Fixed Bed Reactor – 1 Real Reactors (1) The catalyst are held in place and do not move, (2) Material and energy balance must be conducted for fluid in.

Fixed Bed Reactor – 1 Real Reactors

(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 Real Reactors

(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 Fixed Bed Reactors

(1) Single pellet model is established by averaging the microscopic processes that occur within the intra-particle environment,

(2) An effective diffusion coefficient is used to represent the information about the physical diffusion process and pore structure,

(3) A viable commercial catalyst must have sufficientactive sites to maintain a product formation rate

in the order of 1 mol/L h,

4) 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)

General BalancesCatalyst Particle

Fixed Bed Reactors

(1) Material Balance

where

General BalancesCatalyst Particle

Fixed Bed Reactors

(2) Energy Balance

where

Catalyst Fixed Bed Reactors

(1) Catalyst (usually metal sometimes also metal oxides) is often dispersed onto large surface area support material,

(2) 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.

(3) The support often have surface areas between 0.05-100 m2/g.

Catalyst Pellets – 1 Fixed Bed Reactors

(1) Catalyst pellets are made by tableting and extrusion methods. The latter is the more popular method,

(2) Different pellet shape and size could be obtained by simply changing the extruder head,

(3) The pellet shape and size could be optimized to increase mass transfer rates, while minimizing the pressure drop in the reactor.

Catalyst Pellets – 2 Fixed Bed Reactors

(4) The pellet void fraction or porosity, where p is the effective pellet density and Vg is the pore volume,

(5) The pore volume range fro, 0.1-1 cm3/g pellet,(6) 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

Single Pellet Reaction

(1) Material balance

(2) Steady-state

(3) Spherical coordinate system

(4) Boundary conditions

absence of driving force



(5) Dimensionless equation - 1

characteristic length:

dimensionless length: dimensionless concentration:

length scale

concentration scale



(5) Dimensionless equation – 2

where



(6) Simplification

where



(7) General solution

(8) Specific solution



(9) Concentration profile in pellet



(10) Total productivity in pellet

letting



(11) 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 Single Pellet Reaction

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:

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


(2) Solve for Thiele modulus

where


= ( )0.5

=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

0.007 cm2/s

(3) Solve for overall productivity of a smaller pellet


= ( )0.52.61/s (0.3 cm)2

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 ReactionOther Pellet Geometries – 1


(1) Governing equation



(2) Characteristic Lengths

(3) Dimensionless equations




or




Other Reaction OrdersSpherical Pellet – 5


(5) Positive reaction orders

(6) Redefining Thiele Modulus



(7) Redefining the equations



(8) Effectiveness factor as a function of Thiele modulus

n 1



(9) Effectiveness factor as a function of Thiele modulus

n < 1



(10) Concentration profile within pellet with reaction order less than 1

n = 0



(11) Effectiveness factor can be approximated by the analytical solution for first order reaction

n > 0

concentration profile

overall productivity

effectiveness factor



(11) Effectiveness factor can be approximated by the analytical solution for first order reaction

n > 0

concentration profile

overall productivity

effectiveness factor

Hougen-Watson - 1 Single Pellet Reaction

Find the effectiveness factor for a slab catalyst geometry

(1) Governing equation


(2) Transformation into dimensionless equation

where (dimensionless adsorption constant)


(3) Effectiveness factor

(4) Rescaling the Theile modulus


(5) Effectiveness factor versus Thiele modulus

External Mass Transfer - 1 Single Pellet Reaction

Rapid EMT Slow EMT

<


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

(2) Dimensionless boundary conditions

x x


(3) Biot number

(4) Dimensionless equation


(5) Solving the equation

(6) Concentration profile in spherical pellet

small B means large externalmass transfer resistance

large B means no external masstransfer resistance


(7) New definition of effectiveness factor

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

small B means large externalmass transfer resistance

large B means no external masstransfer resistance


(9) Effects of external mass transfer resistance

slope -1

slope -2


(10) Summary


(11) Observed versus intrinsic kinetic parameters - 1

Reaction-limited Diffusion-limited


(11) Observed versus intrinsic kinetic parameters - 2

Diffusion-limited

Internal mass transfer-limited External mass transfer-limited

General BalancesCatalyst Pellet


where

(2) Energy Balance

where

General BalancesCatalyst Pellet

Nonisothermal Condition - 1 Single Pellet Reaction


(2) Energy Balance

Practical catalyst pellet usually have high thermal conductivity and therefore heat transfer couldoften be neglected.


(3) Solving the two balance equations

for constant properties

therefore


(4) Simplification

defining the dimensionless variables

gives

(5) Dimensionless material balance for nonisothermal pellet Weisz-Hicks Problem

with boundary conditions


(6) Effectiveness factor Weisz-Hicks Problem

(7) Rescaling the Theile modulus


(8) Effectiveness factor versus Thiele modulus Weisz-Hicks Problem


Note: at large Thiele modulus that asymptotesare the same for all values of and .

The effectiveness factor could be larger than 1for some of the parameter values, which becomesmore pronounced for more exothermic reaction.

The interior temperature of the pellet could behigher than the surface for exothermic reaction.

Multiple steady-state is possible in the pellet.

(9) Concentration and temperature profiles in pellet Weisz-Hicks Problem


FBR Design – 1 Fixed Bed Reactor

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.


(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


(3) Fluid Phase (a) mole balance

(b) energy balance

(c) pressure drop (Ergun Equation)

(4) Catalyst pellet (a) mole balance

(b) energy balance


(5) Coupling between fluid and catalyst phases (a) mole balance

(b) energy balance


(6) Quick summary


(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.

(7a) FBR design equation

(7b) First order, irreversible reaction Thiele modulus is independent of concentration

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


(7d) Concentration in term of molar flow

(7e) Substituting into the FBR design equation


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

let


Fixed Bed Reactor – 1 Real Reactors (1) The catalyst are held in place and do not move, (2) Material and energy balance must be conducted for fluid in.

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