Acknowledgment This research was sponsored by the National Aeronautics and Space Administration under Grant No. NGR 19001-016 a t Louisiana State University, and continued under RGC Grant No. 726, The University of Alabama. There support is gratefully acknowledged. Nomenclature
A = cross-sectional area ofthe char zone, cm2 = species identification code = concentration, cm3/g mol = heat capacity ofthe gas mixture, cal/g "C k,, = effective thermal conductivity of the gas mixture, cal/cm2 sec "C/cm H,,= enthalpy per unit mass of component;, cal/g K = number of gaseous species n = number of chemical reactions pi, = stoichiometric coefficients of the products y = heat flux, cal/cm2 sec q,, = heat ofpyrolysis, cal/g R, = reaction rate of component;, g mol/cm3 sec r,, = stoichiometric coefficients of the reactants T = temperature ofthe gases within the char, "C t = time, sec I ) = velocity of gases within the pores, cm/sec W , = mass flux of gases within the pores, g/cm2 sec
c,) c b
= porosity gas density, g/cm3 n = Stephan-Boltzmann constant c
cz = refers to char zone i = refers to chemical reactions j = refers to chemical species 0 = refers to initial value L = refers to final value Literature Cited April, G . C.. Ph.D. Dissertation, Louisiana State University, Baton Rouge, La., 1969. April, G. C., Pike, R . W.. del Valie, E. G . . National Aeronautics and Space Administration, Report No. NASA-CR-1903, 1971. April, G. C.. Pike, R. W.. A l A A J . , 9 (e), 11 13 (1971). del Valle, E. G . , April, G. C., Pike, R. W., Paper 13e. 62nd Annual Meeting of the AIChE. Salt Lake City, Utah, May 1967. Madorski, S. L., "Thermal Degradation of Organic Polymers," Wiley-lnterscience, New York, N. Y . . 1964. Pike, R. W., National Aeronautics and Space Administration, Working Paper No. 181, 1966. Sykes. G. F.. National Aeronautics and Space Administration, Report No. NASA TN-D-3819, 1967. Sykes, G. F., Nelson, J. B., Preprint 7b, 61st National Meeting of the AIChE, Houston, Tex., Feb 1967.
Receiued for reuieu' J u n e 19, 1972 Accepted August 2, 1973
Modeling of a Thin-Film Sulfur Trioxide Sulfonation Reactor Gary R . Johnson Chemicals Research Division. Conffnental Of1 Company. Ponca Cfry, Oklahoma 74601
and Billy L. Crynes* Scbool of Chemfcal Engineering. Oklahoma State University Sfillwater Oklahoma 74074
Thin-film sulfonation reactors are becoming more widely used in the detergent industry as a means of directly combining sulfur trioxide with organic materials. The reaction however is highly exothermic and can under certain conditions produce degradation of the product. Presented is an engineering model for predicting the longitudinal temperature and conversion profiles of the organic liquid film during its travel along the reactor tube. The model then predicts product quality under various operating conditions. Results show that a large portion of the total conversion occurs in the first few inches of the reactor length producing a maximum liquid film temperature in that region. Reactor outlet temperatures do not give a clear indication of the magnitude of the front end temperature peak. Variables such as loading, inert gas rate, cooling water temperature, and reactor diameter substantially affected the liquid film temperature profile.
Introduction The manufacture of detergents is a n interesting and highly specialized industry in the United States. At the present time the most common raw material for formulation of household detergents is linear alkylbenzene. The alkylbenzene is sulfonated with sulfur trioxide to make the sulfonic acid.
Following this, the sulfonic acid is then neutralized and mixed with other ingredients to make the final detergent. 6
Ind. Eng. Chern., Process Des. Develop., Vol. 13, No. 1 , 1974
Sulfur trioxide is a n extremely reactive compound, being a n oxidizing as well as a sulfonating agent. The sulfonation reaction rate is instantaneous and exothermic; the heat of reaction is about 900 Btu/lb of SO3 reacted. As a result liquid SO3 cannot be added directly to the organic material to be sulfonated because of safety and product degradation problems. Instead SO3 is commonly vaporized and diluted with dry air. One of the most widely used systems for reacting sulfur trioxide with organic materials is a tubular thin-film sulfonation reactor. Figure 1 illustrates a typical reactor. It consists of a vertical tube into which the organic liquid and the SO3-inert gas mixture are continuously fed. The organic liquid forms a thin-film on the inside of the tube wall, while the SOZ-inert gas mixture travels down the
ORGANIC LlOUlD THl N - F I L M
reactor are significant variables which may have a substantial effect on final product quality. The thermal history of the organic liquid being sulfonated should have an effect on degradation side reactions, higher temperatures promoting more severe oxidation and charring of the material. Yet there are no experimental data nor models of the reactor in the literature to describe temperatures and conversion profiles. This aspect of thin-film sulfonation has not been reported. The purpose of this article is to present a reactor model for thin-film SOa sulfonation of organic materials. The objective of the model is to predict the longitudinal temperature and conversion profiles of the organic liquid film in the reactor. The effects of operating variables on the temperature profiles will be shown and guidelines for lowering the liquid film temperature will be given.
PRODUCT SULFONIC ACID
Figure 1. Tubular thin-film sulfonation reactor.
center of the tube. The system is essentially an annular, two-phase parallel flow system. The so3 diffuses radially through the inert gas stream and reacts with the liquid film. Reaction heat is removed by a cooling water jacket on the outside of the reaction tube. Liquid film residence time in the tube is on the order of 1-10 sec and gas velocities are on the order of 50-300 ft/sec. The system is highly turbulent. The literature on sulfonation is replete with literally thousands of articles on the chemistry and mechanisms of S O 3 additions. From a reactor engineering standpoint, however, very little literature has appeared on thin-film sulfonation. In some respects this may be intentional due to the proprietary nature of thin-film reactor development. One of the few articles t h a t describes actual experimental tests is a paper by Hurlbert, et al. (1967a,b).This work describes the operation of a small scale thin-film sulfonation unit. It relates important process variables and reactor geometry with the properties of the final product. The complexity of the two-phase flow system dictated a n empirical approach to the investigation. In their work they found at least five variables that must be controlled in the sulfonation step in order to prepare products of the highest quality. These variables were: (1) inert gas/SOs mole ratio; (2) reactor length; (3) post-reactor residence time (aging of the product acid at its exit temperature) ; (4) reactor temperature; ( 5 ) SOa/organic mole ratio. The effect of each of these variables on conversion to organic sulfate. and on color in the final product, was studied using as feed a linear C12-C15 primary alcohol, an alcohol ethoxylate. and a linear alkylbenzene. The position where the reactor temperature was measured is not mentioned in the article. One can only assume that some sort of outlet temperature was chosen. In the earlier development stages of sulfonation, batch reaction kettles were extensively used. From the history of such sulfonators it is known that there were maximum temperature restrictions during sulfonation. It was important to keep the organic liquid in the kettle under 140150°F during the sulfonation of dodecylbenzene (Gilbert, et al., 1953). In these experiments it was found t h a t darkening became noticeable at 158-176°F. When a C12 alcohol was batch sulfated, it was important to keep the temperature under 105°F in order to obtain acceptable product quality. It therefore seems reasonable t h a t the longitudinal and even radial temperature profiles in a thin-film sulfonation
Model Development In an effort to make the thin-film model tractable, the following simplifying assumptions are made. (1) KO entrainment of liquid droplets into gas core occurs. ( 2 ) KO entrainment of gas bubbles into the liquid film occurs. ( 3 ) No vaporization of the liquid occurs. ( 4 ) No condensation of the SO3 occurs. ( 5 ) Entrance effects are neglected. (6) The mass transfer of SO3 is entirely controlled by the radial transport of SOa in the gas film. The model then is in fact a special case of Danckwerts' solution (Danckwerts, 1970) for the two-film model of gas absorption followed by instantaneous. irreversible reaction with a dissolved solute. Specifically, the turbulence of the liquid phase is very high and is sufficient to transport fresh liquid reactant to the interface at a much faster rate than the reacting gas can be transported to the interface. The liquid side is starved and the resistance to mass transfer in the gas side is entirely controlling. The limiting rate is the rate at which SO3 can be supplied to the liquid interface. A detailed discussion of these assumptions is found elsewhere (Johnson, 1971). As a basis for the discussion of thin-film sulfonation, Figure 2 will be used. In this diagram all feed materials for the reaction are injected into the top of the tube. The organic liquid is distributed as a thin film on the inside surface of the reactor tube. Vaporized SOs, diluted with dry air, is injected into the top of the tube and the SO3air stream occupies the center core of the tube. Sormal injection pressures are 5-20 psig. The SO3 diffuses radially from the center of the tube to the liquid-gas interface. At the interface there is an instantaneous reaction of the SO3 with the organic liquid to form the sulfonic acid. The heat of reaction must be removed to prevent degradation of the product. This is accomplished by transferring and distributing the reaction heat into three fluids. (1) A portion of the heat of reaction is transferred through the liquid-film and through the reactor wall into the cooling water. (2) Another portion of the heat of reaction is transferred into the moving gas stream and raises the temperature of the gases. (3) A third portion of the heat of reaction raises the temperature of the liquid film. These three statements in essence describe the heart of the model. The length of the tube is divided up into small segments; on Figure 2 the segment length is 1 in. A comprehensive mass and energy balance is performed on the 1-in. segment and the outputs from these calculations are used as inputs for the second 1-in. segment. Mass and energy balances are then performed on the second segment and so on down the tube. The physical properties of the materials as well as the radial heat and mass transfer rates are assumed constant in each segment, hut are adjusted for the next segment according to the output temperatures Ind. Eng. Chem., Process Des. Develop., Vol. 13,No. 1, 1974
the reactor; and czce versa, small changes in the 20 inputs did not significantly affect the temperature and conversion profiles in the tube. The cooling water temperature was held constant for simplicity in programming. Equations Used in t h e Model The equations incorporated in the model are listed in the order used. A brief discussion follows. SO3 Mass Transfer Coefficient.
Liquid Film Heat Transfer Coefficient.
Gas S t r e a m Heat Transfer Coefficient. Figure 2. Illustration of the symbols used in the segmented heat and mass balance.
and mass flow from each previous segment. Practically speaking this requires the segment length to range from 0.1 to 2.0 in. and the number of calculations are best handled on a computer.
Wall Area of One Segment
I n p u t Data T o use the model, the following input data or quantities must be known or available. Reactor Dimensions a n d Properties. U = reactor tube inside diameter, in. FZ = reactor tube wall thickness, in. L = reactor tube length, ft K , = reactor tube thermal conductivity, Btu/(hr ft2 OF,' ft ) Reactor Operating Variables. W , = organic liquid feed rate, lbjhr J = sulfur trioxide feed rate, Ib/hr S = air rate. standard ft3/min P = average total reactor pressure, psig t,.1 = organic liquid feed temperature. "F tg,l = total gas feed temperature, "F t , = average cooling water temperature, O F Physical Property D a t a . A H L , = heat of reaction, Btujlb of SO3 h, = cooling water heat transfer coefficient. Btu/hr ft2
"F ho = cooling water side fouling coefficient. B t u j h r ft2 "F h r = reaction side fouling coefficient, Btu/hr ft2 "F p g = average viscosity of total gas stream, CP p g = average density of total gas stream, lb/ft3 I?, = average thermal conductivity of total gas stream, Btu/hr ft2 "Fift C , = average heat capacity of total gas stream, Btu/lb "F Z),. = average diffusivity of SOs-air system, ft2/hr pI. = average density of the liquid in the film?lb/ft3 I?,, = average thermal conductivity of the liquid in the film, Btu/hr ft2 "F/ft C , , = average heat capacity of the liquid in the film, Btu/lb "F Calculation Variable. SI = number of segments into which the tube length is divided. There are 24 input quantities in the computer model. Of these 24 inputs, 20 inputs remain constant along the tube length. Four inputs are revised as the calculation proceeds down the tube. These are (1) liquid film flow rate, ( 2 ) total gas flow rate. (3) liquid film temperature, ( 4 ) total gas temperature. Twenty inputs were left constant because it was found that their values were not significantly affected by the temperature and pressure changes normally calculated in 8
Ind. Eng. Chern., Process Des. Develop., Vol. 13, No. 1, 1974
R a t e of Radial SO3 Transfer Across the Gas-Liquid Interface in One Segment.
li(AP,, l b m o l / h r
where P, is the SO3 partial pressure in the segment, atm. R a t e of Heat Generation in a Segment.
Q L = (80.06)AHIS,. R t u / h r
R a t e of Radial Heat Transfer into the Gas Core in a Segment.
h m A ( t!,+ - f,! ) . R t u l h r
t a , l - l must be assumed. New Temperature of Gas Section a t Exit from Segment.
Overall Heat Transfer Coefficient between Cooling Water a n d Liquid Film Bulk Temperature.
B t u j h r ft'"F (9) Overall Heat Transfer Coefficient Used to Calculate Inside Wall Temperature.
. Btu/hrft!"F (10) hi R a t e of Radial Heat Transfer into Cooling Water. C,
Qc = U,Ait,, ,+, -
tL), B t u j h r
Inside Wall Temperature. t,, = ( Q j C , A )
Gas Liquid Interfacial Temperature.
: ' t , , + ] - t,,."F
R a t e of Heat I n p u t into the Liquid Film. Q1
Q\ - Q,
QL, B t u / h r
Exit Bulk Temperature of Liquid Film from the Segment.
t a , L + lwas assumed in eq 7 . If t a , i + l calculated from eq 15 equals t,i,r+lassumed in eq 7. then calculations continue through the remaining equations. If not, a new ta,i+l is assumed in eq 7 and calculations continue through eq 15 until convergence. Then proceed to eq 16. New Liquid Film Flow for the Next Segment.
W , ,+,
+ 80.06S,,l b j h r
New G a s Flow R a t e for the Next Segment. Mole P e r Cent Conversion in a Segment.
Cumulative Mole P e r Cent Conversion.
P u r e O r g a n i c Liquid Viscosity T e m p e r a t u r e F u n c tion. p , = 0.0103194 e ~ p ( 3 4 8 1 . ; / ( t , ~ , ,f+ ,460)).
P u r e Sulfonic Acid Viscosity T e m p e r a t u r e Function.
p? = (2.29282 X lo-;) e ~ p ( 1 1 , 9 5 8 . 2 / ( t , , . , + ~460)). CP
(21) Liquid Mixture Viscosity Function. In i p n , ) = ( 1 - X ) In ( p l )
In ( p 2 ) ! CP
Equation 1 is a modification of the empirical correlation of Gilliland and Sherwood (1934) for calculating the mass transfer of vapors in a gas stream flowing through a tube. The Gilliland and Sherwood correlation is based on the vaporization of several different liquids into an air stream flowing through a wetted wall column; the gas side resistance to mass transfer was entirely controlling. The equation has been found generally reliable over the range of Reynolds numbers from 2000 to 35,000, Schmidt numbers from 0.6 to 2.5, and pressures from 0.1 to 3 a t m . The Reynolds number is based on the gas velocity relative to the pipe. Equation 1 is used to calculate the radial mass transfer coefficient of SO3 in the gas phase. Equation 2 is a correlation of Davis and David (1964). The equation correlates purely convective heat transfer within an average absolute error of 6-1770 over a wide range of tube sizes, flow rates, pressures, and heat fluxes. The equation is based on steam-water and air-water data and generally corresponds to the annular or mist-annular flow condition. Equation 3 is a modification of the standard Nusselttype equation used to predict heat transfer coefficients for fluids moving through pipes at Reynolds numbers greater than 10,000. This equation is used to predict the rate of heat transfer from the liquid film into the gas core. The 22 equations are in general solved in the order presented for each successive longitudinal segment of the reactor. In the first segment the first four equations can be calculated directly with the input reactor data. To use eq 5, the SO3 partial pressure is first needed. In this model the partial pressure of SO3 was obtained by multiplying the mole fraction of SO3 in the gas stream times the average total pressure. P, = k;o,,P. Equation 7 requires the assumption of the outlet liquid bulk temperature from tke segment. As a first guess the inlet liquid bulk temperature to the segment may be used. The gas-liquid interfacial temperature is calculated in eq 13 and is based on the assumption that the bulk liquid film temperature is a n arithmetic average of the inside tube wall temperature and the gas-liquid interfacial temperature. The gas-liquid interfacial temperature has no
direct use in calculating heat transfer in this model but is calculated to illustrate its magnitude. Oxidation side reactions would be most severe at the highest temperatures in the reactor and this temperature is at the gas-liquid interface due to the instantaneous reaction rate. Equation 14 is a heat rate statement. Heat from the reaction is transferred into three fluids: cooling water. the gas stream, and the liquid film. If the correct guess for t H , , - l was made in eq 7 . eq 15 will give the same temperature. The quantity t c i . ! - l is updated on each successive iteration on a 0.l"F step. Convergence is very fast on a computer. Equations 16 and 17 are mass balances t u adjust the flow rates of liquid and gas for the next section. Equation 18 calculates the mole per cent conversion in one segment. Since the reaction rate is instantaneous this model assumes that all SO3 transferred across the gas-liquid interface is immediately converted into sulfonic acid. Conversion in a single liquid segment is the rate of SO3 transferred to that liquid segment divided by the SO3 inlet feed rate to the reactor. Equations 20-22 are means of providing a liquid film viscosity which is a function of both conversion and bulk liquid temperature. Equation,20 is a curve fit for pure tridecylbenzene and eq 21 is a curve fit for pure tridecylbenzenesulfonic acid. Viscosity--temperature data for these two compounds can be found elsewhere (Johnson, 1971). After eq 22 is calculated. the 4 revised quantities. the liquid mixture viscosity, and the 20 constant quantities are then used in the next segment. Equations 1-22 are calculated for every segment. This process continues down the tube length until the reactor outlet is reaxhed. The output from this model shows the following longitudinal tube profiles: (1) bulk liquid film temperature, ( 2 ) . gasliquid interfacial temperature, ( 3 ) bulk gas stream temperature, ( 4 ) mole per cent conversion. To show the effect of the segment length on the model stability the program was run at both a 1.0 and 0.1 in. length segment using typical operating conditions. Table I presents the results of these two runs. These results show good stability when changing the segment size from 1.0 to 0.1 in. Model Results This section presents the results of applying the model to a single tube in a thin-film sulfonation reactor. Temperature and conversion profiles for a standard sulfonation run using typical input data are shown and the importance of heat transfer to the cooling water and gas core is presented. Following this all the major operating parameters of the model are singularly varied one at a time. This kind of flexing of the model shows the options that a plant or design engineer would have at his disposal t o modify the thermal history and thus the quality of the final product. S t a n d a r d SulfonaLion Run. In order to have a common or standard basis for comparison, an appropriate set of input conditions were fed into the program to yield a standard sulfonation run. The input data were not necessarily optimum but were within the range of standard practice. The standard run input data are shown in the Table 11. The graph shown in Figure 3 illustrates the temperature and conversion profiles along the reactor length for the standard run. Conversion is typically very rapid a t the tube inlet but quickly decreases in the latter half of the tube. About 50% of total conversion occurred in the first 1.5 ft of the tube. Quite significantly, this also placed 5070 of the total reaction heat in the first 1.5 ft of the tube and caused the bulk liquid temperature and the gas-liquid inInd. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
Table I. Effect of Segment Length on Model Stability Bulk liquid temp,
Distance from reactor inlet, in. 1
12 120 I
Mol % conversion
Bulk gas temp, "F
Segment 1 0 in.
Segment 0 1 in.
Segment 1 0 in.
Segment 0 1 in.
Segment 1 . 0 in.
S9gment 0 . 1 in.
99.84 147.30 104.84
100.00 113,64 111.76
99.68 114.39 111.82
3.853 37.595 99.102
3.788 37,077 99.025
147.51 104,97 I
S O 3 SULFONATION OF TRIOECYLBENZENE 0 6 2 inches TUBE I D
S O 3 SULFONATION OF TRIOECYLBENZENE TUBE I D 0 6 2 inches AIR RATE 20 SCFM PRESSURE 6 PSIP MOLE RATIOI 0 5 SO3 I LIQUID LlOUlD FEED RATE-I008 Iblhr-in-cir COOLING WATER TEMP 80 'F
AIR RATE 2 0 SCFM PRESSURE 6 Dsig MOLE RATIOI 0 5 S O 3 I LIQUID I b l h r - i n -cir LIQUID FEED RATE--1008 COOLING WATER TEMP8 0 'F
HEAT TRANSFER TO COOLING WATER -0.0
GAS CORE -0.0
REACTOR L E N G T H , FEET
Q a ,b
Figure 3. Standard sulfonation run.
3 4 5 6 7 8 REACTOR L E N G T H , FEET
Figure 1. Comparison of heat transfer effects.
Table 11. Standard Sulfonation Run Input Data Reactor i.d., in. Reactor length, ft Tridecylbenzene feed rate, lb hr in. circumference Reactor material of construction, stainless steel SOa tridecylbenzene mole ratio Air rate, standard ft3 min Reactor pressure, psig Inlet liquid temperature, O F Inlet gas temperature, "F Cooling water temperature, O F
0 62 10
10 08 316 1 05 20 6 0
80 100 80
terfacial temperature to peak in this region. There is a rather large rate of heat generation in the first section of the reactor and all of it originates in the liquid film. One must recognize that this sizable heat release in the front portion of the reactor is a result of one basic assumption of the model-instantaneous reaction of SO3. Beyond this then, the relative rates of diffusion of SO3 to the liquid interface and the rate at which heat can be transferred dictate the magnitude of temperature peaking in the front section of the reactor. The reliability of such temperature peaking in the model relative to those temperature profiles of laboratory, pilot, and commercial reactors depends, of course. upon how representative this assumed model is of those transfer and reactive phenomena that actually occur. If, in fact, the reaction is not instantaneous and a reaction zone exists within the liquid near the interface, then less severe temperature peaking could be possible. Interestingly enough, the bulk pas temperature did not rise rapidly a t the reactor inlet. On a mass flow rate basis, air is by far the greatest quantity entering the reactor. Over half of the heat generated in the front end of the tube was transferred into the gas core. but a comparatively large mass flow rate caused its temperature to rise 10
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
much less than the liquid film. The gas stream absorbs reaction heat in the first 4 ft of the tube, but in the latter 6 ft, it unloads about two-thirds of this heat gain back into the liquid film and the cooling water. Thus in the front of the tube the inert gas is helpful in reducing the liquid film temperature but is deterimental in this respect in the latter half of the tube. Heat Transfer to the Cooling Water and the Gas Core. The direction and magnitude of heat transfer in a thin-film sulfonation reactor is vital to product quality. In Figure 4 a graphical plot of various heat transfer effects is shown. Two hypothetical cases are demonstrated where heat transfer to the cooling water and to the gas core are each set a t zero. Note the disastrous effect of allowing no heat transfer into the cooling water. The liquid film quickly rose to 263°F and leveled off. By contrast when heat transfer to the gas core was set at zero the liquid film only rose to 162°F and then gradually dropped back. In most cases, therefore, heat transfer into the cooling water is the more important mechanism for liquid film heat removal. Though not shown, when both the heat transfer to the cooling water and the gas core were set at zero (the liquid film was sulfonated adiabatically) the liquid outlet temperature was 608°F. This represents the adiabatic reaction temperature when pure so3 is allowed to react with tridecylbenzene and no carrier air stream is used. The product would be a black mass of charred material. Liquid Feed Loading Effect. Liquid and SO3 feed rates are operating parameters commonly varied in a sulfonation plant. Figure 5 shows the effect of changing the liquid and SO3 rates to the reactor. (Both the liquid and so3 rates were changed by the same proportional amount so that a 1.05 mol ratio of SO3 to liquid was maintained.) The middle curve is the standard run. Note that doubling
2 SO3 SULFONATION OF TRIDECYLBENZENE
PRESSURE MOLE RATIO
I 0 5 SO, /LIOUID
TUBE I D 062 i n c k PRESSURE 6 v w MOLE RATIO ___ I 0 5 SO3lLIOUID LlOUlD FEED RATED O 8 lblhr-!n-cir COOLING WATER TEMP80 'F
LIQUID FEED RATE
1 1 i
REACTOR LENGTH, FEET
Figure 5. Liquid feed rate effect.
the rate of the reactants increased the peak temperature from 147 to 185°F and moved the peak about 0.5 ft farther along the tube. Since higher reaction film temperatures normally produce more product degradation, increasing the loading on the reactor tends to produce a poorer quality product. As shown in Figure 5 , doubling the liquid reactant loading only increased the outlet film temperature by 15°F. Merely monitoring reactor outlet temperatures does not give a clear picture of the magnitude of temperature peaking inside the reactor. Air R a t e Effect. The air rate to a sulfonating reactor is not usually varied during normal plant operation. Typically the air rate is set at 100% capacity because it is commonly thought that this procedure will yield the best product. Figure 6 shows the effect of air rate on the liquid film temperature profile. Note that the SO3 and liquid feed rates remained unchanged. Decreasing the air rate from 20 scfm ( t h e standard run) to 10 scfm raised the peak temperature from 147 to 173°F and increased the outlet temperature from 105 to 112°F. The two main reasons for the peak temperature increase are (1) decreased volume of air and thus loss of some of the heat sink capability of the gas core and ( 2 ) most important, a 50% decrease in the liquid film heat transfer coefficient due to a substantial loss of gas flow shear rate on the liquid film. The increased concentration of SO3 due to the decrease in air rate did not, however, produce a large change in the conversion profile along the tube length. For example, at 12 in. down the tube length. 10 scfm air rate gave 41% conversion compared to 3870 at 20 scfm. So far we have discussed varying the liquid feed rate and the air rate separately. Table I11 shows the effect of simultaneously doubling the liquid. SO3. and air rate. It is a rather surprising result. If pressure drop and liquid entrainment into the gas core are not severe problems. substantial increases in plant production are possible if the air rate is increased proportionally to the feed rate of the reactants. Note that doubling all of the feeds to the reactor only produced an 11°F higher liquid peak temperature and only a 0.6% drop in conversion. Cooling Water T e m p e r a t u r e Effect. Probably the most commonly altered variable in a sulfonation plant is the reactor cooling water temperature. If something goes wrong with the product quality, plant operators normally
REACTOR LENGTH, FEET
Figure 6 . Air rate effect
S o 3 SULFONATION OF TRIOECYLBENZENE TUBE I O ___ 0 62 inches A I R RATE PRESSURE MOLE RATIO ____ I 0 5 SO, / LIOUID LIOUIO FEED RATE D O 8 IbIhi-In-cir
3 4 5 6 7 8 REACTOR L E N G T H , FEET
Figure 7 . ('ooling water temperature effect.
Table 111. EfTect of Doubling t h e L i q u i d , Sod and Air Rates o n Film T e m p e r a t u i e s a n d C'onveisions
________ Film tern pei a t ure,
Distance om tube inlet, ft
_______ 145 7 3 158 1 134 8 112
0 5 1 0
140 147 126 104
21 37 90 99
G 5 1
18 9 34 2 87 6 98 5
check the mole ratio of SO3 to organic first and secondly. the cooling water temperature. Figure 'ishows the effect of cooling water temperature on the liquid film temperature profile. Note that dropping the cooling water temperature t o 50°F dropped the liquid peak temperature from Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1 , 1974
SULFONATION OF TRIDECYLBENZENE
PRESSURE 6 MOLE RATIO I05 LIQUID FEED RATE 008 COOLING WATER TEMP80
M lLlQUlD lbi%r-!n-ctr
a 4 ; A c ; REACTOR L E N G T H , FEET
S O 3 SULFONATION OF TRIDECYLBENZENE
20 AIR RATE PRESSURE 6 MOLE RATIO I 05 LlPUlD FEED RATE-I008 COOLING WATER TEMP80
SCFM Psl(J I LIQUID IbIhr-in-ctr
REACTOR LENGTH , FEET
Figure 8. Tube diameter-temperature effect.
Figure 9. Tube diameter-cnnversion effect.
147 to 131°F. Thus as one would expect lowering the cooling water temperature will lower the film temperature and improve product color. This variable however is not a panacea for all the reactor ills. Many organic liquids have a freezing point limitation and decreasing the cooling water temperature will solidify the organic material on the inside walls of the reactor where they will severely char and plug the unit. Tube Diameter Effect Under Constant Liquid Loading. The diameter of the reactor tube had a rather surprising effect on the temperature profile as shown in Figure 8. Changes in reactor tube diameter under constant liquid loading, in fact, introduce more than one effect. Not only is the diameter changed, but the partial pressure of SO3 changes also. Since the reaction is assumed to be instantaneous, then this partial pressure does not have a kinetic effect but rather it has a lesser effect on the mass transfer coefficient, eq 1 and, of course, shows up as a change in the mass transfer driving force, eq 5 . In studying the diameter effect the liquid feed loading was held constant at 10.08 lb/hr in. tube circumference and the SOs feed loading was held a t 3.26 lb/hr in. tube circumference. Tube air mass velocity was held constant at 43,810 lb/hr ft2. Decreasing the tube diameter from 0.81 to 0.21 in. increased the peak temperature from 136 to 216°F and yet decreased the outlet temperature from 109 to 87°F. This is a large increase in the temperature peak in the tube. The reason for this effect is shown in Figure 9. Note t h a t decreasing the tube diameter from 0.81 to 0.21 in. increased total conversion from 97 to 100% but more importantly this change in diameter increased the conversion in the first 12 in. from 29 to 83%. The high rate of conversion in the front end of the smaller diameter tube caused the higher peak temperature. The reasons for the higher peak temperature in the smaller tube are (1) higher partial pressure of SO3 (Note t h a t when the air velocity was held constant and tube diameter was decreased the ratio of air to liquid dropped.) and (2) a higher mass transfer coefficient due to the diameter effect in Gilliland’s correlation, eq 1. Most sulfonation plants normally operate a small ( 5 m m ) diameter glass laboratory sulfonation reactor and commonly make changes in the plant reactor based on the
laboratory data. Figures 8 and 9 clearly show that the temperature profiles in a plant reactor and a laboratory reactor may bear little resemblance to each other. Note that the temperature measurement of the outlet of a small diameter tube is totally misleading, for although the smaller diameter tube gave a lower outlet temperature, the internal peak temperature is much higher. Liquid Viscosity Effects. During the travel of the liquid film down the tube length its viscosity is continually changing. In the case of tridecylbenzene sulfonation this viscosity change is due both to conversion and temperature changes in the liquid film. Due to the sizeable effect the liquid viscosity can have on the temperature profile, building a viscosity-temperature conversion function into the model gave a much more realistic physical property basis for heat transfer calculations. These results are available elsewhere (Johnson, 1971). Comparison of the Model with Experimental Results. Although experimental data on thin-film sulfonation reactors are limited, a few results are presented in patents and other sources. Table IV compares reported experimental results with the model results. Appropriate physical property data were used for the various organic liquids sulfonated or sulfated. Considering the wide range of organic materials, reactor sizes, and feed rates used, the model does a good job of predicting outlet temperatures and conversions.
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
Conclusions The purpose of this article was to present a reactor model for thin-film sulfonation of organic materials. The objectives of modeling were to predict the longitudinal temperature and conversion profiles of the organic liquid film in a tubular reactor. The effects of operating variables on temperature profiles were shown as a means of improving product quality. As a result of this study the following conclusions are made. (1) The model represents experimental reactor outlet data well considering the broad range of organic materials, reactor dimensions, and input data covered. (2) Temperature measurement made only at the reactor outlet will not give a clear indication of the magnitude of temperature peaking inside the reactor.
Table IV. A Comparison of Experimental Data with Model Results
Reactor i.d., in.
Dodecylbenzene Lauryl alcohol a-olefin C l r a-olefin Alcohol ethoxylate Alcohol ethoxylate Alcohol ethoxylate
0.43 0.43 1.0 0.9 0.1968 0.1968 0,1968
6.0 6.0 22.0 6.0
Organic liquid feed rate, lb 'hr
feed rate, lb /hr
Air rate, scfm
4.0 2.0 17.8 8.34 0.362 0.362 0.362
Total gas feed temp,
Knaggs (1965) Knaggs 11965) Derrig (1967) Jacobsen (1970) Hurlbert (1967a,b) Hurlbert 11967a,b) Hurlbert (1967a,b)
Organic liquid feed
80 85 80 80 80 80 80
0 0 0 0 0 0 0
Reported experimental results ~~-
Reference Knaggs (1965) Knaggs (1965) Derng 11967) Jacobsen 11970) Hurlbert t1967a,b) Hurlbert (1967a,b) Hurlbert t1967a,b)
11.72 5.03 43.66 19.5 1.51 1.51 1.51
66 77 62 80 80
0 0 0
80 0 80 0
35.0 1.0 1.0
117.5 117.5 105.0 80.0 122.0 122.0 122.0
Reactor pressure, usia
Outlet liquid temp, "F
Outlet conversion, mol %
Outlet liquid temp, "F
Outlet conversion, mol %
6 0 6 0 6 0 4-7
138 94.1 86.0 95
98-99 97-98 97-98 85.0 95.0 97.4 98.8
144.2 83.1 86.9 117.3 127.8 110.1 98.7
99.5 99.5 99.7 84.66 88.7 96.2 98.7
6 0 6 0
(3) The model shows t h a t a large portion of the total conversion occurs in the first few inches o f t h e tube length producing a maximum liquid film temperature in this region. (4) Although heat transfer from the liquid film into the gas core is substantial, heat transfer from the liquid film into the cooling water is the more effective mechanism for supressing the liquid film temperature rise. ( 5 ) Reducing the reactants loading in certain ranges will improve product quality. (6) Increasing the air rate in certain ranges will improve product quality. ( 7 ) If pressure drop and liquid entrainment into the gas core will not become a severe problem, substantial increases in plant production are possible if the air rate is increased proportionally to the reactant rates. (8) Reducing the cooling water temperature will reduce the liquid film temperature. (9) Under conditions of equal reactant loadings per tube circumference and equal air velocities, small diameter reactors give much higher liquid film temperature peaks than large diameter reactors. Conversion also occurs in a much shorter length in a small diameter reactor than in a large diameter reactor. (10) When sulfonating a detergent alkylate, the viscosit y of the liquid film is low in the front end of the reactor but increases substantially in the latter end of the tube. Liquid film viscosity is the only physical property which changes radically during the sulfonation reaction and must be varied accordingly in the model to give representative results. (11) Other variables produce a minor effect on product quality. These are (1) liquid feed temperature, (2) inlet gas temperature, and (3) total reactor pressure. Details are available (Johnson, 1971). (12) One of the limitations of the present model is the lack of experimental temperature and conversion profile data inside the reactor to support the model's predictions. On the other hand the results of the model point to the need for careful experimental determinations of the internal temperature and conversion profiles as a means of correlating product quality; reaction outlet data will not provide this.
Thin-film sulfonation is a very complex two-phase reaction system containing many nonlinear relationships with operating variables. The model presented is an attempt to show how these variables affect temperature and conversion profiles inside the reactor and their product quality. The model can also be a useful design tool in showing scale-up phenomenon, especially the diameter effect. From a pilot research standpoint the model is very useful in predicting product quality in a commercial reactor based on actual data from a small bench scale reactor. Since a number of commercial thin-film reactors are actually large annulus units and not multitube systems, future work on this model to adapt it to an annulus system might be beneficial.
Nomenclature A = gas-liquid interfacial area in a given segment, ft2 A , = inside wall area of the tube, ft2 A,, = outside wall area of the tube, ft2 A, = average wall area of the tube, ft2 GL1 = superficial molar mass velocity of the gas stream, Ib mol/hr ft2 Gt = total gas and liquid mass velocity, lb/hr ft2 h, = heat transfer coefficient for heat transfer from liquid film to gas core, B t u / h r ft2 "F hl, = heat transfer coefficient for heat transfer from liquid film into cooling water, B t u / h r ft2 "F h,, = heat transfer coefficient for tube wall, Btu/hr ft2 "F h,; = mass transfer coefficient for SO3 in gas stream, lb mol/hr ft2 a t m Pl, = log mean of inert gas pressures at the gas film boundaries, a t m P, = partial pressure of SO3 in the gas stream, a t m Pi = partial pressure of SO3 at the gas-liquid interface, atm Qc = rate of heat transfer into the cooling water in a segment, Btu/hr Q, = rate of heat transfer into the gas core in a segment, Btu/hr 41 = rate of heat transfer into the liquid film in a segment, Btu/hr 8, = rate of heat generation due to reaction in a segment, Btu/hr Re = Reynolds number of a stream, dimensionless S;, = rate of S O 3 transferred into the liquid film in a segment, lb mol/hr Ind. Eng. Chem., Process
Des. Develop.,Vol. 13, No. 1, 1974 13
= segment length. in. f , = gas-liquid interfacial temperature.
t , = inside tube wall temperature, "F L', = overall heat transfer coefficient between liquid film and the cooling water, Btu/hr ft2 "F LTx = overall heat transfer coefficient used to calculate the inside wall temperature, Btu/hr ft2 O F W , = gas flow rate, Ih/hr X = gas mass fraction X = mole per cent conversion Y,O3 = mole fraction of SO3 in gas stream tridecylbenzene viscosity, CP pp tridecylbenzenesulfonic acid viscosity, c P pm = a mixture of p1 and p z , c P PI, = liquid film viscosity. c P
Danckwerts, P. V., "Gas-Liquid Reactions," McGraw-Hill, New York, N. Y., 1970, p 148. Davis, E. J.. David, M. M . , Ind. Eng. Chem., fundarn., 3, 11 1 (1964). Derrig, M. J., Gulf Oil Company Sales Department Brochure, March 3, 1967. Gilbert. E. E., Veldhuis. B., Carlson, E. J., Giolito, S. L., Ind. Eng. Chem.. 45,2070 (1953). Gilliland, E. R., Sherwood, T. K., Ind. Eng. Chem., 26, 516 (1934). Hurjbert. R. C., Knott, R. F., Cheney, H. A , , Soap Chem. Spec., 122, 248 (May 1967a). Hurlbert, R . C.. Knott, R. F., Cheney. H. A . , Soap Chem. Spec., 88, 100 (June 1967b). Jacobsen, R. L., Ohren, T. H., U.S. Patent, 3,531,518 (Sept29, 1970). Johnson, G. R., M.S. Thesis, School of Chemical Engineering, Oklahoma State University, July, 1971 Knaggs, E. A , , etal., U.S. Patent, 3,169,142 (Feb 9, 1965).
1 = inlet to a segment 2 = outlet from a segment
Received for review September 25, 1972 Accepted August 6 , 1973
Simultaneous Absorption and Chemical Reaction of Butenes Daniel L. Shaffer, Jennings H. Jones, and Thomas E. Daubert" Departmenl of Chemical Engineering, The Pennsylvania State University. University Park, Pennsylvania 16802
Absorption of gaseous isobutylene and 1-butene in 70% trifluoroacetic acid was studied at conditions of industrial significance in small stirred cell and packed column absorbers. Isobutylene absorption rates in the aqueous perfluoro acid conformed to film and penetration theory predictions for absorption accompanied by fast, pseudo-first-order chemical reaction. Depending upon temperature, solute partial pressure, and liquid agitation the presence of this chemical reaction yielded an absorption rate enhancement factor of 30 to 100 relative to the nonreactive 1-butene. Stirred cell experiments yielded specific absorption rates which, when applied to packed column absorption measurements, produced the important design parameter of interfacial contact area effective for mass transfer.
1nt.roduction Operations such as thermal and catalytic cracking produce quantities of isobutylene mixed with other closeboiling Cq olefins and paraffins. The separation of isobutylene from these complex mixtures is normally accomplished by a n absorption-chemical reaction scheme, frequently liquid-liquid extraction with aqueous sulfuric acid. Nonreactive paraffins and secondary olefins are present in the extract only a t very dilute concentrations because of their low solubility in the acid phase. Sulfuric acid processes generally require dilution of the extract phase before isobutylene regeneration to avoid polymerization and subsequently require reconcentration of the acid for recycle to the extractor. Previous work (Fenske and Jones, 1956; Robin, 1967) showed that 70% trifluoroacetic acid reacts preferentially with gaseous isobutylene in a Cq mixture to yield the ester trrt-butyl trifluoroacetate and tert-butyl alcohol. Isobutylene could be regenerated from the acid with heat, requiring no dilution to suppress polymerization. These gasliquid absorptions were performed batch-wise with no a t tempt at a continuous contacting scheme. Knowledge of the absorption-reaction mechanism and effects of critical processing variables must be obtained before a continuous process can be evaluated and designed. The goal of the present work (Shaffer. 1971) was the experimental confirmation of a quantitative model of absorption and reaction 14
Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 1, 1974
of gaseous isobutylene in 70% trifluoroacetic acid that incorporates the combined effects of critical system variables and establishes a basis for process design. Absorption-Reaction Model The carbonium ion type reaction of isobutylene and 70 wt 90 aqueous trifluoroacetic acid to form tert-butyl trifluoroacetate can be considered to be essentially irreversible at the 25" temperature used throughout this study. Above 50" the equilibrium shifts and this assumption cannot be made. The fundamental relations governing simultaneous diffusion and chemical reaction of a dissolved species have been reviewed by Danckwerts (1970). For one-dimensional diffusion of a single species with diffusivity independent of concentration $a
D.4= ax? at
The reaction rate term r , is generally a function of solute concentration and of one or more liquid reactant concentrations. If these reactant concentrations vary appreciably, continuity equations for each reactant must be solved simultaneously with eq 1 to obtain the solute concentration profile. However, when the liquid reactants are present in great excess relative to a sparingly soluble dissolving solute, their concentrations can be "lumped" with the second-order reaction rate constant to yield a pseudo-first-