Selective conversion of stearic acid into high-added value octadecanedioic acid using air and transition metal acetate bromide catalyst: Kinetics, pathway and process optimization

2.1 Materials and methods

Liquid-phase air-oxidation of SA (purity > 98.5%) at a specified temperature (363–383 K) and pressure (2.8–5.8 barg) was performed using Co(OAc)₂·4H₂O (0–15 mmol L⁻¹; purity > 99.5%), Mn(OAc)₂·4H₂O (0–15 mmol L⁻¹; purity > 99.5%), HBr (0–15 mmol L⁻¹, purity > 47.0%) and AcOH (purity > 99.5%). SA to AcOH with varying weight ratio (i.e., 5:95–20:80) was allowed to react with pre-filtered air at a desired pressure and temperature in an autoclave made of SS-316 (Sultana et al., 2015; 2017). Air was injected to maintain constant pressure to ensure constant oxygen partial pressure in the autoclave. The withdrawn sample was esterified using the methanolic solution of trimethylsulphonium hydroxide (TMSH). An accurately measured 5.0 mg SA oxidation sample was esterified using 250 μL methyl tert-butyl ether and 150 μL methanolic TMSH solutions in a stoppered bottle, which was shaken vigorously for five minutes to obtain complete esterification of acids. The esterified low volatile compounds and solvents were removed by applying the vacuum. The residue was then analyzed using GC–MS (JEOL GC MATE II coupled with the mass spectrometer, model MS-5973 MSD) and GC (TRACE™ 1300: Thermo Fisher Scientific). The oxidation was allowed to carry out for 50 h and then cooled to room temperature after depressurization. A non-dispersive infrared based CO₂-analyzer (IR-1000, TECHNOVATION, India) was used to detect the presence of CO₂ in the exit gas while depressurization.

2.2 Standardization of SA oxidation products

SA oxidation products (at 20 and 50 h) as well as initial feed involving SA, AcOH and catalysts were esterified using a methanolic solution of TMSH, whereas, the vacuum evaporated esterified products were analyzed using GC–MS. The GC–MS analysis was performed using a capillary column DB-5MS (30 m × 0.32 mm × 0.25 μm) and high purity Helium carrier gas at 1.0 mL min⁻¹. The column temperature was ramped at 10 °C min⁻¹ from 50 to 250 °C, whereas injector and detector were kept at 250 °C. 0.1 μL sample was injected using a split mode (split ratio-1:10) and mass spectrometer was scanned (m/z - 50–600 amu) with electron impact (EI) mode of ionization. The details of the total ion chromatogram for feed and oxidation sample at 20 h are shown in Fig. 1a and b, respectively. The peaks in ion-chromatogram were identified from NIST standard database library (NO. NIST 02) and the details of the identified peak are also shown in Fig. 1a and b. The mass spectroscopy analysis methyl esters of SA and ODDA are shown in Fig. 2a and b, respectively. The details of mass spectroscopy analysis of remaining identified compounds were shown in Figs. S1a–S1i (Supplementary file). The total number of identified peaks in the feed (Fig. 1a) and 20 h oxidation products (Fig. 1b) were found to be 10 and 11, respectively. Among the observed peaks, the presence of methyl ester of SA was identified in Fig. 1a (peak No. 7), whereas both SA and ODDA were present in Fig. 1b (peak Nos. 7 and 11) and appeared at 18.95 min and 22.27 min, respectively. The peaks related to the oxidation related intermediates like hydroxyl-, aldehyde- and keto-compound was absent in Fig. 1b, which confirmed the selective oxidation of SA to ODDA only. It was also observed that the peaks at 1–6, 8–10 in feed sample (Fig. 1a) and oxidation sample at 20 h (i.e., Fig. 1b) were common to feed and 20 h oxidation samples and appeared at the identical retention time, indicating the possible impurities, which were present in SA and TMSH solution.

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Fig. 1 GC–MS total ion-chromatograms of trimethylsulphonium hydroxide (TMSH) assisted esterified (a) SA feed and (b) SA oxidation product after 20 h.

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Fig. 2 Mass spectrum composition of the identified (a) methyl ester of octadecanoic acid (i.e., methyl stearate) in feed and (b) dimethyl octadecanedioate in SA oxidation product after 20 h.

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The base peak in all the mass spectra of esters was observed at m/z = 74 which was a product of Mc Lafferty rearrangement process (Mc Lafferty, 1959). For the ester of stearic acid, a peak at [M-43]+ was observed mainly due to the rearrangement of the chain and one hydrogen atom, followed by the expulsion of propyl radical. In addition, β-cleavage of [CH₃OOC(CH₂)_n]+, where n = 2, 3, 4, 5,… was occurred with distinct ions at m/z = 87, 101, 115, 129…, with a difference of 14 amu confirmed the methyl ester of stearic acid. For dimethyl octadecanedioate, a peak was observed at [M-31]+ due to α-cleavage (loss of methoxy group) and ([M-74]+) due to the loss of McLafferty ion. Other characteristic ion peaks of hydrocarbon ions of general formula [C_nH_2n]+ were observed in the lower mass range at m/z, 84, 98, 112, 126.., with a difference of 14 amu, signifying a hydrocarbon series of alkyl ions. Thus, α-cleavage and alkyl series support the identification of esters of fatty acids. The spectra of SA and ODDA were compared and identified from the library matched software (NO. NIST 02), yielding similar results (Fig. 2a and b).

To monitor the oxidation reaction, SA and ODDA were identified and quantified using GC analyzer. Flame ionization detector and capillary column TR-FAME (50 m × 0.22 mm × 0.25 µm) was used for analysis and identical GC operating conditions were employed as described by Hajra et al. (2017). The details of the GC spectra for the feed, 20 h and 50 h oxidation samples are shown in Fig. 3a, which confirmed the presence of SA (retention time: 15.92 min) and ODDA (retention time: 13.36 min) in the oxidation sample. The composition-variant GC plots using pure methyl ester of SA and ODDA as well as calibration plots are shown in Fig. 3b and c, respectively.

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Fig. 3 (a) GC analysis of SA feed and its oxidation product after 20 and 50 h under fixed catalyst and process condition i.e., Co(OAc)₂·4H₂O-350 ppm, Mn(OAc)₂·4H₂O-350 ppm, HBr-858 ppm, temperature-383 K and pressure-2.8 barg. Calibration plots for the standardization of the methyl ester of (b) SA and (c) ODDA using GC analysis.

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2.3 Design of experiments (DOEs) for SA oxidation

The effects of SA loading, temperature and pressure on ODDA yield were determined as per the DOEs in Table 1, whereas Design-Expert software 7.0.0 (Stat-Ease Inc., Minneapolis, USA) based on CCD-RSM was used to select the optimum number of DOEs to account the effect of catalysts [i.e., Co(OAc)₂·4H₂O, Mn(OAc)₂·4H₂O and HBr] and their combination on ODDA yield under fixed SA loading, temperature and pressure. Above Design-Expert software is a proven mathematical tool to select optimum DOEs, build models and analyze the effects of the individual factor along with their interacting effects on the process (Mondal et al., 2018; Kumar et al., 2018). The detailed limits of the catalyst concentration involving levels and corresponding DOEs are given in Tables 2a and 2b, respectively. The limits of catalyst concentration were selected through preliminary studies of the liquid phase oxidation of SA. Among the twenty experiments in Table 2b, four central experiments are repetitive in nature, whereas other axial and factorial designs of experiments are different from each other. In Table 2b, the yield of ODDA is the response variable. The relation between decision variables and response variable was assumed to abide by the following second-order polynomial equation (Montgomery, 2001):

Using twenty response values in Table 2b, the analysis of variance (ANOVA) was performed to determine the coefficients of Eq. (1). A gradient search technique, built in the Design-Expert software, was used to determine the optimum values of the factors for which the yield of ODDA was maximized. The maximum yield of ODDA was obtained by differentiating above polynomial equation (i.e., Eq. (1)) and equated to zero to determine the optimum values of the factors, i.e., ${\text{X}}_{\text{s}}=-0.5{\text{B}}^{-1}\text{b}$ , where B = coefficient matrix and b = coefficient vectors in Eq. (1), which is expressed in terms of Y = b₀ + X^Tb + X^TBX. It is mentioned that all experiments in Tables 1 and 2b were carried out in triplicate (except the central points in Table 2b) and the mean values of ODDA yield are reported in Tables 1 and 2b. The standard deviations were also calculated from the three same experiments and also reported in Tables 1 and 2b.

3.1 Oxidation pathway

The GC–MS (Figs. 1a, b, 2a and b) and GC results (Fig. 3a), revealed that SA was oxidized selectively to ODDA (details discussions are in Section 2.2). It was also observed that no traces of CO₂ were detected while depressurization of the reactor. Therefore, the autoxidation pathway of SA to ODDA using air, Co(OAc)₂·4H₂O, Mn(OAc)₂·4H₂O and HBr in AcOH is shown by the following reaction scheme:

Above SA oxidation is similar to the conversion of the pelargonic acid to azelaic acid and the catalytic activity was explained by the bromine-bromide cycle (Hajra et al., 2017). The details of the bromine-bromide cycle for the autoxidation of SA to ODDA are also shown in Scheme 2. In this cycle, bromide ions converted into bromine radicals in presence of oxygen, Co(II) and Mn(II) ions. The produced bromine radical abstracts hydrogen of SA to produce initiator for further reaction. It was reported that Mn(III)Br or Co(III)Br complex alone is not sufficient to initiate the free-radical reaction, however, the combined effect of Co(II) and Mn(II) ions help to decompose the hydroperoxides to produce free radicals (Raghavendrachar and Ramachandran, 1992; Jolly, 1980).

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Scheme 1 Oxidation of SA using metal (II) acetate-bromide-complex.

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Scheme 2 Oxidation pathways for the autoxidation of stearic acid to octadecanedioic acid using metal acetate bromide complex (where M = Co and Mn).

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3.2 Oxygen solubility

Pressure, temperature and SA loading have the significant influence on oxygen solubility in AcOH that affect the conversion of SA. In this study, the solubility of oxygen was determined under fixed catalyst concentration assuming that no oxidation reaction is taking place during the measurement of solubility. The solubility of oxygen (i.e., [S] in mmol L⁻¹) was calculated from: [S] = 1000ΔP/RT, where ΔP = differential between initial pressure and steady pressure after attending equilibrium (barg), T = temperature (K) and R = universal gas constant = 0.082057 L (bar mol⁻¹ K⁻¹). The variation of [S] with SA loading at different pressure and temperature for fixed catalyst concentration (i.e., Co(II):Mn(II):Br^–(ppm)-350:350:858) are shown in Fig. 4a and b, respectively. The time-variant pressure at 10% SA loading at different pressure and temperature are shown in Fig. 4a and b, respectively, as an insert. It was observed that [S] increased from 15 to 60 mmol L⁻¹ with the increase in pressure at 383 K when SA loading was varied from 0 to 20% (Fig. 4a). Similarly, [S] was decreased from 51 to 15 mmol L⁻¹ with the increase in temperature at 2.8 barg when SA loading was varied from 0 to 20% (Fig. 4b). It was also observed that [S] reduced significantly with the increase in SA loading and found maximum when SA loading is zero (Fig. 4a and b). Above experiments were carried out in triplicate and the average values are reported in Fig. 4a and b.

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Fig. 4 Oxygen solubility under varying SA loading at different (a) pressure and (b) temperature at fixed catalyst loading [i.e., Co(II)-350 ppm, Mn(II)-350 ppm, Br^–-858 ppm].

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3.3 SA and AcOH loading on ODDA yield

Oxidation of SA was carried out in the autoclave as per DOEs in Table 1 (Expt. Nos. 1–4) for 50 h. The variation of SA and ODDA with time with the increase in initial SA loading was quantified using GC analysis and the details are shown in Fig. 5a. It was observed that the yield of ODDA was found to be the maximum (i.e., 81.87%) when SA:AcOH is 5:95, whereas the ODDA yield was reduced with the increase in SA:AcOH and the details of ODDA yield and corresponding operating conditions are given in Table 1. The increase in ODDA yield was due to the increased [S] value at the lower SA loading (Fig. 4a and b). Therefore, the oxidation of SA was enhanced with the increase in [S] that improved the productivity of ODDA. The time-variant GC spectra of SA and ODDA corresponding to Fig. 5a (i.e., Expt. Nos. 1–4 in Table 1) are outlined in Fig. S2 (Supplementary file).

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Fig. 5 Experimental and predicted molar concentration of SA and ODDA under varying (a) SA loading (wt%) in feed (5–20%), (b) pressure (2.8–5.8 barg) and (c) temperature (353–383 K) for fixed catalyst loading: Co(II)-350 ppm, Mn(II)-350 ppm and Br^–-858 ppm.

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3.4 Pressure and temperature on ODDA yield

The effect of pressure and temperature on the conversion of SA to ODDA was established at temperature and pressure as per DOEs in Table 1 (Expt. Nos. 2, 5–7 and 8–10). The detailed variation of SA and ODDA molar concentration at different pressure and temperature are shown in Fig. 5b and c, respectively. It was noted that pressure and temperature have a marked effect on ODDA yield. It was observed that the yield of ODDA was increased from 78.58 to 88.19% when the oxidation pressure was increased to 5.8 from 2.8 (Table 1). The increase in yield with pressure was mainly due to the increased [S] value at the elevated pressure (Fig. 4a). It was also observed that an almost 5.0% increase in ODDA yield was observed with the 10 K rise in the 353–383 K temperature range in spite of the reduction in [S] value with the increase in temperature (Fig. 4b). The yield of ODDA was increased from 61.12 to 78.58% when the temperature was raised from 353 K to 383 K. The time-variant GC spectra of SA and ODDA corresponding to Fig. 5b and c are drawn in the Figs. S3 and S4, respectively (Supplementary file). Comparing the oxidation results in Table 1, it was cleared that the oxygen solubility plays a significant role in improving the yield of ODDA, which is more sensitive to pressure rather than temperature. Though, the higher pressure and temperature reduce the oxidation time, however, the acetic acid mixture is too corrosive at higher temperature and pressure to carry out the oxidation in an SS 316 autoclave. Therefore, the maximum temperature and pressure were limited to 383 K and 5.8 barg, respectively, for SA oxidation.

3.5 Catalyst loading on ODDA yield

SA oxidation was performed as per DOEs in Table 2b under fixed SA:AcOH- 10:90, T-383 K and P-2.8 barg. It was observed that higher yield of ODDA was obtained when total concentration of catalyst (i.e., [Co(II)]+[Mn(II)]+[Br⁻]) was relatively higher (e.g., Run No. 3 in Table 2b), whereas a minimum yield of ODDA was seen when total catalyst concentration was least (e.g., Run No. 15 in Table 2b). However, the role of the individual catalyst along with the interacting effects on ODDA yield was not clear. For this, ANOVA was carried out using DOEs and the corresponding response (i.e., ODDA yield) in Table 2b to select the appropriate model involving the different loadings of Co(OAc)₂·4H₂O (X₁), Mn(OAc)₂·4H₂O (X₂) and HBr (X₃) catalyst. An ANOVA Table was prepared by determining the sum of square, the degree of freedom, mean square, F-value and p-value for ODDA yield (Y); for which the details are given in Table 3. It was observed that p-value <0.0001 with minimum F-value was obtained for the quadratic model, which is given by:

In above equation, the positive and negative coefficients indicate the synergistic and antagonistic effect of catalysts on ODDA yield, respectively. The detailed ANOVA results are also given in Table 4. Coefficient of determination (R2: goodness of fit), adjusted R2 (Adj R2: accuracy of fit), predicted R2 (Pred R2) were determined using Eq. (2) and the R2, Adj R2 and Pred R2 for ODDA yield were found to be 0.9948, 0.9902 and 0.9759, respectively, and above values revealed that the proposed model is accurate to predict ODDA yield within the limits of catalyst concentration (Table 2a). Above regression model was also evaluated by carrying out using lack of fit test and p-value (i.e., prob > F) was found to be 0.45, indicating that the proposed model was satisfactory to predict the experimental ODDA yield and details of the analysis of variance are shown in Fig. 6a–c. The predicted vs. actual ODDA yield is shown in Fig. 6a, whereas the normal percent probability vs. residuals plot and residuals vs. predicted response plot is shown in Fig. 6b and c, respectively. The Fig. 6a shows that the errors are normally distributed in a straight line indicating the significance of the individual catalyst concentration. Similarly, normal percent probability vs. residual plot is also distributed normally in a straight (Fig. 6b). In contrast, the residuals vs. predicted responses were found to be scattered within the narrow range (Fig. 6c), which suggests that the proposed model is accurate.

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Fig. 6 Statistical analysis of ODDA yield (a) predicted vs. actual ODDA yield (b) normal percent probability vs. residuals plot and (c) residuals vs. predicted response plot.

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The order of influence of the individual and interacting effects of [Co(II)], [Mn(II)] and [Br⁻] on ODDA yield was established. The order of dominance of the catalyst concentration on the predicted ODDA yield (Y) was found to be X₂ (Mn-acetate: 40.70%) > X₃ (HBr: 39.57%) > X₁ (Co-acetate: 19.72%), which is shown in Fig. 7a. The variation of ODDA yield with the individual catalyst concentration is also shown in Fig. 7b-7d. It was noted that the predicted yield was enhanced at the higher Co(OAc)₂·4H₂O concentration (Fig. 7b), however, the ODDA yield was reduced after attaining the maximum when Co(OAc)₂·4H₂O concentration was increased further. On the other hand, the higher concentration of Mn(OAc)₂·4H₂O and HBr improved the yield of ODDA (Fig. 7c and d), however, the yield of ODDA was unaffected when the concentration of Mn(II) and Br–were increased beyond 500 and 900 ppm, respectively. The interacting effects among the catalysts were also determined and the order of influence on ODDA yield was found to be X₁-X₂ (81.60%) > X₁-X₂ (9.97%) > X₂-X₃ (8.41%) respectively, which are also shown in Fig. 8a. The interacting effects of catalyst concentration on ODDA yield are shown by the three-dimensional (3D) plots and two-dimensional (2D) contour plots (Fig. 8b–d). It was observed that the interacting effect of Co(OAc)₂·4H₂O and HBr is very significant to increase the yield of ODDA (Fig. 8a) in spite of the minimum effect of Co(OAc)₂·4H₂O concentration on yield (Fig. 7a). In other words, Co(OAc)₂·4H₂O catalyst interacts synergistically with HBr that helped to increase the yield of ODDA. The increased effect of the individual HBr and interacting effect of Co(OAc)₂·4H₂O-HBr revealed that the oxidation of SA proceeds via bromine-bromide cycle.

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Fig. 7 The effect of the individual catalyst on ODDA yield at fixed SA loading-10.0% (wt), 383 K and 2.8 barg. (a) Percentage contribution of the individual catalyst on ODDA yield. Influence of individual factor on ODDA yield under varying (b) X₁: Co(OAc)₂·4H₂O concentration (X₂ = X₃ = 0), (c) X₂: Mn(OAc)₂·4H₂O concentration (X₁ = X₃ = 0) and (d) X₃: HBr concentration (X₁ = X₂ = 0).

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Fig. 8 Interacting effect among the catalysts on ODDA yield at fixed SA loading-10.0% (wt), 383 K and 2.8 barg. (a) Percentage contribution of catalyst interaction on ODDA yield. The 3D response surface plot showing the interacting effects on ODDA yield under varying (b) X₁: Co(OAc)₂·4H₂O concentration and X₂: Mn(OAc)₂·4H₂O concentration (X₃ = 0) (c) X₂: Mn(OAc)₂·4H₂O concentration and X₃: HBr concentration (X₁ = 0) (d) X₁:Co(OAc)₂·4H₂O concentration and X₃: HBr concentration (X₂ = 0) with 2D contour plots.

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Design-Expert software was used to find the maximum yield of ODDA and corresponding optimum values of the catalyst concentration. Among the optimal solutions, ODDA yield with 81.74% was the most desirable solution and corresponding concentrations of cobalt (II), manganese (II) and bromide were found to be 600.4, 455.2 and 1016.6 ppm, respectively (Table 5). Using the optimum catalyst concentration, SA oxidation was carried at 10% SA loading, 2.8 barg and 383 K and it was observed that the actual and predicted ODDA yield was almost similar, which was found to be 81.87%.

3.6 SA oxidation kinetics

Elementary liquid phase pseudo-homogeneous SA oxidation kinetics was determined on the basis of the proposed oxidation pathway (Scheme 1). As the reaction time is much higher than oxygen diffusion time (Fig. 4a, 4b, 5 and 9), therefore overall oxidation process is controlled by the chemical kinetics. It was also assumed that SA reaction follows the first-order kinetics under constant oxygen partial pressure. Therefore, the variation of SA and ODDA molar concentration with time is given by:

Defining the conversion of SA $[\text{i}.\text{e}.\text{,}{\text{X}}_{\text{SA}}=({\text{C}}_{\text{SA,}0}-{\text{C}}_{\text{SA}})/{\text{C}}_{\text{SA,}0}]$ , a plot of $\text{ln}(1-{\text{X}}_{\text{SA}})$ vs. t, gives a straight line and rate constant, k was determined from the slope. It is mentioned that the rate constant in Eqs. (3a) and (3b) is a lumped kinetic parameter, which depends on temperature, ([S]) and total molar concentration of catalyst (i.e., [Σ] = [Co²⁺] + [Mn²⁺] + [Br⁻]) and expressed as

Hence, k₀ in Eq. (4) was determined by knowing k, [S] and [Σ] and Expt. No. 2 of Table 1 was chosen for this. The values of k, [S] and [Σ]for the Expt. 2 in Table 1 were found to be 0.0327 h⁻¹, 0.02198 mol L⁻¹ and 0.02305 mol L⁻¹, respectively and corresponding k₀(383) was found to be 64.5504 h⁻¹mol⁻² L². Using above k₀(383) value, the k-values were calculated under varying pressure (i.e., [S]) and catalyst concentration at a constant temperature. The details of observed [i.e., the slope of $\text{ln}(1-{\text{X}}_{\text{SA}})$ vs. t plot] and calculated k-values are reported in Table 6 under varying feed composition, pressure and catalyst loading. Percent absolute deviation of k-values $\left(\text{i}.\text{e}.\text{,}\%\text{AD}=\left|\frac{({\text{k}}_{\text{expt}}-{\text{k}}_{\text{cal}})}{{\text{k}}_{\text{expt}}}\times 100\right|\right)$ for each experiment in Table 1 (except temperature variation experiments) was determined and the details are given in Table 6. The percent average absolute deviation of k-values $\left(\text{i}.\text{e}.\text{,}\%\text{AAD}=\frac{1}{\text{N}}{\sum }_{\text{i}=1}^{\text{N}}\left|\frac{({\text{k}}_{\text{obs,i}}-{\text{k}}_{\text{pred,i}})}{{\text{k}}_{\text{obs,i}}}\right|\times 100\right)$ was also determined at different SA loading and pressure and found to be ≤3.60, indicating the accuracy of the calculated rate constants using proposed lumped rate constant. The details of the comparison between experimental (filled symbols) and predicted results (continuous/dotted lines) with varying SA loading and pressure is shown in Fig. 4a and b, respectively.

Under varying catalyst loading for the yield of ODDA ≥ 71.53% (i.e., Run Nos. 3, 4, 8 and 20 in Table 2b) and ≤51.96% (i.e., Run Nos. 2, 13, 15 and 19 in Table 2b), the observed and calculated molar concentration of SA and ODDA are shown in Fig. 9a and 9b. Corresponding to Fig. 9a and b, GC spectra of SA and ODDA are also shown in Figs. S5 and S6, respectively (Supplementary file). An AD was also calculated at different catalyst loading (Table 2b) and RSM predicted optimum catalyst concentration, and%AAD was found to be ≤5.0% (Table 6), showing the accuracy of the predicted rate constants.

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Fig. 9 Experimental and predicted molar concentrations of SA and ODDA under varying concentration of catalysts as per the design of experiments for (a) ODDA yield ≥ 71.53% (i.e., Run Nos. 3, 4, 8 and 20: Table 2b) and (b) ODDA yield ≤ 51.99% (i.e., Run Nos. 2, 13, 15 and 19: Table 2b) at fixed SA loading-10.0% (wt), 383 K and 2.8 barg.

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The temperature dependent k₀(T), i.e., the intrinsic rate constant, was determined for known temperature dependent [S] using Fig. 3b, [Σ] (i.e., 0.02305 mol L⁻¹: Table 1) and observed k-values (determined from the slope of $\text{ln}(1-{\text{X}}_{\text{SA}})$ vs. t plot at the different temperature: Expt. Nos. 2 and 5–7 in Table 1 and Fig. 5c). For known catalyst concentration, k₀(T) was calculated from the observed k-values and fitted with Arrhenius equation. The details of lnk₀(T) vs. 1/T plot are shown in Fig. 10 and k0(T) is given by the following equation:

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Fig. 10 Variation of intrinsic rate constant k₀(T) with temperature (T) for the oxidation of SA to ODDA using Arrhenius equation.

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The energy of activation for k₀(T) was found to be 34.55 kJ mol⁻¹. Based on the temperature dependent intrinsic rate constant k₀(T), time variant concentration profiles for SA and ODDA were generated using Eqs. (3a) and (3b) under varying temperature and the results are shown by continuous/dotted lines in Fig. 5c and corresponding AAD was found to be ≤3.28% (Table 6) indicating the accuracy of proposed lumped rate constant relating to temperature, pressure and catalyst concentration.