Screening key parameters affecting stability of graphene oxide and hydrolyzed polyacrylamide hybrid: Relevant for EOR application

Abstract

Graphene oxide-enhanced hydrolyzed polyacrylamide (GOeH) hybrids present a promising advancement for enhanced oil recovery (EOR), addressing a knowledge gap in understanding the stability of these materials under different conditions. The current study investigates how key parameters, including polymer concentration (1000 and 1500 ppm), graphene oxide (GO) concentration (100 and 300 ppm), salinity (seawater and 0.1 seawater), and the presence or absence of divalent ions (Mg²⁺), affect the stability of GOeH hybrids at high temperatures (80 $°C$). A 2^K-full factorial experimental design and analysis of variance (ANOVA) were employed to quantify these effects. GO was synthesized and characterized using common methods, including XRD, FTIR, Raman, and DLS analysis. Zeta potential was used to assess stability over 21 days, while the sedimentation method measured instability. ANOVA results reveal that, within the studied range, neither polymer concentration nor the presence or absence of Mg²⁺ significantly impacts stability. However, both factors seem to contribute positively to long-term stability. Notably, GO concentration has a significant positive effect on stability, with a percent contribution of 38.24 %, suggesting that higher GO concentrations enhance the stability of the GOeH hybrid. Conversely, salinity has a statistically significant negative impact on stability, potentially due to the salt-in effect. Additionally, the interaction between polymer concentration and Mg²⁺ shows a borderline significant effect, indicating that excessive cross-linking at higher polymer concentrations could reduce stability. These findings offer valuable insights into optimizing EOR strategies, aiding in developing more effective approaches to utilizing GOeH hybrids for different conditions.

Nomenclature

Nomenclature	Description
2K-full factorial	Two-level full factorial
AUC	Area Under the Curve
ANOVA	Analysis of Variance
API RP63	American Petroleum Institute Recommended Practice 63
DLS	Dynamic light scattering
DIW	Deionized water
EOR	Enhanced oil recovery
FTIR	Fourier transform infrared spectroscopy
GO	Graphene oxide
GOeH	Graphene oxide-enhanced hydrolyzed polyacrylamide
GOTA	Amphiphilic-modified graphene oxide
HPAM	Hydrolyzed polyacrylamide
ID/IG	Intensity ratio of D and G peaks in Raman spectroscopy
IFT	Interfacial tension
Mg2+	Magnesium ion
MgCl2	Magnesium chloride
Minitab	Statistical software for design of experiments
NaCl	Sodium chloride
OOIP	Original oil in place
ppm	Parts per million
p-value	Probability value for statistical significance
S-GO	Surface-modified graphene oxide
sGOeH	Saline graphene oxide-enhanced hydrolyzed polyacrylamide
SiNP	Silica nanoparticle
Statsmodels	A Python module for statistical models
XRD	X-ray diffraction
ZP	Zeta potential

1. Introduction

Using nanoparticles for EOR purposes has drawn attention in the last two decades due to their specific properties. The primary mechanism of nanoparticles for improving oil recovery is based on their ability to alter the interfacial tension (IFT) between oil and water, thereby enhancing the mobilization of oil droplets trapped in the reservoir rock [1,2]. Additionally, nanoparticles can increase the viscosity of the displacing fluid, improving sweep efficiency and facilitating easier production [3]. Furthermore, nanoparticles can target specific oil reservoirs, such as those with high salinity or temperature, by modifying rock surface properties to interact favorably with the reservoir conditions [4,5].

For EOR, various types of nanoparticle, such as carbon nanotubes [6,7], carbon nanofibers [8], nano oxides, and clay nanoparticles [[9], [10], [11], [12], [13]] have been used. The findings have been encouraging. Silica nanoparticles (SiNPs) have become the most widely used for EOR purposes due to their ability to be surface-modified to control their chemical properties [1]. SiNPs have been shown to significantly improve oil recovery, with some studies reporting recoveries of 8.7 % and 7.7 % of the original oil in place (OOIP) after water flooding [2]. Although nano-enhanced oil recovery (nano-EOR) exhibits considerable promise, the technology is still in its early stages of development. Therefore, more research is needed to prove the effectiveness of nanoparticles in real-world oil field operations [2]. Many researchers have noted that systematic and rigorous studies are needed to develop general guidelines for the optimal use of nanoparticles in EOR; however, due to their potential to be used alongside other EOR agents and generate synergistic effects, hybrid EOR methods are increasingly recommended [2,4,14]. An example of this approach is the use of polymer-nanoparticle hybrids.

A wide range of studies have demonstrated that the synergistic effects of hybridizing polymers and nanoparticles can significantly improve oil recovery compared to using each component individually [[14], [15], [16], [17]]. Hybridizing polymer and nanoparticles improves oil recovery by altering rock wettability, increasing polymer viscosity, and decreasing polymer retention in rock surfaces [17]. Cheraghian et al. studied the effect of using SiNPs on polymer adsorption on the surface of carbonate and sandstone rocks. They observed that nanoparticles played a significant role in preventing polymer adsorption on the rock surface. In the absence of nanoparticles, polymer adsorption increased significantly [18]. Simulation studies that investigated the effect of using SiNPs in the polymer solution on adsorption also indicated that using nanoparticles results in much lower adsorption values than conventional polymer flooding [19,20]. Ulasbek et al. conducted rheology experiments and contact angle measurements to determine the optimal concentrations of hydrolyzed polyacrylamide (HPAM) and SiNP, which resulted in a maximum incremental oil recovery of 26.88 % [17]. Widely used in EOR, HPAM is chosen because it enhances oil displacement by increasing fluid viscosity, has proven field performance, and offers cost-effectiveness in various reservoir conditions [14,21]. Zhangaliyev et al. demonstrated that the addition of polymer positively affects the salinity tolerance of nanoparticles, while the inclusion of nanoparticles increases the viscosity of the polymer solution [15]. These observations imply that the hybrid application of polymers with nanoparticles holds promise for substantially enhancing oil recovery, marking it as a promising area for research in the oil and gas industry.

Recently, the use of carbon-based nanoparticles, particularly graphene oxide (GO) nanoparticles combined with polymers, has shown potential for EOR applications. On its own, GO offers several advantages for EOR purposes. GO modifies rock surfaces from oil-wet to water-wet, facilitating better oil displacement and improving recovery rates [[22], [23], [24]]. It effectively reduces IFT, enhancing oil displacement efficiency, and can achieve significant effects at low concentrations, thereby reducing contact angles without requiring large amounts of material [22,23]. Additionally, GO improves the mobility ratio and minimizes viscous fingering during oil recovery [25]. For instance, ElShawaf et al. examined the effectiveness of GO in lowering the viscosity of heavy asphaltene-rich oil. Their results demonstrated that GO achieved viscosity reductions ranging from 20 % to 65 %, surpassing the performance of eight other nanoparticles. This makes GO a more economical alternative than various other nanoparticles used [26]. Khoramian et al. investigated graphene oxide nanosheets (GONs) in micro-model flooding experiments. Their findings revealed that GONs increased viscosity by 34 % at a concentration of 800 ppm and reduced IFT to 19.4 mN/m. Notably, the GON nanofluid achieved 28 % higher oil recovery than brine, significantly improving mobility and extending the breakthrough time from 55 to 98 min [25]. Kashefi et al. explored a GO-SiO₂ nanohybrid and demonstrated its ability to alter wettability from oil-wet to water-wet, achieving optimal performance at a concentration of 0.015 wt% and a 1:1 ratio, particularly at elevated temperatures [27]. Jafarbeigi et al. explored the use of GO nanofluid for EOR purposes. Their results showed a reduction in contact angle from 161° to 35° and a decrease in IFT from 18.45 mN/m to 8.8 mN/m at a concentration of 500 ppm, indicating the nanofluid's effectiveness in improving EOR outcomes [28]. Additionally, Gu et al. investigated amphiphilic-modified graphene oxide (GOTA) through contact angle and IFT measurements. Their results showed that GOTA exhibited amphiphilicity with contact angles of 34.6° (hydrophilic) and 103.5° (hydrophobic). The IFT was significantly reduced to approximately 16 mN/m, further decreasing to 11.95 mN/m when combined with zwitterionic surfactants. Molecular simulations supported the effectiveness of GOTA in enhancing oil recovery [29]. Being environmentally friendly compared to traditional additives, GO remains a sustainable option for improving oil recovery processes [23]. However, when combined with polymers, these benefits are further amplified. For instance, Aliabadian et al. showed that adding GO decreased viscosity and dynamic modulus. The application of 0.2 wt% surface-modified graphene oxide (S-GO) increased oil recovery by 8 %, reflecting a 7.8 % increase in recovery efficiency compared to an HPAM solution without S-GO, due to the superior dispersibility of S-GO [30]. Lyu et al. studied the synergistic effect of modified surface GO and polyacrylamide. The experimental results showed that the viscosity at elevated temperatures increased by around 20 %. The hybrid exhibits excellent thermal resistance, where more than 85 % of its original viscosity remains in high-salinity conditions [31]. Meanwhile, Haruna et al. studied the effects of GO on HPAM and discovered that adding 0.1 wt% GO greatly enhanced long-term thermal stability, with viscosity increases of 47 % at 85 °C and 36 % at 25 °C. While greater NaCl concentrations lowered viscosity, the HPAM/GO composite showed increased critical salinity tolerance, indicating its suitability for high-salinity applications [32]. Similarly, Haruna et al. investigated a hybrid of HPAM and GO for EOR. They found that the hybrid reduced oil-water IFT from 62.54 mN/m to 42.78 mN/m and lowered the contact angle from 71.08° to 68.84°, increasing viscosity from 9.07 mPa s to 16.49 mPa s. In core-flooding tests, 0.8 wt% GO improved oil recovery to 76.83 %, compared to 67.39 % for pure HPAM, attributed to better mobility ratios from GO's amphiphilic properties [33]. Another study explored the synergistic effect of GO and partially hydrolyzed polyacrylamide for EOR purposes, merging coreflood experimental and CFD modeling approaches. The study demonstrated the potential of the hybrid system to improve oil recovery by altering the wettability of rock surfaces and reducing IFT [34]. Additionally, the impact of modified GO nanofluid on changes in wettability and variations in IFT was investigated by Jafarbeigi et al., highlighting the potential of GO nanofluid in improving oil recovery [28]. Collectively, these studies indicate that the hybrid application of GO and polymer has the potential to substantially improve oil recovery by modifying rock surface wettability, reducing IFT, and enhancing the mobility ratio.

The potential of GO-enhanced HPAM hybrid (GOeH) in EOR applications necessitates a comprehensive investigation into their stability under various conditions. A close look at the existing literature reveals a knowledge gap in thoroughly examining of GOeH hybrid stabilities for EOR applications. Addressing this gap is crucial for developing robust guidelines and methodologies that can be applied in field operations, ultimately contributing to the success of EOR strategies that leverage these advanced materials. Consequently, this research aims to determine how key parameters such as polymer concentration, GO concentration, salinity, and the presence or absence of divalent ions (Mg²⁺) affect the stability of GOeH hybrids at high temperatures of 80 °C. Thus, GO was synthesized, and characterizations were conducted using common methods. Subsequently, GOeH hybrids were prepared, and the effects of the parameters mentioned above, on their stability were assessed using zeta potential and sedimentation methods. A 2^K-full factorial experimental design, and Analysis of Variance (ANOVA) were utilized in this study to differentiate between significant and insignificant features. Using this method, the impacts of various parameters can be measured, and their relative effects on the results can be compared.

2. Materials

Chemicals, including sulfuric acid (95 % purity), sodium hydroxide, potassium permanganate, and hydrogen peroxide, were supplied by Merck Company, while graphite was purchased from Asbury Company. The polymer solution for the study was prepared from "Flopaam 3630S" powder from SNF, HPAM, which was dissolved in deionized water (DIW) to form polymer solution. To prepare the brine, NaCl and MgCl₂ salts (approximately 99 % purity) from Sigma-Aldrich were used.

3. Methods

3.1. Synthesis of graphene oxide

The technique for synthesizing GO involves several distinct stages, as detailed in Refs. [35,36]. Initially, intercalated graphite is heated at 900 $°C$ for a brief duration in an oven, inducing expansion of graphite plates and increasing inter-sheet spacing. To improve graphite oxidation, a mixture of 20 ml of sulfuric acid and 2 g of potassium permanganate was prepared and mixed in an ice bath. After oxidation, the temperature was increased to 40 $°C$. The expanded graphite is then added to the solution and stirred for 2 h using a magnetic stirrer. The resulting paste-like liquid is mixed with 100 mL of cold water and 5 mL of hydrogen peroxide solution. To purify the resultant material, the mixture is washed with sodium hydroxide and centrifuged several times. Next, the washed graphite oxide is exfoliated using a high-shear homogenizer. Finally, GO nanosheets are dispersed and stabilized using probe and bath sonication. The flowchart of the synthesis process can be observed in Fig. 1.

Fig. 1.

Flowchart of the synthesis process of GO.

3.2. GO characterization methods

A systematic approach utilizing various analytical techniques was employed to characterize the synthesized GO. Initially, X-ray diffraction (XRD) was conducted to explore the atomic arrangements of the synthesized GO.

This included the acquisition of GO sludge by centrifuging the GO solution, drying it, and assessing the resultant powder with a PHILIPS PW1730 X-ray diffractometer. Accurate X-rays were produced by the device, which contained a Cu lamp, enabling a detailed investigation of peak positions with an unmatched precision threshold. Following XRD analysis, Fourier transform infrared spectroscopy (FTIR) was performed using a Thermo_Avatar spectrometer to identify chemical bonds, molecular interactions, and functional groups within the GO sample. Surface changes in the nanoparticles were effectively investigated using this approach. After FTIR analysis, Raman spectrometry was carried out using the UniDRON - UniNanoTech Confocal Microscopy system. The Raman spectroscopy equipment can analyze molecular structures and identify chemical interactions. This technology, which utilizes laser light interactions, offers rapid assessments of carbon structures, making it a cost-effective tool for examining materials such as nanotubes, fluorine compounds, and graphene. The current study conducted dynamic light scattering (DLS) and zeta potential (ZP) analyses using a MALVERN Nano ZS ZEN 3600 instrument. DLS facilitated examining particle distribution and size dynamics, while ZP analysis provided insights into the particles’ electric charge. To ensure the validity of the results, each sample underwent rigorous dilution and testing protocols, reinforcing the accuracy and reliability of the analytical outcomes.

3.3. Saline graphene oxide enhanced HPAM (sGOeH) hybrid preparation

The polymer solution was prepared according to the procedure indicated in API RP63 and allowed to rest for 24 h in a heat and light-free environment. The diluted GO dispersion was carefully introduced dropwise into the polymer solution, followed by continuous stirring for 24 h. After that, one-third of the GOeH was mixed into the pre-prepared brine solution and stirred for an additional 2 h, resulting in the formation of a semi-hybrid solution. In the final step, this semi-hybrid solution was mixed with the remaining GOeH hybrid, and the mixture was stirred for a further 2 h. Fig. 2 shows a schematic view of the saline graphene oxide enhanced HPAM (sGOeH) preparation method.

Fig. 2.

Schematic view of the sGOeH preparation method.

3.4. Analyzing the stability of saline graphene oxide enhanced HPAM

Two approaches were used to evaluate the stability of sGOeH hybrids, including the sedimentation test and ZP analysis [32,37,38]. Sedimentation analysis, a typical approach for determining the stability of nanoparticle dispersions, involves observing the sample over time as it remains undisturbed in a container. This method determines the stability of the hybrid material based on the differences in the settling distance or color contrast between the sedimented particles and the supernatant liquid. If a substantial separation or color difference is observed, the sample is considered unstable. However, it is important to note that this approach does not provide quantitative assessments. Therefore, samples with no apparent settling distance or color variation are subjected to ZP analysis, a widely used method for assessing nanoparticle suspension stability, for 21 days. Higher absolute ZP values indicate greater nanoparticle suspension stability [39].

The Area Under the Curve (AUC) of ZP versus time as a quantitative method was used to quantify long-term stability [36]. A higher absolute AUC value indicates enhanced long-term stability, enabling a more detailed analysis of ZP progression throughout the study. To compute the AUC for each solution, the well-established Simpson's integration algorithm was employed. The resulting AUC data was then analyzed using ANOVA, a vital statistical tool for identifying statistically significant differences between group means. This method is widely utilized across various disciplines due to its effectiveness in uncovering patterns and relationships within data, enabling researchers and decision-makers to draw insightful conclusions and make informed decisions. Additionally, ANOVA simplifies hypothesis testing, particularly when comparing outcomes from different treatments or interventions, by assessing variability within and between groups. The “Statsmodels” module in Python was used to conduct ANOVA analyses.

In ANOVA, several key statistical metrics clarify group-level disparities and measure the magnitude of observed effects. The p-value, a key statistic, indicates the probability that observed differences are due to chance, typically with a threshold of 0.1. Conversely, the F-statistic quantifies the variability divergence among specified groups. A lower p-value typically corresponds to a greater spread between group means, increasing the reliability of the analysis. Additionally, effect size evaluations measure the magnitude of disparities among group averages, providing essential insights into the practical implications of the observed outcomes. By incorporating these statistical indices, ANOVA facilitates the exploration of potential relationships between variables and assesses the relative influence of each factor on the overall observed variability in the dependent variable.

3.5. Experimental design

The stability of a sGOeH hybrid was investigated through a series of experiments examining the effects of four key controlling parameters: polymer concentration, GO concentration, salinity (NaCl), and divalent ion presence (Mg²⁺). In experiments where the effects of multiple factors are studied, factorial designs are generally the most efficient approach. These designs investigate all possible combinations of factor levels in each trial or replicate. This structure allows researchers to examine the joint effects of factors on a response, making it ideal for experiments involving multiple variables. Despite the widespread application of the general factorial design, there are specific cases within this design that are particularly significant. These specific cases are widely used in research and form the foundation for other valuable experimental designs. The most important case involves experiments with k factors, each at two levels, offering a primary yet powerful method for understanding complex interactions. The 2^K-full factorial design, used in this study, provides a simple and effective way for understanding complex interactions among factors [40].

The polymer concentration was set at two levels: 1000 ppm (low) and 1500 ppm (high). This range was selected due to its frequent use in literature and because lower concentrations are generally unsuitable for field applications. In contrast, higher concentrations, above 3000 ppm, are prone to mechanical degradation in porous media, making them impractical [41]. Furthermore, the upper limit of 1500 ppm aligns with cost-effectiveness, while higher polymer concentrations may incur significantly higher costs. GO concentrations were set at 100 ppm (low) and 300 ppm (high). This range was chosen to keep nanoparticle concentration low relative to polymer concentration, avoiding the economic burden of higher concentrations. Salinity was set at two levels: high (seawater salinity) and low (0.1 times seawater salinity). These levels were chosen to reflect common environmental conditions and assess their influence on polymer hybrid stability. For the divalent ion concentration, the focus was on magnesium (Mg²⁺). The experimental design included two Mg²⁺ levels: 0.1 times seawater concentration and zero. This choice was based on GO's high sensitivity to divalent ions, particularly at higher concentrations, where GO stability becomes problematic even with polymer present.

The experimental design was structured to maintain a constant ionic strength across salinity levels to ensure consistency. This was made to isolate the effects of salinity and divalent ion concentration on sGOeH stability. For example, the ionic strength of a high-salinity solution without Mg²⁺ was equivalent to that of a high-salinity solution with Mg²⁺, enabling direct comparisons between these scenarios. Controlling the ionic strength at both high and low salinity levels ensured that differences in outcomes could be attributed to the controlling parameters, not to fluctuations in ionic strength. This approach ensured the reliability and robustness of the results, enabling a more accurate evaluation of the factors affecting polymer hybrid stability.

Minitab Statistical Software version 21 was used to design the experiment, while the "Statsmodels" module in Python was employed for statistical analysis, ensuring robustness and accuracy. The software recommended 16 solutions for a comprehensive evaluation. To ensure the reproducibility of result, each experiment was conducted in triplicate. The experimental design, including the variable levels, is detailed in Table 1.

Table 1.

Experimental design table.

Run	Hybrid Solution Namea	Parameter
		Polymer Concentration (ppm)	GO Concentration (ppm)	Salinity (ppm)	Mg2+ Concentration (ppm)
1	LLHA	1000	100	45483	0
2	LLHP	1000	100	44496	643
3	LLLA	1000	100	4549	0
4	LLLP	1000	100	3560	643
5	LHHA	1000	300	45483	0
6	LHHP	1000	300	44496	643
7	LHLA	1000	300	4549	0
8	LHLP	1000	300	3560	643
9	HLHA	1500	100	45483	0
10	HLHP	1500	100	44496	643
11	HLLA	1500	100	4549	0
12	HLLP	1500	100	3560	643
13	HHHA	1500	300	45483	0
14	HHHP	1500	300	44496	643
15	HHLA	1500	300	4549	0
16	HHLP	1500	300	3560	643

^aH: high, L: low, A: absence, P: presence.

4. Results and discussion

The structural characterization of GO was conducted using XRD, FTIR, and Raman spectrometry. Fig. 3a shows the XRD pattern of GO. A strong peak at 11° indicates the formation of GO. Two additional peaks were observed at 2θ values of 24.45° and 34.4°, correlating with interlayer distances of 3.63 nm and 2.60 nm, respectively. These results align with those reported in prior research [32,42]. FTIR spectroscopy was used to analyze chemical bonds, molecular interactions, and identifying functional groups within GO. The FTIR spectrum, shown in Fig. 3b, confirms the formation of GO and reveals distinctive chemical bond configurations, including the in-plane vibration of C=C bonds, carboxyl groups, C-OH vibration, C-O bonds, ketonic species, and hydroxyl groups. These findings confirm the characterization of GO and align with previous studies [[42], [43], [44], [45]]. Raman spectrometry was used along with FTIR spectroscopy to identify carbon structures. The Raman spectrum, presented in Fig. 3c, exhibits D and G peaks at 1342 cm⁻¹ and 1568 cm⁻¹, respectively. The primary in-plane vibration is indicated by the G peak while oxygen-containing functional groups primarily contribute to the D peak [30]. The ratio of D to G peaks (I_D/I_G) was calculated to be 1.02, revealing that the synthesized GO was oxidized [46]. DLS analysis was utilized to measure the hydrodynamic diameter of GO nanosheets, revealing a mean diameter of 286.9 nm (Fig. 3d). The stability of the GO aqueous dispersion was evaluated using ZP analysis, yielding a value of −20.55 mV, indicating the dispersion's stability.

Fig. 3.

Characterization results for XRD (a), FTIR (b), Raman (c), and DLS (d) analyses.

The long-term stability of hybrid solutions is crucial for their performance and potential EOR applications. This section explores the impact of various parameters on the stability of these solutions, such as polymer concentration, GO concentration, salinity, and divalent ions (Mg²⁺). ZP analysis was conducted on different hybrid solutions at a constant temperature of 80 °C over time to assess the stability of the hybrids. The analysis followed the experimental design outlined in Table 1, as illustrated in Fig. 4. Subsequently, ANOVA was performed on the AUC data, with the results shown in Table 2.

Fig. 4.

– ZP vs time for sGOeH under different conditions outlined in Table 1.

Table 2.

ANOVA table for the long-term stability of sGOeH.

Source	DF	Adj SS	Adj MS	Effect	Percent Contribution	F-Value	P-Value
A- Polymer	1	15569	15569	62.4	2.75	0.89	0.389
B- Go	1	277479	277479	263.4	38.24	15.85	0.011 < 0.1
C- Salinity	1	131796	131796	−181.5	18.17	7.53	0.041 < 0.1
D- Mg	1	30092	30092	86.7	4.15	1.72	0.247
AB	1	1702	1702	20.6	0.23	0.10	0.768
AC	1	24087	24087	77.6	3.32	1.38	0.294
AD	1	74681	74681	−136.6	10.29	4.27	0.094 < 0.1
BC	1	51739	51739	−113.7	7.13	2.95	0.146
BD	1	437	437	−10.5	0.06	0.02	0.881
CD	1	30316	30316	87.1	4.18	1.73	0.245
Error	5	87546	17509
Total	15	725444

The stability of the hybrid is not significantly impacted by polymer concentration, as indicated by the ANOVA results, with a p-value of 0.389. This suggests that the stability of the hybrid is not substantially affected by variations in polymer concentration within the examined range. This effect becomes more evident in Fig. 4, where the differences between the left charts (Fig. 4a and c) and the right charts (Fig. 4b and d), attributed solely to polymer concentration, illustrate that these differences do not significantly impact the AUC, indicating the hybrid's long-term stability. However, despite the lack of significance, the positive sign associated with polymer concentration may still indicate a beneficial effect on long-term stability. This notion is supported by the main effect plots of AUC shown in Fig. 5a. Lower polymer concentrations may result in fewer polymer chains to effectively encapsulate or bind with GO sheets, leading to poor dispersion, agglomeration, and uneven distribution. This may weaken the stability of the hybrid due to insufficient interfacial interactions and reduced mechanical strength. Conversely, higher polymer concentrations tend to create a denser hybrid structure, likely enhancing support for GO dispersion and strengthening interfacial adhesion with the polymer matrix.

Fig. 5.

Main effects plot (fitted means) of AUC for polymer concentration (a), GO concentration (b), Salinity (c) and Mg²⁺ (d).

Similar to polymer concentration, the presence or absence of Mg²⁺ ions does not significantly influence hybrid stability, as indicated by a p-value of 0.247 (>0.1). Nevertheless, as seen in Fig. 5d, the presence of Mg²⁺ ions demonstrates a positive impact on long-term stability, likely due to their ability to enhance cross-linking and structural support. This positive effect is evident from the comparison of filled and hollow signs in each chart in Fig. 4, where filled signs represent the presence of Mg²⁺ ions and hollow signs indicate their absence.

As outlined in Table 2, the statistical analysis revealed that GO concentration, salinity, and the interaction of polymer concentration with Mg²⁺ significantly affect the hybrid's long-term stability. Consider Fig. 4, where differences between the upper and lower charts (Fig. 4a and b versus Fig. 4c and d), solely attributed to GO concentration, highlighting that GO concentration significantly impacts the AUC and, consequently, the hybrid's long-term stability. The ANOVA quantified the results. The low P-value (0.011), high F-value (15.85), and high percent contribution (38.24 %) for GO concentration indicate its substantial positive effect on stability. This suggests that increasing GO concentration leads to enhanced stability, probably due to improved interactions within the hybrid structure. A higher GO concentration may create a more robust network, enhancing structural integrity and durability. Fig. 5b illustrates the main effect of AUC on GO concentration.

In Fig. 4, solid and dashed lines in each chart illustrate variations in salinity levels between high and low. It is evident that salinity decreases long-term stability. Furthermore, the statistical significance of the influence of salinity on stability is highlighted by a p-value of 0.041 and a substantial F-value of 7.53, emphasizing its importance. The negative effect (−181.5) of salinity in ANOVA results suggests that increasing salinity correlates with decreased stability. This finding aligns with the notion that critical interactions within colloidal systems may be disturbed by elevated ionic strength. High salinity significantly reduces sGOeH stability due to the salting-out effect. This occurs when water and salt molecules interact, weakening hydrogen bonds between GO and polymer chains, leading to GO sheet aggregation. Elevated salt concentrations modify the ionic strength and dielectric constant, influencing the conformation and stability of polymer chains. Fig. 5c presents the main effect plot of AUC for salinity.

The interaction between polymer concentration and Mg²⁺ also showed a marginally significant effect, with a p-value of 0.094 and a negative effect size of −136.6. This finding indicates that the presence of magnesium, when combined with higher polymer concentrations, may mitigate stability. This suggests a potential negative effect on the hybrid's overall performance.

The interaction plot of AUC for polymer concentration and Mg²⁺ is shown in Fig. 6. As evident, at lower polymer concentrations, the presence of Mg²⁺ seems to enhance stability, likely due to its ability to cross-link polymer chains, providing additional structural support and cohesion. However, at higher polymer concentrations, the presence of Mg²⁺ may induce excessive cross-linking or increase rigidity, leading to reduced stability and a higher risk of agglomeration.

Fig. 6.

Interaction plot of AUC for polymer concentration∗ Mg²⁺.

5. Conclusions

To conclude, GO was successfully synthesized and characterized, focusing on the long-term stability of a sGOeH hybrid at a high temperature of 80 °C. Through a comprehensive investigation, we assessed the impact of various parameters on stability, including salinity, polymer concentration, GO concentration, and the presence of divalent ions (Mg²⁺). The effects of these parameters on the long-term stability of sGOeH hybrids were evaluated using ANOVA statistical analysis and a 2^K-full factorial experimental design. These findings contribute to a deeper understanding of the stability dynamics in sGOeH, particularly in the context of EOR applications. Based on this investigation, the key conclusions are.

• •A comprehensive experimental design was employed to evaluate the influence of several factors on long-term stability, such as polymer concentration, GO concentration, salinity, and divalent ions.
• •The AUC metric was used to quantify the long-term stability of the hybrid solution.
• •The quantified stability data were analyzed using the ANOVA statistical approach.
• •According to the ANOVA, polymer concentration and the presence of divalent ions do not significantly influence the long-term stability of the hybrid solution within the studied range.
• •Among the factors investigated, salinity and GO content were the most influential. Higher salinity decreases stability, while an increased GO content enhances it.
• •The observed effects of salinity and divalent ions on long-term stability suggest that tailored adjustments to polymer and GO concentrations could improve the hybrid's robustness in saline environments.
• •Results showed that, of all parameter interactions, only the interaction between polymer concentration and magnesium (Mg²⁺) significantly impacted the long-term stability of the hybrid.

CRediT authorship contribution statement

M. Iravani: Writing – original draft, Methodology, Investigation, Formal analysis, Conceptualization. M. Simjoo: Writing – review & editing, Supervision, Resources, Project administration, Conceptualization. M. Chahardowli: Writing – review & editing, Supervision, Project administration.

Data availability statement

The data used to support the findings of this study are included in the article.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.