Kinetic Study of a gas – phase catalytic packed bed membrane reactor

8/10/2019 Kinetic Study of a gas phase catalytic packed bed membrane reactor

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Kinetic Study of a gas phase catalytic packed bedmembrane reactor with pressure drop for a reversible

gas phase reaction with a competing side reaction

Applicant: Sukaran Singh Arora Instructor: Prof. Geoffery WildeStudent No.: 72597123

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Outline1. Description of the Problem2. Design of the Reactor

3. Structure to the Solution4. Design Equations, Assumptions and Initial

Conditions5. Numerical Methods Used6. MATLAB Code7. Results and Discussions8. References

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1. Description of the ProblemThe elementary gas phase reactionis carried out in a packed bed reactor with a

surrounding hydrogen permeable membrane. There isa heat exchanger surrounding the reactor, and there isa pressure drop along the length of the reactor,governed by the Ergun equation.

The competing reaction takes place with elementary kinetics. C is the desired product andD is formed in an undesired side reaction

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1. Description of the Problem(cont.)

The aim of the problem is to find the optimumtemperature (T) and pressure (P) for the PFR that willgenerate our desired production of C.Further addressing the factors that may affect our

decision in the design of the reactor based on theresults obtained.

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2. Design of the ReactorReactant B permeablemembrane

Q(Ta)

Q(Ta)

A, B, C A & BPFR

& DTT0

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3. Structure to the SolutionModeling a simple packed bed reactor with heattransfer and transfer of hydrogen through themembraneModifying the design equations and code toaccommodate the complexity introduced by theunwanted side reaction

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4. Design Equations, Assumptionsand Initial Conditions

A. Design EquationsB. AssumptionsC. Initial Conditions

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4. A. Design EquationsThe mass balances are based on the flow conditions andthe assumed reaction scheme. The mass balance can be written as:

The sign of the production term is negative if the substanceis consumed in the chemical reaction. With mathematicalnotations, the mass balance for substance i is

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4.A. Design Equations (cont.) is the amount of the substance, is themolar flow rate, and is the specificproduction/consumption rate of the substance.For gas phase reactions flow rate of the reactants (A &B) is usually specified as F A0 and F B0 as designparameters.

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4.A. Design Equations (cont.)The general design expression for a catalytic reaction interms of conversion is a molar balance on reactant A and istherefore given by:

Similar expressions can be written for the other species as well:

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4.A. Design Equations (cont.)The reaction rate expression for the reversiblereaction and unwanted side reaction is given by:

where k 1A and k 2B are the forward rate constant of thetwo reactions resp. and follow the Arrheniusexpression:

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4.A. Design Equations (cont.)The general energy balance can be written as:

which for only A and B in the initial feed and constantCp values simplifies to

where U a is the overall heat transfer coefficient, Ta isthe temperature of the surroundings, T is thetemperature of the reactor, Hir is the heat of the i th reaction. C pi is the heat capacity of the substance i

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4.A. Design Equations (cont.)The permeability rate of the reactant B is given by:

(Ideal gas law)

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4.A. Design Equations (cont.)The other various values are given by the followingexpressions:

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4.B. AssumptionsThe problem is worked assuming plug f low with noradial gradients of concentrations and temperature atany location within the catalyst bed. X denotes theconversion of A, defined by

and T denotes the temperature, which are bothfunctions of only the axial location within the catalystbed specified by the catalyst weight W.The heat capacities are assumed to be constant forboth the reactants and products.

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4.C. Initial ConditionsTable1. Parameter Values for the ProblemCpA = 40 J g -1 mol -1 K-1

CpB = 40 J g -1 mol -1 K-1

H1R = -40,000 J g -1 mol -1 K-1

H2R = 30,000 J g -1 mol -1 K-1

E1a = 41,800 J g -1 mol -1 K-1

E2a = 73,146.57 J g-1

mol-1

K-1

k 1A = 0.05 dm 9 kg -1 min -1 mol -2 at 450K

k 2B = 0.09 dm 6 kg -1 min -1 mol -1 at 450K

Kc = 25,000 dm 3 mol -1 at 450K

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4.C. Initial Conditions (cont.)Table1. Parameter Values for the ProblemT0 = 450 KR = 8.314 J mol-1 K-1

F A0 = 5 mol min-1

FB0 = 5 mol min -1 Ua = 0.8 J kg-1 min -1 K-1 Ta = 500 K = 0.015 kg-1 k

pB*(1/A*) = 0.5

P0 = 10 atm y A0 = 0.5 (equi molar feed)

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5. Numerical Method usedThe governing design equations combined with thekinetic expressions and auxiliary correlationscomprise nonlinear algebraic, ordinary differentialequations. The formulated model consists of these ordinarydifferential equations as an initial value problem.These set of equations are solved with 4th order

RungeKutta method/ode 45 built in MATLABfunction. At the end of the procedure it is possible to plotthe concentration of components and temperature versus length/weight of catalyst.

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7.A. Conversion, Normalizedpressure and T/1000 down thereactor

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7.A. Concentration of A, B, Cand D down the reactor

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7.B. Conversion, Normalizedpressure and T/1000 down thereactor

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7.B. Concentration of A, B, C andD down the reactor


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7.C. Plot of conversion vs.Temperature

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7.D. Plot of conversion vs. Pressure

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7.E. Optimum Parameters usingfminsearch

The optimum temperature and pressure are:503.535581 K & 45.644620 atm resp.

The final conversion at the optimum parameters is:0.99999999999984013.

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7.F. Some key points for reactordesign

At a constant pressure of 10 atm, we can see that our

conversion reaches a maximum at a temperature ofabout 430 K. If we increase the temperature beyond430 K, the rate of our unwanted reaction increases,and we see a drop in conversion. At a constant temperature of 450 K, we can see thatour conversion reaches a maximum at a pressure ofabout 23 atm. And according to the fminsearch, the optimum parametersare about 504 K and 46 atm.

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7.F. Some key points for reactordesign (cont.)However, usually, exceeding 30 atm in pressure is not

advantageous The gains in production are not worth the higherexpenditures (in capital investment and in operating costs)that would be associated with those operating pressures.Equipment for high pressure applications is much moreexpensive, the feed would need to be pressurized, etc.,and as in the real world, a project's budget must beeconomical, or else the project will never get off theground.

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7.G. Final Conclusion

So, the optimum set of parameters can be atemperature of 504K and pressure of about25 atm with a conversion of

9.999482459268932e-001

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8. References A Collection of 10 Numerical Problems in ChemicalEngineering for various Mathematical SoftwarePackagesThe Permeability of hydrogen in novel membranes atelevated temperatures and pressures ,B.D. Morreale1,3,M.V. Ciocco1, K.S. Rothenberger2, B.H. Howard2, A.V.Cugini2,3, R.M. EnickElements of Chemical Reaction Engineering, 4 th edition, H. Scott Fogler

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Kinetic Study of a gas – phase catalytic packed bed membrane reactor

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