Non-Adiabatic Multitubular Fixed-Bed Catalytic Reactor Model

Article pubs.acs.org/IECR

Non-Adiabatic Multitubular Fixed-Bed Catalytic Reactor Model Coupled with Shell-Side Coolant CFD Model Eric J. Hukkanen,* Michael J. Rangitsch, and Paul M. Witt The Dow Chemical Company, Midland, Michigan 48674, United States ABSTRACT: An overall fixed-bed reactor model that combines a one-dimensional plug flow reactor model with a computational fluid dynamics (CFD) model of the shell-side coolant fluid over a series of individual reactor tubes is presented. The model chemistry is the partial oxidation of o-xylene to phthalic anhydride, a well-studied system for reactor performance. The model is used to investigate the effect of variation in cooling temperature on overall reactor performance: temperature profiles at the wall and centerline and o-xylene conversion. Non-isothermal shell-side cooling temperature profiles are calculated using computational fluid dynamics and heat flux profiles along the reactor tube length. This analysis demonstrates that, with faster coolant flow rates, the coupled fixed-bed reactor and CFD model process outputs approach the nominal case. Alternative shell-side baffle configurations are examined. The calculated coolant velocity profiles, though different between evaluated configurations, result in similar overall reactor performance. However, it should be noted that none of the simulations observe isothermal shell-side coolant temperatures, as is commonly assumed in fixed-bed and plug flow reactor models. This coupled model enables opportunity for further reactor optimization on both the shell-side CFD model and the fixed-bed reactor model, as it can be applied to pilot- and commercial-scale reactors for existing or new chemistries. This model provides a more realistic estimation of the reactor performance, when considering isothermal coolant profiles. Specifically, for the fixed-bed reactor model, alternative catalyst packing schedules (i.e., activity profiles) or feed rates can be considered. Additionally, conditions or individual reactor tubes can be identified that are more prone to runaway.

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INTRODUCTION The multitubular fixed-bed reactor system is used for strongly exothermic reactions, such as partial oxidation reactions. A typical multitubular reactor system can contain several thousand tubes, sometimes up to 20 000 tubes. In these reactor systems, a circulating heat-transfer fluid is used to remove the large heat of reaction and maintain the fixed-bed temperature within a narrow range.1 Proper design, loading, and operation of fixed-bed reactors requires a combination of reactor modeling, pilot plant trials, and catalyst bed grading to achieve desired reactor performance. Fixed-bed reactor models can be classified into two types of models: pseudo-homogeneous or heterogeneous.2 Both model classifications can be modeled in one or two dimensions. The pseudo-homogeneous one-dimensional models assumes concentration and temperature gradients only in the axial direction. Axial mixing and diffusion can also be incorporated into the one-dimensional model. The pseudo-homogeneous twodimensional model incorporates heat and mass transfer in the axial and radial direction. Heterogeneous reaction models are used when it is necessary to distinguish between the fluid phase and catalyst surface (i.e., concentration and temperature of fluid are different than those at the catalyst surface). Computational fluid dynamics (CFD) are more commonly used to investigate the flow patterns within the fixed-bed reactor tube to better understand heat and mass transfer and its influence on reaction kinetics.1,3 As in most cases with fixed-bed reactor models, fixed-bed reactors and reactor performance are evaluated assuming a constant shell-side coolant temperature. Recent advances allow for computational tools that enable more accurate modeling of multitubular fixed-bed reactors. Hybrid gPROMS-CFD © XXXX American Chemical Society

Multitubular software is one such commercial software package that enables modeling of fixed-bed reactors and shell-side temperature profiles using CFD.4 This commercial package was used to evaluate and optimize reactor performance of terephthaldehyde production.5 This paper presents a fixed-bed reactor model that combines a one-dimensional plug flow reactor model with a CFD model of the shell-side coolant fluid over a series of individual reactor tubes. The model chemistry is the partial oxidation of o-xylene to phthalic anhydride. Partial oxidation of o-xylene has been studied extensively by several researchers.2,6−12 Primary research topics focused on reaction kinetics, reactor perfor mance, graded catalyst beds and catalyst activity, and evaluation of hot spots or runaway conditions. Reactor performance resulting from non-isothermal shell-side coolant temperature has not been investigated. In this analysis, the shell-side temperature of the fixed-bed reactor is not isothermal. The fixed-bed reactor model presented is a one-dimensional model based on the work of Hagen et al.13 that accounts for heat generation distribution along the radial direction. The Hagen method is comparable to two-dimensional conservation equations, though other appropriate models can be used. The shell-side coolant temperature is addressed using computational fluid dynamics (CFD). While CFD is well suited to Special Issue: NASCRE 3 Received: March 2, 2013 Revised: May 3, 2013 Accepted: May 6, 2013

A

dx.doi.org/10.1021/ie4006832 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

Article

modeling heat and mass transfer in a tubular packed bed reactor, industrial scale reactors tend to have many individual reactor tubes (reactors with more than 50 000 tubes are not unknown). It is possible to model the detailed flow around each tube, but the size of the problem thus generated would consume vast amounts of computational resources. In cases with large numbers of tubes, it is possible to approximate the shell-side flow domain as a porous medium. Non-isotropic momentum losses are used to add the directional nature of pressure drops in a tube bundle. With this treatment it is possible to achieve fairly good agreement with observed flow distribution and pressure drop.14 The fixed-bed reactor model and CFD model are coupled by the shell-side coolant temperature and reactor heat flux along each tube. Figure 1 illustrates a schematic of a common multitubular

Table 1. Reactor and Reaction Constants constants

description

value

units

ΔHrxn,1 ΔHrxn,2 ΔHrxn,3 A1

heat of reaction 1 heat of reaction 2 heat of reaction 3 pre-exponential reaction 1 pre-exponential reaction 2 pre-exponential reaction 3 Biot number, (hwdt/2kr,e) reactor tube diam. activation energy reaction 1 activation energy reaction 2 activation energy reaction 3 heat transfer coefficient at the wall effective radial thermal conductivity reactor length pressure initial reactor feed mole fraction of o-xylene in air bulk catalyst density

−264 −781 −1045 1.632 × 10−2

kcal/mol kcal/mol kcal/mol mol/(kgcat s atm2)

1.583 × 10−3

mol/(kgcat s atm2)

1.789 × 10−3

mol/(kgcat s atm2)

0.802 0.0254 27.14

m kcal/mol

31.00

kcal/mol

28.60

kcal/mol

30.93

cal/(m2 s K)

0.49

cal/(m s K)

9.0 1.7 0.120 1.12

m atm mol/s mol %

1240

kgcat/m3

A2 A3 Bi dt Ea,1 Ea,2 Ea,3 hw kr,e l P Ftot,i yox ρb

for the partial oxidation of o-xylene reported by Calverley et al.15 The kinetic parameter values are reported in Table 1. The rate equations are

r1 = k1PoxPO2 r2 = k 2PphPO2 r3 = k 3PoxPO2

Figure 1. Multitubuluar fixed bed catalytic reactor modeling schematic.

⎛ E ⎛1 1 ⎟⎞⎞⎟ a, i ⎜ ki = Ai exp⎜⎜− − 600 ⎠⎟⎠ ⎝ Rg ⎝ T

fixed-bed catalytic reactor system. The model is used to investigate impact of coolant flow rate and baffle configuration on the resulting variation in shell-side cooling temperature. The resulting non-isothermal cooling temperature impacts the overall reactor performance: temperature profiles at the wall and centerline and o-xylene conversion. The reactor performance is evaluated for each case.

i = 1, 2, 3

where ri is the reaction rate for reaction i, Ai is the preexponential constant for reaction i, Ea,i is the activation energy for reaction i, ki is the reaction rate constant for reaction i, Pox is the partial pressure of o-xylene, PO2 is the partial pressure of oxygen, and Pph is the partial pressure of phthalic anhydride. Reactor Model. The conservation equations for mass and energy define the fixed-bed reactor model. The mole balance for species i over all reactions j is defined by

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REACTOR MODELING Chemistry. The gas-phase partial oxidation of o-xylene reaction network is defined by the following reactions: C8H10 + 3O2 → C8H4O3 + 3H 2O C8H4O3 +

for

n

dFi = Vrρb ∑ νi , jrj dz j=1

for

i = 1, ..., m (1)

where Vr is the fixed-bed reactor volume and νi,j is the reaction stoichiometric coefficient for species i and reaction j. For simplicity, we assume that the fixed-bed reactor is isobaric. It is recognized that this assumption is unrealistic. Alternative pressure drop correlations may be substituted. The energy balance equation

15 O2 → 8CO2 + 2H 2O 2

21 O2 → 8CO2 + 5H 2O 2 Direct conversion of o-xylene to phthalic anhydride is the primary reaction. Complete combustion of both o-xylene and phthalic anhydride constitute non-selective competing reactions. Partial oxidation of o-xylene has been studied extensively by several researchers.2,6−10,12 This paper uses kinetic information C8H10 +

m

∑ Fi i=1

8αk r,eπl dĤ =− dz A

(2) 13

is defined using the method developed by Hagan et al. The Hagan method estimates the heat transfer between the process B



Article

Figure 2. (a) Nominal reactor wall temperature and centerline temperature for base case analysis, as calculated from eqs 12 and 13. (b) Nominal heat flux at reactor tube wall for base case analysis, as calculated from eq 16.

and the shell coolant. The reactor model is a one-dimensional model that accurately simulates the two-dimensional conservation equations by accounting for the heat generation distribution along the radial direction. The energy balance equation, eq 2, is developed by applying a Taylor’s series expansion of ln f(T) around the radial mean temperature, Tm, where f(T) is of the Arrhenius form and Tc is the coolant temperature ⎛ E ⎞ f (T ) = exp⎜⎜ − a ⎟⎟ ⎝ R gT ⎠

ln f (T ) ≈ −

(3)

Ea + A(T − Tm) + B(T − Tm)2 + ... R gTm

Figure 3. Nominal o-xylene conversion for base case analysis assuming constant shell-side wall temperature (600 K). (4)

Table 2. Nominal Results for Base Case Simulation

where

A=

E̅ R gTm2 R gTm

B =− E̅ A2

⎛ Ea, i − E ̅ ⎞2 1 ⎟ wi + ∑⎜ 2 i= 1 ⎝ E̅ ⎠ n

(6)

n

∑ Ea,iwi

(7)

i=1

riΔHrxn, i n ∑i = 1 riΔHrxn, i

Tw(z = zmax) Tw(z = 1) Tcent(z = zmax) Tcent(z = 1) χox(z = 1) Q̇ r(z = zmax) Qr

T (r , α) = Tc +

(8)

Hagan applied Taylor series expansion and the Karman− Pohlhausen procedure16 resulting in an implicit equation for the α term in eq 2. α=

value 0.267

⎤ Bi ⎡ 1 B 2 ln (1 − α)⎥ ⎢A(Tm − Tc) + ln(1 − α) − ⎦ 4⎣ 3 A2

Tw = Tc +

⎛ ⎛ r ⎞ 2 ⎞⎤ 1 ⎡ 4α ⎢ − 2ln⎜1 − α + α⎜ ⎟ ⎟⎥ ⎝ R ⎠ ⎠⎥⎦ A ⎢⎣ Bi ⎝

(11)

4α BiA

r=R

(12)

and

The reactor heat transfer rate adjusts along the axial direction based on the local reaction rate and local temperature. For simplicity, effective thermal conductivity, kr,e, and the heat transfer coefficient at the wall, hw, are assumed to be constant. Therefore, the Biot number, Bi, is constant as well:

hw d t 2k r, e

K K K K % W/m2 W

Temperature profiles at the reactor wall, Tw, and reactor centerline, Tcent, are of particular interest in work presented here. Evaluation at r = R and r = 0 reduces eq 11 to

(9)

Bi =

620.8 606.9 629.8 609.8 57.7 2693 1242

units

Hagan et al.13 derive the radial temperature profile along the reactor length where

where the weighting, wi, of reaction i is defined by wi =

description normalized axial position at max. temp. max. reactor wall temp. final reactor wall temp. max. reactor temp. at centerline final reactor temp. at centerline final o-xylene conversion max. radial heat flux total radial heat release

(5)

The average activation energy, E̅ , is defined by E̅ =

output zmax

Tcent = Tc +

⎤ 1 ⎡ 4α − 2ln(1 − α)⎥ ⎢⎣ ⎦ A Bi r=0

(13)

The fixed-bed reactor model is coupled to the shell-side CFD model through the heat flux at the reactor tube and the shellside coolant temperature, Tc. The energy flux, Q̇ r, in cylindrical coordinates is defined as17

(10) C



Article

Figure 4. CFD coolant velocity profiles on the reactor shell-side. Sections are along the center point of the zones.

Figure 5. CFD coolant temperature profiles on the reactor shell-side. Sections are along the center point of the zones.

∂T Q̇ r = −k r,e ∂r

Q̇ r =

(14)

The energy flux can also be written as −k r,e

∂T = hw (Tw − Tc) ∂r

4αhw BiA

r=R

(16)

Equation 16 is used to calculate the energy flux from each fixedbed reactor tube model to the CFD model for shell-side coolant temperature. The mass and energy balance equations are solved using Athena Visual Studio, which uses a variant of the DASSL predictor−corrector algorithm to solve the reactor integration problem. The specific enthalpy of the system is calculated using

(15)

where hw is the heat transfer coefficient at the wall and Tcool is the coolant temperature. Equation 14 can be rewritten by substituting eqs 12 and 15 to incorporate the Hagan method into the energy flux D



Article

Table 3. Comparison of Reactor Performance for Disk and Doughnut Baffles and Varying Coolant Flow Ratesa

a

output

description

zmax T̅ c Tw(z = zmax) Tw(z = 1) Tcent(z = zmax) Tcent(z = 1) χox(z = 1) Q̇ r(z = zmax) Qr

normalized axial position at max temp. shell-side wall temp. max. reactor wall temp. final reactor wall temp. max. reactor temp. at centerline final reactor temp. at centerline final o-xylene conversion max. radial heat flux total radial heat release

15 kg/s 0.403 609.0 637.0 624.5 649.6 628.1 76.3 3780 1640

± ± ± ± ± ± ± ± ±

0.028 10.3 3.5 0.3 4.6 0.4 0.8 363 29

30 kg/s 0.289 603.9 626.3 614.5 636.4 617.7 65.3 3071 1354

± ± ± ± ± ± ± ± ±

0.013 4.1 1.0 0.1 1.2 0.1 0.3 115 8

50 kg/s

units

± ± ± ± ± ± ± ± ±

K K K K K % W/m2 W

0.286 602.3 623.9 611.3 633.7 614.4 62.2 2925 1283

0.006 2.3 0.5 0.1 0.8 0.1 0.2 68 4

Mean output values are reported at 95% confidence.

Figure 8. Resulting shell-side wall temperature profiles for 36 zones from CFD modeling. Molten salt flow rate is 30 kg/s. Nominal (initial) shell-side temperature is 600 K (−·−).

Figure 6. Resulting shell-side wall temperature profiles, Tc, for 36 zones from CFD modeling. Molten salt flow rate is 15 kg/s. Nominal (initial) shell-side temperature is 600 K (−·−).

Figure 7. Overall reactor performance for 36 zones from CFD modeling. Resulting heat flux profiles (a), Q̇ r, calculated using eq 16. Reactor temperature at wall, Tw, (b) and centerline, Tcent, (c), as calculated from eqs 12 and 13. Resulting o-xylene conversion profiles (d). Molten salt flow rate is 30 kg/s. Nominal reactor heat flux, temperature, and o-xylene conversion profiles (−·−) are reported for comparison. E



Article

Figure 9. Overall reactor performance for 36 zones from CFD modeling. Resulting heat flux profiles (a), Q̇ r, calculated using eq 16. Reactor temperature at wall, Tw, (b) and centerline, Tcent, (c), as calculated from eqs 12 and 13. Resulting o-xylene conversion profiles (d). Molten salt flow rate is 30 kg/s. Nominal reactor heat flux, temperature, and o-xylene conversion profiles (−·−) are reported for comparison.

considered representative of the temperature of the coolant experienced by each tube located in the zone. The grid was constructed with the ANSYS program GAMBIT. It is a fully hexagonal grid with 2.16 million cells (55 × 55 × 743 cells). The same sized grid was used for all simulations. It was built so that interblock faces could be labeled as walls to create the baffling scheme desired, while keeping the same geometry and cell count. The inter-baffle spacing is set to the diameter of the bundle. The CFD code writes the coolant temperature profile vector for each zone into a series of files that are then copied to the correct location for the reactor model computation. The fixedbed reactor models executes the simulation with the updated shell-side coolant temperature. The fixed-bed reactor model solution is obtained in 10 s. The CFD code then calls the reactor model for each of the bundle zones, and reads the resulting data files (radial heat flux vector). Each computational cell is then identified by tube bundle zone and the distance along the reactor tube. The heat flux (source term) and several other parameters are read from the reactor model results file and stored in user defined memory locations in the ANSYS Fluent code. The parallel nature of the CFD simulation requires that these steps be done only from the master process of the simulation. To avoid numerical instabilities, the computed heat source term is under-relaxed with the heat source term from the previous model iteration. This technique is reasonably robust and converges in approximately 5000 iterations per zone and coolant profile (approximately 30−40 min). Using 32 parallel processors, the complete CFD-fixed-bed reactor model simulation would complete in 18−20 h. Three molten salt flow rates are evaluated and the resulting profiles are compared to the base case. Cross-cocurrent flow of

Figure 10. Resulting shell-side wall temperature profiles for 36 zones from CFD modeling. Molten salt flow rate is 50 kg/s. Nominal (initial) shell-side temperature is 600 K (−·−).

the Athena Visual Studio flash calculation and the physical property database provided with the Athena Visual Studio installation. While this model uses the Hagan method13 to calculate an appropriate radial-mean temperature, it is fundamentally a onedimensional model, so only the axial activity distribution is being investigated with this approach. Shell-Side Model. The linkage between the CFD code and the reactor model is through the heat balance equation. The reactor model is used to set a heat source term in the CFD model. The CFD model generates a cooling medium temperature for the reactor model, using the reactor models calculated wall heat flux as a heat source term in the CFD energy equation. The variations in the local conditions encountered by the individual tubes are accounted for by dividing the tube bundle into a number of zones (36 in this case). The 36 zones were arranged in a 6 × 6 grid. The centroid of each zone is F



Article

Figure 11. Overall reactor performance for 36 zones from CFD modeling. Resulting heat flux profiles (a), Q̇ r, calculated using eq 16. Reactor temperature at wall, Tw, (b) and centerline, Tcent, (c), as calculated from eqs 12 and 13. Resulting o-xylene conversion profiles (d). Molten salt flow rate is 50 kg/s. Nominal reactor heat flux, temperature, and o-xylene conversion profiles (−·−) are reported for comparison.

at 95% confidence. Equation 16 is integrated along the length of the reactor to calculate the total radial heat released. As is expected with faster coolant flow rates, the mean shell-side coolant temperature decreases (i.e., approaches the ideal case of 600 K). The slowest flow rate (15 kg/s) yields the highest reactor centerline temperature further into the reactor bed. As the coolant feed rate increases, the maximum predicted reactor temperature and normalized axial position decreases (i.e., approaches the nominal case). The next sections analyze the results for each flow rate. Case 1: 15 kg/s. Figure 6 reports the resulting shell-side coolant temperature for the 36 zone compared to the nominal case, 600 K. The slower feed rate results in a larger increase in shell-side coolant temperature. The shell-side temperature at the exit of the reactor is more than 15 K larger than the base case. The resulting overall increase in shell-side coolant temperature results in a 32% increase in total radial heat release compared to the base case. The additional heat release and higher shell-side coolant temperature results in an increase of almost 20 K of the maximum reactor temperature along the centerline. This results in a 32% increase in o-xylene conversion. See Figure 7. Case 2: 30 kg/s. Figure 8 reports the resulting shell-side coolant temperature for the 36 zone compared to the nominal case, 600 K. The coolant feed rate is twice as fast as Case 1. The shell-side temperature gradient is reduced due to the increased coolant flow rate. The shell-side temperature at the exit of the reactor is more than 7 K larger than the base case. The resulting overall increase in shell-side coolant temperature results in a 9% increase in total radial heat release compared to the base case. The additional heat release and higher shell-side coolant temperature results in an increase of almost 7 K of the

the molten salt is implemented. Two baffle configuration are also considered: segmented baffles and disk and doughnut baffles.

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RESULTS Base Case Analysis. The first simulation completed assumes a constant, uniform shell-side temperature, 600 K, with no variance in the axial direction (i.e., perfect mixing and isothermal). This simulation establishes the nominal profile for reactor temperature along the reactor wall and centerline, defined by eqs 12 and 13. The nominal heat flux profile along the length of the reactor is calculated, defined by eq 16. Temperature profiles at the wall and centerline and heat flux profile are reported in Figure 2. A maximum reactor temperature and heat flux is achieved at the normalized axial position 0.267 (2.406 m). The maximum wall and centerline temperatures are 620.8 and 629.8 K, respectively. The maximum heat flux is 2693 W/m2. The nominal o-xylene conversion profile across the reactor length is reported in Figure 3. The o-xylene conversion is 57.7%. The complete base case results are summarized in Table 2. Coolant Flow Rate and Impact on Reactor Performance. The subsequent simulations evaluate the impact of shell-side coolant feed rate on reactor performance. Three coolant feed rates were selected: 15, 30, and 50 kg/s. Figure 4 reports the simulated shell-side coolant velocity profiles for each case. Figure 5 reports the simulated shell-side temperature profile for each coolant feed rate. It is evident that the slowest flow rate (15 kg/s) has a larger temperature gradient along the length of the reactor. Conversely, the fastest coolant flow rate (50 kg/s) has a smaller temperature gradient along the length of the reactor. Table 3 summarizes key characteristics from each simulation. For each output, the mean of the 36 zones is reported G



Article

Figure 12. CFD coolant velocity profiles on the reactor shell-side. Sections are along the center point of the zones.

Shell-Side Baffle Configuration. Simulations in this section evaluate the impact of shell-side baffle configuration on reactor performance. Two shell-side baffle configurations were selected: segmented and disk and doughnut. There are alternative baffles, in addition to no baffles, that can be evaluated but are not addressed in this current work. The shell-side coolant (molten salt) flow rate was kept constant (50 kg/s) for each simulation. Figure 12 reports the simulated shell-side coolant velocity profiles for each case. CFD simulations report different coolant velocity profiles for the segmented and disk and doughnut baffled systems, for the same coolant flow rate. Figure 13 reports the simulated shell-side temperature profile for each shell-side configuration. The resulting shell-side coolant temperature profiles for both cases appear to be similar qualitatively. For either case, the resulting shell-side temperature is non-isothermal, as is assumed for the base case. In fact, the shell-side temperature follows an almost linear profile approaching 604−605 K at the reactor outlet (z = 1), with the mean shell-side temperature of 602.3 K. Figure 10 reports the shell-side coolant temperature for the disk and doughnut baffle case; simulations from the segmented baffle case are similar. Table 4 reports the reactor model process outputs for both cases. The reactor performance for both configurations are statistically similar. This analysis illustrates that similar reactor performance is achieved with different external shell-side baffling systems.

maximum reactor temperature along the centerline. This results in a 13% increase in o-xylene conversion. See Figure 9. Case 3: 50 kg/s. Figure 10 reports the resulting shell-side coolant temperature for the 36 zone compared to the nominal case, 600 K. The shell-side temperature gradient is reduced due to the increased coolant flow rate. The shell-side temperature at the exit of the reactor is more than 4 K larger than the base case. The resulting overall increase in shell-side coolant temperature results in a 3% increase in total radial heat release compared to the base case. The additional heat release and higher shell-side coolant temperature results in an increase of almost 7 K of the maximum reactor temperature along the centerline. This results in an 8% increase in o-xylene conversion. See Figure 11. This analysis, as expected, demonstrates that with faster coolant flow rates, the coupled fixed-bed reactor and CFD model approach the nominal case. Variance in reactor performance outputs (i.e., temperature, heat flux, and conversion) for each tube is reduced with increasing coolant flow rate. There is a substantial improvement in overall reactor performance when the flow rate is increased from 15 kg/s to 30 kg/s. The distance in the reactor bed, zmax, where the peak temperature and heat flux is observed is reduced 28%. The resulting o-xylene conversion is reduced 14%. Increasing the coolant flow rate from 30 kg/s to 50 kg/s reduces zmax and χox 1% and 5%, respectively. There may be physical limitations that must be considered and accounted for when considering adjusting flow rates. H



Article

Figure 13. CFD coolant temperature profiles on the reactor shell-side. Sections are along the center point of the zones.

Table 4. Comparison of Reactor Performance for Segmented Baffles and Disk and Doughnut Baffles output

description

zmax T̅ c Tw(z = zmax) Tw(z = 1) Tcent(z = zmax) Tcent(z = 1) χox(z = 1) Q̇ r(z = zmax) Qr

normalized axial position at max temp. shell-side wall temperature max. reactor wall temp. final reactor wall temp. max. reactor temp. at centerline final reactor temp. at centerline final o-xylene conversion max. radial heat flux total radial heat release

segmented baffles 0.287 602.3 623.8 611.2 633.5 614.3 62.1 2903 1281

0.001 2.3 0.4 0.1 0.5 0.1 0.2 36 4

disk/doughnut baffles

units

± ± ± ± ± ± ± ± ±

K K K K K % W/m2 W

0.286 602.3 623.9 611.3 633.7 614.4 62.2 2925 1283

0.006 2.3 0.5 0.1 0.8 0.1 0.2 68 4

reactor performance: temperature profiles at the wall and centerline and o-xylene conversion. This analysis demonstrates that with faster coolant flow rates, the coupled fixed-bed reactor and CFD model process outputs approach the nominal case. Alternative shell-side baffle configurations are examined. The calculated coolant velocity profiles, though different between evaluated configurations, result in similar overall reactor performance. However, it should be noted that none of the simulations observe isothermal shell-side coolant temperatures, as is commonly assumed in fixed-bed and plug flow reactor models. This provides opportunity for further reactor optimization on both the shell-side CFD model and the fixed-bed reactor model, as it can be applied to pilot- and commercial-scale

The CFD models calculated significantly different coolant velocity profiles based on the baffle configuration. The resulting shell-side coolant temperatures were comparable. The fixed-bed reactor model confirms that the overall reactor performance are statistically similar.

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± ± ± ± ± ± ± ± ±

CONCLUSIONS

This paper presents an overall fixed-bed reactor model that combines a one-dimensional plug flow reactor model with a CFD model of the shell-side coolant fluid over a series of individual reactor tubes. The model chemistry is the partial oxidation of o-xylene to phthalic anhydride. The model is used to investigate the variation in cooling temperature on overall I



Article

(4) Process Systems Enterprise Limited, Hybrid gPROMS-CFD Multitubular. http://www.psenterprise.com/gproms/hybrid_ multitubular.html (accessed: Jan. 15, 2013). (5) Shin, S.; Han, S.; Lee, W.; Im, Y.; Chae, J.; Lee, D.; Lee, W.; Urban, Z. Optimize Terephthaldehyde Reactor Operations. Hydrocarbon Process. 2007, 83−90. (6) Anastasov, A. I. An Investigation of the Kinetic Parameters of the o-Xylene Oxidation Process Carried out in a Fixed Bed of HighProductive Vanadia−Titania Catalyst. Chem. Eng. Sci. 2003, 58, 89−98. (7) Anastasov, A. I.; Nikolov, V. A. Optimal Policies of Operation of a Fixed-Bed Reactor for Oxidation of o-Xylene into Phthalic Anhydride. Ind. Eng. Chem. Res. 1998, 37, 3424−3433. (8) Calderbank, P.; Chandrasekharan, K.; Fumagalli, C. The Prediction of the Performance of Packed-Bed Catalytic Reactors in the Air-Oxidation of o-Xylene. Chem. Eng. Sci. 1977, 32, 1435−1443. (9) Castillo-Araiza, C. O.; Lòpez-Isunza, F. Modeling the Partial Oxidation of o-Xylene in an Industrial Packed-Bed Catalytic Reactor: The Role of Hydrodynamics and Catalyst Activity in the Heat Transport. Ind. Eng. Chem. Res. 2010, 49, 6845−6853. (10) Froment, G. F. Fixed-Bed Catalytic ReactorsCurrent Design Status. Ind. Eng. Chem. 1967, 59, 18−27. (11) Orozco, G. A.; Gomez, J. R.; Sanchez, O. F.; Gil, I. D.; Duran, A. Effect of Kinetic Models on Hot Spot Temperature Prediction for Phthalic Anhydride Production in a Multitubular Packed-Bed Reactor. Can. J. Chem. Eng. 2010, 88, 224−231. (12) Papageorgiou, J.; Froment, G. Phthalic Anhydride Synthesis. Reactor Optimization Aspects. Chem. Eng. Sci. 1996, 51, 2091−2098. (13) Hagan, P.; Herskowitz, M.; Pirkle, C. A Simple Approach to Highly Sensitive Tubular Reactors. SIAM J. Appl. Math. 1988, 48, 1083−1101. (14) Alshare, A.; Simon, T.; Strykowski, P. Simulations of Flow and Heat Transfer in a Serpentine Heat Exchanger Having Dispersed Resistance with Porous-Continuum and Continuum Models. Int. J. Heat Mass Transfer 2010, 53, 1088−1099. (15) Calverley, E.; Witt, P.; Sweeney, J. Reactor Runaway Due to Statistically Driven Axial Activity Variations in Graded Catalyst Beds. Chem. Eng. Sci. 2012, 80, 393−401. (16) Goodman, T. R. Application of Integral Methods to Transient Nonlinear Heat Transfer. In Advances in Heat Transfer; Irvine, T. F., Hartnett, J. P., Eds.; Academic Press: New York, 1964; Vol. 1; pp 51− 122. (17) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; John Wiley & Sons, Inc.: New York, 1960.

reactors for existing or new chemistries. This model provides a more realistic estimation of the reactor performance, when considering isothermal coolant profiles. Specifically, for the fixedbed reactor model, alternative catalyst packing schedules (i.e., activity profiles) or feed rates can be considered. Additionally, conditions or individual reactor tubes can be identified that are more prone to runaway. The coupled model does provide flexibility in that such future optimizations are possible.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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NOMENCLATURE A, B = Hagan terms (K−1, K−2) Ai = pre-exponentional factor of reaction i (mol kgcat−1 atm−2 s−1) Bi = Biot number dt = reactor tube diameter (m) Ea,i = activation energy for reaction i (kcal mol−1) E̅ = average activation energy (kcal mol−1) Fi = molar flow rate of component i (mol s−1) Ftot,i = initial reactor feed (mol s−1) hw = heat transfer coefficient at wall (cal m−2 s−1 K−1) Ĥ = specific enthalpy (cal mol−1) ΔHrxn,i = heat of reaction for reaction i (kcal mol−1) ki = rate constant of reaction i (mol kgcat−1 atm−2 s−1) kr,e = effective radial thermal conductivity (cal m−1 s−1 K−1) l = reactor length (m) m = number of components n = number of reactions P = pressure (atm) Px = partial pressure of component x (atm) Q̇ r = energy flux in radial direction (W m−2) Q r = total radial heat release (W) R = reactor tube radius (m) Rg = ideal gas constant (cal mol−1 K−1) ri = rate of reaction i (mol kgcat−1 s−1) T = temperature (K) Tc = shell-side temperature (K) Tcent = reactor centerline temperature (K) Tm = radial mean temperature (K) T̅ c = mean shell-side temperature (K) Tw = reactor wall temperature (K) Vr = fixed-bed reactor volume (m3) wi = weighting of reaction i yox = mole fraction of o-xylene in air z = dimensionless axial position zmax = dimensionless axial position at maximum temperature α = Hagan alpha term ν = stoichiometric coefficient ρb = bulk catalyst density (kgcat m−3) χox = o-xylene conversion (%)

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REFERENCES

(1) Eigenberger, G.; Ruppel, W. Ullmann’s Encyclopedia of Industrial Chemistry; Wiley-VCH Verlag GmbH & Co. KGaA: Berlin, 2000. (2) Froment, G. F.; Bischoff, K. B.; Wilde, J. D. Chemical Reactor Analysis and Design, 3rd ed.; John Wiley & Sons, Inc.: New York, 2011. (3) Dixon, A. G.; Nijemeisland, M. CFD as a Design Tool for FixedBed Reactors. Ind. Eng. Chem. Res. 2001, 40, 5246−5254. J


Non-Adiabatic Multitubular Fixed-Bed Catalytic Reactor Model

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