kinetics research on fast exothermic reaction between cyclohexanecarboxylic

7/31/2019 Kinetics Research on Fast Exothermic Reaction Between Cyclohexanecarboxylic

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Chemical Engineering Journal 169 (2011) 290298

Contents lists available at ScienceDirect

Chemical Engineering Journal

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c e j

Kinetics research on fast exothermic reaction between cyclohexanecarboxylic

acid and oleum in microreactor

K. Wang, Y.C. Lu, Y. Xia, H.W. Shao, G.S. Luo

The State Key Lab of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing 100084, China

a r t i c l e i n f o

Article history:

Received 2 December 2010

Received in revised form 18 February 2011Accepted 24 February 2011

Keywords:

Microreactor

Fast exothermic reaction

Kinetics

Liquidliquid multiphase

CFD simulation

a b s t r a c t

Microreactors are effective tools for the intensification of fast exothermic chemical reactions. In this

work, we focus on thekineticsstudy of a microreactingprocess to provide a deeper understanding of the

transportand reaction performance within microreactors. An experimental setupincorporatingan online

kinetic measurement method was developed based on the temperatureconversion relationship in the

cyclohexanecarboxylicacidoleum reaction a crucial reaction for the preparationof-caprolactam. The

reactant conversion wassuccessfully recorded in a reaction time of less than 1.0s, andit wasdetermined

that the reaction rate was mainly controlled by the mixing of reactants. The mass transfer coefficient

in the microreactor reached 104 m/s, and the observed selectivity of the main-product was higher than

97%.Based on the experimental results, a single-droplet model wasdevelopedto establisha better under-

standing of the temperature and concentration distributions in the reacting system as well as analyze

the effect of drop size on main-product selectivity.

Crown Copyright 2011 Published by Elsevier B.V. All rights reserved.

1. Introduction

Fast exothermic reactions play essential roles in the chemical

engineering industry for their wide applications. Although these

types of reactions have appeared hundreds of years until now,

people still find they are hard to operate. Many fast exothermal

reactions take placein batch reactors with low reaction efficiencies,

low yield and low safety. In recent years, however, the introduc-

tion of micro-structured chemical system has brought about many

new advantages for those reactions,including higherproduct yield,

higher space rate, lower energy consumption and safer operation

[13]. Fast mixing can be obtained in microreactors with residence

times on themillisecondlevel [4] while high volumetricheat trans-

fer coefficients 10 times larger than those observed in common

heat exchangers can be obtained in microcontactors [5]. Because of

their excellent mixing and transport performance, many different

types of chemical reactions have been intensified using microreac-tors, such as fast precipitation reaction for nanoparticles [6], strong

exothermic polymerization for polymer materials [7], and danger-

ous organic synthesis with reactive reactants [8].

Corresponding author at: The State Key Lab of Chemical Engineering, Depart-

ment of Chemical Engineering, Tsinghua University, Gongwu Building 477, Beijing

100084, China. Tel.: +86 10 62783870; fax: +86 10 62783870. Corresponding author. Tel.: +86 10 62783870; fax: +86 10 62783870.

E-mail addresses: [email protected](K. Wang), [email protected]

(G.S. Luo).

Microreactors are effective tools for improving fast exothermic

reaction processes, especially for solving low selectivity problems.

The efficient mixing of reactants,fast heatremoval and controllable

reaction time allow the overall reaction process to be controlled

more effectively, resulting in a higher selectivity of the main-

products. The FriedelCrafts aminoalkylation reaction is a classic

example of a reaction system to which a microreactor can be

applied. Nagaki et al. reported 92% main-product yields by using

micromixing technology [9]. In a differentstudy, Park and Kim car-

ried out an oxidative Heck reaction in a dual-channel microreactor

[10]. Their results showedsignificantimprovements in yield, selec-

tivity, and reaction time in microreactors over traditional batch

reactors. Jovanovic et al. reported a selective alkylation reaction

of phenylacetonitrile in a 250-m internal diameter microchan-

nel reactor [11]. They found both the conversion and selectivity in

their microreactor increased significantly compared with a stirred

reactor. In our previous work, we also studied the enhancementof selectivity in fast exothermic consecutive reactions using the

reaction between cyclohexanecarboxylic acid and oleum, a crucial

process forthe preparation of-caprolactam. Microreactors gener-

ating microdroplets in a liquidliquid multiphase reaction process

were used to enhance reactant mixing and main-product selectiv-

itywhichreached levels(>97%) much higherthan those in common

batch reactors [12,13].

Except for the advantage research of microreactors, deeply

understanding the transport and reaction characteristics of

microreacting process is very importantfor further development of

microreaction technology. In this work we investigate the appar-

1385-8947/$ see front matter. Crown Copyright 2011 Published by Elsevier B.V. All rights reserved.

doi:10.1016/j.cej.2011.02.072
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K. Wang et al. / Chemical Engineering Journal 169 (2011) 290298 291

Nomenclature

AH+ protonated cyclohexanecarboxylic acid

AS mixed anhydride

by-P by-products

CCA cyclohexanecarboxylic acid

Ci concentration, i refers to CCA, H2SO4, HSO4 , SO3,

AS, AH+, by-P (mol/m3)

Cpalkyl heat capacity of alkyl-hydrocarbons, alkyl refers toC6H14, C7H16, C8H18 [kJ/(kg

C)]

CpCCA heat capacity of CCA [kJ/(kgC)]

Cpoleum heat capacity of oleum [kJ/(kgC)]

D diffusion coefficient (m2/s)

Din diffusion coefficient in the droplet (m2/s)

Dout diffusion coefficient out of the droplet (m2/s)

d inner diameter of the reaction pipe (m)

dav average droplet diameter (m)

d32 Sauter-mean droplet diameter (m)

Ha Hatta number ( Ha =

mC0SO3

Din/kC)

k thermal conductivity [W/(m C)]

kC mass transfer coefficient of CCA (m/s)

kCa volumetric mass transfer coefficient of CCA (1/s)kin thermal conductivity in the droplet [W/(mC)]

kout thermal conductivity out of the droplet [W/(mC)]

Kb equilibrium constant of proton exchange reaction

Km equilibrium constant of mixed anhydride formationreaction

MCCA molecular weight of CCA (g/mol)

MH2SO4 molecular weight of H2SO4 (g/mol)

MSO3 molecular weight of SO3 (g/mol)nCCA molar transport rate of CCA (mol/s)

Qoil volume feeding rate of oil phase (m3/s)

Qoleum volume feeding rate of oleum (m3/s)

q heat source in model equation (W/m3)

qr released heat flux of the reacting system (W)

R reaction source in model equation [mol/(m3s)]

s cross-sectional area of the mixing channel (m)

T temperature (C, K)

TinC

inlet temperature of continuous phase (C)

TinD inlet temperature of dispersed phase (C)

uT average velocity in microreactor

[uT= 4(Qoil + Qoleum)/d2, m/s]

uC average velocity of continuous phase in micromixer

(uC= Qoil/s, m/s)

V inner volume of the microreactor (m3)

xCCA mass concentration of CCA in the feeding oil (wt%)

x CCA mass concentration of CCA in the hydrolyzed oil

phase (wt%)

xSO3 mass concentration of SO3 in the feeding oleum(wt%)

Cm concentration driving force (mol/m3)rHM reaction enthalpy of mixed anhydride formation

reaction (kJ/mol SO3)

rHP reaction enthalpy of proton exchange reaction

(kJ/mol H2SO4)

oleum conversion of oleumm kinetic constant of the main reactions [m3/(s mol)]s kinetic constant the of side reactions (1/s) interfacial tension (N/m)C viscosity of continuous phase (Pa s)oil density of oil phase (kg/m

3)

oleum density of oleum (kg/m3)

phase ratio of dispersed phase reaction time (s)

Fig. 1. Sketch view of the working system.

ent kinetics of cyclohexanecarboxylic acidoleum reaction in a

microreactor, a topic which, up to now, has not been frequently

discussed in the literature before. An online kinetic measurement

method was developed to measure the reactant conversions at dif-

ferent reaction times. The mixing performance in the microreactor

was investigated experimentally, and a single droplet model was

established to show the nature of the temperature and concentra-

tion distributions in the micro-scale reacting system.

2. Experiment and simulation

2.1. Working system

The reaction process between cyclohexanecarboxylic acid (CCA)

and oleum, also referred to as the Premixing Reaction in the SINA

process for the preparation of caprolactam [14], was selected as

a representative fast exothermic reaction system. Fig. 1 shows

this multiphase reaction system with a CCA dissolved alkyl-

hydrocarbon solution, as the organic feed solution, and oleum as

the sulfuric phase solution (Fig. A1). Throughout the process, the

phase ratio between the oil and sulfuric acid phase was larger than

6, with the oil phase acting as the continuous phase. CCA first dif-

fused from the continuous phase to the dispersed phase, followed

by reactions between CCA and oleum in the droplet.

Two main reactions take place in this working system [13].

Oneis theproton exchange reaction between CCAand sulfuric acid:

(I)

The other is the mixed anhydride formation reaction between

CCA and sulfur trioxide:

(II)

Themixedanhydride is themain-product,sinceit canreactwith

nitrosylsulfuric acid to form caprolactam in the following process

[15]. Thesetwo mainreactionsare ultra-fastreactions [16,17]. They

take place almost instantaneously when the reactants meet and

stop quickly when the feed stream is terminated [18]. The reac-

tions are always shown as reversible in the literatures [19,20]. We

measured the chemical equilibrium of the proton exchange reac-

tion and determined the equilibrium constant, Kb, shown in Eq.(1). According to previous studies, the equilibrium constant of the

mixed anhydride formation reaction (Km)is1 04 times greater thanthe proton exchange reaction [12,19]. Thus, both reactions can be

seemed as irreversible processes for simplification with stoichio-

metric excess of CCA in all operations.

Kb =CAH+CHSO4

CCCACH2 SO4= 0.06 exp

13, 900

RT

= 19.48.4 ( 20 70 C) (1)

where AH+ refers to the protonated cyclohexanecarboxylic acid.

Both reactions are highly exothermal. Maggiorotti measured their


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292 K. Wang et al. / Chemical Engineering Journal 169 (2011) 290298

reaction enthalpies at rHP=13.86 kJ/mol H2SO4 for the pro-ton exchange reaction and rHM=50.4kJ/mol SO3 for the mixedanhydride formation reaction [18].

Throughout the reaction process, irreversible side reactions

involving mixed anhydride begin, forming undesirable sulphonic

acids such as sulphocyclohexanecarboxilic acid and benzensul-

phonic acid [18]. To simplify the reaction scheme we refer to all

products of side reactions as by-products in this article.

(III)

The kinetic rates of the side reactions are slower than those of

the mainreactions.Maggiorotti measured the yields of by-products

accordingto thereactiontimein a batch reactor with strongstirring

(600 rpm stirring rate) [18]. Based on those results, we determined

that the side reactions can be considered as first-order reaction

processes with an average reaction rate described by (Fig. A2):

dCby-Pd

= sCAS, s = 1.8 109 exp

8.9 104

RT

(30 C < T < 90 C) (2)

where is the reaction time, by-P refers to the by-products andAS refers to the mixed anhydride.The reaction process of the working system can be quenched

by adding water into the system. The protonated CCA and

mixed anhydride quickly hydrolyze and revert to CCA as shown

in the following schemes. The by-products, however, cannot

be hydrolyzed, resulting in the partial consumption of CCA in

the experiments. Using these relations, the yield of by-products

can be analyzed and the main-product selectivitycan be calculated.

(IV)

(V)

3. Methods and setup

For this microreactor kinetics study, the measurement method

is very important. Due to the small size of microreactors, accurate

measurement of reactant conversion with very short reaction time

is very difficult. Because the sampling time may be several times

longer than the reaction time, an online measurement method

is most appropriate for a kinetics study. Several online methods

have been proposed in the literature. In 2003, Song and Ismag-

ilov used fluorescence signals to analyze the turnover kinetics

of Ribonuclease A in their microfluidic chips [21]. In 2009, Han

et al. measured the decomposition kinetics of H2O2 with micro-

electrodes in time-controlled microchannels [22]. In this work, the

relationship between reactant conversion and temperature wasused.

The experimental setup is given in Fig. 2. Fig. 2a is a sketch map

of theexperimental devices and Fig.2b provides an illustration. The

reactantscome from therightside of thedevices with thefeed tem-

peratures controlled by coiled pipes in a water bath. Mini-sensors

(6mm3 mm3 mm metal shell with PT100 thermal resistance

wire in it) placed on the inlet pipes of the micromixer are con-

nected to a data recording system (Beijing Riubohua Co. Ltd.). The

micromixer is a micro-sieve dispersion device, which produces

microdroplets. It consists of a mixing channel (yellowred color in

Fig. 2a), a distributionregion(bluecolor in Fig. 2a) andthree micro-

sieve pores (For interpretation of the references to color in this

sentence, the reader is referred to the web version of the article.).

The mixing channel is10 mmin length, 1mm in width and 0.5 mm

Table 1

Locations of the temperature sensors.

T1 T2 T3 T4 T5 T6 T7 T8

Distances from the

micro-sieve pores

(cm)

10 22 28 36 46 60 75 90

in height. Thevolume of distributionregion is approximately 80L.

The mixing channel and the distribution region are connected via

the micro-sieve pores, which are 0.4 mm in diameter and 0.5mm

in depth. A reaction pipe with a 1 mm inner diameter and 0.3mm

wall thickness is placed at the outlet of the mixing channel to com-

plete the reaction process. Thus, the micromixer and reaction pipe

combine to form a complete microreactor. For the online measure-

ment of reactant conversion, eight mini-sensors are placed on the

reaction pipe to collect temperature data. The pipe temperature

representsthe fluidtemperature during the stable reaction process.

The microreactor is completely insulated with NBRPVC rubber

foam before and during the experiment ensuring that the temper-

ature is only influenced by the reactant conversion. This type of

microreactor has already been shown to exhibit plug flow perfor-

mance [23], and the reaction time can therefore be calculated by

comparing the sensor location to the average velocity of the react-

ing fluids. The locations of the mini-sensors are given in Table 1. At

the end of the reaction pipe a hydrolyzer is introduced to quench

the reacting process for the analysis of main-product selectivity. A

microscope is also used to obtain images of the microdroplets pro-

duced in the microreactor. A polymethyl methacrylate chamber is

introduced to replace part of the reaction pipe for observation.

3.1. Operation and analysis

The CCA solution and oleum were delivered to the microreactor

via metered pumps (Beijing Satellite Co. Ltd.). In each trial, the oil

was injected into the microreactor first followed by the oleum. The

hydrolysis temperature was maintained below 45 C. During the

experiment, temperatures were measured after the reaction had

stabilized and samples of hydrolyzed products were collected atthe outlet.

Oleum conversion and mixed anhydride selectivity were the

mainparameters consideredin this experiment. The oleumconver-

sion was calculated by monitoring the rise in reactor temperature

due to the release of heat as shown in the following equations:

qr =

TTin

C

QoiloilxCCACpCCA + (1 xCCA)Cpalkyl

dT

+

TTin

D

QoleumoleumCpoleumdT (3)

oleum =qr

Qoleumoleum

xSO3 rHM/MSO3 + (1 xSO3 )rHP/MH2 SO4 100% (4)

Here, qr is the released heat flux; oleum is the oleum conversion; T

is the measured temperature; TinC

is theinlettemperature of contin-

uous phase; TinD is the inlet temperature of dispersed phase; Qoil isthevolumetric feed rate of oil(continuousphase); Qoleum is the vol-

umetric feedrate of oleum; oil isthe oildensity; oleum istheoleumdensity;xCCA is themass concentration of CCAin theoil feed;xSO3 is

the mass concentration of SO3 in the oleum feed; CpCCA is the heat

capacity of CCA; Cpalkyl is the heat capacity of alkyl-hydrocarbons;

Cpoleum is the heat capacity of oleum; MSO3 is the molecular weightof SO3 and MH2SO4 is the molecular weight of H2SO4. We use this

definition for oleum conversion not only because of the need for

onlinekinetic measurement,but also dueto thepresent inabilityto

accurately quantify oleum, mixed anhydride and protonated CCA


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Table 2

The heat capacities of the working system [2426].

CpCCA (20100C) 1.67 + 0.0069T[J/(g C)]

CpC6 (2060C)a 2.16+ 0.0043T[J/(g C)]

CpC7 (2080C)a 2.14+ 0.0041T[J/(g C)]

CpC8 (20100C)a 2.16+ 0.0026T[J/(g C)]

Cpoleum (20100C) 1.82 + 0.0025T[J/(g C)]

aC6, C7 and C8 refer to hexane, heptane and octane individually.

in the working system. Although this conversion is not based on

the molar quantity, it still reflects the actual change in reactant

concentration. Heat loss from the experimental setup was tested

by flowing hot n-hexane through the microreactor, and the results

showed that heat dissipation was less than 3% of the total enthalpy

flux (the enthalpy at room temperature was set to zero). Thus heat

loss was neglected in the conversion calculation.

To measure the selectivity, the concentrations of CCA in the

oil feed and the oil phase output with hydrolyzed products were

measured using standard potentiometric titration. An automatic

titrator (Shanghai Leici Co. Ltd.) with a relative error of less than

0.5% was used. A 70% (v/v) acetone/water solution was introduced

as the titration solution, and CCAs equivalence point lies between

pH 10 and pH 11. In hydrolyzed solutions, CCA is water-insoluble

and is concentrated in the oil phase, but the sulphonic by-products

are highly water-soluble substances. Thus, the molar quantity of

CCA converted to by-products can be calculated by the concentra-

tion difference between the oil feed and the hydrolyzed oil output.

At 100% oleum conversion, the main-product selectivity is shown

as:

SM =Qoiloil

xCCA (1 xCCA)/(1 x

CCA)x

CCA

/MCCA

QoleumoleumxSO3 /MSO3 100% (5)

where x CCA is the mass concentration of CCA in the hydrolyzed

oil phase, and MCCA is the molecular weight of CCA. The physical

properties of the working system are given in Table 2 [2426].

3.2. Model simulation

A mathematical model detailing temperature and concentra-

tion fields was developed to gain a deeper understanding of the

reaction process, masstransport andheat dispersioncharacteristics

within the microreactor. The model contained combined mass and

heat transport equations solved using computational fluid dynam-

ics (CFD) software COMSOL 3.4 with a finite element solver. The

running time for each simulation was approximately 5 min on a

personal computer with an Intel Core II CPU and 4GB of RAM.

Fig. 3. The measured temperatures at different pipe positions and the oleum con-

versions according to the residence times.

4. Results and discussion

4.1. Measured kinetics in the microreactor

Using the experimental setup with online temperature sensors,

the reaction kinetics were measured for three working systems

oleum/CCA hexane, oleum/CCA heptane and oleum/CCA octane.

The final temperature of each system did not exceed the boiling

point of the solvent. The measured temperatures are given in Fig. 3.

As shown on the left side of the picture, the temperature increases

near the beginning of the reaction pipe but stabilizes towards the

Fig. 2. (a) The experimental setup and process; (b) picture of the microreactor.


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Fig. 4. (a) The droplet sizes and their distributions. (b) Microscope picture of the

microdroplets.

end of the pipe, suggesting the reaction has reached completion

inside the microreactor. In the figure, uT is the average velocity of

thereactingfluidsin thereactionpipe.The right side ofFig.3 shows

the conversion of oleum with reaction time. The graph shows that

thereactionprogressesquicklyrequiring 1 s orless forthe complete

conversionof oleum. Fig.3 also illustrates the effectof differentflow

conditions on thereactionrate.The reaction rate increaseswith the

increase of flow velocity for all experimental systems and operat-

ing conditions, and the measured kinetic rate, strongly affected bythe mixing process in the microreactor, is therefore the apparent

kinetic rate.

4.2. Mixing performance in the microreactor

Fora liquidliquid multiphase process, flowvelocity is a charac-

terof mixingperformancein themicroreactor.Sincethisis a mixing

controlled reaction, it is important to understand exactly how

mixing influences the overall microreaction process. Liquidliquid

two-phase mixing is primarily determined by droplet size and the

mass transfer coefficient of the working system. In this study, we

used an online CCD camera to record the flowing droplets in the

reaction pipe. The sulfuric acid/CCA alkyl-solutions were chosen as

cold test systems to give investigations on the droplet size. Fig. 4shows the average diameters of droplets and their standard devia-

tions, which were obtained by counting at least 300 droplets in the

recorded images with image-analysis software. Nearlyall the aver-

age droplet diameterswere 60m,with almostno changeresulting

from the variation of flow velocity.

Fig. 4 shows flowvelocity has littleeffecton the droplet size and

only affects the mass transfer coefficient of the working system.

By using the measured average droplet sizes we can estimate the

CCA mass transfer coefficient. Since the main reactions are very

fast, almost all the transported CCA is quickly consumed by the

oleum at the beginning of the process, taking place in the reaction

region between the micromixer and Sensor T1. Assuming the two

main reactions have equal kinetic constants, the transported molar

quantity of CCA can be calculated from the amountof heat released

Fig. 5. (a) The mass transfer coefficients of CCA; (b) the volumetric mass transfer

coefficients of CCA.

Fig. 6. The main-product selectivity at different final temperatures.

by the reacting system as shown in the following equation:

nCCA = T1oleum Qoleumoleum

xSO3 /MSO3 + (1 xSO3 )/MH2SO4

(6)

where nCCA is the molar transportrate of CCAin the reaction region

between the micromixer and Sensor T1, and T1oleum

is the oleum

conversion at the location of Sensor T1. Since CCA is almost con-

sumed at low oleum conversions, the CCA concentration in the

dropletscan beassumedto bezero.Thus, themasstransportdriving

forces can be calculated by the following equation:

Cm =CinCCA CT1CCA

ln(CinCCA

/CT1CCA

)(7)

where CinCCA

is the incoming concentration of CCA in the oil phase,

and CT1CCA

is the CCA concentration in the oil at Sensor T 1. Assum-

ing the average droplet sizes in the cold test systems represent the

average droplet sizes in thereactingsystem, themass transfer coef-

ficient (kC) andvolumetric masstransfercoefficient(kCa)ofCCAcan

be estimated as:

kC nCCA

6V/d32 Cm(8)

and

kCa =nCCA

V Cm

(9)

where is the phase ratio of the dispersed phase, d32 is the Sauter-mean diameter of the droplets, and V is the inner volume of the

microreactor. The calculated results given in Fig. 5 shown the mass

transfer and volumetric mass transfer coefficients increasing with

the increasing velocity of the fluids. The mass transfer coefficient

of CCA in the microreactor is in the range of 104 m/s, much higher

than those in common liquidliquid processes [27]. The volumet-

ric mass transfer coefficient, in the range of 1/s, also increased with

the increase in flow velocity. This enhanced mass transport perfor-

mancein the microreactor allows the reactions to reachcompletion

quickly.

4.3. Main-product selectivity

High reaction selectivity can be obtained by quickly quench-

ing the fast reaction process. Considering that the side reactions

are temperature sensitive, the advantage of using a microreactor

device operating at high temperatures becomes more apparent. In

our previous work we demonstrated that main-product selectivity

higher than 97% can be obtained when the final reactor temper-

ature ranged from 45 to 65 C [12]. In this study, we show that

this high selectivity is maintained even at temperatures near 90 C

(Fig. 6). Obtaining high selectivity at high temperatures is desir-

able especially because the reactions immediately following these

reactions in the SINA caprolactam production process also require

high temperatures. Compared to the results obtained in a common

batchreactor [18], the main-product selectivity in the microreactor

is much higher.


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Fig. 7. The single droplet reaction model.

4.4. Modeling of the reaction process

Knowing the reaction and mass transport details in the react-

ing system is crucial for the in-depth understanding of the overall

microreaction process. However, due to the small sizes, measuring

the temperature and concentration fields in microdroplets is very

difficult, and in this work they are instead expressed with a mathe-

matical model. For the purpose of understanding the characterized

information of thereacting process in detail, a single droplet model

was adopted in this work.

Considering the co-directional flow of the two phases in the

reaction pipe, the continuous phase can be considered static from

the inertial reference frame of the droplet and vice versa. As shown

in Fig.7, the reacting flowconsistsof many differentfluid elements.Neglecting droplet coalescence, we can use a single droplet model

to describe the reaction process. The model is based on one reac-

tion element as shown in Fig. 7b. The element has an axisymmetric

structure.Diffusion and heatconduction equationswith sources are

used to describe the mass transport and heat transport processes

in the model.

Ci

+ (DCi) = Ri (10)

CpT

+ (kT) = q (11)

where i refers to CCA, H2SO4, SO3, AS, AH+ and by-P, D is the diffu-

sion coefficient, and k is the thermal conductivity. R and q are the

rates of mass and heat generation represented as:RCCA = m(CCCA CSO3 + CCCA CH2SO4 ) (12)

RSO3 = mCCCA CSO3 (13)

RH2SO4 = mCCCA CH2SO4 (14)

RAS = mCCCA CSO3 sCAS (15)

Rby-P = sCAS (16)

q = mCCCACSO3 rHM mCCCACH2SO4 rHP (17)

The kinetic equationsof themixed anhydrideformation reaction

and the proton exchange reaction are very important for char-

acterizing the rate of mass generation due to reaction. However,

there has been little or no information on the kinetics of these

reactionsavailable in theliterature.Here in thepresent model,con-sidering both the mixed anhydride formation andproton exchange

reactions are ultra-fast processes, we assume them to be second-

order reactions with equal kinetic coefficients, m, as seen in Eqs.

(12)(14). The value ofm was estimated using the Hatta number(Ha), whose value should be higher than 3 for a mixing controlled

reaction. The Ha number is defined as:

Ha =

mC

0SO3

Din/kC (18)

where Din is the diffusion coefficient in the droplet and C0SO3

is the

feeding concentration of SO3 in oleum. The final value ofm cho-

sen was 0.2m3/(mols) (Ha= 3), andthe calculation results changed

little by increasing m beyond this value. The kinetic equation for

the side reactions is given in Eq. (2), shown above. The parametersfor the model equations are given in Table 3 [24,26]. Because of its

small size, fluid movement within the droplet is neglected and the

moleculardiffusion coefficient is used as shown in thetable. On the

outside of the droplet, the diffusion coefficient is given as the effec-

tive diffusion coefficient. An enhancement factor is introduced to

represent the effect of flow on the mass transfer coefficient. Simi-

lar assumptions are madecorresponding to the heat conductivities.

The effect of CCA mass transport on droplet size is neglected, since

thediameter expansion ratio was less than 1.2post-reaction.How-

ever, the effect of CCA mass transport on the variation of heat

capacity is considered in the model parameters.

The initial and boundary conditions of the model equations are

given as:

For the time = 0,

CCCA = CAS = Cby-P = 0 (in droplet) (19)

CSO3 = CH2SO3 = CAS = Cby-P = 0 (in oil phase) (20)

On the surface of the droplet,

CSO3 = CH2SO3 = CAS = Cby-P = 0 (21)

DinCCCA = DoutCCCA (22)

kinT= koutT (23)

On the external boundary of continuous phase,

CCCA = 0 (24)

T= 0 (25)

Since oleum droplet formation in the micromixer only takes

several milliseconds much shorter than the reaction time we

assume no product exists initially. The partition coefficient of CCA

between the two phases is near unity for the operating conditions

specified (Fig. A3). Thus, the influence of CCA concentration on the

Table 3

The parameters in the model equations (2060C) [24,26].

Diffusion coefficient D (m2/s) Thermal conductivity k [w/(m C)] Heat capacity Cp [kJ/(m3 C)]

Inside of droplet

Din =2.0109 kin =0.31 oleumCpoleum + (CCCA + CAS + Cby)CpCCAMCCA

Outside of droplet

Deff= DCCA =0.5109a keff= koil =0.17 xC6CpC6oil + CCCACpCCAMCCA

a

DCCA =0.5

109

m2

/s measured with metallic diaphragm cell method.


7/9


Fig. 8. The variations of temperature and concentration field according to the reaction time.

Fig. 9. (a) The calculation results of oleum conversion; (b) the intensified factors atdifferent average flow velocities.

two-phase interface is negligible and not considered. The droplet

region covered by this model is shown in Fig. 7c. It is an axisym-

metric structure, scattered with triangle elements. The model was

solved using COMSOL 3.4 CFD software and the results are given in

Fig. 8.

Fig. 8 shows the variation of the temperature and CCA/SO3 con-

centrationfields withreactiontime. The temperature gradient from

the inside tothe outside of the reacting droplet is weak with nearly

no temperature difference between the droplet and its surrounding

solution for all simulation cases in this study. Thus heat gener-

ated by the reaction can be removed quickly from the reacting

droplet. The CCA concentration field shows a very large concen-tration gradient near the droplet surface. Taken together with the

SO3 concentration field, it becomes apparent thatthe concentration

of CCA in the droplet is nearly zero as SO3 has not been completely

consumed. Thus, the reactions mainly taken place near the droplet

surface.

Theenhancementfactor in themodel (Fig.9) was obtained using

the experimental results in Fig. 3. Fig. 9a shows good agreement in

a comparison between the experimental and simulation results.

The enhancement factors, given in Fig. 9b, increase with the accel-

eration of the reacting fluids. These results are in accord with the

variationof the mass transfer coefficient. Accordingto the values of

the enhancement factor, mass transport processes can be intensi-

fied several times over by using microreactor flows to increase the

effective diffusion coefficient.

Fig. 10. (a) The variation of reaction time according to the droplet size; (b) thevariation of reaction selectivity according to the droplet size.

We also analyzed the effect of droplet size on main-product

selectivity using this model. Fig. 10 displays the total reaction time

and main product selectivity (calculated using the by-product con-

centrations) when the amount of transported CCA had reached

95%. The calculated results reflect the variation trend in reac-

tion time and selectivity. The reaction time increases rapidly with

the increase of droplet size, while the main-product selectivity

decreases. Interestingly, the selectivity decreased slowly on the

micrometer scale, and much more quickly on the millimeter scale.

This phenomenon accords with the achievement of high selectivity

using microdroplets with size distributions. Thus, the micro-scalemixing of the liquidliquid multiphase system is crucial for fast

exothermic reactions.

5. Conclusion

In this study,we designed an onlinemeasurementmethod anda

mathematic model to study the apparentkineticsof fastexothermic

multiphase reactions in a microreactor. The online measurement

was based on the relationship between temperature and reac-

tant conversion in the working system an ultra-fast, highly

exothermic, liquidliquid multiphase reaction process between

cyclohexanecarboxylic acid and oleum. The entire reaction process

wascompleted in less than 1 s andthe reaction rate wasdominated

by the mixing of the reactants. A small average droplet diameter


8/9


(60m), reflective of the mixing scale of the system, combined

with high flow velocities in the microreactor enhanced the CCA

mass transportbetween phases. The CCA mass transfer coefficients

were in the range of 104 m/s, much higher than those observed

in common liquidliquid processes. Enhanced mixing performance

andprecise control of thereactiontimeyielded main product selec-

tivity as high as 97% at final temperatures ranging from 40 to 90C.

To gain a deeper understanding of the transport and reaction pro-

cesses occurring on the droplet scale within the microreactor, a

single droplet model was developed to calculate the temperature

and concentration distributions in the working system. The model

showed that heat generated by the reaction is removed quickly

from the reacting droplet, and CCA transport from the oil phase to

the sulfuric acid phase is the rate controlling step of the reaction

process. The reactions mainly take place near the droplet surface

due to the speed with which this fast, multiphase reaction process

occurs. Using this model as an analysis tool, we studied the effects

droplet size on reaction time and selectivity and determined that

the micrometer scale is crucial for the enhancement of selectivity

in fast exothermic multiphase reactions.

Acknowledgements

We would like to acknowledge the support of the National Nat-

ural Science Foundation of China (21036002, 20876084) and the

National Basic Research Program of China (2007CB714302) for this

work.

Thanks to Chris P. Tostado, Ph.D. candidate in our group, for the

English revision of this paper.

Appendix A. Appendixes

Considering the physical similarity of oleum and sulfuric acid,

H2SO4CCAhexane waschosen as a cold test systemin thepresent

work. Fig. A1 gives itstriangle phase diagram. The miscibility of the

two phases is weak with CCA concentration lower than 70 wt%.

For the kinetic study of side reactions, the experimental resultsof Maggiorotti areretreated in the present work [18]. It is found the

side reactions can be seem as first-order processes and their aver-

age kinetic contant with the variation of temperature is given in

Fig. A2. Correlated with those kinetic contants the effect of tem-

perature on the reaction rate can be discribed by Eq. (2) in the

text.

To build the reaction model, the partition of CCA between

two phases is an important parameter. Using the phase diagram

of H2SO4CCAhexane and the equilibrium coefficient of pro-

ton exchange reaction (Eq. (1)), the partition coefficients of CCA

between sulfuric acid phase and oil phase can be calculated. Fig. A3

Fig. A1. The phase diagram of H2SO4CCAhexane system.

Fig. A2. The average kinetic constants of the side reactions.

Fig.A3. The partitioncoefficients of CCA between sulfuric acidphase and oil phase.

givesthe calculation results. For the situationof CCA concentrations

between 1 mol/L and 5 mol/L in oil, the operating concentrations in

the experiment, the partition coefficient nearly equals to 1.0.

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