Kinetic modeling and optimization of n-heptane catalytic isomerization using Box-Behnken experimental design

doi:10.21203/rs.3.rs-2589328/v1

The statistical analysis using response surface methodology approach was conducted for optimization of the kinetic conditions of the n-heptane isomerization reaction over Pt-HZSM-5/HMS catalysts. The conditions of the kinetic experiments were as H₂ flow rate of 20-45 cc min⁻¹, n-C₇ flow rate of 2-4.5 cc h⁻¹, the reaction temperatures in the range of 200-350 °C, and the weight percent of HZSM-5 of 10-40. The results show that the amounts of HZSM-5 into Pt-HMS structure helps the rate of n-heptane isomerization reaction. The surface and contour plots confirm that the reaction rates do not considerably change versus temperature and flow rates of n-heptane and H₂. 0.24 mol g⁻¹s⁻¹ is the highest reaction rate obtained in the 4.5 cc h⁻¹ n-heptane flow rate and 45 cc min⁻¹ H₂ flow rate. The modelling results show both power-law and Langmuir–Hinshelwood model are in agreement with the experimental data.

n-heptane isomerization

kinetics

Langmuir–Hinshelwood model

RSM

The extensive use of petroleum has convert to a serious worry due to the poisonousness of the released pollutants from its combustion in the vehicle engine. Considerable amounts of these pollutants released into the environment will possibly reason detrimental health effects to organisms. ^[1–5] Isomerization reaction has received a renewed attention due to high quality petroleum without production of pollutants such as aromatics and also no a decrease in the octane number of gasoline, which is a measure to show its combustion. This reaction involves a catalytic reaction beginning with n-paraffins to produce a wide distribution of branched hydrocarbons. ^[1–5]

In this process, the catalyst plays the main role in the progression of reaction. There are several reports about the application of different catalysts in this process. Among them and according to our previous researches, ^{[1, 6]} hybrid systems, due to their interesting features, high activity and thermal stability in the various catalytic reactions have attracted our attention.

In our previous research, ^[1] the activities of platinated catalysts supported on hexagonal mesoporous silica (HMS) were modified with HZSM-5 accomplished for the n-heptane (n-C₇) isomerization. A number of characterization analyzes, including X-ray diffraction (XRD), X-ray fluorescence (XRF), temperature programmed desorption of NH₃ (NH₃-TPD), Fourier-transform infrared spectroscopy (FTIR), H₂ chemisorption, nitrogen sorption, and thermogravimetric analysis (TGA) have proceeded. Moreover, numerous catalytic performances for example activity and selectivity to various products, such as mono- and multi- branched iso-heptanes, cracking, hydrogenolysis and also research octane number at a range of temperature and time on the stream have been tested. ^[1] Continuing this work, the kinetics of this reaction over Pt-HZSM-5/HMS catalysts were studied.

The study of reported researches exposes that different parameters can be effected to improve the effectiveness of the kinetics of n-C₇ isomerization reaction: (a) catalytic structural properties; (b) reaction conditions such as temperature and pressure; (c) the flow rates of each reactant; (d) and so on. ^[1–6]

Because examining several variables simultaneously requires a lot of time and money, ^[7] modeling tools were used in combination with experimental methods. One of these multivariate approaches is the Response Surface Method (RSM), which has been applied in experimental design, model building and optimization. This method is the mixture of statistical and mathematical methods and can analyze problems, where a connection between the response and the independent parameters through a response function. ^[8–10] In this research, to discover the maximum reaction rate, the optimal operation with RSM is used to find the best conditions.

In the present work, some effective parameters for example the H₂ and n-C₇ flow rates, temperature, and the weight percent of HZSM-5 were selected as important influences on the catalyst competence. Two models based on power law (LH) and Langmuir–Hinshelwood (LH) mechanism were used to study the kinetics of n-heptane.

According to reported literatures, the kinetic study of the aim reaction on the Pt-HZSM-5/HMS does not report earlier. This comprehensive method can suggest considerable development in the catalytic isomerization process.

2.1. Catalyst preparation

In this experiment, the preparation of Pt-HZSM-5/HMS catalysts refers to related literature. ^[1] The detailed steps are as follows: Dissolve 7 g ethanol in 5 g tetraethyl orthosilicate. After stirring, a solution of 1.2 g of dodecylamine and 0.5 ml of HCl (1 M) in 15 ml of distilled H₂O with various zeolite amounts are slowly added to the previous solution. After stirring for 6 h, the precipitate is washed several times and filtered, and placed in an oven at 110°C overnight. Finally, the Pt catalysts are calcined at 300 ℃ for 4 h. Pt amount in these catalysts is 0.6 wt%. Pt-HZSM-5/HMS catalysts were made by impregnating suitable amounts of HZSM-5 zeolite. ^[1]

The weight percent of zeolite was varied from 10 to 40. These prepared catalysts with different HZSM-5 weights were named as PZH-10, PZH-20, PZH-30, and PZH-40, respectively.

2.2. Kinetic unit

The experiments were done in a continuous laboratory scale unit. The unit consists of feed injector, gas flow meters, fixed bed Pyrex micro reactor, two silica gel for drying the input gas, H₂ gas cylinder, thermometer and cooler with an appropriate control system for heating. The n-heptane as a feed was injected into a vaporizer by a syringe pump and blended with H₂ at different controlled temperatures.

The reaction operated under isothermal conditions. An on-line gas chromatograph (Agilent Technologies 7890A equipped with a flame ionization detector) was also connected to a micro reactor by a controller for analyzing the consumed gas during the reaction in the chosen time interval. The reaction rate (Eq. 1) for the isomerization process was defined as follows:

$$r \left(\text{m}\text{o}\text{l} {\text{g}}^{-1} {\text{s}}^{-1}\right)=\frac{\text{t}\text{h}\text{e} \text{f}\text{l}\text{o}\text{w} \text{r}\text{a}\text{t}\text{e} \text{o}\text{f} \text{n}-\text{h}\text{e}\text{p}\text{t}\text{a}\text{n}\text{e}\times \text{d}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y} \text{o}\text{f} \text{n}-\text{h}\text{e}\text{p}\text{t}\text{a}\text{n}\text{e} \times \text{c}\text{o}\text{n}\text{v}\text{e}\text{r}\text{s}\text{i}\text{o}\text{n}\left(\text{\%}\right)}{\text{m}\text{o}\text{l}\text{a}\text{r} \text{w}\text{e}\text{i}\text{g}\text{h}\text{t} \text{o}\text{f} \text{n}-\text{h}\text{e}\text{p}\text{t}\text{a}\text{n}\text{e}\times \text{w}\text{e}\text{i}\text{g}\text{h}\text{t}\times \text{m}\text{e}\text{t}\text{a}\text{l} }$$

1

2.3. Design of experiments (DOE) and response surface methodology (RSM)

DOE/RSM model of n-heptane isomerization was developed, for which the H₂ flow rate (A: cc min^− 1), n–C₇ flow rate (B: cc h^− 1), temperature (C: ^○C) and the weight of HZSM-5 (D: %) are central factors, impacting on production. This model involves the mathematical and statistical methods which optimize the experimental data by a response of the system (dependent variable) as a function of independent variables influencing the system. ^[11] The ranges of operating conditions (independent variable) were shown in Table 1. Three levels, including low level (− 1), central value (0) and high level (+ 1) were measured for each factor. Box-Behnken was used as an experimental design for RSM. The responses of this design (by Design-Expert Software V.11) as the dependent variables were listed in Table 1.

Table 1

Input parameters and the experimental responses by the CCD design.
Parameters				Levels
Parameters				Low (-1)	Center (0)	High (+ 1)
A: H₂ flow rate (cc min^− 1)				20	32.5	45
B: n-C₇ flow rate (cc h^− 1)				2	3.25	4.5
C: Temperature (^○C)				200	275	350
D: Weight of HZSM-5 (%)				10	25	40
RUN	Parameters				Experimental Responses
-	A	B	C	D	rate (mol g^− 1s^− 1)
1	32.5	3.25	125	25	0.14
2	45.0	2.00	350	40	0.02
3	32.5	3.25	275	25	0.10
4	32.5	0.75	275	25	0.01
5	45.0	4.50	200	40	0.24
6	32.5	3.25	275	25	0.10
7	32.5	3.25	275	55	0.22
8	32.5	3.25	425	25	0.12
9	32.5	3.25	275	25	0.10
10	20.0	4.50	350	40	0.12
11	32.5	3.25	275	25	0.10
12	32.5	3.25	275	25	0.10
13	32.5	3.25	275	25	0.10
14	45.0	2.00	350	10	0.05
15	45.0	4.50	350	40	0.04
16	20.0	2.00	350	40	0.08
17	7.5	3.25	275	25	0.09
18	45.0	2.00	200	40	0.13
19	45.0	2.00	200	10	0.16
20	20.0	2.00	350	10	0.09
21	20.0	2.00	200	40	0.15
22	20.0	4.50	200	10	0.03
23	32.5	3.25	275	5	0.02
24	20.0	4.50	350	10	0.01
25	57.5	3.25	275	25	0.18
26	45.0	4.50	200	10	0.06
27	32.5	5.75	275	25	0.17
28	20.0	4.50	200	40	0.10
29	20.0	2.00	200	10	0.15
30	45.0	4.50	350	10	0.04

The response surface plots are due to the fittings of empirical models to the experimental data. These responses are according to a second order polynomial function of codified factors (Table 2).

Table 2

Coefficients of the final equation versus actual parameters.
Actual Equation = a + bA + cB + dC + eD + fAB + gAC + hAD + iBC + jBD + kCD + lA² + mB² + nC² + oD² + pABC + qABD + rACD + sBCD + tA²B + uA²C + vA²D + wAB² + xAC² + yAD² + zB²C + a`B²D + b`BC² + c`BD² + d`C²D + e`CD² + f`A³ + g`B³ + h`C³ + i`D³
Constant	a	b	c	d	e
response	+ 0.1007	+ 0.0230	+ 0.0397	-0.0049	+ 0.0504
Constant	f	g	h	i	j
response	+ 0.0144	-0.0186	-0.0033	+ 0.0076	+ 0.0265
Constant	k	l	m	n	o
response	-0.0091	+ 0.0037	-0.0072	+ 0.0027	+ 0.0009
Constant	p	q	r	s	t
response	-0.0059	+ 0.0028	-0.0128	-0.0085	-0.0504
Constant	u	v	w	x	y
response	-0.0308	-0.0327	-0.0220	+ 0.0000	+ 0.0000
Constant	z	a`	b`	c`	d`
response	+ 0.0000	+ 0.0000	+ 0.0000	+ 0.0000	+ 0.0000
Constant	e`	f`	g`	h`	i`
response	+ 0.0000	+ 0.0000	+ 0.0000	+ 0.0000	+ 0.0000

The analysis of variance (ANOVA) was done to estimate the statistical importance of the parameters and interactions using Fisher's test, and its associated probability level (p-value). T-tests were also used to investigate the import of the coefficients measured for each model. The goodness of fit of the models to the experimental data was compared by the coefficient of determination (R²). ^[11]

Two kinetic models based on power law (PL) and the Langmuir–Hinshelwood (LH) mechanism were used to obtain the kinetic parameters. A non-linear least-square regression was used to evaluation the kinetic parameters. ^[6]

3.1. Regression equation development and ANOVA analysis

A mathematical relationship between input variables and new experimental predicted responses was obtained for n-heptane in catalytic isomerization over Pt-ZH catalysts. The experiments were done in accordance with the designed matrix as shown in Table 1.

In the present work, the ANOVA analysis established cubic equations were developed in terms of the coded factors with the inclusion of both significant and insignificant terms for n-heptane isomerization under the use of the prepared catalysts as shown in Table 2.

Table 3 lists the linear effect of process variables coded A, B, C, and D, dual interactions as AB, AC, AD, BC, BD, and CD, square interactions as A², B², C², and D², triple interactions as ABC. ABD, ACD, and etc., cubic interactions as A³, B³, C³, and D³ on the response variables.

Table 3

ANOVA of quadratic model for the surface response of suggested model.
Source	Sum of Square	df^a	Mean Square	F-Value	P-Value
Model	0.0939	22	0.0043	4.6500	0.0219	significant
A: H₂ flow rate	0.0042	1	0.0042	4.6000	0.0691	-
B: n-C₇ flow rate	0.0126	1	0.0126	13.7700	0.0075	-
C: Temperature	0.0002	1	0.0002	0.2130	0.6584	-
D: Weight of HZSM-5	0.0203	1	0.0203	22.1200	0.0022	-
AB	0.0033	1	0.0033	3.6100	0.0993	-
AC	0.0056	1	0.0056	6.0500	0.0434	-
AD	0.0002	1	0.0002	0.1903	0.6758	-
BC	0.0009	1	0.0009	1.0000	0.3496	-
BD	0.0112	1	0.0112	12.2200	0.0101	-
CD	0.0013	1	0.0013	1.4500	0.2675	-
A²	0.0004	1	0.0004	0.4133	0.5408	-
B²	0.0014	1	0.0014	1.5400	0.2544	-
C²	0.0002	1	0.0002	0.2177	0.6550	-
D²	0.0000	1	0.0000	0.0225	0.8849	-
ABC	0.0006	1	0.0006	0.6136	0.4591	-
ABD	0.0001	1	0.0001	0.1332	0.7260	-
ACD	0.0026	1	0.0026	2.8500	0.1352	-
BCD	0.0012	1	0.0012	1.2700	0.2966	-
A²B	0.0136	1	0.0136	14.7800	0.0063	-
A²C	0.0050	1	0.0050	5.5000	0.0515	-
A²D	0.0057	1	0.0057	6.2000	0.0415	-
AB²	0.0026	1	0.0026	2.8100	0.1377	-
AC², AD², B²C, B²D, BC², BD², C²D, CD², A³, B³, C³, D³	0.0000	0	-	-	-	-
Residual	0.0064	7	0.0009	-	-	-
Lack of Fit	0.0064	2	0.0032	-	-	-
Pure Error	0.0000	5	0.0000	-	-	-
Cor Total	0.1003	29	Sum of squares is Type III - Partial
^a degree of freedom.

Statistical analysis of variance (ANOVA) has been led to investigate the importance of model and variables for n-C₇ isomerization. The low P-value (0.0219) and high F-value (4.65) obtained for the used model, which confirm the fitness and the significance of the model response. There is only a 2.19% chance that an F-value this large could occur due to noise. Commonly, a significant level (α) of 0.05 is well. ^[12] In this case B, D, AC, BD, A²B, A²D are significant model terms. Values greater than 0.1000 indicate the model terms are not significant.

The model has the R² amount near to unity (0.94) that presents the model predicted data to approach the response data and the association of the model and the dependent parameters. A good correlation between predicted and actual experimental data of n-C₇ isomerization are presented in Fig. 1 Furthermore, the Root Mean Square Error (RMSE) that is the standard deviation of the residuals, ^[12] obtained RMSE = 0.03 for these data. The signal to noise ratio greater than 4 is another major factor for model evaluation. The results show the signal to noise ratios of 9.04 that indicates the used cubic model to be used to direct the design space. According to ANOVA data, the Lack of Fit is 0.0064 of the responses. Compared to the pure errors, the lack of fit is influential. However, the pure errors naturally eliminate and are not significant in this model.

The combined effect of operating parameters as H₂ flow rate (2-4.5, cc h^− 1), n-C₇ flow rate (20–45 cc min^− 1), temperature (200–350 ^○C), and weight of HZSM-5 (10–40%) on the isomerization reaction was studied by 3D response surface achieved from RSM as presented in Fig. 2. The contour graphs were also shown at Fig. 3. Among two variables, the third and fourth variables were fixed at the middle values (A: 32.5, B: 3.25, C: 275, and D: 25). The combined effect of H₂ flow rate and n-C₇ flow rate on this process in the constant temperature (275 ^○C) and weight of HZSM-5 (25%) as surface performances is shown in Fig. 2a. The rest of the parameter pairs are shown in other parts of this figure while the other parameter pairs are kept constant.

According to the surface response and contour plots, the maximum reaction rate (0.24 mol g^− 1 s^− 1) has obtained in the high flow rate of both n-C₇ (4.5 cc h^− 1) and H₂ (45 cc min^− 1). Increasing the H₂ flow rate to 45 cc min^− 1 at a maximum constant flow rate of n-C₇ (4.5 cc h^− 1) promotes the kinetic rate at around 200 ^○C for the PZH-40 catalyst, while this amount decreased to 0.13 mol g^− 1s^− 1 at n-C₇ flow rate (2.00 cc h^− 1).

Among operating parameters of H₂ flow rate, n-C₇ flow rate, temperature, and weight of HZSM-5 perturbation plot show that temperature was a most influencing factor for isomerization reaction followed weight of HZSM-5 as shown in Fig. 4.

Table 4 presents the specific optimal conditions as the input variables and predicted responses by the Design-Expert 11. The experimental results under the optimum conditions of the CCD-surface response confirm the prediction of RSM is very well with a deviation of 0.03%.

Table 4

Best conditions for the reaction rate of n-C₇ isomerization predicted by the CCD-surface response and experimental results.
	Reaction rate	n-C₇ flow rate	H₂ flow rate	Temperature	Weight of HZSM-5
CCD surface	0.24	4.50	43.25	200.00	40.00
The real rate at the best point	0.24	4.50	45.00	200.00	40.00

3.2. PL and LH models

PL and LH models over the conditions cited in the experimental section have been considered. The estimated parameters of these two models were summarized in Table 5. The Arrhenius plots (Fig. 5a) show the activation energies in the range of ~ 31 to ~ 99 kJ/mol (Table 5) for this process.

Table 5

PL and LH parameters and activation energies.
T (^oC)	Orders	PZH-10	PZH-20	PZH-30	PZH-40
	PL model
200	${n}_{H2}$	-0.07	-0.08	-0.02	-0.09
250	${n}_{H2}$	-0.06	-0.06	-0.03	-0.06
300	${n}_{H2}$	-0.03	-0.05	-0.01	-0.05
350	${n}_{H2}$	-0.03	-0.05	-0.01	-0.04
200	${m}_{C7}$	0.47	0.67	0.60	0.57
250	${m}_{C7}$	0.60	0.71	0.62	0.93
300	${m}_{C7}$	0.77	0.72	0.80	0.96
350	${m}_{C7}$	0.96	0.84	1.03	0.98
	${E}_{app}^{act} \left(\text{k}\text{J}{\text{m}\text{o}\text{l}}^{-1}\right)$	86.22	31.09	96.89	99.07
	LH model
$K$	${E}_{app }^{act}\left(\text{k}\text{J}{\text{m}\text{o}\text{l}}^{-1}\right)$	95.2	54.2	99.8	100.6
	$A \left(\text{m}\text{o}\text{l}{\left(\text{g}\text{s}\right)}^{-1}\right)$	1.1×10^− 5	1.1×10^− 9	2.7×10^− 5	9.0×10^− 7
${K}_{C7}$	${-\varDelta H}_{ads-C7}\left(\text{k}\text{J}{\text{m}\text{o}\text{l}}^{-1}\right)$	27.2	15.6	87.5	52.6
	${A}_{C7} \left({\text{a}\text{t}\text{m}}^{-1}\right)$	1.2×10^− 11	1.2×10^− 12	2.7×10^− 5	9.2×10^− 9
${K}_{H2}$	${-\varDelta H}_{ads-H2}\left(\text{k}\text{J}{\text{m}\text{o}\text{l}}^{-1}\right)$	4.5	7.1	7.1	7.1
	${A}_{H2}\left({\text{a}\text{t}\text{m}}^{-1}\right)$	1.4×10^− 2	2.7×10^− 2	2.7×10^− 2	2.7×10^− 2

According to the equation of PL model (Eq. 2), the reaction order concerning hydrogen is -0.01 to -0.09 and the order kinetics for n-C₇ is 0.47–1.03 (see Table 5 and Fig. 5b).

$$r \left(\frac{\text{m}\text{o}\text{l}}{\text{g}\bullet \text{s}}\right)=A {e}^{-\frac{{E}_{\text{a}\text{p}\text{p}}^{\text{a}\text{c}\text{t}} }{\text{R}\text{T}}}{P}_{H2}^{n}{P}_{C7}^{m}$$

2

The H₂ reaction orders suggest low coverage of catalysts by H₂ and the dissociative and strong adsorption of n-C₇. According the results, the reaction rate declines with increasing P_H2.

To evaluate the performance of these models, regressions of the predicted and experimental data were drawn in Fig. 5c & d. The correlation coefficients (R²) were shown both models produce acceptable predicted results. However, the PL model is only a mathematical and unrealistic model, the Langmuir-Hinshelwood model can make better predictions by considering its mechanism (Eq. 3).

$$r=\frac{A {e}^{-\frac{{E}_{\text{a}\text{p}\text{p}}^{\text{a}\text{c}\text{t}} }{\text{R}\text{T}}} .{ P}_{c7} .{ P}_{H2}}{\left(\left(\frac{1}{{A}_{C7} {e}^{-\frac{{\varDelta \text{H}}_{ads-C7} }{\text{R}\text{T}}}} \right)+{ P}_{c7}\right).\left(\left(\frac{1}{{A}_{H2} {e}^{-\frac{{\varDelta \text{H}}_{ads-H2} }{\text{R}\text{T}}}} \right)+{ P}_{H2}\right)}$$

3

The correlation coefficients (R²) valuations of this model (above 0.9) indicate the low error between experimental and predicted data (Fig. 5d). The activation energies obtained this model are in the range of ~ 54 to 100 kJ mol^− 1, which is in accordance with the previous literatures. ^{[6, 13]}

According to Table 5, PZH-20 has the lowest activation energy that it confirms this catalyst fast reaction. The results show A_H2 (the pre-exponential factor of H₂ adsorption) is higher than A_C7. This presents faster adsorption of H₂ than n-C₇. Based on the strong adsorption of the n-C₇, the n-C₇ adsorption heat (ΔH_ads-C7) is higher than H₂ (ΔH_ads-H2).

In this study, the effect of HZSM-5 amounts, temperature and n-C₇ and H₂ flow rates on the kinetics of this reaction were studied over platinated HZSM-5/HMS catalysts. To discover the relationships between these parameters and reaction rates, around 30 different runs of the surface response methodology were designed by Design-Expert software. On the basis of the predicted data, the below conclusions can be obtained:

1) In accordance with the obtained response, RSM can successfully predict the reaction rates.

2) The highest reaction rate (0.24 mol g^− 1 s^− 1) has occurred in the high flow rate of both n-C₇ (4.5 cc h^− 1) and H₂ (45 cc min^− 1).

3) The amount of HZSM-5 in the PZH-x structure is the most effective parameter on the isomerization kinetic rate.

4) Compared to the effect of zeolite content on the activity of catalysts, the other parameters, especially temperature, have not significantly effect on the rate response.

5) PL and LH models were used to evaluate the parameters for this process. These models show good agreement with experimental results.

There is no research involving human participants and/or animals in this work.

There is no competing interests.

The author does the entire work.

There is no funding for this work.

All data and materials are available in the text.

N. Parsafard, M. H. Peyrovi, M. Rashidzadeh, Micropor. Mesopor. Mater. 200, 190–198 (2014).
L.P. Teh, H.D. Setiabudi, S.M. Sidik, et. al. Mater. Chem. Phys. 263, 124406 (2021).
M.H. Peyrovi, N. Parsafard, P. Peyrovi, Ind. Eng. Chem. Res. 53, 14253–14262 (2014).
B. Zhang, W. Zhou, J. Zhang, et. al. CCS Chem. 3371–3382 (2021).
Z. Ghaderi, M.H. Peyrovi, N. Parsafard, BMC Chem. 15, 1–8 (2021).
N. Parsafard, M.H. Peyrovi, M. Jarayedi, Energy Fuel. 31, 6389–6396 (2017).
M.D.G. de Luna, M.M. Sablas, C.M. Hung, et al. Chemosphere. 251, 126254 (2020).
N. Jiang, Y. Zhao, C. Qiu, et al. Appl. Catal. B: Env. 259, 118061 (2019).
M.Y. Ong., S. Nomanbhay, F. Kusumo, et al. Energies. 14, 295 (2021).
P. Gupta, K.K. Nayak, Int. J. Biol. Macromol. 85, 141–149 (2016).
A.F. Silva, P. Neves, S.M. Rocha, et al. Fuel. 259, 116256 (2020).
N. Parsafard, A. Garmroodi, S. Mirzaei, Int. J. Chem. Kinet. 53, 971–981 (2021).
M.H. Peyrovi, N. Parsafard, H.R. Anajafi, Chem. Phys. Let. 713, 32–38 (2018).

No competing interests reported.

Kinetic modeling and optimization of n-heptane catalytic isomerization using Box-Behnken experimental design

Status:

Version 1

Abstract

Figures

1. Introduction

2. Experimental Section

2.1. Catalyst preparation

2.2. Kinetic unit

2.3. Design of experiments (DOE) and response surface methodology (RSM)

3. Results And Discussions

3.1. Regression equation development and ANOVA analysis

3.2. PL and LH models

4. Conclusion

Declarations

References

Additional Declarations

Status:

Version 1

T (^oC)	Orders	PZH-10	PZH-20	PZH-30	PZH-40
	PL model
200	\({n}_{H2}\)	-0.07	-0.08	-0.02	-0.09
250	\({n}_{H2}\)	-0.06	-0.06	-0.03	-0.06
300	\({n}_{H2}\)	-0.03	-0.05	-0.01	-0.05
350	\({n}_{H2}\)	-0.03	-0.05	-0.01	-0.04
200	\({m}_{C7}\)	0.47	0.67	0.60	0.57
250	\({m}_{C7}\)	0.60	0.71	0.62	0.93
300	\({m}_{C7}\)	0.77	0.72	0.80	0.96
350	\({m}_{C7}\)	0.96	0.84	1.03	0.98
	\({E}_{app}^{act} \left(\text{k}\text{J}{\text{m}\text{o}\text{l}}^{-1}\right)\)	86.22	31.09	96.89	99.07
	LH model
\(K\)	\({E}_{app }^{act}\left(\text{k}\text{J}{\text{m}\text{o}\text{l}}^{-1}\right)\)	95.2	54.2	99.8	100.6
	\(A \left(\text{m}\text{o}\text{l}{\left(\text{g}\text{s}\right)}^{-1}\right)\)	1.1×10^− 5	1.1×10^− 9	2.7×10^− 5	9.0×10^− 7
\({K}_{C7}\)	\({-\varDelta H}_{ads-C7}\left(\text{k}\text{J}{\text{m}\text{o}\text{l}}^{-1}\right)\)	27.2	15.6	87.5	52.6
	\({A}_{C7} \left({\text{a}\text{t}\text{m}}^{-1}\right)\)	1.2×10^− 11	1.2×10^− 12	2.7×10^− 5	9.2×10^− 9
\({K}_{H2}\)	\({-\varDelta H}_{ads-H2}\left(\text{k}\text{J}{\text{m}\text{o}\text{l}}^{-1}\right)\)	4.5	7.1	7.1	7.1
	\({A}_{H2}\left({\text{a}\text{t}\text{m}}^{-1}\right)\)	1.4×10^− 2	2.7×10^− 2	2.7×10^− 2	2.7×10^− 2