MS PowerPoint - Catalysis Eprints database
Download
Report
Transcript MS PowerPoint - Catalysis Eprints database
Graduate Workshop Lecture Series
Estimating kinetics parameters in
(photo)catalysis using simple and complex
modeling approaches
Vaidyanathan (Ravi) Subramanian
Associate Professor, Chemical Engineering
University of NEVADA, Reno
Outline for this presentation
At the end of this lecture the following information will
be disseminated:
Refresher on catalysis
Key steps in a catalytic process
General strategies to offset transport limitations
Rate
Definitions, Catalyst-reactant interactions
Definitions, rate expressions
Rate analysis
Non-rigorous approach (Power law model)
Rigorous approach (Langmuir model)
Catalyst: Introduction
What is a catalyst?
A catalyst is a material that favorably influences a reaction
but emerges from the reaction unchanged
Examples
Fuel cell
Photocatalysis
PtRu: Metal catalysts that promote oxidation of a fuel to produce
current in a fuel cell
TiO2: A photocatalyst that promotes degradation of pollutants
without undergoing any change in itself
Value added product formation
Al2O3-Rh: Support – catalyst composite used in high temperature
hydrogen production
Types of catalytic reactions
Homogeneous
Homogenous catalysis concerns processes in which a
catalyst is in solution with at least one of the reactants
Manufacturing of n-isobutylaldehyde
CO, propylene, H2 with liquid phase Co as catalyst
Heterogeneous
Involves more than one phase.
A reaction involving gas and liquid
Examples:
TiO2 photocatalyst is usually in the solid phase while pollutants
can be in liquid or gas phase
Hydrogenation catalysts are in the solid phase whereas
unsaturated oils are in the liquid phase
Catalyst properties
Usually the activities in the presence of a catalyst
occur at the interface
Gas-liquid, gas-liquid-solid
For example, the photocatalytic process occurs at the
surface of TiO2
Crucial physical aspects of the catalyst
Surface area
Pore size, pore volume: What are these?
These dictate the extent of the catalyst surface available and
that can be utilized by a catalytic process
Active sites
Higher the number of active sites greater the activity
Generally, higher the surface area, higher the activity of the
catalyst
Catalyst properties … contd.
Selectivity
Pore size can control the selectivity of the
reaction
Example
Benzene and toluene can react over zeolite to
form xylene mixtures. But the pore of zeolite
only allows a specific type of xylene to come
out.
Supported catalyst
Catalyst is not used by itself but supported
on another material
Example
Fuel
cell catalysts: PtRu on carbon
General catalyst – support configuration
catalyst
Surface
support
Pore
interiors
Pore
mouth
Definitions
Active site
Turn over frequency (TOF-f)
The location on a catalyst where the reactant
undergoes chemistry
Point of the catalyst that facilitates strong interaction
with reactant
Number of molecules reacting per active site per
second
Dispersion
Distribution of the catalyst. This term is usually used
when a catalyst is prepared over a support
One usually requires higher dispersion
Higher dispersion typically yields higher activity
Thermodynamics of a catalytic process
The feasibility of a reaction is decided by the
initial and final energy state of the reactants and
products respectively
Different pathways can be employed to facilitate
a reaction
Pathways mainly differ based on the energy barrier
that exist between the reactant(s) and product(s)
A catalyst promotes the reaction by following a
different, usually a more energy efficient,
pathway
Thermodynamics…contd.
Without catalyst:: higher energy barrier
I impedes reaction
Energy
II
With catalyst:: lower energy barrier facilitates
reaction
A
B
Reaction pathway
Interaction between catalyst and reactant
Prior to reaction the reactants have to
come in contact with the catalyst
Chemisorption
Adsorbed atoms or molecules are held to
the catalyst surface by chemical
bonding(the same type which hold atoms
bonded in molecules)
Physisorption
The atoms are held on the catalyst surface
by physical forces
Main steps in a catalytic reaction
There are in general 7 key steps in a
heterogeneous catalytic reaction
1. mass transport: diffusion of A from bulk phase to the
catalyst surface
2. diffusion of A from pore mouth to pore interior
3. adsorption of A on active site
4. reaction on active site AB
5. desorption
6. diffusion of B from pore interior to pore mouth
7. mass transport: diffusion of B from catalyst surface
to bulk
Steps: Pictorial
A B
Catalyst
Buk
A
B
1
7
Pore
surface
2
Pore
interior
6
5
3
4
Active site
Steps…contd.
Factors that play a role
Diffusion limited:
steps 1,2, and/or 6,7
Kinetic limited :
step 3,4,or 5
Overall rate = rate of the slowest step
Analogous to saying
Strength of chain = strength of weakest link
Step 1
Diffusion from bulk to the external transport
Reactant travels
from bulk
concentration
CAb to CAs at the
catalyst surface
over a boundary
layer thickness
Diffusion rate = kC(CAb-CAs)
Where
kC=mass transport coefficient
kC=f(fluid velocity(U),particle diameter(Dp))
kC 1/
Step 1:…contd.
(Q) what happens to overall rate of diffusion when the velocity
increases for a constant particle diameter?
Overall rate increases
Overall rate
U
External mass
transport no longer
the slowest step
External diffusion is
the slowest step
U/DP
Step 2
Internal diffusion
Assumption: no external diffusion
Internal diffusion = f (pellet size)
For larger pellets
Reactants consumed at the pellet surface
Therefore, bulk of the catalyst may not be used in reaction
For small pellets
Larger the pellet size –
longer it will take to diffuse to the bulk
from the surface
Most of the catalyst surface is used
Rate of transport = krCAs
CAs= concentration at external surface
kr=overall rate constant =f(DP)
Step 2…contd.
(Q) what happens to rate constant when the
diameter of catalyst particle increases?
(hint: higher DP longer time to diffuse)
Rate constant decreases
Surface reaction sequence is
the slowest step
kr
Internal diffusion is
the slowest step
DP
What is the need for estimating kinetic
parameters?
Kinetic parameters are needed to answer several of the
following questions
How fast the reaction can occur?
How efficient of a chemical transformation is the reaction
What is the extent of desired and undesired product(s)
formation
How doe the cost and sustainability (environmental impact)
aspect of the process work out
What supporting infrastructure/ facilities are required to run the
chemical reaction?
Rate is a key measure of kinetics
Rate of a reaction
What is Rate?
Rate of a reaction
Rate can be defined as transformation or changes that
occur causing the concentration of a specie to increase or
decrease with time
Is a measure of how a reaction occurs with respect to time
Examples
Rate of consumption
Depletion of a reactant with time
Rate of formation
Increase in the formation of a product with time
Rate of a reaction…contd.
Rate is generally defined as:
Change in the concentration of a reactant per unit time per unit
volume
It is typically represented by the symbol r
r = dCA/dt
where
dCA = change in concentration of a component A
dt = duration when the change in concentration occurs
Positive : indicate formation of A with time
negative: indicates consumption of A with time
Some examples of units
mol/dm3.s
Kg/m3.hr
Rate of a reaction…contd.
For example consider the
reaction AB
As time progresses
A gets consumed and
B get formed.
i.e. the concentration of A
decreases while the
concentration of B increases.
This can be graphically
represented as shown in
the adjacent plot
B
CA CB
A
Time (t)
CA CB
B
dCA
A
dt
Time (t)
Rate of consumption of A = change in the concentration of A with time = dCA/dt
Other definitions of reaction rate
We saw that rate can be expressed in terms of per unit volume of fluid as shown
bellow:
Based on unit volume of reacting fluid (homogeneous systems)
r1 = 1 dNi
moles of i formed
V dt
(volume of fluid) (time)
What are other possible types?
Heterogeneous systems: more than one phase
Based on unit mass of solid in a fluid – solid reaction
r2 = 1 dNi
moles of i formed
W dt
(mass of solid) (time)
Based on interfacial area in a two phase reaction system
r3 = 1 dNi
moles of i formed
S dt
(surface) (time)
Based on a unit volume of solid in a gas-solid system
r4 = 1 dNi
moles of i formed
Vs dt
(volume of solid) (time)
All rates are related
How you relate them with one another?
r1 =
1 dNi
V dt
dNi =
Vr1
dt
dNi =
Vr1 = Wr2 = Sr3 = Vsr4
dt
Thus, rate expressions can be expressed in different
interchangeable forms
Other facts about rate
It is an algebraic equation
It is independent of reactor configuration
(you will learn about types of reactor later)
It is generally a function of the dependent variables
Meaning, operations in algebra (+,-,x,/) are used for expressing
rate
P,V,T, n, and material properties
It has a few key factors that are critical to understand the
details of the chemical reaction
rate constant,
equilibrium constant,
Molecularity and reaction order
Rate constant (k)
The rate of reaction is proportional to the
concentration of the reactants
rC
(for simplicity the power terms are excluded)
The proportionality constant is called the rate
constant (k)
r=kC or k = r/C
From the above expression the units of rate
constant can be identified as dependent on
time and concentration
Equilibrium constant (K)
Dual site reaction
Adsorbed atom/molecule site can (1) another adsorbed
atom/molecule or (2) react with another site
An adsorbed molecule may isomerizes or decomposes at the said
site
The rate law for reaction 1 is:
A.S+C.S
Example: CO oxidation to CO2 over Pt sites
Forward reaction: rS=kS.CA.S
backward reaction: r-S=k-S. CC.S
So overall rate
RS= forward – backward
=kS.CA.S - k-S. CC.S
=kS(CA.S- CC.S)
KS
Where KS=kS/k-S=reaction equilibrium constant
Molecularity and reaction order
Molecularity
of an elementary reaction is the number of
molecules involved in the reaction
Usually 1, 2, occasionally 3
only applicable to elementary reactions
Order, overall order
if r= kCAaCBb, then
the order of reaction with respect to A is a
order of reaction with respect to B is b
overall order is a+b
Rate dependency on temperature
For elementary reaction of the form
A products,
rate=f1(temperature)xf2(concentration)
This is usually the case with all reactions
The temperature dependency is manifested as a part
of the rate constant
k=f(constant, temperature)
Arrhenius’ law states the relation between rate constant
and temperature
It is written as
k = k0exp(-E/RT)
Where
k0=frequency factor, E=activation energy (calories)
Rate analysis?
The modeling approaches to estimating the rate
parameters can be classified based on rigor
Non-rigorous
Rigorous
Power law model (one size fits all)
Linearized power law model
Numerical based power law model
Langmuir model (iterative and semi empirical)
Highly empirical (statistical analysis driven)
The choice of method to be adapted is driven based on
the (i) accuracy desired, and (ii) the level of details
needed from the analysis.
The rate law (power law model)
The power law model correlates reaction with
two basic parameters: the reaction rate constant
and the order (participating species)
The general expression for the power law model
for an elementary reaction AB is written as:
-rA = kCAn (where n is 1 )
This expression can be applicable to complex
reactions as well.
How will you write the rate expression for the
following reaction if it were elementary?
aA+bBcC+dD
-rA = kCAaCBb
The Langmuir Model
The Langmuir model is a popular kinetics model that can be
applied to heterogeneous photocatalytic reactions
Key aspects include:
Unlike the power law model, it allows for decoupling rate
constant (k) from equilibrium adsorption constant (K).
Allows for an iterative path way to propose and validate
mechanistic aspects associated with the reaction process
Single site
Dual site
Offers options to customize equation to include light –
matter interactions
Adsorption
Adsorption is a prerequisite for a catalytic
process
For the reaction A Products, the adsorption is
symbolically written as
A+S A.S
A= reactant (atom or molecule)
S= active site on catalyst surface with no atom
(or molecule) adsorbed on it
A.S = a reactant adsorbed on the active site
Note: the reaction is shown to be reversible. This is
mainly to indicate that some atoms might just adsorb
and desorb without reaction and represent the
Single site and dual site reaction
A+S products
A
A2+2S products
A
A
Adsorption …contd.
Occupied sites (CA.S ,CB.S)
A
B
Vacant site (CV)
Active site concentration (Ci,S) (mol.g-1.catalyst-1)
where i stands for reactant or product
Number of active sites per unit mass of catalysts
Avogadro number
Units: mol./ g of catalyst
For the system shown, the total concentration (Ct) of sites
(also called as site balance)
Ct=CV+CA.S+CB.S
An exercise on Langmuir model derivation
Derive the expression for the Langmuir singe site model
General approach
Determine the expression for the net adsorption rate.
It is given as:
attachment rate – detachment rate
Define adsorption equilibrium constant as KA=kA/k-A
Perform a site balance
LH isotherm is an expression for the concentration of
adsorbed species
Linearized form is to write the above expression in
Y=mX + C form
Adsorption equilibrium constant
Assume a gas phase reaction as follows
yst
R Photocatal
products
Before the reaction can occur, the molecules needs to interact
with the site via chemisorption or physisorption method
The attachment rate (proportional to the PR and CV)
= kA.PR.CV
The detachment rate
= - k-A.CR.S
The adsorption equilibrium constant (KA) represents the
situation under a dynamic steady state
KA=kA/k-A
Adsorption equilibrium constant
At equilibrium,
Net adsorption rate = attachment rate – detachment rate
(1)
Substituting the adsorption equilibrium constant (KA)
rAD = kA.PR.CV - k-A.CR.S
KA=kA/k-A
And rearranging eq (1) we can get
rAD = kA.(PR.CV - CR.S)
KA
(2)
Site balance
The total number of sites is given as,
At equilibrium,
Ct=vacant sites + adsorbed sites
In this case, Ct=CV+CR.S
(3)
The net rate of adsorption (rAD)should be zero.
(dynamic steady state)
Or rAD = kA.(PR.CV - .CR.S) =0
KA
Rearranging,
CR.S =KAPR.CV
(4)
Site balance… contd.
Rearranging,
Substituting the value of CV from eq (3) in eq(4)
Since in many cases, only the adsorbed sites can only be
identified; it is helpful to substitute CV in terms of CR.S
CR.S =KAPR.CV
CR.S =KAPR. (Ct-CR.S)
Rearranging,
CR.S = KAPR.Ct
(5)
1+ KAPR
This equation gives the concentration of R adsorbed on the
catalyst surface as a function of the partial pressure of R.
This is called the Langmuir adsorption expression after the
Nobel laureate Irving Langmuir.
Langmuir isotherm analysis
Rearrange eq(5),by linearizing,
PR = PR + 1
(6)
CR.S
Ct KACt
Y = mX + C
Which is the linearized form of the Langmuir equation
Thus one can check if
an experimental data
set follows the Langmuir
kinetics
P
R
CR.S
This expression gives the equilibrium
adsorption constant and an estimate of
total sites utilized in the reaction
1
KA.Ct
PCO
1
Ct
Photocatalytic degradation of dye
The power law and LH models can be applied to a
common photocatalytic reaction – the photodegradation
of dyes.
Dyes are often toxic (carcinogenic) and alter the
ecosystems where there are introduced
Photocatalysis is a pathway to remediate this dye.
The options are:
Example: Dye discharge into water stream by textile industries
Complete mineralization (CO2 and Water)
Decontamination to a more benign intermediate
Examples of dyes
Methyl orange, Victoria blue, Acid orange
Overall rate: power law model
0.12
constant
0.10
rMO ,M min
-1
0.08
0.06
0.04
0.02
0.00
0
20
40
60
[MO] x 10
80
-6
Power law model rMO
100
d [ MO ]
dt
The rate vs. methyl orange concentration [MO] plot
Subramanian et.al. Ind. Eng. Chem. Res. (2009)
LH kinetics for photocatalytic reactions
rMO f ( I , s, [ MO ], K )
I Intensity, s area ,
[ MO ] MO concentration ,
K equilbrium const .
rMO
k1as I
1 k1as I
K [ MO ]
1 K [ MO ]
a, , consts.
K [ MO ]
rMO k r
1 K [ MO ]
where
k1as I
kr
1 k1as I
PC: Langmuir Hinshelwood Model
100
1/rMO [min M]
80
60
K [ MO ]
rMO k r
1 K [ MO ]
1
1
1
rMO k r K [ MO ] k r
40
y = 6.451 + 62.28x
2
R = 0.996
20
0
0.0
0.1
0.2
0.3
0.4
0.5
1/[MO]
Single site – single molecule adsorption and reaction
mechanism of MO degradation
Subramanian et.al. Ind. Eng. Chem. Res. (2009)
Other factors influencing kinetics
Other general parameters that influence reaction
kinetics are:
Catalyst loading
External effects (addition of external fields)
Additives (pH adjustors)
Specific to photocatalytic processes other key
parameters that affect the rate reaction rate are:
light intensity,
light screening,
adsorption-desorption equilibrium
Summary
A key aspect in catalysis is the determination of rate of
reactions
The main contributors to rate of reaction are: rate
constant, equilibrium constants, concentration (pressure)
of participating reactant species
The analysis of rate can be carried out using simple and
complex models
Simple: Power law model
Complex: Langmuir Hinshelwood
The models can provide insights into the mechanistic
details of the reaction