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Membrane Reactors Modeling

  • Marcello De Falco
Chapter

Abstract

The present chapter deals with mathematical modeling strategies for reactors and membrane-based separators simulations. Firstly, the various types of models for both fixed bed reactors and hydrogen separation membranes and with different complexity grades are described and assessed. Then, two membrane reactor configurations are modeled: the integrated membrane reactor (IMR), in which the hydrogen selective membrane is assembled inside the reaction environment, and the staged membrane reactor (SMR), where the membrane is assembled outside the reactor in separation units placed after the reaction step. Models’ equations, boundary conditions, and numerical solution strategies are reported in this chapter, in order to clarify criticalities of reactor modeling and benefits achievable for researchers and reactor designers by properly simulating all chemical and physical phenomena occurring in a membrane reactor.

Keywords

Membrane Reactor Hydrogen Partial Pressure Hydrogen Permeation Selective Membrane Retentate Side 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

a

External particles total surface to reactor volume ratio

Ai

Bed size heat exchanging surface

Ao

Heating fluid media heat exchanging surface

Am

Log mean of A i and A o

BH

Hydrogen permeability

CA

Concentration of component A

CA,s

Concentration inside catalyst particle

\( C_{\text{A}}^{\text{S}} \)

A-component concentration on catalyst surface

cH

Hydrogen concentration

\( c_{{{\text{H}}_{2} ,{\text{high}}}} \)

Hydrogen concentrations in high pressure mixture streams

\( c_{{{\text{H}}_{2} ,{\text{low}}}} \)

Hydrogen concentrations in low pressure mixture streams

cp

Gas mixture specific heat

cp,perm

Specific heat in permeation zone

D

Hydrogen diffusion coefficient through membrane

De

Effective diffusivity in catalyst

Dea

Effective axial diffusivity

Der

Effective radial diffusivity

dmem

Membrane diameter

dmem,i

Internal membrane diameter

dmem,o

External membrane diameter

dp

Equivalent catalyst particle diameter

dt

Internal tubular reactor diameter

Ea

Membrane permeability apparent activation energy

f

Friction factor

G

Superficial mass flow velocity

(−ΔH)

Heat of reaction

hex

Heat transport coefficient in the external side

hf

Heat transport coefficient between gas and solid phase

hperm

Heat convective transport coefficient in the permeation zone

hW

Heat transport coefficient in the first layer near the tube wall

J

Hydrogen flux through membrane lattice

\( J_{{{\text{H}}_{2} }} \)

Hydrogen flux through the membrane

Kg

Mass transport coefficient between gas and solid phase

kmet

Tube wall conductivity

P

Reaction pressure

P0

Membrane permeability pre-exponential factor

Pea

Axial Peclet number

Pemr

Mass effective radial Peclet number

\( p_{{{\text{H}}_{2} }} \)

Hydrogen partial pressure

\( p_{{{\text{H}}_{2} ,{\text{r}}}} \)

Hydrogen partial pressures in retentate side (high hydrogen partial pressure)

\( p_{{{\text{H}}_{2} ,{\text{p}}}} \)

Hydrogen partial pressures in permeate side (low hydrogen partial pressure)

R

Universal gas constant

rA

A-component reaction rate

\( r_{{{\text{H}}_{2} }} \)

Hydrogen reaction rate

ri

i-Component reaction rate

Rmem

Selective membrane radius

S

Hydrogen solubility

T

Reactor operating temperature

Tperm

Permeation zone temperature

Tr

Temperature of heating/cooling fluid

Treac

Reaction zone temperature

TS

Temperature on catalyst surface

Ts

Temperature inside catalyst particle

TW

Reactor tube wall temperature

U

Overall heat transport coefficient between the external and reaction bed

U1

Overall heat transfer coefficient between reaction and permeation zone

us

Gas superficial velocity

us,high

Superficial gas velocity in separator high pressure zone

us,low

Superficial gas velocity in separator low pressure zone

us,perm

Superficial gas velocity in permeation zone

Vp

Pellet volume

z

Reactor axial coordinate

zperm

Axial coordinate of membrane module

Greek Letters

αmem

Membrane thermal conductivity

ε

Void fraction of the packed bed

δ

Membrane thickness

η

Catalyst effectiveness factor

λe

Thermal conductivity in catalyst

λer

Effective radial thermal conductivity

ξ

Radial coordinate inside catalyst particle

μg

Gas mixture viscosity

ρB

Catalytic bed density

ρg

Gas molar density

ρg,perm

Gas density in permeation zone

Abbreviations

BVP

Boundary value problem

IMR

Integrated membrane reactor

ODE

Ordinary differential equation

PDE

Partial differential equation

SMR

Staged membrane reactor

References

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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Faculty of EngineeringUniversity Campus Bio-Medico of RomeRomeItaly

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