – 1

  • Catalyst pellets are made by tableting and extrusion methods. The latter is the more popular method,
  • Different pellet shape and size could be obtained by simply changing the extruder head,
  • The pellet shape and size could be optimized to increase mass transfer rates, while minimizing the pressure drop in the reactor.
slide8

Fixed Bed Reactors

Catalyst Pellets – 2

  • The pellet void fraction or porosity, where rp is the effective pellet density and Vg is the pore volume,
  • The pore volume range fro, 0.1-1 cm3/g pellet,
  • The pellet can possess either a uniform pore size or a bimodal pores of two different sizes, a large size to facilitate transport and a small size to contain the active catalyst sites.
slide9

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 1

  • Material balance
  • Steady-state
  • Spherical coordinate system
slide10

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 2

  • Boundary conditions

absence of driving force

slide11

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 3

  • Dimensionless equation - 1
  • characteristic length:
  • dimensionless length: dimensionless concentration:

concentration scale

length scale

slide12

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 4

  • Dimensionless equation – 2
  • where
slide13

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 5

  • Simplification
  • where
slide14

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 6

  • General solution
  • Specific solution
slide15

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 7

  • Concentration profile in pellet
slide16

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 8

  • Total productivity in pellet
  • letting
slide17

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 9

  • Effectiveness factor – 1
  • where
  • = 1 : the entire pellet volume is reacting at the same high rate because reactant is able to diffuse quickly through the pellet,
  • = 0 : the pellet reacts at a slow rate, since the reactant is unable to penetrate into the pellet interior.
slide18

Single Pellet Reaction

First-Order Reaction

(1) Spherical Pellet – 9

  • Effectiveness factor – 2
slide19

Single Pellet Reaction

Example – 1

The first order, irreversible reaction took place in a 0.3 cm radius spherical catalyst pellet at T = 450 K.

At 0.7 atm partial pressure of A, the pellet’s production rate is –2.5 x 10-5 mol/g-s, what is the production rate at the same temperature for a 0.15 cm radius catalyst pellet.

Given:

slide20

Single Pellet Reaction

Example – 2

  • List the equations for (a) overall productivity, (b) effectiveness factor and (c) Thiele modulus for a first order reaction in a spherical pellet.
slide21

Single Pellet Reaction

Example – 2

  • Solve for Thiele modulus
  • where

2.125 mol/cm3–s (0.3 cm)2

=

0.007 cm2/s (1.9 x 10-5 mol/cm3)

k (0.3 cm)2

= ( )0.5

0.007 cm2/s

slide22

Single Pellet Reaction

Example – 2

  • Solve for overall productivity of a smaller pellet

2.61/s (0.3 cm)2

= ( )0.5

0.007 cm2/s

The smaller pellet has about 60 % better overall productivity!

Note: this is only true when the system is within diffusion-limited regime!

slide23

Single Pellet Reaction

First-Order Reaction

Other Pellet Geometries – 1

  • Governing equation
slide24

Single Pellet Reaction

First-Order Reaction

Other Pellet Geometries – 2

  • Characteristic Lengths
  • Dimensionless equations
slide25

Single Pellet Reaction

First-Order Reaction

Other Pellet Geometries – 3

  • Effectiveness factor – 1
  • or
slide26

Single Pellet Reaction

First-Order Reaction

Other Pellet Geometries – 4

  • Effectiveness factor – 2
slide27

Single Pellet Reaction

Other Reaction Orders

Spherical Pellet – 5

  • Positive reaction orders
  • Redefining Thiele Modulus
slide28

Single Pellet Reaction

Other Reaction Orders

Spherical Pellet – 6

  • Redefining the equations
slide29

Single Pellet Reaction

Other Reaction Orders

Spherical Pellet – 7

  • Effectiveness factor as a function of Thiele modulus

n  1

slide30

Single Pellet Reaction

Other Reaction Orders

Spherical Pellet – 8

  • Effectiveness factor as a function of Thiele modulus

n < 1

slide31

Single Pellet Reaction

Other Reaction Orders

Spherical Pellet – 9

  • Concentration profile within pellet with reaction order less than 1

n = 0

slide32

Single Pellet Reaction

Other Reaction Orders

Spherical Pellet – 10

  • Effectiveness factor can be approximated by the analytical solution for first order reaction

n > 0

concentration profile

effectiveness factor

overall productivity

slide33

Single Pellet Reaction

Other Reaction Orders

Spherical Pellet – 10

  • Effectiveness factor can be approximated by the analytical solution for first order reaction

n > 0

concentration profile

effectiveness factor

overall productivity

slide34

Single Pellet Reaction

Hougen-Watson - 1

Find the effectiveness factor for a slab catalyst geometry

(1) Governing equation

slide35

Single Pellet Reaction

Hougen-Watson - 2

(2) Transformation into dimensionless equation

where (dimensionless adsorption constant)

slide36

Single Pellet Reaction

Hougen-Watson - 3

(3) Effectiveness factor

(4) Rescaling the Theile modulus

slide37

Single Pellet Reaction

Hougen-Watson - 4

(5) Effectiveness factor versus Thiele modulus

slide38

Single Pellet Reaction

External Mass Transfer - 1

Rapid EMT

Slow EMT

<

slide39

Single Pellet Reaction

External Mass Transfer - 2

(1) The presence of external mass transfer resistance will only affect the boundary condition

(2) Dimensionless boundary conditions

x

x

slide40

Single Pellet Reaction

External Mass Transfer - 3

(3) Biot number

(4) Dimensionless equation

slide41

Single Pellet Reaction

External Mass Transfer - 4

(5) Solving the equation

(6) Concentration profile in spherical pellet

small B means large external

mass transfer resistance

large B means no external mass

transfer resistance

slide42

Single Pellet Reaction

External Mass Transfer - 5

(7) New definition of effectiveness factor

(8) Effectiveness factor versus Thiele modulus for different Biot numbers

small B means large external

mass transfer resistance

large B means no external mass

transfer resistance

slide43

Single Pellet Reaction

External Mass Transfer - 6

(9) Effects of external mass transfer resistance

slope -1

slope -2

slide44

Single Pellet Reaction

External Mass Transfer - 7

(10) Summary

slide45

Single Pellet Reaction

External Mass Transfer - 8

(11) Observed versus intrinsic kinetic parameters - 1

Reaction-limited

Diffusion-limited

slide46

Single Pellet Reaction

External Mass Transfer - 9

(11) Observed versus intrinsic kinetic parameters - 2

Diffusion-limited

Internal mass transfer-limited

External mass transfer-limited

slide47

Catalyst Pellet

General Balances

(1) Material Balance

where

slide48

Catalyst Pellet

General Balances

(2) Energy Balance

where

slide49

Single Pellet Reaction

Nonisothermal Condition - 1

(1) Material Balance

(2) Energy Balance

Practical catalyst pellet usually have high thermal conductivity and therefore heat transfer could

often be neglected.

slide50

Single Pellet Reaction

Nonisothermal Condition - 2

(3) Solving the two balance equations

for constant properties

therefore

slide51

Single Pellet Reaction

Nonisothermal Condition - 3

(4) Simplification

defining the dimensionless variables

gives

slide52

Single Pellet Reaction

Nonisothermal Condition - 4

(5) Dimensionless material balance for nonisothermal pellet

Weisz-Hicks Problem

with boundary conditions

slide53

Single Pellet Reaction

Nonisothermal Condition - 5

(6) Effectiveness factor

Weisz-Hicks Problem

(7) Rescaling the Theile modulus

slide54

Single Pellet Reaction

Nonisothermal Condition - 6

(8) Effectiveness factor versus Thiele modulus

Weisz-Hicks Problem

Note: at large Thiele modulus that asymptotes

are the same for all values of g and b.

The effectiveness factor could be larger than 1

for some of the parameter values, which becomes

more pronounced for more exothermic reaction.

The interior temperature of the pellet could be

higher than the surface for exothermic reaction.

Multiple steady-state is possible in the pellet.

slide55

Single Pellet Reaction

Nonisothermal Condition - 7

(9) Concentration and temperature profiles in pellet

Weisz-Hicks Problem

slide56

Fixed Bed Reactor

FBR Design – 1

Analysis of a fixed bed reactor with a packed bed of catalyst pellets involves:

(1) fluid phase that transports the reactants and products through the reactor,

(2) solid phase where reaction-diffusion processes occurs.

slide57

Fixed Bed Reactor

FBR Design – 2

(1) Coupling between catalyst and fluid

The two phases communicate by exchanging materials and energy

(2) The following assumptions will be made for the analysis of a FBR

slide58

Fixed Bed Reactor

FBR Design – 3

(3) Fluid Phase

(a) mole balance

(b) energy balance

(c) pressure drop (Ergun Equation)

slide59

Fixed Bed Reactor

FBR Design – 4

(4) Catalyst pellet

(a) mole balance

(b) energy balance

slide60

Fixed Bed Reactor

FBR Design – 5

(5) Coupling between fluid and catalyst phases

(a) mole balance

(b) energy balance

slide61

Fixed Bed Reactor

FBR Design – 6

(6) Quick summary

slide62

Fixed Bed Reactor

FBR Design – 7

(7) Simple examples

The first order, irreversible reaction took place in a 0.3 cm radius spherical catalyst pellet at T = 450 K.

The feed to the reactor is pure A (12 mol/s, 1.5 atm), the pellet’s production rate is –2.5 x 10-5 mol/g-s. The bed density is given to be 0.6 g/cm3. Assume that the reactor operates isothermally at 450 K. External mass-transfer limitations are negligible.

Given:

Find the FBR volume needed for 97 % conversion of A.

slide63

Fixed Bed Reactor

FBR Design – 8

(7a) FBR design equation

(7b) First order, irreversible reaction

Thiele modulus is independent of concentration

(7c) Effectiveness factor is constant along the axial length

slide64

Fixed Bed Reactor

FBR Design – 9

(7d) Concentration in term of molar flow

(7e) Substituting into the FBR design equation

slide65

Fixed Bed Reactor

FBR Design – 9

(7f) What happen when there is external diffusion resistance

let