Reaction engineering notes

  • Langmuir Hinshelwood model

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

relationship between rate of reaction and temperature

  • 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.

relationship between equilibrium constant and pressure for ideal gas

  • Equations for PFR, CSTR and batch reactor
  • Equation for PFR

equation for PFR

  • Equation for CSTR

equation for CSTR

  • Constant volume first order reaction in PFR/batch reactor

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.    

varying volume constant pressure reaction
varying volume constant pressure reaction

  • Rate Constant K for first order irreversible system for any ϵA

rate constant for first order irreversible system for varying volume system

  • Rate constant K for Zero order irreversible system for any ϵA

rate constant for zero order irreversible system for varying volume reaction

  • Varying volume batch reactor

Rate equation for varying volume batch reactor

rate constant for varying volume batch reactor

Rate equation for varying volume batch reactor first order reaction system

rate constant for varying volume batch reactor first order system

Rate equation for Varying volume batch reactor zero order reaction system

rate equation for varying volume batch reactor zero  order 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

conversion for second order constant volume irreversible system in 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

Final rate equation for a constant volume reaction of order n

  • Zero order reaction

Rate equation for zero order reaction is defined such that

rate equation for zero order reaction

  • Arrhenius law

Relationship between different rate constants

arrhenius law

  • Thiele Modulus
  • Thiele modulus for nth order irreversible reaction

thiele modulus for nth order irrversible reaction

  • Thiele modulus for solid catalyzed reaction

Thiele modulus for solid catalyzed reaction

  • Thiele modulus for spherical pellet

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

relation between reaction rates and theile modulus in case of strong pore diffusion resistance

  • 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:

effective order for nth order reaction in case of strong pore diffusin resistance

  • Reactors in series
  • PFR and CSTR in First order reaction

For N CSTR in series each of same volume V in first order reaction

N CSTR in series for first order reaction

For N plug flow reactors in series of same volume in first order reaction

N PFR in series for first order reaction

  • Space time and holding time
  • Holding time in batch reactor

holding time in batch reactor

  • Space time in plug flow 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

exit age distribution

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

exit age distribution

The fraction of the fluid that leaves the reactor with an age greater than t1

exit age distribution

E is defined as

exit age distribution

  • Exit age distribution for CSTR

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

exit age distribution for CSTR

  • Exit age distribution for PFR

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

exit age distribution for PFR

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

controlling activation energy among actual activation energy and diffusion activation energy

  • Interfacial area per unit volume of dispersion in gas-liquid contactor

interfacial area per unit volume of dispersion in gas-liquid contactor

  • Peclet number

Peclet number for ideal CSTR and ideal PFR

peclet number for ideal CSTR and ideal PFR

  • Conversion
  • Conversion in adiabatic reactor

conversion in adiabatic reactor

  • Finding conversion given heat of reaction

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

effectiveness factor of a catalyst

  • Effective rate constant

Effective rate constant in case of first order gaseous phase reaction catalyzed by non-porous solid

Effective rate constant for 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

temperature and pressure correction for concentration inside a reactor

  • Semi-batch reactor

Rate equation for semi batch reactor

rate equation for semi-batch reactor

  • Packed bed reactor

Rate equations for packed bed reactor

Rate equations for packed bed reactor

  • Equlibrium constant and gibbs energy

Calculating equilibrium constant for reaction Equlibrium constant and gibbs energy given gibbs energy for the reaction

calculating Equlibrium constant from gibbs energy

  • Reaction in series

Calculating time for concentration of B to be maximum

Calculating time for concentration of B to be maximum in a series reaction

  • Reversible reaction

For a reversible reaction reversible reaction

relationship between final concentration of A and equilibrium concentrationo of A in reversible reaction

  • Instantaneous fractional yield

Instantaneous fractional yield in case of pore diffusion

Instantaneous fractional yield in case of pore diffusion

    1. For reaction 

Instantaneous fractional yield in case of pore diffusion
Instantaneous fractional yield in case of pore diffusion

  • Concentration inside and outside catalyst surface

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

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

fractional yield

  • 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

selectivity of a reaction

  • 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

Fractional conversion of reactant

  • Half life of a reactant

Half life of a reactant in a first order system is defined as follows

Half life of a reactant in a first order system

  • Dispersion of PFR and CSTR

Zero dispersion implies reactor is plug flow reactor (PFR) and infinite dispersion implies reactor is CSTR

Dispersion of PFR and CSTR

  • Rate of reaction of species j

For homogenous system rate of reaction for species j is defined as

homogeneous rate of reaction for a particular species

  • First moment of RTD function

First moment of RTD function is mean residence time

First moment of RTD function is mean residence time

  • Mean residence time

In a pulse tracer experiment mean residence time is given by

pulse tracer experiment mean residence time

  • 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

recycle ratio

  • Ratio of volume of reactors

In CSTR ratio of volumes V1 and V2 for different conversion x1 and x2

ratio of volume of reactors for different conversion

  • 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

rate equation for second order batch/Plug flow constant volume reactor

  • Time required for conversion F

Time required in a reaction for conversion F (conversion F is the fraction of reactants converted to products)

time required for conversion F

  • Plug flow reactors in parallel

If two plug flow reactors PFR1 and PFR2 are in parallel then

equation for plug flow reactors in parallel

  • Vapour phase catalytic reaction

Vapour phase catalytic reaction with equimolar reactants and surface reaction is rate controlling then rate equation becomes

rate equation for vapour phase catalytic reaction with equimolar reactants when surface reaction is rate controlling

  • Least square regression method

least square regression  method

  • Second order unimolecular reaction rate

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

relationship between rate constant and 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

mean conversion in the exit stream for a second order liquid phase reaction in a non-ideal flow reactor

  • 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.