Kinetic Model of Olefins/Isobutane Alkylation Using Sulfuric Acid as Catalyst

Abstract

The alkylation of isobutane and low molecular olefins using strong acid as catalysts is an important process in the petrochemical field, and its product, alkylate, is an ideal gasoline blending component due to high octane number, low vapor pressure, low sulfur, and lack of aromatics. To better meet the optimization process of the simulation of the alkylation unit, a reaction kinetic model with 20 reactions based on industrial data was developed, in which the alkylation products were divided into lumped components in detail. The reactor model was established based on the flow state and structural pattern of the industrial reactor, considering the internal circulation flow, and is suitable for the simulation of the DuPont alkylation process. Also, eventually, the model parameters were solved by the nonlinear least-squares fitting method. The results of the validation calculations showed that the kinetic model fitted the experimental data with good agreement. In addition, the reaction kinetic model was used to predict the influence of operating conditions, which is consistent with the trend in actual industrial production.

1. Introduction

In the oil refining industry, the alkylation process is an important process in which isobutane is used as the raw material and reacts with C₃–C₅ olefins using strong acid as catalyst to produce alkylates. The product has high octane number, low sulfur content, and no olefins or aromatics, which makes it a very ideal gasoline blending component.^1,2 The alkylate as a blending component of gasoline can not only increase its octane number but also dilute other gasoline components as a solvent and reduce the content of sulfur, olefins, and aromatics in gasoline.

With the continuous development of the automobile manufacturing industry, high-octane number gasoline with good antiknock performance has received more and more attention. In addition, the environmental regulations also have increasingly strict requirements for olefin, benzene, and aromatic content in gasoline. In China, the National VI standard³ for gasoline released in 2016 has made significant downward adjustments to the upper limits of aromatic, olefin, and benzene content, which requires the aromatic content to be no more than 35%, benzene content to be no more than 0.8%, and olefin content to be no more than 18%, which indicates that high-octane number alkylates with the advantages of no aromatics, benzene, and olefins are becoming more and more popular.

Alkylation reactions need to be carried out in the presence of strong acid,^4,5 so the alkylation can be divided into three categories according to the physical properties of catalysts: liquid acid alkylation, solid acid alkylation, and ionic liquid acid alkylation. Liquid acids mainly include sulfuric acid and hydrofluoric acid, which are widely used in the alkylation process in the industry,⁶ but there are many problems in safety and environmental protection. In response to the shortcomings of traditional liquid acids, solid acids and ionic liquid acids have received much attention in recent years because of their green and environmental advantages and have great potential to become the mainstream direction of alkylation catalyst development in the future. However, large-scale industrial production has not yet been realized because of the problems such as the easy deactivation of solid acid catalysts⁷ and the expensive cost of ionic liquids.⁸ Most of the alkylation processes currently used in the industry are processes using sulfuric acid as the catalyst because of the good economics of the sulfuric acid process and safer and more environmentally friendly operation than the hydrofluoric acid process.⁹

The alkylation reaction is a process controlled by both chemical reactions and diffusion, which is very complex and contains a series of reactions based on carbonium ions as intermediates.¹⁰⁻¹² It is generally believed that the mass transfer from isobutane to the acid phase is the controlling step to determine the reaction rate. In the alkylation process, the mixing state of acid and hydrocarbon has a great influence on the selectivity and yield of the reaction because of the large difference in density and viscosity of the two phases. In addition, the reaction temperature, acid concentration, the volume ratio of acid to hydrocarbon, and the molar ratio of isobutane to olefins also have a significant effect on the yield.¹³ The alkylation process must choose suitable conditions to operate efficiently. Daily analytical sampling alone is not only small in the amount of data obtained but also time-consuming. The study of kinetics, on the other hand, can not only provide information about the alkylation reaction under different conditions so as to effectively control the reaction and improve the efficiency of chemical production but also understand the kinetics of the side reactions, which can save raw materials and make the later products easy to separate, and it can also solve the kinetic equations to derive the optimal operating conditions of the device so that the device can operate efficiently under the best condition.

Many studies have been reported on the kinetics of alkylation. In the early 1940s, Schmerling^14,15 proposed a mechanism based on the carbonium ion principles to explain the alkylation process of olefins and isobutane. Subsequently, Albright et al.^16,17 explained the formation mechanism of acid–soluble hydrocarbons and red oil cations based on the abovementioned chain reaction principles. The author also pointed out that the isomerization of trimethylpentane (TMPs) carbonium ions was not the main source to produce dimethylhexane (DMH) carbonium ions because the amount of DMHs will change significantly with residence time and agitation conditions. Lee and Harriott¹⁸ investigated the alkylation reaction and solved the kinetic model containing a main reaction and a polymerization reaction based on experimental data using the theory of mass transfer and chemical reaction simultaneously. Langley and Pike¹⁹ established a 17-reaction mechanism model for the alkylation reaction kinetics of propylene and isobutane and treated the reaction rates of carbonium and olefin intermediates based on the assumption of steady-state rates to obtain the rate constants and activation energies of the model. Schilder et al.²⁰ studied the kinetics of the reaction of isobutane with 2-butene in a stirred tank reactor, focusing on the droplet size distribution of the IL catalyst BMIMCI/AlCl₃ dispersed in C₄ hydrocarbons. The intrinsic chemical rate constant was derived from the mean droplet size and the measured effective rate constant (including a possible influence of external or internal diffusion). According to the classical carbonium mechanism, Sun et al.²¹ developed a kinetic model of alkylation reaction using sulfuric acid as catalyst and predicted the concentration changes in TMPs, DMHs, and heavy ends (HEs). The experimental and simulation data were in good agreement. However, most of the alkylation kinetics are based on laboratory research, and studies based on industrial data have not been carried out systematically.

In this paper, the reactor model was determined according to the structural pattern and flow state of the reactor. A kinetic model of alkylation reaction using sulfuric acid as catalyst was established to simulate the alkylation process, and its kinetic parameters were estimated through industrial data regression. Industrial data and model calculation results are consistent with each other.

2. Study Subject

2.1. Description of the Alkylation Process

The subject of the research is a sulfuric acid alkylation unit developed by Dupont^22,23 to produce high-octane gasoline blending components. Data were obtained from the industrial alkylation unit, including DCS data, monthly technical reports, material balances in a wide range of raw material composition, and flow rates. The principal scheme of the alkylation process implemented in the industry is presented in Figure 1.

Figure 1.

Brief procedure of the alkylation process.

After removing butadiene from the preparation unit, the raw material is mixed with the circulating isobutane stream recovered from the top of the de-isobutane tower and the circulating refrigerant stream obtained from the refrigeration cycle unit and then enters the alkylation reactors in three streams. At the same time, sulfuric acid from the acid settler and fresh acid are mixed into the alkylation reactor and mixed with the feed hydrocarbon in the reactor. Olefins and isobutane react under the catalysis of sulfuric acid to produce alkylates. After the reaction product and sulfuric acid flow out from the reactor, they flow through the acid settler, in which the hydrocarbon phase is separated from sulfuric acid. Then, sulfuric acid circulates back to the inlet of the reactor; the hydrocarbon phase from the acid settler passes through the pressure valve to lower the pressure to about 20 kPa where the light hydrocarbons are vaporized, thus absorbing the heat released from the alkylation reaction. The products from the tube side of the three reactors are mixed after heat exchange and then enter the downstream tank. Information about the flow of the alkylation reactor module is shown in Figure 2.

Figure 2.

Alkylation reactor module.

2.2. Industrial Conditions

In the data collected, the operating conditions of the alkylation unit are as follows: the feed flow rate for the single reactor is at around 30–70 tons/h; the reactor inlet temperature is at about 2.0–4.0 °C; the reactor outlet temperature is at around 6.0–6.5 °C; the ratio of isobutane to olefins (molar ratio) at the reactor inlet is between 7:1 and 12:1; the acid-to-hydrocarbon ratio (volume ratio) inside the reactor is around 1.1; and the acid concentration (wt %) of the three reactors is roughly around 92–96%. The reactor pressure is maintained at about 0.48 MPa, which is to keep the liquid phase of reactants and has no other effect on the alkylation reaction. The reactor volume of the industrial alkylation unit is 48.41 m³, in which the volume of the space between the hydrocarbon phase inlet and the reactor outlet including the draft tube and agitation area is 24.86 m³. It is considered as the reaction zone in the model since no olefins are present at the reactor outlet. Also, the olefins are completely converted in the reaction zone. In industrial production, the gas chromatograph with an Al₂O₃ (PLOT) chromatographic column and hydrogen flame ionization detector was used to identify and quantify all components.

Analyzing the influences of feed flow rate, acid-to-hydrocarbon ratio, acid concentration, the ratio of isobutane to olefins, reaction temperature, and other factors on the distribution of alkylation products and properties such as octane number, it is found that the feedstock feed rate had a greater effect on the distribution and properties of the products than other factors.

Figure 3 shows the effect of the total feedstock flow on the C₈ distribution and research octane number (RON) of the product from the three reactors. A message from the graph is that the selectivity of C₈ for the alkylation reaction becomes worse as the feed load increases, which is very important for kinetic modeling.

Figure 3.

Influence of feed flow rate on the distribution of C₈ and RON.

3. Kinetic Model

3.1. Lumped Model and Reaction Network

The main alkylation reaction is the addition reaction of isobutane and olefins. The commonly used catalysts for alkylation reactions are sulfuric acid, hydrofluoric acid, alumina, and so on. The sulfuric acid catalyst is used in this device. From the composition of the alkylation reaction products, alkylation reactions are complex and involve not only the main reaction but also many side reactions: isomerization, polymerization, cracking, and so forth. Thus, in the study of kinetics, the compounds in the complicated reaction system can be divided into several pseudo-components, or lumps, based on the principle that their kinetic properties are similar. Therefore, the reaction network is simplified which is facilitated to the kinetic study of the complex reaction system.²⁴

According to the daily analysis from the refinery, the reaction products (except carbon eight) are classified by carbon numbers, which are C₅, C₆, C₇, C₉, C₁₀, and C₁₁, respectively. Considering that the reaction of isobutane with different butenes may give different alkanes, C₈ is divided into two lumps according to the chain length: TMP and DMH.

Daily industrial data from the commercial alkylation unit show that the raw materials for the alkylation reaction are olefins and isobutane, with a small amount of isopentane. In the raw materials, there are also some diluents, also known as inert components, respectively, propane and n-butane, which are not involved in the reaction, so they are not considered in the model. However, it should be noted that their content will affect the relative concentration of butene and isobutane due to their dilution effect.

With the continuous exploration of the mechanism of the alkylation reaction, it is well-accepted that the alkylation follows the classic carbonium ion mechanism.^25,26 The alkylation products are produced by a chain reaction mechanism, which consists of three processes: chain initiation, chain growth, and chain termination.

First, in the alkylation reaction with sulfuric acid as catalyst, the hydrogen proton dissociated from sulfuric acid reacts with isobutene to form the tert-butyl carbon cation, which is the chain initiation process. Then, the tert-butyl carbon cation adds to the butene molecule to form the C₈ carbon cation, which is the chain growth process. After that, the C₈ carbon cation follows the hydrogen transfer reaction with isobutane to produce isooctane and regenerate the tert-butyl carbon cation, which is the chain termination process.

At the same time, the C₈ carbon ion may also undergo an addition reaction with olefins to form the C₁₂ carbon cation, which is then cracked to form the lighter carbon cation and the corresponding lighter olefin.²⁷ This can be used to explain part of the light hydrocarbon formation, but based on the analysis of the products, this is far from sufficient.

Figure 4 shows that the molar flow rate of light hydrocarbons (C₅–C₇) is greater than the molar flow rate of heavy hydrocarbons (C₉–C₁₁). To be specific, the molar flow rate of C₅ is slightly smaller than the molar flow rate of C₆ and they are both greater than the molar flow rate of C₇ alkanes. The molar flow rate of C₉ and C₁₁ alkanes is approximately the same in the products, and the molar flow rate of C₁₀ is about 1/3 of the molar flow rate of C₁₁. This result suggests that it is not reasonable to treat the light hydrocarbons (C₅–C₇) as being produced only by the cracking reaction of C₁₂⁺ because the creaking reaction of C₁₂⁺ is equimolar, which is not consistent with the actual results. Therefore, it is necessary to add further information on the mechanism of light hydrocarbon generation.

Figure 4.

Molar flow rate of byproducts (left) and main products (right).

Albright and Doshi²⁸ described the degradation and isomerization reactions of isobutane and light hydrocarbons and speculated on the most likely mechanism of DMH⁺ degradation. DMH⁺ and dimethylhexenes (formed from DMH⁺) react to generate C₁₆⁺, which eventually undergoes a cracking reaction to form small-molecule degradation products.

Based on the abovementioned discussion and analysis, the reaction network of alkylation reaction is proposed, as shown in Figure 5.

Figure 5.

Reaction network.

3.2. Reaction Kinetic Equation

Based on the reaction network mentioned above, the obtained reaction rate equations are shown in Table A1.

Table A1. Reaction Rate Equations^a.

serial number	reaction rate equations
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)

^aNote: c_i (i = 1–20) denotes the concentration of each lumped component, which are, respectively, butene, TMP⁺, DMH⁺, isobutane, C₅, C₆, C₇, TMP, C₉, C₁₀, C₁₁, C₁₂, DMH, iC₄⁺, C₅⁺, C₆⁺, C₇⁺, C₅⁼, C₆⁼, and C₇⁼ (mol/kg).

In the alkylation process, TMP⁺ or DMH⁺ is produced by a chain reaction in which iC₄⁺ adds to a butene molecule to form C₈⁺, followed by the hydrogen transfer reaction from isobutane to form TMP or DMH and regenerate the iC₄⁺. C₁₂⁺ is fragmented to smaller isoalkyl cations and olefins.¹⁸ Usually, the fragmentation position is near the middle of the chain, and the probability of fragmentation at the side is smaller, which is proved by the product analysis that the mass of C₃ did not change much when making material balance. Based on actual industrial data, considering that 1-butene, cis-2-butene, trans-2-butene, and isobutene are controlled by chemical equilibrium, olefins can be regarded as a lump, and the concentration of different olefins within the butene lump can be calculated using the equilibrium constant.²⁹

Figure 6 shows the isomerization reactions between the four olefins.

Figure 6.

Isomerization reaction between olefins.

If C_4,n, C_4,c, C_4,t, and C_4,i are used to, respectively, represent the concentrations of 1-butene, cis-2-butene, trans-2-butene, and isobutene and C₄ represents the concentration of lumped butene, then

1

2

3

4

where

5

6

7

4. Reactor Model

According to the introduction of the alkylation unit, it can be found that three horizontal flow reactors are used in the alkylation process, and each of which is matched with an acid settler. The flow of the hydrocarbon phase in each reactor is parallel. The acid phase is circulated between the reactor and the acid settler to maintain the volume ratio of acid to hydrocarbon in the reactor, where the catalyst in the first and second reactors is supplemented with a little fresh acid, while the catalyst in the third reactor is supplemented with a little acid from the first and second acid settlers.

When the acid and hydrocarbon materials enter the reactor inlet, the stirring impeller will rapidly disperse the hydrocarbon phase into the sulfuric acid catalyst to form an acid–hydrocarbon emulsion, which will be discharged from the other side of the impeller and enter the sealing side along with the space between the draft tube and the reactor shell under the influence of the hydraulic head, part of which flows into the acid settler as a reaction product along the rising line and the other part returns to the draft tube to form a cycle in the reactor. The fluid flow state in the alkylation reactor²³ is shown in Figure 2.

For the industrial alkylation reactor, the flow pattern inside the reactor cannot be measured directly, and it is difficult to build the reactor model accurately when only the reactor operating conditions and the content of each component are known. Cai and Dai³⁰ performed CFD analysis of the alkylation reactor using a standard k–ε model to investigate the relationship between the circulating flow rate, the impeller speed, and the impeller diameter in the reactor. By calculating the flow field at different operating speeds, it is found that the circulating flow rate in the draft tube is proportional to the rotational speed of the impeller, which is not frequently adjusted under normal operating conditions, so it can be assumed that the circulation flow rate in the draft tube is a fixed value.

In this way, according to the flow state of the fluid in the reactor and the structure pattern of the reactor, the reactor can be simplified to a plug flow reactor with circulation, and its structure is shown in Figure 7.

Figure 7.

Reactor model.

Alkylation reactions using sulfuric acid as catalyst are relatively complicated heterogeneous reactions that involve diffusion and chemical reaction. In order to simplify the model reasonably, the following assumptions are made:

• (a)The reactor operates under constant pressure (0.48 MPa) and steady-state conditions.
• (b)The flow model of the hydrocarbon and acid phases in the reactor is handled as PFR with circulation, and since the alkylation reaction is very fast and no olefins are found at the reactor outlet according to the daily analysis, the reaction is finished before reaching the reactor outlet and the circulation part does not involve the alkylation reaction.
• (c)The circulating flow in the reactor is proportional to the speed of the stirring impeller, and due to the high-speed rotation of the stirring impeller in the reactor, the chemical reaction can be considered as the rate-determining step.
• (d)According to the DCS data, the outlet temperature of each reactor does not change much, and there will be a large circulation flow inside the reactor to quickly remove the heat released from the alkylation reaction inside the reactor, which will make the temperature difference inside the reactor not change considerably, so the alkylation reactor is supposed to be an isothermal reactor.
• (e)The residence time of the hydrocarbon phase in the reactor depends on the ratio of acid to hydrocarbon, feed flow rate, and circulating flow rate in the draft tube.

Based on the reaction network and assumptions, the model can be calculated using the following eqs 8–27.

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

where c_j (j = 1–20) denotes the concentration of each lumped component, which are, respectively, butene, TMP⁺, DMH⁺, isobutane, C₅, C₆, C₇, TMP, C₉, C₁₀, C₁₁, C₁₂, DMH, iC₄⁺, C₅⁺, C₆⁺, C₇⁺, C₅⁼, C₆⁼, and C₇⁼; AO is the acid-to-hydrocarbon ratio; w is the concentration(wt %) of sulfuric acid; and f(AO,wcor) is a correction function introduced for the main reaction;

In actual alkylation industrial production, the operating conditions are relatively homogeneous, and the variation range of acid concentration and the acid-to-hydrocarbon ratio are small. However, large variations in acid concentration and acid-to-hydrocarbon ratio can have a significant effect on the distribution of reaction products and RON.

In the alkylation process, the concentration of sulfuric acid is strictly controlled as an important operating variable. The impurities³¹ affecting sulfuric acid concentration are generally divided into two types: water and acid-soluble hydrocarbons.^32,33 The presence of water facilitates the dissociation of sulfuric acid and provides the H⁺ required for the alkylation reaction, and acid-soluble hydrocarbons are also highly ionized, which can make isobutene into the tert-butyl carbon cation and induce the alkylation reaction. The abovementioned is the favorable side of impurities, but an increase in the concentration of either water or acid-soluble hydrocarbons causes the sulfuric acid concentration to decrease and the unfavorable side reactions are strengthened.³⁴ The increase in water makes the corrosion ability of sulfuric acid enhanced, while the increase in acid-soluble hydrocarbons may increase the viscosity of acid, and these have important effects on the distribution of alkylation products.

Also, the acid-to-hydrocarbon ratio is also a very important variable. In the reactor, the acid phase and hydrocarbon phase form an emulsion phase under the high-speed agitation of the impeller. If the acid–hydrocarbon ratio is relatively small, it cannot make the acid become a continuous phase, which increases the generation of byproducts and leads to poor quality of the generated alkylates and high acid consumption.

In general, when the sulfuric acid concentration reaches 95–96%, the performance of sulfuric acid-catalyzed alkylation reaction is the best, which is beneficial to the generation of main alkylation products and can improve the octane number of products. In addition, the lower acid concentration and acid-to-hydrocarbon ratio will favor the alkylation side reactions and reduce the selectivity of C₈ main reactions. The reason may be that some macromolecules will be generated in the side reaction, such as the reaction of some olefins and sulfuric acid to form sulphate;³⁵ it may also intensify the olefin polymerization reaction and increase the HEs in the alkylation products, and these results will lead to the lower octane number of the alkylates. Therefore, a correction function³⁶ for the main reaction is introduced in the model to reflect the influence of the change in acid concentration and acid–hydrocarbon ratio on the selectivity of the main reaction. The type of the correction function is as follows.

28

where AO is the ratio of acid to hydrocarbon and wcor is the coefficient after renormalizing the acid concentration, which can more clearly reflect the influence of acid concentration on C₈ selectivity.

Lee and Harriott¹⁸ studied the acid-catalyzed reaction of isobutane with 1-butene and the 1-butene oligomerization. It is found that the rate constant for isobutane with 1-butene goes up as the acid strength increases. However, in this paper, there are no such reaction steps that correspond exactly to the reaction in the literature. Even so, it can be found that the chain growth and chain termination reaction steps of the main reactions in our model are similar to the alkylation reaction of isobutane with 1-butene. Therefore, it is reasonable to correct the reaction rate of the main reaction by adjusting the acid concentration and the acid-to-hydrocarbon ratio.

5. Parameter Estimation

To ensure the reliability of the kinetic parameters, most of the data (52 sets) are needed for parameter estimation. Left data (10 sets) with quite different conditions are selected to validate the reliability and adaptability of the model. The variation range of component concentrations and operating conditions are shown in Figure A1.

Figure A1.

Variation range of material concentrations and operating conditions.

Based on the kinetic model mentioned above, the model has 20 reaction rate constants, one circulating flow rate and three equilibrium constants between olefins. Thermodynamically, K₁, K₂, and K₃ are a function of temperature and can be calculated using the Gibbs free energy of the isomerization reaction between olefins. In this paper, the REquil module in Aspen plus is used to calculate the chemical equilibrium and obtain the equilibrium constants K₁, K₂, and K₃. The equilibrium constants K₁, K₂, and K₃ were 9.207, 2.636, and 9.248 at 279.2 K, respectively. Therefore, the values of α, β, and γ can be calculated as 0.0038, 0.0354, and 0.0934, respectively.

For the calculation of the circulation flow rate in the reactor, when fitting the parameters based on the actual data, it was found that when the circulation flow rate was larger, that is, when the reactor model was closer to the CSTR model, the trend of the calculated reaction product concentration and the fresh feed flow rate was opposite to the actual trend. Therefore, considering to reduce the fitting error, the value of the circulation flow rate was determined by minimizing the absolute deviation.

To estimate rate constants in eqs 8–27, the nonlinear least-squares fitting method was used with the following object function

29

where x_j,exp and x_j,cal represent the measured value and model calculation value of component j at the outlet of the reactor, respectively; z denotes the number of lumps; and n represents the number of sets of data. In this work, the Isqnonlin function in Matlab is used to estimate k₁–k₂₀, which is based on the principle of minimizing the sum of squares of errors. The Gear method with variable step size and order is used to solve the stiff kinetic differential equations.³⁷ It should be noted that there are three reactors with different acid and hydrocarbon concentrations, and therefore, each reactor needs to be calculated separately when performing the numerical analysis, and then, the results of the three reactors are mixed and compared with the actual values.

All substances involved in the alkylation reaction, including propane, n-butane, olefins, and isobutane, are shown in Appendix A. 2. In the fresh feed, there is no dissociation of the catalyst and therefore no intermediate components are present, so the initial concentrations of all components except butene and isobutane are 0 mol/kg. Moreover, according to the data of the industrial plant, the concentration of olefins at the reactor exit is almost 0 mol/kg, so it can be assumed that the olefins are completely converted in the reactor. This is also in accordance with the feature that the alkylation reaction is fast and is completely converted before the reactor exit.

When solving the reactor model, it is assumed that the composition of the circulating flow stream is initially the same as that of the fresh feed, and the outlet stream after each calculation will be circulated partly back to the reactor inlet until the relative deviation of the outlet composition of two consecutive calculations does not exceed 1%, which can be considered as iterative convergence, and its value can be regarded as the reactor outlet concentration.

In this work, 52 sets of data from the alkylation unit are used to estimate the kinetic parameters in the model, using nonlinear least squares to minimize the objective function. The results obtained using nonlinear least squares are shown in Table 1.

Table 1. Kinetic Parameters of the Model with 95% Confidence Intervals^38a.

reaction rate constant	numerical value	reaction rate constant	numerical value
k1 (min–1)	11.63 ± 3.58	k11 (kg2 mol–2 min–1)	86.89 ± 19.32
k2 (min–1)	16.44 ± 4.62	k12 (kg2 mol–2 min–1)	22.82 ± 6.05
k3 (kg mol–1 min–1)	862.37 ± 187.20	k13 (kg2 mol–2 min–1)	90.22 ± 27.73
k4 (kg mol–1 min–1)	1.54 ± 0.26	k14 (kg mol–1 min–1)	14.28 ± 3.61
k5 (kg mol–1 min–1)	12956.94 ± 4072.1	k15 (kg mol–1 min–1)	4.56 ± 1.24
k6 (kg mol–1 min–1)	0.2187 ± 0.11	k16 (kg mol–1 min–1)	51.22 ± 17.54
k7 (kg2 mol–2 min–1)	1.36 ± 0.34	k17 (kg mol–1 min–1)	3521.91 ± 797.47
k8 (kg mol–1 min–1)	89.41 ± 16.49	k18 (kg mol–1 min–1)	1.28 ± 0.16
k9 (kg mol–1 min–1)	90.67 ± 9.60	k19 (kg mol–1 min–1)	2.06 ± 0.73
k10 (kg mol–1 min–1)	119.86 ± 20.33	k20 (kg mol–1 min–1)	3.71 ± 0.96

^aNote: all values of the reaction rate constants are greater than 0.

It can be seen from the abovementioned table that the reaction rates for chain growth are much larger than those for chain initiation and chain termination, which are particularly prominent in the TMP⁺ and DMH⁺ production. From the point of view of the chain reaction mechanism, it is a very normal phenomenon that the alkylation reaction rate increases after the chain initiation process due to the continuous accumulation of iC₄⁺. In the chain termination stage, the reaction rate decreases because of the decrease in olefins.

Since the data were collected from an industrial unit, there was inevitably more deviation in the data collection and analysis process compared with experimental kinetic investigation in the laboratory. As shown in Table 1, almost all confidence intervals are one magnitude smaller than their own parameters, which confirms the reliability of the estimated rate constants.

It can also be found that the subsequent reaction rate of DMH⁺ is large. From the analysis of the products, the light hydrocarbons are not only produced by the crack of C₁₂⁺ but also by the subsequent reaction of DMH⁺ to produce C₅ and C₆ alkanes. This reaction rate will affect the distribution of C₅ and C₆ in the product.

The value of the circulating flow rate inside the reactor is about 425 tons/h, which is about 10 times the flow rate of fresh feed to the reactor. The alkylation reaction is an exothermic reaction; the heat released by the reaction is quite large. In order to remove the heat, it is necessary to form a large flow circulation inside the reactor.

According to the abovementioned kinetic model of the alkylation reaction, the reaction kinetic model was solved by the Gear method of solving a rigid system of differential equations, and the average relative deviations of C₅, C₆, C₇, C₈, C₉, C₁₀, and C₁₁ in alkylates were calculated as 9.24, 5.42, 4.66, 1.84, 8.72, 21.20, and 8.49%, respectively. The fitting effect of the main alkylation product is good, and the relative deviation for the byproducts is relatively large, which is due to the proportion of byproducts in the alkylation product being small especially the C₁₀ hydrocarbons. In general, the data of the model fit well, indicating that the established kinetic model based on the classic carbonium ion mechanism is relatively reasonable.

6. Model Verification

In order to verify the reliability of the established kinetic model and its kinetic parameters, prediction calculations should be performed with additional industrial data, and the reliability of the model can be judged by the degree of agreement between the predicted values and actual values. In this paper, 10 left sets of data from the alkylation unit with different reaction conditions and feedstock compositions were selected for validation calculation of alkylation product distribution.

The range of the feed flow rate selected in the validation is approximately about 35–60 tons/h. The relative deviations of C₅, C₆, C₇, C₈, C₉, C₁₀, and C₁₁ were 12.78, 5.32, 5.36, 1.95, 25.51, 17.72, and 10.98%, respectively. The relative deviations indicate that the kinetic model and kinetic parameters are reliable and can achieve accurate product distribution prediction for industrial alkylation plants.

7. Model Prediction

In actual industrial production, the product distribution and product quality may be influenced by inert components, the ratio of isobutane to olefins, the flow rate of reaction feedstock, and so on. Based on the developed kinetic model of alkylation reaction using sulfuric acid as catalyst, the trend along the alkylation reactor and the effects of reaction conditions at different feed flows were studied.

7.1. Trend along with the Alkylation Reactor

Based on the abovementioned model parameters, the changes in material composition in each reactor can be predicted reliably. The concentration profiles of each intermediate and C₈ produced in the alkylation of isobutane with olefins are plotted in Figure 8. It shows that all the carbonium ions are created and lost quickly during alkylation. This demonstrates that the alkylation is a very rapid reaction. Almost after 0.5 min, each of the species reaches a platform individually.

Figure 8.

Trend of carbonium ion (left) and C8 (right) along the reactor.

In general, the residence time of alkylation reactors in the industry is about 5–20 min, which is the value of the whole reactor volume divided by the volume flow rate of the fresh feed hydrocarbon. In this paper, the reaction zone includes only the draft tube and the agitation zone in the model, and its residence time is affected by the feed flow rate of fresh hydrocarbon, the flow rate of circulating hydrocarbon, and the ratio of acid to hydrocarbon. Since the circulation flow rate is about 10 times the fresh feed flow rate, the residence time is about 1 min.

7.2. Influence of the Propane and n-Butane Content in the Feedstock

The impurities in the feedstock are low-molecular alkanes that do not participate in the reaction. Based on the daily analysis data of the petrochemical industry, it is known that the low-molecular alkanes are mainly propane and n-butane, which can dilute the hydrocarbon phase and thus reduce the concentrations of isobutane and butene.

Figure 9 shows the effect of propane and n-butane in the feedstock on the quality of the alkylates at different feed flows.

Figure 9.

Influence of the impurities in the feedstock on alkylate yield and RON at different feed flows.

Model calculation results show that the RON changed slightly when the propane and n-butane concentrations changed, but the alkylate yield changed significantly. This can be explained by the fact that propane and n-butane do not participate in the reaction in alkylation, and the increase in the concentration of these impurities reduces the yield of alkylates.

According to the model calculation results, the differences in the content of these dilution components are not significant and have a negligible effect on the octane number of alkylates within their variation range.

7.3. Influence of the Ratio of Isobutane to Olefins

During the alkylation process, this ratio is the molar ratio of isobutane to olefins in the feed hydrocarbon, and the reaction process is strongly influenced by the ratio. The ratio of each reactor can be adjusted by changing the flow rate of circulating isobutane. Daily analysis data from the plant shows that an addition of the molar ratio of isobutane and olefin in the feed hydrocarbon leads to the increase in the RON. In the simulation process, the effect of the ratio was investigated by keeping the respective reaction conditions such as feed flow rate, temperature, acid concentration, and acid-to-hydrocarbon ratio constant and adjusting the isobutane concentration at the reactor inlet to keep the alkene ratio varying in the range of 7–12.

Figure 10 shows the effect of the ratio of isobutane to olefins on the RON of alkylates at different feed flows. Obviously, increasing the ratio is beneficial to obtain higher octane alkylates. According to the relevant literature,³⁹ the diffusion coefficient of butene is greater than that of isobutane. This means that butene is more likely to diffuse in sulfuric acid than isobutane, which leads to a phenomenon that butene at the interface or in sulfuric acid will be prone to a rapid polymerization reaction, which is not conducive to the generation of high-quality alkylated oil products. Therefore, maintaining a high isobutane concentration in the reactor is necessary to reduce the probability of collisions between olefins and to ensure the selectivity of the main alkylation reaction.

Figure 10.

Influence of the ratio of isobutane to olefins on RON at different feed flows.

7.4. Influence of the Feed Flow Rate

During the alkylation process, the feed flow rate can be adjusted by changing the proportion of the mixed feed from the catalytic cracking unit to the alkylation unit. Small changes in the feed flow rate can change the residence time, but considering that the alkylation reaction is very rapid and the alkylation reactor is a PFR with circulation, the circulation flow rate is large than the fresh feed rate, so the change in residence time has less effect on the product distribution.

During the simulation, the temperature, hydrocarbon phase concentration, catalyst concentration, and acid-to-hydrocarbon ratio inside the reactor are kept constant, and only the feed rate is changed. The effect of the feed flow rate on the octane number of alkylates is shown in Figure 11.

Figure 11.

Influence of the feed flow rate on RON.

It can be seen from the graph that as the feed flow rate increases, RON gets lower. The change in the feed flow rate is mainly due to the change in the ratio of isobutane to olefins of the reactor inlet, as iterative convergence is required for each reactor when calculating the reactor model. If the feed flow rate is different, the ratio of isobutane to butene after mixing will be different, which will affect the distribution of alkylation products.

7.5. Influence of Sulfuric Acid

Sulfuric acid, as a catalyst for the alkylation reaction, its concentration in the reactor and the volume ratio of it to hydrocarbon are very important parameters of the process. As mentioned above, for the alkylation reaction unit, the acid concentration in the first and second reactors is somewhat higher than that in the third reactor, which is around 92%.

In the prediction simulation, the reactor temperature, feed flow rate, and hydrocarbon phase concentration were kept constant, and the acid concentration and acid-to-hydrocarbon ratio were, respectively, varied to predict their effects on the product octane number, and the results are shown in Figure 12. Increasing the acid concentration and acid-to-hydrocarbon ratio can improve the selectivity of the alkylation reaction, so the octane number of the alkylated oil will be increased.

Figure 12.

Influence of sulfuric acid on the mass fraction of C8 and C11 and RON at different feed flows.

In general, maintaining a higher acid concentration is beneficial for alkylation reactions, and industrial production generally maintains the acid concentration at about 95% to obtain high-octane alkylate products. It is also very important to maintain a certain acid-to-hydrocarbon ratio in the reactor. Maintaining this ratio allows the acid to exist as a continuous phase and the hydrocarbon as a dispersed phase, which can reduce the probability of collision between olefins and inhibit the polymerization reaction.

8. Conclusions

• (1)Based on the alkylation of isobutane with olefin carbonium ion mechanism, a kinetic model was developed for the actual alkylation reactor using sulfuric acid as a catalyst. The model parameters were regressed using industrial data, and the calculated values of the model and the actual data were in good agreement.
• (2)According to the actual data of the normal operation of the oil refinery and the calculation results of the model, increasing the reaction feed flow will be conducive to the generation of byproducts (C₅–C₇ and C₉–C₁₁) and the decrease in RON.

Glossary

Nomenclature

T

temperature, K

P

pressure, MPa

i

the number of the reaction

j

the number of the component

r_i

rate of reaction i, mol kg^–1 min^–1

k_i

rate constant of reaction i, kgⁿ mol^–n min^–1

c_j

the concentration of component j, mol kg^–1

R

circulation ratio in the reactor

C_A0

fresh material concentration at reactor inlet, mol m^–3

v₀

feed volume flow rate, m³ h^–1

C_A1

material concentration after mixing of fresh feed with circulation stream, mol m^–3

V

reactor volume, m³

v_R

circulation volume flow rate of the reactor, m³ h^–1

C_Af

material concentration at reactor outlet, mol m^–3

α

conversion coefficient between 1-butene and lumped butene

β

conversion coefficient between cis-2-butene and lumped butene

γ

conversion coefficient between trans-2-butene and lumped butene

K₁

equilibrium constant of 1-butene and cis-2-butene

K₂

equilibrium constant of cis-2-butene and trans-2-butene

K₃

equilibrium constant of trans-2-butene and isobutene

C_4,n

the concentration of 1-butene, mol kg^–1

C_4,c

the concentration of cis-2-butene, mol kg^–1

C_4,t

the concentration of trans-2-butene, mol kg^–1

C_4,i

the concentration of isobutene, mol kg^–1

C₄

the concentration of lumped butene, mol kg^–1

f(AO,wcor)

the correction function of main reactions

w

the weight fraction of sulfuric acid, wt %

wcor

the calibrated weight fraction of sulfuric acid

Glossary

Abbreviations

C₅

iso-paraffins with carbon number 5

C₆

iso-paraffins with carbon number 6

C₇

iso-paraffins with carbon number 7

C₈

iso-paraffins with carbon number 8

DMH

dimethylhexane

TMP

trimethylpentane

C₉

iso-paraffins with carbon number 9

C₁₀

iso-paraffins with carbon number 10

C₁₁

iso-paraffins with carbon number 11

C₁₂

iso-paraffins with carbon number 12

HES

heavy hydrocarbon components

LES

light hydrocarbon components

AO

the volume ratio of acid to hydrocarbon

RON

research octane number

Appendix A

Figure A1 and Table A1.

The authors declare no competing financial interest.