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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.

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

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)

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.

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.

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.

First-Order Reaction

(1) Spherical Pellet – 1

- Material balance
- Steady-state
- Spherical coordinate system

First-Order Reaction

(1) Spherical Pellet – 2

- Boundary conditions

absence of driving force

First-Order Reaction

(1) Spherical Pellet – 3

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

concentration scale

length scale

First-Order Reaction

(1) Spherical Pellet – 6

- General solution
- Specific solution

First-Order Reaction

(1) Spherical Pellet – 8

- Total productivity in pellet
- letting

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.

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:

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.

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

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!

First-Order Reaction

Other Pellet Geometries – 2

- Characteristic Lengths
- Dimensionless equations

Other Reaction Orders

Spherical Pellet – 5

- Positive reaction orders
- Redefining Thiele Modulus

Other Reaction Orders

Spherical Pellet – 7

- Effectiveness factor as a function of Thiele modulus

n 1

Other Reaction Orders

Spherical Pellet – 8

- Effectiveness factor as a function of Thiele modulus

n < 1

Other Reaction Orders

Spherical Pellet – 9

- Concentration profile within pellet with reaction order less than 1

n = 0

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

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

Hougen-Watson - 1

Find the effectiveness factor for a slab catalyst geometry

(1) Governing equation

Hougen-Watson - 2

(2) Transformation into dimensionless equation

where (dimensionless adsorption constant)

External Mass Transfer - 2

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

(2) Dimensionless boundary conditions

x

x

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

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

External Mass Transfer - 6

(9) Effects of external mass transfer resistance

slope -1

slope -2

External Mass Transfer - 8

(11) Observed versus intrinsic kinetic parameters - 1

Reaction-limited

Diffusion-limited

External Mass Transfer - 9

(11) Observed versus intrinsic kinetic parameters - 2

Diffusion-limited

Internal mass transfer-limited

External mass transfer-limited

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.

Nonisothermal Condition - 2

(3) Solving the two balance equations

for constant properties

therefore

Nonisothermal Condition - 3

(4) Simplification

defining the dimensionless variables

gives

Nonisothermal Condition - 4

(5) Dimensionless material balance for nonisothermal pellet

Weisz-Hicks Problem

with boundary conditions

Nonisothermal Condition - 5

(6) Effectiveness factor

Weisz-Hicks Problem

(7) Rescaling the Theile modulus

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.

Nonisothermal Condition - 7

(9) Concentration and temperature profiles in pellet

Weisz-Hicks Problem

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.

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

FBR Design – 3

(3) Fluid Phase

(a) mole balance

(b) energy balance

(c) pressure drop (Ergun Equation)

FBR Design – 5

(5) Coupling between fluid and catalyst phases

(a) mole balance

(b) energy balance

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.

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

FBR Design – 9

(7d) Concentration in term of molar flow

(7e) Substituting into the FBR design equation

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