Ind. Eng. Chem. Res. 2008, 47, 4317–4324
4317
Kinetic Modeling of Propene Hydroformylation with Rh/TPP and Rh/CHDPP Catalysts Andreas Bernas,† Pa¨ivi Ma¨ki-Arvela,† Juha Lehtonen,‡ Tapio Salmi,† and Dmitry Yu. Murzin*,† Process Chemistry Centre, Åbo Akademi, FI-20500 Åbo/Turku, Finland, and Technology Centre, Perstorp Oy, P.O. Box 350, FI-06101 Borgå/PorVoo, Finland
Hydroformylation of propene to isobutyraldehyde and n-butyraldehyde was studied in the kinetic regime in a semibatch stainless steel reactor at 70-115 °C and 1-15 bar overpressure in 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate solvent with rhodium/cyclohexyl diphenylphosphine (Rh/CHDPP) and rhodium/triphenylphosphine (Rh/TPP) catalysts. The influence of process parameters such as Rh concentration (50-250 ppm), ligand mass fraction (0-10 wt %), H2-to-CO ratio, and stirring power was investigated and the influence of solvent concentration was studied by using mixtures of valeraldehyde and 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate as solvent. The solubility of propene, H2, and CO in 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate was measured in the same reactor. Rh/CHDPP showed lower normal/isometric aldehyde ratio (n/i) than Rh/TPP. The rate was temperature and pressure dependent, while the Rh concentration or syngas composition did not have any significant impact. The n/i ratio was always independent of the conversion, but dependent on the ligand concentration: higher ligand concentration promoted isobutyraldehyde formation. Based on experimentally recorded kinetic data, a stoichiometric scheme was proposed and parameters of power-law rate models were determined by using nonlinear regression analysis. The experimental system was described as a perfectly mixed gas-liquid reactor. As showed by sensitivity analysis, the kinetic parameters were well identified and physically reasonable and they were in accordance with qualitative observations. The kinetic models with a degree of explanation of more than 0.9 described the formation of the products with satisfying accuracy.
2. Experimental Section
triphenylphosphine (TPP, 99%, Acros Organics) or cyclohexyldiphenylphospine (CHDPP, PA, Acros Organics) were dissolved in 150 mL of 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate or valeraldehyde (97%, Aldrich) in a vessel under nitrogen bubbling on a heating plate equipped with magnetic agitation at a temperature slightly less than the reaction temperature. After a period of 20-30 min the ligand-modified complexes were formed as the solution turned into a yellow-green color. All chemicals were nitrogen treated and stored under nitrogen in order to avoid any contact with air to prevent oxidation. The experiments were carried out in a stirred and pressurized 300-ml Parr 4561 stainless steel reactor, which was designed to withstand a pressure of 300 bar at 350 °C. It had an internal cooling loop and was equipped with an automatic temperature control system consisting of an external electric heating jacket coupled to a steering unit (Parr 4843), which was also used to control the stirring speed. The temperature could be maintained within (1 °C. The reactor had facilities for sampling of the liquid phase as well as the gaseous content and it was connected to reservoirs of propene (99.5%, AGA) and nitrogen (99.999%, AGA). Synthesis gas containing a H2/CO mixture of the composition 50.5 mol % CO and 49.5 mol % H2 (99.995%, AGA) or 45.0 mol % CO and 55.0 mol % H2 (99.995%, AGA) was fed at a constant pressure to the reactor with a pressure controller (Brooks 5866, Brooks 0154)). The reactor was equipped with transducers for online measurements of temper-
In a typical experiment, the catalyst precursor (acetylacetonato)dicarbonylrhodium(I) (99%, Alfa Aesar) and the ligand
Scheme 1. Hydroformylation of Propene to Isobutyraldehyde and n-Butyraldehyde
1. Introduction Hydroformylation of alkenes with carbon monoxide and hydrogen is a homogeneously catalyzed gas-liquid reaction, which is used for the production of linear and branched aldehydes. A wide range of aldehydes, having applications in perfumes, surfactants, plasticizers, and solvents, is produced by this reaction, which is a typical case of simultaneous absorption of two or more gases, with reaction in a liquid medium or in an interfacial regime in the presence of a homogeneous catalyst.1–6 A lot of studies have been devoted to the chemical aspects of the process, such as catalyst and ligand selection, but precise kinetic investigations, which are the basis of reaction engineering, are very scarce. In the present work, we have determined the kinetics of propene hydroformylation on rhodium-based homogeneous catalysts. The ligands used were cyclohexyl diphenylphosphine (Rh/CHDPP) and rhodium/triphenylphosphine (Rh/TPP). The reaction is given in Scheme 1. The aim is to investigate ligands giving different normal/ isometric aldehyde ratio (n/i), to experimentally determine quantitative reaction kinetics, and to develop a mathematical model, which is the basis of rational reactor design and operation, by using measured gas solubility in the reaction mixtures.7
* To whom correspondence should be addressed. Tel.: +358 2 215 4985. Fax: +358 2 215 4479. E-mail:
[email protected]. † Åbo Akademi. ‡ Perstorp Oy. 10.1021/ie071401r CCC: $40.75 2008 American Chemical Society Published on Web 06/12/2008
4318 Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008
ature and pressure (Keller type PA21 SR/80520.3-1), which was followed up on a PC for continuous data logging. After charging the catalyst solution, the reactor was sealed tight and the heating jacket was attached. Gases fed into the reactor were dispersed in the liquid phase by the aid of a sinter. Initially, the PC logging of temperature and pressure was started and the reactor was pressurized with 6 bar (overpressure) of nitrogen with all valves closed to check for leakage. Thereafter, the agitation was switched on at 1000 rpm and nitrogen was flushed through the reactor for 3 min at atmospheric pressure to remove any residues of oxygen prior to the experiment. The pressure was increased to 10 bar and kept at this level for 10 min. After equilibrium between gas and liquid phases was reached, the outlet was carefully opened. A propene volume of 2 L was flushed though the liquid phase with the flow 22 L/h for 7 min at 2.2 bar and ambient temperature. The reactor was kept closed for 25 min to await gas-liquid equilibrium resulting in ∼0.15 mol of propene in the liquid phase and thereafter heated to the reaction temperature while the pressure increased at the same time. After stabilization of the temperature, a zero sample was taken from the liquid phase. The stirring was kept on during this entire procedure. The reaction time was initialized to zero as soon as the reactor was pressurized with hydrogen-carbon monoxide mixture. Samples of 1 mL were withdrawn from the liquid phase at certain time intervals. Waste samples of ∼1 mL were also taken prior to sampling. The weight was measured for all samples, and the loss of the total liquid volume was taken into account in the calculations of the concentration profile. The temperature was slightly increasing in the beginning of the reaction. Typically, the conversion reached the value of 1 at 20 to 40 min; however, the total reaction time of 180 min was used to follow up possible changes after complete propene conversion. The experiments included in the kinetic model were carried out in the kinetic regime, which was confirmed by special experiments conducted at varied stirring rates. The influence of solvent concentration on the hydroformylation kinetics was investigated by using mixtures of 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate and n-pentanal as solvent. After the run, the outlet was opened carefully and after reaching atmospheric pressure the reactor was cooled by the aid of cooling water and nitrogen flushing. The reactor was washed first with water and technical acetone, and, following this, with acetone and methanol of PA grade. Between some 5 and 10 experiments, blank runs were performed in order to check for catalysis of metal residues in the reactor. No catalytic activity was ever detected in these runs. Analyses of hydroformylation products for reaction followup were carried out by an internal standard method using a gas chromatographic technique for determination of isobutyraldehyde, n-butyraldehyde, propene, and propane in 2,2,4-trimethyl1,3-pentanediol monoisobutyrate solvent. Because of propene and propane evaporation from the samples, the required initial amount of propene was calculated from the aldehyde products since no side reactions were detected. A Hewlett-Packard 5890 series II gas chromatograph with flame ionization detector operating at 300 °C and split/splitless injector with HP GC Chem Station Rev. A.06.03 509 electronic integrator using a J&W Scientific DB-1 capillary column of the length 60 m and inner diameter 0.25 mm with 1 µm film thickness was used. The injector operated in the split mode at 250 °C and 1.93 bar, the oven temperature program was 30 °C (0 min):1 °C/min:60 °C (0 min), 15 °C/min:300 °C (40 min), and gas flow rates of 3 mL/min carried gas helium, 28 mL/min makeup gas helium,
Figure 1. Influence of stirring rate on conversion at 30 min and n/i ratio at conversion 1 in hydroformylation of propene on rhodium catalyst. Conditions: ligand compound, cyclohexyldiphenylphosphine; solvent, 150 mL of 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate; reaction temperature, 100 °C; syngas overpressure, 10 bar; ligand fraction, 0.5 wt %; rhodium fraction, 100 ppm; H2-to-CO ratio, 1:1; reaction time, 180 min.
245 mL/min air, 41 mL/min hydrogen, and 202 mL/min split were applied. 3. Results and Discussion 3.1. Mass Transfer. Rh/CHDPP catalyzed propene hydroformylation experiments were carried out with varied stirring rate in order to get a picture of the mixing properties of the system. The experiments were conducted in the interval from 100 to 1000 rpm. An experiment at 400 rpm was repeated in order to verify the reproducibility. The conversion and the n/i ratio increased with increased stirring rate. The conversion after a reaction time of 30 min and the n/i ratio at 100% conversion dependences on the stirring rate are presented in Figure 1. A stirring rate of 100 rpm gave the slowest conversion of 0.16 after a reaction time of 3 h. Thereafter the conversion systematically increased with the agitation speed. The initial rate was the same at 800 rpm and at 1000 rpm. Consequently, the system was agitated at 1000 rpm in all further runs. The n/i ratio was independent of the conversion slightly increasing with the stirring rate. The rate data at 1000 rpm were found to be in the kinetic regime and the results revealed that the diluted system was well mixed and that the hydroformylation experiments were performed on the plateau of the initial reaction rate versus the mixing power dependence. 3.2. Solvent Effects. Experiments with varied solvent composition were carried out at 100 °C and 15 bar over 100 ppm Rh using 0.5 wt % of CHDPP ligand in order to investigate the influence of the solvent on catalyst activity and selectivity. Figure 2 shows the conversion versus time patterns. The solvent was varied from pure 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate via 10, 20, 40, and 60 wt % of valeraldehyde (pentanal) in 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate to pure valeraldehyde. The n/i ratio was conversion independent and remained at a constant value of 1.7. The conversion versus time approximately followed the same curve in all these experiments. 3.3. Cyclohexyldiphenylphosphine Ligand. 3.3.1. Influence of Ligand Mass and Rhodium Concentration. The effect of ligand amount was investigated by performing hydroformylation experiments over catalysts with varied ligand concentrations. Two series of runs were carried out: one series at 100 ppm Rh concentration and another at 250 ppm. Activity data
Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008 4319
Figure 2. Influence of solvent composition on conversion versus time dependences in hydroformylation of propene on Rh/CHDPP catalyst. Conditions: syngas overpressure, 15 bar. Other conditions same as in Figure 1. Note: wt % valeraldehyde ) wt % of valeraldehyde in 2,2,4trimethyl-1,3-pentanediol monoisobutyrate. Table 1. Activity Data on Rh/CHDPP Catalyst for Varied Ligand Concentration at Different Rhodium Concentrationsa N
Rh mass (ppm)
ligand mass (wt %)
n/i
TOF (min-1)b
conversionc
propene (mol)d
1 2 3 4 5 6 7 8 9 10
250 250 250 250 250 100 100 100 100 100
0.5 1 2 3.34 10 0 0.025 0.1 0.25 0.5
1.56 1.78 1.86 1.94 2.13 s 1.33 1.44 1.63 1.78
39.25 39.67 26.49 19.71 13.35 s 62.72 95.01 92.29 75.59
1.00 0.97 0.93 0.95 0.64 0.00 0.96 0.73 0.99 1.00
0.1532 0.1502 0.1430 0.1492 0.1467 s 0.1616 0.1706 0.1588 0.1525
a
Conditions: ligand compound, cyclohexyldiphenylphosphine; solvent, 150 mL of 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate; reaction temperature, 100 °C; syngas overpressure, 10 bar; H2-to-CO ratio, 1:1; reaction time, 180 min. b Turnover frequency. TOF ) total moles of propene converted after 10 min per unit time and moles of rhodium. c Conversion after 30 min. d Least required amount of propene for achieving the observed amounts of aldehydes via analysis.
on Rh/CHDPP at varied ligand concentrations is demonstrated in Table 1. The conversion decreased and the n/i ratio increased with the CHDPP concentration. The hydroformylation rate versus ligand concentration dependence passed a maximum at rather low ligand amount and the precursor alone was not active in absence of ligand. It was seen that the ligand concentration had a dramatic effect on the hydroformylation kinetics using 250 ppm of rhodium, as shown in entries 1-5 of Table 1. As demonstrated in Figure 3a, the hydroformylation rate is rather slow at a ligand amount of 10 wt % of CHDPP and the rate systematically increases when the amount of CHDPP is decreased via 3.34, 2, and 1 wt % to 0.5 wt %. As seen in entries 6-10 of Table 1, also at the rhodium concentration 100 ppm, the rate increased as the CHDPP concentration was decreased from 0.5 wt % via 0.25 wt % to 0.1 wt %. The concentration 0.1 wt % CHDPP showed the highest TOF value of 95.01 min-1 (Table 1, entry 8). When the ligand mass thereafter was decreased to 0.025 wt % the rate started to decrease. An experiment was carried out with total absence of ligand (Table 1, entry 6) in order to check if any reaction occurs with only the precursor present. In this experiment, only trace amounts of aldehydes were detected.
Figure 3. Dependence of conversion on metal and ligand concentrations in hydroformylation of propene on Rh/CHDPP catalyst. (a) Influence of CHDPP concentration on conversion using 250 ppm Rh. (b) Influence of Rh concentration on conversion using 2 wt % CHDPP. Conditions: reaction temperature, 100 °C; syngas overpressure, 10 bar. Other conditions are the same as in Figure 1. Table 2. Activity Data on Rh/CHDPP Catalyst for Varied Metal Concentrationa N
Rh mass (ppm)
n/i
TOF (min-1)
conversion
propene (mol)
1 2 3 4
50 75 100 250
1.82 1.82 1.82 1.82
31.44 33.41 31.00 26.49
0.41 0.56 0.77 1.00
0.1451 0.1630 0.1586 0.1430
a
Ligand fraction, 2 wt %. Other conditions same as in Table 1.
Experiments using varied rhodium concentrations were carried out at 100 °C and 11 bar at the CHDPP amount 2 wt %. As seen in Table 2, the n/i ratio is not dependent on rhodium concentration at these conditions. The n/i ratio kept a constant value of 1.82 at any conversion as the rhodium concentration was varied within a large concentration range. Similarly, the TOF did not vary with the rhodium concentration, which is an indication of good experimental setup accuracy. As demonstrated in Figure 3b, the conversion increased systematically with rhodium concentration when the Rh concentration is increased from 50 via 75 and 100 to 250 ppm. The ligand concentration was the single found variable affecting the n/i ratio. Figure 4 illustrates the effect of ligand concentration on the n/i ratio in propene hydroformylation. 3.3.2. Influence of Temperature and Syngas Pressure. Activity data on Rh/CHDPP at varied temperature and pressure
4320 Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008
Figure 4. Influence of ligand concentration on n/i ratio in hydroformylation of propene on Rh/CHDPP catalyst at rhodium concentrations 250 ppm and 100 ppm. Conditions are the same as in Figure 1.
are presented in Table 3. The reaction temperature was varied at pressures 10 and 15 bar and the pressure was varied at predominantly 100 °C using 0.5 wt % ligand and 100 ppm rhodium concentration. Moreover, the pressure was varied at 100 °C using higher ligand and Rh amounts of 2 wt % and 250 ppm, respectively. First of all, it can be concluded that neither temperature nor pressure affects the n/i ratio significantly, which kept a conversion independent and rather constant value of around 1.7 using 0.5 wt % CHDPP (Table 3, entries 1-11) and at 1.86 using 2 wt % CHDPP (entries 12 and 13), since the n/i ratio increases with the ligand concentration. Figure 5 shows the dependence of TOF on temperature. At both pressures 10 bar (entries 1-4) and 15 bar (entries 5-8) the TOF showed strong temperature dependence. It is obvious that the dependence of rate on temperature is more pronounced at lower temperatures such as 70-100 °C than for the interval 100-115 °C. The propene conversion increased with pressure and the n/i ratio kept a constant value of 1.6 to 1.7 as the pressure was increased from 8 via 10 and 12 to 15 bar using 0.5 wt % CHDPP and 100 ppm Rh (Table 3, entries 3 and 9-11). A varied pressure at 2 wt % CHDPP and 250 ppm Rh (Table 3, entries 12 and 13) also showed a similar increase of conversion with pressure, while the n/i ratio remained unchanged at 1.86. Some experiments were carried out using nitrogen as an inert gas to study the influence of a very low syngas pressure. In these experiments with the initial syngas partial pressures 1, 2, and 3 bar, the conversion increased with pressure, and the n/i ratio was approximately 1.56 at any conversion. The influence of syngas composition was studied by performing hydroformylation experiments over 100 ppm Rh on 0.5 wt % CHDPP at 100 °C and 10 bar using the hydrogen-to-carbon monoxide ratios 0.5:0.5 and 0.55:0.45. However, the hydroformylation kinetics was not found to be dependent on the H2/CO ratio. In both cases, the conversion versus time dependence followed the same curve and the n/i ratio showed a constant time and conversion independent value of about 1.78. In both cases, some trace levels of 0.02 wt % of propane was detected in the liquid phase. No propane was found in the gas phase. 3.4. Triphenylphosphine Ligand. 3.4.1. Influence of Ligand Mass. The kinetics of propene hydroformylation on Rh/ TPP was investigated at varied ligand concentration, temperature, and pressure. Similarly to the CHDPP ligand, the reaction rate increased and the n/i ratio decreased when the ligand
concentration was decreased. The hydroformylation rate versus ligand concentration dependence passes a maximum at a low ligand amount. The outcome of this investigation is presented in Table 4. The effect of ligand amount was investigated by performing hydroformylation experiments over Rh/TPP catalysts with varied ligand concentration at the temperature 100 °C and the total pressure 10 bar using the rhodium fraction 100 ppm. As demonstrated in Figure 6, the hydroformylation rate is rather slow at a ligand amount of 8 wt % of TPP and the rate systematically increases when the amount of TPP is decreased via 4 and 2 wt % to 0.5 wt %. The TPP concentration 0.5 wt % showed the highest TOF value of 78.79 min-1 (Table 4, entry 1). The n/i ratio increased with the TPP concentration. 3.4.2. Influence of Temperature and Syngas Pressure. Activity data on Rh/TPP catalyst at varied reaction temperatures is presented in Table 5. The temperature was varied in experiments using 0.5 and 2 wt % of TPP. The temperature does not affect the n/i ratio significantly, which kept a conversion independent and constant value of approximately 2 while using 0.5 wt % of the TPP ligand (entries 1-4) and 3 with 2 wt % of TPP (entries 5-7), since the n/i ratio increases with the ligand concentration. Similarly to the CHDPP ligand (Figure 5), when using TPP the dependence of rate on temperature is more pronounced at lower temperatures such as 85-100 °C than for the interval 100-115 °C. A possible explanation for this might be that the increase of reaction rate by elevated temperature is retarded by the decrease of the propene solubility. The activity and selectivity data at varied syngas pressure are presented in Table 6. The TOF increased with pressure. When using 0.5 wt % of TPP ligand (entries 1-4), the lowest investigated pressure of 6 bar gave only 22% conversion at a reaction time of 180 min. The n/i ratio was not affected by pressure. On the other hand, when 2 wt % of TPP ligand was used (entries 5-7), the n/i ratio slightly decreased with pressure. 3.5. Kinetic Modeling. 3.5.1. Model A: Cyclohexyldiphenylphosphine Ligand. The hydroformylation systems using Rh/ CHDPP and Rh/TPP catalysts are modeled separately. These two models are hereafter referred to as models A (Rh/CHDPP) and B (Rh/TPP). The concentrations of propene, isobutyraldehyde, and nbutyraldehyde were used in the parameter estimation. The concentration of propene in the liquid phase was calculated from the concentrations of the aldehyde products. The concentrations of ligand and metal are expressed by unit mass fraction and the liquid phase concentrations of hydrogen and carbon monoxide are used. Hydroformylation of propene can be described as two catalytic routes: (1) the reaction of propene, CO, and H2 to isobutyraldehyde and (2) the reaction of propene, CO, and H2 to n-butyraldehyde. The generation rates of the reaction products isobutyraldehyde and n-butyraldehyde are denoted by r1 and r2, respectively, and the consumption rate of propene is the sum of the rates of the two steps -
dcA ) rA ) r1 + r2 dt
(1)
where dci ) k1cAn1cH2n2cCOn3[Rh]n4[L]-n5 dt
(2)
dcn ) k2cAm1cH2m2cCOm3[Rh]m4[L]-m5 dt
(3)
r1 ) and r2 )
Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008 4321 Table 3. Activity Data on Rh/CHDPP Catalyst for Varied Reaction Temperature and Pressure at Different Rhodium Concentrations and Ligand Amountsa N
Rh mass (ppm)
ligand (wt %)
T (°C)
P (bar)
n/i
TOF (min-1)
conversion
propene (mol)
1 2 3 4 5 6 7 8 9 10 11 12 13
100 100 100 100 100 100 100 100 100 100 100 250 250
0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 2 2
75 85 100 115 70 85 100 115 100 100 100 100 100
10 10 10 10 15 15 15 15 8 12 15 10 15
1.78 1.86 1.78 1.56 1.70 1.70 1.63 1.56 1.70 1.63 1.63 1.86 1.86
16.30 44.68 75.59 93.16 10.64 65.26 86.75 103.49 57.86 87.79 87.57 26.49 37.40
0.49 0.82 1.00 0.97 0.31 0.80 0.97 0.96 0.95 0.96 0.97 0.93 1.00
0.1493 0.1650 0.1525 0.1594 0.1557 0.1691 0.1492 0.1559 0.1512 0.1425 0.1499 0.1430 0.1594
a
Conditions same as in Table 1.
the exponential factors ni and mi. The kinetic constants k1 and k2 are assumed to follow the Arrhenius dependence
( (
k ) A exp
Figure 5. Temperature dependence of the turnover frequency at 10 bar (2) and 15 bar (∆) in hydroformylation of propene on Rh/CHDPP catalyst. Conditions are the same as in Figure 1. Table 4. Activity Data on Rh/TPP Catalyzed Hydroformylation of Propene for Varied Ligand Concentrationa N ligand mass (wt %) 1 2 3 4
0.5 2 4 8 a
n/i
TOF (min-1) conversion propene (mol)
1.86 2.70 3.00 4.00
78.79 71.20 43.59 24.84
0.95 0.98 0.87 0.67
0.1376 0.1554 0.1339 0.1570
Rhodium fraction, 100 ppm. Other conditions same as in Table 1.
In eqs 2 and 3, cA (mol/dm3), ci (mol/dm3), cn (mol/dm3), cH2 (mol/dm3), cCO (mol/dm3), [Rh] (mass fraction), and [L] (mass fraction) denote concentration of propene, concentration of isobutyraldehyde, concentration of n-butyraldehyde, concentration of hydrogen and carbon monoxide, mass fraction of rhodium, and mass fraction of ligand. The solubility of H2 and CO in 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate solvent follows the dependence7 B + C ln(T/K) (4) (T/K) where A, B, and C are 10.972, -1466.01, and -2.3931 as well as 17.413, -1398.4, and -3.419 for H2, and CO, respectively. The pressure dependence of the gas solubility is at low solubility and moderate pressure given by Henry’s law. The total concentration of the liquid phase was calculated to 5.315 mol/ dm3, and the concentrations of H2 and CO in the liquid phase are obtained by multiplication of solubility with total concentration. In the expressions above, describing model A, the constants to be estimated are the kinetic constants k1 and k2 as well as
-Ea 1 1 Rgas T Tmean
))
(5)
In the expression above, A, Ea, Rgas, T, and Tmean denote frequency factor, activation energy, the gas constant, reaction temperature, and mean temperature of the experiments. The differential eqs 2 and 3 portraying model A are still not possible to solve numerically. The model is considerably overparametrized and needs to be simplified. An essential simplification that will be of assistance in the parameter estimation can be done. As described earlier, the reaction temperature did not affect the selectivities to the two aldehydes. The n/i ratio versus conversion dependence for varied reaction temperature at pressures 10 and 15 bar showed a constant value. Such a result indicates that the rates r1 and r2 of the catalytic steps (1) and (2) have the same activation energy Ea. Thereafter a solution of model A could be obtained. Based on this preliminary approach, the model was simplified in order to further drop unnecessary parameters and to get more reliable parameter estimation statistics, i.e., to suppress the standard errors of the parameters. It was observed that the propene concentration versus reaction time multiplied by metal mass fraction dependences fell on the same curve for every experiment made with varied rhodium concentration; hence it can be concluded that the metal mass fraction dependence of the model is of first order. Similarly, the propene concentration versus reaction time multiplied by reaction pressure fell on the same curve for the experiments made using varied pressure. The product distribution and thereby the selectivities were not affected by metal mass fraction, partial pressure of CO, nor partial pressure of H2. Thus the parameters n2, n3, n4, m2, m3, and m4 were set to the value 1. The rate of the two steps including the parameters k1, k2, n1, n5, m1, and m5 are then given by r1 )
ln(xg) ) A +
dci ) k1cAn1cH2cCO[Rh][L]-n5 dt
(6)
and dcn ) k2cAm1cH2cCO[Rh][L]-m5 (7) dt Moreover, the following measures were taken. The exponents n1 and m1 were fixed to 1 because the kinetics was found to be first order with respect to propene concentration. A plot of the natural logarithm of the propene concentration versus time showed a straight line with a negative slope for all involved r2 )
4322 Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008
experiments. The exponents k1, k2, n5, and m5 were let to float during the parameter estimation. The new shape of the model is given by r1 )
dci ) k1cAcH2cCO[Rh][L]-n5 dt
(8)
r2 )
dcn ) k2cAcH2cCO[Rh][L]-m5 dt
(9)
and
which was solved numerically. 3.5.2. Model B: Triphenylphosphine Ligand. The hydroformylation system using Rh/TPP catalyst, model B, is modeled is a similar manner as the Rh/CHDPP catalyst. The generation rates of the two aldehydes r1 and r2 in eq 1 are given by r1 )
dci ) k1cAcH2cCO[Rh][L]-n5 dt
(10)
r2 )
dcn ) k2cAcH2cCO[Rh][L]-m5 dt
(11)
and
where the constants to be estimated are the frequency factors and the activation energies in the kinetic constants k1 and k2 as well as the exponential factors n5 and m5. 3.5.3. Parameter Estimation. The systems of differential equations portraying models A and B were solved numerically in the parameter estimations with the backward difference method by minimization of the sum of residual squares, SRS, with nonlinear regression analysis using the Simplex and Levenberg-Marquardt optimization algorithms implemented in the software Modest.8 The sum of squares was minimized with respect to using a step size of 0.1 and a value of 1 × 10-6 for both the absolute and relative tolerances of the Simplex and Levenberg-Marquardt optimizer, starting with Simplex and thereafter switching to Levenberg-Marquardt. The parameter correlation matrixes of the models are given in Tables 7 and 8. Although there is some negative correlation between parameters A1 and n5 as well as A2 and m5 in model A (Table 7) and between A1 and n5 as well as A2 and m5 in model B (Table 8), correct and independent variable variation is indicated by a correlation coefficient matrix of values close to zero, as can be seen from these tables. The values of the estimated parameters, the estimated standard errors, and the estimated relative standard errors (in %) are shown in Tables 9 and 10. A decreased number of parameters suppressed the degree of explanation and increased the sum of residual squares. Models A and B have SRS and R2 values of SRS ) 0.3495 × 101 and R2 ) 92.01% as well as SRS ) 0.1371 × 101 and R2 ) 95.00%, respectively. At the same time, decreasing the number of parameters decreases the standard errors, which are reasonably low. Both models have degree of explanation larger than 0.9, although the number of parameters has been dramatically diminished. Moreover, the kinetic parameters of the models are physically reasonable and they are in accordance with qualitative observations. The models describe the formation of the products very well. Parity diagrams of the models are shown in Figure 7. It was possible to find minima of the objective function for all the parameters. A sensitivity analysis using the same software showed that the parameter identifiability is optimized. Contour plots of the sum of residual squares from sensitivity analysis of the estimated parameters of the models
Figure 6. Influence of ligand concentration on (a) conversion and (b) n/i ratio in hydroformylation of propene on Rh/TPP catalyst. Conditions are the same as in Figure 1. Table 5. Activity Data on Rh/TPP Catalyzed Hydroformylation of Propene at Varied Reaction Temperaturea N
ligand mass (wt %)
reaction temp (°C)
n/i
TOF (min-1)
conversion
propene (mol)
1 2 3 4 5 6 7
0.5 0.5 0.5 0.5 2 2 2
85 100 110 115 85 100 115
2.13 1.86 1.94 1.94 3.00 2.70 3.00
25.18 78.79 92.70 86.48 16.33 71.20 95.36
0.75 0.95 0.95 0.96 0.42 0.98 0.97
0.1457 0.1376 0.1447 0.1411 0.1507 0.1554 0.1627
a
Rhodium fraction, 100 ppm. Other conditions same as in Table 1
Table 6. Activity Data on Rh/TPP Catalyzed Hydroformylation of Propene at Varied Syngas Pressurea N
ligand mass (wt %)
total press. (bar)
n/i
TOF (min-1)
conversion
propene (mol)
1 2 3 4 5 6 7
0.5 0.5 0.5 0.5 2 2 2
6 8 10 13 8 10 13
s 2.33 1.86 2.33 3.35 3.00 2.85
1.94 75.89 78.79 88.23 61.98 70.39 82.09
0.03 1 0.95 0.98 0.93 0.92 0.95
0.1400 0.1417 0.1376 0.1471 0.1591 0.1640 0.1692
a
Rhodium fraction, 100 ppm. Other conditions same as in Table 1
A and B are available in the Supporting Information. The contour plots showed well-defined minima of the SRS for all parameter combinations.
Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008 4323 Table 7. Correlation Matrix of the Parameters of Model A
A1 A2 n5 m5 Ea
A1
A2
n5
m5
Ea
1.000 0.470 -0.955 -0.450 -0.049
1.000 -0.463 -0.944 -0.068
1.000 0.507 0.107
1.000 0.139
1.000
Table 8. Correlation Matrix of the Parameters of Model B
A1 A2 n5 m5 Ea
A1
A2
n5
m5
Ea
1.000 0.476 -0.983 -0.466 0.038
1.000 -0.490 -0.978 0.050
1.000 0.501 -0.027
1.000 -0.032
1.000 a
Table 9. Values of the Estimated Parameters for Model A est value
est std error
est rel std error (%)
0.151 × 10-2 0.325 × 10-2 0.308 × 10 ° 0.260 × 10 ° 0.447 × 105
(0.113 × 10-3 (0.184 × 10-3 (0.153 × 10-1 (0.119 × 10-1 (0.236 × 104
7.5 5.7 5.0 4.6 5.3
parameter A1 A2 n5 m5 Ea
a Dimensions: [Ea] ) J mol-1, [A1] and [A2] ) dm8 mol-2 min-1. SRS ) 0.3495 × 101, R2 ) 92.01%.
Table 10. Values of the Estimated Parameters for Model Ba parameter
est value
est std error
est rel std error (%)
A1 A2 n5 m5 Ea
0.231 × 105 0.171 × 106 0.544 × 100 0.298 × 100 0.681 × 105
(0.307 × 104 (0.145 × 105 (0.289 × 10-1 (0.192 × 10-1 (0.263 × 104
13.3 8.5 5.3 6.5 3.9
a Dimensions: [Ea] ) J mol-1, [A1] and [A2] ) dm8 mol-2 min-1. Model A: SRS ) 0. 1371 × 101, R2 ) 95.00%.
4. Conclusions The kinetics of homogeneously catalyzed hydroformylation of propene to isobutyraldehyde and n-butyraldehyde was studied in a semibatch stainless steel reactor over rhodium/cyclohexyldiphenylphosphine (Rh/CHDPP) and rhodium/triphenylphosphine (Rh/TPP) catalyst using 2,2,4-trimethyl-1,3-pentanediol monoisobutyrate solvent. The influence of temperature, syngas pressure, rhodium mass fraction, ligand mass fraction, hydrogento-carbon monoxide ratio, and solvent concentration was investigated. The hydroformylation experiments were carried out in the kinetic regime, which was confirmed when the stirring rate was varied from 100 to 1000 rpm. The ligand CHDPP showed lower hydroformylation rate and n/i ratio than that for TPP. The n/i ratio versus conversion always showed a linear dependence, which was on a lower level for CHDPP than that for TPP at similar conditions. The hydroformylation rate versus ligand concentration dependence passed a maximum at a rather low ligand amount. The ligand concentration was the only variable affecting the n/i ratio versus conversion dependence. Rate increased and n/i ratio decreased when the ligand concentration was decreased for both investigated ligands. Power-law rate models were developed, and the parameters of the models were determined by nonlinear regression analysis. The experimental system was described as a perfectly mixed semibatch gas-liquid reactor. The concentrations of propene, isobutyraldehyde, n-butyraldehyde, carbon monoxide, and hydrogen were used in the parameter estimation. The kinetic models showed the R-squared value of more than 0.9 and
Figure 7. Parity diagrams of models A and B.
reasonably small estimated relative standard errors of the parameters. Independent variable variation was indicated by a correlation coefficient matrix of values close to zero and it was possible to find minima of the objective function for the parameters. As showed by sensitivity analysis, the kinetic parameters were well identified and physically reasonable and they were in accordance with qualitative observations. The model predicted the propene hydroformylation kinetic system very well. The rate equations with the kinetic parameters can be used for reactor modeling. Acknowledgment This work is part of the activities at the Åbo Akademi Process Chemistry Centre within the Finnish Centre of Excellence Programme (2000-2011) by the Academy of Finland. Financial support from Perstorp Oy is gratefully acknowledged. Supporting Information Available: Contour plots of the sum of residual squares from sensitivity analysis of the estimated parameters of model A for hydroformylation of propene on Rh/ CHDPP catalyst and of model B for hydroformylation of propene on Rh/TPP catalyst. This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature Rh/CHDPP ) rhodium/cyclohexyldiphenylphosphine Rh/TPP ) rhodium/triphenylphosphine
4324 Ind. Eng. Chem. Res., Vol. 47, No. 13, 2008 n/i ratio ) normal/isomeric aldehyde ratio TOF ) turnover frequency at 10 min model A ) model using Rh/CHDPP catalyst model B ) model using Rh/TPP catalyst r1 ) isobutyraldehyde generation rate r2 ) n-butyraldehyde generation rate cA ) concentration of propene ci ) concentration of isobutyraldehyde cn ) concentration of n-butyraldehyde cH2 ) concentration of hydrogen cCO ) concentration of carbon monoxide t ) unit time [Rh] ) mass fraction of rhodium [L] ) mass fraction of ligand A ) constant in gas solubility dependence B ) constant in gas solubility dependence C ) constant in gas solubility dependence k1 ) kinetic constant (isobutyraldehyde) k2 ) kinetic constant (n-butyraldehyde) Ai ) frequency factor Ea ) activation energy Rgas ) the gas constant T ) reaction temperature Tmean ) mean temperature of the experiments ni ) parameter in rate equations mi ) parameter in rate equations
SRS ) sum of residual squares R2 ) R-squared value
Literature Cited (1) (a) Van Leeuwen, P.; Claver, C. Rhodium Catalyzed Hydroformylation; Kluwer Academic Publishers: Dordrecht, The Netherlands, 2000. (b) Falbe, J. New Syntheses with Carbon Monoxide, Springer Verlag: Berlin, 1980. (c) Torrent, M.; Sola, M.; Frenking, G. Theoretical Studies of Some Transition-Metal-Mediated Reactions of Industrial and Synthetic Importance. Chem. ReV. 2000, 100, 439. (2) Beller, M.; Cornils, B.; Frohning, C. D.; Kohlpaintner, C. W. Progress in Hydroformylation and Carbonylation. J. Mol. Catal. A 1995, 104, 17. (3) Heck, R. F. Synthesis and Reactions of Alkyl Cobalt and Acyl Cobalt Tetracarbonyls. AdV. Organomet. Chem. 1966, 4, 243. (4) Orchin, M.; Rupilius, W. Mechanism of the Oxo Reaction. Catal. ReV. 1972, 6, 85. (5) Suess-Fink, G.; Meister, G. Transition Metal Clusters in Homogeneous Catalysis. AdV. Organomet. Chem. 1993, 35, 41. (6) Papadogianakis, G.; Sheldon, R. A. Catalytic Conversions in Water: Environmentally Attractive Processes Employing Water Soluble Transition Metal Complexes. New J. Chem. 1996, 20, 175. (7) Still, C.; Salmi, T.; Ma¨ki-Arvela, P.; Era¨nen, K.; Murzin, D. Yu.; Lehtonen, J. Solubility of Gases in a Hydroformylation Solvent. Chem. Eng. Sci. 2006, 61, 3698. (8) Haario, H. Modest User’s Guide, Helsinki, 2001.
ReceiVed for reView October 17, 2007 ReVised manuscript receiVed February 29, 2008 Accepted April 24, 2008 IE071401R
