An experimental investigation into the rheological behavior and filtration loss properties of water-based drilling fluid enhanced with a polyethyleneimine-grafted graphene oxide nanocomposite

The modern oil and gas industry, driven by a surging global energy demand, faces the challenge of exploring deeper geological formations. Ensuring the robust performance of drilling fluids under harsh wellbore conditions is paramount, with elevated temperatures and salt contamination recognized as detrimental factors affecting the rheological and filtration loss properties of drilling fluids. We successfully synthesized a polyethyleneimine-grafted graphene oxide nanocomposite (PEI-GO), and its functional groups formation and thermal stability were verified through Fourier Transform Infrared Spectroscopy (FTIR) and Thermogravimetric Analysis (TGA). Our findings demonstrated a significant improvement in the plastic viscosity and yield point of the base drilling fluid with the addition of PEI-GO. The inclusion of 0.3 wt% PEI-GO outperformed the base drilling fluid at 160 °C, improving the yield point/plastic viscosity (YP/PV) value and reducing filtration loss volume by 42% and 67%, respectively. The Herschel–Bulkley model emerged as the superior choice for characterizing rheological behavior. PEI-GO exhibited compatibility with high-salt formations, maintaining satisfactory filtration volumes even when subjected to sodium chloride (NaCl) and calcium chloride (CaCl2) contamination concentrations of up to 20 and 10 wt%, respectively. The remarkable rheological and filtration properties of PEI-GO are attributed to its electrostatic interactions with clay particles through hydrogen and ionic bonding. These interactions lead to pore plugging in the filter cake, effectively preventing water infiltration and reducing filtration loss volume. This study emphasizes the potential of PEI-GO in water-based drilling fluids, particularly in high-temperature and salt-contaminated environments.


Introduction
Drilling uids are a key aspect in the success of oil and gas exploration and drilling operations.These uids can be categorized into water-based, oil-based, and synthetic-based uids, with water-based uids being preferred to reduce high operational cost and because of their cost-effectiveness and environmental safety.However, water-based uids impose certain wellbore issues owing to water's reactivity with reactive formations like shale.The water might intrude into the formation, leading to shale hydration and swelling, weakened formations, and wellbore collapse. 1,2Simultaneously, the water loss can result in the formation of a dense lter cake on the borehole wall, causing borehole damage and pipe sticking. 3To avoid these issues, it is crucial to control drilling uids' properties, particularly rheology and ltration loss, to ensure efficient drilling operations. 4Rheological properties determine the uid's ow behavior and its ability to suspend and transport cuttings, while ltration loss properties dictate the uid's ability to control uid loss into the formation. 5,6Stable rheological features and low uid loss in downhole conditions were crucial for maintaining well stability, preventing formation damage, and optimizing drilling productivity.Consequently, rheology modiers and uid loss additives such as surfactants, polymers, and nanoparticles were incorporated into the formulation to improve the rheological properties and minimize the uid loss to the formation. 7,8olyethyleneimine (PEI) is categorized as a cationic polymer, indicating its positivity is derived from the inclusion of amino groups (-NH 2 ) within its polymer chain, rendering it cationic in nature.This property, stemming from the amino groups, further underlined the feasibility of employing positively charged polymers as drilling uid's additive within high-temperature reservoirs.The interaction of electrostatic forces among particles within drilling uid is recognized as a major factor in improving rheological properties. 9Branched PEI exhibited greater efficacy in inhibiting clay hydration and swelling when compared to 1,6-hexamethylenediamine. 10 The addition of less than 1% branched PEI resulted in enhancements in rheological parameters and effective control of uid loss.In a different study, PEI with high molecular weight had better shale inhibition capability but had worse water solubility and increased cost. 11,12Although PEI had the capability to engage with clay via hydrogen bonding and electrostatic interactions, it exhibits limited resilience when exposed to temperatures exceeding 120 °C. 12Meanwhile, only a slight improvement in viscosity was observed when PEI was used to formulate a polymer-based drilling uid. 13,14][17] In recent years, the application of polymer nanocomposite (PNC) in drilling uid has been investigated to improve rheological properties, lter loss control and shale inhibition. 18,19NC encompasses inorganic nanoparticles that are either graed with polymer chains on their surface or are integrated within a polymer matrix. 19,20This amalgamation capitalizes on the attributes of both elements, thereby heightening the material properties of the resultant product.These PNCs were formed through various polymerization methods such as radical, adsorption of polymeric dispersants, and in situ surface modication. 21Furthermore, comprehending the phase behavior of polymer nanocomposites holds paramount importance in evaluating their thermal degradation tendencies.Siddique et al. 22 investigated the structural and thermal degradation patterns of reclaimed clay nano-reinforced lowdensity polyethylene nanocomposites.Their study underscored the signicance of discerning distinct phases within the polymer matrix, particularly the crystalline and amorphous phases.These structural attributes of the polymer, such as the degree of substitution and molar mass, exhibit multifunctional behavior, exerting inuence over various properties of the drilling uid. 23The phase behavior of polymer nanocomposites within drilling uids is pivotal for optimizing drilling uid performance.A profound understanding of the diverse phases inherent in the polymer matrix, coupled with judicious nanoparticle selection and achieving uniform dispersion, can yield signicant enhancements in the rheological, thermal, and ltration properties of the drilling uid.
The polyethyleneimine-graphene oxide (PEI-GO) composite belongs to the category of PNCs and has been investigated for its potential as a rheology enhancer and uid loss reducer in drilling uids.The ndings from ref. 16 demonstrated a slight improvement in the rheological properties of PEI-GO in comparison to the base drilling uid.However, this study is limited to a single concentration and a lower aging temperature of 65 °C.A recent study by Zhao et al. 17 explored different PEI-GO and montmorillonite concentrations, along with elevated aging temperatures up to 150 °C, regarding rheology and American Petroleum Institute (API) ltration loss.The results indicated that the montmorillonite solution with PEI-GO had lower plastic viscosity (PV) and exhibited the lowest yield point (YP), compared to most inhibitors except potassium chloride (KCl) which signied improved rheological behavior.The inhibitor's compatibility with drilling uids was evident in the viscosity and API ltration loss differences before and aer its addition.Notably, PEI-GO's inuence on drilling uid's reliability was minimal post-aging, suggesting good compatibility with standard drilling uid additives.
The utilization of the PEI-GO in drilling uids has been a subject of considerable interest and research in recent years.The motivation of this study lies in addressing the following critical gaps in the current understanding of PEI-GO as a rheology modier and ltration loss control agent in waterbased drilling uids.Despite the available literature, there has been a limited study to determine the most suitable rheological model for describing the ow behavior of this novel PNC.In addition, the suitability of PEI-GO under high salt concentration is yet to be studied.Examining the drilling uid's tolerance in high salinity is crucial, as it has the potential to degrade the uids' rheological characteristics and diminish their stability to high temperatures.Further research is needed to investigate the PEI-GO's specic inuence on rheological behavior and ltration loss performance, particularly concerning HPHT conditions and salt contamination.This study aims to examine the performance of PEI-GO in water-based drilling uids under elevated aging temperatures and high salinity conditions, with a focus on its rheological and ltration properties.Additionally, we also assess the suitability of various rheological models in describing the ow behavior of this modied drilling uid.To ensure the effective organization of the discussion, this article is divided into subsections.The owchart in Fig. 1 illustrates the structure and ow of the research, encompassing the experimental design, data collection, and analysis.

Materials
Functionalized GO, PEI and dicyclohexylcarbodiimide (DCC) were procured for the synthesis of PEI-GO.The composition of water-based drilling uids comprised of varied chemical additives: bentonite, KCl, xanthan gum (XG), carboxymethyl cellulose (CMC), sodium hydroxide (NaOH), and barite.These additives were formulated in a specic sequence and duration to achieve the desired formulation.Sodium chloride (NaCl) and calcium chloride (CaCl 2 ) were acquired to examine the impact of salt contamination on drilling uid performance.NaCl and CaCl 2 were chosen as materials in salt contamination analysis of drilling uid due to their ability to mimic the salt content in oil basins, their impact on rheological behavior and their interaction with polymers and biopolymers in drilling uids. 24,25ll materials were commercially available and procured from Sigma-Aldrich.

Methods
2.2.1 Synthesis of PEI-GO.PEI-GO composite was synthesized via the in situ solution polymerization method. 16The GO nanosheets were rst dispersed in deionized water with a concentration of 1 mg mL −1 by ultrasonication at 40 kHz and 350 W for 30 minutes.The resultant GO nanouid and a controlled amount of PEI solution were mixed in a beaker using a magnetic stirrer hot plate.Next, DCC was slowly added to the solution to act as a cross-linking reagent for the PEI-GO polymerization process.The system was kept under continuous stirring at a constant temperature of 60 °C for 24 hours.Then, the solution was centrifuged at 15 000 rpm for 30 minutes with ethanol to separate the PEI-GO from the residual polymer.Finally, the PEI-GO was subjected to drying in an oven set at 80 °C for 4 hours and the PEI-GO powder was collected and used for  characterization analysis and performance evaluation.The schematic representation of the PEI-GO synthesis process is depicted in Fig. 2.
2.2.2 Preparation of water-based drilling uids.The base drilling uid was formulated by mixing distilled water with bentonite, KCl, XG, CMC, NaOH, and barium sulfate, following specic mixing times and order, as well as their designated functions outlined in Table 1.While the addition of additives to drilling uids lacks an exact standard, their introduction aimed to maintain the total uid volume under 350 mL, in accordance with API standard. 26The addition of NaOH was implemented to increase the pH, aligning with the common pH range of 8-11 in drilling uids.This adjustment enhances bentonite dispersion, facilitates sufficient dissolution of additives in the drilling uids, and minimizes corrosiveness to drilling tools as recommended in literature. 27efore blending the nanocomposite with the base drilling uid, the PEI-GO sample underwent a preparation process using the ultrasonication technique to prevent aggregation. 28,29nitially, the PEI-GO was dispersed in deionized water using an ultrasonic homogenizer for 30 minutes.Subsequently, it was introduced into the mixing cup to generate drilling uids with varying PEI-GO concentrations.The solution underwent an additional 10 minutes of mixing to achieve a homogeneous drilling uid mixture.All formulations aimed to yield 350 mL of water-based drilling uids with a density of 9.5 ppg.Achieving a consistent 9.5 ppg density across different formulations might necessitate minor adjustments in the quantities of distilled water and barium sulfate, owing to variations in PEI-GO concentrations. 30These drilling uid samples were placed in an aging cell under 500 psi and subjected to temperature aging at 80 and 160 °C for 16 hours to replicate the borehole's uid circulation and to investigate the effect of temperature and salt resistance on drilling uid's rheology and ltration loss properties.

Material characterization
2.3.1 Fourier transform infrared spectroscopy (FTIR).FTIR analysis was conducted to conrm the successful graing of PEI molecules onto the GO surface and study the chemical structure of PEI-GO.The analysis was accomplished using PerkinElmer Frontier-01 FTIR equipment, which had a wavelength range of 4000 to 400 cm −1 .Data were collected at a spectral resolution of 1 cm −1 under ambient conditions.The FTIR spectra obtained for GO, PEI, and PEI-GO were analyzed for characteristic peaks and bands that indicated the presence of functional groups. 31.3.2Thermogravimetric analysis (TGA).TGA was performed to assess the thermal stability of the developed PEI-GO, and a comparison between GO and PEI was established.This analysis was conducted using a PerkinElmer Simultaneous Thermal Analyzer 6000 under a nitrogen environment.Samples of GO, PEI, and PEI-GO were prepared and heated from 29 to 900 °C at a heating rate of 10 °C min −1 , and the mass change of the samples was measured.The TGA curves were analyzed for signicant differences in mass loss and thermal stability between the samples.

Performance evaluation
2.4.1 Rheological properties.The rheological characteristics of the drilling uids were assessed, encompassing measurements of PV and YP.These measurements were conducted utilizing a FANN rotational viscometer at six speeds, specically 600 rpm, 300 rpm, 200 rpm, 100 rpm, 6 rpm, and 3 rpm.It is noteworthy that both pre-and post-aging assessments were performed on all drilling uid samples.Based on API 13B-1 recommendations, the PV and YP values were subsequently calculated by employing the following formulas: 32 where F 600 and F 300 are the viscometer dial readings at 600 rpm and 300 rpm, respectively.2.4.2Rheological modeling.Rheological models are essential for characterizing the behavior of drilling uids, serving as key parameters for accurately calculating pressure drop, ensuring efficient hole cleaning, and managing drilling hydraulics. 33,34Choosing the right rheological model reduces computational errors and improves prediction accuracy during drilling operations.Drilling uids oen display non-Newtonian behavior due to factors like clay particles and electric charges on clay surfaces, causing viscosity to change with shear rate. 8,35The Bingham plastic, power law, and Herschel-Bulkley models are employed to predict the rheological behavior of drilling uid, as outlined below: 2.4.2.1 Bingham Plastic Model.This model is applied to uids demonstrating Bingham plastic behavior, characterized by linear s/g behavior beyond an initial shear stress threshold.The PV represents the slope of this line, and the YP signies the threshold stress.It can be expressed as follows: 2.4.2.2 Power Law Model.Fluids exhibiting power law behavior can be characterized by the following expression: 2.4.2.3 Herschel-Bulkley Model.This model also well-known as a yield power-law model, is expressed as follows: where s is the shear stress (Pa), s 0 is YP (Pa), _ g is the shear rate (1/s), m p is the PV, K is the uid consistency coefficient, and n is the uid behavior index.In this study, the most appropriate rheological model is determined by measuring the required rheological parameters (PV and YP) using a FANN rotational viscometer.Subsequently, these values are integrated into the rheological models to calculate the coefficient of determination (R 2 ) to assess the degree of alignment between the obtained outcomes and the desired values, with a value nearing 1 signifying a highly accurate prediction.
2.4.3Filtration loss.API uid loss tests were conducted for all drilling uid samples at a standard temperature of 25 °C and pressure of 100 psi.For each sample, 350 mL of drilling uid was loaded into the cell body, and the volume of liquid ltrate was measured every 5 minutes for 30 minutes.A high-pressure high-temperature (HPHT) uid loss test was conducted by loading 175 mL of each drilling uid sample into HPHT lter press cells and conducting the test at a temperature of 160 °C and a differential pressure of 500 psi.The mechanism of ltration loss improvement was analyzed using scanning electron microscopy (SEM) on lter cake samples of drilling uids.

Material characterization
Fourier Transform Infrared Spectroscopy (FTIR) analysis was performed to identify the functional group of GO and conrm the surface modication of PEI-GO as shown in Fig. 3. Based on GO peak characteristics, the broad peak located at 3421 cm −1 was related to the O-H stretching vibration.Two absorption spectra were observed at 2927 and 2860 cm −1 owing to C-H groups of graphene. 16The peak at 1718 cm −1 arose from the C]O stretching vibration in COOH groups.Two peaks located at 1635 and 1576 cm −1 were attributed to C]C stretching vibration.The alkoxy C-O and epoxy C-O groups were identied through the stretching peaks at 1188 and 1094 cm −1 , respectively.All of GO's distinctive peaks found in this study were consistent with earlier ndings. 39,40As for PEI-GO, the functionalization of PEI by graing onto GO surfaces was demonstrated by the absence of the epoxy C-O peak at 1188 cm −1 .The peak at wavelength 3434 cm −1 was attributed to the hydrogenbonded hydroxyl group (-OH) and amino group (-NH 2 ) hydrogen stretching bands. 41In addition.the N-C]O and C-N ionic bonds at 1650 cm −1 and 1387 cm −1 were formed, indicating the successful absorption vibration of the amide group in the molecular chain of PEI, respectively.
The TGA analysis for GO, PEI, and PEI-GO is shown in Fig. 4. PEI displayed weight loss beginning at 150 until 337 °C which accounts for 14%.Then, major weight loss was observed up to 400 °C where 86% of PEI was lost and only 0.1% residue was le until the end of the TGA test.This pattern was comparable to that seen by Liu et al. 42 As for GO, no signicant weight loss was observed between 30 and 285 °C.Only 6% weight loss occurs around 490 °C and the weight loss decreases linearly until 900 °C where the remaining residue for GO was around 43%.In the case of PEI-GO, a different trend of TGA was observed where weight loss was about 7% between 150 and 258 °C due to the efficient removal of oxygen-functional groups. 31,43At 700 °C, the intersection between GO and PEO-GO occurred and showed that the decrease in weight loss is higher for GO as compared to PEI-GO.At 900 °C, 50% of PEI-GO was lost and 50% residue was

Rheological properties
In this study, the rheological characteristics of drilling uids were described through PV and YP.PV is a measure of ow resistance of drilling uids, which is inuenced by the solid content and electrochemical forces between the reactive particles. 44,45YP represents the initial stress required to initiate the ow of non-Newtonian uids and indicates the drilling uid's effectiveness in cleaning the borehole. 46YP is inuenced by both the volume and electrochemical attractive forces among solid particles added to the drilling uid. 47s illustrated in Fig. 5a, the PV of the drilling uid increased with the increasing concentration of PEI-GO at ambient temperature.This nding aligns with the report made by Li et al., 48 indicating that graphene can establish strong interactions with the polymer matrix, leading to heightened viscosity.The increase in PV observed in the drilling uids upon the addition of PEI-GO can be attributed to the formation of hydrogen bonds and amide groups' intercalation between bentonite particles and the PEI-GO nanocomposite.The presence of these functional groups has been conrmed through the earlier FTIR characterization analysis in this study.When cationic PEI-GO was introduced into the base drilling uid, led to ion xation and exchange which resulted in heightened electrostatic attractive forces between the negatively charged bentonite platelets and the incorporated PNCs. 49,50Notably, a concentration of 0.1 to 0.3 wt% PEI-GO resulted in a minimal increase in PV.However, when 0.4 wt% and 0.5 wt% PEI-GO were added, the PV experienced a signicant rise to 15 and 18 mPa s.This can be attributed to stronger attraction forces between the clay surface and PNCs caused by a higher solid content, resulting in the occulation and aggregation of PNCs.This phenomenon is caused by increased attraction, poor distribution, and reduced separation between solid components. 47gh temperatures typically degrade polymers such as XG and CMC, leading to a decrease in rheological parameters.However, Fig. 5a shows a slight increase in the PV of the base drilling uid aer thermal aging.The addition of a low concentration of XG and CMC did not signicantly affect the rheological properties of the base drilling uid.Instead, the viscosity aer aging was primarily inuenced by the dispersion of bentonite in the base drilling uid at elevated temperatures. 51he effect of temperature aer the addition of PEI-GO can be assessed as PV increased signicantly when the PEI-GO concentrations increased for drilling uids sample before aging and aer aging at 80 °C, while at 160 °C, the increase in PV was minimal.The increment of PV is happening since both side and main chains of the nanocomposite remain intact aer aging.Consequently, the increased number of PEI-GO molecules, due to the extended chains enveloping the interlayer spaces of the bentonite, resulted in an increased surface area and greater ow resistance. 51Other studies observed that elevated temperatures led to greater kinetic activity among the solid particles present in the drilling uid. 47This increased interparticle interaction resulted in the thermal dispersion of bentonite particles, ultimately contributing to the heightened viscosity of the drilling uid sample. 49,52However, when comparing PV between temperatures at the same PEI-GO concentration, the PV exhibited an opposing trend.The PV of drilling uids aer aging at 80 °C is higher than that of drilling uids before aging, especially at lower PEI-GO concentrations, with marginal differences at higher PEI-GO concentrations.In contrast, aging at 160 °C results in a reduction in PV compared to both the drilling uids before aging and those aged at 80 °C, especially aer using 0.3 to 0.5 wt% of PEI-GO.At higher temperatures, PEI-GO molecules form due to increased dissociative adsorption of water by amine groups on side chains, resulting in decreased adsorption of the polymer nanocomposite on clay particles. 51Nonetheless, it is advantageous to employ a drilling uid with a lower PV value for efficient drilling operations, which can lead to an improved rate of penetration, reduced wellbore pressure, and decreased risks of formation fractures and differential pipe sticking. 53,54Hence, the PV remains most stable across all temperature conditions when adding up to 0.3 wt% PEI-GO, and concentrations beyond 0.4 wt% adversely affect the drilling uid's PV.
The effect of increasing PEI-GO concentrations on the YP is exhibited in Fig. 5b.It was shown that the YP of base drilling uids was increased with the increment of PEI-GO concentrations, as a result of PNCs addition that increased the solid content and caused the attractive electrostatic forces among the particles to amplify.This increasing trend is similar for drilling uid samples that underwent aging at 80 and 160 °C.The nding also showed that higher temperatures caused the YP to drop at the same PEI-GO concentrations.The lower YP at higher temperatures is a result of the thermal degradation of solid particles in the drilling uid, which increases the distance between molecules and reduces ow resistance. 55Having a high YP in drilling uids is advantageous as it signies improved cutting transport.Nonetheless, an excessively high YP can negatively impact the cutting carrying capacity, whereas an excessively low YP can lead to the sagging of barite and drill cuttings. 44Therefore, it is recommended to nd the optimal formulation by analyzing the YP/PV ratio of the drilling uid.
The YP/PV ratio serves as a crucial indicator of shearthinning behavior and the overall carrying capacity of the drilling uid. 47,56This ratio plays a pivotal role in optimizing drilling uid efficiency, favoring a combination of low plastic viscosity and high yield point.A higher YP/PV value not only signies improved shear-thinning behavior but also enhances the uid's ability to efficiently transport rock cuttings at low shear rates and facilitate effective rock fragmentation at high shear rates. 57,58This balance in rheological properties is instrumental in achieving optimal drilling performance.Table 2 provides the YP/PV ratios for drilling uids with increasing concentrations of PEI-GO at varying aging temperatures.The highest YP/PV ratios are observed at 0.1 wt% PEI-GO before aging and at 0.3 wt% PEI-GO aer aging at 80 °C.Additionally, maximum YP/PV values are found at 0.2 wt% and 0.3 wt% PEI-GO aer aging at 160 °C.It can be concluded that the concentration of 0.3 wt% PEI-GO is the most effective among various concentrations, exhibiting a consistently high YP/PV value, even under elevated temperatures of 80 and 160 °C.The exceptional performance of PEI-GO under elevated temperatures suggests a high degree of thermal stability.In summary, the comparison of rheological properties demonstrates a signicant enhancement and stability in the rheology of drilling uids with the addition of PEI-GO, irrespective of temperature conditions.

Rheological modeling and shear thinning behaviour
Rheological modeling is crucial for characterizing the ow behavior of drilling uids, which, in turn, is essential for optimum wellbore hydraulics management. 59Fig. 6 presents the rheogram, depicting the shear stress-shear rate relationship of the drilling uids with varying PEI-GO concentrations before aging.At low shear rates, the drilling uid's rheological behavior appears unaffected by PEI-GO concentrations.However, at high shear rates, increasing PEI-GO concentrations markedly inuence the drilling uid's rheological behavior, evident from the differences in shear stress among the concentrations.Table 3 compiles parameters derived from tting various rheological models, including the Bingham plastic, power law, and Herschel-Bulkley models, all based on the shear stress-shear rate relationship.In this study, the Herschel-Bulkley model stands out as the most suitable choice for describing the shear stress-shear rate curve, as indicated by higher R 2 values approaching 1 and considerably lower rootmean-square error (RMSE) values nearing 0. It surpasses both the power-law and Bingham plastic models in terms of tting accuracy.This accentuates the Herschel-Bulkley model's superior accuracy in portraying the rheological behavior of the drilling uids investigated in this study.
In Table 3, it's evident that as the PEI-GO concentration increased, both the uid behavior index (n) and uid consistency coefficient (K) exhibited uctuations, with distinct highest and lowest values.The arrangement of n values, from lowest to highest, was 0.1 < 0.3 < base < 0.2 < 0.4 < 0.5 wt%, while for K values, it was arranged from highest to lowest as 0.3 > 0.4 > 0.1 > 0.2 > base> 0.5 wt%.A lower n value indicated a more pronounced non-Newtonian characteristic in the drilling uid, which is desirable for achieving effective shear-thinning behavior and enhanced cutting transport, with a corresponding increase in the K value enhanced cutting transport. 58herefore, it can be concluded that 0.3 wt% PEI-GO in base drilling uid consistently performed well in terms of rheological behavior, enhancing the shear-thinning behavior and  The results indicate that the 0.3 wt% PEI-GO consistently displayed signicantly higher K values compared to the base drilling uid across all temperature conditions.The higher values of K indicate greater viscosity, which promotes efficient transport of cuttings from the borehole to the surface; conversely, a lower K may result in cuttings settling owing to gravity. 60Furthermore, for samples before aging, the n values of PEI-GO were slightly lower than the base drilling uid.However, as the temperature changes to 80 and 160 °C, the difference between the base drilling uid and the 0.3 wt% PEI-GO becomes signicantly pronounced.It can be observed that 0.3 wt% PEI-GO maintained a low n value under both low and high temperature conditions.A lower n value improves the drilling uid's ability to transport cuttings effectively, emphasizing the importance of a lower n value for better cuttings carrying capacity. 60Overall, drilling uids with higher K values and lower n values have a better ability to suspend solid particles and cleaning borehole. 61Collectively, these ndings highlight the ability of the base drilling uid with 0.3 wt% PEI-GO to retain and suspend solid particles, even at high temperature conditions.
The inuence of temperature on the rheological characteristics of the drilling uid was examined by analyzing the Herschel-Bulkley model parameters, K and n values.These parameters are intrinsically linked, with alterations in one directly impacting the other. 62The investigation encompassed both the base drilling uid and the variant containing 0.3 wt% PEI-GO, as depicted in Fig. 7 and Table 4.The outcomes reveal a discernible pattern, as temperature ascends, K values decline while n values ascend, a phenomenon observed in both the base drilling uid and the 0.3 wt% PEI-GO.This trend signies a reduced tendency of the drilling uid to suspend solid particles at elevated temperatures. 63indicated that the incorporation of PEI-GO resulted in a significant decrease in the amount of API ltration loss seen in the base drilling uid.Furthermore, it is noteworthy that an increase in the ageing temperature resulted in a more noticeable disparity in the API ltration volume between the base drilling uid and the base drilling uid added with PEI-GO.For instance, the percentage difference in API ltration volume for the 0.3 wt% PEI-GO compared to base drilling uid was only 18.31% before aging.However, aer aging at 80 and 160 °C, this difference increased to 48.04% and 56.83%, respectively.These results showed that PEI-GO reduces uid loss better than base drilling uid aer aging at temperature up to 160 °C.PEI-GO enhanced base drilling uid by maintaining stable rheology and reducing ltrate loss volume at high temperatures, making it a better additive option for high-temperature applications.Fig. 9 presents visual and scanning electron microscopy (SEM) images of lter cakes formed from the base drilling uid and base drilling uid containing 0.3 wt% PEI-GO aer aging at 160 °C.The visual of these lter cakes, as shown in Fig. 9a and b, indicates that the base drilling uid exhibits larger pores on the surface of the lter cake in comparison to the 0.3 wt% PEI-GO-containing drilling uid, which displays fewer and smaller pores on its lter cake surface.Furthermore, the lter cake created by base drilling uid is signicantly thicker compared to that of the 0.3 wt% PEI-GO-containing uid.To be specic, the thickness of the base drilling uid lter cake measures 4.32 mm, whereas the PEI-GO lter cake is notably thinner at 1.24 mm.It is noteworthy that an excessively thick lter cake can lead to wellbore-related issues, including tight holes, causing differential sticking, and inducing elevated pressure surges. 3A closer examination through SEM at 1000-and 5000 times magnication reveals the distinct characteristics of each lter cake, as shown in Fig. 9c-f.The lter cake from the drilling uid containing 0.3 wt% PEI-GO displays a atter and smoother surface in comparison to the lter cakes from the base drilling uid.This is attributed to the presence of the PEI-GO nanocomposite, which forms a hydrophobic lm that seals the pores, preventing uid ow and resulting in a thinner and densely packed lter cake with reduced ltration loss volume compared to the base drilling uid. 16he impact of PEI-GO concentration on ltration loss reduction is also clearly demonstrated in Fig. 8.The addition of 0.1 and 0.2 wt% of PEI-GO led to a decrease in ltration loss of 4.23% and 8.45%, respectively, compared to the base drilling uids in the pre-aging sample.This reduction effect became more pronounced when 0.3 to 0.5 wt% PEI-GO were employed, resulting in ltration loss reductions between 18.31 to 23.94%.This trend remained consistent when the samples were subjected to elevated temperatures of 80 and 160 °C, with 0.3-0.5 wt% PEI-GO demonstrating the highest percentages of uid loss reduction which ranging between 48.04-51.40%and 60.43-61.96%.This nding indicates that a concentration range of 0.3 to 0.5 wt% PEI-GO had high thermal resistance.

Filtration properties
To further validate the temperature resistance between 0.3 to 0.5 wt% PEI-GO, high-pressure high-temperature (HPHT) ltration tests were conducted at a differential pressure of 500 psi and temperatures of 80 and 160 °C.As illustrated in Fig. 10, the HPHT ltration volume of 0.3 and 0.5 wt% PEI-GO consistently remained lower than that of base drilling uid.In contrast to base drilling uid, as temperatures increased, 0.3 to 0.5 wt% PEI-GO exhibited substantially lower ltration volumes, indicating their capability to withstand temperatures as high as 160 °C.This is supported by the high thermal stability characteristics of PEI-GO nanocomposite as identied in the TGA analysis.Moreover, when comparing the API and HPHT ltration loss between 0.3-0.5 wt% PEI-GO, the difference between them was minimal, less than 5%.This nding indicates that the augmentation of PEI-GO concentration did not provide a substantial improvement in the ability to reduce uid loss.In some cases, a further increase in nanoparticle concentration adversely impacted rheological properties and ltration loss performance. 47,60This was attributed to nanoparticle agglomeration, mirroring the behavior of larger particles and resulting in an elevated level of ltration loss. 64he rheological characteristics and ltration performance of a drilling uid containing 0.3 wt% PEI-GO align with the operational requirements of drilling uids.Thus, taking into account both cost considerations and performance, this study concludes that the most optimal concentration is 0.3 wt% PEI-GO.This nding is in line with the enhancement of rheological and ltration loss properties observed at optimal nanoparticle concentrations, as reported by Arain et al. 47

Inuence of high salinity condition on PEI-GO performance in drilling uid
The introduction of sodium (Na + ) and calcium (Ca 2+ ) ions has been seen to disturb the diffusion double-layer arrangement of bentonite, resulting in a fast decline in the rheological and ltration characteristics of the solution composed of bentonite. 65This occulation phenomenon might result in a thick lter cake, which oen leads to differential pressure sticking in permeable zones.Table 5 summarizes the rheological properties (PV, YP, and YP/PV) of the 0.3 wt% PEI-GO drilling uid before and aer aging under elevated concentrations of NaCl and CaCl 2 .
In general, the augmentation of NaCl and CaCl 2 concentrations resulted in a reduction in the rheological characteristics of the drilling uid.However, the impact on PV and YP was minimal with increasing salt concentrations.It was evident that the YP/PV values signicantly decreased at salt concentrations of 25 wt% NaCl and 15 wt% CaCl 2 , indicating the detrimental effect of higher salt concentrations on the shear-thinning behavior and carrying capacity of drilling uids.Aer high-  temperature aging, the rheological properties of the drilling uids decreased at the same NaCl and CaCl 2 concentrations, indicating that aging temperature had a more substantial inuence on PEI-GO compared to salt concentrations.Nevertheless, the YP/PV value of the PEI-GO drilling uid remained stable before and aer aging at 160 °C, indicating that it was able to maintain the uid's cuttings carrying capacity and wellbore cleaning efficiency even under high salinity conditions. 66It is worth noting that, when comparing the two salt types, CaCl 2 had a more pronounced adverse effect on the performance of the PEI-GO drilling uid compared to NaCl.Fig. 11 and 12 present the evaluation of how well base drilling uid enriched with 0.3 wt% PEI-GO, withstands high salinity environments of NaCl and CaCl 2 in terms of ltration loss volume.This assessment is conducted both before and aer subjecting the uids to aging at 160 °C.Fig. 11a demonstrates that the addition of 0.3 wt% PEI-GO signicantly reduces ltration loss volume, even when tested for NaCl contamination at concentrations up to 20 wt%, prior to aging.This observation remains consistent aer aging the drilling uid sample at 160 °C, as depicted in Fig. 11b.However, at a NaCl concentration of 25 wt%, both ltration loss volume and rate sharply increase for both temperature conditions.Turning to Fig. 12a and b, a slight increase in ltration loss volume is noticeable at 5 and 10 wt% CaCl 2 , but it substantially rises at 15 wt% CaCl 2 .It can be concluded that 0.3 wt% PEI-GO exhibits excellent tolerance to NaCl and CaCl 2 , particularly at concentrations of 20 wt% and 10 wt%, respectively.This makes it a suitable choice for application in high-salinity formations, even at high temperatures up to 160 °C.The outcomes of this investigation regarding the impact of NaCl and CaCl 2 salinity on rheological and ltration loss properties align with ndings reported in the literature. 66

Conclusion
The polymerization of low molecular weight PEI with GO was successfully performed, demonstrating the formation of PEI-GO  nanocomposite, as conrmed by FTIR analysis.The high thermal resistance of the nanocomposite was evident through TGA analysis.This study comprehensively investigated the rheological properties, rheological modeling, ltration properties, and the inuence of high-temperature and high-salinity conditions on drilling uid performance enhanced with varying concentrations of PEI-GO nanocomposite.The experimental ndings lead to the following conclusions: The rheological properties evaluated in this study: PV, YP and YP/PV were improved with the increasing concentration up to 0.5 wt% of PEI-GO in the water-based drilling uids.
The Herschel-Bulkley model emerged as the most accurate in describing drilling uid rheological behavior, as evidenced by the best t to the shear stress-shear rate curve.Additionally, the uid behavior index (n) and uid consistency coefficient (K) demonstrated improvements when using base drilling uid containing PEI-GO, indicating superior shear-thinning behavior and overall rheological properties.
PEI-GO effectively reduced both API and HPHT ltration loss volumes of the base drilling uid.Visual and SEM analyses revealed that PEI-GO led to the formation of a thinner and denser lter cake, further enhancing ltration loss reduction.
This study determines that a concentration of 0.3 wt% of PEI-GO is the most effective, indicating that a modest quantity of the nanocomposite is sufficient to enhance the rheological and ltration loss properties of water-based drilling uids.
Furthermore, PEI-GO exhibited excellent resistance to NaCl and CaCl 2 , particularly up to concentrations of 20 wt% and 10 wt%, respectively.The PEI-GO's outstanding rheology and ltration properties are due to its electrostatic interaction with clay particles through hydrogen and ionic bonding, resulting in pore plugging within the lter cake.This, in turn, prevented water inltration and reduced ltration loss volume, thereby mitigating wellbore instability issues.
The high thermal stability of PEI-GO is evident according to the assessment of PEI-GO performance in rheological and ltration loss properties when compared to the base drilling uids, even at temperatures as high as 160 °C.
In this study, PEI-GO nanocomposite consistently maintained stable ltration loss reduction and rheological properties, even under high-salinity conditions and elevated temperatures, making it a suitable choice for challenging drilling environments.An extension of this research work could explore the applicability of PEI-GO as a shale inhibitor agent under harsh wellbore conditions, further enhancing its versatility in drilling operations.

Fig. 1
Fig. 1 Flowchart outlining the experimental procedures conducted in this study.

Fig. 4
Fig.4TGA curves of GO, PEI, and PEI-GO.Fig.3FTIR spectra of GO and PEI-GO.

Fig. 5
Fig. 5 (a) Plastic viscosity and (b) yield point, of base drilling fluid with increasing PEI-GO concentration at different temperatures.

Fig. 6
Fig. 6 Rheogram of base drilling fluids with various PEI-GO concentrations before aging (dash lines represent the fitted lines using the Herschel-Bulkley model).

Fig. 8
Fig. 8 illustrates the inuence of PEI-GO on the ltration properties of the base drilling uid.The experimental results

8
API filtration volume comparison between the base drilling fluid and the base drilling fluid with varying concentrations of PEI-GO under varying temperatures: (a) before aging, (b) after aging at 80 °C, and (c) after aging at 160 °C.

Fig. 9
Fig. 9 Images of filter cakes and SEM analysis formed by the base drilling fluid (a, c and e) and base drilling fluid containing 0.3 wt% PEI-GO (b, d and f) after aging at 160 °C.

Fig. 10
Fig. 10 Filtration volumes under high-pressure, high-temperature (HPHT) conditions for the base drilling fluid from 0.3 to 0.5 wt% PEI-GO at various temperatures.

Fig. 11
Fig. 11 Filtration loss of the base drilling fluid added with 0.3 wt% PEI-GO under different NaCl concentrations: (a) before aging and (b) after aging at 160 °C.

Fig. 12
Fig. 12 Filtration loss of the base drilling fluid added with 0.3 wt% PEI-GO under different CaCl 2 concentrations: (a) before aging and (b) after aging at 160 °C.

Table 1
Formulation of drilling fluids

Table 2
YP/PV of the drilling fluid with increasing PEI-GO concentrations at different temperature conditions

Table 3
Calculated parameters of Bingham plastic, power law, and Herschel-Bulkley models for base drilling fluid with different PEI-GO concentrations

Table 4
Calculated parameters for base drilling fluid and base drilling fluid added with 0.3 wt% PEI-GO under varying temperatures via the Herschel-Bulkley model

Table 5
Rheological values of the base drilling fluid containing 0.3 wt% PEI-GO for different concentrations of NaCl and CaCl 2 before aging and after aging at 160 °C