Chemical Reaction EngineeringâII

33 Practical Model of the Benzoic Acid Oxidation Step as a Means towards Optimization of the Phenol Process

Downloaded by CORNELL UNIV on October 7, 2016 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch033

L. VAN DIERENDONCK, P. DE JONG, J. VON DEN HOFF, and H. VONKEN Central Laboratory, DSM, P.O. Box 18, Geleen, The Netherlands R. VERMIJS CIR, P.O. Box 1021, Rozenburg, Rotterdam, The Netherlands

In the preparation of phenol from toluene by the toluene-benzoic acid route, the economics of the process largely depend on the process conditions used in the benzoic acid oxidation step. It is possible to describe the chemical and physical phenomena in the reactor by a mathematical model. The information needed to develop this model was taken from plant test runs and from additional laboratory research on the kinetics in the process step. Study of the model has furnished more insight into what occurs in the process, thus permitting the settings to be better adapted to the process conditions.

T

oluene is oxidized to phenol in two independently operated units (Figure 1). The process starts with partial conversion of toluene to benzoic acid in a gas-stirred oxidation reactor. The resulting mixture is fractionated in several successive operations, yielding purified benzoic acid. In the reactor of the second oxidation section this benzoic acid stream is converted to phenol by a homogeneous catalyst consisting of copper and magnesium benzoates. The air needed enters the reactor base via a gas distributor together with steam. The steam causes the phenylbenzoate initially formed as an intermediate product to hydrolyze to phenol, which is stripped from the reaction medium by the effluent gas. This effluent is fed to a column separator to recover crude phenol and unconverted benzoic acid; the latter is then recycled via evaporators. Byproducts formed in the oxidation predominantly consist of low volatile components, i.e., tar. The tar concentration in the reactor is controlled by discharging reactor liquid to the extraction unit where the byproducts are removed, and the benzoic acid, copper, and magnesium are recycled to the oxidation reactor. The residual streams from the first and second oxidation section are burned together. 432

Hulburt; Chemical Reaction Engineering—II Advances in Chemistry; American Chemical Society: Washington, DC, 1974.


33.

Benzoic Acid Oxidation

VAN DIERENDONCK ET A L .

I

REACTOR fOXIDATION

DISTILLATION COLUMNS

433

1—»-TAR

REACTOR 2 OXIDATION e

TAREVAPORAEXTRACTORS TION

SEPARA - SEPARATOR TION COLUMN

Figure 1. Flowsheet Points of Investigation To improve the economics of phenol production, the efficiency output and onstream times of the process had to be increased. Our study was directed at several aspects, such as the development of a model for the second oxidation stage. The required information was derived partly from plant measurements. The kinetics of each step, for example, were determined in a reactor of ca. 1 liter. Some other aspects were not as well suited to laboratory investigation because of scale-up problems. These include: (a) The relation between rate of mass transfer (K S) and superficial gas velocity ( V ) . In view of the process conditions, laboratory research would call for a superficial gas velocity so low that production rates comparable with those realized in practice could be attained only under conditions of mechanical stirring. (b) The relation between reaction conditions and tar formation. The long residence times obtained in the industrial reactor, in combination with recycling light tar components, would make it impossible for a semitechnical reactor to be scaled down to the point where the costs are no longer prohibitive. (c) The influence of the oxidation temperature above the boiling point of benzoic acid. Studying this point on a laboratory scale would involve large experimental problems of evaporation rate, benzoic acid recycle, and sealing the equipment. Partly for these reasons, the data needed in our model study were taken from test runs done in the plant reactor. As far as possible, the kinetic and physico-technological information obtained from these test runs has been used for the ultimate model. Only in some cases did we use equations derived from a regression analysis of measuring data. Research during model building was done by workers from the plant staff and from several departments of the D S M Central Laboratory. The team included specialists from organic chemistry, technology, and systems engineerh

s


434

CHEMICAL REACTION ENGINEERING

II

ing who worked closely with the production division. This guaranteed assem bling of the relevant information and offered the possibility of regularly check ing the validity of the model.


Basis of the Model Reaction Scheme and Stoichiometry. The preparation of phenol from benzoic acid (second oxidation) is done by oxidative decarboxylation with air in the presence of copper and magnesium (1, 2, 3, 4, 5, 6, 7, 8, 9, 10). Nor mally, phenylbenzoate is regarded as an intermediate product. The hydrolysis of phenylbenzoate—the actual phenol formation—is effected in the oxidation reactor by steam; magnesium is the catalyst. Practice has shown that phenol production along this route invariably entails several consecutive and side reactions in which, e.g., tar is formed. The formation of tar via a consecutive reaction appeared from the fact that in an experiment using radioactive phenol, phenol was incorporated in the tar. Also, part of the tar forms directly from benzoic acid or cupric benzoate. H-0*CO2

k

1 20-COOH*teO •

k

2(0-COO) Cu-

2

• 0 - C O O - 0 *2(0-ΟΟΟ) Cu •COg

2

H 0 2

CO2*H*0 0-OU0-COOH

φ—Ο-Ό—φ phenyl benzoate

(2)

2

(b) reoxidation of cuprous benzoate to cupric benzoate 0

0

Ο

2 Cu—Ο—C—Φ + 2 φ—C—OH cuprous benzoic benzoate acid (c)

-f I 0 ^

• 2 Cu(0—C—Φ)2 + Η 0 cupric benzoate

2

2

(3)

hydrolysis of phenol benzoate Ο II Mg catalyst φ—Ο—C—Φ -f- Η 0 τ± phenyl benzoate 2

Ο || φ—OH + Φ—C—OH phenol benzoic acid

(4)

2. Formation of tar (1 + 2), which proceeds in agreement with the gross equation Ο + 0.9 η 0

η φ—C—OH benzoic acid 3.

• (CeH O .e)» + η C 0 tar 1 = tar 2

2

4

0

2

+ η Η 0 2

(5)

Formation of benzene by decarboxylation of benzoic acid Ο • φ—H + C 0 benzene

Φ—C—OH benzoic acid 4.

(6)

2

Ring degradation Ο Φ—C—OH + 7.5 0 benzoic acid

2

•7 C0

2

+ 3 H 0 2

(7)

These reactions have been incorporated in the reaction scheme, which served as a basis for the model (Figure 2). Kinetics. The kinetics of the partial steps in the reaction scheme were studied in bench-scale experiments. The reactor—a glass, stirred, gas-liquid



436


II

contactor—was normally operated on the batch principle, and was provided with the necessary feeding, measuring, and analytical equipment. The majority of the components were analyzed by gas-liquid chromatography. The amount of tar formed was determined after fractionation of the reactor contents. The amounts of phenol, tar, and benzene were measured as functions of several variables, such as temperature, pressure, copper and magnesium content, gas load, and residence time (independent variables), and phenol concentra tion, degree of hydrolysis, cupric-cuprous ratio, oxygen partial pressure, etc. (dependent variables). The results of these experiments were used to derive the order of the various reactions as well as the reaction rate constants and their temperature dependencies. Similar measurements were done under plant conditions to assemble sup plementary information and to check the validity of the model. These measure ments were done in many strictly defined test runs in which the production of phenol, the consumption of toluene, the temperature, the pressure, the liquid level, and the air and steam loads were varied. The test runs also yielded information on specific aspects such as ring degradation, oxygen content of the tar, gas holdup, and tar viscosity. All this information was used to describe the individual reactions which are discussed below. OXIDATION OF CUPROUS TO CUPRIC BENZOATE. The oxidation of cuprous to cupric benzoate under the process conditions proceeds at a fast rate; the reduction of cupric benzoate, on the other hand, is a much slower reaction. Hence, the equilibrium lies entirely on the side of the cupric compound. This implies that during the oxidation the cupric benzoate concentration is fairly constant and high with respect to the amount of copper present. Thus, a given [ C u ] / [ C u ] is a function of the reaction conditions. The reaction rate equation r 2+ = k · C + · C (8) was derived from measurements of the rate of oxygen consumption as a func tion of the temperature, the oxygen partial pressure, and the [Cu ]/|[Cu ] ratio. This problem is analyzed below, under Oxygen Absorption. 2 +

+

A

C u

Cu

o 2

2+

+

FORMATION OF PHENOL AND HYDROLYSIS OF PHENYL BENZOATE. Phenyl benzoate (phb), which forms from the cupric benzoate, has a distinctly lower vapor pressure than benzoic acid ( B Z O H ) and thus accumulates in the reaction liquid. It is removed by hydrolysis with water; M g benzoate is the catalyst. Phenol (ph) is stripped from the reaction medium by the offgas stream. The rate of the homogeneous hydrolysis as a function of temperature, water concentration, phenyl benzoate concentration, and magnesium content was measured in a separate pressure assembly. At a sufficiently high water:phenyl benzoate mole ratio the reaction is zero-order with respect to water and first order with respect to phenyl benzoate. When the magnesium concentration exceeds a given minimum, its influence on the hydrolysis is nil. Since the equilibrium of the reaction phenyl benzoate + H 0 k k phenol + benzoic acid lies far enough to the right (k » k ), at the phenyl benzoate and water concentrations used under plant conditions the forward reaction (k C ) will predominate. The rate of hydrolysis was derived from data assembled from laboratory and plant measurements (see Figure 3) : 2

2

2

2

s

3

vhh

rh = k

where k

2

(9)

· Cphb

2

p

= k

2o

X er ' E

RT

Ε (activation energy) = 80 kj/mole.


(10)

33.

437


VAN DIERENDONCK E T A L .

>J 2

UUIU —

Ch-

1

— 4» - labc>ratory

CJ - plant )-


1

)°-

10 Τ

3

Λ •κ" )

Ι ι ι1.8 Figure 3.

1

I

M — 1.9

2.0

2.1

2.2

2.3

Reaction rate constant for the hydrolysis of phenyl benzoate as a function of temperature

BENZENE FORMATION. Oxidative decarboxylation of benzoic acid to phenol also yields benzene, under the action of the copper component in the catalyst system. The amount of benzene formed can be easily measured in laboratory experiments. The results are described by the zero-order reaction rate equation : Tbenzene

=

&7

=

& 7

0

X

* T

B

'

R

(H)

T

where £ = 147 kj/mole, which implies that the rate of formation is inde pendent of the copper concentration. FORMATION OF TAR 1. As shown in the reaction scheme (Figure 2), phenol formation is attended by a side reaction in which tar is formed. In bench-scale experiments (9) the phenol concentration can be kept extremely low (little formation of tar 2), with the result that the rate of tar 1 formation can be measured. The rate of tar 1 formation appears to depend on the benzoic acid consumption, the temperature, and the oxygen partial pressure. Test runs in the plant have proved the correctness of the above relations. In interpreting the experimental results, ζ in ( C H 0 ~ ) was taken equal to the average value of 0.8. To calculate the production of tar 1, the following relation was used in the model: 6

4

n

tar 1 production = o -f Οι X BZOH consumption + α Χ Τ + a · p 0

2

3

Q2

(12)

One mole of tar in the above relation means 1 mole of C H O (aromatics) incorporated in the tar. FORMATION OF TAR 2. The formation of tar in the consecutive reaction (tar 2) can be followed if the phenol concentration is increased by passing additional phenol through the reaction mixture. The kinetics of this reaction are represented by: G

4

0 8


438


-

= fee X C

(13)

p h

The activation energy of the reaction amounts to approximately 77.5 k J/mole. RING DEGRADATION. Analysis of byproducts formed both in industrial installations and in the laboratory equipment (La., carbon monoxide and diacetyl) clearly shows that aromatic rings are degraded. Since the various products could not be determined exactly, we assumed that the degradation goes as far as C 0 and H 0 (see Equation 7). The data on ring degradation were obtained by separately quantifying the amounts of tar 1 and degradation products by oxygen and benzoic acid balances, starting from the test run values. As stated above, we used a fixed value for ζ (0.8) in these calculations. How ever, another value for ζ will yield a different distribution of the amounts of tar 1 and ring degradation products in the mass balance. The sensitivity of the reaction system to this change has not been satisfactorily established; however, the consequences for the total model seem to be of secondary importance. The amount of degradation products has been correlated with the oxygen consumption and the temperature by the following equation: 2


-

II

2

ring degradation = a

Q

+ αϊ X 0

2

consumption + o Χ Γ 2

(14)

Losses. As in most processes, losses occur, and here they have been taken into account in drawing up the balances. The principal losses occur in the following sections: (1) primary oxidation (losses assumed to be constant); (2) extraction; (3) distillation (phenol). On the basis of plant experience, all these losses were determined with a fair degree of accuracy and are expressed as a fixed percentage of the phenol production. Balances. BENZOIC ACID BALANCE. Making allowance for the above men tioned reactions leading to benzoic acid consumption, as well as for the principal losses, we set up the following benzoic acid balance: ΒΖΟΗ consumption = phenol production + production of (tar 1 + tar 2) + benzene production + ring degradation + losses (15) OXYGEN BALANCE. Summation of the amounts of oxygen consumed in the various reactions (including the amount lost with the phenol losses) yields the following oxygen balance: oxygen consumption = 0.5 phenol production +0.9 (tar 1 + tar 2) + 7.5 ring degradation +0.5 phenol distillation losses

(16)

It will be evident that the effect of ring degradation manifests itself particularly in this oxygen balance. TOLUENE CONSUMPTION PER T O N OF PHENOL. A practical quantity for expressing the total efficiency of the first and second oxidation steps is the toluene consumption per ton of phenol produced. This is, in fact, the reciprocal of the overall yield or the yield of the first oxidation step multiplied by that of the second. The former yield is measured; the latter is calculated from the model. Physical Aspects of the Oxidation Reactor The chemical aspects of the process as discussed in the previous section are now considered as they relate to the physical aspects of the reactor. Inside the reactor the contacting gas and liquid flows exchange oxygen, water, phenol,


33.

439



and benzoic acid. These mass transfer processes depend partly on physical factors, partly on the chemical reaction rate. Coupling such physicochemical relations, including those for the solubility, the vapor pressure, and the residence time distributions of the gas and liquid phases, to the kinetic model yields a computer program whereby the situation in the plant reactors can be simulated. Oxygen Absorption. An important transfer relation in the process is the absorption of oxygen in the oxidation medium. The oxygen is used mainly to oxidize cuprous to cupric benzoate and must be transferred from the gas to the liquid phase. This process can be described by:


r

= K

0 2

ov

(17)

S AC

Information on this transfer process has been obtained from laboratory experi ments in which the oxygen absorption was studied in a stirred reactor (1 liter volume). The results are given below: (a) r

= Kov S po

0 2

/R Τ He (at constant V , T, and F ,o)

2

OXLT

(18)

L

S

(b) ro = α VL,O (at constant po , V , and T), 2

2

where

V

(Ν - Ν J) ^]

L)0

(c) K

ov

(19)

B

= ko Ccu+

1/2

e~ ' E

RT

(at constant S and V )

(20)

B

From these data it can be concluded that: (1) the resistance to mass transfer is controlled by the liquid phase ( K > > K " ) ; (2) mass transfer is chemi cally enhanced because Ko ( : ) C + and E = 50.4 kj/mole. It appears therefore that the oxidation reaction is in fact a film reaction in which the bulk concentration is extremely low. For such a case the value of the mass transfer coefficient can be derived from the Hatta number, which is defined as: L

V

_ 1

C u

( K o v )

1 / 2 « -ψ- ( — - - k Co2,r C + A L \n + 1

Ha = Keff/K

l

L

x

g

1 / 2

C u

\ #o ) /

1 / 2

m

2

, where K

ov

= Ku e

(21)

The chemical enhancement factor (φ) shows how much the mass transfer coefficient K is increased. It also gives the ratio between actual consumption and maximum physical mass transport: h

?* a c t

ro2, phys. max.

rθ2,

a

c

t

Kj, S Cou

(22)

If H a > 2, then Ha = φ since ^ » 10 C 02,i

(23)

The absorption of oxygen then satisfies the equation: r

02

= Φ KL S C , i = Kett S POÎA/R 02

Τ He

(24)

The effective mass transfer coefficient is proportional to the root of the copper concentration and independent of the oxygen concentration. This leads to the conclusion that in our case m and η in the Hatta number are equal to unity, so that tfeff = (ki C

and

ki — ki e~ Q

C u +

Do ) 2

1/2

, where EM ~ 2 Ε(Κον)

E,RT


(25)

440


II

It follows, therefore, that the oxidation of cuprous benzoate mentioned above is first order with respect to copper and oxygen. Since the solubility of oxygen in benzoic acid is unknown, k can be calculated only after the Henry coefficient (He) is estimated in similar system. However, in calculations regarding the plant reactor, it is enough to use the value of K / H e , and this can be derived experimentally. To calculate the 0 transfer in the plant reactor, both K and the specific interfacial area S must be known. The size of S depends mainly on the super ficial gas velocity V (no mechanical stirring). The relation between S and V is known from the literature (10, 11): 4

e f f

2

e f f

s

8

S = a Downloaded by CORNELL UNIV on October 7, 2016 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch033

0

(26)

V*

where a = 1, if the gas holdup ε < 0.3 and a ^ 1 if ε > 0.3. Further, the temperature dependence of S over a limited range is small. The interdependence of oxygen absorption and reactor variables can therefore be derived from a mass balance taken over a very small part of the reactor volume, dV (dV = FdH), on the assumption that plug flow occurs in the gas phase: ^

dpo* -

S g l l ^ FdH

-K

e{{

(27)

Further /F = V and H = height of the gas-liquid dispersion. After integrating over the height H, it follows from Equations 26 and 27 that g

g

to

Pot, out

.

a

o

(28)

Ε ϊ ψ ° 2 Η

He

We can assume that V remains approximately constant when the height is varied and that the gas holdup changes only slightly with variations in V if V > 0.3 m/sec. A good approximation of Equation 28, obtained by a regres sion analysis, reads: s

8

s

In (1 - X) = (o„ + α, Τ + a 7.) H . s

(29)

e{{

where X = 1 — ( p , out)/(p > ) ^ **eff. = effective absorption height. The sum of the terms in brackets is negative in sign. This relation enables the total oxygen consumption to be calculated within the entire range of operating conditions. It is also the basic equation needed to calculate the phenol production, which is one of the terms in the oxygen and benzoic acid balances. Phenol Stripping. The required yield is one of the factors determining the phenyl benzoate and phenol concentrations to be maintained in the reaction liquid. In adjusting the phenol concentration, the rate of transfer from the liquid to the gas phase is important. In view of the consecutive reaction which leads from phenol to tar, the bulk concentration of phenol must be kept as low as possible. The transfer process is described by: 02

02

m

a n c

t

n

e

(30)

r h = &2Cphb = KhS(Chph — C\ ) P

ph

Under the conditions prevailing in our reactor, the transfer rate K S is of the order one (sec ) (II, 12, 13). At the production rate of 0.3-1 kmole/m hr L

-1


3

33.

441


VAN DIERENDONCK ET A L .

reached in our bench-scale experiments, the driving force equals A C = C i — CL = (0.9

• 3) Χ ΙΟ" kmole/m 4

3

The difference between the concentrations in the bulk and at the interface is related to the bulk concentration by AC _

10-4

C

10"

10-

1

L


which shows that the bulk concentration may be taken approximately equal to the concentration at the interface. This also holds under the conditions in the plant reactor. Hence, the bulk concentration is related to the partial pressure as: p h = a Cp P

h

(31)

The magnitude of the proportionality constant for phenol-benzoic acid can be derived by Raoult's law, whose validity has also been demonstrated in bench-scale experiments. Hence,

p

ph

= yP

(32)

and

p

ph

= χ Pph

(33)

t

where x, y denote the mole fractions of phenol in the liquid and gas phases, respectively, and P is the vapor pressure of pure phenol. Since part of the phenol dissolves in the condensing benzoic acid, it is recycled with the latter to the evaporators and subsequently resupplied to the reactor. Thus, the phenol partial pressure is increased by a given factor (recycle parameter), which adversely affects the yield. However, the consecutive reac tion of phenol can be suppressed by leading inert gases through the reactor to lower the phenol partial pressure. Application of this principle enabled labora tory yields to be raised to ca. 90% (see Figure 4). Under plant conditions efficiency could also be improved in this way (passage of additional steam). Water Solubility. As stated above, the rate of the phenyl benzoate hy drolysis is a function of the water concentration. Like the phenol concentration, the concentration of water in the liquid is defined by the direct relation between partial pressure and bulk concentration. Therefore: p h

CH?O = a xmo = α ρ mo/Ρmo Pmo = 1/a Cmo Pmo (Raoult's law)

(34) (35)

where P = vapor pressure of pure water. Bench-scale experiments proved the validity of these relations. Thus, to achieve the required water concentration in the liquid, the partial pressure of the steam in the reactor must not be allowed to drop below a given minimum. Benzoic Acid Evaporation. Compared with the other reactants, benzoic acid is always present in excess, even if the amount bound to copper and mag nesium (in benzoate form) is disregarded. The excess benzoic acid partly comes from the first and partly from the recycle streams of the second oxidation step. Because of the smooth exchange between the gas and liquid phases, it takes little time for gas-liquid equilibrium to be established. The ultimate vapor pressure again conforms to Raoult's law provided the copper and magnesium salts, as well as the heavy tar products, are not regarded as volatile constituents. H 2 0


442


II

90-,

Ν ·

Laboratory experiments

X \

85-^

515 Κ

Δ

508 Κ

•

483 Κ

\

\ Downloaded by CORNELL UNIV on October 7, 2016 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch033

•

80- Yield (TJ ) in mole 1»

\ \

N

\

\

\ \

\

Δ

\

^

Δ \

\

75-

70-

— —

—ι—

0.1

0.2

1

Chemical yield vs. phenol concentration

Figure 4. Hence

(36)

PBZOH = x PBZOH

where FBZOH vapor pressure of pure benzoic acid. Gas Holdup. The passage of large quantities of benzoic acid vapor, air, and steam results in a high superficial gas velocity (V = $ astot./F)> limited by the entrainment factors in the condensation column and the reactor. The super ficial gas velocity ( V ) determines the magnitude of the gas holdup ( ε ) , and thus the specific interfacial area and the effective reactor volume. According to the literature, ε and V are related as follows =

g

s

s

(37)

ε = 1.2 If we allow for the reaction conditions, this relation can be simplified to e = o F 0

s

3 / 4

provided ε < 0.3

(38)

The surface tension and viscosity of this system are difficult to determine under the reaction conditions, so the magnitude of the constant in Equation 38 was calculated from measurements in the plant reactor. From the value of the gas holdup thus found, the specific interfacial area S can be estimated


33.

VAN DiERENDONCK ET AL.

443

Benzoic Acid Oxidation S « 6 β/Α

(39)

Equation 38 can be substituted in Equation 39. Since d ^ V " (10), S ~> ν · ° (see Equations 26 and 27) provided that ε < 0.3. The holdup rela tion is also used in the model to calculate the effective reactor volume ( V ) : h

β

s

1 / 4

ι

L

V


L

- (l - ) V » (l _ ) F H e

(40)

e

T

where H is the height of the gas-liquid dispersion. Residence Time Distribution of the Gas and Liquid Phases. Besides knowledge of kinetics and mass transfer, information is needed about the degree to which production rate and yield are influenced by the residence time distri bution of the gas and liquid phases. Some data on the mixing times can be found in the literature (11, 12, 14). The mixing time in the liquid phase (11) is given by t

m

« 4.7 H + 1

provided V > 0.03 m/sec

(41)

a

Applied to the liquid heights and gas velocities used in practice, Equation 41 yields a t value of 25-40 sec. Considering the mixing time in its relation to certain important reaction times in the model, the reaction time/mixing time ratio (t /t ) is around 5-100. These values are large enough to allow calcula tions for a perfectly mixed liquid phase. The mixing pattern in the gas phase must be derived from data on backmixing the gas bubbles. This backmixing is accounted for by the Péclet number—i.e., Pe = ( V H ) / ( e D ) = transport by the gas flow/transport by axial mixing. As to the magnitude of the axial mixing coefficient in the gas phase in industrial reactors, little information is available. The assumption regarding plug flow in the gas phase, which forms the basis of Equation 29, is not refuted by the outcome of the test runs done at various liquid levels in the reactor. On the other hand, under these conditions the Péclet number would have to be larger than 3, which implies that the mixing coefficient derived from it for the system discussed will have to be of m

r

m

g

mg

PARAMETERS

• P H E N O L PRODUCTION - TOLUENE CONSUMPTION

- B E N Z E N E PRODUCTION TEMPERATURE

\

\

m TAR PRODUCTION

•tc.

Figure 5.

The model

the order of 3 m /sec. Considering the observations by Towell and others (12) and the results of gas mixing experiments in fluid beds (15), this is a likely value. 2

Model and Results General. The mathematical model comprises all the previous relations combined into a system of algebraic nonlinear equations (Figure 5). Beside the numerous dependent variables in the system, five independent variables, or


444


II


degrees of freedom, can be distinguished; they are all related to operationally controlled factors and are: reactor temperature, reactor pressure, height of the gas-liquid dispersion in the reactor, air load, and steam load. In addition to these, other parameters exist which, under certain conditions, may deviate and thus must be accounted for in the computer program—e.g., the reactor diameter and the recycle characteristics. The calculation procedure comprises two iteration loops, which do not present any convergence problems. Besides the essential model equations, the program also includes several derived equations which ensure comprehensive results (e.g., partial pressures and superficial gas velocity). This brings the number of equations used in the model to approximately 50 (Fortran V ; terminal Univac 1108; calculation time: a few msec).

Figure 6.

Phenol production in tons Iday. Plant test runs performed under various conditions.

Reliability and Accuracy. In estimating the reliability of the model, two points should be taken into account: (a) the fundamental physical, technological, and chemical relations; (b) the incorporation in the model of a few regression equations based on some 20 plant measurements. Whereas point (a) affords certainty as to the reliability of the interpolations in most cases, the regression approach in (b) calls for some limitation of the range over which the extrapolations are carried out. The two most essential quantities in the process and, hence, in the model are the phenol production (tons/day) and the consumption of toluene per ton of phenol produced (kg/ton). To illustrate the accuracy obtained in the model-building stage, we have plotted the measured vs. the calculated values of the two quantities. The data were obtained from 20 selected runs and are Hulburt; Chemical Reaction Engineering—II Advances in Chemistry; American Chemical Society: Washington, DC, 1974.

33.

VAN. .DIERENDONCK ET A L .


445


Calculated

Fiant test Toluene consumption in kg I ton phenol. runs performed under various conditions.

Figure 7.

the same as those used in the model building. Beside the graphical representa tion in Figures 6 and 7, characteristic values are compiled in Table I. These indicate the accuracy of the model, both in an absolute sense and its relation Table I.

Absolute and Relative Accuracy of the Model Related to the 20 Test Runs

Description Range of data actually occurring in the plant (Am) Mean error of prediction (ε) Standard deviation of error e (σ ) (square root of variance) Relative error of prediction β

(Δ?ΤΙ ^

Phenol Production, Tons/Day 70 0.1 2.5 3.6%

Toluene Consumption per Ton Phenol, kg 200 -2 30.7 15.4%

100%)

to the intervals between the maxima and minima in production and consump tion. Recent test runs, done under more widely varied conditions, confirm the predictive quality of the model (see Figures 6 and 7; symbols + ). Results. Implemented with a cost function, the model can be used as a tool in economic optimization efforts where technological, marketing, or other constraints must be observed (efficiency optimization vs. production optimi zation). Hulburt; Chemical Reaction Engineering—II Advances in Chemistry; American Chemical Society: Washington, DC, 1974.


I

C O N S T A N T

1000 Kgs/h

— Air kgs/h

/

J 5 tons/day

I

/

phenol-production

I

|

Ν ,

JlOkgs/ton phenol

STEAM-

A

toluene-consumption

KXX)kgs/h

,

Figure 8.

Steam kgs/h

\

Β

D Ε

2

/ 1m

——Height m

Sensitivity of the model

0.2-K) N/m

5

-—Pressure N/m*

|

2.5 Κ

——-Temperature Κ

/ , / , \

c



33.



447

We examined the sensitivity of the model to changes in air or steam feed, pressure, liquid level, and temperature. An illustration of these sensitivities regarding phenol production and toluene consumption under a given opera tional condition is shown in Figure 8A-E. It is seen here that, e.g., the conse quences of a pressure rise can be largely offset by increasing the steam feed. The model has also been used to calculate process adjustments required by operational troubles (e.g., one reactor out of service) or unpredictable cir cumstances (e.g., toluene shortage). Finally, the model has been very helpful in designing a reactor extension where the reactor diameter was used as the main parameter. However, in cal culations involving a change in such an essential dimension of the process equipment, extrapolations cannot be carried too far. We obviated this hazard by fixing temperature-dependent maxima with regard to the specific oxygen consumption (kmole/m sec). These were derived from the maximum values measured in the current plant reactor. Weighing the costs of this investigation against the profits, we see that cost of the research for developing the model is returned within one year. In summary, this intensive research work has made it possible for the phenol production per reactor to be increased to 300% of the 1964 design capacity, thereby enabling the original phenol process to hold its own against the compe tition from alternative technologies, next to other cost price decreasing means. 3

'Nomenclature o, ι, 2... η general constant C concentration, kmole/m sec Cj concentration at interface, kmole/m sec C bulk concentration, kmole/m sec D diffusion coefficient, m /sec d bubble diameter, m D mixing coefficient in the gas phase, m /sec d reactor diameter, m d stirrer diameter, m È activation energy, kj/mole F cross-sectional area of the reactor, m g acceleration of gravity, m /sec H height, m a

3

3

3

L

2

b

2

mg

T

s

2

2

Ha

Hatta-number = ^ - q r y * k ·

He H k ^eff. Kg K Ko m, η η Ν N ρ Ρ P Pe r

Henry coefficient = p/R · Τ · C effective height of the gas-liquid dispersion, m reaction rate constant, k m o l e ~ / n i ~ effective mass transfer coefficient, m /sec mass transfer coefficient in gas phase, m/sec mass transfer coefficient in liquid phase, m/sec overall mass transfer coefficient, m/sec reaction order coefficient revolution number, 1 /sec minimum revolution number required for bubble dispersion, 1 /sec partial pressure, kg/m pressure of pure component, kg/m total pressure, kg/m Péclet number reaction rate, kmole/m sec

et(

L

V

0

t

·C

( 1

n )

3 ( 1

L

B

· D

n ) s e c

2

2

2

3



448 R S t Τ t t V V V V χ y ζ

2

m T

3

3

L L o

T


gas constant, k j / mole °K specific interfacial area, m / m time, sec temperature, °K mixing time, sec reaction time, sec volume of the liquid in the reactor, m effective stirrer speed, m /sec volume of the gas-liquid dispersion in the reactor, m superficial gas velocity, m /sec mole fraction in the liquid phase mole fraction in the gas phase oxygen content in the tar

II

s

Greek Letters a exponent Δ difference ε gas holdup η viscosity, Ν = Newton, Nsec/m ρ density, kg/m σ surface tension, N / m φ chemical enhancement factor gas flow rate, m /sec

3

2

3

3

g

Subscripts Β component b bubble disp dispersion eff effective g gas i interface in inlet L liquid out outlet s stirrer r reactor t total

Literature Cited 1. Reading, W. W., Lindblom, R. O., Temple, R. G., Ind. Eng. Chem. (1961) 53, 805. 2. Reading, W. W.,J.Org. Chem. (1961) 26, 3144. 3. Reading, W. W.,J.Org. Chem. (1962) 27, 3551. 4. Reading, W. W.,J.Org. Chem. (1963) 28, 1063. 5. Reading, W. W.,J.Org. Chem. (1964) 29, 2556. 6. Reading, W. W.,J.Org. Chem. (1965) 30, 3750. 7. Reading, W. W.,J.Org. Chem. (1965) 30, 3754. 8. Schoo, W., etal.,Rec. Trav. Chem. (1961) 80, 134. 9. Schoo, W., etal.,Rec. Trav. Chem. (1963) 82, 172, 954, 959. 10. van Dierendonck, L. L., Fortuin, J. M. H., Venderbos, D., 4th Europ. Symp. Chem. Reaction Eng., 1968. 11. van Dierendonck, L. L., Thesis Technical Highschool Twente, 1970. 12. Towell, G. D., Ackerman, G. H., 5th Europ. 2nd Intern. Symp. Chem. Reaction Eng., 1972. 13. van Dierendonck, L. L., 4th Chisa Congr., 1972. 14. Reith, T., Thesis Technical Highschool Delft, 1968. 15. Kunii, D., Levenspiel, O., "Fluidization Engineering," Wiley, New York, 1969. RECEIVED January 2, 1974.


Chemical Reaction EngineeringâII

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