Gas‐phase catalytic isomerization of n ‐heptane using Pt/(CrO x /ZrO 2 )‐HMS catalysts: A kinetic modeling

A systematic study has been conducted to optimize the process conditions and to evaluate the kinetic parameters for the isomerization reaction of n‐heptane on the novel platinum‐chromium/zirconium‐ hexagonal mesoporous silica (Pt/(CrOx/ZrO2)‐HMS) catalysts (PCZH). The kinetic experiments were performed in a fixed‐bed reactor at the reaction temperatures of 200–350°C, Cr/Zr molar ratio of 5–35, the n‐C7 flow rate of 2–4.5 cc h−1, and H2 flow rate of 20–45 cc min−1. The statistical analysis of all experimental data was carried out using analysis of variance to optimize the operating conditions for n‐heptane reactions. The results show that the incorporation of Cr into the Pt‐Zr‐HMS structure promotes the kinetic rate of the isomerization reaction. Sharp elevation from 0.08 to 0.3 mol g−1 s−1 in the isomerization kinetic rates can be observed in the PCZH(35) and a temperature of 350 °C, when the H2 flow rate increases from 20 to 45 cc min−1 at a constant flow rate of n‐C7 (4.5 cc h−1). The surface and contour plot verifies that the kinetic rate does not significantly vary with respect to studied temperatures and Cr/Zr ratio when the flow rate of isomerization feeds is considerably low. The experimental kinetic rate obtained on the optimum condition is in good agreement with the prediction of the response surface method. The kinetic model of Langmuir–Hinshelwood as well as a power‐law model was developed for this reaction. A reasonably good fit of the obtained data shows that the Langmuir–Hinshelwood model has a better performance to define the isomerization of the n‐heptane process.

Keywords: kinetics; Langmuir–Hinshelwood model; n‐heptane isomerization; optimization; response surface methodology

INTRODUCTION

Isomerization of straight‐chain alkanes to its corresponding branched‐chain isomers is an effective technique to upgrade the gasoline quality and create more ecofriendly fuel to fulfill the new environmental regulations.1 Catalytic isomerization is proved to be an efficient and economical approach for improving the octane number of gasoline and reducing its aromatic content. Various catalysts such as bifunctional catalysts,2,3 zeolite‐containing catalysts, including noble metals like Pt1 or Pd,4 Friedel–Crafts catalyst,5 tungsten sulfide,6 and other complicated forms were utilized in the isomerization process.7 Generally, bifunctional solid catalysts include metallic sites in the dehydrogenating process and acidic sites for isomerization/cyclization functionalities. The addition of another metal part such as Zr,8 Fe,9 Cr,10,11 Al,12 Sn,13 Re,13 and Ir14 to modify the properties of a metallic section, which mainly utilized noble metals (specifically Pt), has been studied for isomerization reactions in recent years. These metals can closely interact with Pt which can affectthe selectivity, activity, and stability of catalysts.

Investigation of previous research reveals that various techniques can be utilized to improve the efficiency of the isomerization reaction: (a) employing high acidic catalysts and superacidic materials can proceed the isomerization reaction at lower temperatures and boost the formation of isomerization products, (b) the cracking process can be significantly diminished using hydride transfer agents, and (c) the synthesis of composite zeolites structures including the zeolite component with a meso‐ or macroporous material, which accelerates the diffusion properties and elevates the yield of isomerized final products.15 Mesoporous molecular sieves absorbed much attention of researchers for further investigation in the catalytic reactions.16,17 Although the silica surface of these materials has weak reactivity, however various benefits such as uniform and tunable pore structure, high surface area, and Si exchangeable by other elements are fascinated to use these compounds. The weak reactivity is attributed to the fact that the available silanol groups accomplished only hydrogen bonds with adjacent gaseous molecules or barely ionizing in aqueous solutions. Several elements such as Co,18 Ti,19,20 Al,21 V,22 Fe,23 and Mn 24 were added to the mesoporous frameworks to elevate their acid and/or redox properties. In our previous researches, several modifications to the catalytic activities of Pt catalysts supported hexagonal mesoporous silica (HMS) and also its composite with other materials is accomplished for the n‐heptane isomerization.1,11–13,15 The synthesis of a series of Pt/ZSM‐5/HMS, Pt/Zr‐HMS, Pt/Al‐HMS/HZSM‐5, Pt/Zr(x)‐HMS/HZSM‐5, and Pt‐(Sn, Re)/HZSM5‐HMS reveals that HMS can be considered as a proper candidate for isomerization processes. In the new approaches, a novel Pt–Cr/Zr(x)‐HMS catalyst with different molar ratios of Cr/Zr was synthesized in our past research and utilized for n‐C7 isomerization. Various characterization tests, including X‐ray powder diffraction (XRD), X‐ray fluorescence (XRF), NH3 temperature programmed desorption (TPD), Fourier‐transform infrared spectroscopy (FTIR), H2 chemisorption, nitrogen sorption, and thermogravimetric analysis (TGA), were carried out. Also, several catalyst performances such as activity and various forms of the selectivity, including MOB (monobranched) heptane, MUB (multibranched) heptane, i‐C7 (MOB + MUB), cracking, hydrogenolysis, and RON (research octane number) at an extended range of feed temperature and exposure time have been tested.11

In continuation of the previous work, the kinetics of n‐heptane isomerization measurements over trimetallic Pt–Cr/Zr(x)‐HMS catalysts were investigated in this article. Effective parameters such as the flow rate of H2 and n‐C7, temperature (T), and catalyst molar ratio (M) were selected as influential factors on the catalyst efficiency in the isomerization reactions. The kinetics of n‐heptane as a model component of heavy naphtha during the isomerization reaction using power law15 and Langmuir–Hinshelwood models15 is studied. Moreover, a response surface methodology11 (RSM) is recruited to explore the relationship between the aforementioned parameters. To find the maximum amount of the kinetic rate, the optimization procedure on input variables (n‐H2, n‐C7, T, and M) is applied to find the best conditions. Three distinct points of views are highlighted in this article: (a) the kinetic study of the novel Pt–Cr/Zr(x)‐HMS catalyst with various chromium‐to‐zirconium (Cr/Zr) molar ratios for n‐heptane isomerization, which has not been addressed in the previous studies, (b) remarkable performance of RSM in finding the relationship between the reaction rate with respect to studied influential input parameters, and (c) finding suitable kinetic models for n‐C7 isomerization over the novel catalysts.

To the best of our knowledge, the kinetic study of n‐heptane isomerization on the Pt/(CrOx/ZrO2)‐HMS has not been reported in the literature to date. This comprehensive approach can offer considerable development in catalytic isomerization processes.

EXPERIMENTAL

Catalyst preparation

A series of Pt/(CrOx/ZrO2)‐HMS catalysts with different molar ratios of Cr/Zr were prepared using the impregnation method. These molar ratios were varied from 5 to 35. Novel Pt/(CrOx/ZrO2)‐HMS catalysts with different Cr/Zr molar ratios were named as PCZH(5), PCZH(10), PCZH(20), and PCZH(35), respectively. In all catalysts, the Pt amount was maintained at 0.6 wt%. In this method, an aqueous solution was prepared using the required amounts of ammonium dichromate and zirconyl(IV) nitrate hydrate. Pt/(CrOx/ZrO2)‐HMS catalysts were prepared by impregnating appropriate solutions of hexachloroplatinic acid on a (CrOx/ZrO2)‐HMS catalyst. The details of the preparation, plus all the characterization tests, including XRD, XRF, NH3‐TPD, FTIR, H2 chemisorption, nitrogen sorption, and TGA procedures are given elsewhere.11

Kinetic setup

In the kinetic study, two distinct gas cylinders including H2 (>95% purity) was used to provide the required gas feed stream for the isomerization reactions. The volumetric flow rate of gas feed into the reactor was adjusted by a precalibrated flow meter. To prevent moisture from entering into the fixed reactor, two separate cylinders containing silica gel were utilized to dry the incoming gas. For each experiment, the liquid n‐C7 feed was pumped into a feed system vaporizer via a syringe pump and blended with the H2 stream at various controlled temperatures. A fixed‐bed Pyrex microreactor packed with 1 g of the prepared catalyst was utilized for the investigation of kinetic study. The aforementioned reactor operated under isothermal conditions and connected to an online gas chromatograph (Agilent Technologies 7890A equipped with a flame ionization detector) by a controller. The exhaust gas of the reactor was analyzed several times during the reaction in the desired time interval. Liquid feed (n‐heptane) and inlet gas (hydrogen) are mixed by a glass tube at the top of the reactor and by passing through the catalyst bed. A stainless‐steel tube equipped with a thermal coating to prevent the condensation process was employed to convey products of the reactor to a gas chromatograph. A Lindberg furnace is employed to provide the necessary temperature for the isomerization reaction. Also, the K‐type thermocouple was used to measure the reactor bed temperature.

Design of experiments

It has been proved that mathematical models are powerful tools for simulation and optimization of chemical reaction systems.25,26 Among them, the statistical models would facilitate correlating operating parameters and provide a better view of the performance of the experimental processes. Mainly, three distinct steps were completed in the design of experiments (DOE): (a) statistical design of experiments, (b) estimation of coefficients through a mathematical model with the prediction of response, and (c) analysis of the model's applicability.

In the present work, a response surface experimental design was applied for the investigation of n‐heptane isomerization with Pt/(CrOx/ZrO2)‐HMS catalysts. The most popular response surface method is the central composite design (CCD) procedure, which can be employed for developing the proper polynomial modeling and determining the various parameter efficiency. A detailed discussion about the CCD method can be found elsewhere.27 To assist the PCZH(x) catalyst for n‐heptane isomerization, a set of various data with 30 different preparation experiments were proposed by Design‐Expert Software V.11, as shown in Table 1. According to that, four independent factors, including the H2 flow rate (A: cc min−1), n‐C7 flow rate (B: cc h−1), feed temperature (C: °C), and a catalyst molar ratio (D) were utilized in the RSM with the CCD technique and three levels of 1 (factorial points) plus the center point.27,28 All the aforementioned parameters are varied in a particular range of values in which the minimum, central, and maximum amount concerning their values in the actual and coded form are shown in Table 1. Experiments were performed at the temperatures, molar ratios of Cr/Zr, n‐heptane, and H2 flow rates of 200–350°C, 5–35, 2–4.5 cc h−1, and 20–45 cc min−1, respectively. The selection of these parameters with their specific experimental ranges was meticulously based on the preliminary screening test. Many attempts have been made to select parameters which are frequently used in the literature and also have effective impact on the kinetic rate.12,13,15 The selection of these variables were purposefully chosen after the preliminary screening test, and these variables are regularly used in the literature. All experiments were performed in a fixed‐bed reactor containing 1 g of a prepared catalyst which was kept constant in all the test runs. The CCD routine is employed to determine the least experiments supposed to be accomplished for optimizing the input variables and output responses.27 It can be ensured that employing a CCD routine leads to obtain the least tests that are believed to be accomplished by optimizing the input variables and output response. Process and analysis of variance (ANOVA) are very useful and essential for analyzing datasets.29 It allows comparisons to be made between three or more groups of data. To obtain the kinetic parameters, experimental data were analyzed using a power law and the Langmuir–Hinshelwood model. The kinetic model derived from the Langmuir–Hinshelwood approach was developed considering surface reaction mechanisms of n‐heptane isomerization. The kinetic parameters were estimated using a nonlinear least‐square regression by fitting the expression to the experimental data.

1 TABLEMatrix of input variables and the observed response by the CCD design

	Level
Parameter	Low (−1)	Center (0)	High (+1)
A: H2 flow rate (cc min−1)	200	275	350
B: n‐C7 flow rate (cc h−1)	5	20	35
C: Temperature (°C)	20.0	32.5	45.0
D: Molar ratio of catalyst	2.00	3.25	4.50

1 TABLEMatrix of input variables and the observed response by the CCD design

Run	Parameter	Observed responses
–	A	B	C	D	Rate (mol g−1 s−1)
1	40.0	4.50	300	5	0.193
2	30.0	2.00	350	20	0.162
3	32.5	3.25	275	35	0.166
4	20.0	2.00	350	5	0.123
5	45.0	2.00	250	20	0.152
6	30.0	2.00	250	35	0.147
7	40.0	4.50	300	35	0.259
8	45.0	2.00	200	5	0.118
9	32.5	3.25	200	20	0.101
10	30.0	2.00	300	20	0.160
11	20.0	2.00	350	35	0.164
12	40.0	4.00	300	20	0.231
13	20.0	2.00	250	35	0.151
14	40.0	4.50	200	10	0.153
15	20.0	4.50	200	5	0.079
16	32.5	3.25	275	5	0.121
17	30.0	4.00	250	5	0.074
18	40.0	3.00	250	10	0.128
19	20.0	2.00	350	35	0.174
20	45.0	2.00	350	35	0.156
21	30.0	2.00	250	5	0.125
22	20.0	4.50	350	5	0.072
23	30.0	3.00	200	20	0.057
24	20.0	3.25	275	20	0.064
25	40.0	4.50	300	10	0.170
26	20.0	4.50	200	35	0.095
27	45.0	2.00	200	35	0.143
28	40.0	2.00	300	10	0.107
29	30.0	3.00	250	10	0.034
30	20.0	4.50	350	35	0.055

RESULTS AND DISCUSSION

Modeling and optimization using RSM

In the RSM approach, the actual responses achieved from the DOE were utilized to construct appropriate mathematical correlations between the input variables and new predicted values. The CCD was applied to entire sets of experiments, and the ANOVA table will be utilized to confirm the adequacy of the model. The quadratic equation was fitted with the experimental results attained on the basis of CCD. The final equation obtained in terms of coded factors is presented in Table 2.

2 TABLECoefficients of the final equation in terms of actual factors

Actual equation = a+bA + cB + dC+eD+ fAB+ gAC + hAD+iBC + jBD+kCD+lA2+ mB2+ nC2+ oD2
A: H2 flow rate (cc min−1), B: n‐C7 flow rate (cc h−1), C: Temperature (°C), D: Molar ratio of catalyst
Coefficient	a	b	c	d	e
Rate	+0.610	−0.020	−0.288	+0.001	+0.002
Coefficient	f	g	h	i	j
Rate	+0.003	+6.912E−06	+0.005E−02	−0.001E−02	+0.012E−02
Coefficient	k	l	m	n	o
Rate	+3.784E−07	+0.002E−01	+0.030	−2.321E−06	−0.007E−02

This equation in terms of actual factors may be utilized to make estimates about the response at given levels of each factor. Figure 1 depicts the performance of RSM for the output data. R‐squared (R2) is a goodness‐of‐fit measure for linear regression models, which show the strength of the relationship between the model and the dependent variable. Also, the root mean square error (RMSE) is the standard deviation of the residuals (prediction errors).30 According to statistical analysis, it can be concluded that RSM can successfully predict the kinetic rate with respect to studied independent input data (R2 = 0.989, RMSE = 0.007). The ANOVA results for fitting the suggested model are shown in Table 3.

3 TABLEAnalysis of variance (ANOVA) for the surface response of the suggested model

	ANOVA for quadratic model (R2 = 0.989)
Source	Sum of square	Df0001	Mean square	F‐value	p‐Value
Model	0.059	14	0.004	4.90	0.002	Significant
A: H2 flow rate	0.022	1	0.022	25.28	0.002E−01	–
B: n‐C7 flow rate	0.002	1	0.002	2.67	0.123	–
C: Temperature	0.001	1	0.001	1.42	0.253	–
D: Molar ratio of catalyst	0.006	1	0.006	7.51	0.015	–
AB	0.026	1	0.026	29.97	<0.001E−01	–
AC	0.005E−01	1	0.005E−01	0.57	0.464	–
AD	0.001	1	0.001	1.20	0.290	–
BC	0.000	1	0.000	0.02	0.903	–
BD	0.001E−01	1	0.001E−01	0.10	0.754	–
CD	2.487E−06	1	2.487E−06	0.00	0.958	–
A2	0.001	1	0.001	1.56	0.231	–
B2	0.006	1	0.006	6.39	0.023	–
C2	0.005E−01	1	0.005E−01	0.64	0.438	–
D2	0.007E−01	1	0.007E−01	0.87	0.365	–
Residual	0.013	15	0.009E−01	–	–	–
Lack of fit	0.013	14	0.009E−01	20.10	0.173	Not significant
Pure error	0.0003	1	0.000	–	–	–
Cor total	0.072	29	–	–	–	–

1 a Degree of freedom.

The F‐value for the model is the test statistic used to define whether any term in the model is related to the response, including blocks and factor terms.31 It can be achieved by dividing the model mean square by its residual mean. A large F ratio can be obtained when the null hypothesis is wrong (the data are not sampled from populations with the same mean) and when random sampling happened to end up with large values in some groups and small values in others. The statistic is only one measure of significance in the F test, then it should be considered the p‐value. The p‐value is determined by the F statistic and indicates the probability of occurrence of the results. Also, the probability that measures the evidence against the null hypothesis is gained by the p‐value. Lower probabilities offer stronger evidence against the null hypothesis.32 A p‐value lower than the significance level describes variation in the response, while in the larger amount no clear deduction can be made for variation in the response and offers to find a new model. Usually, a significance level (denoted as α) of 0.05 works well.31 According to Table 3, the F‐value of the kinetic rate model is obtained to be 4.90 which implies the model is significant.

An additional significant parameter for model evaluation is an adequate precision measure of the signal‐to‐noise (S/N) ratio. The S/N ratio denotes that the effect on the average responses and noises is computed by the influence on the deviations from the average responses, which will disclose the sensitiveness of the experiment output to the noise factors. The suitable S/N ratio should be chosen according to previous knowledge, expertise, and understanding of the process. Regardless of the category of the quality characteristics, a higher S/N ratio corresponds to a better quality characteristic. Therefore, the optimal level of the process parameters is at the same level with the highest S/N ratio. Totally, a ratio greater than 4 is desirable.33,34 Hence, the quadratic models of the kinetic rate with the S/N ratio of 8.960 indicate adequate precision signals for the models to be applied to navigate the design space. Also, the lack of fit is insignificant for the responses as indicated in the ANOVA table. It shows that lack of fit is not influential relative to the pure errors, and naturally eliminated terms are not significant for the models.

To see the overall operation of RSM methods, both surface performances and contour plots over the entire input domain will be presented. For a better comparison of three‐dimensional figures, the surface response was sketched against two input parameters while the other two remaining parameters were kept constant at maximum and minimum values. As it was mentioned before, the variation extent of the n‐C7 flow rate, H2 flow rate, temperature, and catalyst molar ratio is 2–4.5 cc h−1, (20–45 cc min−1‐, (200–350°C, and 5–35, respectively. Figure 2 shows the surface response (right) and contour plot (left) for a kinetic rate of n‐heptane isomerization as a function of two input variables of n‐C7 plus H2 flow rate at maximum temperature (350 °C) and a maximum catalyst molar ratio (35). Surface response and contour figures revealed that the maximum kinetic rate of n‐heptane isomerization (0.3) was observed at the high flow rate of both n‐C7 (4.5 cc h−1) and H2 (45 cc min−1). Increasing the H2 flow rate from 20 to 45 cc min−1 at a maximum constant flow rate of n‐C7 (4.5 cc h−1) leads to the sharp elevation of around 275% (from 0.08 to 0.3) in the kinetic rate of the isomerization process over the PCZH(35) and temperature of 350°C, while this amount decreased to 22% (from 0.14 to 0.17) at a minimum constant flow rate of n‐C7 (2 cc h−1). Generally, the minimum isomerization kinetic rate occurs at a minimum flow rate of H2 (20 cc min−1) in which variation in the n‐C7 flow rate has no significant effect on the output response. Increasing the n‐C7 flow rate at the high flow rate amount of H2 has a more profound effect on the isomerization kinetic elevation compared to a lower flow rate. The surface and contour plot of n‐heptane kinetic rate at a minimum temperature (200°C) and a minimum catalyst molar ratio (5) is shown in Figure 3. Similar to the previous figure, the highest kinetic rate was measured at the maximum flow rate of both n‐C7 and H2. At n‐C7 and H2 flow rate of (4.5, 45), decreasing temperature from 350 to 200°C and catalyst molar ratio from 35 to 5 leads to around 29.5% reduction in the isomerization kinetic rate. Again, the minimum kinetic rate can be observed at a minimum H2 flow rate and average extent range of n‐C7. Around 263% elevation in the output response can be observed with increasing the H2 flow rate from 20 to 45 cc min−1 at 4.5 cc h−1n‐C7 flow rate. Comparison of both Figures 2 and 3 reveals that variation in feed temperature and catalyst molar ratio does not have any significant effect on the overall shape of surface plots.

The variance in the isomerization kinetic rate against temperature and catalyst molar ratio of highest and lowest flow rates of n‐C7 and H2 is sketched in Figures 4 and 5, respectively. At a molar flow rate of n‐C7 (4.5 cc h−1) and H2 (45 cc min−1), increasing the temperature from 200 to 350°C and catalyst molar ratio of 5–35 leads to 42.85% elevation in the kinetic rate (see Figure 4). At the low amount of n‐C7 and H2 flow rates, the surface figure shows the very low slope variation through the entire input domain (see Figure 5). It means that the kinetic rate does not significantly vary with respect to studied temperatures and catalyst molar ratio when the flow rate of isomerization feeds is considerably low.

To find the maximum isomerization kinetic rate with respect to studied four input parameters, the optimization techniques by the Design‐Expert 11 has been performed. The specific optimal condition, including all the input variables and predicted response, is exhibited in Table 4. The optimization results of the CCD‐surface response were validated by the synthesis of the novel PCZH(x) catalyst and test under the reported optimum condition. The experimental results under the optimum condition validate the prediction of RSM very well (see Table 4) with a deviation of 0.21%.

4 TABLEOptimum conditions for the isomerization kinetic rate predicted by the CCD‐surface response and experimental results

	Kinetic rate (mol g−1 s−1)	n‐C7 flow rate (cc h−)	H2 flow rate (cc min−1)	Temperature (°C)	Catalyst molar ratio
CCD surface	0.26	4.19	44.87	328.41	27.82
The real rate at the optimum point	0.26	4.20	45.00	330.00	30.00

Power‐law and Langmuir–Hinshelwood models

The experimental data for the n‐heptane isomerization over four different Pt‐(CrOx/ZrO2)‐HMS catalysts have been kinetically modeled for the specific range mentioned in the Experimental section. Two distinct models have been studied to estimate the parameters for the n‐C7 isomerization reaction. Table 5 shows the parameter estimates of a regression of the kinetic rate data with the power law and Langmuir–Hinshelwood model for all synthesis catalysts at the various temperature ranges. The activation energies of catalysts were calculated using Arrhenius plots. Figure 6 shows the linear Arrhenius plots for this reaction. The activation energies for isomerization of n‐C7 using the power‐law model were obtained in the range of 5.76–19.98 kJ mol−1 (see Table 5). These results are lower than the values reported in the literature.12,15 The overall reaction rate (Equation 1) and also the power‐law model (Equation 2) are defined as follows:

$$rmolg-1s-1=n-C7flowrate\times n-C7density\times conversion(\%)n-C7molarweight\times weightofcatalyst\times impregnatedmetal,$$

$$r\left(\mathrm{mol}{\mathrm{g}}^{-1}{\mathrm{s}}^{-1}\right)=A{e}^{-\frac{E_{\mathrm{app}}^{\mathrm{act}}}{RT}}{P}_{\mathrm{H}2}^n{P}_{\mathrm{C}7}^m.$$

netics parameters and activation energies obtained from power law and Langmuir–Hinshelwood models

T (°C)	Order	PCZH(5)	PCZH(10)	PCZH(20)	PCZH(35)
Power law model
200	nH2	−0.09	−0.08	−0.08	−0.08
250	nH2	−0.08	−0.07	−0.07	−0.07
300	nH2	−0.07	−0.07	−0.06	−0.06
350	nH2	−0.06	−0.06	−0.06	−0.06
200	mC7	0.56	0.56	0.53	0.54
250	mC7	0.57	0.56	0.57	0.56
300	mC7	0.57	0.58	0.58	0.58
350	mC7	0.58	0.58	0.60	0.60
$Eappact(kJmol−1)$	5.76	9.59	19.26	19.98
Langmuir–Hinshelwood model
K	$Eappact(kJmol−1)$	61.3	67.7	43.6	59.6
	A (mol g − 1s − 1)	2.6 × 10−8	3.2 × 10−7	1.1 × 10−8	1.6 × 10−8
KC7	− ΔHads‐C7(kJ mol−1)	56.6	60.6	36.5	52.5
	AC7 (atm−1)	5.0 × 10−9	1.4 × 10−7	2.1 × 10−9	7.2 × 10−9
KH2	− ΔHads‐H2(kJ mol−1)	4.4	7.1	7.1	7.1
	AH2(atm−1)	1.3 × 10−2	2.7 × 10−2	2.7 × 10−2	2.7 × 10−2

This equation gives the apparent activation energies ( $E_{\mathrm{app}}^{\mathrm{act}}$ ), preexponential factors (A), the partial pressure of n‐C7 (PC7) and H2 (PH2) and the partial orders of H2 (n) and n‐C7 (m).

The power‐law model shows that the isomerization of n‐C7 follows 0.5‐order kinetics (on average) for all catalysts (see Table 5 and Figure 6B). The reaction order is −0.06 to −0.09 concerning hydrogen, suggesting low coverage of catalysts by H2 and 0.5 to 0.6 for n‐C7, indicating dissociative and strong adsorption of n‐C7. These results show that the reaction rate decreases with increasing H2 pressure.

The comparison between the predictions of the power‐law model and experimental data is shown in Figure 6(C). According to excellent correlation coefficients (R2), it can be claimed that the power‐law model can successfully predict the isomerization kinetic data for a novel synthesis catalyst. Other forms of the kinetic equation and related parameters for the n‐C7 isomerization reaction were derived on the assumption of the Langmuir–Hinshelwood model (see Table 5). The following reaction rate equation (Equation 3) was suggested based on the Langmuir–Hinshelwood mechanism:

3 $$r=Ae-EappactRT.Pc7.PH21AC7e-\Delta Hads-C7RT+Pc7.1AH2e-\Delta Hads-H2RT+PH2.$$

The adsorption heats of n‐C7 and H2 (ΔHads), the pre‐exponential factor of H2 adsorption (AH2), and the n‐C7 (AC7) are used in this equation.

As can be seen from Figure 6(D), this model exhibits good accuracy for all prepared catalysts. The correlation coefficient (R2) valuations for all catalysts were above 0.9, indicating that the error between experimental and calculated results is relatively low. Regarding this model, the activation energies on the Pt‐(CrOx/ZrO2)‐HMS catalysts were found to be ∼43 to 68 kJ mol−1, which is in agreement with the previous reports.12,15 So, it can be concluded that the Langmuir–Hinshelwood seems to be a suitable model for this reaction. Comparison of all kinetic data revealed that the (PCZH(20)) catalyst has shown the lowest activation energy for the used temperature region. According to Table 5, AH2 (the preexponential factor of H2 adsorption) is higher than AC7. This suggests faster adsorption of H2 over these catalysts. Also, the values for the adsorption heats of n‐C7 (ΔHads‐C7) are higher than H2 (ΔHads‐H2) that is based on the strong adsorption of the n‐C7.

CONCLUSION

The goal of the present study was to investigate the kinetic rate of a new solid catalyst for n‐heptane isomerization. In this way, the kinetic rate of various Pt‐Cr/Zr(x)‐HMS catalysts with different Cr/Zr molar ratios was obtained for isomerization purposes. The effect of diverse amounts of Cr/Zr, feed temperature, and flow rate of hydrogen and n‐heptane on the kinetics of the isomerization reaction was investigated. Around 30 different experiment runs were suggested by Design‐Expert software. The surface response methodology was utilized to find the relationships between input parameters and kinetic rate. Also, two distinct models have been studied to estimate the parameters for the n‐C7 isomerization reaction. Based on the obtained results, the following conclusions can be drawn:

• According to statistical analysis, it can be concluded that RSM can successfully predict the kinetic rate output response.
• At the maximum temperature and Cr/Zr ratio, the highest kinetic rate of n‐heptane isomerization was observed in the high flow rate of both n‐C7 (4.5 cc h−1) and H2 (45 cc min−1).
• The incorporation of Cr in the Pt‐Zr‐HMS catalyst structure can promote isomerization kinetic rate considerably.
• The kinetic rate does not significantly vary with temperature and catalyst molar ratio when the flow rate of isomerization feeds is considerably low.
• Validation of the optimized condition with experimental results shows the reliability of RSM for the prediction of the isomerization kinetic rate.
• Langmuir–Hinshelwood models show good agreement with experimental results.

ACKNOWLEDGMENT

The study was supported by Kosar University of Bojnord with the grant number 9907131736.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available within the article. Also these data are available from the corresponding author upon reasonable request.

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By Nastaran Parsafard; Ali Garmroodi and Shohreh Mirzaei

Reported by Author; Author; Author