1066
Ind. Eng. Chem. Res. 1993,32, 1066-1070
Kinetic Study of Naphthalene Sulfonation Reaction Salwa Hawash,’ Nahed Kamal, Guzine El-Diwani, and Sherif Eissa Chemical Engineering and Pilot Plant Department, National Research Centre, Dokki, Cairo, Egypt
Sayed Sherif Faculty of Engineering, Cairo University, Cairo, Egypt
This study represents a mathematical procedure for the kinetic analysis of naphthalene sulfonation using sulfuric acid a t molar ratios ranging from 0.7 to 1.5 and reaction temperatures from 115 to 180 O C . The overall sulfonation comprises many consecutive, parallel, and reversible reactions. Representative samples of the reaction mixture are analyzed by high-performance liquid chromatography for quantitative evaluation of the sulfonic acid isomers produced and by alkalimetric determination of acidity. The model suggested includes the concentration of the five components in the reaction mixture, considering five reactions. The kinetic parameters for these reactions are estimated for “best fit” of the experimental data by the weighted least squares method based on minimizing the deviation between measured data and those calculated according to the model. This model describes fairly well the process kinetic through the evaluated parameters. It is observed from the results that, with respect to the yield of the target (@-sulfonicacid), the optimum reaction temperature is 170 O C for equimolar acid to naphthalene ratio. 1. Introduction
Table I. List of Compound Symbols and Chemical Formulas of Compounds
The aim of this work is to study the production of the 8-sulfonic acid which by its condensation with formaldehyde is used as a cement additive to improve the concrete properties (Hattori, 1979;ACI, Manual 1973. The naphthalene sulfonation technique is known, but there is still a lack in chemical engineering data for the process description and design concerning the different sulfonic acid isomers produced. The reaction conditions of sulfonation should be optimized in order to yield the highest conversion in the intended product, minimizing time as much as possible to minimize energy consumption in heating the system. The main aim of this work is to enlarge the knowledge of the processes occurring during the sulfonation or to obtain data of the time dependence of the composition of the reaction mixture and to develop a mathematicalmodel describing the overall kinetics. The experimental conditions were chosen on the basis of previous results (Nowickiand Zarzychi, 1987;Serwinski et al., 1987). 2. Theoretical Section
The present study treats the overall kinetics of a complex reaction system. A differential representation or “kinetic model” is developed to describe the system kinetic of the naphthalene sulfonation. This sulfonation leads to different sulfonic acids through a complex reaction system, constituted of many parallel, consecutive, and reversible reactions. A simplified kinetic model is supposed to be the most probable, and ita corresponding mathematical model is deduced. In the actual study it is assumed that the experimental data are obtained from an isothermal intensively mixed batch reactor providing homogeneous reaction. Thus, the data can be represented by a set of simultaneous first-order nonlinear ordinary differential equations, which are, however, linear in the coefficients to be estimated. A suitable method is chosen to adopt the solution concerning the proposed model. 0888-588519312632-1066$04.00/0
compound symbol chemical formula
compound naphthalene sulfuric acid a-naphthalenesulfonic acid
8-naphthalenesulfonic acid naphthalenedisulfonic acid
Table I summarizes the components which amear (Nowickiand Zarzychi, 1987;SeAnski et al., 1987)i i the reaction system under study. For simplicity, the compound symbols given in Table I are used to denote the corresponding compounds assumed to take part in the applied set of reactions when naphthalene and sulfuric acid are allowed to react under the studied conditions. The following reactions are assumed to be the most significant for the description of the process under study: N +S+ A
+ H20 N + S ==B + H20 N + 2s
D + 2H,O
A + S*D
+ H20
D +H20+A
+B +S
(1) (11)
(IV) (VI
(VI)
The rate of concentration change of a component can be expressed in general form as 0 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 1067 for a product:
rj = dCi/dt
for a reactant:
rj = -dCi/dt
... i = 1,2,3, ...
i = 1,2,3,
( 1 ) Heating Manlle ( 2 ) Mercury Seal ( 3 ) Resistanl Thermancter
( 4 )h a t Controller ( 5 ) Electric Stirrer
where ri is the rate of reaction for the homogeneous, isothermal, and constant-volume reaction mixture. The rate equation is however a function of the unknown reaction rate constants: dCi/dt = kJ(Ci)
at constant temperature
dk
(1)
where the index n is related to the number of unknown reaction rate constants. According to the above reactions, the number of unknowns k, is to be less than or equal to the number of the available differential equations (rj) related to the dependent variable (Cj) for the possibility of numerical solution. However, the number of these unknowns must be reduced by the followingconsiderations: The reversible reaction rate constants for reactions I and I1 can be taken as fractions of the forward reaction rate constants. In addition, some reactions can be neglected because of low probability of occurrence. For this reason, the following assumptions are made: 1. Most of the water of reaction is stripped off as it is formed (from experimental results), so that the reversibility of reactions I and I1 is nearly neglected. 2. In the case of equal molar reactant ratio (acid/ naphthalene) or less than equimolar ratios, reactions IVVI can be neglected since they require more sulfuric acid than present. 3. All reactions listed are considered second order with reaction rate constants k, (L mol-' h-l), where index n is related to the compounds of the reaction mixture. 4. Sulfones or tar whichmay be formed at the operating conditions are of very small amounts compared to the other products and are neglected. 5. Stripped water volume is neglected compared to the reactant mixture volume, so the reaction volume is assumed constant since water is evaporated at the reaction temperature (170 OC). The actual procedure used in solving the rate equations is based on numerical integration using the RungeKutta method,followed by the nonlinear least squares technique. By solving the set of rate equations, best estimates of the coefficientsk, are obtained and the validity of the proposed model for the description of experimental data is checked. The differential equation can be formulated by dC/dt = &t,C(t),&)
( 6 ) Teflon Stopper
(2)
where C is the vector of the dependent variables. 6 is the reaction constant of the differential equations that give the following solution. (3) where subscript i refers to the number of time during the reaction and subscript j refers to the number of components forming the kinetic model. Equation 4 formulates (4)
the deviation 6 i j using the predicted values of the dependent variable (Cjj)m,which are the experimental concentrations (measured), and (Cj), which are the calculated concentrations according to the model.
0 Figure 1. Bench-scale sulfonation setup.
The criterion used to estimate the rate constants is to minimize the sum of the squares of the deviation 6i~,so the objective function to be minimized is represented by the following equation: (5) e is a function of k's and represents a surface with a minimum in kk-dimensional space (kk is number of rate constants). By Marquard's technique a minimum objective function e (eq 5 ) can be obtained, and consequently the optimum values of k's are also obtained at different reaction conditions.
3. Experimental Section 3.1. Sulfonation Setup (Figure 1). The system consists mainly of the glass reaction vessel (0.5-L capacity) provided by a propeller type mixer adjusted (1200 rpm) to assure a perfectly mixed reaction mixture necessary to enhance dissolution of naphthalene and to obtain representative samples. In order to verify that the rate measurements were not distorted by mass-transfer limitations, sulfuric acid conversion was measured at various stirring speeds. Above a stirring speed of about 600 rpm the sulfuric acid conversion remains constant. Therefore, to be on the safe side, the kinetic measurementa were carried out at a stirrer speed of about 1200 rpm (Nowicki and Zarzychi, 1987; Anoshin et al., 1978). The reactor is heated electrically,and temperature is kept constant using a contact thermometer connected to a controller. 33. ExperimentalProcedure. The measured volume of sulfuric acid (93.7 mL) is charged to the reactor and heated to the required reaction temperature. The amount of previously melted naphthalene (80 "C) is added spontaneously (15-20 s) so that the temperature is raised to the required value and kept constant during the whole reaction time, Conditions are changed according to Table 11.
1068 Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 Table 11. Exwrimental Conditions acid to run no. temp ("C) naphthalenea mole ratio 1 115 1.1 2 120 1.1 3 140 1.1 4 165 1.1 5 170 1.1 6 176 1.1 7 180 1.1 8 170 0.7 9 170 0.9 10 170 1.0 11 170 1.4 a
vol of sulfuric acid (mL) 93.7 93.7 93.7 93.7 93.7 93.7 93.7 59.6 76.6 85.1 119.2
acid concn (wt %) 98 98 98 98 98 98 98 98 98 98 98
wt of total volb sulfuric acid, (gm) of reaction mixture (mL) 172 335.29 172 335.29 172 336.29 172 335.29 172 335.29 172 335.29 172 335.29 109 166.93 140 243.66 156 287.80 219 495.57
200 g of naphthalene wed for each run = 1.56 mol. Based on average density a t the reaction temperature, which was 1.25 g/mL.
< m z 100
t
I00
~
A
.
t-
A -
4
U
z
0
SIN
E 6ot
11
v 170OC 176OC
a
50 /
I
/
,
I
15
30
45
60
90
I
120
150
180
Reaction time, (min)
Figure 2. Conversion-time curves for different temperatures (runs 1-3, 5, and 6).
At predetermined time intervals about 2-mL test samples are sucked through Teflon tubing, quenched, and analyzed. Unreacted sulfuric acid is determined by volumetric titration using barium chloride; the sulfonic acid isomers (a, 8, and di) are detected using highperformance liquid chromatography. 4. Results and Discussion 4.1. Time-Concentration Relationship. 4.1.1. Effect of Temperature on Naphthalene Sulfonation. Sulfonation was studied at a constant molar ratio of acid to naphthalene (1.1) and temperatures ranging from 115 to 180 "C. Figure 2 shows the change in total conversion of naphthalene at the different reaction temperatures. 4.1.2. Effect of Acid to Naphthalene Molar Ratio. Different runs are operated at the optimum temperature (170"C) in order to investigate the effect of change in reactant molar ratios from 0.7 to 1.4. Figure 3 shows that up to 1.1:l molar ratio no naphthalene disulfonicacidsare formed. At higher molar ratios diacids are produced; their concentration reaches a maximum value and then begins to decrease parallel with the increase in the &monoisomer. 4.2. Kinetic Parameter Determination. 4.2.1. Development in the Model. Five probabilities were attempted to obtain the best values of the reaction rate constants which minimize the objective function given in eq 5. However, after going over these five probabilities, it was observed that naphthalenedisulfonic acids are formed by sulfonation of naphthalene-&sulfonic acid with
30
I
,
,
I
I
sulfuric acid, but unsubstituted naphthalene and sulfuric acid do not form the disulfonic acids directly. Whenever naphthalenedisulfonicacids are formed at the early stages of reaction, they are hydrolyzed to the more stable &isomer, but not the a-isomer or to the a- and @-isomers. The reverse of reactions I and I1 is attempted with different values of fractions from the forward reaction rate, resulting in a high value of the objective function. However, the model, through which optimum values of sulfonation reaction rate constanta are obtained, is represented by the following chemical reactions: ki
N + S-A N +S
+ H,O
-+ h
B
H,O
ha
A-B k4
A + S -.D
+ H,O
D + H,O
-.B + S ki
The corresponding rate equations can be represented by the following matrix:
Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 1069 Table 111. Values of Kinetic Rate Constants
4.2.2. Values of Kinetic Rate Constants. The model is developed by the following sequence: 4.2.2.1. Preliminary values of specific rate constants were evaluated by considering a second-order reversible reaction between naphthalene and sulfuric acid as the predominating reaction in the system. Specific reaction rates from second-order reversible reactions can be calculated using integral methods (Levenspiel, 1975) for linearization of the rate equations, plotting In CN/CS against time, from which K1 is determined, and then determining the equilibrium constant, from which K2 is evaluated. 4.2.2.2. Five model probabilities were attempted to obtain the best values of the reaction rate constants indicated by minimum values of the objective function
acid to naphthalene 4 molarratio kl kz ka kr ka [E(Cm-C)'I 0.9 0.04 9.02 12.18 0.00 0.00 0.15 1.0 0.00 10.20 19.90 0.00 0.00 1.79 1.4 1.95 8.90 0.59 17.20 3.38 1.90
-
I
I
4 -
% 6/Cm 1.62 1.70 0.23
/---
7
Temp. 170°C SIN 0 9 0 Ncph V p-NSA
V 3 r
0
H~SOL
A
oc-NSA
2 --
(0.
The following conclusions were derived from the probabilities: 1. Naphthalenedisulfonic acid (formed theoretically through reactions IV and V) is formed only through reaction V and is significant at higher ratios of HzSO$ naphthalene. 2. Naphthalenemonosulfonic acid @-isomeris most probably formed through the hydrolysis of the disulfonic acid,formed at the initial stagesof the sulfonation (reaction VI). However, from probabilities reaction VI is developed to
Reaction time, (min)
Figure 4. Calculated concentrations according to the kinetic model compared with the experimental concentrations (run 9).
5t
k6
D + H,O -B + S 3. The reversibility of reactions I and I1 is tested by assuming reversible reaction rate constants kl' and kz' as fractions of the forward kl and k2 (kl' = flkl,k2' = f2k2). By determination of objective functions at different f values, the minimum is obtained by neglecting the reversibility, which is in accordance with the assumption that water is stripped off as it is formed. The following scheme represented the model which led to the miniiumvalue of the objectivefunctionrepresented in Table 111.
1
2
Reaction time, (min)
kl
+ H20
ka
+ H20
N + S -A N + S-B ka
A-B ki
A + S-D
+ H20 k6
D + H 2 0 -B
+S
4.2.2.3. The final model was checked out on the experimental data selected to represent a variety of conditions in the experimental work. The first two runs had acid to naphthalene molar ratios of 0.9 and 1.0 and the third run had a high acid to naphthalene ratio (1.4); that all runs were carried out at the same optimum reaction temperature (170 "C). At each kinetic run applied, the rate constants which were estimated fit the obtained data.
Figure 6. Calculated concentrations according to the kinetic model compared with the experimental concentrations (run 10).
One hundred iterations were sufficient to obtain the best fit. The values of the kinetic rate constants, the objective function (e), and the percentage deviation from the experimental concentrations for different applied ratios are given in Table 111. The graphical representation and comparison between the measured and calculatedconcentrationsare illustrated in Figures 4-6. The overall comparison between measured concentrations of individual reaction components and those calculated through the model is illustrated in Figure 7. Table IV shows the results of an evaluation procedure which illustrates the speed of the decrease in the objective function according to the number of function evaluations corresponding to the values of parameters estimated. 5. Conclusion
From the comparison of the measured and calculated concentration dependences it may be seen that the model
1070 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 S/N
1.4
Noph. V p-NSA 0
Temp =17LfC
YSOL A W-NSA di-NSA 0
. -
I
I
1
0
E
t
.-e ? 2
sulfonation process only by taking the mentioned limitation into account, i.e., if the composition of the reaction mixture does not differ substantially from the conditions described in this study. From the comparison of the change of product concentrations with time for different experimentalconditions studied, it is clear that the highest concentration of the intended @-sulfonicacid is produced at 170 OC, 1.1:l molar ratio, after a 90-min reaction time and then constitutes 95% of the product, as shown in Figure 2.
C
U
1
15
60
30
120
Reacliar time, (min)
Figure 6. Calculated concentrations according to the kinetic model compared with the experimental concentrations (run 11). 5
o Naphthalene
H2SO4
‘ 4
i-
v p-NSA
c U 0
DO(-
c
Y
2 3
NSA
mdi-NSA
Y
E
u 0
u
- 4 2
-
0.4)
Y
rn a u c
r~ = rate of consumption of naphthalene (mol/(L.h)) rs = rate of consumption of sulfuric acid (mol/(L.h)) S = sulfuric acid S/N = sulfuric acid to naphthalene molar ratio T = temperature (K) t = time (h)
2 1
Measured concentratlons mol/L
Literature Cited
Figure 7. Overall comparison between measured and calculated concentrations. Table IV. Test of Evaluation Procedure (Run 11)
no. of functionevaln guess 61 96 exact values
Nomenclature A = a-naphthalenesulfonicacid B = 8-naphthalenesulfonicacid C = calculated concentration (mol/L) CA = concentration of naphthalene-a-sulfonicacid (mol/L) CB = concentration of naphthalene-@-sulfonic acid (mol/L) CD = concentration of naphthalenedisulfonicacid (mol/L) C, = measured concentration (mol/L) CN = concentration of naphthalene (mol/L) CS = concentration of sulfuric acid (moVL) D = naphthalenedisulfonicacid k = reaction constants of differential equations (h-1) k’ = reversible reaction constants of differential equations (h-9 L = number of components M = number of interval time N = naphthalene r A = rate of production of naphthalene-a-sulfonicacid (mol/ (LW) r~ = rate of productionof naphthalene-8-sulfonicacid (mol/ (LW) rD = rate of production of naphthalenedisulfonicacid (mol/
kl 7.000 0.152 0.163 0.160
k2
ks
kd
k6
9.000 15.000 0.300 1.500 2.146 7.563 12.810 0.265 2.443 7.148 12.530 0.227 2.400 7.300 12.600 0.230
value of objfunction 43.000 1.533 1.144 1.100
with estimated parameter values describes fairly well the course of the sulfonation reaction under the experimental conditions chosen. Nevertheless, these parameters cannot be considered as free values of the corresponding reaction rate constants with regard to the limited extent of the information and the simplificationsmade. Consequently these parameters can be used for the design of the
ACI. Manual of Concrete Practice; American Concrete Institute: Detroit, 1973; Part I, pp 309-11. Anoahin, S. A.; Makarova, E. G.; Molodtsova, V. I.; Sizov, 5. Yu.; Sukhanov, S. V.; Fokina, 0. L.; Shkolnyl, V. G. Effect of Intensity of Mixing on the Sulfonation of Naphthalene. Khim. Prom.-St. (Moscow) 1978, 7, 496. Hattori, K. Superplasticizer in Concrete; American Concrete Institute Detroit, 1979; SP-62, pp 37-66. Nowicki, L.; Zarzychi, R. Kinetics of Naphthalene Sulfonation with 96 wt. 7% Sulfuric Acid. J. Chem. Technol. Biotechnol. 1987,39, 149. Levenspiel, 0. Chemical Reaction Engineering; Wiley Eastern University Eddition: New Delhi, Bangalore, Bombay, 197%p 127. Serwinski, M.; Zarzychi, R.; Nowicki, L. Kinetics of Naphthalene Sulfonation in Sulfuric Acid Solutions. Znz. Chem. Procesowa 1987, 8 (l),81. Received for review February 12, 1993 Accepted February 23,1993
