Kinetics of long chain n-paraffin dehydrogenation over a commercial Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst

A kinetic modeling study on long chain n -para ﬃ n dehydrogenation using a commercial Pt-Sn-K-Mg/ γ -Al 2 O 3 catalyst was carried out in a continuous ﬂ ow set-up using n -dodecane as a model component at various temperatures (450-470 °C), pressures (0.17-0.30MPa), H 2 /para ﬃ n mole ratios (3:1-6:1) and space times (0.22-1.57gh mol − 1 ). The commercial catalyst was characterized by XRD, BET, MIP, SEM and CO chemisorption. An empirical exponential equation was found to predict the mono-and di-ole ﬁ n yields very well. In addition, 6 mechanistic models based on the LHMW mechanism were derived and tested by non-linear least squares ﬁ tting of the experimental data. The model which assumes that surface reactions and particularly the dehydrogenation of the metal-alkyl chain to the adsorbed mono-ole ﬁ n and di-ole ﬁ n as the rate determining steps was found to give the best ﬁ t with the experimental data. In addition, activation energies and adsorption enthalpies for each elementary reaction were obtained. The kinetic testing and modeling have shown that the high mono-ole ﬁ ns selectivity for long chain para ﬃ n dehydrogenation can be obtained by operating at low space time (when P, T and m are same), high pressure (when τ , T and m are same) and high H 2 /para ﬃ n ratio (when τ , P and T are same), as well as low reaction temperature (when τ , P and m are same) but with little e ﬀ ect.


Introduction
Dehydrogenation of long chain, kerosene range, n-paraffins to mono-olefins over a Pt-Sn/γ-Al 2 O 3 based catalyst operated at high temperatures (475-490 °C) and low pressures (0.1−0.25 MPa) is an important step in the production of linear alkylbenzene sulfonates (LAS), with widespread applications as biodegradable detergents.The commercial feedstock is a mixture of n-paraffins with different chain lengths (generally n-C 10 -C 13 ), each of which has a different dehydrogenation rate [1] and as such, the reaction network for n-paraffin dehydrogenation is very complicated.In addition, other reactions occur as well [2,3], examples are (i) cracking to lighter fractions, (ii) consecutive dehydrogenation and formation of aromatics via dehydrocyclization, and (iii) coke formation.These reactions take place on the metal and/or acid sites of the typically used bi-functional Pt-Sn/γ-Al 2 O 3 catalysts.In order to obtain high mono-olefin selectivity, these side reactions forming dienes, trienes/aromatics [4,5], etc., must be suppressed kinetically or inhibited by proper modification of the Pt-Sn/ γ-Al 2 O 3 catalyst.The high temperatures used for n-paraffin dehydrogenation to overcome thermodynamic equilibrium limitations also results in the formation of substantial amounts of coke.Modifications of the Pt-Sn/γ-Al 2 O 3 catalyst by e.g., the introduction of (i) alkaline [6][7][8], alkaline earth [9][10][11] and transition metals [12][13][14], (ii) rare earth elements [15], and (iii) the use of carbon as support [16,17], have been reported to improve the mono-olefin selectivity and catalyst life-time.Recently, a Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst has been commercialized in PetroChina, PR China [18], which is characterized by longer life-time (72 vs. 58 days), higher operation temperature (490 vs. 481 °C) and higher daily production (333.6 vs. 321.5 tons day −1 ), as compared to Pt-Sn-K/γ-Al 2 O 3 catalyst.The better performance of Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst was attributed to the higher mechanical strength and better thermal stability of Mg-Al-O support, as well as the moderated acidity, enhanced interaction of Pt and support, and the increased pore volume and pore size diameter resulted from adding Mg [9].However, detailed kinetic studies on long chain paraffin dehydrogenation are scarce, although is of high importance for determining (i) the reaction mechanism, (ii) to establish reaction networks and (iii) to be used for reactor engineering studies, e.g., for the proper simulation and design of commercial reactors.
Krylova et al. [19] investigated the kinetics of n-decane dehydrogenation over Pt-W-Li/Al 2 O 3 catalyst using hydrogen/deuterium isotope exchange experiments and proposed a stepwise reaction scheme, in which the desorption of mono-and di-olefins was regarded as the rate determining step.This kinetic model was further expanded by Sadykhova et al. [20,21], and allowed determination of the kinetic parameters for n-decane, n-undecane and n-dodecane dehydrogenation over a Pt-Sn/Al 2 O 3 catalyst.Basrur et al. [22] investigated the kinetics of n-decane dehydrogenation over the promoted Pt/Al 2 O 3 catalyst using a Box-Wilson method and developed an empirical model for predicting paraffin conversion/olefin selectivity vs. operational parameters.Padmavathi et al. [23] studied the kinetics of n-dodecane dehydrogenation over a Pt-Sn-In-Fe-Li/Al 2 O 3 catalyst and discriminated five possible reaction schemes using a Box optimization method.Their results indicate the occurrence of a stepwise mechanism for long chain paraffin dehydrogenation over such promoted Pt/Al 2 O 3 catalysts.In addition, the most suitable kinetic model based on Langmuir-Hinshelwood-Hougen-Watson (LHHW) mechanism was determined in which the surface reaction was identified as the rate determining step.This kinetic scheme was further adopted by Vafajoo et al. [24] to optimize the rate parameters for commercial plant data by a Nelder-Mead (NM) simplex method.Ivashkina et al. [25] analyzed the thermodynamics of C 9 -C 14 dehydrogenation by means of quantum chemistry and established a kinetic model including deactivation due to coke formation.Kinetic models for deactivation of long chain paraffin dehydrogenation catalyst were also discussed by Gaidai et al. [26] and Saeedizad et al. [27].It was shown [26,27] that coking was mainly caused by the formation of dienes.In previous studies by our group [28], it was found that three different types of coke were present at a deactivated Pt-Sn-K/Al 2 O 3 catalyst used for long chain paraffin dehydrogenation.The coke was present at different positions on the catalytically active surface, viz. on Pt nanoparticle sites, acid sites on the Al 2 O 3 support in close proximity of the Pt nanoparticles and discrete acid sites on the Al 2 O 3 support.
It is generally accepted [29] that the dehydrogenation reactions (e.g., dehydrogenation of paraffins and mono-olefins) are catalyzed by the metal (e.g., Pt) sites of the bi-functional Pt-Sn/γ-Al 2 O 3 catalyst whereas most of the side reactions (e.g., isomerization and coking) take place on the Lewis acid sites of the catalyst.To the best of our knowledge, kinetic studies on long chain n-paraffin dehydrogenation considering both sites of the bi-functional Pt-Sn/γ-Al 2 O 3 catalyst have not yet been considered, although it is highly relevant for designing an efficient catalyst with respect to mono-olefin selectivity and coking/ catalyst deactivation.In this context a "bi-functional mechanistic model" is proposed for the first time.The kinetics of long chain nparaffin dehydrogenation over an industrial Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst [18] using n-dodecane as the model component will be reported, applying LHHW mechanisms which were reported earlier [23,24] and commonly used for describing the catalytic dehydrogenation reactions [30].The models include both surface reaction steps on metal nanoparticles (Pt) and acid sites.The best model was selected using appropriate model discrimination methods.Finally, relations to predict the mono-and di-olefin yield at different reaction conditions (temperature, pressure and H 2 /paraffin ratio) were established and verified.

Catalyst characterization
X-ray diffraction (XRD) spectra of the catalyst were obtained using a PAN Alytical X′ Pert PRO instrument with Cu Kα radiation (40 kV and 40 mA) in the scan 2θ range of 20-80°.
The specific surface area of the catalyst was calculated from the adsorption isotherms obtained from nitrogen physisorption experiments at 77 K using a Micromeritics ASAP system (2010, USA) based on Brunauer-Emmett-Teller (BET) theory [31].Pore size distributions (PSD) were calculated from the desorption branches of the isotherms according to the BJH (Barrett-Joyner-Halenda) method [32].The catalyst was degassed at 300 °C prior to these measurements.
The total pore volume of the catalyst was measured using mercury intrusion porosimetry (MIP, Micromeritics Autopore 9520, USA).The catalyst was pre-degassed in vacuum (0.01 torr) for 1 h at 95 °C.
Scanning Pt dispersion of the catalyst was determined by CO pulse chemisorption using a Micromeritics AutoChem II 2920 (USA).The catalyst was pre-reduced under pure H 2 (99.99%, 20 ml min −1 ) at 500 °C for 1 h, purged with helium (99.99%, 20 ml min −1 ) at 520 °C for 1 h and then cooled to 50 °C in He. 100 μL pulses of 5 vol.%CO/He were used and the time between pulses was 4 min.The adsorbed CO was determined by TCD and Pt dispersion calculations were based on the assumption that the value of CO/Pt s is 1 [33].

Experimental setup and kinetic measurements
The experimental setup for n-dodecane dehydrogenation consisted of a micro-catalytic setup [34] with a fixed-bed reactor (tubular stainless steel, 10-mm-inner-diameter).The reactor was loaded with the commercial Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst (0.24 g), which was grounded to particle sizes between 0.25−0.6mm to eliminate axial back-mixing and channeling effects in the catalyst bed.The catalyst was pre-reduced in-situ by hydrogen (99.995%, 500 ml min −1 ) at 470 °C for 2 h.Reaction temperatures (T, 450, 460 and 470 °C) were measured by a thermocouple in the catalyst bed and used to control the reactor temperature by adjusting the electronic furnace temperature.Reactor pressures (P, 0.17, 0.24 and 0.30 MPa) were measured by a pressure gauge at the bottom of the catalyst bed and controlled by a back pressure regulator.n-Dodecane was fed to the reactor using an HPLC pump, and space times (τ = W/F P ) between 0.22-1.57g catalyst (mol h −1 ) −1 were applied.The hydrogen flow was measured and controlled by mass flow controller and two hydrogen to paraffin mole ratios (m, 3:1 and 6:1) were applied.For each set of reaction conditions (e.g., for each combination of T, P and m), 5 data points were collected by varying the space time (τ) over the catalyst.In total, 60 data points were collected for the modeling and an overview of the data is given in Table S1 (Supporting Information).
After reaction, the products and un-reacted paraffins were condensed and analyzed using an Agilent 7890 A (USA) Gas Chromatograph equipped with a flame ionization detector (FID) and an HP-FFAP column (30 m × 0.53 mm × 1.0 mm, Agilent, USA) [9].The conversion of n-dodecane (X P ) was derived from its GC peak area percentage (A P , Eq. 1).The selectivities (S) to mono-(C 12 = , S O ) and diolefins (C 12 = = , S D ) were defined based on their fraction in the total products (Eq.2).The corresponding yields (Y) were calculated using Eq. 3.

Determination of external and internal diffusion limitations and heat transfer limitations
To study the effect of external diffusion on the kinetic data, two experiments were performed at 450 °C with different catalyst intakes (0.24 g and 0.48 g).The n-dodecane feed (F P ) and not the catalyst intake was varied to compare the n-dodecane conversion at equal space times (τ = W/F) and the results are shown in Fig. 3.The curves for the n-dodecane conversion versus space time are similar for both catalyst intakes, implying that external diffusion effects are negligible when the space time is smaller than 1.5 g (mol h −1 ) −1 .Accordingly, the space time for all the kinetic experiments was below this value to eliminate external mass transport limitations.
The Weisz-Prater criterion (Eq.4) was used to evaluate the relevance of internal diffusion effects.
where r P,obs is the observed average reaction rate of n-dodecane (mol kg −1 s −1 ), ρ cat is the density of the catalyst (kg m -3 ), R p is the average radius of the catalyst particles (m), C P is the average concentration of ndodecane (mol m -3 ) and D P is the internal diffusion of paraffin in the catalyst pores, assuming Knudsen diffusion (m 2 s −1 ).Details on the calculation of the Weisz-Prater criterion are given in the Supplementary Information.
The calculated values of N WP are shown in Table S1 for each experimental run.None of the experimental values exceeds 0.2, indicating the absence of internal diffusion limitation of n-dodecane.In addition, earlier experimental studies by us in the same reactor at similar reaction conditions as the present kinetic study with different catalyst particle sizes [34] also showed that internal diffusion effects were absent when using a catalyst with particle sizes in the range of 0.85-1.0mm.
Possible internal heat transfer limitations were analyzed using the coupled concentration and temperature profiles inside the catalyst particles [35,36].From the analysis, the calculated temperature differences inside the catalyst particles, ΔT particle = T surface -T center , were found as 0.03 K on average with a maximum value of 0.085 K (Table S1).These differences were considered too small to take into consideration.
Possible temperature differences due to external heat transfer limitations are quantified from a balance equating the rate of heat removal via the film with the rate of heat production in the catalyst particle.The results in the form of the calculated temperature differences over the film surrounding the catalyst particles, ΔT film = T g -T surace , are given in Table S1 and are on average 1.5 K with a maximum value of 3.85 K.These differences were considered too small to take into consideration as well.
In parallel, isomerization, dehydrocyclization (of paraffins), cracking and coking also take place.The latter pathway is particularly catalyzed by the acid sites of the catalyst.When the acidity of the catalyst is reduced (e.g., by alkali doping), the latter pathway is suppressed.
When using modified catalysts (Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst, [5]), as in this study, tri-olefins at any given time were too low for detection, in line with the observation from the industrial long chain paraffin process and the analysis of reaction products using temperature-programmed reaction/single-photon ionization time-of-flight mass spectrometry (TPRn/SPI-TOF-MS) measurements [4,5], which is likely due to that they are the transient species and get converted at a very fast rate to aromatics.As such, tri-olefins are not considered in the model.Accordingly, the consecutive reaction pathway (RP1) can be simplified to RP2.Langmuir -Hinshelwood -Hougen -Watson (LHHW) and Power -Law (P-L) models are commonly used in heterogeneous catalysis.Padmavathi et al. [23] and Vafjoo et al. [24] have shown that LHHW based models fitted the experimental data well, though without specifying catalytic sites.We here consider two types of adsorption sites on the bi-functional Pt-Sn/γ-Al 2 O 3 based catalyst, viz., metal nanoparticle sites (Pt, denoted as M) and Lewis acid sites (denoted as L).The proposed reaction scheme consists of 13 reactions, including adsorption/ desorption equilibria and surface reactions (Table 1).All reactions were considered to be reversible, elementary reactions, the only exceptions being dehydrogenation of adsorbed di-olefins on M sites (Reaction No. 8 in Table 1) and for the formation of aromatics from adsorbed diolefins on L sites cooperated with M sites (Reaction No. 11 in Table 1).These two reactions were considered as irreversible [2,3] as thermodynamically most stable product, viz., aromatics, is formed and the backward reactions are expected to occur with very low rates.The reaction scheme is summarized in Scheme 1 and was set up using the following assumptions (H1-H10).
H1. Existence of three different active sites [28], viz., Pt nanoparticles, Al 2 O 3 support acid sites with Pt naoparticles in close vicinity and isolated acid sites on the Al 2 O 3 support.As experimental techniques allow only to measure the total number of Lewis acid sites and it is not possible to estimate the fraction of the above two types of acid sites, they are lumped as Lewis acid sites to simplify the kinetic model.The Lewis acid sites of interest are a fixed fraction because there is only one catalyst being used, it will be incorporated in the rate constants for the steps where the Lewis acid sites are involved.
H3. Adsorption of paraffins occurs only on the Pt sites.H4.Dehydrogenation of paraffins on Pt sites proceeds step-wise, viz., first formation of adsorbed M-alkyl and M−H species.In the next step, the M-alkyl species react to yield an adsorbed mono-olefin and a second M−H species.
H5. Hydrogen gas is formed by a surface reaction between two adsorbed M−H species on Pt sites [23,30].
H6.The adsorbed mono-olefins, di-olefins, aromatics and H 2 species on Pt sites can be desorbed to form the corresponding products.
H7.The desorbed di-olefins can also be adsorbed on the Lewis acid sites.The desorbed mono-olefins from metal sites was not considered to re-adsorb on Lewis acid sites due to the adsorption on Lewis acid sites is always weaker than metal sites and minor.And practically, the catalyst design and reaction conditions (e.g., low contact time) for long chain paraffin dehydrogenation are optimized to render the mono-olefins desorption a facile process.
H8.The adsorbed di-olefins on Lewis acid sites can be transformed into aromatics via dehydrocyclization in cooperation of Pt sites [29] follows step-wise reaction mechanisms.These stepwise reactions are lumped in one reaction to simplify the model, due to the fact that dehydrocyclization is not the core reaction and minimized in long chain paraffin dehydrogenation process.
H9.The adsorbed aromatics on the Lewis acid sites can be desorbed to form aromatics.
H10. Coking and cracking reactions are not included in the model.This is due to the fact that their reaction rates are so low that the corresponding products are not detectable at the reaction conditions applied.This can also be indicated by the reported long life-time of and low coke deposition on the catalysts for long chain n-paraffins dehydrogenation, which were 30 days and 8 wt.% for Pt-Sn-Li/Al 2 O 3 [38], 37 days and 7.9 wt.% for Pt-Sn-In-Fe/Al 2 O 3 [39], and 72 days and 3.8 wt.% for the Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst investigated in this kinetic study [18].

From reaction network to kinetic models
To obtain expressions for the three reaction rates r P , r O and r D (RP2), the Langmuir-Hinshelwood-Hougen-Watson (LHHW) approach was followed, assuming that certain reactions among those presented in Table 1 are rate determining (rds).A total of 6 different kinetic models were derived: 3. Dehydrogenation of adsorbed paraffins on M sites -2nd step (non-equilibrium) L: Lewis acid sites; M: Pt sites.The dependency of kinetic parameters and equilibrium constants on temperature can be indicated by Arrhenius equation (Eq.5) and Van 't Hoff equation (Eq.6), separately.
Hence, for each parameter stated in the formulae above, two kinetic constants were estimated, viz., the pre-exponential factor (k 0,i or K 0,i ) and the activation energy (Ea i ) or enthalpy (ΔH i ).Most parameters were imposed to be positive, in order to be physically meaningful.However, the enthalpy of adsorption reactions (e.g., for reactions No. 1, 4, 7, 10 and 12, Table 1) were set to be negative because adsorption is an exothermic process.

Reactor modeling and parameter estimation
The reactions were carried out in a fixed bed reactor and it was assumed that the reactor behaves as a PFR reactor.Volume expansion in the reactor was not considered as it is limited due to the low conversion of n-dodecane (e.g., < 10%) and very high amount of hydrogen gas (e.g., H 2 /paraffin mole ratios was 3:1 -6:1) was used as the dilution gas.As such, the following 5 ordinary differential equations (ODEs, Eqs.7-11) were used for reactor modeling.2 ) where P T is the total pressure and τ is the space time.The initial conditions are represented by the initial partial pressures of n-dodecane and hydrogen, which can be calculated from the experimental pressure and the hydrogen to paraffin ratio in the feed (m).By integrating the system between 0 and the desired space time τ, it is possible to determine the partial pressures of all the species involved.Eqs.7-11 were implemented in the software package Matlab™ (The Mathworks, Inc.) and solved using the function ode15 s.
Parameter estimation was performed in MatLab™ using the function lsqnonlin, which is based on a non-linear least square minimization method and involved all 60 experimentally obtained data points (Table S1).The sum of the normalized squared deviations (NSD) was optimized.For the i th species and the j th experiment, the normalized deviation NSD i,j is defined as Eq.12.
where x is the conversion (for paraffins) or yield (for mono-olefins and di-olefins) for model and experiments.The use of normalized deviations was preferred over relative errors as the latter method gives an excessive weight to the smaller values, resulting in a poor fitting for the higher ones.
For model discrimination, the root mean squared error (RMSE) and the Pearson's correlation coefficient R 2 for each model were calculated for each species.

Characteristics of the industrial Pt-Sn-K-Mg/γ-Al2O3 catalyst
The Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst was characterised using XRD, nitrogen physisorption, mercury intrusion porosimetry (MIP) and SEM and the results are shown in Fig. 1 and summarised in Table 2. XRD patterns of the catalyst (Fig. 1a) show h-k-l reflections characteristic of the γ-Al 2 O 3 phase (JCPD No. 04-0858).The nitrogen adsorption/desorption data (Fig. 1b) of the catalyst show a type IV isotherm and a H1type hysteresis loop [40], indicating the presence of mesoporous and macroporous cylindrical pores.This is further illustrated by the PSD obtained by the BJH method (Fig. 1b) and the MIP data (Fig. 1c).The bimodal PSD structure (Fig. 1c, centered at 14.6 nm and 1300 nm) is typical for long chain paraffin dehydrogenation catalysts.

Effect of the process conditions on n-dodecane dehydrogenation
The yields of mono-olefins and di-olefins during n-dodecane dehydrogenation over Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst at different temperatures (T), pressures (P), H 2 /paraffin ratios (m) and space times (τ) are plotted in Fig. 2. It can be seen from Fig. 2 that when P, m and τ are constant (e.g., P = 0.24 MPa, m = 6:1 and τ = 0.45), higher reaction temperature leads to an increase in the yields of mono-olefin (Y O , Fig. 2a, c and  e) and di-olefin (Y D , Fig. 2b, d and f).When T, m and τ are the same (e.g., T = 450 °C, m = 6:1 and τ = 0.45), increasing the reaction pressure decreases the yields of mono-olefin (Y O , Fig. 2a) and di-olefin (Y D , Fig. 2b).When T, P and τ are same (e.g., T = 460 °C, P = 0.17 MPa and τ = 0.45), increasing the H 2 /paraffin ratio (m) the yields of mono-olefin (Y O , Fig. 2c) and di-olefin (Y D , Fig. 2d).When T, P and m are constant (e.g., T = 470 °C, P = 0.30 MPa and m = 6:1), increasing the space time (τ) over the catalyst favors higher yields of mono-olefin (Y O , Fig. 2e) and di-olefin (Y D , Fig. 2f).These trends follow from the thermodynamics of dehydrogenation of long chain paraffins to olefins, which is an endothermic reversible reaction accompanied by volume expansion.
The effect of the space time (τ) and yields of mono-and di-olefins (Y O and Y D ) was modeled using a simple empirical approach (Eq.13).
The results are shown in Fig. 2 (solid lines) and the equations with parameter values are given in the Supplementary Information.Agreement between the experimental data and the predicted values is very good.The Empirical modeling (Eqs.13, S1 and S2) and our kinetic testing (Fig. 2) reveal that the increased selectivity of mono-olefins (or the ratio of mono-olefins yields to di-olefins yields) can be obtained by operating at low space time (when P, T and m are same), low reaction temperature (when τ, P and m are same), high pressure (when τ, T and m are same) and high H 2 /paraffin ratio (when τ, P and T are same).

Table 2
Characteristics of the Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst used in this study.

Kinetic modelling results
The experimental data set with 60 experiments at a range of conditions was used for kinetic modeling.The model quality indicators (NSD, RMSE and R 2 ) for the 6 different models tested are provided in Table 3 whereas the corresponding kinetic parameters for each model are given in Table 4.The models based on adsorption (Model 1) and desorption (Model 6) as the rds show significantly higher values for the NSD and RMSE and lower values for R 2 than the models based on surface reactions (Models 2-5).As such, models with surface reactions as the rate determining steps seem to fit the experimental data better, which is consistent with previous research [23].This is also supported by considering the parity plots in Fig. 4 and Figs.S2-S5.
At first sight, the model quality indicators for the remaining four models with surface reactions as the rds are rather similar (Table 3).However, Model 4 and 5 present slightly lower values for the RMSE and NSD compared to the other two surface-reaction-based models (Models 2 and 3).Both Models 4 and 5 assume that the rds is the dehydrogenation of half-dehydrogenated C 12 H 23 M species adsorbed on Pt sites to the adsorbed di-olefin, viz., the second step of mono-olefin dehydrogenation to di-olefin (Reaction 6, Table 1).These findings imply that the second step of mono-olefin dehydrogenation is slower than the first.
The activation energies of Model 4 (54.5 KJ mol −1 ) and Model 5 (59.3 KJ mol −1 ) for dodecane dehydrogenation to mono-olefins are in the range (31.4-78.0KJ mol −1 ) reported for dodecane dehydrogenation by Sadykhova et al. [21], Kang et al. [41], Padmavathi et al. [23] and Jiang et al. [42].Further detailed comparison between Models 4 and 5 show that the Pearson's correlation coefficient for Model 5 is better than for Model 4, in line with the parity plots in Fig. 4. Thus Model 5 was selected as the best model for this kinetic study, which assumed that the rate determining steps are represented by the second step in the dehydrogenation of both paraffin and mono-olefin (r P and r O ).
The activation energies of Model 5 for dodecane dehydrogenation to mono-olefins (59.3 KJ mol −1 ) and for mono-olefins dehydrogenation to di-olefins (53.9 KJ mol −1 ) are very close, indicating the formation of mono-olefins and di-olefins have similar sensitivity with the temperature increase.This is also well reflected by the small change of monoolefins to di-olefins ratio when the temperature increases from 450 °C to 470 °C during the kinetic testing.Practically, we have also observed that the selectivity of mono-olefins is relatively stable (or slightly decreased) during the life-span of 72 days when the operation temperature in the industrial plant increases from 478 °C to 490 °C to keep the productivity [18].This can be kinetically explained from our kinetic modeling which proves that the increase of temperature (e.g., 450-490 °C) has little effect on mono-olefins to di-olefins ratio related to their similar reaction activation energy.As such, other operation parameters, e.g., pressure, should be resorted to more effectively tune the mono-olefin selectivity for long chain paraffins dehydrogenation, indicated by the above kinetic testing and modeling.
A previous mechanistic study [29] has shown that the metal sites are required to cleave the C-H bond of the adsorbed paraffin (or monoolefin).Only when the two neighboring C atoms are activated, the corresponding mono-olefin (or di-olefin) can be formed (RP3).The present kinetic results reveal that the half-dehydrogenated paraffin and mono-olefin adsorbed on the metal sites are more difficult to be dehydrogenated (Step 2, Reactions No. 3 and 6, Table 1) on the neighboring metal sites than the first step (dehydrogenation of the paraffin and mono-olefin adsorbed on the metal sites, Reactions No. 2 and 5, Table 1).This is due to the fact that the second dehydrogenation step requires extra metal sites which are present and adjacent to those adsorbing the half-dehydrogenated species.Thus lowering the liquid hourly space velocity (LHSV) of paraffins (viz., increasing τ) while keeping T, P and m same can decrease the concentration of the adsorbed paraffin (or mono-olefins) on metal sites (e.g., Pt) surface, leading to the increased yields of mono-olefins and di-olefins which is in line with the observation from our kinetic testing (Fig. 2).Alternatively, increasing the loading of the noble metal (e.g., Pt) on the long chain paraffin dehydrogenation catalyst might be another option to increase the overall reaction rate.However, it was often observed that increasing Pt loading decreases the Pt dispersion [43], resulting in a lowering of the rate of olefin formation [44].Our kinetic results also indicates that the noble metals (e.g., Pt) are not required in large quantities but are needed to be highly dispersed on the support (e.g., γ-Al 2 O 3 with high surface area) [2] to generate high concentration of Pt particle surface per support surface area.

(RP3)
It is interesting to notice that the reaction rate for the aromatization step (Table 1) for the best model (Model 5) includes two additive terms.One involves K DL which takes into account the synergy between Pt and acid sites (Reaction 11, Table 1) and the other one is K DM , where the

Table 4
Reaction rate constants, reaction equilibrium constants and adsorption constants for n-dodecane dehydrogenation over Pt-Sn-K-Mg/γ-Al  pathway only involves the reaction on Pt sites (Reaction No. 8, Table 1).The estimated kinetic parameters in Table 4, along with the simulation results, indicate that the former pathway is predominant.Thus, the above calculations prove the reported assumption that aromatization and further coking are accelerated by acid sites together with Pt sites [2].Because highly dispersed metal (Pt) sites are required for high reaction rates for long chain paraffin dehydrogenation to olefins, neutralization of the Lewis acid sites is expected to lower aromatics and coke formation rates for improved olefin selectivity and prolonged catalyst lifetime.Indeed, this is done in practice by modifying the catalysts with alkali metals such as Li [7,8], Na [45], K [6,7] and Cs [45].

Conclusions
The empirical model presented here for the kinetics of n-dodecane dehydrogenation over the Pt-Sn-K-Mg/γ-Al 2 O 3 catalyst shows promise by successfully predicting the yields of mono-and di-olefins within the industrially relevant conditions (450-470 °C, 0.17−0.30MPa, H 2 /paraffin mole ratios between 3:1 and 6:1, space times between 0.22-1.57g h mol −1 ).Operation at low space time, high pressure, high H 2 /paraffin ratio and low reaction temperature is favorable to high mono-olefins selectivity.The bi-functional model is relevant because it is based on the elementary reactions on Pt and Lewis acid sites, key characteristics of this dehydrogenation catalyst.Within the six reaction rate models tested, the surface step involving the interaction of Pt-H and Pt-alkyl species to result in an absorbed mono-olefin or di-olefin is observed to be the kinetically relevant rate determining step.The kinetic modeling indicates that the increased temperature within a certain range (e.g., 450-490 °C) has little effect on mono-olefin selectivity, which opens the opportunity for the industry to maintain the productivity at later period of catalyst life-time by increasing the operation temperature while keeping relatively stable product selectivity.Kinetic data also suggests that aromatization was majorly caused by Pt and Lewis acid sites in a concerted way.This is critical in the design of an efficient catalyst as, lowering the aromatics formation by neutralizing Lewis acid sites can (i) improve olefin selectivity and (ii) prolong catalyst life-time as aromatics are precursor to coke.Both are extremely relevant of commercial operation of long chain paraffins dehydrogenation catalysts.
The values of activation energy are given in kJ mol −1

Financial
support from the Liaoning Provincial Natural Science Foundation of China (Grant No. 2013020111) and a visiting professor program from the King Saud University, Saudi Arabia for this research are acknowledged.S.He also thanks Prof. C. Sun at Dalian Institute of Chemical Physics, Chinese Academy of Sciences for collaborations on R
electron microscopy (SEM) measurements were performed

Table 3
Model quality indicators for the 6 kinetic models.