Lec 3 Multiphase reacting systems-Gas-Solid Systemseacademic.ju.edu.jo/z.hamamre/Material/Advance...

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan

Tel. +962 6 535 5000 | 22888

1

Dr.-Eng. Zayed Al-Hamamre

Multiphase Reacting Systems:

Gas-Solid Systems

Advance Chemical Reaction Engineering


Tel. +962 6 535 5000 | 22888

2

Content

Introduction

Constant-Size Particle

Shrinking Particle


Tel. +962 6 535 5000 | 22888

3

Gas-solid reacting systems can be classified as systems in which

o The solid is reacted to another solid or other solids,

Or generally

Introduction


Tel. +962 6 535 5000 | 22888

4

Such a reaction is frequently encountered in the process industry (e.g., in coal gasification, in

ore processing, iron production in the blast-furnace, and roasting of pyrites.

The rate of such reactions depends on the relative magnitudes of the rate of transport and the

rate of reaction whether or not important gradients inside and around the particle are built up

or not.

Introductiono The solid disappears in forming gaseous product(s).


Tel. +962 6 535 5000 | 22888

5

Any of the following mass transfer resistances can be important

o Film diffusion: With a fast surface reaction on a nonporous particle, mass transfer

limitations can arise in the fluid phase.

o Pore diffusion: With porous particles, pore diffusion is likely to limit reaction rates at the

internal surface.

o Product layer diffusion: Many fluid-solid reactions generate ash or oxide layers that impede

further reaction.

o Sublimation: Some solids sublime before they react in the gas phase. Heat transfer can be

the rate-limiting step.

The surface reaction itself can be rate limiting.

Introduction

With gas-solid reactions the conditions inside the particle change with time, since the solid

itself is involved in the reaction.

The process is therefore essentially of a non-steady-state nature.


Tel. +962 6 535 5000 | 22888

6

Geometries Reacting Solids


Tel. +962 6 535 5000 | 22888

7

Geometries Reacting Solids


Tel. +962 6 535 5000 | 22888

8

Reaction Rate of Solids The reaction of solids occurs in the monolayer of molecules adsorbed on the surface of the

solid B,

The molecules of the solid react with the gaseous molecules to form a gaseous product and

remove solid molecules.

s


Tel. +962 6 535 5000 | 22888

9

Since is independent of the conversion of the solid, it is constant as long as any solid is

present.

The concentration of solid B at the surface is constant because new surface is exposed

continuously so that the concentration of exposed solid B, is always one monolayer

Reaction Rate of Solids

s


Tel. +962 6 535 5000 | 22888

10

A gas reacting with a solid of low porosity to

yield a porous non-reacted layer, often called

"ash" layer.

The reaction then takes place in a narrow zone

that moves progressively from the outer

surface to the center of the particle.

Such a situation is described by the so-called

heterogeneous shrinking-core model

Concentration proms of gas and

solid reactants

Qualitative Analysis


Tel. +962 6 535 5000 | 22888

11

When the transport rates through the two layers are not

too different and the true rate of reaction is not infinitely

fast,

o The situation is no longer as clear cut, and

o The sharp boundary between reacted and unreacted

zone no longer exists.



Tel. +962 6 535 5000 | 22888

12

When the transport through both reacted

and unreacted structures is usually fast

compared with the true reaction rate,

o The reaction rate, is governing the rate

of the overall phenomenon.

o Then there are no gradients whatever

inside the particle.



Tel. +962 6 535 5000 | 22888

13


Assumption

The reacting particle is isothermal.

The particle size remains constant during reaction.

The integrity of the particle is maintained (it doesn’t break apart),

The densities of solid reactant B and solid product (surrounding B) be nearly equal.

The single particle acts as a batch reactor in which conditions change with respect to time t.

The solid does not disappear or appear but rather transforms from one solid phase into another

as the reaction proceeds ,

Any effect of external mass transfer is the same in all cases, regardless of the situation within

the particle


Tel. +962 6 535 5000 | 22888

14


In a nonporous solid B,

Reactant A initially reacts with

the exterior surface of B,

As product solid (assumed to be

porous) is formed, A must

diffuse through a progressively

increasing thickness of porous

product to reach a progressively

receding surface of B.

There is a sharp boundary

between the porous outer layer of

product and the nonporous

unreacted or shrinking core of

reactant B


Tel. +962 6 535 5000 | 22888

15

In a very porous solid B,

Τhere is no internal diffusional resistance, all parts of the interior of B are equally accessible

to A, and reaction occurs uniformly (but not instantaneously) throughout the particle.

Ιn the general case

The reactant and product solids are both relatively porous, the concentration profiles for A and

B with respect to radial position (r) change continuously

is either zero (completely reacted outer layer) or ρBm (unreacted core of

pure B);



Tel. +962 6 535 5000 | 22888

16

For an isothermal spherical particle of radius R, a material balance for reactant A(g) around

the thin shell (control volume) of (inner) radius r and thickness dr, taking both reaction and

diffusion into account,

B.C 1

B.C 2



Tel. +962 6 535 5000 | 22888

17

the amount of B present in a particle is

The decrease in volume or radius of unreacted core accompanying the disappearance of dNB

moles of solid reactant is

For the reaction

I.C



Tel. +962 6 535 5000 | 22888

18

Two idealized models can be used to describe the reaction process

i. Progressive-Conversion Model

ii. Shrinking-Core Model

Uniform reaction model

Reactant gas enters and reacts

throughout the particle at all times,

most likely at different rates at

different locations within the

particle.

Thus, solid reactant is converted

continuously and progressively

throughout the particle

Progressive-Conversion

Model



Tel. +962 6 535 5000 | 22888

19

o Step 1: Diffusion of gaseous reactant A

through the film surrounding the particle

to the surface of the solid.

o Step 2: Penetration and diffusion of A

through the blanket of ash to the surface

of the unreacted core.

o Step 3: Reaction of gaseous A with solid

at this reaction surface.

Shrinking-Core ModelShrinking-Core Model

The reaction occurs first at the outer skin

of the particle.

The zone of reaction then moves into the

solid, leaving behind completely converted

material and inert solid (ashes)


Tel. +962 6 535 5000 | 22888

20

Shrinking-Core Model

Then, the conversion is

o Step 4: Diffusion of gaseous products through the ash back to the exterior surface of the

solid.

o Step 5: Diffusion of gaseous products through the gas film back into the main body of fluid.

Film formation model


Tel. +962 6 535 5000 | 22888

21


There is a sharp boundary (the reaction

surface) between the nonporous

unreacted core of solid B and the

porous outer shell of solid product

(sometimes referred to as the “ash

layer

Outside the particle, there is a gas film

reflecting the resistance to mass

transfer of A from the bulk gas to the

exterior surface of the particle.

As time increases, the reaction surface

moves progressively toward the center

of the particle; that is, the .unreacted

core of B shrinks.


Tel. +962 6 535 5000 | 22888

22

Shrinking-Core Model To find the time required to reach a fraction of B converted, for a spherical particle of species

B of radius R undergoing reaction with gaseous species A

The material balance across a thin spherical

shell in the ash layer at radial position r and with

a thickness dr,

G/S systems the shrinkage of the unreacted core is

slower than the flow rate of A toward the unreacted

core by a factor of about 1000, which is roughly the

ratio of densities of solid to gas.

Because of this it is reasonable to assume, in

considering the concentration gradient of A in the ash

layer at any time, that the unreacted core is stationary.


Tel. +962 6 535 5000 | 22888

23


B.C 1

B.C 2


Tel. +962 6 535 5000 | 22888

24



Tel. +962 6 535 5000 | 22888

25


and substitution of the resulting expression for


Tel. +962 6 535 5000 | 22888

26


But


Tel. +962 6 535 5000 | 22888

27

The resistances act in series and are all linear in concentration.

Shrinking-Core Model The time required for complete conversion of the particle


Tel. +962 6 535 5000 | 22888

28

Diffusion Through Gas Film Controls


No gaseous reactant is present at the

particle surface;

The concentration driving force is

constant at all times during reaction of

the particle

Where Sex is the unchanging exterior surface of a particle


Tel. +962 6 535 5000 | 22888

29


The variation of the

unreacted core with time


Tel. +962 6 535 5000 | 22888

30

Diffusion through Ash Layer Controls


Both reactant A and the

boundary of the unreacted

core move inward toward the

center of the particle.

In the ash layer, no reaction

of A take place (inert layer),

The shrinkage of the

unreacted core is slower than

the flow rate of A toward the

unreacted core by a factor of

about 1000,

Constant

The unreacted core is stationary

And


Tel. +962 6 535 5000 | 22888

31

Thus the rate of reaction of A at any instant is given by its rate of diffusion to the reaction

surface, or



Tel. +962 6 535 5000 | 22888

32


The progression of reaction in terms of the time required for complete conversion


Tel. +962 6 535 5000 | 22888

33



Tel. +962 6 535 5000 | 22888

34



Tel. +962 6 535 5000 | 22888

35

Chemical Reaction Controls


The progress of the reaction is unaffected by

the presence of any ash layer,

The rate is proportional to the available

surface of unreacted core


Tel. +962 6 535 5000 | 22888

36


The decrease in radius or increase in fractional conversion of the particle in terms of τ is


Tel. +962 6 535 5000 | 22888

37

Shrinking (Dissolving) Solid Particle When no ash forms, as in the burning of pure carbon in air, the reacting particle shrinks during

reaction, finally disappearing

o Step 1: Diffusion of reactant A

from the main body of gas

through the gas film to the

surface of the solid.

o Step 2: Reaction on the surface

between reactant A and solid.

o Step 3: Diffusion of reaction

products from the surface of the

solid through the gas film back

into the main body of gas.

There is no product or “ash” layer, and hence no ash-

layer diffusion resistance for A


Tel. +962 6 535 5000 | 22888

38

Shrinking (Dissolving) Solid Particle

The reacting particle is isothermal.

The particle is nonporous, so that reaction occurs only on the exterior surface.

The surface reaction between gas A and solid B is first-order

Model Assumption


Tel. +962 6 535 5000 | 22888

39



Tel. +962 6 535 5000 | 22888

40



Tel. +962 6 535 5000 | 22888

41

But



Tel. +962 6 535 5000 | 22888

42

Shrinking (Dissolving) Solid ParticleGas Film Diffusion Controls


Tel. +962 6 535 5000 | 22888

43

Example

Rearranging


Tel. +962 6 535 5000 | 22888

44

Example

Rearranging


Tel. +962 6 535 5000 | 22888

45

Example Cont.

The mass-transfer-limited growth time is much shorter than the reaction-limited growth time,

Therefore, the reaction should be nearly reaction controlled with a reaction time of 2.77 min.

Date post:	11-Feb-2020
Category:	Documents
Upload:	others
View:	19 times
Download:	0 times

Lec 3 Multiphase reacting systems-Gas-Solid Systemseacademic.ju.edu.jo/z.hamamre/Material/Advance...

Documents