Optimization of process-specific catalytic packing in

Accepted Manuscript Optimization of process-specific catalytic packing in catalytic distillation process: A multi-scale strategy Qinglian Wang, Chen Yang, Hongxing Wang, Ting Qiu PII: DOI: Reference:

S0009-2509(17)30593-6 https://doi.org/10.1016/j.ces.2017.09.040 CES 13817

To appear in:

Chemical Engineering Science

Received Date: Revised Date: Accepted Date:

7 June 2017 12 August 2017 19 September 2017

Please cite this article as: Q. Wang, C. Yang, H. Wang, T. Qiu, Optimization of process-specific catalytic packing in catalytic distillation process: A multi-scale strategy, Chemical Engineering Science (2017), doi: https://doi.org/ 10.1016/j.ces.2017.09.040

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Optimization of process-specific catalytic packing in catalytic distillation process: A multi-scale strategy *

Qinglian Wang, Chen Yang, Hongxing Wang, Ting Qiu

College of Chemical Engineering, Fuzhou University, Fuzhou 350116, Fujian, China Corresponding author: [email protected] (T. Qiu)

Abstract A novel two-way coupling multi-scale model was proposed to investigate the catalytic distillation process. In the model, a microscopic model that focuses on the reactive performance of structure catalytic packing was used to calculate actual rate for catalytic distillation process, which is the basic parameter for process simulation. Furthermore, the traditional process simulation was used to provide proper boundary conditions for microscopic model. In order to validate the multi-scale model, heterogeneously catalyzed hydrolysis of methyl acetate was employed as a test system. The simulated final conversions of methyl acetate and catalyst layer efficiency factors were in good agreement with experimental results. The results indicated that as the equivalent diameter of catalyst layer decreases from 25.4mm to 8.1mm, the catalyst layer efficiency factor rises to 200% approximately. This study could provide a theoretical guide for the optimization of catalytic packing structure.

Keywords： Catalytic distillation; Two-way coupling; Multi-scale model; Reactive performance; Efficiency factor

1 Introduction Catalytic distillation (CD), which integrates the catalytic reaction and distillation in a single multifunctional process unit, is a well-known example of process intensification. Due to vast advantages such as high reaction conversion, low energy consumption, energy savings and simple operation, it has been successfully applied in esterification, 1

etherification, hydrolyzation of ester, hydration of olefins, etc (Harmsen, 2007). The type, geometry and structure of internals influence the whole process performance significantly in the catalytic distillation process. Thus, the developed catalytic packings have to enhance both separation and reaction, and maintain a sound balance between them. At present, a variety of structured catalytic packings have been developed (Subawalla et al., 1997; Götze et al., 2001; Odziej et al., 2005; Ding et al., 2015). However, these packings cannot be efficiently suitable for all the catalytic distillation process. Therefore, the development of a process-specific and high-separation-efficiently structured catalytic packings is desirable. Nevertheless, due to the complexity resulting from the nonideality of components and integrations among hydrodynamics, vapor-liquid mass transfer, inter diffusion and chemical kinetics, our cognition to the catalytic distillation process is insufficient. Until now, the design and optimization of structured catalytic packings mainly rely on engineering experience and empirical correlations. In recent years, computational fluid dynamics (CFD) was widely used to investigate the local flow and mass transfer characteristics, and provided a new idea for the design of process-specific catalytic packing. For instance, the works by Higler et al. (1999), Van Baten et al. (2001), Van Baten and Krishna (2001; 2002), Dai et al. (2012), Li et al. (2012) and Ding et al. (2014). Nevertheless, influence of catalytic packing structure on macro variables such as conversion, yield and production purity which take many attentions in the actual industrial processes are unavailable simply based on CFD simulations. These macro variables can be obtained via process simulation which is widely described by equilibrium (EQ) and non-equilibrium (NEQ) models (Klöker et al., 2005; Zhang et al., 2011). However, influence of structure on macro parameters cannot be considered directly during the process simulation. Therefore, it is impossible to realize optimization of process-specific structured catalytic packings simply based on either CFD simulation or process simulation.

Multi-scale model is an efficient method to establish the relationship between micro phenomenon and macro process (Sun et al., 2013). Liu et al. (2013) proposed a multi-scale model which combined CFD with process simulation to investigate the process of removal of acetic acid from water. Fluent software was used to calculate the tray efficiency in the element scale. And the calculated results were input into process simulation. With respect to the development of structured catalyst packing, 2

Klöker et al. (2003), Górak et al. (2005) and Egorov et al. (2005) proposed a novel multi-scale model to obtain simulated results associated with hydraulic properties and mass transfer performance of different internals by using CFD approach, which were input into the rigorous, rate-based process simulation approach. Actually, not only the hydrodynamic and mass transfer characteristic of catalytic packing internal, but also the multicomponent mass transfer and reaction process in the catalyst layers influence the efficiency of catalytic distillation process. For the development of high-efficiency and process-specific catalytic packing, the determination of structural parameters of catalyst layers is also a key problem. To the best of our knowledge, none of the previous multi-scale models considered the influence of structural parameters of catalyst layers. In the study, a novel two-way coupling multi-scale model that focuses on reactive performance of structured catalytic packing is proposed with the consideration of the inter influence between catalyst layer structure and catalytic distillation process. A microscopic model is used to investigate the multicomponent mass transfer and reaction process in the catalyst layer. The catalyst layer efficiency factor which is introduced to assess the rationality of catalyst layer structure parameter and obtained by experimental data or empirical method normally (Sundmacher and Hoffmann, 1993; Xu et al., 1995) can be calculated via the microscopic model. Then the actual reactive rate during catalytic distillation process which is the basic parameter for process simulation can be obtained. The traditional process simulation is used to provide proper boundary conditions for the microscopic model. A well-known reference system heterogeneously catalyzed hydrolysis of methyl acetate is employed as a test system, so as to validate the proposed novel multiscale model. By the utilization of this proposed multi-scale model, the corresponding catalyst layer structural parameter can be determined for different engineering processes.

3

2 A multi-scale strategy 2.1 Multi-scale structures of catalytic distillation column Catalytic distillation is characterized by hierarchical multi-scale structure in nature, as shown in Fig. 1, ranging from catalyst layer scale to the catalytic distillation column scale. This decomposition was based on the need of our study. The catalyst layer scale is namely the microscopic scale in this work, which is generated by porous catalyst pellets packing. In this scale, multicomponent mass transfer and catalytic reaction are taken place. The structured catalytic packing internal such as bale packing, KATAPAK® and MULTIPAK®, is called meso-scale structure, which contains catalyst layers and vapor-liquid mass transfer units. The CD column scale is the macro scale. The mass balance and heat balance of the whole system are considered in the scale, which can be described by the traditional EQ stage model or NEQ stage model.

Catalyst layer scale

Catalytic packing scale

(~mm)

(~m)

CD column (~10m)

Fig. 1 Multi-scale structures in catalytic distillation column

2.2 Establishment of multi-scale model In this subsection, the objective is to establish a two-way coupling multi-scale model for catalytic distillation process. The multi-scale simulation framework is shown in Fig. 2. The macroscopic process simulation results can provide proper boundary conditions for the microscopic simulation. At the same time, the microscopic simulation results can be input

4

into macroscopic process simulation as parameters to simulate the reactive distillation process. The established two-way coupling model is quite different with the multi-scale model for reactive distillation process found in the literature. The multi-scale approaches mentioned in the literature are commonly involving a one-way coupling model. The comparisons are listed in Table 1.

5

Macroscopic process simulation

Microscopic numerical simulation

Start

Input specification of column

Specify geometry domain

Input physical property data

Specify governing equations

Input manipulated conditions

Calculate boundary conditions

Input thermodynamics data

Mesh grid

Calculate reaction rate

Solve

Simulation

Convergence？

No

Yes

No

Concentration distribution of catalyst layer

Convergence？ Yes Concentration and temperature distributions

Convergence?

No

Yes End

Fig. 2 Multi-scale simulation framework Table 1 Comparisons of multi-scale models in the literature and the present model 6

Reactive distillation

Catalytic distillation

Literature

Literature

The present model

CFD simulation

CFD simulation

CFD simulation

Tray efficiency

Pressure drop and mass transfer coefficients

Catalyst layer efficiency factor

EQ simulation

NEQ simulation

Process simulation

Optimal process

Optimal packing

Optimal packing

Coupling way

One-way

One-way

Two-way

Goal

Optimize process

Optimize packing

Optimize packing

Result

Completed

Failed

Completed

Model framework

Liu et al. (2013) calculated the tray efficiency by using CFD simulation in fluid mechanical scale (element scale), and the calculation results are input into the process simulation, thus establishing the multi-scale model. The multi-scale method for heterogeneous catalytic distillation process suggested by Klöker et al., (2003), Górak et al., (2005) and Egorov et al., (2005) is still a one-way coupling model. The CFD method was used to predict hydraulic properties and mass transfer performance, and then, the calculated results was input into the process simulation. Due to the substantial difficulties related to the CFD model, especially for the description of extremely complex hydrodynamic phenomena above the load point, however, the combination was not successful. This work realized the multi-scale simulation study for catalytic distillation process from another perspective. The relationship between catalyst packing internal structure and reaction rate was investigated. For the development of catalytic packing, it is worthy to acknowledge that the necessity to investigate the relationship between catalytic packing internal structure and hydrodynamics and mass transfer performance. Furthermore, reaction performance that serves as an important part for catalytic distillation process should not be ignored and the 7

determination of catalyst layer structure parameter is also important for the development of catalytic packing. The necessity of two-way coupling model can be analyzed as follows. Firstly, the conventional catalytic distillation column contains rectification, reactive and stripping sections. The reactive section is packed with catalytic packing and the rectification and stripping sections are packed with structured packing. This complex structure of CD column results in the enormous difficulties to simulate the catalytic distillation process within the whole CD column due to the limitations of computation level. Although Liu et al. (2013) successfully used the one-way coupling model to simulate reactive distillation process, the studied hydrodynamic phenomena of tray column is much simpler than that of catalytic packing. Secondly, hydrodynamics, vapor-liquid mass transfer and reaction characteristics of catalytic packing influence the efficiency of catalytic distillation and the catalytic distillation process also influence fluid flow, mass transfer, and reactive processes within catalytic packing. Hence, the design of process-specific catalyst packing is desirable. Although hydrodynamics and vapor-liquid mass transfer can be simulated by reconstructing the representative units of catalytic packing in the small scale (Higler et al. 1999; Van Baten et al. 2001; Van Baten and Krishna 2001; 2002), the confirmation of corresponding boundary conditions reflected the characteristics of catalytic distillation process is still a difficult problem for the one-way coupling model. Thus, the two-way coupling model was established in this work.

2.3 Microscopic scale model (catalyst layer scale) 2.3.1 Analysis of reaction and mass transfer process The schematic diagram of packing structure and flow distribution of liquid-vapor phase are shown in Fig. 3 (b). In the catalytic distillation process, since the voidage of the catalyst layers is far less than that of vapor-liquid mass transfer channels, most of the downward liquid flows along the surface of catalyst layers and forms liquid films. Reactant molecules diffuse into the catalyst layers structure under the effect of concentration gradient, where they react either on the catalyst pellets surfaces or in the particles interior. Similarly, the product molecules diffuse onto the catalyst layer surfaces from the opposite direction, and then mass transfer with contranatant vapor phase. In this way, the reactive distillation process is completed. Therefore, the diffusion/reaction inside catalyst layers has significant influence on the catalytic distillation process. In this section, a microscopic model was established to describe the multicomponent mass transfer and reaction in the catalyst layer. Based on the above analysis, some assumptions are put forward: 8

(1) The internal resistance of catalyst beds is isotropic. (2) Each component diffuses along with the radial direction, while the axial diffusion and seepage flow inside catalyst layers in single catalyst packing internal can be ignored. (3) Temperature in radial direction is uniform in a small transfer element, and the reaction heat can be neglected, thus the reaction process could be regarded as isothermal process.

2.3.2 Geometry domain Catalyst layer is porous media made up of porous catalyst pellets. Because of the obvious difference of voidage between catalyst layers and mass transfer units, the seepage phenomenon of catalytic sheet interior is not considered to simplify the physical structure. The macroscopic governing equations reported in the literature focused on reaction rates involving first-order kinetics, irreversible second-order kinetics, Michaelis-Menten kinetics and first-order reversible kinetics (Mitra and Muhammad, 2007; Ding et al., 2013; LugoMéndez et al., 2015; Qiu et al., 2017), while for the catalytic distillation process, the reactive processes inside catalyst layers are commonly involving reversible multicomponent reaction. It is difficult to handle the complex multicomponent mass transfer and reaction process at the macroscopic level due to the current limitations in mathematical capabilities. In this work, the diffusion/reaction problem in the porous catalyst layer was investigated at the microscopic level. Since the entire structured catalytic packing in the whole catalytic distillation column can hardly be modeled because of computational limitation, the small representative element was used. Kenig (1997) proposed hydrodynamic analogy (HA) approach to model the distillation process, reactive stripping process and reactive absorption process in the columns equipped with structured packing (Schildhauer et al., 2005; Shilkin et al., 2005; Shilkin et al., 2006; Kenig et al., 2007; Brinkmann et al., 2010; Brinkmann et al., 2014). This approach was established based on the structural similarities between complex flow in real units and simplified model flow pattern. Firstly, by analyzing the fluid dynamics in the structure packings, an appropriate physical model was built considering all the flow characteristics. The structure parameters such as the number of channels and their diameter were determined based on the real packing geometric characters. And then the partial differential equations of momentum, energy and mass transfer can be used to describe the 9

transport phenomenon in the whole column. As with the hydrodynamic analogy approach, the microscopic model for multicomponent mass transfer and reaction process in the catalyst layer was established. A reaction/separation unit is selected in the axial direction of reaction zone of CD column (macro-scale), in which the concentration distribution and temperature profile are uniform in the axial direction based on the assumption of process simulation. It is assumed that the liquid phase and vapor phase uniformly distributed in radial direction, indicating that in the selected unit, the diffusion/reaction performance in each catalyst layer is identical. Thus, mass transfer and reaction process in single catalyst layer could be used to approximately characterize the process in single reaction/separation unit. The schematic diagram of geometry simulated is shown in Fig. 3. (a)

(b) stage1

Mass transfer units

Catalyst layers

Distillate V2

stage2 L2

(c) Feed

V j-1

stage j-1 Vj L j-1

stage j V j+1 L j

stage j+1

Microscopic model

L j+1

V N-1

Vapor phase flow direction

stage N-1 LN-1

Liquid phase flow direction

stage N Bottoms

Catalytic column

Catalyst packing Fig. 3 Schematic diagram of simulated geometry

Based on the proposed assumptions, multicomponent diffusion and reaction process in porous catalyst layer is only considered and the seepage flow is ignored. Due to the fact that the heterogeneous reaction occurs in the catalyst beds, the closure problem obtained from the deviation process of species diffusion in porous media (Valdés-Parada et al. 2011) can be used to confirm an appropriate microstructure of single porous catalyst layer. The method is as follows (Quintard et al., 2006; Yang et al., 2015a, 2015b): (1) The representative region of microstructure was determined.

10

(2) The representative unit cell was constructed by using Comsol Multiphysics package and the closure problems derived by Valdés-Parada et al. (2011) were solved. (3) The effective diffusivity tensor was calculated by means of the simulation results. In order to confirm a proper microstructure, the calculated results were compared with the literature model values established by Maxwell (1873) and Weissberg (1963), which can be used to describe the diffusion process in porous media. (4) Based on the actual characteristics of porous catalyst layer such as the voidage of catalytic sheet and the single catalytic sheet equivalent diameter, the established geometry domain was confirmed.

2.3.3 Governing equation Based on the model assumptions, the governing equation of diffusion/reaction inside catalyst layers was established, according to Maxwell-Stefan multicomponent mass transfer theory (Curtiss and Bird, 1999; Taylor and Krishna, 1993). The governing equation expression can be given by Eq. 1 E  N 1         DiE wE   0 E 1  

（1）

where  is mixture density, kg  m 3 ; wE is mass fraction of each component in reaction system; DiE is diffusion coefficient of each component, m 2  s 1 .

2.3.4 Boundary conditions A. Flux boundary The reactive process is considered to take place on the outside surface of catalyst particles. The flux boundary was preset:

 E  N 1  - n     DiE wE   Ri  E 1 

11

（2）

where n represents the unit normal vector pointing from the fluid phase toward the solid phase. Ri is chemical reactive source and represents the rate of production or consumption of each component, kg  m 2  s 1 . It is important to notice that the effect of diffusion inside the catalyst particles have to be taken into account when the reaction source was added. Ri can be expressed as Eq. 3.

Ri  ri surfaceM i 103

（3）

where ri-surface is the rate of production or consumption of each component on the reactive surface, mol  m2  s 1 ; M i is molar mass, kg  kmol 1 . B. Mass fraction boundary

According to the characteristics of catalytic distillation process, the left face of the physical model was selected as entrance boundary. And the boundary condition was set as mass fraction boundary:

wi  wib

（4）

where wib is the mass fraction of liquid component on the external surface of catalyst beds. C. Symmetric boundary In order to reduce the calculation magnitude, except for the left face of physical model and the surfaces of particle, all the rest of faces were set to the symmetric boundary.

 E  N 1  - n     DiE wE   0  E 1 

（5）

2.4 Macroscopic scale model (process model) The widely used models for catalytic distillation are equilibrium (EQ) stage model and nonequilibrium (NEQ) stage model. The equilibrium (EQ) stage model is the simplest and conventional model for catalytic distillation. It assumes that the vapor and liquid stream leaving the stage are in equilibrium with each other. The influence of chemical reaction is considered via rate expressions integrated into the mass and energy balances. In the non12

equilibrium (NEQ) stage model, the mass transfer process is described by Maxwell-Stefan equations. Non-equilibrium (NEQ) stage model is more rigorous approach and can gain better simulation results than EQ stage model. Accordingly, the solving difficulty increases since the model complexity increases. For the catalytic distillation process simulation, the choice of appropriate model approach must comprehensively consider the model accuracy and program convergence. Baur et al. (2000) used the EQ and NEQ stage models to simulate the production process for methyl tert-butyl ether (MTBE). It has been found that the conversion calculated by NEQ model was higher than that of EQ model. Sundmacher et al. (1999) simulated the production process for methyl tert-butyl ether (MTBE) and tert amyl methyl ether (TMAE) via both EQ and NEQ stage models. They found that for the TMAE process, the NEQ model was needed; while for the MTBE process, both the EQ and NEQ stage models could obtain accurate results. As a consequence, alternative model can be chosen for the specific reactive system according to the requirement.

3 Solution of multi-scale model To validate the proposed multi-scale model, the catalytic distillation process for hydrolysis of methyl acetate was employed as a test system. The following study was based on our previous work (Wu et al., 1999a) which can help us to obtain the basic parameters for simulation easily. We studied the heterogeneously catalyzed hydrolysis of methyl acetate in a pilot plant. The flow chart for hydrolysis of methyl acetate is shown in Fig. 4.

Reflux

Feed

Reaction zone

Stripping

Bottom products

Fig. 4 Flow chart for hydrolysis of methyl acetate

13

The inner diameter of CD column packed with catalyst capsules was 200 mm. Methyl acetate and water were fed at the top of reaction zone. The total reflux operation was used and the products were obtained from the bottom of column. Table 2 lists the column specifications. Table 2 Specifications for the catalytic distillation column Items

Configuration

Column diameter (mm)

200

Height of each bale (mm)

168

Height of catalytic packing（m）

3.024

Volume of catalytic packing（m3）

0.0995

Mass of catalyst packed (kg)

20

Height of reaction zone（m）

3.6

Height of stripping zone（m）

2

3.1 Solution geometry domain for microscopic model As mentioned in section 2.3.2, it was considered to deal with the multicomponent mass transfer and reaction at the microscopic level and it is important to establish an appropriate microstructure. In this section, based on the proposed assumptions of microscopic model, the effect of microstructure on diffusion process in porous media was studied. About three situations of catalyst packing may happen in the actual process： (1) As the catalyst particles packed in the catalyst beds in bulk, the microstructure is disordered. (2) Due to the limitation of the space structure of catalytic sheet, catalyst pellets may deform under a certain extrusion. (3) The catalyst particles are non-uniform and the size of catalyst particle diameter is

14

unequal. Fig. 5 shows six different representative unit cells of catalytic sheets. Thereinto, the ordered architectures can refer to the literature (Desmet and Deridder, 2011a, 2011b; Yang et al., 2015a, 2015b). (a)

(b)

(c)

(d)

(e)

(f)

Fig. 5 Six different represent unit cells of catalytic sheets

Note that (a) represents the random sphere packed structure which was generated with MATLAB. The diameter of listed catalyst particles is 0.49mm; (b) shows the body center cubic (BCC) ordered architecture, where the displayed particles diameter is 0.4mm; (c) represents simple cubical (SC) ordered architecture, in which the listed particles diameter is 0.5mm; (d) is face centered cubical ordered geometry (FCC), where the displayed particles diameter is 0.35mm; (e) shows the situation of uneven distribution of particles diameter where the listed diameters are 0.4mm and 0.45mm (in the center of cubic), respectively, considering the industrial particle size distribution; and (f) represents the circumstance that catalytic particles are deformation, where the geometric shape of pellets change into ellipsoids from the initial spheres because of its swelling ability and the limitation of the space structure of catalytic sheet. The x-direction, y-direction, and z-direction lengths of the listed particles are 0.4mm, 0.4mm and 0.35mm, respectively. 15

According to the method introduced in section 2.3.2, the closure problems in the literature were solved by using Comsol Multiphysics package for different porous media structures and the diffusive coefficients were calculated. The results are shown in Fig. 6. The lines in Fig. 6 represent the literature model results, where one can see the simulation calculated values seem to be in line with the model results, although the microstructures are quite different. The average relative errors of all points in Fig. 6 are less than 10%. Therefore, each component diffuses in the ordered architecture can be used to describe the process in catalytic sheets in the admissible error. It is important to note that the minimum voidage of SC architecture is 0.476, and that of BCC or FCC architecture is approximately 0.3. Therefore, in the practical application process, it is necessary to confirm an appropriate structure according to the characteristics of porous catalyst layers. For the hydrolysis process of methyl acetate, the voidage of catalytic sheet was 0.32 and the single catalytic sheet equivalent diameter was 12.7mm. The experimental catalyst particle diameter varied from 0.3mm to 1.2mm. Thus the established geometry domain is shown in Fig. 7.

1.0

0.8

Deff/D

0.6 Maxwell Weissberg Disorder BCC FCC SC Uniform Deformation

0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

 Fig. 6 Relationship between simulated values and the model results

y

z x

y Fig. 7 Established geometry domain for hydrolysis process of methyl acetate

16

Table 3 lists the geometry structure parameters for simulation of microscopic model. Table 3 The parameters for simulation of microscopic model Parameters

Values

Catalyst particle diameter d p (mm)

0.5

Voidage of catalytic sheet



0.32

Single catalytic sheet equivalent diameter D (mm) Volume of simulated geometry domain Vregion ( m 3 ) Surface area of catalyst particles inside the geometry domain A ( m 2 )

12.7

6.99  10 -10

1.5710-5

3.2 Solution parameters of microscopic model For the microscopic model, considering the nonideality of methyl acetate hydrolysis system, the Maxwell-Stefan diffusion coefficient matrix calculated by using MATLAB can be expressed as:

D  Gwi xi 1 D* xi wi 1 G1  w x GAB   AB  wA 1  N B  x w N B 

w  i

A, B  1,2, N  1

 w A  0      0

0 wB  

 0   0       wN 1 

 x A  0      0

0 x B  

 0          x N 1 

x  i

 ,  

（6） （7）

（8）

（9）

 

where D* is Fick diffusion coefficient matrix;

D   B  *

1

17

（10）

 BAA  B B   BA     BN 1 A

BAA 

x A

EN

xE

E 1 EN

DAE



DAN

 1 1 BAB   x A    DAE DAN AB   AB  x A

 BAN 1          BN 1N 1 

BAB BBB  

 ln  A  xB

（11）

A  1,2, N  1

  

A  1,2,, N  1 A, B  1,2,, N  1

T , P , xE ,E  B

1, A  B

（12）

（13） （14） （15）

 AB   0, A  B where D AE is binary Maxwell-Stefan diffusion coefficient;



0 DAB  DAB



1 xB  x A

0 DAB 

2

D 

1 x A  xB 0 BA

2

（16） （17）

K1T  BLVA1/ 3

where V is molar volume of solute at normal boiling point, cm3  mol 1 ; xi is mole fraction of each component;  L is viscosity, cp; T is reaction temperature and can be obtained from EQ simulation results, K; K1 can be expressed as

K1

  3V 1   B   V A 

 8.2  10  12

  

2

3

   

（18）

where V can be expressed as

V  0.285VC1.048

（19）

where VC is critical molar volume, cm3  mol 1 . In this paper, the flux boundary was used. For the process of hydrolysis of methyl acetate, the rate of production or consumption of each component on the reactive surface

ri-surface could be described by the following expression:

18

ri  surface  Z l

mcat Vregion k  CMeOAc CH2O  k  CMeOH CHAC   BC Vbed A

（20）

where mcat is the catalyst mass in one stage, g; Vbed is the volume of catalyst bales in one stage, m 3 ;  BC is volume ratio of catalytic sheets to catalyst bales and set as 0.75 according to the our fabricated method of catalyst bales; Vregion is the volume of simulated geometry domain, m 3 ; A is the surface area of catalyst particles inside the geometry domain, m 2 ;

k  , k  are the forward and backward reaction rate constants, respectively, m6  mol 1  s 1  gcat  ; Zl is the liquid holdup of reaction zone which was introduced by 1

considering that only the catalyst pellets surrounded by the liquid participate in the reactive process actually. The holdup equations published in the work by Wu (1999) were used. The dynamic holdup was expressed as:

ln Z d  6.074  1.353G  0.257  0.44G ln L

（21）

The total holdup was expressed as:

Z l  Z d  2.5468 10 2

（22）

In the mass fraction boundary condition, mass fraction of liquid component on the external surface of catalytic sheets wib was obtained from the macroscopic process simulation results. Except for the feed stage, the liquid-phase concentration in the catalytic sheet was derived from the upper equilibrium stage. While for the feed stage, the liquid mass fraction was calculated according to the mass balance law:

L  L  qF

（23）

where L is the liquid molar flow rate at the feed stage, kmol  h 1 ; L is liquid reflux molar flow rate, kmol  h 1 ; q is the liquid fraction of feed; F is the feed molar flow rate,

kmol  h 1 .

19

3.3 Solution parameters of macroscopic model For the macroscopic process simulation, Pöpken et al. (2001) pointed out that the EQ model is sufficient to model the hydrolysis process of methyl acetate by the comparison of simulation results with experimental data. Therefore, a typical EQ model was built and solved by Aspen Plus using the RadFrac module in this work. Table 4 lists the input parameters for simulation of the EQ model, where the kinetics of hydrolysis of methyl acetate was measured in a batch stirred reactor with SK-1A cation exchange resin as catalyst. A more detailed study of this reaction kinetic has been done in our previous work (Wu et al., 1999b);  is the catalyst layer efficiency factor, which can be calculated by the following expression according to the microscopic numerical simulation results:



rfact rideal



 

A

A

ri-surface Ci dA

（24）

ri-surface Ci 0 dA

where Ci is the actual concentration of each component inside the catalytic sheets,

mol  m-3 ; Ci 0 is the initial concentration of each component, mol  m-3 ; A is the interface of liquid phase and solid phase. The NRTL parameter model was selected to calculate the activity coefficients, and the binary interaction parameters can refer to our work (Zhao et al., 2010).

Table 4 The input parameters for simulation of the EQ model Parameters

Values

Water to methyl acetate molar ratio Rm

1.5~2

Reflux rate to feed rate Rf

3~4.5

Space velocity Sv

0.27~0.45

Pressure of feed (atm)

1

Operation pressure (atm)

1

Total stages

22

20

(including condenser and reboiler) Reaction stages

10

Stripping stages

10

Feed stage

1

Catalyst loaded (kg)

20

Kinetic equation

rMeOAc actual  W k  CMeOAc CH2O  k  CMeOH C HAC 

Forward reaction rate constant

k  3.1809 104 exp  7149.3 / T 

Backward reaction rate constant

k  4.5556 104 exp  6656.5 / T 

In this paper, the proposed multi-scale model was solved by Aspen Plus combining with Comsol Multiphysics package. The macroscopic process simulation was solved by Aspen Plus using the RadFrac module. And the microscopic numerical simulation of mass transfer and reaction within catalyst layers was solved by Comsol Multiphysics package combining with MATLAB. Moreover, the residuals of all equations are less than 10-6, and the sensitivity analysis was conducted in order to guarantee that all of the results in the present study are independent of the grid step size.

4 Results and discussion 4.1 Validation of multi-scale model The proposed two-way coupling multi-scale model was used to simulate the hydrolysis process of methyl acetate under different conditions. The operation conditions for hydrolysis process of methyl acetate were selected as the initial condition for multi-scale model. The calculated conversions of methyl acetate were compared with our previous experimental results (Wu et al., 1999a), which is shown in Table 5. As can be seen from Table 5, the simulation results and experimental data are in good agreement. The average relative error is 4.03%, indicating the validation of the multi-scale model.

21

4.2 Comparison of one-way and two-way coupling multi-scale models Liu et al. (2013) proposed the similar multi-scale simulation framework to successfully simulate the reactive distillation. The difference is that the framework in their work is a oneway coupling model while in this work the framework is a two-way coupling model. In this section, in order to explain the necessity of two-way coupling model, the similar one-way coupling multi-scale simulations were conducted. Table 5 Comparisons of the multi-scale results with experimental data in the literature Conversions of methyl No.

Water to Reflux rate Space acetate（%） methyl acetate to feed velocity Sv molar ratio Rm rate Rf Experimental Calculation value value

Error

Absolute error

Relative error%

1

1.5

3.3

0.356

38.75

39.47

0.72

1.86

2

2

3.8

0.356

51.62

52.07

0.45

0.87

3

2

4.5

0.356

53.50

51.18

2.32

4.34

4

2

3.3

0.25

56.00

58.34

2.34

4.18

5

2

3.3

0.3

53.28

55.73

2.45

4.60

6

2

3.3

0.4

48.00

50.66

2.66

5.54

7

2

3.3

0.45

46.72

48.7

1.98

4.24

8

2

3

0.27

54.56

57.42

2.86

5.24

9

2

3

0.3

53.10

55.96

2.86

5.39

2.07

4.03

Average error

The simulated method is described as follows: (1) The reactive temperature and boundary conditions of microscopic model were set as arbitrary values and the multicomponent mass transfer and reaction process in catalyst beds were simulated. (2) The microscopic simulation results were used to calculate the catalyst layer efficiency factors and the reaction rates were obtained. 22

(3) The calculated reaction rates were used as the basic parameters for macroscopic process simulation, thus completing the multi-scale simulation. In this work, two groups of simulation were conducted and the corresponding boundary conditions and simulation results were listed in Table 6. Table 6 Boundary conditions of one-way coupling model and simulation results No.

T (K)

wMeOAc

wH2O

wMeOH

wHAC

η%

1

50

0.7

0.1

0.1

0.1

73.38

2

50

0.7

0.2

0.01

0.09

80.64

According to the microscopic simulation results, the macroscopic process simulations were conducted and the simulation results were shown in Table 7. The calculated conversions of methyl acetate were compared with the simulation results of two-way coupling model proposed in this work. The relative errors with experimental data were also listed in Table 7. As can be seen, the calculated results of one-way coupling model have larger deviations than that of two-way coupling model proposed in this work. The larger deviations indicated that the two-way coupling model has advantage over one-way coupling model for our study. On the other hand, the different errors of group 1 and group 2 indicate that for one-way coupling model, the boundary conditions of microscopic simulation have influence on the simulation results. Thus, the confirmation of boundary conditions is the key problem for one-way coupling model as described in section 2.2. Table 7 Comparisons of calculated methyl acetate conversions and relative errors of one-way and two-way coupling models

relative errors

methyl acetate conversions No. Group 1 (%)

Group 2 (%)

Group 1 (%)

Group 2 (%)

This work (%)

1

43.70

45.09

12.78

16.35

1.86

2

53.27

55.15

3.19

6.83

0.87

3

52.08

54.11

2.56

1.23

4.25

4

59.50

60.59

6.25

8.19

4.18

5

56.90

58.32

6.80

9.46

4.60

23

6

51.85

53.69

8.02

11.85

5.54

7

49.31

51.32

5.55

9.85

4.24

8

58.49

59.63

7.21

9.29

5.24

9

57.05

58.35

7.44

9.89

5.39

Average

-

-

6.64

9.22

4.03

4.3 Effect of process conditions According to the proposed two-way coupling multi-scale model, the catalyst layer efficiency factors at different position of CD column for different process conditions can be calculated. The results were shown in Fig. 8.

78 No.1 No.2 No.3 No.4 No.5 No.6 No.7 No.8 No.9

76 74 72

%

70 68 66 64 62 60 2

4

6

8

10

12

stage number Fig. 8 Catalyst layer efficiency factors profiles for different process conditions

As can be seen, for the hydrolysis system of methyl acetate, the catalyst layer efficiency factors decrease gradually from the top to the bottom of reactive zone. This can be ascribed to the total reflux operation. Fig. 9 is the liquid concentration and temperature profiles, respectively, at the molar ratio of water (H2O) to methyl acetate (MeOAc) of 2.0, reflux rate to feed rate of 3.3, space velocity of 0.45. As can be seen, from the top to the bottom of reaction zone, methyl acetate and water are consumed continuously as reactants, while the molar fractions of products acetic acid and methanol increase continuously. The reaction process is constantly close to equilibrium state. In this way, when the amount of catalysts 24

packed inside the catalytic sheets is identical, the utilization ratio of catalysts decreases gradually, thus leading to the decrease of catalyst layer efficiency factor. 1.0

332.0

MeOAC H2O MeOH HAC T (K)

0.8

331.6 331.2

0.6

330.4

0.4

T (K)

x i

330.8

330.0 0.2 329.6 0.0 2

4

6

8

10

12

14

16

18

20

329.2 22

stage number Fig. 9 Concentration and temperature profiles for liquid phase (molar ratio Rm=2.0, reflux rate to feed rate Rf=3.3. Space velocity SV=0.45 )

Furthermore, from Fig. 8, one can see that the process conditions have slight influence on catalyst layer efficiency factors, which can be ascribed to the influence of intrinsic reaction kinetic.

4.4 Concentration distributions inside catalyst layers According to the multi-scale simulation results, the concentration profiles of each component inside catalyst layers were analyzed in this section. Fig. 10 depicts the concentration profiles of each component inside catalyst bed at z=0.2mm, where the initial concentration of methyl acetate, water, methanol and acid were 8968.94mol·m-3, 5244.10mol·m-3, 2273.61mol·m-3, and 954.27mol·m-3, respectively, the reaction temperature was 331.02K, and the EQ stage was 7 stage. The process condition was at the molar ratio of water (H2O) to methyl acetate (MeOAc) of 2.0, reflux rate to feed rate of 3.3, space velocity of 0.45.

25

y (mm)

(a) MeOAc (mol·m-3)

1

MeOAc: 8450 8500 8550 8600 8650 8700 8750 8800 8850 8900 8950

0.5 0

0

1

2

3

4

5

x (mm)

y (mm)

(b) H2O (mol·m-3)

1

H2O: 5090 5100 5120 5140 5150 5170 5180 5190 5210 5220 5230 5240

0.5 0

0

1

2

3

4

5

x (mm)

y (mm)

(c) MeOH (mol·m-3)

1 MeOH: 2280 2300 2340 2380 2400 2440 2480 2500 2540 2580 2600 0.5 0

0

1

2

3

4

5

x (mm)

y (mm)

(d) HAc (mol·m-3)

1 HAC: 1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 0.5 0

0

1

2

3

4

5

x (mm) Fig. 10 Concentration profiles of each component inside catalytic sheets at Z=0.2mm

26

It is obvious that the concentrations of each component vary acutely in the entrance region of catalyst layer. Nevertheless, as the position approaches to the center of catalyst pocket, the concentrations change only slightly. It can be explained that as the component is closer to the center of catalyst layer, the longer diffusion distance leads to the greater diffusion resistance and the smaller diffusion flux. This gives us a revelation that the catalyst layer efficiency factor would increase with the decrease of equivalent diameter of catalyst pocket.

4.5 Effect of equivalent diameter of catalyst layer According to the simulation results in section 4.4, the multicomponent mass transfer and reaction process under the different catalyst layer structure was investigated. As the established microscopic model was based on the process simulation results, and the concentration and temperature profiles do not depend on the axial channel coordinate in single reaction/separation unit, the effect of radial structure parameters on the reaction rate was only considered in this work. Several assumptions were put forward: (1) The final conversions of MeOAc keep constant under different catalytic packing internals. (2) The packing density of catalyst particles in the catalyst layers is equal. (3) The influence of radial structure of catalyst layers on hydrodynamics and mass transfer performance of catalyst packing internal was ignored, which may be considered in our future work. Based on these assumptions, only the influence of radial structure parameters of catalyst layers on reactive performance was discussed. The boundary conditions for microscopic simulation were selected from the convergence results of multi-scale model at the molar ratio of water (H2O) to methyl acetate (MeOAc) of 2.0, reflux rate to feed rate of 3.3, space velocity of 0.45. The studied equivalent diameters of catalyst layer are 25.4mm, 17.3mm, 12.7mm, 8.1mm, respectively, considering the actual industrial size and that of pilot plant experiments. The results are shown in Fig. 11.

27

As can be seen, the equivalent diameter of catalytic sheet has significant influence on catalyst layer efficiency factor. When the equivalent diameter decreases from 25.4mm to 8.1mm, the catalyst layer efficiency factor increases to nearly double. This important conclusion was validated by experimental method in order to further validate the reliability of the proposed multi-scale model which was shown in Appendix. Therefore, the equivalent diameter of catalyst layer plays an important role in the design and optimization of catalytic packing structure. When the catalytic sheet is designed too large, the low catalyst layer efficiency factor leads to the increase of investment costs. While, if catalytic sheet diameter is too small, the manufacture and installation of catalyst packing internal may be difficult. Thus in the practical application process, there is a tradeoff between manufacture complexity and profit. 100 D=8.1mm D=12.7mm D=17.3mm D=25.4mm

90 80

%

70 60 50 40 30 2

4

6

8

10

12

stage number Fig. 11 Effect of equivalent diameter of catalytic sheets on catalyst layer efficiency factor

According to above simulation results, the calculated catalyst layer efficiency factors under different equivalent diameters of catalytic sheet were used as basic parameter for process simulation at the molar ratio of water (H2O) to methyl acetate (MeOAc) of 2.0, reflux rate to feed rate of 3.3, space velocity of 0.45. The conversions of methyl acetate under the different catalyst layer structures were calculated. The results are shown in Fig. 12. As can be seen, the conversions of methyl acetate increase with the decrease of equivalent diameter, which conforms to our knowledge that under the same circumstance, the conversion of methyl acetate increases with the rise of catalyst layer efficiency factor.

28

52 50 48 46

xA %

44 42 40 38 36 34 32 6

8

10

12

14

16

18

20

22

24

26

D (mm) Fig. 12 Effect of equivalent diameter of catalytic sheets on conversions of methyl acetate

5 Conclusion An innovative two-way coupling multi-scale model that combines the microscopic model with macroscopic process simulation was proposed to improve the traditional process simulation model. The microscopic model focused on the phenomenon of diffusion/reaction in catalyst layer. The macroscopic process simulation results provide proper boundary conditions for the microscopic simulation. At the same time, the microscopic simulation results are input into macroscopic process simulation as parameters to simulate the reactive distillation process. The developed multi-scale model was used for the simulation of the hydrolysis of methyl acetate by heterogeneously catalyzed reactive distillation. Both the simulation obtained final conversions of methyl acetate and catalyst layer efficiency factors were in good agreement with experimental data. The influence of equivalent diameter of catalyst layer was investigated. The results indicate that the equivalent diameter of catalyst pocket has significant influence on catalyst layer efficiency factor. When the equivalent diameter of catalytic sheet decreases from 25.4mm to 8.1mm, the catalytic sheet efficiency factor rises to 200% approximately and the conversion of methyl acetate increases from 33.7% to 51.11%, where the molar ratio of water to methyl acetate, reflux rate to feed rate and space velocity were set to 2.0, 3.3, and 0.45, respectively.

29

It should be mentioned that, for the microscopic model established in this work, only radial diffusion process was considered based on the typical catalytic packing structure and flow distribution of liquid-vapor phase, as discussed in section 2.3.1. Indeed, radial flow also exists in the catalyst layer. For different internals, the radial distribution of liquid inside catalytic packing is different, leading to the discrepancy of radial flow phenomenon of catalytic sheet interior. Furthermore, the radial flow in the catalyst layer also influences the catalyst layer efficiency factor which attracted attention in our work. In order to simplify the model, however, the multicomponent mass transfer and reaction process in the catalyst layer was not comprehensively described in this work. It is definitely worth investigating the radial flow phenomenon of catalytic sheet interior in our future work.

Acknowledgments The authors wish to acknowledge the financial support by the National Natural Science Foundation of China (Project Nos. 91534106 and 21506032).

Appendix. Validation of catalyst layer efficiency factor In order to further validate the proposed multi-scale model, the calculated catalyst layer efficiency factors under different catalyst layer structures were compared with experimental data. Four kinds of catalyst capsules were fabricated and the equivalent diameters of catalytic sheet were approximately 25.4mm, 17.3mm, 12.7mm and 8.1mm, respectively, while all the heights and diameters of catalyst bales were 155mm and 100mm, respectively. The image of catalyst packings is shown in Fig. A-1. The structure parameters are listed in Table A-1. The macrokinetic behaviors of four kinds of catalyst capsules were investigated.

D=25.4mm

D=12.7mm

D=17.3mm

30

D=8.1mm

Fig. A-1 Diagram of fabricated catalyst capsules

The experimental operation processes are same as our previous work. The kinetic data of catalyst were measured in a batch stirred reactor and the macrokinetic behavior was investigated in a batch cycling unit. A more detailed study of this reaction kinetic can refer to our previous work (Wu et al., 1999b). The kinetic data of hydrolysis of methyl acetate catalyzed by common industrial catalyst C-100E were measured which had not been reported in the literature to the best of our knowledge. Table A-1 Structure parameters of the fabricated catalyst capsules Items

Parameters

Equivalent diameter of catalyst layer (mm)

25.4

17.3

12.7

8.1

Height of catalyst loaded (mm)

155

155

155

155

Diameter of catalyst capsules (mm)

100

100

100

100

Mass of catalyst particles (g) (dry basis)

280.5

256

192.5

110

Type of corrugated packing

CY®

CY®

CY®

CY®

The catalyst reaction kinetic experiments were performed in reactive kettle at agitation speed of 400 rpm, molar ratio of H2O to MeOAc of 4, catalyst loaded of 20g, and reactive temperature of 323.15 K. It should be mentioned that the external diffusion effect was negligible at the agitation speed of 400 rpm. According to the experimental results, the chemical equilibrium constants can be calculated. Because of the nonideality of hydrolysis system of methyl acetate, the nonideality of the liquid phase should be corrected by replacing the concentrations of components with activities normally. Nevertheless, in order to correspond with the kinetic data used in the micro-scale simulation, the equilibrium constants and reaction rate constants were still calculated based on the concentrations of components. The calculated equilibrium constant K at 323.15 K is 0.1754 and the forward reaction rate constant k+ is 3.325 10-12 m6  min 1 mol 1  g .

31

60 50

Cal. D=25.4mm D=17.3mm D=12.7mm D=8.1mm

xA %

40 30 20 10 0 0

100

200

300

400

500

600

t (min) Fig. A-2 Effect of equivalent diameters of catalytic sheet on the reaction rate and the conversion of MeOAc (%): symbols, experimental data; and solid lines, best fit for experimental data

By the utilization of the batch cycling unit, the macrokinetic behaviors of four kinds of catalyst capsules were investigated at molar ratio of H2O to MeOAc of 4, reaction temperature of 323.15K and sprinkle density of 19.75m/s. The results are shown in Fig. A-2. The reaction rates at various catalyst bales were calculated by the pseudohomogeneous reaction kinetic model. The calculated values are shown in Table A-2. The continuous lines in Fig. A-2 represent the calculated results. The catalyst layer efficiency factors can be calculated by comparing the forward reaction rate constant in reactive kettle at 323.15K with that of catalyst capsules. The results are also shown in Table A-2.

Table A-2 Macro forward reaction rate constant and efficiency factor Equivalent diameter of catalytic sheet (mm)

k  ×1012/ m6·min-1·mol-1·g

η%

25.4

1.3666

41.10

17.3

1.7818

53.59

12.7

2.2511

67.70

32

8.1

2.5758

77.46

The simulation averaged results were compared with experimental data, as shown in Fig. A-3. As can be seen this figure, the simulation values and experimental results are in good agreement. The average relative error is 5.25% and the maximum relative error is 10.15%, thus further proving the reliability of multi-scale model. 80

Simulation results Experimental results

75 70

%

65 60 55 50 45 40 35 6

8

10

12

14

16

18

20

22

24

26

D (mm) Fig. A-3 Comparisons of micro-scale simulation results with experimental data

Nomenclature A

= surface area of catalyst particles inside the geometry domain, m 2

A

= interface of liquid phase and solid phase

B

= the matrix defined by Eq.11

Ci 0

= initial concentration of each component, mol  m-3

Ci

= actual concentration inside the catalytic sheets, mol  m-3

DiE

= diffusion coefficient of each component, m 2  s 1

D AE

= binary Maxwell-Stefan diffusion coefficients, m 2  s 1

D

= equivalent diameter of catalytic sheets, mm 33

dp

= catalyst particle diameter, mm

F

= feed molar flow rate, kmol  h 1

K

= chemical equilibrium constant

K1

= the constant defined by Eq.17

k , k-

= forward and backward reaction rate constant, m6  mol 1  s 1  gcat 1

L

= liquid molar flow rate at the feed stage, kmol  h 1

L

= liquid reflux molar flow rate, kmol  h 1

mcat

= catalyst mass in one stage, g

Mi

= molar mass, kg  kmol 1

n

= unit normal vector pointing from the fluid phase toward the solid phase

q

= liquid fraction of feed

Rm

= water to methyl acetate molar ratio

Rf

= reflux rate to feed rate

Ri

= chemical reactive source, kg  m 2  s 1

ri-surface

= reaction rate on the reactive surface, mol  m2  s 1

rfact

= actual reaction rate of catalytic distillation process, mol  s 1

rideal

= reaction rate in reactive kettle, mol  s 1

Sv

= space velocity

T

= reaction temperature, K

V

= molar volume of solute at normal boiling point, cm3  mol 1

VC

= critical molar volume, cm3  mol 1

Vbed

= volume of catalyst bales in one stage, m 3

Vregion

= volume of simulated geometry domain, m 3

wE

= mass fraction of each component in reaction system 34

wib

= mass fraction of liquid component on the external surface of catalyst beds

W

= concentration of catalyst pellets, g  m 3

x i

= mole fraction of each component

xA

= conversion of methyl acetate

Zl

= dynamic holdup, m3  m3

Zd

= total holdup, m3  m3

Greek letters



= void fraction of porous media



= mixture density, kg  m 3

L

= viscosity, cp



= catalyst layer efficiency factor

 BC

= volume ratio of catalytic sheets to catalyst bales

AB

= thermodynamic factor defined by Eq.14

 AB

= the constant defined by Eq.15

Abbreviations CD

= catalytic distillation

CFD

= computational fluid dynamic

EQ

= equilibrium

H2O

= water

HAC

= acetic acid

MeOAc

= methyl acetate

MeOH

= methanol

35

NEQ

= non-equilibrium

36

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Highlights



A microscopic model focused on reactive performance was established.



A two-way coupling multi-scale model was proposed for catalytic distillation.

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The simulation results were in good agreement with experimental data.

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The effect of equivalent diameter of catalyst layer on efficiency factor was studied.

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