ISSN 0012-5008, Doklady Chemistry, 2006, Vol. 406, Part 2, pp. 26–29. © Pleiades Publishing, Inc., 2006.Original Russian Text © S.A. Mustafina, A.V. Balaev, R.S. Davletshin, S.I. Spivak, U.M. Dzhemilev, 2006, published in Doklady Akademii Nauk, 2006, Vol. 406, No. 5,pp. 647–650.

26

In modeling nonisothermal processes in reactorswith the participation of a gas, a liquid, and a fixed solidcatalyst, it is necessary to take into account that thechange in the composition of the reaction mixturedepends significantly not only on the chemical reactionitself but also on phase transitions in the catalyst bed.Taking into account these factors is virtually decisive inconsidering processes accompanied by the release of alarge amount of heat in the reaction zone. Among suchprocesses are the reactions of hydrogenation of unsat-urated compounds [1, 2].

In this work, using a mathematical model, the

α

-pinene hydrogenation in a reactor with a fixed bed ofa nickel silicate catalyst is studied with consideration ofsimultaneous chemical and phase transformations. Themain purpose of this study is to determine the type ofreactor and the operating conditions for which the yieldof the desired product,

cis

-pinane, is maximal.The interest in this problem is caused by the great

practical importance of the

α

-pinene hydrogenationproduct,

cis

-pinane, whose oxidation yields a stablehydroperoxide used as the initiator of low-temperaturebutadiene–styrene polymerization. Numerous studiesdetermined [3] that the use of

cis

-pinane hydroperoxideas a polymerization initiator significantly improves theperformance and specifications of butadiene–styrenerubbers, especially those produced at high monomerconversions.

Analysis of experimental data showed [3] that, onthe chosen catalyst, chemical reactions can occur inboth the liquid and the gas phases. A two-step schemeof

α

-pinene hydrogenation is proposed, which com-prises an irreversible step of

α

-pinene interaction withhydrogen to form

cis

-pinane and a reversible step of

α

-

pinene isomerization. As an

α

-pinene isomer, an ana-logue averaged between dipentene and

α

-terpinene ischosen.

Pinene + H

2

Pinane or C

1

+ H

2

C

2

,

Pinene Isomers or C

1

C

3

.

The kinetic equations for these steps have the fol-lowing form:

for the liquid phase,

where

,

where

for the gas phase,

w

1

=

C

1

C

H

=

k

4

y

1

y

H

,

where

k

4

= ,

w

2

=

C

1

–

C

3

=

k

5

y

1

–

k

6

y

3

,

where

k

5

=

C

G

,

k

6

=

C

G

.

Here,

C

G

and

C

L

are the molar densities (kmol/m

3

) ofthe gas and the liquid phases, respectively;

x

i

and

y

i

arethe mole fractions of the components in the liquid andthe gas phases, respectively; and

W

i

and

w

i

are the ratesof the reactions (kmol/(m

3

h)) in the liquid and the gasphases, respectively.

To describe the

α

-pinene hydrogenation in the gas–liquid–solid catalyst system, a two-phase mathematicalmodel has been developed, which takes into accountthe change in the number of moles in the reaction sys-tem: first of all, the significant decrease in the numberof moles in the gas phase because of the hydrogen con-sumption in the hydrogenation and also the change inthe number of moles in both phases because of theevaporation or condensation of the components.

The mathematical description of the nonisothermal

α

-pinene hydrogenation in a tubular reactor with a

W1 k1C1PH k1x1yH,= = k1 k1PCL,=

W2 k2C1 k3C3– k2x1 k3x3–= =

k2 k2CL, k3 k3CL;= =

k4 k4CG2

k5 k6

k5 k6

Modeling of Gas–Liquid a-Pinene Hydrogenationin Tubular Reactors

S. A. Mustafinaa, A. V. Balaevb, R. S. Davletshina, S. I. Spivakb, and Corresponding Member of the RAS U. M. Dzhemilevb

Received August 10, 2005

DOI: 10.1134/S0012500806020042

a Sterlitamak State Pedagogical Institute, pr. Lenina 37, Sterlitamak, 453103 Bashkortostan, Russia

b Institute of Petrochemistry and Catalysis, Russian Academy of Sciences, pr. Oktyabrya 141, Ufa, 450075 Bashkortostan, Russia

CHEMICALTECHNOLOGY

DOKLADY CHEMISTRY Vol. 406 Part 2 2006

MODELING OF GAS–LIQUID α-PINENE HYDROGENATION IN TUBULAR REACTORS 27

fixed catalyst bed is given by the set of material andheat balances

(1)

Yi = {xi at Vvap > 0} or {yi at Vvap < 0}, ϕ = under

the boundary conditions at l = 0

xi = , yi = , L = L0, G = G0, T = T0. (2)

Here, Qj are the heats of reactions, kcal/kmol; arethe heats of evaporation of the components, kcal/kmol;

and are the molar specific heats of the gas andthe liquid phases, respectively, kcal/(kmol K); Cc is themass heat capacity of the coolant, kcal/(kg K); Gc is themass flow rate of the coolant, kg/h; Sc is the externalspecific heat-transfer surface area, m2/m3; αc is theheat-transfer coefficient, kcal/(m2 h K); L and G are themolar flow rates of the liquid and the gas phases,respectively, kmol/h; l is the axial coordinate along thereactor length, m; S is the cross-sectional area of tubes,m2; Vvap is the molar evaporation rate, kmol/h; νij are thestoichiometric coefficients; and ϕ is the mole fractionof the gas phase.

Of fundamental importance for developing themodel is the approach to determining the phase transi-tion rate. There are two main approaches thereto: ther-modynamic equilibrium between the two phases isassumed [4] and Vvap is calculated using a certain equa-

1S--- CP

L L CPGG+( )dT

dl------ Q j 1 ϕ–( )W j ϕw j+[ ]

j 1=

2

∑=

–Vvap

V p

---------- ∆HiVYi αcSc Tc T–( ),+

i 1=

3

∑

±GcCc

S------------

dTc

dl--------- αcSc T Tc–( ),=

1S---dL

dl------

Vvap

V p

----------– FL,= =

1S---

dxi

dl-------

Fi xiFL–L

---------------------,=

Fi 1 ϕ–( )v ijW j

Vvap

V p

----------Yi, i–j 1=

2

∑ 1 2 3,, ,= =

1S---dG

dl------- 1 ϕ–( )W1– ϕw1–

Vvap

V----------+ ΦG,= =

1S---

dyi

dl-------

Φi yiΦG–G

-----------------------, Φi ϕνijw j

Vvap

V p

----------Yi,+j 1=

2

∑= =

1S---

dyH

dl---------

1 ϕ–( )W1– ϕw1– yHΦG–G

-----------------------------------------------------------------,=

GG L+--------------

xi0 yi

0

∆HiV

CPG CP

L

tion [5]. In the model advanced, it is suggested that Vvapin set (1) be determined as the difference between theequilibrium value G* and the actual value G. G* is cal-culated from the total composition of the reaction mix-ture and current values of the phase variables P and T,and G is the solution of set (1). Then, the evaporationrate Vvap = G* – G. In evaporation, this value is positive,and in condensation, it is negative. If the equilibriumvalue of the mole fraction of the gas phase should be 1,then the evaporation rate is taken to be maximal andequal to L.

All the kinetic and thermophysical parameters areavailable in the literature [3]. The thermophysicalparameters (phase equilibrium constants, enthalpies ofthe components, their molar specific heats in the gasphase, and heats of evaporation of the components) arecalculated according to published procedures [6].

At an inlet temperature of about 30°C under adia-batic conditions, because of the high exothermicity ofα-pinene hydrogenation, the temperature in the reactorexceeds 300°C [3]. This temperature is much higherthan the experimentally recommended limiting temper-ature 140–150°C [3] (above the latter temperature,there are thermal decomposition of the components,coking, and catalyst deactivation). Therefore, the pro-cess should be performed in reactors with sufficientlygood heat removal, e.g., in tubular reactors, which canbe designed in two variants: with cocurrent and withcountercurrent flows of the reaction mixture and thecoolant.

Depending on the variant of reactor design, the signof the left-hand side of the equation for the coolant inset (1) can be either plus or minus for a cocurrent orcountercurrent reactor, respectively.

Then, set (1) is closed by the following boundaryconditions:

(3)

Using set (1) under boundary conditions (2) and (3),a computational experiment was performed for a tubu-lar reactor with tubes 3.5 m3 in volume, 50 mm in diam-eter, and 2 m in length at an average constant pressureof 5 atm with water as a coolant. The volume of theintertubular space is approximately 1.5 times largerthan that of the reaction space. The initial conditionsare T0 = 30°ë, L0 = 1.95 kmol/h, and G0 = 2.45 kmol/h.The coolant flow rate Gc is a parameter being varied.

Some of the calculation results are presented inFigs. 1–4 (the solid and dashed lines show the data forthe cocurrent and countercurrent reactors, respec-tively).

With an increase in the coolant flow rate Gc, the tem-perature Tmax in the reactor naturally decreases, but atequal coolant flow rates, the temperature in the counter-current reactor is always higher than that in the cocur-

T x l 0= T x0 for the cocurrent reactor=

and T x l Lmp= T x0 for the counter current reactor.=

28

DOKLADY CHEMISTRY Vol. 406 Part 2 2006

MUSTAFINA et al.

rent reactor (Fig. 1). However, to reach the same tem-perature in the reactor, the coolant flow rate in the coun-tercurrent reactor should be significantly higher thanthat in the cocurrent reactor.

A convenient characteristic for estimating the oper-ating conditions is the average temperature Tav in thereactor. The maximal temperature Tmax in the reactorand the α-pinene conversion X as functions of Tav arepresented in Figs. 2 and 3, respectively.

Figure 2 shows that, lest Tmax exceed a limiting valueof 150°C, Tav should be 96°C in the cocurrent reactorand 70°C in the countercurrent reactor. In this case,

X exceeds 99% and is about 96%, respectively (Fig. 3).The coolant flow rates Gc for these reactors are 550 and2600 kg/h, respectively. The latter value is technologi-cally unrealistic and economically unacceptable. Char-acteristic profiles of the temperature in the reactorsunder such operating conditions are presented in Fig. 4.

The determining process parameter is Tmax. Com-parison of Figs. 1–4 shows that, at the same Tmax, in thecocurrent reactor, the average temperature Tav in thereactor, the coolant temperature, and the average cool-ant temperature are higher. In the countercurrent reac-tor, only Gc is higher. This is because the temperature

500

60

ímax, °C

Gc, kg/h1000 1500 2000 2500 3000

80

100

120

140

160

180

200

70

100

íav, °C80 90 100 110 120

80

120

140

160

180

200

ímax, °C

íav, °C100 110 120908070

0.85

0.90

0.95

1.00ï í, °C

160

140

120

100

80

60

40

200 0.2 0.4 0.6 0.8 1.0

ξ

1

2

2

1

Fig. 1. Maximal temperature in the reactor vs. coolant flowrate.

Fig. 2. Maximal temperature in the reactor vs. average tem-perature.

Fig. 3. α-Pinene conversion in the reactor vs. average tem-perature.

Fig. 4. (1) Catalyst and (2) coolant temperature profilesalong the relative reactor length.

DOKLADY CHEMISTRY Vol. 406 Part 2 2006

MODELING OF GAS–LIQUID α-PINENE HYDROGENATION IN TUBULAR REACTORS 29

of the water cooling the reaction zone through the tubewalls in the cocurrent reactor is lower than that in thecountercurrent reactor, in which much of the heatshould be removed in the tail part of the reactor, wherethe reaction rate and, hence, the heat release are insig-nificant. Therefore, in the countercurrent reactor, thecoolant begins to contact the reaction zone at a highertemperature, which leads to the necessity of increasingthe coolant flow rate. It is seen that the presence of aheat source—a chemical reaction—makes cocurrenttubular reactors more efficient, in contrast to ordinaryheat exchangers.

If, to increase the reactor operation reliability, Tmaxis decreased to 140°C, then X will be 98.6% for thecocurrent reactor and below 95% for the countercurrentreactor. In this case, Gc should be increased to 600 and2800 kg/h, respectively. It is clear that such conditionsin the countercurrent reactor are impossible to imple-ment.

The numerical analysis demonstrated that the α-pinene hydrogenation to form cis-pinane can be effi-ciently performed in a tubular reactor with a fixed bedof a nickel silicate catalyst with cocurrent flows of thereaction mixture and the coolant. Figures 1–3 show thatsuch a reactor has quite a high technological flexibility.Even with a decrease in Tmax to 130°C, the operatingconditions remain suitable: X = 97% at Gc = 720 kg/h.

Thus, the fundamental novelty of the results of thisstudy consists in using a thermodynamic approach fordetermining the phase transition rate and also in obtain-ing evidence that gas–liquid hydrogenation in tubularreactors can be efficient only in the case of cocurrentflows of the reaction mixture and the coolant.

ACKNOWLEDGMENTS

This work was supported by the Russian Foundationfor Basic Research (grant no. 05–01–97908–r–agidel’).

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1999, no. 4, pp. 61–65.2. Datsevich, L.B., Iess, A., Kambur, M.P., and Mukhor-

tov, D.A., Katal. Prom-sti., 2004, Special Issue, pp. 18–26.

3. Kas’yanova, L.Z., Extended Abstract of Cand. Sci.(Chem.) Dissertation, Ufa, 2002.

4. Kirillov, V.A. and Drobyshevich, V.I., Teor. Osn. Khim.Technol., 1998, vol. 32, no. 1, pp. 72–81.

5. Kirillov, V.A., Kuz’min, V.A., Kuzin, N.A., et al., Teor.Osn. Khim. Technol., 1993, vol. 27, no. 5, pp. 508–513.

6. Reid, R.C., Prausnitz, J.M. and Sherwood, T.K., TheProperties of Gases and Liquids, 3rd ed., New York:McGraw Hill, 1977. Translated under the title Svoistvazhidkostei i gazov, Leningrad: Khimiya, 1982.