Catalysis Today 79–80 (2003) 89–95

Tubular reactor for liquid reactions with gas release

Peter Stahl, Adrian Wegmann, Philipp Rudolf von Rohr∗Institute of Process Engineering, Swiss Federal Institute of Technology (ETH) Zurich, CH-8092 Zurich, Switzerland

Abstract

A design procedure for tubular reactors is developed for liquid-phase reactions with gas release in horizontal tubes ofsmall diameters. It is based on a one-dimensional calculation approach, which assumes a stationary turbulent flow. For eachstream-wise position on the tube axis, the model delivers the actual temperature, void fraction, chemical composition andslip of the mixture. The possible retardation of the gas release from the liquid proves to be a decisive factor. Approachesto handle this phenomenon are described. The calculation of the tubular flow reactive system requires the knowledge of thereaction macro kinetics. It can be determined separately in suitable small scale batch experiments as shown. Experimentswith a homogeneous model reaction in a tubular pilot plant validate the theoretical method.© 2003 Elsevier Science B.V. All rights reserved.

Keywords: Tubular reactor; Retardation; Reaction; Multiphase flow

1. Introduction

Profitable chemical reactions often require criticalreaction conditions. In case of fast exothermic or en-dothermic reactions, large reaction volumes lead todifficulties in controlling the process variables pres-sure and temperature. Conducting the reaction in smallvolumes enables not only a proper control, but pre-vents also severe damages in case of inhomogeneitiesor instabilities. Thus, it is often advisable to prefercontinuous processing to batch processing[1,2]. Thetwo basic continuous reactor types are the continuousstirred-tank reactor and the tubular plug-flow reactor.

Tubular reactors are simple and easy to construct.Furthermore, a narrow residence time distribution canbe achieved by turbulent flow conditions. In case ofsmall tube diameters, the geometry allows operation athigh pressures. The favorable ratio of surface to vol-ume enhances heat transfer and thus simplifies the ad-

∗ Corresponding author.E-mail address: vonrohr@ivuk.mavt.ethz.ch (P.R. von Rohr).

justment of a desired axial temperature profile. Theseadvantages make the turbulently operated tubular re-actor with small diameter the most recommendablecontinuous reactor type for critical reaction processes.

Tubular reactors are however disadvantageous forslow reactions, which require long reactor tubes, thatcause high pressure drops. The same is true for highlyviscous liquids. In this case uneconomic high pump-ing power can only be avoided, if solely the most crit-ical phase of the reaction is conducted in the tubularreactor.

The design and calculation of tubular reactors cancause problems, because fluid mechanics, reaction ki-netics and thermodynamics are coupled and difficultto describe mathematically especially in case of reac-tions with phase transitions. In practical use this meansthat a special reactor design is required for each ap-plication in order to achieve an optimal process[2–4].

The aim of this work is to develop a design methodfor homogeneous liquid-phase reactions with gas re-lease in horizontal tubes with small diameters. Thisincludes a one-dimensional calculation approach,

0920-5861/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0920-5861(03)00014-2

90 P. Stahl et al. / Catalysis Today 79–80 (2003) 89–95

which—assuming a stationary turbulent plug-flow—takes into account both the fluid dynamics and thereaction process. For each stream-wise position onthe tube axis, the model delivers the actual tempera-ture, void fraction, chemical composition and slip ofthe mixture. It is compared to experiments, carriedout in a pilot facility, that allowed measurements alsowithin the reaction zone.

2. Reactor dimensions

In order to be able to assume a turbulent plug-flow,it is necessary to dimension the reactor in a way thatthe axial dispersion of the reacting phase—here theliquid phase—can be neglected. For superficial liquidReynolds numbers ofReL > 10,000 Lali et al.[5]find independently of the flow pattern a constant ax-ial dispersion, which is not higher than that of liquidsingle-phase flow at same Reynolds numbers.

For smaller Reynolds numbersReL < 10,000 theaxial dispersion of two-phase flow can be significantlyhigher than the dispersion of single-phase flow.

The internal diameterd of the reactor tube has tobe chosen small enough to remove almost instanta-neously the heat released by an exothermic reaction,respectively, to supply the necessary heat for an en-dothermic reaction. This means that thermal stabilitymust be guaranteed along the tube axis. Fluidmechanicdesign fundamentals, i.e. pressure drop calculation,critical flow, hold up, are summarized by Stahl[6].

3. Model reaction

The autocatalytic oxygen releasing reaction ofpotassium permanganate with hydrogen peroxideunder acid conditions is chosen as model reaction:

5H2O2+2MnO4− +6H+ → 2Mn2+ + 8H2O + 5O2

H2SO4 is used as acid. The reaction is homoge-neous, all reactants are in aqueous solutions. It featuresa color change, as the degradation of the permanganateions leads to a decolorization of the initially violet so-lution.

The knowledge of densityρ, viscosityη, specificheat capacitycp and thermal conductivityλ and sol-ubilities as a function of temperature and pressure of

all reactants and products and their aqueous solutionsis needed to describe the continuous reaction processthoroughly and predict the behavior within the tubularreactor.

An expression for the reaction macro kinetics isnecessary in order to calculate tubular reactors. Simoyiet al.[7] found the reaction between the permanganateions and hydrogen peroxide under acid conditions tooccur in three stages: a fast initial, an induction periodand a main autocatalytic step. While the first two stepstake a few milliseconds, the main step can last severalseconds.

In the literature, no complete reaction kinetics isgiven for all three steps. For the essential autocatalyticmain step, the following rate law may be applied[8]:

dcMnO4−

dt= kca

MnO4−(cMnO4

−,0+cMn2+,0 − cMnO4−)r

(1)

According to the measurements of Simoyi et al. theexponents can be approximated witha = 1 andr =1.5.

In order to determine the dependency ofk, measure-ments of the reaction time are conducted in a batchfacility. The reaction times were measured opticallyby evaluation of videorecordings (50 pictures per sec-ond).

The trend of the obtained data corresponds to lit-erature data at lower absolute concentrations[9]. Thereaction time is found in the range between 0.8 and10 s. An increase of temperature and initial surplusof sulfuric acid leads to higher reaction rates, while ahigher surplus of hydrogen peroxide inhibits the auto-catalytic reaction. Thus, varying the initial hydrogenperoxide concentration is an elegant means to adjustthe reaction time to a desired value.

Eq. (2)directly gives the following relation betweenk and the reaction timetR:

tR = C

k1.5MnO4

−(2)

For a 99% degradation of the permanganate ions,the constant isC ∼ 12. Thus, a correlation for the re-action kinetics is resulting with the measured reactiontimestR. It has to be kept in mind that this macro ki-netics does not give any information about the reactionmechanism.

P. Stahl et al. / Catalysis Today 79–80 (2003) 89–95 91

To transfer the obtained macro kinetics to the tubu-lar reactor, it is necessary that both reactors havesimilar mixing times. The mixing time of the tubularreactor used is given inSection 4. The comparabilityof heat transfer in both reactors is ensured by theanalogy of geometry, wall material (glass) and wallthickness, as well as the choice of the same heat car-rier (water). A sufficiently high heat transfer withinthe heat carrier is assumed.

4. Experimental

A tubular reactor pilot plant was designed to con-duct the experimental work. Its reactor tube has alength of 5 m (five modular elements, each 1 m long)and an internal diameter of 7 mm.Fig. 1 shows theexperimental set-up schematically.

The maximum total volume flow is 12 l/min, whatleads to a maximum entrance Reynolds number ofRein = 30,000 at ambient temperature. At mixturetemperature ofT = 50◦C this value increases toRein = 60,000, due to the lower viscosity. Beforeentering the reactor, the three solutions pass a heatexchanger, which allows a stationary tempering at tem-peratures betweenT = 15 and 50◦C.

While the KMnO4- and the H2SO4-solution, whichdo not react with each other, are premixed beforethe inlet, the H2O2-solution is added in a coax-ial mixing nozzle at the reactor entrance. The tubejacket enables temperature control by heat exchange.The modular design offers the possibility to pro-vide measuring points for temperature, pressure and

Fig. 1. Schematic representation of the test set-up. P: membrane pumps, H: heat exchanger.

void fraction in the couplings between the modules.Furthermore, elements as orifice plates can be in-serted here, in order to disturb and homogenize theflow.

Experiments were conducted in a temperature rangebetweenT = 15 and 50◦C and in a mass flow rangebetweenM∗

tot = 0.028 and 0.112 kg/s. At ambienttemperature these mass flows correspond to entranceReynolds numbers of 5000≤ Rein ≤ 20,000. TheKMnO4-massflow fractionx∗

KMnO4= M∗

KMnO4/M∗

tot

was varied betweenx∗KMnO4

= 0.39×10−3 and 5.8×10−3, that leads to volume flow fractions of the re-leased oxygen at the reactor outlet (ambient pressure)of 0.1 ≤ ε∗

G ≤ 0.7. The volume flow fraction is de-fined asε∗

G = V ∗G/V ∗

tot.Pressure and temperature are measured at the reac-

tor in- and outlet as well as within the reactor betweenthe modules. The temperature is detected by NiCr–Ni-thermocouples, the pressure is transduced by ceramicsdiaphragm sensors (Type Endress+ Hauser Cerabar).The void fraction is measured at the couplings, too.The chosen method is gamma-densitometry with anIodine-125 gamma-source.

5. Calculation method

The basic requirements of a calculation method fortubular reactors are summarized inSection 1. In Fig. 2,a schematic flowsheet of the calculation procedureis shown. The one-dimensional calculations are car-ried out iteratively, basing on the method of finitedifferences. The following input data is needed: the

92 P. Stahl et al. / Catalysis Today 79–80 (2003) 89–95

Fig. 2. Schematic flowsheet of the calculation procedure[10].

tube geometry (length, diameter, orifice plates), theentrance conditions (temperature, mass flow, concen-trations) and the pressure at the reactor outlet. Theprogram calculates for each stream-wise position the

tube axis pressure, temperature, chemical composi-tion, void fraction and the velocities of both phases.All other quantities can be derived from this. For fur-ther details see[6].

P. Stahl et al. / Catalysis Today 79–80 (2003) 89–95 93

Fig. 3. Undisturbed tubular reactor flow: comparison of calculated and measured temperature, pressure and void fraction development. Massflow: M∗ = 0.061 kg/s, entrance Reynolds numberReL,in = 12,400, initial concentrations: 5.96 g KMnO4/kg solution, 24.25 g H2O2/kgsolution, 21.06 g H2SO4/kg solution, entrance temperatureTin = 25◦C, jacket temperatureTjack = 26◦C.

6. Comparison with experimental results

Fig. 3 shows in detail the comparison of the cal-culation with the experimental results for one exam-ple. The flow is not disturbed, that means no orificeplates are inserted into the reactor. The experimentis conducted at ambient temperature with an en-trance Reynolds number ofReL = 10,000 (M∗

L,in =

εL,out M∗G,out (g/s) pin (bar) Tout (◦C) tR (s)

Theory 0.352 0.181 1.96 27.95 0.79± 0.05Experiment 0.36± 0.04 0.17± 0.01 1.99± 0.03 27.91± 0.32 0.72± 0.04

0.062 kg/s). The initial concentrations are listed inFig. 3.

The essential quantities to compare are reactiontime, temperature and pressure development, voidfraction development and the mass flow of releasedoxygen. The following table shows the comparison.Since the gas mass flow is only measured at thereactor outlet, it is not included inFig. 3.

94 P. Stahl et al. / Catalysis Today 79–80 (2003) 89–95

Experiment and measurement show a good agree-ment, that is within the measurement accuracy.

All experiments with undisturbed flow agree wellwith the calculations for reaction time and tempera-ture development. However, the void fraction develop-ment often displays a deviation between the measuredand predicted values, that cannot be explained withthe uncertainties in measurement. These deviations re-sult from an erroneous estimation of the retardationof gas release. The equilibrium assumption, that allgas passes directly into the gaseous state when theliquid is saturated with solved gas, is not justified inmost cases. Usually the system is in non-equilibriumafter reaction, i.e. the mass of gas solved in the liq-uid exceeds the equilibrium solubility. The liquid issuper-saturated and the release of the gas phase is re-tarded.

Deviations in the prediction of the void fraction al-ways cause errors in the prediction of pressure drop,too.

The experiments concerning disturbed flow werecarried out using an orifice plate in order to dis-turb the reacting flow. It is inserted in 2 m dis-tance from the reactor inlet what is according tothe reaction zone length, adjusted by the reactiontime.

The flow disturbance proves to reduce the retarda-tion of gas release. The experiments do not indicatethat the orifice diameter necessary for an instanta-neous gas release depends on the Reynolds number,whereas this diameter obviously depends on theamount of produced oxygen, as shown in the followingtable.

KMnO4-concentration(g/kg solution)

0.39 1.20 2.65 5.8

ε∗G,out 0.1 0.3 0.5 0.7

Orifice-φ (mm) 2 2 3 4

7. Conclusion and outlook

The design of gas–liquid tubular reactors requiressignificantly more effort than in the single-phasecase. In this work tubular reactors for homogeneousliquid reactions with gas release were examined. Adesign procedure for turbulent flow conditions waselaborated and experimentally verified on the basis

of a model reaction. This method includes criteria todetermine the reactor dimensions, the measurementof a reaction macro kinetics and a program for reactorcalculation. This program is based on experimentallyverified suitable correlations to calculate the pressuredrop, the slip, the temperature development and thecritical flow phenomenon for small tube diameters.It does not need any adjustable parameters. Besidesthe reaction kinetics and the pressure drop corre-lations, the gas release proves to be an importantparameter to describe the process. It does not de-pend on the reaction kinetics alone, as the gas can bereleased retarded from super-saturated reaction mix-ture. The retardation time can be influenced by flowperturbation.

Future work will focus on the formulation of amore basic and universal correlation in order topredict this retardation as a function of physicalproperties, flow conditions and perturbation. The ex-amination of heterogeneous liquid–liquid reactionswill be a further task, as this reaction type is industri-ally relevant. The oxidation of 2-octanol with nitricacid is an example for such a heterogeneous reactionwith an undesired side reaction, since NOx-gases areformed[10]. The prediction and measurement of thespecific phase interface between the liquid phaseswill have high significance, because it governs themass transfer and thus influences the reaction macrokinetics.

Acknowledgements

The financial support provided by the Emil BarellFoundation (Switzerland) is acknowledged.

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