Additive-mediated interfacial engineering of H₂SO₄-catalyzed isobutane alkylation from molecular design to industrial process intensification

Abstract

Understanding and correlation of the multiscale interfacial mass transport behaviors mediated by the additive for liquid/liquid dispersion system is challenging. Here, we propose interfacial mass transfer flux through the quantitative coupling between microscopic interfacial parameters and mesoscopic droplet mass transfer model for H₂SO₄-catalyzed isobutane alkylation with emphasis on additive molecular design to industrial process intensification. Microscopic interfacial parameters are incorporated into CFD-PBM model to determine interfacial mass transfer flux of isobutane (N_isobutane). Based on the ratio of N_isobutane in the system with and without the additives, the interfacial enhancement factor E is proposed and validated as an indicator for optimal additive screening. Decoupled N_isobutane from apparent kinetic model, mass transfer-free kinetic parameters of isobutane alkylation are determined, quantitatively confirming the reaction is mass transfer controlled. Additive-mediated process intensification reveals PPG400 additive increases alkylate capacity by 24.85% up to 99.83 kt/a from 79.96 kt/a in additive-free system.

Introduction

Immiscible liquid–liquid interfacial reactions exhibit distinct energetic states and organizational behaviors compared to those in the bulk phases^1,2,3,4. The interfacial intensification of the liquid–liquid systems mediated by amphiphilic additives is a noteworthy development, which has emerged as a promising technique in the oil recovery⁵, pharmaceutical production⁶, and solvent extraction⁷, primarily because of increased Marangoni convection and enhanced interfacial mass flux^8,9,10,11. A typical case of heterogeneous liquid–liquid interfacial reaction is the isobutane alkylation with C3–C5 olefins under conditions of strong acid (H₂SO₄) and intense shear forces to generate C₈ alkylate product, where numerous rapid reactions and mass transport take place simultaneously at the acid/hydrocarbon interfacial regions^12,13. The promising green catalysts, such as ionic liquids (ILs), have been extensively investigated, yet remain challenging due to high operating costs, difficult disposal of spent salts, and insufficient stability under industrial operating conditions. In contrast, concentrated H₂SO₄-catalyzed isobutane alkylation still represents the dominant industrial process, owing to its high stability and excellent catalytic performance. Due to the polarity difference, the nonpolar isobutane exhibits lower solubility in the acid phase and undergoes slower diffusion across the acid/hydrocarbon interface compared to butene, and thus the interfacial mass transfer of isobutane is the rate-determining step for the isobutane alkylation^14,15,16. Over the past decades, the high ratio of isobutane to olefins (I/O ratio > 8) in feedstock and the inadequate mixing between the C4 hydrocarbons phase and the H₂SO₄ phase have seriously hindered the further increase in the capacity of a single reactor of the H₂SO₄-catalyzed isobutane alkylation^17,18. Alternatively, the introduction of intensified additives (e.g., ILs, deep eutectic solvents, surfactants, etc.) proved to be one of the promising ways to reduce the interfacial tension, promote the bi-phase mixing, increase the interfacial I/O ratio, inhibit the butene oligomerization, and thus improve the quality and capacity of alkylate, which has attracted considerable attention^19,20. However, the quantitative correlations of the additive-intensified behaviors for the H₂SO₄-catalyzed isobutane alkylation from microscale interfacial properties to mesoscale mass transfer behaviors and to industrial process intensification still remain greatly ambiguous.

The prerequisite to bridge the gap between the microscale interfacial properties to mesoscale mass transfer behaviors and to industrial process intensification for the isobutane alkylation relies on the estimation of the isobutane mass transfer across the acid/hydrocarbon interface to quantify how it tunes the multiscale transport behaviors and related kinetics. From the mesoscale perspective, the utilization of the electron microscope, clear photos of the isobutane mixing with catalytic systems found that the addition of ammonium surfactant can significantly decrease droplet size and enhance the dispersion of isobutane²¹, which mainly arises from the improvement of trace additives on the microscale interfacial properties at the liquid/liquid acid/hydrocarbon interface of H₂SO₄-catalyzed isobutane alkylation^22,23. At the molecular scale, furthermore, the understanding of interfacial properties altered by additives (e.g., ILs, deep eutectic solvents, and surfactants) has been considerably investigated to elucidate the interfacial transport behaviors of isobutane using molecular dynamics (MD) simulation ^24,25,26. It is found that additives with long-chain and organic aromatic structures have a propensity to align perpendicularly to the interface, which is conducive to their accumulation at the interface, thereby enlarging the interfacial thickness (σ), reducing the interfacial tension (γ), and giving rise to the different mesoscopic mass transport behaviors and kinetics^27,28. These behaviors and kinetics are also influenced with respect to the proportion of the dispersed phase, mechanical mixing conditions, physicochemical characteristics of reactants and catalyst, and reactor geometry^29,30,31,32. Recently, according to the volume of fluid model, the flow behaviors of the hydrocarbon phase in the acid phase for H₂SO₄-catalyzed isobutane alkylation were investigated in detail, which indicates strong vortices can accelerate surface renewal and significantly enhance the mass transfer of isobutane^16,20, but the effect of the additive on the interfacial behaviors was not considered³³. Despite the considerable microscale and mesoscale investigations for the H₂SO₄-catalyzed isobutane alkylation, there is a large gap in the quantitative correlation between the microscale interfacial properties and mesoscale droplet dispersion behaviors. Fortunately, obtaining microscopic key interfacial parameters and further combining them with the mesoscopic flow behaviors to obtain interfacial mass transfer flux (N_isobutane) could potentially allow to bridge the gap for the quantitative correlation between the microscale interfacial properties and mesoscale droplet dispersion behaviors, and simultaneously quantitatively evaluate the enhancement effect of additives on the acid/hydrocarbon interfacial properties of H₂SO₄-catalyzed isobutane alkylation.

In addition, reliable kinetic parameters are essential for fundamentally assessing whether additives facilitate the crucial steps in alkylation reactions^34,35. These reactions are extremely complex, involving simultaneous pathways, such as alkylation, polymerization, cracking, disproportionation, and self-alkylation, which proceed via carbonium ion intermediates^36,37,38. Early efforts have systematically studied the apparent kinetics of additive-mediated alkylation systems to elucidate the formation pathways of key components, including trimethylpentanes (TMPs), dimethylhexanes (DMHs), and heavy ends (HEs, C₉⁺) in alkylate³⁹. Moreover, the increased selectivity of TMPs components observed in systems with additives like [N_1,1,1.1][C₁₀SO₄] is attributed to an increased rate constant for hydride transfer from isobutane to TMPs cations, a phenomenon linked to accelerated mass transfer of isobutane⁴⁰. However, these apparent kinetic parameters are inherently confounded by mass-transfer effects under varying conditions, which cannot isolate and accurately quantify the transport enhancement solely attributable to the additive, making direct comparisons unreliable and hindering the establishment of a theoretical basis for rational screening of additives. To address this challenge, this study aims to develop a mass transfer-free kinetic model that decouples chemical reaction rates from mass-transfer limitations, thereby providing a more robust framework for evaluating additive efficacy from the perspective of kinetics.

In this work, we proposed an interfacial mass transfer flux through the quantitatively coupling between the microscopic interfacial parameters and mesoscopic droplet mass transfer model of the liquid/liquid dispersion system of H₂SO₄-catalyzed isobutane alkylation with emphasis on the additive molecular design to the industrial process intensification based on the complex reaction/mass transfer coupling kinetics (Fig. 1). Firstly, for the H₂SO₄-catalyzed isobutane alkylation system with nonionic additives and ionic amphiphilic additives at controlled interface coverage as well as varying temperature, three representative microscopic interfacial parameters, including γ, interfacial concentration (c*), and diffusion coefficients (D) were determined, underscoring the role of additives in regulating interfacial properties. Upon incorporating the microscopic interfacial parameters into the mesoscopic liquid–liquid mass transfer model, the simulated droplet size distribution, specific surface area (a), mass transfer parameters (k_L, k_La), and crucial N_isobutane were determined by CFD-population balance model (PBM) simulation and semi-empirical formula calculation, respectively. Thereafter, based on the ratio of N_isobutane in the system without and with the additives, the interfacial enhancement factor (E) was proposed as an indicator to quantitatively assess the mass transfer intensification degree of isobutane. Significantly, it shows good agreement with macroscopic enhanced catalytic performance in the isobutane alkylation systems with diverse additives. In particular, by leveraging the N_isobutane into the apparent kinetic models of isobutane alkylation to decouple the rate-determining step of isobutane mass transfer, mass transfer-free reaction rate constants of the isobutane alkylation were obtained, and the activation energies of the ultrafast hydride ion transfer reactions were calculated. Furthermore, the kinetic parameters were inserted into the process simulation to predict the additive-intensified industrial C4 alkylation process, which predicts the production capacity of alkylate with propylene glycol with a molecular weight of 400 (PPG400) additives can be increased by about 24.85% up to 99.83 kt/a from the typical 79.96 kt/a in the additive-free system for the typical industrial alkylation unit. The strategy we proposed not only deepens the comprehension of additive-intensified isobutane alkylation but also has a great potential to be extended into more liquid–liquid heterogeneous systems from microscale properties to macroscale process optimization.

Fig. 1: Schematic representation of additive-intensified isobutane alkylation.

A multiscale framework is proposed for additive-mediated alkylation, coupling microscopic interfacial parameters with a mesoscopic mass-transfer model to quantify the interfacial mass-transfer flux. The detailed interfacial properties of interfacial tension (γ), diffusion coefficients (D), and interfacial isobutane concentration difference (∆c_isobutane^*) for the H₂SO₄-catalyzed isobutane alkylation system without and with additive at various interface coverage and temperature are investigated using MD simulations. By incorporating key microscopic interfacial parameters (D, γ, ∆c_isobutane^*) into the mesoscopic liquid–liquid mass transfer model, the simulated hydrocarbon droplet diameter (d_p), specific surface area (a), mass transfer parameters (k_L, k_La), and N_isobutane for the corresponding system are determined. A dimensionless parameter, the interfacial enhancement factor, representing the tunability degree in the N_isobutane induced by the additive, is constructed. By decoupling N_isobutane from the apparent kinetic model, a mass transfer-free kinetic model for the instantaneous H₂SO₄-catalyzed alkylation is developed.

Results

Effects of PPG400 additive on microscale acid/hydrocarbon interfacial properties

Initially, PPG400 was selected as the surfactant additive for the reaction reinforcement due to the numerous advantages, such as low price, no halogen, and metallic elements, and reactive functional groups at the terminal sites^41,42. Considering the enrichment of additives at the interface can alter the physical properties and concentration gradients to a large extent, detailed interfacial properties for the H₂SO₄-catalyzed isobutane alkylation system without and with PPG400 additive at different interfacial coverage and temperature was initially studied via MD simulations with the optimized structures of each moiety shown in Supplementary Fig. 1. The equilibrated snapshots and mass density profiles along the z-axis of PPG400 distribution at various concentrations across the acid/hydrocarbon interface for H₂SO₄-catalyzed isobutane alkylation are presented in Fig. 2a. The PPG400 molecules tend to accumulate at the acid/hydrocarbon interface (Supplementary Figs. 2–4) exhibiting a distinct peak in the interfacial region, and the distribution of 2-butene is closer to the acid phase compared to isobutane. In particular, the interfacial coverage is defined as the number of PPG400 molecules per interfacial area (molecule/nm²)²⁹. As the interfacial coverage of the PPG400 additive increases, the intensity of this peak rises significantly (Supplementary Fig. 4). The orientation of the long carbon chains of PPG400 towards the acid phase enables a more substantial penetration of C4 hydrocarbons into the interface (Supplementary Fig. 3).

Fig. 2: Effects of PPG400 additive on interfacial properties.

a Equilibrated snapshots and mass density profiles along the z-axis of the simulated H₂SO₄ and C4 hydrocarbons interfacial systems with 0.3 wt% PPG400 additive. b The obtained interfacial tension (γ) and thickness (σ) as a function of interfacial coverage. c The obtained interfacial isobutane concentration difference (∆c_isobutane^*) and diffusion coefficient (D) of isobutane as a function of interfacial coverage. d The obtained γ and σ for the PPG400-system as a function of temperature. e The obtained ∆c_isobutane^* and D of isobutane for the PPG400-system as a function of temperature. It should be noted that the ratio of isobutane to olefins (I/O ratio) is 16:1 for the MD simulations, the same as the following experimental conditions. Error bars represent the statistical error in MD trajectories, originating from finite sampling and interfacial fluctuations.

To fully elucidate the effect of PPG400 additive on the regulation of microscopic interfacial transport, the y and interfacial thickness (σ) for the PPG400-aiding system as a function of interfacial coverage were further studied (Fig. 2b and Supplementary Notes 1, 2). σ is positively correlated with interfacial coverage, whereas γ exhibits an inverse relationship. Specifically, γ and σ of the fresh H₂SO₄ system are 26.20 mN/m and 0.24 nm, respectively. Upon incorporation of PPG400, as the interfacial coverage increases from 0.028 to 0.194 molecule/nm², γ decreases from 26.17 to 24.95 mN/m, while σ rises from 0.254 to 0.328 nm (Fig. 2b and Supplementary Fig. 5). Consequently, the PPG400 additive reduces γ and concurrently enhances σ compared to the additive-free system.

On the other hand, the microscopic interfacial parameters, including interfacial isobutane concentration difference between the interface and the acid phase (∆c_isobutane^*) and D of isobutane, altered by the addition of PPG400, were quantified. ∆c_isobutane^*, identified as the key mass transfer driving force in H₂SO₄-catalyzed alkylation (Fig. 2c and Supplementary Note 3), is significantly higher than that of the fresh H₂SO₄ system. Notably, ∆c_isobutane^* reaches a maximum value of 4.81 × 10⁻³ mol/kg at the interfacial coverage of 0.055 molecule/nm², equivalent to the PPG400 concentration of 0.3 wt%. The effect of PPG400 coverage on ∆c_isobutane^* presents a trade-off relationship. At moderate coverage, PPG400 can enrich the isobutane at the interface by optimizing thermodynamic driving forces, whereas excessive coverage introduces larger steric hindrance, causing a slight decline in ∆c_isobutane^*. Concurrently, the D of C4 reactants across the interface as a function of interfacial coverage was calculated (Supplementary Note 4 and Fig. 2c). Compared to the additive-free system, the existence of PPG400 at the interface restricts the isobutane diffusion, reducing D to a minimum value of 0.115 × 10⁻¹⁰ m²/s at the highest interfacial coverage. This suppression of interfacial dynamics is primarily attributed to the increased σ, which elongates the diffusion path for isobutane molecules and imposes transport limitations due to interfacial blocking by the long chains of PPG400. To quantitatively assess the thermodynamic standard free energy of the key isobutane molecule, the potential of mean force (PMF) of isobutane was calculated under varying PPG400 concentrations (Supplementary Note 5 and Table 1). The interfacial PMF difference (ΔPMF), defined as the energy barrier for isobutane transfer from the interface to the acid phase, decreases markedly from 35.40 kJ/mol in the fresh H₂SO₄ system to a minimum of 28.92 kJ/mol at 0.3 wt% PPG400. This reduction reveals a significantly lowered mass transfer resistance, since the additive accumulates at the interface and improves its properties to favor the isobutane penetration.

In addition, the elevated temperature decreases the γ from 26.92 to 25.60 mN/m, while increasing the σ from 0.253 to 0.279 nm (Fig. 2d). This interfacial remodeling is driven by intensified molecular dynamics, which enhances hydrocarbon penetration across the phase boundary. Consequently, the D of isobutane rises significantly (Fig. 2e). The accelerated diffusion promotes rapid equilibration, which shortens the residence time of isobutane at the interface and thereby suppresses the buildup of a high concentration gradient, leading to a decrease in ∆c_isobutane^* (Fig. 2e).

It should be noted that the simulated I/O ratio is 16:1 for MD simulations, which is the same as the following experimental alkylation conditions. To eliminate significant differences in isobutane and butene concentration, MD simulations are also conducted under a 1:1 I/O ratio. Significantly, the interfacial properties with 1:1 I/O ratio (Supplementary Figs. 6–10) are aligned with those observed in the system with 16:1 I/O ratio, confirming the reliability of the MD simulation results.

Quantitative correlation of microscale interfacial characteristics with mesoscale mass transfer coefficients

According to the above MD simulations, the effects of the additive on microscopic interfacial thermodynamics and dynamics properties are well explained, but such efforts remain inadequate to clarify the mechanism of additive-mediated isobutane mass transfer enhancement at the mesoscopic scale. Mesoscale N_isobutane is an effective and reasonable parameter for quantifying the amount of isobutane entering the acid phase via interfacial mass transfer. Upon incorporating the microscopic interfacial parameters (D, γ, ∆c_isobutane^*) without and with the PPG400 additive at different concentrations into the mesoscopic droplet mass transfer model (Supplementary Note 6), the hydrocarbon droplet diameter (d_p), a, k_L, k_La, and N_isobutane in the corresponding system can be determined by semi-empirical heterogeneous droplet mass transfer model and CFD-PBM simulations based on the same size of the batch experimental alkylation reactor with the actual dimensions. For each simulation case, the d_p and hydrocarbon volume fraction were allowed to fully converge to an equilibrium state prior to data acquisition, ensuring that the reported results are representative of steady state conditions (Supplementary Fig. 11).

In isobutane alkylation processes, the hydrocarbon phase, acting as the dispersed phase, is sheared into droplets in the acid continuous phase. Evidently, butene is rapidly and completely oligomerized within seconds of mixing, and the isobutane mass transfer across the droplet interface is the determining step for the alkylation^43,44. Under certain operating conditions, the rate of energy dissipation (ε), dispersed phase dispersion rate (ϕ), and physical properties, such as viscosity (μ), density (ρ), stirrer geometry, and reaction conditions are all fixed. Only the microscopic interfacial properties (D, γ, ∆c_isobutane^*) mediated by additives have an impact on the mesoscale mass transfer. The decrease of γ induced by the incorporation of PPG400 permits the dispersed droplets with smaller d_p, which means the enlarged a of hydrocarbon phase (Fig. 3a, d, and Supplementary Fig. 12). As the dosage of the PPG400 increases, the d_p distribution shifts toward smaller values and render spatial distribution as homogeneous as possible (Supplementary Fig. 13). This phenomenon improves the mesoscopic dispersion efficiency between hydrocarbon phase and acid phase for isobutane alkylation, all of which exert a positive effect on the alkylation process. While the value of k_L exhibits a continuous downward trend first and then almost remains unchanged as the PPG400 concentration increases (Supplementary Fig. 14), which is consistent with the variation of the microscopic D restricted by the interfacial hindrance effect of the additive. The overall mass transfer coefficient (k_La), determined by k_L and a, first decreases from 0.424 to 0.421 s⁻¹ as the dosage of the PPG400 increases from 0.1 to 0.6 wt%, and then increases to 0.430 s⁻¹ as the dosage of the PPG400 further increases to 1.0 wt% (Fig. 3b, e). Generally, the values of k_La in liquid–liquid heterogeneous reactors are between 0.1 and 100 s⁻¹, which proves that the obtained values of k_La for the H₂SO₄-catalyzed isobutane alkylation are within a reasonable range^45,46.

Fig. 3: Quantitative calculation of mesoscopic mass transfer coefficients.

a Comparison and validation of hydrocarbon droplet diameter (d_p) from CFD-PBM simulations and those calculated via the empirical formula. b Comparison and validation of the overall mass transfer coefficient (k_La) from CFD-PBM simulations and those calculated via the semi-empirical formula. c Comparison and validation of interfacial mass transfer flux of isobutane (N_isobutane) from CFD-PBM simulations and those calculated via the empirical formula. d The d_p distribution of the H₂SO₄-catalyzed isobutane alkylation as a function of PPG400 concentration. e The k_La of the H₂SO₄-catalyzed isobutane alkylation as a function of PPG400 concentration. f The N_isobutane of the H₂SO₄-catalyzed isobutane alkylation as a function of PPG400 concentration. Interfacial parameters acquired from the I/O ratio of 16:1 system. Error bars represent the propagated deviation originating from statistical error in MD-calculated liquid–liquid interfacial tension. No independent experiments were performed.

Integrating multiple parameters (k_La, ϕ, ∆c_isobutane^*), a quantitative N_isobutane can be acquired using the following equation:

$${N}_{{{\mathrm{isobuatne}}}}= {k}_{{{{\rm{L}}}}}a\frac{\phi }{1-\phi }\left({c}_{{{\mathrm{isobuatne}}},{{\mathrm{interfacial}}}\,{{\mathrm{region}}}}^{\ast }-{c}_{{{\mathrm{isobuatne}}},{{{{\rm{H}}}}}_{2}{{{\mathrm{SO}}}}_{4}{{\mathrm{region}}}}^{\ast }\right) \\= {k}_{{{{\rm{L}}}}}a\frac{\phi }{1-\phi }\Delta {c}_{{{\mathrm{isobutane}}}}^{\ast }$$

(1)

where ϕ is the fraction of the dispersed phase, as a constant (Supplementary Note 6). Based on the semi-empirical calculated results of N_isobutane distribution in Fig. 3c, f, it is observed that the addition of the PPG400 additive significantly promotes the distribution shift of N_isobutane in the alkylation reactor toward higher magnitudes, compared to the additive-free system. Specifically, at a dosage of 0.3 wt%, the N_isobutane value reaches a peak of 0.121 mol kg^-1 min^-1, corresponding to the most remarkable enhancement of mass transfer of isobutane. Moreover, comparison of the semi-empirical calculated results with those from CFD-PBM simulations (see Fig. 3a–c and Supplementary Figs. 13, 14) shows that the d_p, a, k_L, k_La, and N_isobutane data fall within a 5% error margin, confirming the reliability of the semi-empirical calculated results.

Furthermore, a multi-scale validation framework was established, in which CFD-PBM simulations under varying interfacial tension conditions were used to predict key parameters d_p and a. Values predicted by the CFD-PBM model show excellent agreement with calculations from semi-empirical formulas that incorporate microscopically derived parameters from following 35 distinct ILs additive systems (Supplementary Figs. 15–17). And a model experiment was designed using the pendant drop method to verify the water/n-octane interfacial tension reduction caused by PPG400 additive in heterogeneous liquid–liquid system (Supplementary Fig. 18 and Table 2).

Correlation of interfacial mass transfer flux with reaction performance

PPG-based additives were employed to experimentally explore the effects of molecular weight, additive amount, reaction time, and temperature on the H₂SO₄-catalyzed isobutane alkylation (Supplementary Figs. 19, 20, and Table 3). Research octane number (RON) is derived from the proportion of alkylate components and correlates with the changes in selectivity of C₈ components and improved performance⁴⁷. Among PPG with various molecular weights of 200–1500, PPG400 shows the best catalytic performance with the highest yield of C₈ components (Supplementary Fig. 20). The effects of the PPG400 concentration on the alkylate components (Fig. 4a) as well as C₈ components (Supplementary Fig. 21) in fresh H₂SO₄ systems were investigated. As the dosage of PPG400 increases from 0.1 wt% to 0.3 wt%, the RON and C₈ components show a marked increase from 96.40 to 97.07 and 77.66 wt% to 81.37 wt%, respectively, with the 2,2,4-TMP and 2,3,3-TMP components reaching the maximum values of 29.98 wt% and 22.45 wt%, respectively. However, excessive PPG400 concentration facilitates butene oligomerization and the generation of by-products, with the maximum content of HEs components up to 11.18 wt% at the amount of 1.0 wt%. Furthermore, a lower reaction temperature leads to further improvement in the quality of alkylate with higher selectivity of targeted TMPs components (Fig. 4b and Supplementary Fig. 22). The effects of the fresh H₂SO₄ with and without PPG400 on the alkylate components as a function of reaction time were investigated, as depicted in Supplementary Fig. 23. Upon the addition of PPG400 at the optimized dosage of 0.3 wt%, the alkylate RON is 94.97 at 5 min, and 96.97 at 10 min, versus 90.36 at 5 min and 92.36 at 10 min in the fresh H₂SO₄ system, respectively, which reveals that PPG400 plays an important role in accelerating the reaction rate.

Fig. 4: Enhanced catalytic performance and reaction kinetics mediated by additives and criterion for the interfacial enhancement factor E.

a Alkylate components as a function of PPG400 concentrations. b The difference of alkylate components for H₂SO₄ alkylation with 0.3 wt% PPG400 as a function of temperature. c Verification of parameter E with RON of the generated alkylate for different PPG400 concentrations. d The simplified C4 alkylation reaction pathway. e Kinetic parameters k₄ and k_6, as well as enhancement factor E as a function of PPG400 concentration. f The establishment of the mass transfer-free reaction kinetic model. g Fitting concentration profiles of key components for the additive-free system along time in the mass transfer-free kinetic model. h Predicted concentration profiles of key components for the PPG400-0.3 wt% system along time in the mass transfer-free kinetic model. i Arrhenius relationship between ln(k₄) and 1/T. j Arrhenius relationship between ln(k₆) and 1/T. k Arrhenius relationship between ln(k₇) and 1/T. l Arrhenius relationship between ln(k₁₅) and 1/T. Reaction conditions: stirring rate 3000 r/min, volume ratio of H₂SO₄/hydrocarbon 1.5:1, volume ratio of I/O 16:1. The data in Fig. 4a, c comes from n = 3 independent experiments. Error bars in Fig. 4c represent the standard error from n = 3 independent experiments. Error bars in Fig. 4e represent the 95% confidence intervals. Abbreviations used include research octane number (RON), trimethylpentanes (TMPs), dimethylhexanes (DMHs), light ends (LEs, C₅– C₇) and heavy ends (HEs, C₉⁺).

In particular, a dimensionless parameter, the interfacial enhancement factor E, representing the enhanced degree of the N_isobutane, was constructed to quantitatively evaluate the impact of additive-mediated microscopic interfacial regulation on mesoscopic mass transfer. E can be derived using Eq. 2.

$$E=\frac{{({k}_{{{{\rm{L}}}}}a)}_{{{{\rm{i}}}}}}{{({k}_{{{{\rm{L}}}}}a)}_{0}}\times \frac{{(\Delta {c}_{{{\mathrm{isobuatne}}}}^{\ast })}_{{{{\rm{i}}}}}}{{(\Delta {c}_{{{\mathrm{isobuatne}}}}^{\ast })}_{0}}$$

(2)

where (k_La)₀ and (∆c_isobutane^*)₀ are the mass transfer coefficient and interfacial concentration difference of isobutane in the additive-free system, and (k_La)_i as well as (∆c_isobutane^*)_i are those in the additive-adding system. Notably, the variation trends of the parameter E and macroscopic enhanced catalytic performance in the systems with different PPG400 concentrations were in complete alignment (Fig. 4c). At the optimal dosage of 0.3 wt%, the parameter E attains a peak value of 1.14, corresponding to the most significant enhancement in alkylate RON. Similarly, parameter E calculated by substituting the microscopic interfacial parameters obtained from I/O ratio of 1:1 MD model with different PPG400 concentrations into the empirical formula, agrees well with the macroscopic enhanced catalytic performance of the corresponding PPG400-aiding systems (Supplementary Fig. 24). This concordance robustly demonstrates that E is invariant to the macroscopic I/O ratio, thereby serving as a reliable descriptor exclusively capturing the interfacial mass transfer enhancement induced by additive. To sum up, the introduction of the PPG400 can markedly enhance the acceleration of N_isobutane, thereby inhibiting the oligomerization of butene and shortening residence time for isobutane alkylation, which can benefit the alkylate quality³⁶.

Generally, the formation of key alkylate components (e.g., TMPs, DMHs) proceeds via instantaneous hydride ion transfer from an isobutane molecule to a larger carbonium ion intermediate (e.g., TMPs⁺, DMHs⁺), in which mass transfer of isobutane to the acid phase is the rate-determining step, effectively controlling the overall rate of the alkylation process. The apparent kinetic model based on the C4 alkylation reaction pathway (Fig. 4d) is initially fitted. To avoid overfitting, the simplified model is used⁴⁸ (details in Supplementary Notes 7, 8, and Supplementary Fig. 25). The apparent kinetics is actually a comprehensive reaction that integrates both the reaction itself and the mass transfer of isobutane. The limiting steps relevant to the mass transfer of isobutane are mainly associated with key rate constants to generate TMPs, DMHs, and HEs, including k₄, k₆, k₇, and k₁₅, which within the apparent kinetic model, remain susceptible to alterations regulated by the mass transfer of isobutane^39,48.

Apparent kinetic model accurately predicts the concentration variations of key alkylate components (Supplementary Notes 7, 8, and Supplementary Figs. 26–28), enabling the determination of detailed kinetic constants. For the kinetic parameters k₄ and k₆ in the apparent kinetic model, as the dosage of PPG400 rises from 0.1 wt% to the optimal 0.3 wt%, the value of k₄ relative to the generation of TMPs components varies from 1.35 to 1.75 kg mol⁻¹ min⁻¹. However, upon excessive addition of PPG400, reaching up to 1.0 wt%, the value of k₄ diminishes to 1.60 kg mol⁻¹ min⁻¹. Notably, the remaining kinetic parameters relative to hydride ion transfer demonstrate the same tendency (Supplementary Tables 4–6). Notably, the k₄ and k₆ for TMPs and DMHs, respectively, show a good agreement as the enhancement factor E (Fig. 4e). The positive correlation between the enhancing effectiveness of the additive and the magnitude of apparent key kinetic parameters further supports that the reaction rate is primarily determined by mass transfer of isobutane.

To unravel the mass transfer-free kinetics behaviors, a mass transfer-free kinetic model for isobutane alkylation was successfully developed by decoupling N_isobutane from the apparent kinetic model (Fig. 4f and Supplementary Note 9). Excellent agreement exists between the fitted results from the additive-free system and our previous experimental data³⁹ (Fig. 4g), with confidence intervals for kinetic parameters an order of magnitude smaller than the rate constants. Specifically, the apparent kinetic parameters (k₄, k₆, k₇, k₁₅) for this system are significantly lower, with the values of 1.03 kg mol⁻¹ min⁻¹, 4.36 kg mol⁻¹ min^-1, 108.49 kg mol⁻² min⁻², and 32.62 kg mol⁻² min⁻², respectively, than those derived from the mass transfer-free model, which yields constant values of 192.87 kg mol⁻¹ min⁻¹, 863.92 kg mol⁻¹ min⁻¹, 1688.16 kg mol⁻² min⁻², and 8457.40 kg mol⁻² min⁻², respectively, regardless of additive presence (Supplementary Table 7). The markedly higher values of mass transfer-free kinetics are consistent with the characteristics of instantaneous reaction, underscoring the need to decouple the mass transfer effect.

The invariance of mass transfer-free kinetic parameters across varying PPG400 concentrations definitively confirms that the PPG400 enhancement on the isobutane alkylation process operates exclusively through modulating the N_isobutane, without altering the reaction kinetics. This conclusion is robustly supported by the precise predictions of the mass transfer-free kinetics, which successfully predicted the time-dependent evolution of key product concentrations across systems with different PPG400 dosages, all showing strong agreement with experimental data (Fig. 4h and Supplementary Fig. 30).

To further elucidate the mass transfer-free nature of the alkylation reaction, Arrhenius parameters for key steps (k₄, k₆, k₇, and k₁₅) were derived by plotting the logarithm of each rate constant ln(k_i) against 1/T, as shown in Fig. 4i–l and Supplementary Fig. 29, with the detailed activation energies and pre-exponential factors in Supplementary Table 8. The calculated activation energies for these elementary steps are consistently below 15.00 kJ/mol, a remarkably low value. These exceptionally low values are characteristic of ultrafast hydride transfer reactions, consistent with prior literature reporting values of 5–20 kJ/mol⁴⁹. The term activation energies herein refer to the values derived from the chemical rate constants obtained after mathematically decoupling the mass transfer resistance. They are distinguished from the energies of individual elementary steps.

This theoretical insight explains the instantaneous reaction behavior and underscores why the process rate is predominantly governed by N_isobutane rather than mass transfer-free chemical kinetics. The accurate predictive capability of the model, grounded in these mass transfer-free kinetic parameters, provides a powerful tool for optimizing the industrial alkylation process with additive.

Verification and comparison of additive enhancement performance

To further validate the rationality and reliability of the enhancement factor E, we systematically investigated the microscopic interfacial properties (γ, σ, D, ∆c_isobutane^*) and mesoscopic mass transfer parameters (d_p a, k_L, k_La, N_isobutane) in systems with different ILs additives ([N_111m][C_nSO₄], where m = 4,8,14, and n = 1,10,14, Fig. 5a) at a fixed ILs dosage of 0.3 wt%. MD simulation results (Supplementary Figs. 31–33 and Fig. 5b, c) confirmed that both cations and anions synergistically enhance interfacial properties. ILs additives with longer alkyl chains exhibited a more pronounced peak at the interface, leading to increased σ and ∆c_isobutane^*, and reduced D as well as γ^47,50. At the mesoscopic level, as the length of alkyl chains increases, a increases by reducing the d_p, while concurrently elevating steric hindrance at the interface. This heightened hindrance impedes the diffusion of isobutane, leading to a decrease in k_L (Fig. 5d). The net effect of these competing factors is a decrease in k_La, as exemplified by the [N_1,1,1,14][C₁₄SO₄] system, where a 7.31% reduction in k_L outweighed a 6.48% gain in a, resulting in a drop in k_La from 0.445 to 0.413 s⁻¹ (Fig. 5e). However, N_isobutane is determined not only by k_La but also by the ∆c_isobutane^*, which serves as the fundamental driving force. The increase in N_isobutane with longer alkyl chains is dominated by the significant rise in ∆c_isobutane^* resulting from IL-mediated optimization, rather than being limited by the reduction in k_La.

Fig. 5: Verification of the adaptability of the enhanced factor E.

a Molecular structures of the cation, anion ([N_111m][C_nSO₄], m = 4, 8, 14, and n = 1, 10, 14). b The obtained interfacial tension (γ) and thickness (σ) for ILs additives with different alkyl chain lengths. c The obtained interfacial isobutane concentration difference (∆c_isobutane^*) and diffusion coefficient (D) of isobutane for ILs additives with different alkyl chain lengths. d The obtained mass transfer parameters (k_L) and hydrocarbon droplet diameter (d_p) for the ILs additives with different combinations of cations and anions. e The obtained overall mass transfer parameters (k_La) and specific surface area (a) for the ILs additives with different combinations of cations and anions. f Verification of enhanced parameter E for 35 distinct ILs additive systems. g Parameter E for the ILs additives with different combinations of cations and anions. h Performance comparison with different additives. Error bars represent the standard deviation. Abbreviations used include research octane number (RON).

Most importantly, the variation trends of parameter E across different ILs additive systems were in complete alignment with the experimentally measured RON (Fig. 5f), where the RON data were referenced from previous work³⁷. The highest E, at 1.34, was observed in the [N_1,1,1,14][C₁₄SO₄] additive system, attributable to the greatest improvement in the N_isobutane, demonstrating its superior mass transfer intensification effect. Furthermore, the parameter E, calculated from microscopic interfacial parameters obtained via MD simulations under a 1:1 I/O ratio, consistently matched the macroscopically observed enhancement in catalytic performance (Supplementary Fig. 34). This comprehensive validation strongly confirms the robustness of the parameter E as a predictive metric for interfacial enhancement.

To address concerns about generalizability, additional analyses were conducted to evaluate the E across 35 distinct ILs additive systems featuring diverse cationic structures and anionic species (Fig. 5g). This comparative analysis was conducted under a 1:1 I/O ratio model, which was selected for its more pronounced variation in the E value, thereby providing a more sensitive basis for comparison (Supplementary Figs. 35–37). Among all systems screened, [C₁₂C₁₂Phyr][C₁₂SO₃] emerged as the most effective additive, yielding the highest E value of 5.87. The superiority of [C₁₂C₁₂Phyr][C₁₂SO₃] can be attributed to its unique molecular structure, which is optimized to simultaneously maximize both k_La and ∆c_isobutane^*, synergistically enhancing the N_isobutane.

Furthermore, the model successfully identifies optimal additives based on multidimensional evaluation beyond a single parameter. A comparative analysis of key metrics demonstrated PPG400 has distinct advantages in terms of enhancement performance, cost-effectiveness, and low dosage requirement compared to other ILs (Fig. 5h). These practical benefits, combined with its environmentally benign advantages, specifically the absence of halogens and metallic elements, validate parameter E not only as a robust theoretical indictor but also as a practical tool for screening and identifying ideal additives like PPG400 for industrial alkylation.

Industrial alkylation process intensification

Actually, the alkylate production capacity in industry using pure H₂SO₄ as catalyst with 98.3 wt% acid content is unreliable. Instead, the concentrated H₂SO₄ in typical industrial reactors generally contains 6.0–7.0 wt% organics, 1.0–3.0 wt% water, and 90.0–92.0 wt% H₂SO₄, referred to as the used H₂SO₄ to distinguish it from the fresh one^40,51,52. The systematic alkylation experiments employing the used H₂SO₄ as catalyst without and with the PPG400 additive were conducted, as described in Supplementary Figs. 38–40. Due to the positive effect induced by acid-soluble oil, the experimental results identified an optimal PPG400 dosage of 0.2 wt% in the used H₂SO₄-catalyzed system, which maximized the beneficial effects on alkylate quality with an elevated RON of 0.24 compared to the used H₂SO₄ system. The detailed kinetic constants of the used H₂SO₄ catalytic system without and with the addition of PPG400 additive were obtained, as listed in Supplementary Fig. 41 and Table 9.

A detailed process simulation of the reaction effluent refrigeration process for C4 alkylation was conducted using the Aspen Plus simulation platform, with a custom user model based on complex reaction kinetics. The main unit equipment of the effluent refrigeration process is illustrated in Fig. 6a, and its specific process units are depicted in Supplementary Note 10 and Table 10^18,53. Specifically, the influences of key operating parameters, including space time and feedstock I/O ratio, on the C4 alkylation process were systematically investigated for the system without and with the PPG400 additive. The quality and process capacity of alkylate were employed as the core indicators to assess the performance of the additive on the process intensification of C4 alkylation.

Fig. 6: Process intensification in isobutane alkylation.

a The main unit devices of the effluent refrigeration process. b Space time-dependent alkylate components as well as RON for the used H₂SO₄-catalyzed alkylation without and with the PPG400 additive. c The comparison of RON and conversion for the used H₂SO₄-catalyzed alkylation without and with the PPG400 additive as a function of process capacity. d The comparison of capacity and RON for the used H₂SO₄-catalyzed alkylation without and with the PPG400 additive as a function of the molar ratio of I/O. Conditions: PPG400 concentration 0.2 wt%, volume ratio of H₂SO₄/hydrocarbon 1.1:1, reaction temperature 281.15 K. All process simulations are based on used H₂SO₄ as the catalyst.

To achieve the optimal yield and quality of the alkylate, it is critical to maintain a sufficient space time (τ) of 20–30 min to ensure full emulsification between the acid and hydrocarbon phases^40,43. The influences of space time on the alkylate composition, RON, and product yield were systematically investigated under a fixed reaction temperature, with comparisons between the system without and with the PPG400 additive, as illustrated in Fig. 6b. The alkylate composition under varied space times in both systems are further provided in Supplementary Fig. 42. The RON of the alkylate for the PPG400-aiding system with a space time of 20 min reaches 97.05, which is still higher than that of 96.71 in the used H₂SO₄ system at 30 min. These results indicate that PPG400 effectively enhances both the RON and yield of the alkylate even under a shorter space time.

Two process intensification strategies were developed to utilize the advantages of the PPG400 additive in enhancing the quality and process capacity of alkylate, with the core goal of increasing process capacity while ensuring the quality of alkylate is superior to the additive-free system. For the first strategy, increasing the feed quantity shortens the space time at a fixed reactor volume, thus leading to lower quality of alkylate (Fig. 6c and Supplementary Fig. 43). Notably, the PPG400-aiding system performed well even at a higher capacity of 100 kt/a within 20 min, achieving an alkylate RON of 96.90 and a C₈ yield of 76.64%. This result is better than the RON of 96.52 and C₈ yield of 75.42% obtained in the used H₂SO₄ system at 80 kt/a with a space time of 25 min.

For the strategy of reducing the I/O ratio, the impacts of the I/O ratio on the composition of the alkylate, along with the capacity and RON in the used H₂SO₄-catalyzed alkylation process, both without and with the addition of the PPG400 additive, were explored (Fig. 6d). In the used H₂SO₄ system, when the I/O ratio declines from 10:1 to 4:1, the RON gradually declines from 96.46 to 95.35, and the proportion of the low-RON components, including HEs, LEs, and DMHs, rises significantly (Supplementary Fig. 44). Despite the negative impact on product quality, reducing the I/O ratio substantially enhances process capacity. Specifically, when the I/O ratio is lowered from 10:1 to 4:1, the alkylate production capacity increases dramatically by 117.79%, from 84.90 to 184.90 kt/a. Excessively reducing the I/O ratio in pursuit of increased capacity will significantly exacerbate the load on the refrigeration and distillation sections. Against this backdrop, reducing the molar I/O ratio to 6:1 is a more suitable option for practical application. At an I/O ratio of 6:1 in the PPG400 system, the RON of the alkylate can be maintained at 96.66, with capacity reaching 133.67 kt/a, representing a 28.71% increase compared to the used H₂SO₄ system without additive operating at the industrially standard I/O ratio of 8:1. These findings demonstrate that the addition of PPG400 additive can remarkably enhance product quality while simultaneously increasing production capacity, achieving by reducing the space time or feedstock I/O ratio.

Discussion

Additive intensification has been widely explored as a feasible approach to improve the quality of alkylate generated by H₂SO₄-catalyzed isobutane alkylation. Previous studies were mainly focused on the impact of additives (e.g., ILs, deep eutectic solvents, surfactants, etc.) on the microscale interfacial environment and macroscale catalytic performance based on the representative interfacial properties as well as the C₈ components selectivity, respectively. With the deep multiscale understanding of heterogeneous systems, the mesoscale mass transfer plays an important role in bridging the microscale interfacial properties and the macroscale reaction performance, serving as a critical link that determines the overall efficiency of the alkylation process. Therefore, upon incorporating the microscopic interface parameters into the mesoscopic liquid–liquid mass transfer model, we presented an unconventional strategy to bridge this scaling gap between microscale liquid–liquid interfacial parameters and mesoscale mass transfer coefficients. The N_isobutane with mass transfer properties (d_p, a, k_L, k_La) were provided, which was fine-tuned by the additives. Inspired by mass transfer of isobutane as the rate-determining step for the whole alkylation, the enhancement effect indicator of additives, E, was established by the ratio of N_isobutane with and without additive. Through the decoupling of the N_isobutane from the apparent kinetics, the mass transfer-free kinetics are defined as the inherent chemical rate independent of mass transfer, which makes it possible to individually quantify the contributions of the additive-induced enhancement in N_isobutane and accurately predict the macroscopic catalytic performance. Potentially, such strategy focused on establishing a quantitative structure-performance relationship between the molecular structures of additives and the enhancement factor E could be extended to the design and screening of optimized additives for sustainable chemical processes.

In summary, our results underscore the pivotal role of microscale interfacial properties regulated by the introduction of additives in governing mesoscale mass transfer behaviors in liquid–liquid heterogeneous instantaneous reactions of H₂SO₄-catalyzed isobutane alkylation. The introduction of PPG400 enables a diminution of the γ and an increase in the relatively larger solubilization of isobutane, resulting in a significant improvement of a by 1.42% and ∆c_isobutane^* by 24.37%. A dimensionless parameter, interfacial enhancement factor E, has been formulated by the N_isobutane derived from integrating microscopic interfacial parameters into the droplet mass transfer model to evaluate the intensification in mass transfer across various additive systems. The variation trends of the parameter E and macroscopic enhanced catalytic performance during the addition of diverse additives (nonionic additives and ionic amphiphilic additives) were in complete alignment, which further proves the rationality and reliability of the parameter E. The N_isobutane was further isolated from the apparent kinetic model to establish the mass transfer-free kinetic model for the isobutane alkylation. Furthermore, the decoupled mass transfer-free kinetics serve as a universal benchmark, enabling the prediction of how structural modifications in additives will ultimately influence the macroscopic catalytic output (e.g., RON, alkylate yield) across different industrial conditions. From the perspective of actual production predication, a customized user model based on the kinetic modeling was established and integrated into the Aspen Plus simulation platform to facilitate the process simulation without and with PPG400 additive, achieving the goal of improving the processing capacity by at least 24.85% while ensuring the quality of alkylate.

Methods

MD simulation details

To simulate the behaviors of PPG400 additives at the H₂SO₄/C4 hydrocarbons interface, the OPLS-AA force field was employed to treat the interaction among the additives, H₂SO₄, and C4 hydrocarbons. The structures and force field parameters for the concentrated H₂SO₄ (including the H₂SO₄ molecule, bisulphate ion, and hydronium ion), as well as C4 hydrocarbons for MD simulations, were directly taken from our previous research^22,54. The force field parameters of PPG400 were obtained from LigParGen. The charges of the additives were optimized through the ChelpG method at the basis set of 6–311++G(d,p) level, utilizing the Gaussian 09 program.

In each simulation system, the C4 reactant box comprises 160 molecules of 2-butene and 2560 molecules of isobutane, with the box size of 8.0 × 8.0 × 4.0 nm³. The size of the H₂SO₄ box (8.0 × 8.0 × 24.0 nm³) contains 5696 H₂SO₄ molecules, 168 hydronium ions, and 168 bisulphate ions⁵⁵. For the interfacial simulation, a gap of 2 nm was maintained between the H₂SO₄ box and the C4 hydrocarbons box to place PPG400 additives. The number of additives in the gap was 1, 4, 8, and 12, corresponding to the concentrations of 0.1, 0.3, 0.6, and 1.0 wt%, respectively. An initial energy minimization of 100000 steps was conducted to eliminate the unreasonable initial structure. The canonical (NVT) simulations were performed at 281.15 K using nose-hoover thermostat for 10 ns. Subsequently, the isothermal-isobaric (NPT) ensemble was further carried out for 40.0 ns. To ensure full equilibration, the number density distribution of each component was sampled every 2.0 ns, and no apparent density deviations could be found. A further 30.0 ns NPT was performed for data collection with the time steps of 1.0 fs. To maintain a stable interface, the semi-isotropic Parrinello Rahman barostat method was applied along the z-axis, with a relaxation time of 2.0 ps at 1 bar for all NPT ensembles.

For all MD simulations, GROMACS software was employed with periodic boundary conditions in three dimensions. Both Lennard-Jones interaction and Coulombic interaction were cut off at 1.2 nm. The LINCS algorithm was employed to manage all covalent bonds involving hydrogen atoms. Maxwell distribution was employed to obtain the initial atomic velocity. Long-range electrostatic interactions were addressed using the particle mesh Ewald method. It should be noted that the interface model constructed in this work can be considered as a pseudo-phase model, which is used to quantify the interfacial composition, thermodynamic driving forces, and microscopic interfacial parameters (D, σ, γ, ∆c_isobutane^*) of the additive-modified alkylation system. More detailed information for interfacial properties calculation was included in the Supplementary Notes 1–5.

CFD simulation details

To model the multiscale phenomena, 3D steady and transient CFD-PBM simulations were performed by ANSYS Workbench 2022 R2. The simplified structure of the stirring tank reactor was constructed by Space Claim 2022 R2. The Euler method for incompressible fluid is used to study the flow field in the liquid–liquid dispersion process. The reactor has three-blade flat impellers. The fluid domain was divided into a stationary domain and a rotational domain. The rotation of the impeller was simulated by multiple reference frames. The PBM was solved by the discrete method, which discretizes the droplet population into a finite number of size intervals.

Materials

All chemicals were purchased commercially and used as received. Fresh H₂SO₄ (98 wt%) was bought from Sinopharm Chemical Reagent Co., Ltd. Polypropylene glycols (PPGs) were obtained from Shanghai Titan Scientific Co., Ltd. The Nitrogen (99.99%) gas was purchased from Air Liquide (Shanghai) Gas Co., Ltd. Mixed C4 hydrocarbons were obtained from Shanghai Weichuang Standard Gas Analysis Technology Co., Ltd. The detailed composition of Mixed C4 hydrocarbons is listed in Supplementary Table 3.

Experimental procedures

C4 alkylation was performed in a batch glass reactor at the temperature range of 273.15 to 285.15 K and an operating pressure of 0.5 MPa¹⁸. The dosages of PPG400 were 0.33, 0.66, 1.00, 2.00, and 3.30 g, corresponding to the mass percentages of 0.1, 0.2, 0.3, 0.6, and 1.0 wt%, respectively. A certain amount of PPG additives was dissolved in 180 ml of H₂SO₄ and added to the reactor, followed by purging with N₂ gas three times to remove air. Subsequently, 120 mL of a mixed C4 hydrocarbon feed, with a volume ratio of I/O 16:1, was introduced into the reactor while maintaining the pressure at 0.5 MPa to ensure the mixture remained in the liquid phase. The agitator was then adjusted to a stirring speed of 3000 rpm to achieve a uniform dispersion between the hydrocarbon phase and acid phase. Simultaneously, the temperature within the reactor was regulated using a thermostatic bath. After the given reaction time, the product mixtures were collected at the sampling outlet. The alkylate samples were then extracted and separated from the acid phase using carbon tetrachloride. The colorless transparent liquid in the upper layer was analyzed via gas chromatography (GC) to determine the octane number, with further analytical details provided in Supplementary Fig. 19.

Kinetic modeling

The fundamental understanding of reaction kinetics is crucial for gaining insights into reaction mechanisms and optimizing reactor design and processes. The alkylation reaction is complex, involving simultaneous reactions, such as alkylation, polymerization, cracking, disproportionation, and self-alkylation, all mediated by carbonium ions^56,57. With over thirty iso-paraffins present, detecting each one using current analytical methods is challenging, particularly in a strong acid reaction system. Due to the close molecular weight, i.e., TMPs, DMHs, HEs, and LEs are treated to be one pseudo component, respectively. It is widely recognized that the C4 alkylation reaction occurs via the classical carbonium ion mechanism¹⁵. Building upon our prior work and informed by insights into the isomerization reactions of butene and the pathways for the formation of HEs, the alkylation kinetic model has been further refined³⁹. Detailed kinetic modeling for information was included in the Supplementary Notes 7–9 and Tables 4–9.