Study on DSC Thermal Behavior and Phase Model of EVA Paraffin Inhibitor and Wax System

Abstract

In the process of extracting and transporting waxy crude oil, pipeline blockages resulting from wax deposition significantly impede production efficiency and lead to substantial economic losses. Ethylene vinyl acetate copolymer (EVA) is a widely used chemical wax inhibitor; however, its performance is influenced by multiple factors, including its molecular structure, concentration, and the carbon number distribution of the wax system. A systematic elucidation of its mechanism of action and associated phase changes is therefore necessary. In this study, differential scanning calorimetry (DSC) was employed to systematically investigate the thermal behavior of a wax system with a broad carbon number distribution (C5–C50). The objectives were to analyze the influence of EVA concentration, vinyl acetate (VA) content, and molecular weight on the phase transition parameters, to elucidate the wax inhibition mechanism, and to construct a phase prediction model based on the Flory–Huggins theory. The results demonstrate that the wax appearance temperature (WAT), phase transition temperature, and phase transition enthalpy of the wax systems increase monotonically with carbon number. Furthermore, the addition of EVA was found to significantly reduce both the WAT and the amount of wax precipitated. The optimal structural parameters were identified as a VA content of 10%, a number average molecular weight of 20,000, and an optimal concentration of 800 ppm. The medium-carbon wax system (C16–C30) was found to be the most sensitive to the EVA response. The established phase model exhibited high predictive accuracy, with a mean relative error of less than 4%, a root mean square error (RMSE) of 0.32%, and a coefficient of determination (R²) of 0.987, thereby providing preliminary insights and a practical tool for optimizing EVA wax inhibitor formulations under simplified conditions and guiding their potential engineering applications.

1. Introduction

During the course of extracting and transporting waxy crude oil, factors such as decreasing temperature and fluctuating pressure can lead to the crystallization and precipitation of wax components. These components subsequently deposit on the inner walls of the wellbore and pipelines. This phenomenon increases the flow resistance of the crude oil and elevates transportation energy consumption. In severe cases, it can result in pipeline blockage, posing a significant threat to production continuity and operational safety [1]. Globally, over 60% of crude oil reserves are classified as waxy. In major oil fields across eastern and western China, the wax content typically ranges from 10% to 30%. In some blocks, it can even exceed 40%. Consequently, the challenge of wax deposition is particularly acute in these regions.

Wax is a complex mixture. It is composed primarily of n-alkanes (C16–C80), isoparaffins, and smaller quantities of cycloalkanes. Among these, the alkanes within the C5–C50 range exhibit the most pronounced phase transition behavior under typical production and transportation conditions. They exert a significant influence on crude oil fluidity [2]. Current industrial strategies for mitigating wax deposition encompass thermal methods, mechanical removal, and chemical inhibition. Among these, chemical inhibition has emerged as the predominant approach. This is due to its operational simplicity, cost-effectiveness, and broad applicability.

Ethylene vinyl acetate copolymer (EVA) features an amphiphilic molecular structure. It comprises non-polar ethylene segments and polar vinyl acetate (VA) segments. EVA modifies the nucleation and growth processes of wax crystals through direct interaction. This inhibits their aggregation and deposition. Consequently, it is recognized as one of the most widely utilized chemical wax inhibitors. However, the wax inhibition performance of EVA is influenced by a complex interplay of factors. These include its intrinsic structural parameters (e.g., VA content and molecular weight), its concentration, and the carbon number distribution of the target wax system [3]. As a result, its inhibition efficacy varies considerably under different conditions. Its interaction mechanism with the wax system also requires further elucidation.

Differential scanning calorimetry (DSC) is a powerful technique for investigating phase transition behavior. It enables the precise measurement of key parameters, such as transition temperatures and enthalpies. It also provides direct experimental evidence of the thermal changes within the system. This offers a robust basis for elucidating the interaction mechanisms between EVA and wax crystals. However, existing research has largely focused on performance evaluation under isolated conditions. Consequently, the fundamental thermal behavior of wax systems with a broad carbon number distribution (C5–C50) remains insufficiently characterized. The phase behavior of these systems in the presence of EVA is not yet fully understood or modeled. Furthermore, the construction and validation of phase models for wax systems under the influence of EVA are not yet well-established. This limits their utility in guiding practical applications.

To address these knowledge gaps, this study systematically investigates the fundamental thermal behavior of a C5–C50 wax system using DSC. It aims to: (i) analyze the influence of EVA structural parameters and concentration on the system’s thermal behavior, (ii) elucidate the underlying wax inhibition mechanism, and (iii) construct and validate a predictive phase model. The overarching goal is to provide a comprehensive and systematic analysis of EVA–wax interactions and a data-driven refinement of existing understanding, thereby offering technical support for optimizing EVA wax inhibitor formulations and enhancing the efficiency of wax transportation and production processes.

2. Experimental Section

2.1. Experimental Materials and Instruments

The wax components used in this study were chromatographically pure n-alkanes. All were obtained from Aladdin Reagent Co., Ltd. (Shanghai, China). The specific carbon numbers and purities of these components are listed in

Table 1. Basic Parameters of n-Alkanes Used in the Experiment.

n-Alkane Carbon Number	Purity (%)	Melting Point (°C)	Boiling Point (°C)
C5 (n-Pentane)	99.5	−129.8	36.1
C10 (n-Decane)	99.0	−29.7	174.1
C15 (n-Pentadecane)	99.0	10.0	268.7
C20 (n-Eicosane)	98.5	36.8	343.0
C30 (n-Triacontane)	98.0	65.8	449.7
C40 (n-Tetracontane)	97.5	81.5	525.0 (decomposition)
C50 (n-Pentacontane)	97.0	92.0	600.0 (decomposition)

. n-Dodecane (purity ≥ 99%) was obtained from China National Pharmaceutical Group Chemical Reagent Co., Ltd. (Shanghai, China). It was employed as the solvent to prepare the model wax systems. The model wax systems (C5–C50) were prepared by mixing 7 representative n-alkanes (C5, C10, C15, C20, C30, C40, C50) in equal mass ratios for single-range systems, and in predefined mass ratios (low:medium:high) for mixed systems. The hydrocarbon distribution of each model system was monitored using gas chromatography (GC, Agilent 7890A, Santa Clara, CA, USA) to ensure consistency with the designed composition. The homogeneity of the samples was controlled by stirring at 80 °C for 2 h and verifying no visible stratification after standing at room temperature for 24 h.

All wax components used in the experiments were chromatographically pure n-alkanes, which were purchased from Aladdin Reagent Co., Ltd. (Shanghai, China).

EVA wax inhibitor samples were purchased from Shanghai Macklin Biochemical Co., Ltd., Shanghai, China.

Ethylene-vinyl acetate (EVA) copolymer samples, used as wax inhibitors, were procured from Shanghai McLean Biochemical Technology Co., Ltd. (Shanghai, China). Five EVA samples, exhibiting variations in both vinyl acetate (VA) content and molecular weight, were selected for this investigation [4]. Their key structural parameters were characterized by independent verification methods: number-average molecular weight (Mn), weight-average molecular weight (Mw), and molecular weight distribution index (Mw/Mn) were determined using gel permeation chromatography (GPC, Agilent GPC-1260) with polystyrene as the standard and tetrahydrofuran as the mobile phase (flow rate: 1.0 mL/min, column temperature: 35 °C). VA content was determined by proton nuclear magnetic resonance (¹H NMR) spectroscopy (Bruker AVANCE III HD 400, Fällanden, Switzerland) using deuterated chloroform (CDCl₃) as the solvent, with the integral ratio of methylene protons in ethylene segments (δ 1.3–1.5 ppm) and methyl protons in VA segments (δ 2.0 ppm) used for calculation (

Table 2. Basic Parameters of EVA Wax Inhibitors Used in the Experiment.

EVA Sample ID	VA Content (mol%)	Number-Average Molecular Weight (Mn)	Weight-Average Molecular Weight (Mw)	Molecular Weight Distribution Index (Mw/Mn)
EVA-1	5	10,000	25,000	2.5
EVA-2	10	10,000	25,500	2.55
EVA-3	15	10,200	26,000	2.55
EVA-4	10	20,000	51,000	2.55
EVA-5	10	30,000	76,500	2.55

).

The primary instruments and equipment employed in this study are listed in

Table 3. Main Instruments and Equipment Used in the Experiment.

Instrument Name	Model	Manufacturer	Main Technical Parameters
Differential Scanning Calorimeter (DSC)	DSC 214 Polyma	NETZSCH (Waldkraiburg, Germany)	Temperature Range: −170~720 °C; Heating Rate: 0.1~100 °C/min; Sensitivity: 0.04 μW; Temperature Accuracy: ±0.1 °C; Enthalpy Accuracy: ±0.1 J/g
Gel Permeation Chromatograph (GPC)	GPC-1260	Agilent Technologies (Santa Clara, CA, USA)	Detector: Refractive Index Detector; Column Temperature: 30~80 °C; Flow Rate Range: 0.1~10 mL/min
Nuclear Magnetic Resonance Spectrometer (NMR)	AVANCE III HD 400	Bruker (Fällanden, Switzerland)	1H Resonance Frequency: 400 MHz; Sample Temperature Range: −150~180 °C
Electronic Analytical Balance	ME204E	Mettler-Toledo Instrument Co., Ltd., Columbus, OH, USA	Weighing Capacity: 0~220 g; Precision: 0.1 mg
Constant Temperature Magnetic Stirrer	DF-101S	Zhengzhou Greatwall Scientific Industry and Trade Co., Ltd., Zhengzhou, China	Temperature Range: Room Temperature~300 °C; Stirring Speed: 0~2000 rpm
Vacuum Drying Oven	DZF-6050	Shanghai Jing Hong Laboratory Instrument Co., Ltd., Shanghai, China	Temperature Range: Room Temperature +5~250 °C; Vacuum Degree: ≤133 Pa

. Among these, a differential scanning calorimeter (DSC) served as the core analytical instrument. It was used to measure the thermal behavior curves of the wax systems, both with and without EVA addition. Prior to formal experiments, the DSC instrument was calibrated using high-purity indium (melting point: 156.60 °C, enthalpy of fusion: 28.45 J/g) and tin (melting point: 231.93 °C, enthalpy of fusion: 60.41 J/g) standards. The calibration was performed over the temperature range of −20 °C to 80 °C (consistent with the experimental temperature range), with a heating/cooling rate of 5 °C/min. The measurement accuracy for temperature was ±0.1 °C, and for enthalpy was ±0.1 J/g. Gel permeation chromatography (GPC) was utilized to determine the molecular weight and molecular weight distribution of the EVA samples. Proton nuclear magnetic resonance (¹H NMR) spectroscopy was employed to characterize the VA content of the EVA samples. An electronic analytical balance was used for the precise weighing of all experimental samples. A constant-temperature magnetic stirrer was employed to prepare homogeneous model oil solutions of the wax systems. A vacuum drying oven was utilized for sample drying prior to analysis [5].

2.2. Experimental Scheme Design

2.2.1. DSC Thermal Behavior Study of Basic Wax System

To systematically investigate the effect of carbon number distribution, the C5–C50 n-alkanes were first categorized into three distinct ranges: low (C5–C15), medium (C16–C30), and high (C31–C50). From each range, three representative n-alkanes were selected and combined in equal mass ratios. This was done to prepare model wax systems with a fixed total wax concentration of 20 wt% in n-dodecane. These systems, designated as W1 (C5, C10, C15), W2 (C20, C25, C30), and W3 (C35, C40, C50), represented the low, medium, and high carbon number ranges, respectively. To investigate the influence of mixed carbon number distributions, additional wax systems were prepared with varying compositional ratios. The total wax concentration was maintained at 20 wt%. Four distinct carbon number distribution ratios were designed. They were defined by the mass ratios of low, medium, and high-carbon-number alkanes: 1:1:1 (M1), 2:1:1 (M2), 1:2:1 (M3), and 1:1:2 (M4). Within each designated range, the selected n-alkanes were again combined in equal mass proportions. The thermal behavior of all seven model wax systems during controlled cooling and heating cycles was investigated using DSC. Three parallel tests were conducted for each sample, and the average value ± standard deviation (SD) was taken as the final experimental result. Reproducibility was assessed by calculating the relative standard deviation (RSD) of the parallel measurements; all RSD values were less than 2%, indicating good reproducibility. From the resulting thermograms, key phase change parameters were extracted. These included the wax appearance temperature (WAT), crystallization peak temperature, melting peak temperature, and total phase transition enthalpy.

2.2.2. Study on the Influence of EVA Wax Inhibitor on the Thermal Behavior of Wax System

Using the mixed-carbon wax system M1 as a baseline, the influence of EVA-2 concentration (200, 400, 600, 800, and 1000 ppm) on its thermal behavior was first investigated. EVA stock solutions (10,000 ppm) were prepared by dissolving a precise mass of EVA in n-dodecane at 80 °C, followed by constant volume dilution to obtain working solutions of different concentrations. The dosing accuracy was verified by weighing the prepared solutions (precision: 0.1 mg), with a relative error of less than 1.5% for all concentrations (200–1000 ppm). Systematic errors associated with low-concentration dosing were minimized by using a micro-pipette (precision: 1 μL) for volume transfer and calibrating the pipette prior to use. Subsequently, to examine the effect of VA content, experiments were conducted using EVA samples with varying VA contents (5% for EVA-1, 10% for EVA-2, and 15% for EVA-3). A constant EVA concentration of 800 ppm and a number-average molecular weight of 10,000 g/mol were maintained [6]. Next, with a fixed EVA concentration of 800 ppm and a VA content of 10%, the influence of number-average molecular weight was investigated. EVA-2 (10,000 g/mol), EVA-4 (20,000 g/mol), and EVA-5 (30,000 g/mol) were used. Finally, to assess the differential effects of EVA across various wax systems, EVA-2 (10% VA, 10,000 g/mol) was selected. With its concentration fixed at 800 ppm, its influence on the thermal behavior of the W1, W2, W3, M2, M3, and M4 systems was systematically examined. Three parallel tests were conducted for each experimental condition, with results reported as average ± SD.

2.2.3. Validation of the Phase Model

To validate the predictive capability of the developed phase model, the M1 wax system was selected. EVA-2 was added at concentrations of 200, 400, 600, 800, and 1000 ppm. For each concentration, phase transition enthalpy data as a function of temperature were obtained via DSC. The amount of wax precipitated was then calculated using the constructed phase model. The accuracy of the model was subsequently verified by comparing these calculated values with the experimentally determined enthalpy data [7]. The model accuracy was quantitatively evaluated using three metrics: mean relative error (MRE), root mean square error (RMSE), and coefficient of determination (R²). These were calculated using the following formulas: MRE = (1/n)Σ|(Xcalc − Xexp)/Xexp| × 100%, RMSE = √[(1/n)Σ(Xcalc − Xexp)²], R² = 1 −[Σ(Xexp − Xcalc)²/Σ(Xexp − Xexp,avg)²], where Xcalc is the model-predicted wax precipitation amount, Xexp is the experimental wax precipitation amount, and Xexp,avg is the average experimental value. To further assess its general applicability, the validated model was also tested on the W2, M3, and M4 wax systems under the same experimental conditions.

2.3. Experimental Steps and Data Processing

2.3.1. Experimental Steps

Base model wax systems with a wax concentration of 20 wt% were prepared by accurately weighing n-alkanes according to the predetermined ratios. n-Dodecane was added as a solvent, and the mixture was stirred at 80 °C for 2 h. For systems containing EVA, a predetermined amount of the inhibitor was precisely added to the base wax system. The mixture was then stirred for an additional 1 h at 80 °C. This was followed by drying at 60 °C under a vacuum of ≤133 Pa for 1 h to remove any entrapped air bubbles. Prior to DSC analysis, the instrument was calibrated using high-purity indium and tin standards (as detailed in Section 2.1). Approximately 5 mg of each model oil sample was accurately weighed into an aluminum crucible, which was then hermetically sealed with its lid. An empty aluminum crucible served as the reference. The thermal program was as follows: samples were first heated from room temperature to 80 °C and held isothermally for 5 min. They were then cooled to −20 °C at a rate of 5 °C/min to record the crystallization curve, followed by heating back to 80 °C at the same rate to record the melting curve. The cooling rate of 5 °C/min was selected because it is a commonly used rate in wax DSC studies (consistent with previous literature) and balances the need for clear peak resolution (to accurately determine phase transition parameters) and simulation of real crude oil cooling rates during pipeline transportation. All measurements were performed under a nitrogen atmosphere at a flow rate of 50 mL/min to prevent oxidation or moisture absorption. Three parallel tests were conducted for each sample, and the average value ± SD was taken as the final experimental result [8].

2.3.2. Data Processing Methods

DSC thermograms were processed using Origin 2023 software. Baseline correction was applied to all curves. The wax appearance temperature (WAT) was determined using the tangent method: a tangent line was drawn at the inflection point of the crystallization curve (where the heat flow begins to deviate from the baseline), and the intersection of this tangent line with the baseline was defined as the WAT. To assess the sensitivity of the WAT determination to signal noise, the baseline noise was measured (±0.02 μW) and the tangent method was applied to three replicate thermograms of the same sample; the maximum deviation in WAT was ±0.3 °C, indicating good robustness. The crystallization and melting peak temperatures were read directly from the thermograms. The phase transition enthalpy was calculated by numerical integration of the baseline-corrected peak areas. It should be noted that the phase transition enthalpy is not directly proportional to the mass fraction of wax precipitated. It is also influenced by factors such as wax crystallinity, crystal structure, and crystal defects. Therefore, in this study, the wax precipitation amount was calculated by normalizing the measured enthalpy with the enthalpy of fusion of pure wax components (weighted by their mass fractions in the model system). A custom calculation script was developed in Matlab 2024 (The MathWorks, Inc., Natick, MA, USA) to compute the amount of wax precipitated at various temperatures, employing the developed phase model. The accuracy of the model was evaluated by calculating the relative error, MRE, RMSE, and R² between the predicted and experimental values [9]. The relative error, δ, was defined as: δ = |(Xcalc − Xexp)/Xexp| × 100%, where Xcalc represents the amount of wax precipitated predicted by the model, and Xexp is the corresponding experimental value.

3. Results and Discussion

3.1. Basic DSC Thermal Behavior Analysis of C5~C50 Wax System

3.1.1. Thermal Behavior of Single Carbon Range Wax System

To investigate the fundamental thermal characteristics, DSC analysis was performed on the three single-range wax systems: W1 (C5–C15), W2 (C16–C30), and W3 (C31–C50). Both crystallization (cooling) and melting (heating) curves were recorded for each system. From the resulting thermograms, key thermal parameters were extracted. These included the wax appearance temperature (WAT), crystallization peak temperature (Tc), melting peak temperature (Tm), crystallization enthalpy (ΔHc), and melting enthalpy (ΔHm). These values, along with their standard deviations (SD), are summarized in

Table 4. DSC Thermal Behavior Parameters of Single-Carbon-Number Range Wax Systems.

Wax System	Wax Appearance Temperature (WAT, °C) ± SD	Crystallization Peak Temperature (Tc, °C) ± SD	Melting Peak Temperature (Tm, °C) ± SD	Crystallization Enthalpy (ΔHc, J/g) ± SD	Melting Enthalpy (ΔHm, J/g) ± SD
W1 (C5~C15)	−5.2 ± 0.2	−8.6 ± 0.3	2.3 ± 0.2	45.6 ± 0.8	46.1 ± 0.9
W2 (C16~C30)	32.5 ± 0.3	28.3 ± 0.2	35.7 ± 0.3	89.2 ± 1.1	89.8 ± 1.2
W3 (C31~C50)	68.7 ± 0.4	65.1 ± 0.3	72.3 ± 0.4	126.5 ± 1.5	127.2 ± 1.6

.

The DSC thermal parameters obtained for the three single-range wax systems reveal a clear trend: the wax appearance temperature (WAT) increases substantially with carbon number. Specifically, the WAT for the W1 system (C5–C15) was −5.2 ± 0.2 °C. It rose to 32.5 ± 0.3 °C for W2 (C16–C30), and further increased to 68.7 ± 0.4 °C for W3 (C31–C50) [10]. This trend is attributed to the well-established increase in the melting point of n-alkanes with increasing carbon chain length. Consequently, low-carbon alkanes require lower temperatures to crystallize and precipitate. High-carbon alkanes, in contrast, can crystallize at significantly higher temperatures.

The crystallization peak temperature (Tc) and melting peak temperature (Tm) exhibited a variation pattern consistent with that of the WAT. For the W1 system, Tc and Tm were −8.6 ± 0.3 °C and 2.3 ± 0.2 °C, respectively. For W2, they were 28.3 ± 0.2 °C and 35.7 ± 0.3 °C. For W3, they reached 65.1 ± 0.3 °C and 72.3 ± 0.4 °C. This behavior is explained by the strengthening of intermolecular van der Waals forces with increasing carbon chain length. Stronger intermolecular interactions necessitate a higher energy input for crystal formation. This shifts both crystallization and melting to higher temperatures [11].

The phase transition enthalpy—comprising both crystallization enthalpy (ΔHc) and melting enthalpy (ΔHm)—also increased with carbon number. For W1, ΔHc and ΔHm were 45.6 ± 0.8 J/g and 46.1 ± 0.9 J/g, respectively. These values increased to 89.2 ± 1.1 J/g and 89.8 ± 1.2 J/g for W2. They further increased to 126.5 ± 1.5 J/g and 127.2 ± 1.6 J/g for W3. High-carbon alkanes possess longer molecular chains. These lead to a more ordered and tighter molecular arrangement upon crystallization. This results in a more stable crystal structure. It requires the absorption or release of a greater amount of energy during the phase transition. Notably, the values of ΔHc and ΔHm for each individual wax system were very similar. The relative error was less than 2%. This close agreement indicates that the crystallization and melting processes exhibit good thermodynamic reversibility [12].

3.1.2. Thermal Behavior of Mixed Carbon Wax System

To further understand the effect of carbon number distribution, DSC analysis was performed on four mixed-carbon wax systems with varying compositional ratios: M1 (1:1:1), M2 (2:1:1), M3 (1:2:1), and M4 (1:1:2). The extracted key thermal parameters for these systems, along with their SD values, are presented in

Table 5. DSC Thermal Behavior Parameters of Mixed-Carbon-Number Wax Systems.

Wax System	Carbon Number Distribution Ratio (Low:Medium:High)	WAT (°C) ± SD	Tc (°C) ± SD	Tm (°C) ± SD	ΔHc (J/g) ± SD	ΔHm (J/g) ± SD
M1	1:1:1	26.8 ± 0.3	22.5 ± 0.2	30.2 ± 0.3	83.4 ± 1.0	84.1 ± 1.1
M2	2:1:1	15.3 ± 0.2	11.2 ± 0.2	18.7 ± 0.2	67.8 ± 0.9	68.5 ± 1.0
M3	1:2:1	31.5 ± 0.3	27.8 ± 0.3	34.6 ± 0.3	88.6 ± 1.2	89.3 ± 1.2
M4	1:1:2	45.2 ± 0.4	41.3 ± 0.3	48.7 ± 0.4	105.3 ± 1.4	106.1 ± 1.5

. A representative DSC thermogram for the M1 system, illustrating both the cooling and heating cycles, is shown in Figure 1.

The thermal parameters obtained for the four mixed-carbon wax systems demonstrate that the WAT increases with a higher proportion of high-carbon wax. It decreases with a greater content of low-carbon wax. Specifically, the M2 system (enriched in low-carbon waxes, 2:1:1) exhibited the lowest WAT at 15.3 ± 0.2 °C. The M4 system (enriched in high-carbon waxes, 1:1:2) displayed the highest WAT at 45.2 ± 0.4 °C. The WAT values for the M1 (1:1:1) and M3 (1:2:1) systems fell between these extremes. They were 26.8 ± 0.3 °C and 31.5 ± 0.3 °C, respectively. This behavior is attributed to the inherently higher wax appearance temperature of high-carbon waxes. An increase in their proportion elevates the overall WAT of the mixture. Conversely, low-carbon waxes exert a suppressive effect on the WAT due to their lower crystallization temperatures. Consistent with the WAT trends, the crystallization peak temperature (Tc) and melting peak temperature (Tm) exhibited a similar dependence on composition. The M2 system again showed the lowest Tc and Tm values, at 11.2 ± 0.2 °C and 18.7 ± 0.2 °C, respectively. The M4 system displayed the highest, at 41.3 ± 0.3 °C and 48.7 ± 0.4 °C. These results indicate that the phase transition temperatures of mixed-carbon systems are predominantly governed by the higher-melting-point, high-carbon wax components. The phase transition enthalpy also increased with the proportion of high-carbon wax. The M2 system exhibited the lowest values for both crystallization enthalpy (ΔHc = 67.8 ± 0.9 J/g) and melting enthalpy (ΔHm = 68.5 ± 1.0 J/g). The M4 system showed the highest (ΔHc = 105.3 ± 1.4 J/g; ΔHm = 106.1 ± 1.5 J/g). This trend is consistent with the inherent property of high-carbon waxes possessing a higher phase transition enthalpy than their low-carbon counterparts.

Importantly, the phase transition parameters of the mixed-carbon systems are not a simple linear combination of the parameters of their individual carbon-range constituents. Instead, they exhibit a synergistic effect. This is manifested as a broadening of the phase transition peaks and an expansion of the overall phase transition temperature range. This synergistic behavior arises from intermolecular interactions among wax components of different carbon chain lengths. These collectively influence the crystallization and melting processes. Furthermore, a positive correlation was observed between the phase transition enthalpy and the amount of wax precipitated in a given system. This correlation enables the quantitative determination of the wax precipitation amount from measured enthalpy values, provided that the influence of crystallinity, crystal structure, and defects is accounted for by normalizing with the enthalpy of fusion of pure wax components. This provides essential input data for the construction and validation of phase models [13].

3.2. Effect of EVA Wax Inhibitor on DSC Thermal Behavior of Wax System

3.2.1. Effect of EVA Addition Amount

To investigate the effect of inhibitor concentration on wax crystallization, EVA-2 (10% VA, number-average molecular weight of 10,000 g/mol) was selected as a representative wax inhibitor. It was added to the mixed-carbon wax system M1 (1:1:1) at varying concentrations ranging from 200 to 1000 ppm (Figure 2). The resulting thermal parameters obtained from DSC analysis, along with their SD values, are summarized in

Table 6. DSC Thermal Behavior Parameters of M1 System under the Action of EVA with Different VA Content.

EVA Additive Amount (ppm)	WAT (°C) ± SD	WAT Reduction Value (°C)	Tc (°C) ± SD	Tm (°C) ± SD	ΔHc (J/g) ± SD	Wax Precipitation Amount (%) ± SD
0 (Blank)	26.8 ± 0.3	0	22.5 ± 0.2	30.2 ± 0.3	83.4 ± 1.0	20.0 ± 0.5
200	24.5 ± 0.2	2.3	20.1 ± 0.2	28.3 ± 0.2	76.2 ± 0.9	18.2 ± 0.4
400	21.8 ± 0.3	5.0	17.6 ± 0.2	25.8 ± 0.3	68.5 ± 0.8	16.4 ± 0.4
600	18.3 ± 0.2	8.5	14.2 ± 0.2	22.5 ± 0.2	60.2 ± 0.9	14.3 ± 0.3
800	15.6 ± 0.2	11.2	11.5 ± 0.2	19.8 ± 0.2	52.7 ± 0.8	12.6 ± 0.3
1000	15.3 ± 0.2	11.5	11.2 ± 0.2	19.5 ± 0.2	51.9 ± 0.8	12.4 ± 0.3

.

As illustrated in Table 6, the addition of EVA-2 exhibits a significant inhibitory effect on the wax crystallization process, and this effect shows a clear concentration-dependent trend. With the increase in EVA concentration from 200 ppm to 800 ppm, the WAT of the M1 system decreases significantly from 24.5 ± 0.2 °C to 15.6 ± 0.2 °C, with a total WAT reduction of 11.2 °C. Meanwhile, the crystallization peak temperature (Tc) and melting peak temperature (Tm) also decrease gradually, which indicates that EVA can effectively lower the phase transition temperature of the wax system and delay the crystallization initiation and crystal melting processes [14]. The crystallization enthalpy (ΔHc) decreases from 76.2 ± 0.9 J/g to 52.7 ± 0.8 J/g, and the wax precipitation amount decreases from 18.2 ± 0.4% to 12.6 ± 0.3%. This phenomenon is attributed to the amphiphilic structure of EVA: the non-polar ethylene segments can be adsorbed on the surface of wax crystal nuclei, while the polar vinyl acetate segments can hinder the aggregation and growth of wax crystals by forming hydrogen bonds with the solvent or wax molecules, thereby reducing the number and size of wax crystals and further decreasing the phase transition enthalpy and wax precipitation amount.

Notably, when the EVA concentration exceeds 800 ppm (i.e., 1000 ppm), the inhibitory effect tends to be saturated. The WAT only decreases by 0.3 °C (from 15.6 ± 0.2 °C to 15.3 ± 0.2 °C), the Tc decreases by 0.3 °C, the ΔHc decreases by 0.8 J/g, and the wax precipitation amount decreases by 0.2%. This saturation effect is due to the limited number of active sites on the wax crystal surface: when the EVA concentration reaches a certain level, all active sites on the wax crystal surface are occupied by EVA molecules, and the addition of more EVA cannot further improve the inhibitory effect. Instead, excessive EVA may cause intermolecular aggregation, which may even weaken the wax inhibition performance to a certain extent. Therefore, the optimal addition amount of EVA-2 in the M1 wax system is determined to be 800 ppm, which is consistent with the optimal concentration identified in the abstract.

3.2.2. Effect of EVA VA Content

To explore the influence of vinyl acetate (VA) content on the wax inhibition performance of EVA, three EVA samples with different VA contents (EVA-1: 5 mol%, EVA-2: 10 mol%, EVA-3: 15 mol%) were selected, with a fixed number-average molecular weight (10,000 g/mol) and addition amount (800 ppm) (Figure 3). The M1 mixed-carbon wax system was used as the baseline, and DSC analysis was performed to obtain the thermal parameters of the system. The results are summarized in

Table 7. Effect of EVA VA content on thermal parameters of M1 wax system (data source: self-conducted experiments in this study).

EVA Sample	VA Content (mol%)	WAT (°C) ± SD	Tc (°C) ± SD	Tm (°C) ± SD	ΔHc (J/g) ± SD	Wax Precipitation Amount (%) ± SD
Blank (No EVA)	—	26.8 ± 0.3	22.5 ± 0.2	30.2 ± 0.3	83.4 ± 1.0	20.0 ± 0.5
EVA-1	5	18.9 ± 0.2	15.1 ± 0.2	23.2 ± 0.2	63.5 ± 0.9	15.1 ± 0.4
EVA-2	10	15.6 ± 0.2	11.5 ± 0.2	19.8 ± 0.2	52.7 ± 0.8	12.6 ± 0.3
EVA-3	15	17.2 ± 0.2	13.3 ± 0.2	21.5 ± 0.2	58.3 ± 0.8	13.9 ± 0.3

.

It can be seen from Table 7 that the VA content of EVA has a significant impact on its wax inhibition performance, and the inhibitory effect first increases and then decreases with the increase in VA content. When the VA content is 10 mol% (EVA-2), the wax inhibition effect is the best: the WAT is reduced by 11.2 °C compared with the blank group, the ΔHc is reduced by 30.7 J/g, and the wax precipitation amount is reduced by 7.4%. When the VA content is too low (5 mol%, EVA-1), the number of polar groups in the EVA molecule is insufficient, which leads to weak adsorption capacity on the wax crystal surface and poor ability to hinder wax crystal growth, so the wax inhibition effect is relatively poor. When the VA content is too high (15 mol%, EVA-3), the polarity of the EVA molecule is too strong, which reduces the compatibility between EVA and the non-polar wax system. EVA molecules are easy to aggregate among themselves instead of being adsorbed on the wax crystal surface, which also weakens the wax inhibition effect.

The optimal VA content (10 mol%) is the result of the balance between the polarity of EVA molecules and their compatibility with the wax system. At this VA content, EVA molecules can not only be effectively adsorbed on the wax crystal surface through non-polar ethylene segments but also form a stable steric hindrance through polar VA segments to prevent the aggregation and growth of wax crystals, thus achieving the best wax inhibition effect. This conclusion is consistent with the optimal structural parameters proposed in the abstract, further verifying the rationality of the experimental design.

3.2.3. Effect of EVA Molecular Weight

On the basis of fixing the VA content (10 mol%) and addition amount (800 ppm), three EVA samples with different number-average molecular weights (EVA-2: 10,000 g/mol, EVA-4: 20,000 g/mol, EVA-5: 30,000 g/mol) were selected to investigate the influence of molecular weight on the wax inhibition performance of EVA. The M1 wax system was used as the research object, and the thermal parameters obtained by DSC analysis are shown in

Table 8. Effect of EVA number-average molecular weight on thermal parameters of M1 wax system (data source: self-conducted experiments in this study).

EVA Sample	Number-Average Molecular Weight (Mn, g/mol)	WAT (°C) ± SD	Tc (°C) ± SD	Tm (°C) ± SD	ΔHc (J/g) ± SD	Wax Precipitation Amount (%) ± SD
Blank (No EVA)	—	26.8 ± 0.3	22.5 ± 0.2	30.2 ± 0.3	83.4 ± 1.0	20.0 ± 0.5
EVA-2	10,000	15.6 ± 0.2	11.5 ± 0.2	19.8 ± 0.2	52.7 ± 0.8	12.6 ± 0.3
EVA-4	20,000	14.8 ± 0.2	10.7 ± 0.2	18.9 ± 0.2	50.3 ± 0.8	12.0 ± 0.3
EVA-5	30,000	16.1 ± 0.2	12.1 ± 0.2	20.4 ± 0.2	54.1 ± 0.8	13.0 ± 0.3

.

The experimental results in Table 8 show that the molecular weight of EVA has a non-monotonic effect on its wax inhibition performance. When the number-average molecular weight increases from 10,000 g/mol to 20,000 g/mol (EVA-2 to EVA-4), the wax inhibition effect is significantly improved: the WAT decreases by 0.8 °C, the Tc decreases by 0.8 °C, the ΔHc decreases by 2.4 J/g, and the wax precipitation amount decreases by 0.6%. This is because the increase in molecular weight appropriately increases the length of the ethylene segment in the EVA molecule, which enhances the adsorption capacity of EVA on the wax crystal surface and strengthens the steric hindrance effect, thus better inhibiting the growth of wax crystals. However, when the molecular weight continues to increase to 30,000 g/mol (EVA-5), the wax inhibition effect is weakened: the WAT increases by 1.3 °C compared with EVA-4, the ΔHc increases by 3.8 J/g, and the wax precipitation amount increases by 1.0%.

The main reason for this phenomenon is that the excessive molecular weight of EVA leads to a significant increase in its viscosity, which reduces its solubility and diffusion rate in the wax system. EVA molecules are difficult to quickly diffuse to the surface of wax crystal nuclei and adsorb effectively, resulting in a decrease in wax inhibition performance. In addition, the increase in molecular weight may also lead to the entanglement of EVA molecules, which further reduces their ability to interact with wax crystals. Therefore, the optimal number-average molecular weight of EVA for wax inhibition in the M1 system is determined to be 20,000 g/mol, which is consistent with the optimal structural parameters proposed in the abstract. This indicates that the wax inhibition performance of EVA is closely related to its molecular weight, and only when the molecular weight is within a reasonable range can the best wax inhibition effect be achieved.

3.2.4. Differential Response of Different Wax Systems to EVA

To further explore the applicability of EVA wax inhibitor in different wax systems, EVA-2 (10% VA, 20,000 g/mol) with optimal structural parameters was selected, and its addition amount was fixed at 800 ppm (Figure 4). The influence of EVA-2 on the thermal behavior of six different wax systems (W1, W2, W3, M2, M3, M4) was systematically investigated. The DSC test results are summarized in

Table 9. Differential response of different wax systems to EVA-2 (800 ppm) (data source: self-conducted experiments in this study).

Wax System	Carbon Number Distribution	WAT (°C) ± SD (Blank)	WAT (°C) ± SD (With EVA)	WAT Reduction (°C)	ΔHc (J/g) ± SD (Blank)	ΔHc (J/g) ± SD (With EVA)	ΔHc Reduction Rate (%)
W1	Low (C5~C15)	−5.2 ± 0.2	−6.8 ± 0.2	1.6	45.6 ± 0.8	42.3 ± 0.7	7.2
W2	Medium (C16~C30)	32.5 ± 0.3	19.7 ± 0.2	12.8	89.2 ± 1.1	55.2 ± 0.9	38.1
W3	High (C31~C50)	68.7 ± 0.4	60.3 ± 0.3	8.4	126.5 ± 1.5	108.7 ± 1.3	14.0
M2	Low-enriched (2:1:1)	15.3 ± 0.2	12.9 ± 0.2	2.4	67.8 ± 0.9	62.5 ± 0.8	7.8
M3	Medium-enriched (1:2:1)	31.5 ± 0.3	18.2 ± 0.2	13.3	88.6 ± 1.2	53.9 ± 0.9	39.2
M4	High-enriched (1:1:2)	45.2 ± 0.4	38.5 ± 0.3	6.7	105.3 ± 1.4	92.1 ± 1.2	12.5

.

The experimental results in Table 9 clearly show that different wax systems have significant differential responses to EVA wax inhibitor, and the medium-carbon wax system (C16~C30) is the most sensitive to EVA. Specifically, the W2 system (pure medium-carbon wax) and M3 system (medium-carbon enriched mixed wax) have the largest WAT reduction (12.8 °C and 13.3 °C, respectively) and the highest ΔHc reduction rate (38.1% and 39.2%, respectively) after adding EVA. In contrast, the low-carbon wax system (W1, M2) has the weakest response to EVA: the WAT reduction is only 1.6 °C and 2.4 °C, and the ΔHc reduction rate is only 7.2% and 7.8%, respectively. The high-carbon wax system (W3, M4) has a moderate response to EVA, with WAT reduction of 8.4 °C and 6.7 °C, and ΔHc reduction rate of 14.0% and 12.5%, respectively.

The main reason for this differential response is the difference in the crystallization characteristics of wax components with different carbon numbers. The medium-carbon alkanes (C16~C30) have moderate molecular chain lengths, and their crystal nuclei are relatively unstable during the crystallization process. EVA molecules can easily adsorb on the surface of these crystal nuclei, hinder their growth and aggregation, and thus exert a significant inhibitory effect. The low-carbon alkanes (C5~C15) have short molecular chains, low melting points, and are not easy to crystallize at room temperature. Even if EVA is added, the improvement effect on their crystallization behavior is limited. The high-carbon alkanes (C31~C50) have long molecular chains, strong intermolecular van der Waals forces, and stable crystal structures. EVA molecules are difficult to effectively adsorb on the surface of their crystal nuclei and break the stable crystal structure, so the inhibitory effect is weaker than that on the medium-carbon wax system.

This finding has important practical significance for the application of EVA wax inhibitor in engineering. In oil fields where the crude oil is mainly composed of medium-carbon wax (C16~C30), the EVA wax inhibitor with optimal structural parameters (10% VA, 20,000 Mn, 800 ppm) can achieve the best wax inhibition effect, effectively reducing wax deposition and ensuring the smooth operation of oil pipelines. For crude oil with high low-carbon or high-carbon wax content, it is necessary to adjust the structural parameters of EVA or combine it with other wax inhibitors to improve the wax inhibition effect.

3.3. Construction and Validation of Phase Model

Based on the Flory–Huggins theory, a phase prediction model for the EVA–wax system was constructed to quantitatively describe the relationship between the phase transition parameters (such as WAT, phase transition enthalpy) and the structural parameters of EVA (VA content, molecular weight), EVA concentration, and wax system carbon number distribution. The core of the model is to establish the thermodynamic equilibrium relationship between the wax crystal phase and the liquid phase, and the model equation is derived as follows:

$$\ln {\mathsf{\varphi }}_w=\ln {\mathsf{\varphi }}_{w0}+{\chi }_{we}{\mathsf{\varphi }}_e^2+{\displaystyle \frac{\mathsf{\Delta }{H}_m}{R}}\left({\displaystyle \frac{1}{T_0}}-{\displaystyle \frac{1}{T}}\right)$$

where: phi_w is the volume fraction of wax crystals in the system; phi_{w₀} is the volume fraction of wax crystals in the blank system (without EVA); chi_{we} is the Flory–Huggins interaction parameter between wax and EVA; phi_e is the volume fraction of EVA in the system; Delta H_m is the melting enthalpy of wax; R is the gas constant (8.314 J/(mol·K)); T₀ is the phase transition temperature of the blank system (K); T is the phase transition temperature of the system with EVA (K).

The interaction parameter chi_{we} is related to the structural parameters of EVA and the carbon number distribution of the wax system. It was fitted using the experimental data of the M1 wax system and EVA-2 with different concentrations. The fitting results show that chi_{we} is 0.38 ± 0.02, which indicates that there is a weak repulsive interaction between EVA and wax molecules, which is conducive to EVA molecules adsorbing on the wax crystal surface and inhibiting crystal growth.

3.3.1. Model Validation

To verify the accuracy and reliability of the constructed phase model, the experimental data of the M1 wax system with different EVA-2 concentrations (200~1000 ppm) were used for validation. The volume fraction of EVA (phi_e) and wax crystals (phi_w) in the system were calculated based on the experimental parameters, and the phase transition temperature (T) was predicted using the model equation. The comparison between the predicted values and the experimental values of WAT (consistent with the phase transition temperature T in the model) is shown in

Table 10. Comparison between predicted and experimental WAT values of M1 wax system (data source: self-conducted experiments in this study; predicted values calculated based on the phase model).

EVA Additive Amount (ppm)	Experimental WAT (°C) ± SD	Predicted WAT (°C)	Relative Error (%)
200	24.5 ± 0.2	24.1	1.63
400	21.8 ± 0.3	22.0	0.92
600	18.3 ± 0.2	18.5	1.09
800	15.6 ± 0.2	15.4	1.28
1000	15.3 ± 0.2	15.5	1.31

, and the relative error between the two was calculated to evaluate the model’s prediction accuracy.

As shown in Table 10, the relative error between the predicted WAT values of the phase model and the experimental values is between 0.92% and 1.63%, with an average relative error of 1.25%. This indicates that the constructed phase model has high prediction accuracy and can effectively describe the relationship between EVA concentration and the phase transition temperature of the wax system. The small relative error also verifies the rationality of the model derivation and the reliability of the fitting parameterchi_{we} (0.38 ± 0.02).

To further verify the applicability of the model in different wax systems, the experimental data of W2 (medium-carbon wax) and W3 (high-carbon wax) with 800 ppm EVA-2 were selected for additional validation. The results are shown in

Table 11. Model validation results for different wax systems (data source: self-conducted experiments in this study; predicted values calculated based on the phase model).

Wax System	Experimental WAT (°C) ± SD	Predicted WAT (°C)	Relative Error (%)
W2 (Medium-carbon)	19.7 ± 0.2	19.3	1.78
W3 (High-carbon)	60.3 ± 0.3	59.1	2.03

. It can be seen that the relative errors of the predicted WAT values for W2 and W3 are 1.78% and 2.03%, respectively, which are slightly higher than those of the M1 system but still within the acceptable range (≤2.5%). This indicates that the phase model has good applicability to different types of wax systems, especially medium-carbon and high-carbon wax systems, which are more prone to wax deposition in engineering practice.

3.3.2. Model Applicability and Optimization

The validation results show that the phase model based on Flory–Huggins theory can effectively predict the phase transition behavior of the EVA–wax system, but its applicability is affected by the carbon number distribution of the wax system and the structural parameters of EVA. For low-carbon wax systems (such as W1), the relative error of the model prediction is relatively large (up to 3.52%, as calculated from additional validation data), which is mainly due to the low crystallization tendency of low-carbon alkanes. The model assumes that the wax system is in a thermodynamic equilibrium state, but low-carbon alkanes are often in a liquid state at room temperature, and the crystallization process is not obvious, leading to deviations between the model prediction and the experimental results.

To improve the applicability of the model to low-carbon wax systems, two optimization strategies were proposed: first, introduce a correction factor alpha related to the carbon number distribution of the wax system, which is used to adjust the interaction parameter chi_{we}; second, modify the model equation by considering the solubility of EVA in low-carbon wax systems. The optimized model equation is as follows:

$$\ln {\mathsf{\varphi }}_w=\ln {\mathsf{\varphi }}_{w0}+\alpha \cdot {\chi }_{we}{\mathsf{\varphi }}_e^2+{\displaystyle \frac{\mathsf{\Delta }{H}_m}{R}}\left({\displaystyle \frac{1}{T_0}}-{\displaystyle \frac{1}{T}}\right)+\ln S$$

where: alpha is the carbon number correction factor (α = 0.85 for low-carbon wax, α = 1.0 for medium-carbon wax, α = 1.1 for high-carbon wax); S is the solubility of EVA in the wax system (dimensionless), which is measured by the mass fraction of EVA dissolved in the wax system at the phase transition temperature.

After optimization, the relative error of the model prediction for the W1 low-carbon wax system is reduced to 1.87%, which significantly improves the model’s applicability to different types of wax systems. This optimized model can provide a theoretical basis for the quantitative design and application of EVA wax inhibitors in different crude oil systems.

3.3.3. Mechanism Analysis of Phase Model

The phase model reveals the intrinsic mechanism of EVA inhibiting wax crystallization from a thermodynamic perspective. The interaction parameter chi_{we} (0.38 ± 0.02) indicates a weak repulsive interaction between EVA and wax molecules, which is the key to EVA’s wax inhibition effect. On the one hand, the weak repulsive interaction prevents EVA molecules from being completely dissolved in the wax phase, making it easier for EVA molecules to adsorb on the surface of wax crystal nuclei; on the other hand, it avoids excessive aggregation of EVA molecules, ensuring that EVA can effectively exert a steric hindrance effect to hinder wax crystal growth.

The model also shows that the phase transition enthalpy (Delta H_m) and EVA volume fraction (phi_e) are important factors affecting the phase transition temperature of the wax system. With the increase in EVA concentration, phi_e increases, and the repulsive interaction between EVA and wax molecules is enhanced, leading to a significant decrease in the phase transition temperature. This is consistent with the experimental results in Section 3.2.1, further verifying the consistency between the model and the experimental data.

4. Conclusions and Prospect

4.1. Main Conclusions

This study investigated the interaction between an EVA wax inhibitor and model wax systems with varying carbon number distributions. Using differential scanning calorimetry (DSC), the influence of EVA structural parameters and wax carbon number distribution on the thermal behavior of the system was systematically examined. The underlying wax inhibition mechanism of EVA was elucidated, and a predictive phase model for the EVA–wax system was constructed and subsequently validated. The main conclusions drawn from this work are as follows:

(1)

EVA concentration exerts a significant influence on the thermal behavior of the wax system, with an optimal dosage range identified. Within the experimental range investigated, increasing the EVA concentration from 200 ppm to 800 ppm led to a progressive decrease in the wax appearance temperature (WAT), crystallization enthalpy (ΔHc), and the amount of wax precipitated for the M1 system, corresponding to a steady enhancement in inhibition efficacy. When the concentration exceeded 800 ppm, the inhibition effect plateaued and, in some cases, exhibited a slight decline, likely attributable to self-aggregation of the EVA polymer at higher concentrations. The optimal EVA concentration was therefore determined to be 800 ppm.

(2)

The VA content and molecular weight of EVA exert a synergistic influence on wax inhibition performance. At a VA content of 10%, the EVA molecular chain possesses an optimal number of polar sites, maximizing its binding efficiency with wax crystals. At a number-average molecular weight of 20,000 g/mol, a balance between chain diffusion and entanglement is achieved, enabling the polymer to most effectively hinder wax crystal growth. Consequently, the EVA wax inhibitor with a VA content of 10% and a number-average molecular weight of 20,000 g/mol exhibited the most favorable comprehensive performance.

(3)

The responsiveness of wax systems to EVA varied significantly with carbon number distribution. The medium-carbon-range system (C16–C30) exhibited the most pronounced response, with a WAT reduction of up to 12.4 °C and a 40.0% decrease in crystallization enthalpy. The high-carbon-range system (C31–C50) showed an intermediate response, while the low-carbon-range system (C5–C15) demonstrated the weakest response. The response characteristics of mixed-carbon systems were governed by the dominant wax component. Among these, the M3 system (1:2:1), which is enriched in medium-carbon waxes, exhibited the most favorable response.

(4)

The wax inhibition mechanism of EVA was elucidated as a synergistic process involving heterogeneous nucleation, adsorptive encapsulation, and crystal habit modification. Specifically, the ethylene segments act as heterogeneous nucleation sites, altering the wax crystal nucleation pathway; the polar ester groups of the VA segments adsorb onto the crystal surfaces, hindering growth; and the EVA molecular chains become incorporated into the crystal lattice, disrupting its regularity. The combined effect of these three phenomena results in a reduction in both the WAT and the total amount of wax precipitated. The thermal parameters obtained from DSC analysis provide thermodynamic evidence supporting this proposed mechanism.

(5)

The phase model constructed in this study, based on the Flory–Huggins theory, accurately predicts the wax precipitation behavior of EVA–wax systems. The relative error between the model-calculated values and experimental measurements is consistently less than 4%, demonstrating its suitability for wax systems with varying carbon number distributions and across a range of EVA concentrations. The model thus provides a robust theoretical foundation for guiding wax management strategies in the practical engineering of waxy crude oil production and transport.

4.2. Future Outlook

While this study has systematically investigated the interaction and phase behavior of EVA–wax systems, several avenues for future research remain to be explored:

(1)

Expanding the scope to multi-component inhibitor systems: The current work focused on a single EVA inhibitor. Future studies should investigate combinations of EVA with other inhibitor types (e.g., polyolefins, surfactants) to explore potential synergistic effects and enhance adaptability to wax systems with diverse carbon number distributions.

(2)

Advancing the phase model to incorporate kinetic effects: The current model is based on thermodynamic equilibrium and does not account for kinetic factors. Future work should aim to incorporate dynamic parameters, such as wax crystal nucleation and growth rates, to develop a kinetic phase model that more accurately reflects the non-equilibrium nature of wax deposition during crude oil transport.

(3)

Deepening mechanistic understanding through microscopic characterization: Subsequent research should employ advanced microscopic and diffraction techniques, such as polarized light microscopy, scanning electron microscopy (SEM), and X-ray diffraction (XRD), to directly visualize changes in wax crystal morphology, size distribution, and crystal structure upon EVA treatment. This would provide more direct, microstructural evidence to complement the thermodynamic findings. We acknowledge this limitation. Microscopic characterization will be further carried out in future work to reveal the morphology and structural changes in wax crystals under the action of EVA.

(4)

Conducting field-scale validation studies: The optimal EVA formulation and parameters identified in this laboratory-scale study should be tested under real-world conditions in waxy crude oil pipeline operations. Field trials are essential to validate the inhibitor’s efficacy and the model’s predictive accuracy in practical engineering scenarios, thereby facilitating the translation of these research findings into industrial practice.