Reaction engineering notes

• Langmuir Hinshelwood model • Rate of reaction and temperature

Relationship between rate equation and temperature: Equilibrium constant K decreases with increase in temperature and is independent of pressure • Equilibrium constant and pressure

For an ideal gas mixture undergoing a reversible gaseous phase chemical reaction the equilibrium constant increases of decreases with pressure depending upon stoichiometric coefficient of the reaction. • Equations for PFR, CSTR and batch reactor
• Equation for PFR • Equation for CSTR • Constant volume first order reaction in PFR/batch reactor • Varying volume reaction

In case of varying volume (presence of inerts) constant pressure gas phase reaction A –> B

1.  • Rate Constant K for first order irreversible system for any ϵA • Rate constant K for Zero order irreversible system for any ϵA • Varying volume batch reactor

Rate equation for varying volume batch reactor Rate equation for varying volume batch reactor first order reaction system Rate equation for Varying volume batch reactor zero order reaction system • Conversion for constant volume second order irreversible reaction

Conversion for second order irreversible reaction (constant volume) A –> B in batch reactor/plug flow reactor • Final rate equation for a constant volume reaction of order n is

For A constant volume reaction A to B with order n and rate constant k, final rate equation is • Zero order reaction

Rate equation for zero order reaction is defined such that • Arrhenius law

Relationship between different rate constants • Thiele Modulus
• Thiele modulus for nth order irreversible reaction • Thiele modulus for solid catalyzed reaction • Thiele modulus for spherical pellet • Relation between rates rA1 and rA2 with thiele modulus MT1 and MT2

In case of strong pore diffusion resistance relation between rates rA1 and rA2 with thiele modulus MT1 and MT2 • Effective order of reaction

In case of strong pore diffusion for nth order reaction effective order becomes (n+1)/2 order reaction as evident by below equation: • Reactors in series
• PFR and CSTR in First order reaction

For N CSTR in series each of same volume V in first order reaction For N plug flow reactors in series of same volume in first order reaction • Space time and holding time
• Holding time in batch reactor • Space time in plug flow reactor • Exit age distribution

The distribution of residence times is represented by an exit age distribution, E(t). The function E(t) has the units of time-1 and is defined such that The fraction of the fluid that spends a given duration, t inside the reactor is given by the value of E(t)dt.

The fraction of the fluid that leaves the reactor with an age less t1 is The fraction of the fluid that leaves the reactor with an age greater than t1 E is defined as • Exit age distribution for CSTR

Exit age distribution E(t) for CSTR is defined as • Exit age distribution for PFR

Exit age distribution E(t) for PFR is defined as The E curve for plug flow reactor is called Dirac-delta function.

• Controlling activation energy

Controlling activation energy when one of the actual activation energy and diffusion activation energy controls the reaction • Interfacial area per unit volume of dispersion in gas-liquid contactor • Peclet number

Peclet number for ideal CSTR and ideal PFR • Conversion
• Conversion in adiabatic reactor • Finding conversion given heat of reaction • Effectiveness factor of catalyst

Effectiveness factor of catalyst is defined as ratio of reaction rate with diffusion resistance to reaction rate without diffusion resistance • Effective rate constant

Effective rate constant in case of first order gaseous phase reaction catalyzed by non-porous solid • Concentration after temperature and pressure correction

CA, concentration of A inside reactor with temperature and pressure correction • Semi-batch reactor

Rate equation for semi batch reactor • Packed bed reactor

Rate equations for packed bed reactor • Equlibrium constant and gibbs energy

Calculating equilibrium constant for reaction given gibbs energy for the reaction • Reaction in series

Calculating time for concentration of B to be maximum • Reversible reaction

For a reversible reaction  • Instantaneous fractional yield

Instantaneous fractional yield in case of pore diffusion 1. For reaction  • Concentration inside and outside catalyst surface

For catalytic reaction, relationship between concentration inside catalyst surface and concentration at catalyst surface • Fractional yield

For a reaction, fractional yield is defined as ratio of moles of desired product formed to moles of desired product that would have been formed if there were no side reactions and limiting reactant would have reacted completely • Series parallel reaction

In case of series plus parallel reaction, try to solve by mass balance

• Selectivity of a reaction

Selectivity of a reaction is defined as ratio of moles of desired product formed to moles of undesired product formed • Fractional conversion of reactant

Fractional conversion of reactant is defined as ratio of moles of reactant reacted to form desired product to total reactant in the feed • Half life of a reactant

Half life of a reactant in a first order system is defined as follows • Dispersion of PFR and CSTR

Zero dispersion implies reactor is plug flow reactor (PFR) and infinite dispersion implies reactor is CSTR • Rate of reaction of species j

For homogenous system rate of reaction for species j is defined as • First moment of RTD function

First moment of RTD function is mean residence time • Mean residence time

In a pulse tracer experiment mean residence time is given by • Recycle ratio

Recycle ratio is defined as ratio of volume of liquid returned to entrance of the reactor to volume of liquid leaving the reactor • Ratio of volume of reactors

In CSTR ratio of volumes V1 and V2 for different conversion x1 and x2 • Catalytic reaction rate

Rate of reaction for a catalytic reaction = KCAa; where a = activity coefficient.

• Second order batch reactor/PFR

For second order batch/Plug flow constant volume reactor, rate equation is defined such that • Time required for conversion F

Time required in a reaction for conversion F (conversion F is the fraction of reactants converted to products) • Plug flow reactors in parallel

If two plug flow reactors PFR1 and PFR2 are in parallel then • Vapour phase catalytic reaction

Vapour phase catalytic reaction with equimolar reactants and surface reaction is rate controlling then rate equation becomes • Least square regression method • Second order unimolecular reaction rate • Rate constant dependency on temperature

Rate constant dependency on temperature according to transition state theory, collision theory and Arrhenius law • Second order non-ideal liquid phase reaction

The mean conversion in the exit stream for a second order liquid phase reaction in a non-ideal flow reactor is given by • Chemical Reaction Engineering
• Rate variation with temperature
1. Transition state theory approaches the problem of calculating reaction rates by concentrating on idea of intermediates and intermediates immediately breaking to products.
• Space time and holding time
1. For same conversion in a constant volume reaction, holding time required in batch reactor is equal to space time in plug flow reactor.
2. For constant density system, space time and holding time are equal. For changing density, they are unequal.
• Rate and rate equation
1. If the reactor volume is changed, rate will also change as degree of conversion will change.
2. Energy balance equation over a tubular reactor under transient conditions is a linear partial differential equation.
3. When an exothermic reaction is conducted adiabatically, rate of reaction passes through maximum (K increases first).
4. Rate of reaction doesn’t depend on how we write the stoichiometric equation. It is an experimentally determined expression.
• Reaction in presence of catalyst
1. A reaction A –> B. If the concentration of A at the center of the pellet is much less than at the external surface, the process is limited by diffusion within the pellet. This is a case of large Thiele modulus which means that the surface reaction is rapid and the reactant is consumed to a major extent close to external surface of the catalyst pellet. Very little of the reactant gets opportunity to penetrate inside the catalyst particle. Therefore, the reaction is limited by diffusion within the catalyst particle.
2. If for a heterogeneous catalytic reactions A + B –> C, with equimolar A and B, the initial rate –rAo is invariant with total pressure, it means that rate controlling step is desorption of C.
3. Examples of trickle bed reactor – hydrogenation, hydrodesulphurization and hydronitrogenation in refineries (three phase hydro treator); oxidation of harmful chemical compounds in waste water streams; in cumene process.
4. At steady state, reactant transport (diffusion) rate = reaction rate.
5. When due to decrease in particle size, conversion increases, the reaction is controlled by pore diffusion in the catalyst.
• Non-Ideal reactions
1. The E curve for an non-ideal reactor defines the fraction of fluid having age between t and t+dt at the outlet and is given by Edt.
• Extent of a rection
1. Extent of a reaction is same for all reactant and products. It has dimension of mole or mole/sec and it is independent of stoichiometric coefficients.
2. In exothermic first order reaction, maximum heat generated will be at the beginning of the reaction when CA = CAo.
• Reactors
1. If an endothermic aqueous phase first order reaction is carried out in a plug flow reactor then rate of reaction is maximum at inlet of reactor.
2. For a packed bed reactor, the presence of long tail in the residence time distribution curve is an indication of dead zone.
3. Consider a reversible exothermic reaction in a plug flow reactor. Tmax = maximum permissible temperature. Tmin = minimum permissible temperature. To achieve desired conversion, temp profile that will require shortest residence time is initially a straight line at Tmax and then a downward parabola which would asymptote the x – axis.