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Design reactors via CFD

Article  in  Chemical Engineering Progress · December 2001

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Reactor Design

André Bakker,
Ahmad H. Haidari and
Elizabeth M. Marshall,
Fluent Inc.

designreactors
viaCFD
I n addition to their work in the
chemical and oil industries,
chemical engineers (ChEs) are
employed in a wide variety of
other industries, such as the produc-
tion of plastics and synthetic resins,
man-made fibers, polymers, paints
Using computational
fluid dynamics to
design commercial-size
batch and continuous
reactors can eliminate
means of a chemical reaction in an
environment that involves fluid flow.
Depending upon the physical state
of the materials being converted and
the operating conditions, different
types and scales of reactors are
used. These include, but are not lim-
and varnishes, drugs and pharma- ited to, batch; continuous stirred-
ceuticals, agricultural chemicals, subjective experience tank reactors (CSTRs); plug-flow,
fats and oils, foods and beverages, fluidized, fixed or moving-bed reac-
and many others. ChEs are respon-
and empiricism, and tors; bubble columns or airlifts; and
sible for the design, operation, opti-lead to better-designed, film reactors. In this article, some of
mization and troubleshooting of today’s most popular methods for
manufacturing operations, and can more-efficient units. simulating reactive flow are re-
be involved in applications that viewed. Examples will emphasize
range from combustion to biological reactions. All of the variety of applications and methods for tackling this
these industrial applications have one thing in common complex behavior.
— raw materials are converted into final products by To successfully implement a chemical reaction

30 www.cepmagazine.org December 2001 CEP

developed in the laboratory on an industrial scale, many When modeling chemical reactors using CFD, the
hurdles are usually encountered. Often, these are related fluid-flow pattern and temperature field are calculated
to difficulties in maintaining the same temperatures, from conservation equations for mass, momentum and
pressures, and level of homogeneity of the reactants on a enthalpy. These equations can be found in textbooks and
large scale. Furthermore, while the reaction time-con- will not be reiterated here. For reacting flows, the mix-
stants stay the same on scaleup, other time constants ing and transport of chemical species must also be cal-
change. Usually, there are significant differences be- culated using species-transport equations. Each equation
tween the residence, feed and mixing times in the labo- is a statement of conservation of a single species. Multi-
ratory and those on the production floor. In addition to ple-species equations can be used to represent compo-
scaleup issues, there is a strong interaction between the nents in a mixture, each of which has different physical
molecular reaction process itself, and the thermodynam- properties. To balance the mass transfer from one
ic, hydrodynamic and mass-transfer processes in the re- species to another, reaction rates are used in each
actor. A detailed understanding of all of these phenome- species-conservation equation, and have as factors, the
na helps the engineer to design a productive and molecular weights, concentrations and stoichiometries
efficient operation. for that species in all reactions. For the species i´, the
This article continues where a prior one on computa- conservation equation is for the mass fraction of that
tional fluid dynamics (CFD) modeling ended (1). The species, mi´, and has the following form:
basics of CFD will not be reiterated here. We will dis-
cuss how to model chemical reactions and the effects of ∂ ρm i′ ∂ ρu im i′ ∂J
+ = – i′,i + R i′ + S i′ (1)
fluid flow on the reaction process. Examples will in- ∂t ∂x i ∂x i
clude Fischer-Tropsch synthesis in a bubble column,
polymerization in an autoclave reactor, and ozone de- In this equation i represents one of the three coordinate
composition in a fluidized bed. directions and Ji´,i is the ith component of the diffusion
flux of species i´ in the mixture. For laminar flows, Ji´,i
Chemical reaction overview is related to the diffusion coefficient for the species and
Chemically reacting flows are those in which the the local concentration gradients. For turbulent flows,
chemical composition, properties and temperatures Ji´,i also includes a turbulent diffusion term, which is a
change as the result of a simple or complex chain of re- function of the turbulent Schmidt number. Ri´ is the rate
actions in the fluid. The reactor is typically simulated at which the species is either consumed or produced in
using a chemical-reaction model coupled with one of the one or more reactions, and Si´ is a general source term
following four fluid-modeling approaches: for the ith species. Note that i is a coordinate index,
1. A perfectly mixed stirred tank (either batch, semi- while i´ is a species index. The general source term can
batch or continuous) be used for nonreacting sources, such as the evaporated
2. A plug-flow reactor vapor from a heated droplet, for example.
3. A network of a relatively small number of perfect- When two or more species are present, the sum of the
ly mixed and plug-flow reactors mass fractions in each cell must add to one. For this reason,
4. A full CFD model. if there are n species in a simulation, only n – 1 species
The calculation time is relatively short for the first equations need to be solved. The mass fraction of the nth
three methods. However, such models may not correctly species can be computed from the required condition:
predict the effects of the reactor hydrodynamics on its
Σm
n
performance. For example, in a large-scale reactor, the =1
ι′
i′ (2)
reaction process may be slowed down by local starva-
tion of one of the reactants, poorly mixed reactants,
nonuniform catalyst distributions or settled catalysts, For a single-step, first-order reaction, say, A + B →
thermal nonuniformities or ignition delays. R, the reaction rate is given by:
Thermal nonuniformities may also accelerate reaction
processes, and, in some cases, local hot spots may result R ∝ C AC B + c Ac B
(3)
in product decomposition, or even in thermal runaways
or explosions. These phenomena cannot be captured
when modeling the reactor using simplified hydrody- CA and CB denote the mean molar concentrations of
namics assumptions (such as perfect mixing), but can be reactants A and B, while cA and cB denote the local con-
depicted with reasonable accuracy using full CFD mod- centration fluctuations that result from turbulence. When
els. These have been successfully used for homogenous the species are perfectly mixed, the second term on the
reaction systems (same state), and heterogeneous reac- right-hand side approaches zero. If the species are not
tions (different phases). perfectly mixed, this term will be negative and will re-

CEP December 2001 www.cepmagazine.org 31

 Reactor Design

Nomenclature
a = interfacial area per volume, m–1
A, B = Magnussen mixing rate constants
Ak = Arrhenius constant for reaction k is consumed in reaction k. The constants Ak and Ek, the
Cj´ = concentration of species j´, mol/m3 Arrhenius pre-exponential factor and activation energy,
Ek = activation energy for reaction k, J/mol respectively, are adjusted for specific reactions, often as
Ji´,i = diffusion flux of species i´ in direction I, kg/m2•s the result of experimental measurements. The stoi-
k = turbulent kinetic energy, m2/s2 chiometry for species i´ in reaction k is represented by
ki = mass-transfer rate, mol/m3•s
the factor νi´,k, and is positive or negative, depending
kl = liquid-side mass-transfer coefficient, m/s
Ki´,k = reaction rate of species i´ in reaction k
upon whether the species serves as a product or reactant.
mi´ = mass fraction of species i´ The molecular weight of the species i´ appears as the
Mi´ = molecular weight of species i´ factor Mi´. The temperature, T, appears in the exponen-
R = universal gas constant, J/mol•K tial term and also as a factor in the rate expression, with
Ri´ = generalized source term for reactions in the species i´ an optional exponent, βk. Concentrations of other
transport equation, kg/m3•s species, j´, involved in the reaction, [Cj´], appear as fac-
RK_i´,k = kinetic reaction rate for species i´ in reaction k, kg/m3•s tors with optional exponents associated with each. Other
RM1-i´,k = mixing-limited reaction rate for the reactant species i´ in
factors and terms not appearing in Eq. 4, can be added
reaction k, kg/m3•s
RM2-i´,k = mixing-limited reaction rate for the product species i´ in
to include effects such as the presence of nonreacting
reaction k, kg/m3•s species in the rate equation. Such so-called third-body
S = strain rate, s–1 reactions are typical of the effect of a catalyst on a reac-
Si´ = Net species source term in the species i´ transport equation tion, for example. Many of the factors appearing in Eq.
t = time, s 4 are often collected into a single rate constant, Ki´,k.
T = temperature, K In addition to the Arrhenius rate, two mixing rates are
Ui = velocity in the direction i, m/s computed that depend upon the local turbulent kinetic
xi = spatial coordinate in direction i, m
energy and dissipation rate. One rate, RM1_i´,k, involves
Greek letters
the mass fraction of the reactant in reaction k, mR, that
βk = temperature exponent in Arrhenius rate expression returns the smallest rate:
ε = turbulent kinetic energy dissipation rate, m2/s3
R M1_i′,k = vi′,kM i′Aρ ε
mR
ηj´,k = exponent for concentration of species j´ in reaction k
k vR,k M R (5)
νi´ = stoichiometry of species i´
ρ = liquid density, kg/m3
where the subscript R refers only to the reactant species,
duce the reaction rate. The estimation of this correlation i´ = R. The other mixing rate, RM2_i´,k, involves the sum
term is not straightforward and numerous models are over product-species mass-fractions, mP:

Σm
available for this purpose. Its presence shows, however,
that the reaction rate should incorporate not only the
R M2_i′,k = vi′,kM i′ABρ ε
P
P
mean concentrations of the reactant species, but also in-
Σ v′ M
k N
clude the turbulent fluctuations of the reactant species as j′,k j
(6)
j′
well, since the latter give an indication of the degree to
which these species are mixed.
One popular method for computing the reaction rates For gaseous-combustion models, constants A and B
as a function of both mean concentrations and turbu- often have values of 4.0 and 0.5, respectively. These val-
lence levels is through the Magnussen model (2). Origi- ues can be adjusted for different types of reactions, such
nally developed for combustion, it can also be used for as those involving liquids (3).
liquid reactions by tuning some of its parameters. The After the rates in Eqs. 4, 5 and 6 are computed, the
model consists of rates calculated by two primary smallest or slowest, is used as a source term in the
means. An Arrhenius, or kinetic rate, RK_i´,k, for species species-transport equations for all species involved in any
i´ in reaction k, is governed by the local mean species given reaction. The basic idea behind the Magnussen
concentrations and temperature in the following way: model is that, in regions with high-turbulence levels, the
eddy lifetime, k/ε, is short, mixing is fast, and, as a result,
Π
N
Ek η j′,k the reaction rate is not limited by small-scale mixing. In
R K_i′,k = – vi′,kM iA kT β k exp – C j′ =
RT j′ = 1 this limit, the kinetic rate usually has the smallest value.
On the other hand, in regions with low turbulence levels,
small-scale mixing may be slow and limit the reaction
Π
N
η j′,k
K i',kM i′ C j′ rate. In this limit, the mixing rates are more important.
j′ = 1 (4)
This common model has been most extensively used
with turbulence models such as the k-ε style and
This expression describes the rate at which species i´ Reynolds stress models. However, there is a trend to-

32 www.cepmagazine.org December 2001 CEP

wards combining chemically reacting flow modeling final CFD solution. While this model has many benefits
with large-eddy-simulation (LES) and even direct-nu- for gaseous combustion systems, it is not the best choice
merical-simulation (DNS) turbulence modeling meth- for liquid reactions that are typical of most chemical
ods. These models do not explicitly calculate the eddy process industries (CPI) applications, where reaction
dissipation rate ε, and so it is necessary to replace ε in rates can fall anywhere from very fast to very slow when
the above rate equations with a suitable substitute. This compared with typical mixing rates.
is typically done by replacing the term ε/k, which is the Another reaction modeling approach incorporates the
reciprocal of the eddy lifetime, with the magnitude of methodology used to describe micromixing, or mixing
the local strain rate S : on the smallest scales (5, 6). In the context of a CFD cal-
∂u j ∂u i culation, micromixing is on a scale that is smaller than a
S = 2S ijS ij S ij = 1 + typical computational cell. Macromixing, on the other
2 ∂x i ∂x j (7)
hand, is responsible for large-scale blending, and me-
somixing is in between. The identification of these mix-
The Magnussen model was initially developed for ing regimes is drawn from assumptions at the core of tur-
simple, one- or two-step reaction sets, in which all reac- bulence modeling theory, namely that turbulence energy
tion rates are fast relative to the small-scale mixing. is generated in large eddies within a domain, and it cas-
However, this model has even found use for more com- cades to successively smaller eddies before being dissi-
plex systems. Recently, for such a system, an extension pated on the smallest scales. This cascade of turbulence
of the Magnussen has been developed (4), termed the is associated with a cascade of mixing, from macromix-
eddy-dissipation-concept (EDC) model. This model as- ing on the large scales, to mesomixing throughout the
sumes that the reaction occurs in small, turbulent struc- mid-scales, to micromixing on the sub-grid scales.
tures, called fine-scales. A volume fraction of the fine- One motivation for the interest in micromixing in liq-
scales is calculated, which depends on the kinematic uid reactions is that micromixing must occur before re-
viscosity of the fluid, the energy-eddy-dissipation rate, actions can take place. It therefore plays an important
and the turbulent kinetic energy. Reactions are then as- role when the reaction times are on the same order as
sumed to occur in the fine, turbulent structures, over a the mixing times. Micromixing models typically use a
time-scale that depends upon the kinematic viscosity mixture-fraction approach, employing a PDF formula-
and the energy-dissipation rate. A source term for each tion for the turbulence-chemistry interaction. The mi-
chemical species is then calculated that depends upon cromixing models are incorporated through calculating
the volume fraction of the fine-scales, the time-scale, the variance of the mixture fraction.
and the difference in species concentrations between the
fine-scale structures and the surrounding fluid. This ex-
tension of the Magnussen model provides improved ac- Fischer-Tropsch synthesis
curacy for complex, multistep reaction sets in which not in a bubble column
all reactions are fast relative to the rate at which small- Bubble columns are used in the CPI for many applica-
scale mixing occurs. tions, one of which is Fischer-Tropsch synthesis. In this
Numerous other reaction models exist that can be process, steam/oxygen gasification of coal or other hy-
coupled to the CFD calculation. For example, a collec- drocarbons produces a mixture of hydrogen and carbon
tion of reacting species can be described by a mixture monoxide. These gases react in a column of water to
fraction, which, under certain circumstances, is a con- form a variety of hydrocarbons in the liquid state. The
served quantity. This so-called PDF modeling approach products are collectively referred to as synthesis liquids
takes its name from the probability-density-function and the gas-to-liquid conversion process is called syngas
method used to describe the turbulence/chemistry inter- conversion. Both hydrodynamics and chemical reactions
action in the model. It is based on the assumptions of in- are important in determining the amount of syngas con-
finitely fast reactions and chemical equilibrium at all version that takes place in any given system. To simulate
times. Rather than solve conservation equations for mul- the hydrodynamics of the liquid/gas system, the Eulerian
tiple species, these equations are solved for the mean multiphase model is used. As described in Ref. 1, this
and variance of the mixture fraction. The variance in the model uses separate sets of fluid equations for each
fraction is representative of fluctuations in the species phase, in this case the gas and liquid, and couples them
concentrations. Thus, while the kinetic-rate expression through pressure, mass, momentum and heat exchange.
uses time-averaged values for species mass fractions, To simulate the chemical reaction between the phases,
the PDF model allows for fluctuations in these quanti- chemical species are defined in each phase. The reac-
ties. Auxiliary reaction calculations allow for the extrac- tions give rise to interphase mass transfer and the results
tion of intermediate and product species as a function of are used to predict syngas conversion in an industrial-
the mixture fraction and temperature distributions in the sized bubble column — the reactor.

CEP December 2001 www.cepmagazine.org 33

Reactor Design

■ Figure 1. Liquid-phase volume-fraction at 5, 10, 15, 20 and 60 s. ■ Figure 2. Liquid-product concentration at 5, 10, 15, 20 and 60 s.

tom of the column injects a mixture of CO (87.5%) and

As an example, consider the reaction between two H2 (12.5%) at a speed of 0.15 m/s. The chemical reac-
gas-phase reactants, CO (g) and H2 (g), in a column of tions are accounted for as balanced- species sources in
water (7). The gases enter the column through an inlet each phase. The model also computes the mass-transfer
on the bottom. The products are in the liquid phase, and rate across the gas/liquid interface.
are water, H2O (l), and a collection of hydrocarbons in Figure 1 shows the volume fraction of liquid after 5,
the methylene group, –(CH2) (l): 10, 15, 20 and 60 s of operation. Red corresponds to
pure liquid, and blue, to pure gas. As time progresses,
CO (g) + H2 (g) → –(CH2) (l) + H2O (l) (8) gas fills the liquid, and caus-
es the liquid level to rise.
The reaction rate is assumed to be dominated by mass The makeup of the liquid be-
transfer across the gas/liquid interface: gins as pure water, but
changes over time to include
ki´ = kl a( [Ceq, i´] – [Ci´]) (9) hydrocarbon products, as
well. The gas is injected
where i´ represents the reactants, either CO or H2. The through a circular opening
quantity kl is the liquid-side mass-transfer coefficient with a diameter slightly less
and a is the gas/liquid interfacial area. [Ceq, i´] is the than the column diameter.
equilibrium concentration of the gas species, i´, in the The inlet velocity profile is
liquid phase and can be estimated by the partial pressure constant, but already starts
of the species. [Ci´] is the local concentration of the re- to deform in the liquid after
actant gas species i´. Values for ki´ are computed for 5 s, as is evident in the left-
each of the gas-phase species, and the smallest (or slow- most graphic in Figure 1.
est) one is used in the calculation. Additional reaction Figure 2 shows the mass
steps produce CnH2n, CnH2n+2, CnH2n+1OH and CO2. fraction of the methylene-
These are not modeled here. group hydrocarbons (one of
A two-dimensional (2-D) axisymmetric model of the the products in the liquid
an industrial-sized bubble column is used. The column phase) at 5, 10, 15, 20 and
is 7 m in dia. and the initial liquid level is 30 m in 60 s. The increased amount
height. Two gas-phase species are used in the model, as of product near the bottom
are two-liquid phase species. The column is initially of the column is the result of ■ Figure 3. Stream-function
contours lines at 60 s for the
filled with pure water, and the gas space on top is ini- recirculation currents that liquid (left) and gas (right)
tially filled with pure hydrogen. A gas inlet at the bot- become established during phases.

34 www.cepmagazine.org December 2001 CEP

 that complex simulations of this type can be carried out
1 0.45 successfully using CFD.
0.9 0.4
Polymerization in an autoclave reactor
0.35
0.8 Low-density polyethylene (LDPE) reactors are used
0.3 to manufacture polymer products. The reactors are typi-

Gas Holdup
Conversion

0.7 0.25 cally of the tubular or autoclave variety. To make the

polymer, a minute amount of initiator is added to a (sin-
0.6 0.2
gle-molecule) monomer. Several reaction steps take
0.15 place in which the monomer is transformed to a polymer
0.5
0.1 with a range of chain lengths (corresponding to a range
0.4 of molecular weights). Heat is released in many of the
0.05
reactions, and one goal of LDPE reactor design is to pre-
0.3 0
0.15 0.2 0.25 0.3 0.35 vent hot spots that give rise to thermal runaways, which
are characterized by an undesired product distribution.
Gas Velocity, m/s In this example (7), the nearly infinite set of reactions
in the chain is approximated by the following six finite-
rate reactions using the method of moments (8).
■ Figure 4. The conversion rate (green) and gas holdup (orange) as
functions of the gas velocity.
Reaction Initiator decomposition: I → 2A
1:
operation. These currents are radially outside the rising Reaction Chain initiation: A + M → R1
2:
gas stream at the center of the column, which can be Reaction Chain propagation: M + Rx → Rx+1
3:
seen forming in Figure 1. Reaction Chain transfer to monomer: M + Rx → Px
4:
In Figure 3, stream-function contour-lines for the liq- + R1
uid (left) and gas (right) phases are shown after 60 s. At Reaction 5: Disproportionation termination: Rx + Ry
this point, the system has reached steady operation, even → Px + Py
though fluctuations in the flow patterns continue. The Reaction 6: Combination termination: Rx + Ry → Px+y
liquid phase is characterized by a strong recirculation
current. The gas phase, on the other hand, has some re- where I is the initiator, A the initiator radical, M the
circulation, and some short-circuiting of gas from the monomer, Rx is a radical of arbitrary length, R is the total
inlet to the outlet at the top of the column. It is the recir- radical, ΣRx, and P is the total polymer, ΣPx. As a conse-
culation of gas and liquid in the vessel that continues to quence of the method of moments, quantities that de-
feed the reaction and produce the highest concentration scribe the product distribution can also be computed.
of product near the bottom of the column, as was shown These include the molecular-weight distribution, which, if
in Figure 2. narrow, indicates a high-quality (uniform) product.
Figure 4 shows the gas holdup and the syngas conver- Other predicted quantities include initiator con-
sion as functions of the gas velocity. For low gas rates, sumption rate, monomer conversion, total
the gas momentum is low, so the gas cannot lift the liq- radical and total polymer concentra-
uid high enough to hold a significant quantity of gas. tion gradients, and the tempera-
Thus, the gas holdup at low gas rates is low. At high gas ture profile.
rates, there is more momentum in the gas phase to push A 3-D model of an
the liquid up, so that it can hold more gas. The gas autoclave reactor
holdup in this regime is high. This expected hydrody-
namic result is predicted by the CFD calculation.
At low gas rates, the residence time in the unit is
high, so conversion of the gas-to-liquid is high. For high
gas rates, the opposite is true. The residence time for the
gas is lower, and the subsequent conversion is reduced.
This result is also shown in Figure 4. The results in Fig-
ures 1 and 2 correspond to the lowest flowrate shown,
0.15 m/s.
This example shows how a reacting multiphase flow
can be modeled. The problem definition is further com- ■ Figure 5. The hybrid
plicated by the fact that the reactants are in one phase, mesh for the autoclave reactor
while the products are in the other. The results illustrate contains 166,000 cells.

CEP December 2001 www.cepmagazine.org 35

Reactor Design

■ Figure 6. The velocity field is ■ Figure 7. Temperature ■ Figure 8. Contours of the ■ Figure 9. Viscosity is shown to
highly swirling. increases from 460 K to molecular-weight distribution are increase as the makeup of the poly-
540 K in the reactor. used to assess the range of molec- mer mixture changes within the re-
ular weights in the product. actor.

is described here. It incorporates the method of moments for vary from 41,500 to 41,900, or by about 1%. The nar-
the reaction with a CFD calculation for the flow field. The rower this distribution, the higher the quality of the
monomer used is ethylene. The viscosity of the mixture is product. The molecular viscosity is computed by a cus-
computed as a function of the temperature and concentrations tom function that incorporates the concentrations of the
of these species and those of the intermediate polymers (or various species in the vessel, as well as the temperature.
radicals) and product polymers. Its value increases from a low of about 0.019 kg/m•s to
Figure 5 shows the hybrid mesh of 166,000 cells used a high of about 0.026 kg/m•s, as the chains of radicals
for the simulation. The reactor contains both paddle and and polymer product increase in length in the reactor, as
twisted-blade impellers, which are modeled using a sliding shown in Figure 9.
mesh, a technique that is common for accurate simulation The results of this simulation are in reasonably good
of rotating equipment. The initiator is premixed with the agreement with Ref. 9. They provide information about
monomer and injected into the reactor through an annular important reactor characteristics, including the tempera-
ring. The RNG k-ε model is used to account for the turbu- ture and viscosity distribution, as well as the spread of
lence in the highly swirling flow. molecular weights in the resulting product. Comprehen-
The velocity vectors in Figure 6 show the high swirl sive results such as these can be used to troubleshoot
induced by the rapidly rotating (250 rpm) impellers in (and help redesign) problem installations in which the
the unbaffled vessel. Four axial slices are used in the product quality is not optimal.
next three figures (Figures 7–9) to show the progression
of different problem variables as the mixture advances Ozone conversion in a fluidized-bed reactor
through the reactor. In these figures, the inlet annulus is The conversion of ozone gas to oxygen gas is another
at the top of the figure and the outflow annulus is at the example of a reactions in a multiphase system (10). The
bottom. (Both are shown as grey circles.) decomposition process occurs in a fluidized bed, where
In Figure 7, the temperature contours increase from the particles in the bed serve as a catalyst. “Bed conver-
the inlet temperature of 460 K to a high of 544 K near sion” refers to the process by which the passage of one
the exit. The thermal decomposition of the ethylene material through the bed is converted to another during
monomer could occur at 544 K, giving rise to a poor transit. Design of the system for optimum conversion
product distribution. This high temperature is partly the strongly depends upon knowledge of both hydrodynam-
result of an adiabatic thermal boundary condition on the ics and chemical reactions. It is essential, therefore, to
reactor walls that was used in the simulation. The con- model both phenomena together in a CFD simulation.
tours of the molecular weight distribution in Figure 8 An Eulerian-granular multiphase flow model is used,

36 www.cepmagazine.org December 2001 CEP

 O2

O3
■ Figure 11. The fluidized bed after 0.5 s of operation.
■ Figure 10. A schematic of the ozone decomposition system.

which has a special treatment for the granular phase that

constitutes the bed. It is combined with a multispecies,
reacting gas phase model to predict ozone decomposi-
tion (and conversion to oxygen) in the fluidized bed.
A 2-D axisymmetric problem is a useful means of
studying this process. A column 0.229 m in dia. and
0.25 m high is used, modeled with a grid of 110 × 70
cells. At rest, the bed is 0.115 m high. It contains cata-
lyst particles 117 µm in dia. The decomposition of
ozone is brought about by sand particles impregnated
with iron oxide in the bed. The decomposition reaction
is first-order for the two gas species:

O3 → 1.5 O2 (10)

The decomposition rate is expressed as:

K = 1.57 a [O3] (11)

where a is the volume fraction of the catalyst and [O3] is ■ Figure 12: The fluidized bed after 1.0 s of operation.
the concentration of ozone. The reaction takes place in
the bed region only. The calculations are done for super- dent. When a coarse mesh is used, the bubbles are fewer in
ficial velocities in the range from 4 to 14 cm/s. number and rounder. When a fine mesh is used, the bubbles
A schematic of the device is shown in Figure 10. Ozone are denser and more irregular. The number of bubbles has a
enters the bed in a uniform flow from the bottom. As it significant impact on the conversion. The more bubbles in
passes through the bed, it interacts with the catalyst and is the domain, the higher the conversion.
converted to oxygen. Figure 11 shows the gas volume frac- Figure 12 shows the gas volume fraction at a t = 1 s.
tion in the bed at t = 0.5 s. The flow field is the same Notice how the upper surface of the bed is lifted by the
whether the reaction in the gas phase is taking place or not. approaching bubbles. While some large bubbles stand
The bubbles are formed near the bottom of the bed and mi- out, the bed itself is filled with small bubbles to a greater
grate upwards. The bubble shape and size are grid-depen- or lesser degree (as indicated by the shades of blue and

CEP December 2001 www.cepmagazine.org 37

 Reactor Design

0.8 0.5
of molecular chemistry, however, combined with empiri-
cal combinatorial chemistry methods promise to signifi-
0.7 cantly reduce the cycle times related to the discovery of
0.45
0.6
new chemical products.
The requirements to develop and produce new prod-
0.5 0.4 ucts to create revenue growth, and more stringent effi-

Gas Holdup
Cout/Cin

ciency requirements to improve profitability, directly af-

0.4 0.35 fect the chemical engineer’s job. New products may re-
0.3 quire new and more-difficult-to-operate chemical reaction
0.3 processes to be productive in mass quantities. Improved
0.2 efficiency requirements may require fine-tuning of exist-
0.25 ing processes, or the replacement of tried-and-true meth-
0.1
ods with completely new ones. An example of the latter
0 0.2 would be the replacement of large, batch reactors with
0 2 4 6 8 10 12 14 smaller continuous units to obtain process intensification.
Gas Velocity, cm/s The classical working methods of chemical engi-
neers, which rely heavily on empiricism, practical expe-
rience, extensive consultation of printed handbooks, and
■ Figure 13. The orange circles show the predictions for the ratio manual calculations, may no longer be suited for this
between Cout/Cin for O3, which is equal to (1 - conversion). The green new and changing environment. More-advanced design
circles show the corresponding experimental data (9). The red circles are
and analysis tools are needed. And indeed, many com-
the predictions for the gas holdup. All data are shown as functions of
superficial gas velocity. puter-based design tools have been developed.
Flowsheet-modeling software can analyze the opera-
tion of complete plants. To make the models tractable,
green). A bed filled with bubbles in this manner is the simplified hydrodynamic models with reduced reaction
desired hydrodynamic state for optimum conversion. sets are often used for the individual chemical reactors.
Figure 13 shows the conversion curve and gas holdup On the other end of the spectrum, specialized software
as functions of the gas velocity at the inlet on the floor exists to model complex chemistry. Such software can
of the bed. The gas holdup is defined as the ratio of the handle stiff (i.e., those with a large difference in time-
gas in the bed to the total volume of the bed. The curve scales and are especially difficult) reaction sets with
shows that the gas holdup increases with gas velocity up hundreds of surface and volumetric reactions, but the
to a point, after which saturation occurs. At low veloci- software is neither suitable to model complete plants nor
ties, the increasing gas velocity forces the bed to lift able to take into effect the hydrodynamics of the reactor.
more. At higher velocities, the bed can no longer rise In between these two extremes falls CFD software,
and hold additional gas, and saturation occurs. which can model both chemical reactions and the link
The conversion curve is plotted along with data from with reactor hydrodynamics dynamics. CFD software is
the literature (9), and good agreement is in evidence. When generally used to model individual plant components,
the quantity Cout/Cin is small, a small amount of ozone exits and not the whole process at once. When tied to flow-
at the top of the bed, meaning that conversion to oxygen is sheet-modeling software, however, it can provide more
high. This occurs at low velocities, where the residence accurate flow-field data (averaged velocities or tempera-
time of ozone in the bed is long. At high velocities, Cout/Cin tures) about unit operations than the simplified assump-
is large, meaning that the conversion to oxygen is poor. tions normally used for input.
This is due to the fact that the residence time is shortened, Indeed, the current trend is to integrate these various
allowing less time for the catalytic reaction to occur. The pieces of software. New chemical products are being de-
technique used in this example could be applied to deter- veloped by using a combination of molecular modeling
mine optimum flowrates for the incoming ozone flow, or to software and combinatorial chemistry. Once the new
test modifications of the bed design, such as the aspect materials and the operating conditions required for the
ratio or the addition of baffles or other internals. Validation reaction process have been identified in the laboratory,
of a laboratory-scale model could also be the basis of the production process can be designed by using the
scaleup designs for an industrial setting. flowsheet model as the basis.
The flowsheet model uses its standard models for
Expanding the toolbox non-reaction-critical components such as pipelines,
In the CPI, new chemical materials traditionally were pumps and conveyors. For the critical components, an
developed empirically via trial-and-error processes that advanced CFD model automatically replaces the one-di-
took years. Recent advances in the computer modeling mensional models currently included in the flowsheet

38 www.cepmagazine.org December 2001 CEP

software. The CFD software automatically exchanges out of the question. However, in the past, scaleup based
the required data with the flowsheet model. It models on a purely theoretical approach was also considered im-
both the fluid dynamics of the reactor and the chemical possible. Current methods therefore rely on a hybrid ap-
reaction process. For complex reaction sets, the CFD proach that combines extrapolation of laboratory- and
software may automatically call a specialized chemical pilot-scale data, dimensional analysis, theoretical analy-
reaction program that replaces its standard chemical re- sis, empirical correlations and practical experience.
action solver, and solves the complex reaction set for The rapid increase in computer power, combined with
every cell in the CFD domain at every fluid-flow time- theoretical advances in the fields of chemical reaction
step. Although not yet generally commercially available, and fluid dynamics, are increasing the role of theoretical
such integrated systems have been implemented on a analysis. This is accelerated by the changes in training
custom basis. It is expected that within a few years, soft- ChEs currently receive in college. In the past, ChEs
ware will be commonly available that includes flowsheet were trained by getting their hands dirty, performing
modeling, reactor hydrodynamics modeling, and fully laboratory experiments and interpreting the results using
integrated complex reaction models. dimensional analysis. Today’s engineers are much more
As discussed, one of the most challenging tasks for a familiar with designing equipment on a computer than
ChE is the scaleup of a laboratory-scale reactor to a full- actually building it by hand. It is therefore to be expect-
size chemical plant. Full-scale experimentation is usually ed that in the future, the design and scaleup of chemical
plants will be done completely based on theoretical and
computational analysis, reducing the role of subjective
personal experience and empiricism. CEP
Literature Cited
1. Bakker A., et al., “Realize Greater Benefits from CFD,” Chem.
Eng. Progress, 97 (3), pp. 45–53 (Mar. 2001).
2. Magnussen, B. F., and B. H. Hjertager, “On Mathematical Mod- ANDRE BAKKER is the regional consulting manager at Fluent Inc.(10
els of Turbulent Combustion with Special Emphasis on Soot For- Cavendish Court, Centerra Resource Park, Lebanon, NH 03766-1442;
mation and Combustion,” Proc. 16th Int. Symp. on Combustion, Phone: (603) 643-2600; Fax: (603) 643-3967; E-mail: ab@fluent.com).
The Combustion Institute, Pittsburgh, PA (1976). Bakker is an internationally recognized expert in industrial mixing and
CFD modeling of chemical engineering applications. His specialization
3. Bakker, A., and J. B. Fasano, “Time Dependent, Turbulent Mix-
includes experimental and computational fluid mixing. He holds
ing and Chemical Reaction in Stirred Tanks,” paper presented at engineering and doctorate degrees from Delft Univ. of Technology in
AIChE Annual Meeting, St. Louis, MO (Nov. 1993), also pub- the Netherlands, both in applied physics. He has coauthored more than
lished in “AIChE Symposium Series,” No. 299, 90, “Industrial 50 technical articles and presentations on fluid dynamics and mixing.
Mixing Technology: Chemical and Biological Applications,” G. B. Bakker is a member of AIChE.
Tatterson, volume editor, pp. 71–78 (1994).
4. Gran, I. R., and B. F. Magnussen, “A Numerical Study of a AHMAD H. HAIDARI is the chemical team leader at Fluent Inc. (Lebanon,
Bluff-Body Stabilized Diffusion Flame: Part 2; Influence of Com- NH; Phone: (603) 643-2600; Fax: (603) 643-3967; E-mail:
bustion Modeling and Finite-Rate Chemistry,” Combustion Sci. ah@fluent.com). Haidari has 15 years of experience in the application
of flow modeling in addressing industrial-process-equipment design,
and Tech., pp. 119–191 (1996).
process troubleshooting, analysis and scaleup. He holds a PhD in
5. Fox, R. O., “On the Relationship between Lagrangian Micromix- mechanical engineering from Lehigh Univ., is a member of AIChE, and
ing Models and Computational Fluid Dynamics,” Chem. Eng. and has made numerous presentations and written publications on
Proc., 37, pp. 521–535 (1998). modeling chemical process equipment.
6. Hannon, J., “Mixing and Chemical Reaction in Tubular Reactors
and Stirred Tanks,” PhD thesis, Cranfield Inst. of Technology, ELIZABETH M. MARSHALL is the technical marketing archive manager at
Cranfield, U.K. (1992). Fluent Inc. (Lebanon, NH; Phone; (603) 643-2600; Fax: (603) 643-3967;
7. Zhou, W., et al., “Application of CFD in Modeling Multiphase E-mail: emm@fluent.com). She has been with Fluent for more than ten
Reactors,” paper presented at Chemical Reaction Engineering VII: years. She has extensive experience in a wide range of industrial
applications, with special focus in the chemical process and mixing
Computational Fluid Dynamics, Quebec City, Canada — spon-
areas. She holds a bachelor’s degree in mathematics from St. Lawrence
sored by the United Engineering Foundation, New York — (Aug. Univ. and a PhD in physics from Dartmouth College.
6–11, 2000).
8. Kiparissides, C., et al., “Dynamical Simulation of Industrial
Poly(vinyl chloride) Batch Suspension Polymerization Reactors,” Acknowledgment
Ind. Eng. Chem. Res., 36 (4), p. 1253 (1997).
The authors wish to acknowledge the contributions of the following
9. Read, N. K., et al., “Simulations of a LDPE Reactor Using Com- individuals: Jay Sanyal and Wei Zhou for their contributions to the
putational Fluid Dynamics,” Reactors, Kinetics, and Catalysis, 43 Fischer-Tropsch model; Bin Yang, Wei Zhou, Madhava Symlal, and
(1), p. 104 (1997). Sergio Vasquez for their contributions to the ozone decomposition
10. Fryer, C., and O. E. Potter, “Experimental Investigation of Mod- model; Wei Zhou for her contributions to the LDPE model; and
els for Fluidized Bed Catalytic Reactors” AIChE J., 22, pp. 38–47 Heshmat Massah, Jeff Ma and Madhusuden Agrawal for many useful
(1976). discussions and advice.

CEP December 2001 www.cepmagazine.org 39

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