Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor

8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor

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Department of Chemical and Biomolecular Engineering

Modelling and simulation of water gas shift reaction in a packed-bed membrane reactor

system

Wu Chengliang (A0086696H)

Final Report

In partial fulfilment of the requirements for the Bachelor of Engineering (Chemical) Degree.


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Foreword

So, there was an Asian guy, you see, hunkered down at a table, in a cafe in Israel. Hes the

only one whos doing any hardcore studying there, with the obligatory, presence-justifying

cappuccino. Hes processing these equations which no layman really understands, with lots of

triangles, dots, and d-something over d-something. Hes reading up on these things called

Fluid Mechanics, Reaction Engineering, Particle Technology and Numerical Simulation. He

seems unsure of whats going to happen, and appears to be contemplating as to whether hed

bitten off more than he can chew.

Fast forward to December, this guys more or less got his simulations in place. They take

approximately 5 minutes to solve each, the rainbow plots look beautiful, and hes got a whole

new depth of understanding in an alien CFD software.

Its been a long, long journey, but a very meaningful FYP. Something that integrates 4 -5

courses worth of content is by no means an easy endeavour, compounded by the youre-on-

your-own nature of a computational FYP. Ive had a couple of hair-tearing and sleepless

nights, but I guess the patchwork quilt of data, tips and guidance from 1001 sources from

Singapore to Romania, came together eventually.

Thanks aside, during this intensive period of studying and simulating, I have bumped into

many sources of literature where the content appeared excessively-complex, and was just

plain impossible for an undergraduate, much less a layman, to digest. Intentional or not,

nobody, Professor, Graduate, Undergraduate, should have to endure incomprehensible

content. Therefore, every attempt has been made in this report to explain concepts that are

relatable to undergraduate chemical engineering content, so that anybody who reads this

thesis doesnt have to bang his head against the wallso much.

Chengliang, WU


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Abstract

Packed-bed membrane reactors (PBMRs) have shown promise in improving conversions of

equilibrium reactions, through their ability to remove the product as it is formed, forcing the

forward reaction to be favoured even further.

The research group has expressed interest in understanding the various phenomena, as well as

sensitivity of hydrogen production/CO conversion to various parameters, in one such PBMR

for the water-gas shift (WGS) reaction. This PBMR utilizes a Pd-Ag alloy hollow fiber

membrane separation module and Ni-Cu catalyst particles, and operates under experimental

conditions stipulated by said group.

To this end, a 2D-axisymmetric mathematical model has been developed and simulated in a

Finite Element Method (FEM) solver, COMSOL Multiphysics (Ver 4.4), under said materials

and conditions. The model is capable of describing concentration, velocity, density, viscosity,

and pressure profiles inside the reactor in both radial and axial coordinates, and its behaviour

has been validated, and determined to be consistent with phenomena expected of a PBMR.

In addition, the model has also performed a sensitivity study, inspecting the effect of 8

different parameters on the reactor performance. These parameters include reaction

temperature, flow rate, steam-carbon ratio, and product presence in the feed. The individual

studies produce and compare H2 production/CO conversion/CO equilibrium conversion in

response to parameter variations, and culminate in recommendations for operating said

reactor.

The objectives, observations, and conclusions have been placed in table form towards the end

of this paper, as a concise reference for the readers convenience. In addition, a guide is

appended at the end (Appendix II) to facilitate replication of this model for further study,

along with advice to achieve numerical convergence more quickly.


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Contents

Foreword .................................................................................................................................... 2

Abstract ...................................................................................................................................... 3

1. Background ......................................................................................................................... 6

1.1. Water-Gas Shift Reaction and Membrane Reactors ................................................... 6

1.2. Model Set-up ............................................................................................................... 7

1.3. Objectives of Project ................................................................................................... 8

2. Theoretical Background/Literature Review ....................................................................... 9

2.1. Fundamentals .............................................................................................................. 9

2.2. Literature Review ...................................................................................................... 10

3. Modelling Process ............................................................................................................ 12

3.1. Major Assumptions ................................................................................................... 12

3.2. Key points ................................................................................................................. 13

3.3. Modelling Approach (Shell Side) ............................................................................. 14

3.3.1. Momentum TransportDarcys Law ................................................................ 14

3.3.2. Mass Transport and ReactionMaxwell-Stefan Diffusion .............................. 16

3.3.3. Mass Transport and ReactionHeterogeneous Rate Law ................................ 17

3.3.4. Energy TransportPseudo-homogeneous Assumption .................................... 19

3.4. Modelling Approach (Tube Side) ............................................................................. 20

3.4.1. Momentum TransportNavier-Stokes Equations ............................................ 20

3.4.2. Mass TransportFicks Law of Diffusion ........................................................ 21

3.4.3. Energy TransportHomogeneous Fluid ........................................................... 22

3.5. Boundary Conditions................................................................................................. 22

3.5.1. Momentum Transport Boundary Conditions ..................................................... 23

3.5.2. Mass Transport Boundary Conditions ............................................................... 24

3.5.3. Sieverts Law Boundary Condition................................................................... 25

3.5.4. Heat Transport Boundary Conditions ................................................................ 26

3.6. Glossary of Symbols ................................................................................................. 29

4. Simulation of WGS ReactionFirst Study and Validation ............................................. 31

4.1. Meshing and Solver Configuration ........................................................................... 31

4.2. Model Study and Validation - Conditions................................................................. 32

4.2.1. Momentum Transport Study and Validation ..................................................... 33

4.2.2. Mass Transport Study and Validation................................................................ 37


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4.2.3. Heat Transport Study ......................................................................................... 44

4.3. Counter-Current versus Co-Current Configuration .................................................. 45

5. Simulation of WGS ReactionDetailed Sensitivity Studies ........................................... 48

5.1. Experimental ConditionsSet 1 (Effect of Temperature) ....................................... 48

5.1.1. ResultsSet 1 (Effect of TemperatureConcentration Profiles) ................... 50

5.1.2. ResultsSet 1 (Effect of TemperatureCO Conversion Profiles) ................. 51

5.2. Experimental ConditionsSet 2 (Effect of Flow Rates) .......................................... 53

5.2.1. ResultsSet 2 (Effect of Flow RatesHydrogen Concentrations).................. 53

5.2.2. ResultsSet 2 (Effect of Flow RatesCO Conversion Profiles) .................... 55

5.3. Experimental ConditionsSet 3 (Effect of Steam-Carbon Ratio) ........................... 56

5.3.1. ResultsSet 3 (Effect of SC RatiosHydrogen Concentrations).................... 57

5.3.2. ResultsSet 3 (Effect of SC RatiosCO Conversion Profiles) ...................... 59

5.4. Experimental ConditionsSet 4 (Effect of Shell Pressure) ..................................... 61

5.4.1. ResultsSet 4 (Effect of Shell PressureHydrogen Concentrations) ............. 62

5.4.2. ResultsSet 4 (Effect of Shell PressureConversion Profiles) ...................... 63

5.5. Experimental ConditionsSet 5 (Effect of Sweep Gas Rate) .................................. 64

5.5.1. ResultsSet 5 (Effect of Sweep RateConversion Profiles) .......................... 65

5.6. Experimental ConditionsSet 6 (Effect of Inlet H2 Presence) ................................ 67

5.6.1. ResultsSet 6 (Effect of Hydrogen PresenceConversion Profiles) .............. 68

5.7. Experimental ConditionsSet 7 (Effect of Inlet CO2 Presence) .............................. 69

5.7.1. ResultsSet 7 (Effect of Inlet CO2 PresenceConversion Profiles) ............... 70

5.8. Experimental ConditionsSet 8 (Effect of Permeability) ....................................... 72

5.8.1. ResultsSet 8 (Effect of PermeabilityConversion Profiles)......................... 73

6. Conclusions ...................................................................................................................... 75

7. Future Work ...................................................................................................................... 77

8. Acknowledgements .......................................................................................................... 78

9. References ........................................................................................................................ 79

Appendix IDerivation of Rate Constant for Rate Law ........................................................ 81

Appendix II - Step-by-Step Modelling Guide in COMSOL 4.4 Update 1 .............................. 81


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1.

Background

1.1.

Water-Gas Shift Reaction and Membrane Reactors

The water-gas shift reaction is a widely-utilized industrial reaction used in the production of

hydrogen gas, and can be found in examples such as shift converters downstream of steam-

methane reforming units. It is a mildly-exothermic reversible reaction.

CO(g)+ H2O(g) CO2(g)+ H2(g) H = -41.8kJ/mol

It has been of interest to conduct this reaction in a membrane reactor, which is an integrated

reaction-separation device that removes H2 as it is being produced, allowing equilibrium

limits to be bypassed, and achieving greater production as a result. A pictorial representation

can be seen below:

Fig 1.1Dynamics of a packed-bed membrane reactor (PBMR)

Multiple types of membrane reactors are available (Doraiswamy, 2014), but in the context of

this simulation, the packed bed membrane reactor, (PBMR), also known as the inert

membrane reactor (IMR) model, will be considered. This model consists of a packed bed


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reactor in the annular region, containing an inert, selectively-permeable membrane tube as the

tubular region. Its schematic will be visualized and discussed in the next section.

1.2.

Model Set-up

Fig 1.2The experimental set-up for the reaction.

The experimental set-up stated by the research group consists of a hollow fiber membrane

module inserted into a packed bed of fine catalyst particles (5Ni/5Cu supported on CeO 2),

with bed porosity of 0.4, synthesized by Saw et. Al (2014). The feed, whose temperature and

flow rate varies between 400-600C and 50-100mL, is inserted into the annular region of the

PBMR, where the catalytic reaction occurs at 2 barg, and product H2 gas subsequently

diffuses into the gaseous sweep region, maintained at 1 atm, with a helium sweep gas set at

0.5m/s by the candidate. The default mode of operation is co-current.


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1.3. Objectives of Project

Through this process, the candidate hopes to achieve the following:

S/N Objective Achieved via

1 Produce and simulate a sufficiently-rigorous

model for the reactor.

Modelling with reference to

appropriate literature sources.2 Verify the operational advantage that a

membrane reactor offers, over an equivalent

reactor without membrane activity.

Using a validation model,

comparing the outlet CO2concentrations between 2 reactors;

1 whose membrane is enabled, 1

whose membrane is disabled.

3 Study and validate the general phenomena

associated with the experimental conditions,

including velocity, density, and pressure profiles.

Simulating a validation model,

based on median experimental

conditions, and performing a study

of said parameters.

4 Study of effect of operating temperature on H2

production and conversion.

Temperature Sweep

5 Study of effect of residence time (flow rate) on

H2production and conversion.

Flow Rate Sweep

6 Study of effect of steam-carbon ratio in feed on

H2production and conversion.

Steam-Carbon Ratio Sweep

7 Study of effect of reaction (shell) pressure on H2production and conversion.

Pressure Sweep

8 Study of effect of Helium gas sweep rate on CO

conversion.

Helium Gas Sweep

9 Study of effect of inlet H2on CO conversion. H2 inlet concentration Sweep

10 Study of effect of inlet CO2 on CO conversion CO2 inlet concentration Sweep11 Study of effect of various membrane

permeabilities on CO conversion

Membrane permeability Sweep

Table 1.3.1Various Objectives to be achieved in the Project

Four terminologies in the above table warrant further elaboration; (1) Sufficiently-rigorous

refers to modelling with minimal simplifying assumptions, to assume only when clearly

validated/not a major consideration in literature. A case in point is to use the momentum

conservation equation to create velocity profiles instead of assuming a constant velocity

profile, which is a common practice in undergraduate Reactor Engineering coursework. (2)

Sweep refers to performing the same simulation, under similar conditions, with variations to

a single variable to study its impact. CFD terminology refers to this as a Parametric Sweep,

henceforth the Sweep term. (3) H2 Production refers to H2 produced in terms of

concentration, in the tube side, considering that the objective of the membrane reactor is to

produce high purity, usable H2 (which is basically the H2 in the tube side). (4) Study refers


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to identifying trends, as well as the sensitivity, between a certain parameter and the result (in

terms of H2 production or CO conversion or both, where appropriate), and providing a

recommendation at the end of the evaluation.

2. Theoretical Background/Literature Review

2.1.

Fundamentals

In typical undergraduate coursework, the end goal of a Reactor Engineering coursework is to

calculate conversion upon a certain reactor volume or catalyst weight. This approach

normally assumes 1D plug-flow behaviour, meaning that there is a constant, flat velocity

profile that has no r-component. This practice allows one to synthesize a mole balance

equation around a differential section of the plug flow, packed-bed reactor, and integrate the

constant velocity value into said equation. According to Doraiswamy (2014), such an

approach is valid for an isothermal situation where no axial or radial gradients exist

(temperature/velocity gradients in this case). However, this method of thinking falls apart in

this project, because PBMRs are characterized by marked compositions and temperature

radial profiles (Falco, Marrielli, & Iaquaniello, 2011), and therefore require a 2D approach at

the minimum. This claim is further justified by the non-isothermal nature of the water-gas

shift reaction, and fluid property alterations, such as density and viscosity, along the length of

the reactor due to reaction and departure of H2 species.

Therefore, 2D fundamental equations of momentum, mass, and energy transport have to be

solved in order to evaluate concentration profiles of individual species. The momentum

equations calculate pressure and velocity profiles in the reactor, which will be coupled to

mass and energy transport equations, to solve for concentration and temperature profiles.

Simultaneously, the mass and energy transport equations will register changes in fluid

properties (density/viscosity/temperature/heat capacities), in turn affecting the momentum


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equations. Therefore, the coupling of these 3 aspects, in both the shell and tube side, will be

elaborated upon, and simulated in the next chapter, to enable the reader to fathom their

interplay.

2.2. Literature Review

Modelling of PBMRs in the literature, specifically with a shell packed-bed and a tube sweep,

are generally few and far in between, mainly because there are many different configurations

of membrane reactors. This issue is exacerbated when the reaction in question is the water-

gas shift. As of this date, no literature source has been found which utilizes similar CFD

software (COMSOL Multiphysics), for the project PBMR.

With the lack of a direct reference to build upon, a fresh modelling approach is necessary.

Therefore, the scope of the review has expanded to include mainly membrane reactors of

different configurations/reactions, simulated in COMSOL, which contain useful modelling

information that will be deployed in the project PBMR. In this section, 3 major references

which helped in determining the modelling equations/practices in this project will be

discussed and their relevancies elaborated upon briefly.

Iyoha (2008)Modelling and simulation of high temperature water gas shift reaction.

Iyoha (2008), in his PhD thesis, modelled the water-gas shift reaction in the case of a non-

packed bed reactor, where the reaction was in the tube side, and the permeation was in the

shell side. His model, which considered only the reaction side, assumed laminar flow,

Maxwell-Stefan diffusion, and was isothermal. His results managed to achieve a good

agreement with his experimental data.

Iyohas context starklyvaried from this version in terms of operating configuration (reaction

was on the tube side instead), packed bed presence (his had none), and isothermality (his

context is, this project is not). Nonetheless, his Maxwell-Stefan diffusivity data, which


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reflects the interaction between all 4 components of the water-gas shift reaction, can be used

as a good approximation of mass diffusion in the shell side of the project PBMR, given the

good agreement with experimental data.

Carcadea, Varlam, & Stefanescu, (2012) Heat transfer modelling of steam methane

reforming

Carcadea et.al (2012) utilized a model which was much closer to the project PBMR, using a

shell side packed bed (albeit with a serpentine shape, which is not practised here) and a tube

side sweep as well. However, the major difference is that the reaction in their model is the

steam-methane reforming reaction, and not the water-gas shift.

Nonetheless, there were useful observations made; the work deployed Darcys Law in the

packed bed, along with Maxwell-Stefan diffusion, and the heat equation. In particular,

Caracadea et.als assumption of Darcys Law as the momentum transport equation in the

packed bed is verified by a separate article (Manundawee, Assabumrungrat, & Wiyaratn,

2011), which meant that Darcys Law is a credible momentum transport equation in the

packed bed. In addition, the heat equation is also a good lead to pursue for this project.

COMSOL Inc., (2008)Fixed Bed Reactor for Catalytic Hydrocarbon Oxidation

This demonstration model provided by COMSOL Inc, a simulation software company,

illustrated reacting flow through a packed bed with heat transfer effects (no membrane). The

noteworthy point is that a pseudo-homogeneous assumption was applied for heat transfer,

meaning that the catalyst pellets and fluid in the packed bed were assumed to be a single

phase. This simplified the modelling, but required an effective thermal conductivity for this

single phase. The pseudo-homogeneous assumption will later be deployed in the modelling of

the project PBMR.


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3.

Modelling Process

Drawing upon the theoretical background acquired earlier, the modelling equations will be

applied. A summary of the modelling approach is enclosed here.

Fig 3: Modelling Summary

3.1.

Major Assumptions

These following assumptions will be deployed in the entire model. Subsequent assumptions

made will be specific to the context of that particular phenomenon to facilitate structure in

explanation.

Ideal Gas Law:

Owing to the high temperature (>500C), and relatively low pressure (


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discussion, it will be assumed that these phenomena do not manifest to a significant extent.

Moreover, these effects were also not captured in the 3 references.

Gravity effects not considered:

To simplify the modelling process, it is assumed that the impact of gravity is negligible.

Similarly, these effects were not captured in the references.

Properties do not vary in the angular direction:

This allows the model to be simplified to a 2D, axisymmetric model, drastically-reducing

computational time. This approach has been validated in the literature, including (Carcadea et

al., 2012; Iyoha, 2007).

Modelling is steady-state:

All time-dependent derivatives are automatically eliminated from the governing equations, as

there are no transient properties necessitating inspection.

Membrane is reflected as having negligible thickness in the model:

This is to facilitate ease of visual comparison between shell and tube sides. Also note that the

effect of thickness on conversion/hydrogen production has been absorbed into the membrane

permeability term, which will be discussed downstream of this report as a sensitivity study.

3.2. Key points

Before the modelling approach is discussed in-depth, the reader is requested to consider that:

1. All velocities listed in the governing equations are velocity fields, and are vector

quantities, unless otherwise stated (for instance, through the z suffix, to indicate the

z-direction velocity). Therefore, the word velocity refers to the vector quantity.


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2. The gradient and divergence operators operate in a cylindrical geometry. However,

because of the axi-symmetric nature, angular derivatives (theta) are eliminated.

3.3.

Modelling Approach (Shell Side)

3.3.1. Momentum Transport Darcys Law

As the shell side of the reactor consists of a packed bed with spherical catalyst pellets, the

governing equations describing flow and pressure drop must be compatible with this

phenomenon. Before determining the appropriate transport phenomena, some understanding

of flow properties has to be applied.

Laminar Flow

The flow is assumed to be laminar, owing to the low velocity of the fluid. This property can,

and will be verified using the simulation results downstream.

Incompressible Flow

As the reactor is operating at a moderate pressure (2 barg maximum), and that Mach number

(that is, the fluid velocity compared to the speed of sound) is easily less than 0.3,

incompressible flow is assumed. This is not to imply that fluid density is an absolute constant

throughout the reactor; incompressible flow merely decouples pressure from density. Owing

to H2 diffusion, the velocity profile is expected to be impacted. This will be reflected in terms

of changes to gas dynamic viscosity and density, which are molar averaged values of their

individual components, as per the following equations:

Where , and refer to dynamic viscosity, molecular weight, and density respectively.


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Darcys Law

Darcys Law is a simplified version of the Navier-Stokes equations. Darcys law assumes

laminar flow, an incompressible fluid, and considers bed porosity and permeability. This law

generally applies to low velocity fluids (i.e. Rep< 10), and has been utilized by similar IMR

models, including Carcadea, Varlam, & Stefanescu, (2012) and Manundawee,

Assabumrungrat, & Wiyaratn, (2011). The governing equations are as follows:

Continuity

Discharge rate per unit area (m/s), or Darcy Velocity, or Superficial Velocity

Where

for a packed bed should be determined by the work of Carman-Kozeny (Reed,

2008), which states that:

Where K = 5 for packed beds, and the bed porosity, , is 0.4, according to the conditions ofthe experiment for which this model is tied to.

It is important to note that Darcys Velocity is not the true velocity at which the fluid moves

(Honrath, 1995). This can be explained with a simple analogy; suppose fluid is leaving a

nozzle at velocity U. Thereafter, an object blocks part of the nozzle. As a result, the true

velocity of the fluid, u, is faster due to the smaller flow area, even though the discharge rate

per unit area (i.e. Darcys Velocity) remains unchanged.


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Therefore, the true velocity, u, is Darcys Velocity divided by the porosity of the bed, as

expressed by:

As COMSOLs Darcys Law interface produces Darcy velocity fields, it is important to

correct the Darcy Velocity to the true velocity when integrating this physics with the

subsequent sections (heat and momentum balance).

3.3.2. Mass Transport and Reaction Maxwell-Stefan Diffusion

As the reaction system is a concentrated one, where reactants are of comparable orders of

magnitude, and there is no single solvent, rules for a binary system (i.e. Ficks Law) cannot

be applied. The alternative is the Maxwell-Stefan diffusion, which describes mass transport in

multi-component systems. In such a system, for instance, a ternary system, where species A,

B, C are concerned, the interactions between A-B, A-C, and B-C have to be considered in the

evaluation of the molar fluxes. In a similar vein, the interactions between the 4 species in the

water-gas shift system have to be considered, which the Maxwell-Stefan equations are

capable of illustrating. Considering these interactions gives rise to the individual Maxwell-

Stefan component mass transport equations, which are listed as follows, for each of the 4

water-gas shift components.

Component Mass Balance

Mass Flux Vector, relative to mass-averaged velocity, ji


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Mass Flux Vector, relative to fixed axis,

The diffusional driving force in the relative mass flux vector, , can be represented as:

Most prominently, reflects the Maxwell-Stefan diffusivity between 2 distinct species, theith and kth. Its values for a water-gas shift system, is described by (Iyoha, 2007) as 2e-5 for all

species. As can be seen, the inter-species interactions have been considered.

One noteworthy point is the thermal diffusion coefficient, , which is not to be confusedwith thermal diffusivity. Thermal diffusion is the coupled effect between gradients of

concentration and temperature (Leahy-Dios, Zhuo, & Firoozabadi, 2008). This phenomenon

is also referred to as the Soret effect. Values for these coefficients have to be determined

experimentally, and none have been found for the water-gas shift reaction as of the time this

report is made. Therefore, they are assumed to be zero. While this inadvertently leads to some

loss in accuracy, this assumption is partially-validated by the mildly-exothermic nature of the

water-gas shift reaction; temperature gradients are expected to manifest, but should not

interfere with the diffusion phenomena too significantly. The validity of this assumption will

be evaluated in the Results section.

3.3.3. Mass Transport and Reaction Heterogeneous Rate Law

The rate law in this context derives from the work of (Saw et al., 2014), which has been

converted to concentration basis instead of partial pressure basis, via the ideal gas law. This

measure is necessary to allow COMSOL, which produces concentration profiles throughout

the entire reactor, to calculate the rate of reaction. The original rate law is reflected here for

its conciseness, which allows further elaboration in the next section.


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The original form is as below:

)]There are a few noteworthy points in this rate law. Firstly, the value of the pre-exponential

factor , was not published along with the rate law for unknown reasons. However, anestimated value was back-calculated using the initial conditions from an experiment (see

Table 3 of Saws work), and was deduced to be ~5493(units are not covered here to avoid

confusion). This may not be the exact value, but is in the same order of magnitude

nonetheless, which is critical for accuracy. The derivation is covered in Appendix I.

A second point which warrants elaboration is the effectiveness factor, which is a factoraccounting for the mass transfer resistance encountered when the reactants diffuse from the

bulk fluid to catalyst surface. The effectiveness factor is limited to this context because the

catalyst particle has little pore, and therefore the assumption follows that mass transfer

resistance to reaction occurs solely through external mass transfer. Subsequently, the value of

0.9 has been agreed upon with one of the authors of the rate law to be a valid representation

of the effectiveness factor.

Thirdly, the term represents the reversibility factor, which is common in catalytic rate lawswhere equilibrium is concerned. It is a function of concentrations of individual species, in this

case,

Where:

The variables involved in the reversibility factor will also be treated as such; they will be

input into COMSOL as variables which have to be evaluated at every single position along

the reactor.


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3.3.4. Energy Transport Pseudo-homogeneous Assumption

To evaluate heat transfer, the heat equation is deployed. The heat equation is essentially the

differential form of the First Law of Thermodynamics combined with Fouriers Law of heat

conduction. This equation can be solved separately from the Navier-Stokes equations because

of the incompressible assumption (Incompressibility means that an additional equation of

state relating density to pressure does not need to be solved, since they are decoupled). In

addition, there is an application of the pseudo-homogeneous assumption. This assumption,

commonly-used in modelling approaches where 2D concentration profiles within the reactor

are required (Gallucci, 2011), assumes that the catalyst pellets and fluid phase form a single

coherent phase. This assumption has been utilized in a packed-bed reactor model (COMSOL

Inc., 2008).

In this equation, the density, fluid heat capacity, true velocity, and enthalpy of reaction have

all been factored in. Details of the implementation will be reflected in Appendix II.

Of particular interest is the effective thermal conductivity, term. This is an empiricalvalue which describes the combined thermal conductivity of the packed bed and its fluid.

Extensive literature studies have been performed for heat transfer in packed beds,

corresponding to different shapes, packing patterns, and reactor geometries. Owing to time

constraints, it is not possible to sieve out the most accurate one, and therefore a classic model

by Bruggemann (1935), as proposed by Madhusudana, (2014), is used, which is less

convoluted to use compared to most correlations. The model states the following

relationships:


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)Where

= Ratio of effective to fluid thermal conductivities, and

= Ratio of solid to fluid

thermal conductivities.

The following values were used to arrive at the value of .Species Thermal Conductivity Source

Ni-Cu catalyst 40 W/m.K (Ho, Ackerman, Wu, Oh, &

Havill, 1978)

Fluid (mass-averaged

thermal conductivity, assume

5:1 steam-carbon ratio)

0.01664 W/m.K National Institute of

Standards and Technology,

US Dept of Commerce

(1984)Pseudo-homogeneous phase 35.46 W/m.K Calculated by Bruggemann

relation

Table 3.3.4: Values used in calculating Lambda.

As the value of effective thermal conductivity lies between fluid and catalyst particle

conductivities, the Bruggemann relation has proven to yield a logical value, which will be

used in the simulation.

3.4. Modelling Approach (Tube Side)

The tube side is also known as the sweep region. Hydrogen diffuses through the membrane

from the shell to this region, where a flowing fluid, also known as a sweep gas, carries it

away for usage. In this context, helium gas will be used, for its inerting characteristic.

3.4.1. Momentum Transport Navier-Stokes Equations

This region assumes the incompressible Navier-Stokes equations, owing to the generally low

velocity of the sweep gas. These equations read:

Continuity

Momentum


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Note that the density, velocity, viscosity and pressure values are appended with a 2 suffix to

indicate that they are in the tube side. The volume force term, F, which reflects gravity, is

ignored for simplicity purposes, as per the assumption in the earlier chapter.

3.4.2. Mass Transport Ficks Law of Diffusion

The tube side consists of helium gas and a much smaller quantity of hydrogen. Therefore, this

is a binary system, for which Ficks Law of diffusion is valid (FicksLaw applies to dilute

systems or binary systems). However, it is of interest to consider only the hydrogen

concentration profile in the reactor. Therefore, only one mass transport equation for hydrogen

is necessary. Note that H2is referred to as component i for standardization purposes.

It is important to also note that the right hand side of the equation is zero. This is because

there is no reaction term in the sweep/tube region, and therefore the equation is purely a

transport-based version, with diffusion and convection transport modes reflected in the first

and second source terms of the equation.

The diffusion coefficient, , in the tube side, reflects the diffusion of H2 through the sweepgas. Its mass diffusivity can be evaluated by the correlation of Hirschfelder et.al (1949), as

proposed by (Welty, Wicks, Wilson, & Rorrer, 2008), where:

At 293K and 1 atm, Welty et al., (2008) has identified as 1.64cm2/s. Using theHirschfelder correlation, at 773K and 1 atm, becomes 7.02cm2/s. Note that thisrelation assumes weak temperature dependency of the collision integral, a term which existed

in the original correlation (this claim was also verified by the earlier authors), allowing the

relation to be simplified to the above. In addition, there is an assumption that the temperature


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does not vary significantly during the course of the reaction, so as to allow a fixed value of

diffusivity to manifest for simplification purposes. This assumption will later be proven valid.

3.4.3.

Energy Transport Homogeneous FluidThe energy balance in the tube side is more straightforward as the fluid is almost 100%

helium. Therefore, the same heat equation as seen in the shell side will be deployed, this time,

with the thermal conductivity of helium factored in. Also note that there is no heat source

term Q,due to the absence of reaction.

3.5.

Boundary Conditions

The boundary conditions for each of the 6 phenomena above will be described. As the model

is 2D, 3 sets of 4 boundary conditions each are needed. 3 sets reflect momentum, mass and

energy conservation equations, each set having 2 r and z-direction boundary conditions (4).

As stated in the initial section, the modelling is 2D-axisymmetric, meaning that COMSOL

will only solve a segment of the model, and perform a solid of revolution to get a 3D model,

as is visualized below. Therefore, the boundary condition images subsequently do not imply

that the modelling in COMSOL is done as per the images; these images are purely for

informative purposes.

Fig 3.5: 2D Axisymmetric method of solution


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3.5.1. Momentum Transport Boundary Conditions

Fig.3.5.1: Momentum physics and boundary conditions

The boundary conditions for the momentum balances depend upon the experimental

conditions. Defining r = 0 as the centreline of the tube side, and z = 0 as the reactor base,

Shell Side (Darcys Law)

Inlet Velocity Outlet Pressure No Flow No Flow Tube Side (Navier-Stokes Equations)

Inlet Velocity Outlet Pressure No-Slip No-Slip


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Tube Side (Ficks Law) Inlet Concentration Convective Dominance Sieverts Law (H2) Sieverts Law (H2)

.

3.5.3. Sieverts LawBoundary Condition

The seventh noteworthy phenomenon (aside from heat, mass, and momentum balances for

each side) is the Sieverts Law boundary condition. Sieverts Law basically describes the flux

of a species across a membrane, and is a function of the partial pressures of hydrogen on each

side of the IMR. In the context of hydrogen, the relationship is:

= where is an empirical value known as the base-case membrane permeability, and is themembrane thickness. The actual membrane permeability is scaled via the Arrheniusrelation, as shown from the exponent term.

Owing to the lack of a permeability value for the membrane in question, an arbitrary value of

1.5e-5 (mol/m2Pa0.5s), from Iyoha (2007) will be used for the entire permeation term (this

factors in the membrane thickness as well) . A study of the impact of this parameter on CO

conversion will be discussed in Chapter 5.


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3.5.4. Heat Transport Boundary Conditions

Fig.3.5.4: Heat transport physics and boundary conditions

The heat transport boundary conditions are slightly more unique; the wall surrounding the

shell is assumed to be of constant temperature, and therefore serves as a heat sink for the

exothermic water-gas shift reaction. The tube side is also another sink as there is no reaction.

Convective heat transfer coefficients have to be determined for 3 cases, wall to shell fluid,

shell fluid to membrane, and membrane to tube fluid as a result, which will be performed

immediately.

Shell Side (Pseudo-homogeneous Model)

Inlet Temperature Convective Dominance Heat Flux (to tube) Heat Flux (to wall)


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Tube Side (Homogeneous Model) Inlet Temperature Convective Dominance Heat Flux (to shell) Heat Flux (to shell)

Convective Heat Transfer Correlations

Wall to Shell fluid, and shell fluid to membrane wall

The shell region is an annulus, which is the space between 2 concentric cylinders. To

evaluate the heat transfer coefficient, Incropera & Dewitt, (2011) have cited the need to first

evaluate the ratio of the inner to outer diameter of the tube and shell regions, which is:

Based on this, the Nusselt numbers for fully-developed flow in a circular annulus with one

surface insulated, and the other at constant temperature can be evaluated according to the

text. The values are:

0.25 7.37 4.23

0.375 6.55 4.33

0.5 5.74 4.43

While there is some loss in accuracy due to the condition of an insulated surface, the loss in

accuracy is mitigated once again by the low temperature gain of the WGS reaction (to be

proven in the validation model), which means that heat transfer from shell to fluid will be of a

very low quantity, allowing the insulated surface condition to hold well.


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Based on the above 2 relations, h1 and h2 are evaluated as 309684 W/m2K and 76770.9

W/m2K. It is important to note that these high values arise out of considering the shell phase

as pseudo-homogeneous, and therefore the effects of the high thermal conductivity of the bi-

metallic catalyst and the small diameter are prominently featured in these coefficients.

Membrane wall to tube fluid

In this context, fluid can be visualized as flowing in a closed conduit. To evaluate the heat

transfer coefficient, the pipe flow Reynolds Number has to be evaluated.

Fluid density, viscosity, and velocity are assumed to be identical to that of heliums, since

hydrogen is of a much lower concentration compared to helium. Based on helium property

data below, sourced from the National Institute of Standards and Technology, US Dept of

Commerce (1984),

Density 0.524 Kg/m

Velocity 0.5 m/s

Viscosity 1.81*10- Pa.s

Thermal Conductivity 0.1513 W/(m.K)

Membrane tube diameter 0.0015 m

The Reynolds number is calculated to be 22. This indicates that flow is laminar (Red 2 barg), such that the difference between tube and shell H2partial pressures is

reduced, cutting H2 flux back to the shell side. Having said that, the initial experimental

condition of co-current configuration remains preferable, and this mode of operation will be

practised for the detailed sensitivity studies in the next Chapter.

5. Simulation of WGS Reaction Detailed Sensitivity Studies

5.1.

Experimental Conditions Set 1 (Effect of Temperature)

With the modelling complete and validated, the sensitivity studies will be performed,

pertaining to Objectives 4 through 11. The first study is on the effect of inlet shell

temperature on hydrogen production and CO conversion. The conditions are similar to those

seen in the validation model, and are as follows:

Shell Side

Boundary Parameter Value Remarks

Outlet Absolute Pressure 3 bar Experimental condition is at

2 barg, therefore absolute

pressure should be ~3 bar.

Inlet Mass Fractions CO 0.1666

H2O 0.833

H2 1e-

CO2 1e

-

5-1 steam-carbon ratio is

preserved, with a small

quantity of product gases

added for convergence

purposes.


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Inlet and wall

temperatures*

673, 723, 773, 823, 873K Wall and inlet temperatures

are kept the same to preserve

temperature constancy.

Inlet Feed Rate 75 mL/min

Tube Side


Outlet Absolute Pressure 1 atm Experimental condition:

Tube side to be maintained at

atmospheric pressure.

Inlet Concentration H2 1e- mol/m Small quantity of H2 added

for tube side convergence

Tube Inlet

Temperature*

673, 723, 773, 823, 873K Tube inlet temperature to be

kept the same as shell and

wall temperatures to preserve

temperature consistency.Inlet Feed Velocity 0.5m/s Arbitrary value specified.* Denotes a parameter whose effects are to be studied

The method of inspection will be through center-line profiles, marked in blue in the picture

below. This method of inspection will be deployed for the rest of the studies as well.

Fig 5.1: Center-line plot analysis. Note that this center-line approach was also deployed forthe previous examples.


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5.1.1. Results Set 1 (Effect of Temperature Concentration Profiles)

The effect of varying operating temperatures on the yield of hydrogen is reflected as below.

Fig 5.1.1.1: H2concentration profile in shell and tube sides, study of inlet temperature effect.

Based on the above plot, it can be seen that a temperature increase enhances the forward

reaction based on the increased yield of hydrogen in shell and tube sides. While this may

seem counter-intuitive based on the exothermic nature of the water-gas shift, it has been

verified that at this temperature, the kinetic effect overrides the thermodynamic effect. This

can be checked using the rate law supplied, through evaluating its constituent parameters, to

determine the cumulative effect on the rate of reaction (see column rate constant *(1-B))

T (K) Rate Constant KEQ Beta 1-Beta Rate Constant * (1-B)

673 3.41 11.85 0.084 0.92 3.12

773 8.86 4.91 0.203 0.80 7.06

873 18.51 2.49 0.401 0.60 11.09Table 5.1.1.2: Evaluation of kinetic versus thermodynamic effects.


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In the above table, it can be seen that a temperature increment of 200K raised the kinetic

effect (rate constant), by 6X, whereas the thermodynamic effect, (1-Beta), reduced by 33%,

therefore, it comes as no surprise that the rate of reaction receives a net enhancement from an

increase in temperature. With an increase in rate of reaction, equilibrium position is further

rightward at the end of the reactor, which explains the higher hydrogen production achieved.

Based on the data provided, the tube side hydrogen yield ranged from 0.04-0.09 mol/m3. As

stated earlier in the verification section, these results may be taken as an indicator of the

average hydrogen concentration in the tube side. In addition, this value range can be used as

an order-of-magnitude estimate for the reader in downstream sections.

5.1.2. Results Set 1 (Effect of Temperature CO Conversion Profiles)

The conversion profiles for CO in the shell side is defined by (Iyoha, 2007) as:

As can be seen, calculating the inlet mole fraction of CO, which is , requires aconversion from mass to mole fractions, given that the Maxwell-Stefan relations have been

used previously. The mole fraction of any species i, , can be evaluated via the followingrelation:

As an example, for steam-carbon ratio of 5:1, the molecular weight of the mix is 19.66g/mol.

Applying the above relations, the conversion profiles of CO are as follows:


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Fig 5.1.1.2 : CO conversion profile in shell side, Equilibrium conversions are labelled EC.

Conversion of CO is generally low based on the experimental conditions, which is expected

given the low H2yields compared to those seen in the validation section. As observed, the

range varies from 0.035 to ~0.09mol/m3. Equilibrium conversions were determined by

increasing the residence time by 1000X (flow rate of 75mL/min reduced to 0.075mL/min),

which created a plateauing conversion profile. The plot is not reflected here to avoid

confusion with the actual results, but the equilibrium conversions are reflected as ECs.

At 873K, equilibrium conversion of CO is observed to be 98%, and is therefore the most

ideal temperature to operate the shift reaction. On the other end of the spectrum, at 673K,

equilibrium conversion was significantly lower, clocking at 68.5%.


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5.2. Experimental Conditions Set 2 (Effect of Flow Rates)

The study will now switch to inspect the effect of flow rate, or more appropriately, residence

time, on H2production. Experimental conditions are as follows:

Shell Side


Outlet Absolute Pressure 3 bar Experimental condition is 2

barg, therefore absolute



H2O 0.833

H2 1e-

CO2 1e-




added for convergencepurposes.

Inlet and wall

temperatures

500C/773K Wall and inlet temperatures



Inlet Feed Rate* 50, 60, 70, 80, 90, 100 mL/min

Tube Side



Tube side to be maintained atatmospheric pressure.



Tube Inlet Temperature 500C/773K Tube inlet temperature to be



temperature consistency.

Inlet Feed Velocity 0.5m/s Arbitrary value specified.* Denotes a parameter whose effects are to be studied

5.2.1. Results Set 2 (Effect of Flow Rates Hydrogen Concentrations)

The effect of varying operating inlet flow rates on the production of hydrogen was studied by

taking the centreline positions of shell and tube sides as well.


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Fig 5.2.1.1 : H2profile in shell and tube sides (effect of Flow Rate). Tube H2 concentrationsare reflected as dotted lines (not elaborated upon in the legend due to space constraints)

As the flow rate decreases, the residence time increases in the reactor. As the reactor is still

far from equilibrium, this means that there is further forward reaction. Interestingly enough, it

can be seen that increasing the residence time by a fixed quantity produces increasing returns,

as evidenced by the increasing hydrogen concentration. This can be further verified by

inspecting the CO2 concentration in Figure 5.2.1.2, which follows a similar progression of

increasing returns.


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Fig 5.2.1.2 : Line flow rate CO2profile in shell side. Note that CO2 remains trapped in theshell side and therefore there is no tube profile.

Based on the plot in Figure 5.2.1.1, tube side H2 production ranges from 0.055 to

0.075mol/m3, for flow rates of 100mL/min to 50mL/min respectively. This value range is in

the same order of magnitude as seen in the temperature study, and serves as a source of

verification for the expected low hydrogen production in the reactor.

5.2.2.

Results Set 2 (Effect of Flow Rates CO Conversion Profiles)

As seen in Section 5.2.1, the same expression for conversion was used, and the results

plotted. As the reaction is conducted only at 773K, the equilibrium conversion is 89.5%, or

0.895 (see Fig. 5.1.1.2).


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Fig 5.2.1.3 : CO conversion profile in shell side, Equilibrium conversions are labelled EC.

In a similar vein to the earlier section, the conversion is low at the same order of magnitude,

ranging from 0.045 to 0.075. Therefore, a longer residence time is recommended, alongside

operating at 873K, to get the maximum CO conversion possible.

5.3.

Experimental Conditions Set 3 (Effect of Steam-Carbon Ratio)

The steam-carbon (SC) ratio is a common terminology, specifically-referring to the ratio of

H2O-CO at the inlet. In this Set, it is of interest to inspect the effect of varying SC ratios on

reactor performance. Note that the ratios are on a mass fraction basis, given the Maxwell-

Stefan relations. The experimental conditions as per listed below will be deployed.

Shell Side


Outlet Absolute Pressure 3 bar Experimental condition is 2

barg, therefore absolute


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methane cracking can occur, leading to coking of the reactor. Annesini, Piemonte, &

Turchetti, (2002) state that to mitigate such an outcome, reactions practised in an industrial

context generally adhere to a 3:1 ratio for the steam-methane reforming process

(recommended ratios for the WGS could not be found in the literature, but considering its

manifestation in the reforming process, this value was used). Using this value as a

benchmark, it can be observed that the tube side hydrogen concentration is 0.076mol/m3,

which is still a respectable increase from 0.06mol/m3, a 27% increase. Therefore, in

accordance with industrial practices, it is recommended to operate the reactor at a 3:1 SC

ratio, instead of 5:1.

5.3.2. Results Set 3 (Effect of SC Ratios CO Conversion Profiles)

The CO conversion profiles are reflected as follows in the below plot.

Fig 5.3.2.1 : CO Conversions under varying Steam-CO Ratios.


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Fig 5.3.2.2 : Equilibrium CO Conversions under varying Steam-CO Ratios.

There are 2 points to discuss based on the above plots. The first is that as the SC ratio tends

towards 1:1, the faster the initial rate of reaction, which is expected by virtue of the 1:1

stoichiometric ratio. This explains the discontinuities observed at the entry point of the

reactor; at a 1:1 ratio, the CO conversion is already at ~0.047. The reader is encouraged to

think of this high starting point as a spike in conversion from 0.

The second is the cross observed at the 1:1 SC ratio; that is, initially, the 1:1 ratio sees the

highest conversion, but it becomes the lowest at the end as well. Further verification can be

seen by increasing the residence time by 10000X to capture equilibrium conversion (See Fig

5.3.2.2); the 1:1 ratio saw a dismal 71% conversion, compared to the 5:1 ratio which saw a

92% conversion. This appears to contradict the earlier discovery in Section 5.3.1, that a 1:1

ratio is the most ideal operating regime. However, there is actually no contradiction, because

(1) The absolute values of CO were different to begin with for each run, therefore, comparing


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conversions to determine which SC ratio was ideal is inherently flawed and should not be

done, and (2) A high SC ratio (5:1) will naturally produce a higher conversion; since the ratio

of water to CO molecules is much greater, therefore, the chance of a CO molecule reacting

(and therefore CO conversion) is higher.

Conclusively-speaking, as far as operating regime is concerned; the lowest ratio permissible

by industry standards, that is, 3:1, is ultimately the way to go. This yields an 87.5%

conversion under the set experimental conditions, and produces a tube hydrogen

concentration yield that is 27% above the originally-quoted 5:1 ratio.

5.4. Experimental Conditions Set 4 (Effect of Shell Pressure)

As observed in the validation section, shell pressure plays a role in Sieverts Law, governing

the net flux of H2 into the tube side, and ultimately affecting the yield available for usage.

Therefore, it is also of interest to assess the impact of this quantity on hydrogen production

and conversion as well. The experimental quantities are as below:

Shell Side


Outlet Absolute

Pressure*

1 bar, 2 bar, 3 bar, 4 bar, 5 bar To be varied


H2O 0.8333

H2 1e-

CO2 1e-

5:1 SC Ratio

Inlet and walltemperatures

500C/773K Wall and inlet temperaturesare kept the same to preserve


Inlet Feed Rate 75mL/min

Tube Side





Inlet Concentration H2 1e- mol/m Small quantity of H2 addedfor tube side convergence


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Inlet Feed Velocity 0.5m/s Arbitrary value specified.

Denotes a parameter whose effects are to be studied

5.4.1. Results Set 4 (Effect of Shell Pressure Hydrogen Concentrations)

Fig 5.4.1.1: Hydrogen Shell and Tube side concentrations under varying Shell Pressures

(units: mol/m3)

The observation here is that the higher the shell side pressure, the greater the shell and tube

hydrogen production. The tube case can be explained by the higher partial pressure of

hydrogen at the shell side, which resulted in a greater flux, according to Sieverts Law. The

shell increment in hydrogen concentrations, on the other hand, is harder to prove qualitatively

due to the complex rate law involved, but it can be seen from the results that the rate law

generally favors a higher pressure operation, as a higher shell pressure led to more H2

production at the exit of the shell side. It is also good to note that such a measure generally


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produces diminishing returns, as can be seen from the shell and tube concentration profiles,

whose increments in H2 production decrease per bar increase in pressure. Therefore, it is

recommended to operate the process at a high pressure, but not to the extent that the costs of

maintaining a high pressure outweigh the benefits in hydrogen production. This can be

achieved via simulation of the scaled-up unit, with cost estimation studies factored in.

5.4.2. Results Set 4 (Effect of Shell Pressure Conversion Profiles)

In this context, conversions are generally not a useful indicator of reactor performance,

because the variations in pressure also lead to variations in velocity through the momentum

balance. Given that the conversion expression is a function of velocity as well as CO mole

fraction, the result becomes more convoluted and is not useful. That being said, it is still

useful to evaluate the equilibrium conversion, which is approximated in this case by

increasing the residence time by 10,000X, upon which the conversion profiles plateau-ed.

Fig 5.4.2.1: CO Equilibrium Conversions under different shell pressures


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Based on the plot as shown above, the lowest pressure has the greatest conversion of 0.93,

whereas the highest has a conversion of 0.89. Considering that the difference in equilibrium

conversion is minute (and that equilibrium is unlikely to be totally reached in a practical

scenario, considering that throughput has to be extremely low), the recommendation of

operating at maximum yet economical pressure, stands as is.

5.5. Experimental Conditions Set 5 (Effect of Sweep Gas Rate)

Helium sweep gas is used in the tube side, to push, or more appropriately, sweep out the

product H2 formed from the shift reaction. Research by Chein, Chen, & Chung, (2015) has

demonstrated improved reactor performance in terms of increased CO conversion, with

increased sweep flow rates. This is presumed to be due to the faster depletion of H 2 in the

tube sides, which induces more hydrogen flux from shell to the tube side, and consequently

further conversion of CO. This claim will be verified with the following experimental

conditions.

Shell Side


Outlet Absolute Pressure 3 bar Experimental conditions


H2O 0.8333

H2 1e-

CO2 1e-

5:1 SC Ratio

Inlet and wall

temperatures




Inlet Feed Rate 75mL/min

Tube Side






for tube side convergenceTube Inlet Temperature 500C/773K Tube inlet temperature to be


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Inlet Feed Velocity* 0.1, 0.3, 0.5, 0.7, 0.9m/s To be varied*Denotes a parameter whose effects are to be studied

5.5.1. Results Set 5 (Effect of Sweep Rate Conversion Profiles)

The conversion profiles will be discussed only as the primary objective is to confirm the

presence of increased CO conversion.

Fig 5.5.1.1: CO Conversions under different sweep rates; sweep at 0.9m/s shows the highest

CO conversion. Graph has been zoomed-in.

As evidenced from Fig 5.5.1.1, the highest sweep rate of 0.9m/s saw the highest conversion

of CO, verifying that the higher the sweep rate, the greater the conversion. The difference in

conversions is small in the context of this reactor due to its relatively-small size.


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The simulation is run to equilibrium once more, by increasing the residence time by 10,000X

to get a plateauing concentration profile, so as to illustrate the impact of sweep rate on

equilibrium conversions.

Fig 5.5.1.2: Equilibrium CO Conversions under different sweep rates; sweep at 0.9m/s shows

the highest CO conversion. Graph has been zoomed-in.

From the study above, the effect of sweep rate on equilibrium conversion is not excessively-

significant; a 9X increase in sweep velocity raised the equilibrium conversion from 0.896 to

0.924, with diminishing returns to boot. Taking into account that costs go up with increase in

helium sweep rate, it is recommended to operate at the most cost-effective regime, rather than

the regime with the highest permissible helium sweep rate.


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5.6. Experimental Conditions Set 6 (Effect of Inlet H2 Presence)

As stated earlier, the WGS is unlikely to occur on its own in an industrial application. For

instance, in the steam methane reformer (SMR), the primary steam-reforming reaction always

takes place first, resulting in the production of some hydrogen.

As evidenced from the SMR equation, hydrogen presence is guaranteed when the water-gas

shift reaction occurs subsequent to the SMR, and therefore it is of interest to inspect the

impact of existing H2 on CO conversion. Hence, the following experimental condition is

proposed. Inlet hydrogen fractions are kept on the low end, to ensure that CO conversions

remain within the same neighbourhood for easier visual comparison.

Shell Side



Inlet Mass Fractions CO Maintained in a

5:1 ratio, after

subtracting H2and CO2 mass

fractions.

H2O

H2* 0.01, 0.015,

0.02, 0.025, 0.03

CO2 1e-

5:1 SC Ratio, with variations

in H2 inlet fractions. Note

that inlet fractions are kept

low.

Inlet and wall

temperatures




Inlet Feed Rate 75mL/minTube Side








kept the same as shell andwall temperatures to preserve


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Inlet Feed Velocity 0.5m/s To be varied*Denotes a parameter whose effects are to be studied

5.6.1. Results Set 6 (Effect of Hydrogen Presence Conversion Profiles)

In a similar fashion to the above Set, only the conversion profiles will be considered in this

context as qualitative evaluation of H2 impact is more important. The results are displayed as

follows:

Fig 5.6.1.1: CO Conversion Profiles under different inlet mass fractions of hydrogen.

In the diagram above, the starting conversions are above zero owing to the presence of

hydrogen in the feed. Therefore, it is difficult to make a visual comparison. A more effective

method of ascertaining the impact of hydrogen in feed is calculating change in CO

conversion, which is tabulated below.


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H2Inlet Fraction Initial Conversion Final Conversion Change

0.03 0.202 0.211 +0.009

0.025 0.178 0.188 +0.01

0.02 0.152 0.163 +0.011

0.015 0.1245 0.136 +0.0115

0.01 0.0945 0.108 +0.0135Fig 5.6.1.2: Conversion Changes under different H2fractions

As the inlet fraction of H2 increases (feed becomes less pure) by a fixed size, it can be seen

that the increase in conversion diminishes. In simpler terms, the operational advantage

offered by this PBMR diminishes the more the feed gets contaminated with H2. Therefore,

this PBMR is not viable for applications where the feed is likely to be impure, namely the

SMR application, where the bulk of the hydrogen is yielded from the reforming reaction, as

the diminishing return effect means that the PBMR will not be effective. That being said, it is

definitely possible to counterbalance this effect through measures such as improving the

membrane permeability. Such a measure increases the draw rate of hydrogen into the tube

side, and forces more CO conversion.

Conclusively-speaking, it is recommended to operate the PBMR in a context where hydrogen

will be of a negligible quantity in the feed, otherwise, further changes to the reactor will be

needed if it is to have an appreciable contribution to the WGS.

5.7. Experimental Conditions Set 7 (Effect of Inlet CO2 Presence)

In a similar fashion to the purposes of Set 6, the implications of CO2presence in the feed on

conversion will be studied as well. The conditions are as below.

Shell Side



Inlet Mass Fractions CO Maintained in a

5:1 ratio, after

subtracting H2and CO2 mass

fractions.

H2O

H2 1e-

5:1 SC Ratio, with variations

in H2 inlet fractions. Note

that inlet fractions are kept

low.


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CO2 0.01, 0.015,

0.02, 0.025, 0.03

Inlet and wall

temperatures




Inlet Feed Rate 75mL/minTube Side










Inlet Feed Velocity 0.5m/s To be varied*Denotes a parameter whose effects are to be studied

5.7.1. Results Set 7 (Effect of Inlet CO2 Presence Conversion Profiles)

The results collected from the sweep are as below:

Fig 5.7.1.1: CO Conversion Profiles under different inlet mass fractions of CO2.


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There are 2 observations to note here. The first is that the CO2 equilibrium quantity appears to

be much smaller than that of hydrogen. This is because at a small inlet quantity (mass

fraction ~0.0175, based on interpolation from Fig 5.7.1.1) and above, the initial conversion

becomes negative, that is, the backward reaction manifests, which is clearly undesirable, even

if there is a net positive conversion in the end. Therefore, the feed should ideally contain a

CO2 inlet mass fraction which is less than the aforesaid value.

The second observation is that it is not recommended to operate this reactor completely if the

inlet CO2 fraction exceeds 0.025, as the net conversion is less than 0.005 (or


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The equilibrium conversions as can be seen, generally do not differ significantly based on the

inlet CO2 mass fractions (0.917 versus 0.907, 1% difference, between the lowest and highest

inlet fractions), however, this is considering that the mass fractions are low in value to begin

with. Differences in equilibrium conversion are expected to become more significant as CO2

inlet fraction increases.

5.8. Experimental Conditions Set 8 (Effect of Permeability)

The membrane forms the linchpin of the PBMR by giving it an operational advantage over

the conventional annular packed-bed reactor, as seen in the validation section. It is easy to

qualitatively-reason that as membrane permeability increases, CO conversion will increase as

well. However, the sensitivity of conversion increment to permeability change is a topic of

interest. Therefore, the last study will be the effect of varying membrane permeabilities on

CO conversion. The experimental context will be as below, which is identical to the

validation condition.

Shell Side


Outlet Absolute Pressure 3 bar Experimental condition is at

2 barg, therefore absolute



H2O 0.833

H2 1e-

CO2 1e-




added for convergence

purposes.Inlet and wall

temperatures

500C Wall and inlet temperatures



Inlet Feed Rate 75mL/min Median value of flow rate

(range 50-100mL) used. Thisreasoning is retrospective.

Tube Side

Boundary

Parameter

Value Remarks

Outlet Absolute 1 atm Experimental condition:


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Pressure Tube side to be maintained at




Tube Inlet

Temperature

500C Tube inlet temperature to be



Inlet Feed Velocity 0.5m/s Arbitrary value specified.

Membrane

Permeability*

0.375e-

,0.75e-

, 1.5e-

, 3e-

, 6e-

(mol/m2Pa

0.5s)

Permeabilities proposed are

quarter, half, double,

quadruple that of the original

value, 1.5e-5.*Denotes a parameter whose effects are to be studied

5.8.1.

Results Set 8 (Effect of Permeability Conversion Profiles)

Fig 5.8.1.1: CO Conversion Profiles under different inlet membrane permeabilities.

Based on the results above, increased membrane permeability does improve CO conversion,

to the tune of increasing returns, that is, a 1X to 2X permeability yields more conversion

change, compared to a 0.5X to 1X permeability. However, in terms of absolute values, the


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difference remains highly insignificant. At 4X the usual membrane permeability, conversion

increased barely from 0.05835 to ~0.0587 (0.6% improvement in conversion). Considering

that these values are in the same order of magnitude as those seen in the literature, and

therefore unlikely to see a drastic increment in permeability in the near future, it is

recommended to harness multiple membrane tubes instead of a single one within a reactor, to

gain a more prominent CO conversion advantage.

That being said, these differences become more significant as equilibrium is being

approached. At 100X the residence time, the difference is in the order of percentages in CO

conversion, indicating that a longer residence time will harness the positive effect of the

membrane tube to a greater extent.

Fig 5.8.1.2: CO Conversion Profiles under different inlet membrane permeabilities, 100X

residence time.


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6.

Conclusions

To sum up the report, a packed-bed membrane reactor has been studied and modelled with

reference to the appropriate literature. Appropriate boundary conditions and heat/mass

transfer correlations have been developed and integrated into the said model.

From the validation model proposed, it can be seen that the model holds good promise for

future studies as the momentum, mass, and heat transfer studies generally agree with the

assumptions made, and that the behaviour of the model adheres to that of a membrane

reactor, such as greater conversion and H2 transfer across the membrane.

In addition, the studies performed with regards to the 8 parameters have provided insights

into recommended operating regimes. However, CO conversion/hydrogen production under

these conditions is generally low, as a result of the small residence time afforded for reaction.

One recommendation for future work is for the research group to increase the residence times

in the experimental contexts, especially if the PBMR is to be scaled-up to industrial

production levels.

Returning to the list of 11 objectives seen in Section 1-3, the outcomes and conclusions are

tabulated as follows:

S/N Objective Outcome/Conclusion

1 Produce and simulate a

sufficiently-rigorous model for the

reactor.

2D-axisymmetric model developed, utilizing

fundamental differential equations of momentum,

mass, and energy balances, with appropriateheat/mass transfer correlations from literature.

2 Verify the operational advantage

that a membrane reactor offers.

A PBMR is verified to produce more CO2

compared to an annular packed-bed reactor under

the same conditions.

3 Study and validate the general

phenomena associated with the

experimental conditions,

including velocity, density, and

pressure profiles.

Validation model operated, with the following

discoveries:

Momentum:Laminar flow, pressure drop and entrance length

validated.

Velocity/Density not expected to vary


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significantly based on set conditions.

Mass:H2 departure from shell side confirmed.

Radial profiles consistent with two-phase masstransfer phenomena, tube centre-line H2concentrations found to be accurate indicator of

average H2 concentrations.

Reaction equilibrium effect captured in model.

Heat:Reactor operation is discovered to be virtually

isothermal, Thermal diffusion coefficient value

/Hirschfelder relation validated.

Counter-vs-Co-CurrentCounter-current produces stronger initial rise in

H2 concentration, but co-current outperforms

counter-current in terms of H2production in tube.

4 Study of effect of temperature on

yield and conversion.

Higher inlet temperature favours conversion

owing to kinetic effect >> thermodynamic effect.

Recommended to operate at 873K due to 98%

equilibrium conversion.

H2production in the range of 0.04-0.09mol/m3,

which sets a range of expected values.

5 Study of effect of residence time

(flow rate) on H2production and

conversion.

Lower flow rate favours conversion due to longer

residence time.

Increasing returns to be had per unit increment in

residence time.

6 Study of effect of steam-carbon

ratio in feed on H2production and

conversion.

Lower SC ratio favours more CO conversion/H2production from a stoichiometry standpoint.

However, a 1:1 ratio is not feasible due topossibility of side reactions. Recommended to

operate at a steam:CO ratio of 3:1, an industrial

practice. This creates a 27% increase in H2production compared to 5:1 ratio.

7 Study of effect of reaction (shell)

pressure on H2production and

conversion.

Hydrogen production in both shell and tube sides

increases with shell-side pressure increase, due to

rate law and Sieverts Law.

However, the returns are diminishing, and

therefore recommended to operate at a cost-

effective pressure.8 Study of effect of Helium gas CO conversion increases as sweep rate increases,


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sweep rate on CO conversion. albeit not significant.

CO conversion increment diminishes as sweep

rate increases, therefore, recommended to operate

the sweep at a cost-effective rate, rather than as-

high-as-possible.9 Study of effect of inlet H2on CO

conversion.

Inlet H2presence diminishes operational

advantage conferred by PBMR, but does not

create negative conversion.

As inlet H2presence increases, the operational

advantage diminishes. Therefore, this PBMR is

not appropriate for high H2inlet contexts such as

a steam-methane reformer.

10 Study of effect of inlet CO2 on CO

conversion

CO2presence begins to create negative

conversion effect if inlet mass fraction >0.0175,

although there is still a positive net conversion.

PBMR will have a detrimental effect instead

(reverse WGS) if CO2inlet mass fraction >0.025,

unless residence time is increased from the

experimental context to allow system to

equilibrate.

Equilibrium conversion generally insensitive to

inlet CO2mass fractions.

11 Study of effect of variousmembrane permeabilities on CO

conversion

Increased membrane permeability raises COconversion to the tune of increasing returns, but

effect is highly-muted in this context.

Recommended to operate PBMR utilizing

multiple membrane tubes to stack the positive

effects.

Table 6-1: List of objectives and corresponding outcomes.

7.

Future WorkBased on the Gantt Chart as provided in the interim report, the project has reached total

completion.

Fig 7: Gantt Chart depicting project progress


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Nonetheless, it is desirable to verify the work with an experimental set-up, which could not

be achieved by the research group within this period in time. Also, further optimization of the

heat and mass transfer coefficients can be done, as more relevant literature becomes

available.

8.Acknowledgements

The candidate would like to express his acknowledgements to:

1. Assoc Prof Kus Hidajat and Dr Usman Oemar for the FYP opportunity.

2.

Dr Eldin Lim for CFD and convergence-related advice.

3. Dr Elena Carcadea for her guidance.

4. Authors of membrane reactor modelling texts.


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9.

References

Annesini, M. C., Piemonte, V., & Turchetti, L. (2002). Carbon Formation in the Steam

Reforming Process: a Thermodynamic Analysis Based on the Elemental Composition.

Borman, V. D., & Chuzhinov, V. A. (1971). The Influence of an Electric Field on the

Thermal Diffusion Coefficient for Gases, 33(5), 89.

Carcadea, E., Varlam, M., & Stefanescu, I. (2012). Heat Transfer Modelling of Steam

Methane Reforming. COMSOL Conference, 2012, Milan, (4).

Chein, R. Y., Chen, Y. C., & Chung, J. N. (2015). Sweep gas flow effect on membrane

reactor performance for hydrogen production from high-temperature water-gas shift

reaction.Journal of Membrane Science, 475, 193203.

doi:10.1016/j.memsci.2014.09.046

COMSOL Inc. (2008). Fixed-Bed Reactor for Catalytic Hydrocarbon Oxidation. Burlington,

MA: COMSOL.Inc.

Doraiswamy, L. K. (2014). Chemical Reaction Engineering, Beyond the Fundamentals. Boca

Raton, FL, USA: CRC Press.

Falco, M. de, Marrielli, L., & Iaquaniello, G. (2011).Membrane Reactors for Hydrogen

Production Processes(1st ed.). Springer. doi:10.1007/978-0-85729-151-6

Gallucci, F. (2011).Modeling of Membrane Reactors for Hydrogen Production and

Purification(Vol. 2, pp. 139). doi:10.1039/9781849733489-00001

Ho, C. Y., Ackerman, M. W., Wu, K. Y., Oh, S. G., & Havill, T. N. (1978). Thermal

Conductivity of Ten Selected Binary Alloy Systems.Journal of Physical Chemistry,

7(3). Retrieved from http://www.nist.gov/data/PDFfiles/jpcrd123.pdf

Honrath, R. E. (1995). Mass Transport Processes. Retrieved from

http://www.cee.mtu.edu/~reh/courses/ce251/251_notes_dir/node4.html

Incropera, F. P., & Dewitt, D. P. (2011).Fundamentals of Heat and Mass Transfer

(Seventh.). Jefferson, MI, USA.

Iyoha

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Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor

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