The document discusses surface kinetics and pore diffusion resistance in solid catalyzed reactions. It presents the following key points: 1. Surface kinetics models assume reactions occur on active sites through adsorption, reaction, and desorption steps. Rate equations can be derived from different proposed mechanisms. 2. For a single cylindrical pore with first-order reaction, a material balance relates the diffusion and reaction terms. This yields a differential equation relating concentration to position. 3. Boundary conditions of known concentration at the pore entrance and zero flux at the closed end allow solving the equation. The solution shows an exponential drop in concentration into the pore dependent on the Thiele modulus.

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2. Solid Catalyzed Reactions
Under the Supervision of: Dr. Imran Nazir Unar
Mujeeb UR Rahman 17CH106
Chemical Engineering Department
Chemical Reaction Engineering (CH314)
Mehran University of Engineering &
Technology
Jamshoro, Pakistan

3. Lecture Objectives
Discussion on:
• Rate Equation for Surface Kinetics
• Pore Diffusion Resistance Combined with Surface Kinetics

4. THE RATE EQUATION FOR SURFACE KINETICS
Introduction
 Because of the great industrial importance of catalytic reactions, considerable
effort has been spent in developing theories from which kinetic equations can
rationally be developed.
 The most useful for our purposes supposes that the reaction takes place on an
active site on the surface of the catalyst.
 Thus three steps are viewed to occur successively at the surface.

5. THE RATE EQUATION FOR SURFACE KINETICS
Introduction - Steps
 Step 1. A molecule is adsorbed onto the surface and is attached to an active
site.
 Step 2. It then reacts either with another molecule on an adjacent site (dualsite
mechanism), with one coming from the main gas stream (single-site
mechanism), or it simply decomposes while on the site (single-site mechanism).
 Step 3. Products are desorbed from the surface, which then frees the site.
 In addition, all species of molecules, free reactants, and free products as well as
site-attached reactants, intermediates, and products taking part in these three
processes are assumed to be in equilibrium.

6. THE RATE EQUATION FOR SURFACE KINETICS
Rate Expression
 Rate expressions derived from various postulated mechanisms are all of the
form:
 For Example, for reaction
 occurring in the presence of inert carrier material U, the rate expression when adsorption of A
controls is
 When reaction between adjacent site-attached molecules of A and B controls, the rate
expression is
 whereas for desorption of R, controlling it becomes
(1)

7. PORE DIFFUSION RESISTANCE COMBINED WITH SURFACE KINETICS
Single Cylindrical Pore, First-Order Reaction
 First consider a single cylindrical pore of
length L, with reactant A diffusing into the
pore, and reacting on the surface by a
first-order reaction:
 Taking place at the walls of the pore, and
product diffusing out of the pore, as shown
in Fig. 1.
 This simple model will later be extended.
(2)
Fig. 1: Representation of a cylindrical catalyst pore.

8. PORE DIFFUSION RESISTANCE COMBINED WITH SURFACE KINETICS
Single Cylindrical Pore, First-Order Reaction
Fig. 2: Setting up the material balance for the elementary slice of catalyst pore.

9. PORE DIFFUSION RESISTANCE COMBINED WITH SURFACE KINETICS
Single Cylindrical Pore, First-Order Reaction
 The flow of materials into and out of any section of pore is shown in detail in
Fig.2.
 At steady state a material balance for reactant A for this elementary section
gives:
 or with the quantities shown in Fig. 2.
 Rearranging gives:
 and taking the limit as Δx approaches zero, we obtain:
 Note that the first-order chemical reaction is expressed in terms of unit surface
area of the wall of the catalyst pore; hence k" has unit of length per time.
(3)

10. PORE DIFFUSION RESISTANCE COMBINED WITH SURFACE KINETICS
Single Cylindrical Pore, First-Order Reaction
 In general, the interrelation between rate constants on different bases is given
by:
 Hence for the cylindrical catalyst pore:
 Thus in terms of volumetric units Eq. 3 becomes:
 This is a frequently met linear differential equation whose general solution is
 Where:
 and where M and M are constants
(4)
(5)
(6)
(7)

11. PORE DIFFUSION RESISTANCE COMBINED WITH SURFACE KINETICS
Single Cylindrical Pore, First-Order Reaction
 It is in the evaluation of these constants that we restrict the solution to this system
alone.
 We do this by specifying what is particular about the model selected, a procedure
which requires a clear picture of what the model is supposed to represent.
 These specifications are called the boundary conditions of the problem.
 Since two constants are to be evaluated, we must find and specify two boundary
conditions.
 Examining the physical limits of the conceptual pore, we find that the following
statements can always be made.
 First, at the pore entrance:
 Second, because there is no flux or movement of material through the interior end of
the pore
(8a)
(8b)

12. PORE DIFFUSION RESISTANCE COMBINED WITH SURFACE KINETICS
Single Cylindrical Pore, First-Order Reaction
 With the appropriate mathematical
manipulations of Eqs. 7 and 8 we
then obtain:
 Hence the concentration of reactant
within the pore is:
 This progressive drop in
concentration on moving into the pore
is shown in Fig.3, and this is seen to
be dependent on the dimensionless
quantity mL, or MT, called the Thiele
modulus.
(9)
(10)
Fig. 3: Distribution and average value of reactant concentration
within a catalyst pore as a function of the parameter mL =𝑳 𝒌/𝑫

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