modelling and simulation of the water-gas shift in a packed bed membrane reactor
TRANSCRIPT
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
1/87
1
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
2/87
2
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
3/87
3
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
4/87
4
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
5/87
5
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
6/87
6
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
7/87
7
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
8/87
8
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
9/87
9
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
10/87
10
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
11/87
11
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
12/87
12
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 (
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
13/87
13
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
14/87
14
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
15/87
15
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
16/87
16
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
17/87
17
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
18/87
18
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
19/87
19
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:
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
20/87
20
)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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
21/87
21
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
22/87
22
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
23/87
23
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
24/87
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
25/87
25
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
26/87
26
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)
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
27/87
27
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
28/87
28
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
49/87
49
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
Boundary Parameter Value Remarks
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
50/87
50
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
51/87
51
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:
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
52/87
52
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%.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
53/87
53
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
Boundary Parameter Value Remarks
Outlet Absolute Pressure 3 bar Experimental condition is 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 convergencepurposes.
Inlet and wall
temperatures
500C/773K Wall and inlet temperatures
are kept the same to preserve
temperature constancy.
Inlet Feed Rate* 50, 60, 70, 80, 90, 100 mL/min
Tube Side
Boundary Parameter Value Remarks
Outlet Absolute Pressure 1 atm Experimental condition:
Tube side to be maintained atatmospheric pressure.
Inlet Concentration H2 1e- mol/m Small quantity of H2 added
for tube side convergence
Tube Inlet Temperature 500C/773K 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
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
54/87
54
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
55/87
55
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).
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
56/87
56
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
Boundary Parameter Value Remarks
Outlet Absolute Pressure 3 bar Experimental condition is 2
barg, therefore absolute
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
57/87
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
58/87
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
59/87
59
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
60/87
60
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
61/87
61
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
Boundary Parameter Value Remarks
Outlet Absolute
Pressure*
1 bar, 2 bar, 3 bar, 4 bar, 5 bar To be varied
Inlet Mass Fractions CO 0.1666
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
temperature constancy.
Inlet Feed Rate 75mL/min
Tube Side
Boundary Parameter Value Remarks
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 addedfor tube side convergence
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
62/87
62
Tube Inlet Temperature 500C/773K 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
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
63/87
63
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
64/87
64
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
Boundary Parameter Value Remarks
Outlet Absolute Pressure 3 bar Experimental conditions
Inlet Mass Fractions CO 0.1666
H2O 0.8333
H2 1e-
CO2 1e-
5:1 SC Ratio
Inlet and wall
temperatures
500C/773K Wall and inlet temperatures
are kept the same to preserve
temperature constancy.
Inlet Feed Rate 75mL/min
Tube Side
Boundary Parameter Value Remarks
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 convergenceTube Inlet Temperature 500C/773K Tube inlet temperature to be
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
65/87
65
kept the same as shell and
wall temperatures to preserve
temperature consistency.
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
66/87
66
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
67/87
67
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
Boundary Parameter Value Remarks
Outlet Absolute Pressure 3 bar Experimental conditions
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
500C/773K Wall and inlet temperatures
are kept the same to preserve
temperature constancy.
Inlet Feed Rate 75mL/minTube Side
Boundary Parameter Value Remarks
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 500C/773K Tube inlet temperature to be
kept the same as shell andwall temperatures to preserve
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
68/87
68
temperature consistency.
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
69/87
69
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
Boundary Parameter Value Remarks
Outlet Absolute Pressure 3 bar Experimental conditions
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
70/87
70
CO2 0.01, 0.015,
0.02, 0.025, 0.03
Inlet and wall
temperatures
500C/773K Wall and inlet temperatures
are kept the same to preserve
temperature constancy.
Inlet Feed Rate 75mL/minTube Side
Boundary Parameter Value Remarks
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 500C/773K Tube inlet temperature to be
kept the same as shell andwall temperatures to preserve
temperature consistency.
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
71/87
71
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
72/87
72
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
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.Inlet and wall
temperatures
500C Wall and inlet temperatures
are kept the same to preserve
temperature constancy.
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:
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
73/87
73
Pressure 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
500C Tube inlet temperature to be
kept the same as shell andwall temperatures to preserve
temperature consistency.
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
74/87
74
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
75/87
75
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
76/87
76
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,
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
77/87
77
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
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
78/87
78
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.
-
8/9/2019 Modelling and Simulation of the Water-Gas Shift in a Packed Bed Membrane Reactor
79/87
79
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