Self Assessment Quiz

Q2.2.The elementary irreversible isothermal gas phase reaction A = products is carried out in a fluidized CSTR. The rate of decay is first order in present activity and order q (=1 in reactant concentration). Express activity and conversion as a function of time. Sourced from Fogler

Q2.3. Consider the reactions
A => D                            (1)
A => U                            (2)
The catalyst decay rate constant for the reactions are k_d1 = 10^{- 4}/min and k_d2 = (5)(10^{- 5})/min. The reaction rate constant for formation of both D and U are k₁ = 2/min and k₂ = 0.2/min.

Q2.4. The catalyst cracking of gas oil A to form C₅ + (component B) and coke/dry gas (component C) is to be carried out in moving bed reactor at 480⁰C.
Pure hydrocarbons are known to crack according to first order rate law. However, gas oil exhibits wide spectrum of cracking rates and a lumped cracking rate expression is given as
r_A = -0.60 C_A2 mol/g.cat.min

Deactivation is independent of gas phase concentrations and follows a first order decay law with a rate constant 0.72/min.

Q2.5. Vinyl chloride monomer (C₂H₃C_l) can be produced by reacting HCl and acetylene (C₂H₂) over mercuric chloride catalyst, supported on activated carbon. Studies reveal that catalyst undergoes deactivation and this kinetics in needed to suitably design and operate commercial processes.

Accordingly a continuous stirred tank reactor containing 10 g catalyst (20 ml) is used to obtain isothermal deactivation data. In the laboratory reactor of 1.0 lit volume 4 catalyst baskets are fitted to the spinning stirred, each basket with a capacity to carry up to 7.5 g catalyst. Measurement of pressure, temperature, flow and composition of the inlet and outlet streams are carried out to obtain the data required.
Let us say that the deactivation rate function follows power law model.
r_d = k_d a^m C_A^p C_B^q C_C^r

where ‘a’ refers to activity. Let the concentration dependence  p, q, r are all zero. Table 2.5.1 summarizes the data obtained at different conditions. Activity is defined as the reaction rate expressed with respect to the reference state specified for each temperature.

Table: Q2.5.1: Deactivation data for acetylene hydrochlorination for 10 g mercuric chloride on activated carbon. Reactor pressure 1.0 atm. ‘O’ refers to inlet conditions. Herein “a” refers to activity

Q2.5.1. Assuming that quasi steady state approximation applies determine the deactivation parameters, p,q,r, k₁, m and activation energy for deactivation Ed

Q2.5.2.Verify whether concentration independence is a satisfactory assumption.

Q2.5.3.Under what condition do you expect the quasi-steady state approximation to break down in this system?

Q2.5.4.Cite another example of a commercial process in which catalyst deactivation is a major problem. Specify the cause of deactivation, and how industries manage the problem of catalyst deactivation, catalyst regeneration and catalyst reuse.

Q2.6.   Reactor Design for Deactivating Catalyst System ( adapted from Fogler)
An elementary reversible liquid phase catalytic reaction A↔B is to be carried out in an isothermal plug flow tubular reactor. The reactor effluents pass through a separator where A is completely recovered and recycled.

Even though the reaction is exothermic, isothermal assumption can be considered reasonable in view of efficient wall heat transfer and turbulence inside the reactor.
The catalyst deactivates as per a first order law. The rate constant for deactivation is available. In order to compensate for this loss of activity the reactor operating temperature is adjusted suitably so that throughput is as close to design as possible. Sometimes throughputs have to be scaled down also. The suggested range to temperature for adjusted typically after 30 days.
In order to achieve the necessary temperature of operation, PFR has a jacket through which suitable utility can be circulated and in order to keep separations costs low the exit composition is kept at or above 75 mole percent B.
Data for problem Q2.6:
Reaction rate constant  
Deactivation velocity constant
Equilibrium constant
Feed pure Liquid A = 250 mol/s
Product pure Liquid B = 250 mol/s
Feed temperature = available as desired
Reactor temperature = 150 to 250 (to be chosen)
Feed concentration of A = 50 mol/lit
Gas constant R = 1.987 cal/mol⁰K

Q2.6.1   Set up the balance equation and obtain the relationship between residence time and reactor parameter (Rate constant and catalyst activity).

Q2.6.2   Specify a process design for fresh catalyst. Specifications should include reactor temperature, recycle ratio, residence time, reactor volume.

Q2.6.3   Tabulate a process design for your deactivating catalyst of Q.6.2 during the first reset period of 30 days. Specifications should include against time, the old and new values of (a) reactor temperature (b)  reaction velocity (c) equilibrium constant (d) composition at reactor exit (e) recycle ratio (f) residence time V/v0

Q2.6.4 Overview the manufacture and applications of supported catalysts with reference to their advantages and disadvantages.

Q2.7 The elementary reaction A <==> B is carried out in an isothermal fixed bed plug flow catalytic reactor containing a supported metal catalyst. A and B are liquids at process conditions and there is no volume change due to reaction.Sourced from Fogler

Side reactions are not serious but they deactivate the catalyst. To increase reaction rate and partially offset the deactivation the reactor temperature is raised on a predetermined schedule from 450 K to 477 K. At the end of the operating cycle the catalyst is discarded and replaced by a new batch.

The normal feed employed is 0.39 lit/s measured at 32⁰C. The unconverted A is separated in a column and recycled. Total feed to the reactor is

A company offers an alternative in which catalyst is to be regenerated in situ with a solvent of proprietary composition. The cost is attractively low compared catalyst replacement. It guarantees at least (a) 90 percent of fresh catalyst activity or (b) 2.25 times the activity of the spent catalyst.

Table 2.7.1.Data on the performance of fresh, spent and regenerated catalyst is given below.

You are to review the data and verify if the guarantees are satisfied prior to ratifying the purchase of the regeneration process.

Q2.7.1. Set up the balance equation and express α k₁V for each case as a function of v_o, Y₂, K_e where α is reactor volume and Y₂ is conversion at reactor exit, expressed with respect to position “o”.

Q2.7.2 . Determine catalyst performance parameter α k₁V for the fresh catalyst

Q2.7.3. Determine the catalyst activity α for spent catalyst.

Q2.7.4. Determine catalyst activity α for regenerated catalyst and verify whether the guarantees are met.