Performance and Characteristics of Low-Molecular-Weight Cross-Linked Grafting Terpolymers as Thickening Agents in Reservoir Fracturing Processes

Abstract

A novel fracture fluid based on a grafting polymer, PAM-co-PAMS-g-PEG (PAM-AMS-AEG), cross-linked by an organic Zr reagent was successfully produced via free-radical polymerization and an in situ cross-linking reaction with a high conversion rate of 96%, resulting in a low molecular weight of 250 kg·mol⁻¹. The effect of fluid constitution on the rheological behavior demonstrates that the P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35/TBAC_0.1 (PASG/[Zr]) aqueous solution has the best comprehensive performance. The PASG/[Zr] solution with a low critical associating concentration (CAC) of 0.15 wt% showed faster and steadier disassociation–reassociation processes. The synergy of ionic hydrogen bonds between sulfonic and amine groups and Zr⁴⁺-coordination results in steady interactions and fast reconstitution of association, leading to remarkable temperature resistance from 30 to 120 °C and a fast response during thixotropic processes. The PASG/[Zr] solution reduces the damage under high pressure based on the rheological characteristics and compatibility with sand, leading to a low filtration loss of the artificial cores. The PASG/[Zr] solution exhibits a good sand-carrying ability based on the rheological and interfacial performance, resulting in slow settlement and fast suspension. The filtration performance of the PASG/[Zr] fracturing fluid showed that it is not sensitive to the shearing rate, core permeability, or pressure. The comprehensive performance of the PASG/[Zr] fracture fluid is better than that of traditional guar fluid, suggesting that it can be used under various conditions for stratum protection and shale gas extraction.

1. Introduction

Over the past two decades, the rapid expansion of unconventional hydrocarbon development has intensified the demand for advanced stimulation technologies that ensure efficient shale gas recovery while preserving the integrity of sensitive, clay-rich formations [1,2,3]. Without these processes, shale gas reservoirs with low permeability and weak beddings are extremely vulnerable to the invasion of aqueous fluids. The negatively charged basal surfaces of clay minerals can interact with invading fluids [3], leading to the propagation of micro-fractures due to the stress exceeding the tensile strength of the shale matrix. Traditional mitigation strategies include increasing the salinity, adding KCl, or converting to oil-based mud; however, these strategies either pollute the environment or fail under the elevated temperatures (>150 °C) encountered in deep shale clays [4,5].

Polyacrylamide (PAM)-based fracturing fluids have emerged as a new generation of intelligent viscous fluids, serving both as rheology modifiers and as interfacial barriers between the fracturing fluid and shale surfaces [6,7,8,9,10,11]. However, conventional PAM systems suffer from limited thermal stability and poor viscoelasticity under harsh reservoir conditions [12,13,14,15,16]. In order to improve the low thermal stability and viscoelasticity of PAM solutions [12,13,14,15,16], 2-acrylamido-2-methyl-1-propanesulfonic acid (AMS) can be copolymerized with AM monomers [17,18,19,20], resulting in high-density ionic hydrogen bonds [21,22] between the sulfonates and amides in mutually exclusive sulfonic side groups along the unfolding and expanding chain [23]. AMS-containing PAM copolymers retain a high viscosity in brines, which is critical when reusing flowback water as the base fluid in shale operations [24]. Their active ionic hydrogen bonds (iHBs) increase interchain interactions [25,26,27,28]. Grafting polymers with unique topological structures can produce special rheological characteristics, and can be used as pseudoplastic or thixotropic agents [29,30,31,32,33,34,35,36,37]. The dynamic network formed by cross-linked PAM-g-poly(ethylene oxide) (PAM-g-PEG) delays fracture closure, allowing for the deeper penetration of the proppant into complex fracture networks, leading to high-gel preserves under high-temperature and -stress conditions [29,30,31] and enhancement in their thermal stability and salt tolerance [32,33,34]. Furthermore, their Zr⁴⁺-coordination can form dynamic network cross-linkers with partial PAMs [38], resulting in active but steady supramolecular interactions in a wide temperature range [39]. Zr⁴⁺ coordination in ultra-high-temperature fracturing fluids has been successfully field-tested [40]. Therefore, to the best of our knowledge, a fracture fluid consisting of grafting P(AM-AMS) and with Zr⁴⁺-coordination that combines all the advantages mentioned above has never been reported.

Despite these advances, no prior study has reported a fracturing fluid that integrates grafting P(AM-AMS) with Zr⁴⁺ coordination to simultaneously leverage the benefits of iHBs, graft architecture, and metal–ligand cross-linking. In this work, we developed a novel fracturing fluid based on low-molecular-weight grafting terpolymers (PAM-AMS-AEG), an organic Zr⁴⁺ cross-linker, a surfactant (TBAC), and a gel breaker ((NH₄)₂S₂O₈). The adjustable rheological behavior of the fracture fluid is due to the multiple polymer networks being mixed with a sol-associator, which improves its shearing resistance and thixotropy. The high compatibility of the fracture fluid and artificial core leads to efficient sand-carrying and a low filtration loss, which are not sensitive to the environmental conditions, and the fluid shows better performance than a traditional fluid (guar gum).

2. Design of Experiments

Materials: Acrylamide (AM, 99%, Sinopharm Chemical Reagent Co., Ltd, Beijing, China), acrylamido-2-methyl-1-propanesulfonic acid (AMS, 99%, Sinopharm Chemical Reagent Co., Ltd, Beijing, China), and acryloyl polyethylene glycol (AEG, 99%, M_n = 1000 g·mol⁻¹, Shandong Asia Chemical Co., Ltd, Dongying, China) were obtained and purified before polymerization to remove the polymerization inhibitor. K₂S₂O₈ (96%, Chengdu Chron Chemicals Co., Ltd, Chengdu, China), Na₂SO₃ (98%, Chengdu Chron Chemicals Co., Ltd, Chengdu, China), (NH₄)₂S₂O₈ (96%, Chengdu Chron Chemicals Co,. Ltd, Chengdu, China), NaOH (96%, Chengdu Chron Chemicals Co., Ltd, Chengdu, China), tetrabutylammonium chloride (TBAC, 98%, Chengdu Chron Chemicals Co., Ltd, Chengdu, China), ZrOCl₂·8H₂O (98%, Chengdu Chron Chemicals Co., Ltd, Chengdu, China), isopropyl alcohol (99%, Chengdu Chron Chemicals Co., Ltd, Chengdu, China), L-lactic acid (LLA, 99%, Chengdu Chron Chemicals Co., Ltd, Chengdu, China), and guar gum (98%, M_w = 2000 kg·mol⁻¹, Dongying Xinde Chemicals Co., Ltd, Dongying, China) were also used.

Polymerization of P(AM-AMS-AEG). The free-radical copolymerization of AM, AMS, and AEG was carried out in aqueous solution. The typical process is described as follows: 2.27 g of AM, 1.33 g of AMS, and 4.48 g of AEG were dissolved in 5 mL of deionized water in a flask. The NaOH solution (20 wt%) was added to this flask to adjust the pH = 7, and then 0.09 g of TBAC was added under stirring. The flask was vacuumed and filled with N₂ 3 times. Amounts of 0.09 g of K₂S₂O₈ and 0.04 g of Na₂SO₃ were dissolved in 5 mL of deionized water. This initiating solution was injected into the AM/AMS/AEG/TBAC solution to initiate the free-radical copolymerization of AM, AMS, and AEG under stirring, and the polymerization was conducted at 80 °C for 6 h. The conversion of resulting polymers was calculated using the ratio of the original mass of monomers to the resulting mass of polymers.

Preparation of Organic Zr⁴⁺-based Cross-linker ([Zr]). The inorganic Zr⁴⁺-based cross-linker was prepared by dissolving ZrOCl₂·8H₂O in deionized water. An amount of 10 mL of ZrOCl₂ aqueous solution (30 wt%) in a flask was mixed with 2 eq of isopropyl alcohol under N₂ atmosphere. An amount of 2 eq of LLA was added fast into the solution and reacted for 1 h at 20 °C. This solution was neutralized by NaOH solution (20 wt%) at 80 °C for 4 h and vacuumed for 30 min to remove volatiles. The resulting solution was [Zr] solution.

Cross-linking reaction of P(AM-AMS-AEG). The polymerizing solution was injected above the ZrOCl₂ aqueous solution (30 wt%) with various dosages to prepare P(AM-AMS-AEG) cross-linked by the inorganic Zr⁴⁺-based cross-linker. The polymerizing solution was injected above [Zr] with various dosages to prepare P(AM-AMS-AEG) cross-linked by the organic Zr⁴⁺-based cross-linker. The cross-linking reaction was conducted at various temperatures for various durations, and the apparent viscosity of the resulting solution was recorded.

Measurements. Fourier Transform Infrared Spectroscopy (FTIR). Chemical structure analysis of the resulting polymers was performed via Nicolet 6700 FTIR spectroscopy (Thermo Co., MA, USA). All samples were ground on a KBr wafer and dried at 105 °C for 24 h before measurement. IR spectra were recorded at 20 °C in the wavenumber range of 4000~400 cm⁻¹ for 32 scans at a resolution of 4 cm⁻¹.

Proton Nuclear Magnetic Resonance (¹H NMR). ¹H NMR analysis of the resulting polymers (D₂O solution) was carried out. ¹H NMR spectra were recorded via a Bruker AV III 400 spectrometer (Bruker Co., MA, USA, 400 MHz) with tetramethylsilane (TMS) as the internal reference.

Gel Permeation Chromatography (GPC). The number-average molecular weight (M_n) and polydispersity index (PDI, M_w/M_n) of terpolymers were determined by an Alliance e2695 chromatographic system (Waters Co., MA, USA) at 30 °C. Terpolymers were dissolved in deionized water (10 μg·mL⁻¹) and deionized water was used as the mobile phase at a flow rate of 1.0 mL·min⁻¹. The column was calibrated against the standard PAM samples.

Viscosity. The apparent viscosity (η_app) of solution was measured via a CAP 2000+H viscometer (BROOKFIELD Co., MA, USA) at various temperatures and shearing rates. To evaluate the relationship between lnτ and ln$\dot{\mathsf{\gamma }}$, the cross-linking polymer solution (0.27 wt%) was poured into an Ubbelohde viscometer (d = 1 mm) in a DZ-80 constant-temperature bath and the apparent viscosity (η_app) was recorded at various temperatures.

Interfacial Tension. The interfacial tension of terpolymer solutions was determined by using a JYW-200A interfacial tension meter (Suzhou Qile Electronic Technology Co., LTD).

Rheological Test. The rheological tests of polymer solutions were performed via an MCR 302 rheometer (Anton Paar Co., Graz, Austria). The oscillation stress sweep was performed on the samples with a conical plate (1 Hz, 20 °C). The oscillation frequency sweep was performed on the samples with a conical plate (1000 s⁻¹, 20 °C). The thixotropic loop was recorded in a shearing–recovery cycle in the shearing rate range of 0~450 s⁻¹.

DFT Analysis. Both the geometry optimization and the frequency calculations were performed with the Gaussian 09 program package and run at the D3-corrected levels of the B3LYP functional with an ultrafine grid [41,42].

Low-Field Time-Domain Proton Nuclear Magnetic Resonance (LF-NMR). The transversal relaxation time spectra (T₂ spectra) of core samples were recorded on a Magnet2000 spectrometer (NIUMAG Co., Suzhou, China) at 20 °C with the CPMG sequence and inverted by the SIRT algorithm [43,44,45,46].

Static Settling Experiment. An amount of 100 mL of fracturing fluid was poured into a graduated cylinder. Proppant particles with various sizes were placed on the upper surface of the liquid. The settling height, H, of the proppant particles at various observing times, t, was measured and recorded. The settling velocity, v_settle, was determined by the ratio of H to the corresponding t.

Dynamic Settling Experiment. The device used for the dynamic sand-carrying test for fracturing fluid is shown in Figure S9. The fracturing fluid in the storage tank was smoothly injected into the pipeline through a screw pump and processed by the sand addition device to form the mixture with a fixed sand ratio. The mixture through the buffer pipe section entered the horizontal test sections with various diameters. The data acquisition system was connected to display the recording data on the computer. The settling rate of the proppant and the sand-laying pattern were observed with a high-speed camera.

Filtration Experiment. A dynamic filtration system for fracturing fluid was designed in the laboratory, which can simulate the formation environment and the flow and shearing process of fracturing fluid in shales. The schematic diagram of the experimental device is shown in Figures S10 and S11. The artificial cores with a diameter of 25.4 mm and length of 50 mm were soaked in standard brine (2.0% KCl + 5.5% NaCl + 0.45% MgCl₂ + 0.55% CaCl₂) to saturation. Subsequently, the cores were put into the experimental device, and the fracture fluid was injected into the device. The filtration loss was recorded at various times under various conditions. Finally, the cores were taken out until the environmental medium was replaced with standard brine. The core permeability of artificial cores with a diameter of 25.4 mm and length of 50 mm was determined, and the damage of the core was determined by the ratio of dry core permeability to filtrated core permeability.

3. Results and Discussions

3.1. Synthesis and Chemical Structure of Fracture Fluid Based on Low-M_w Cross-Linking Terpolymer

3.1.1. Polymerization of Terpolymer

The fracture fluid based on the low-molecular-weight cross-linking terpolymers was successfully produced via free-radical polymerization in aqueous solution and subsequent coordination with Zr-based reagent. Considering the viscous nature of the aqueous fracture fluid, acrylamide (AM) was selected as the primary monomer of the terpolymer, due to the good sand-carrying performance. In order to improve the rheological performance of the aqueous fracture fluid, the general functional molecule, 2-acrylamido-2-methylpropanesulfonic acid (AMS), was selected as the second monomer, since the ionic hydrogen bonds can in situ generate between sulfonic groups and amide groups. Moreover, monoacryl poly(ethylene glycol) (AEG) was selected as the third monomer to improve the amphipathy of the fracture fluid to improve compatibility with the formation fluid. In addition, the Na₂SO₃-K₂S₂O₈ initiating system (I) was selected to realize highly efficient initiation in aqueous solution.

The terpolymer was synthesized through free-radical copolymerization of AM, AMS, and AEG in aqueous solution using a Na₂SO₃–K₂S₂O₈ initiator system at elevated temperature, as illustrated in Scheme 1. To investigate the influence of polymerization temperature (T_p) and time (t_p) on the process, the apparent viscosity (η_app) and monomer conversion (conv.) were monitored under various conditions, with the molar ratio of AM:AMS:AEG:I fixed at 10:2:1.4:0.18. As shown in Figure 1a, both η_app and conv. increased with prolonged reaction time at 80 °C: η_app rose from 0 to 552 mPa·s, while conv. increased from 0% to 92%. The conversion versus time profile followed an exponential trend, indicating that the copolymerization follows apparent first-order kinetics. The effects of temperature were examined by measuring η_app and conv. after 6 h at temperatures ranging from 30 to 90 °C. As T_p increased from 30 to 80 °C, η_app increased from 0 to 552 mPa·s, but further increasing the temperature to 90 °C resulted in a decline to 384 mPa·s. Similarly, conversion reached a maximum of 92% at 80 °C. These results indicate that the optimal polymerization time and temperature are 6 h and 80 °C, respectively.

The monomer concentration is a critical factor in the preparation of fracture fluids, as the rheological properties of the solution are highly dependent on it. Given that the rheological behavior is primarily influenced by the concentration of the first monomer, the apparent viscosity (η_app) was examined by increasing the total monomer content (f_m) while maintaining a constant molar ratio of AM:AMS:AEG:I at 10:2:1.4:0.18. The polymerization was carried out at 80 °C for 6 h. As shown in Figure S1, η_app increased from 498 to 569 mPa·s as f_m rose from 20% to 30%, but decreased to 506 mPa·s when f_m further increased to 40%. Additionally, the initiator concentration (f_i) significantly affects the polymerization process, as it determines the average molecular weight of the polymer and consequently alters the rheological properties of the resulting fracture fluid. To explore the correlation between f_i and η_app, measurements were conducted with f_i varying from 0.06% to 0.24%, while keeping the monomer ratio unchanged (AM:AMS:AEG:I = 10:2:1.4:0.18) and maintaining the reaction at 80 °C for 6 h. As depicted in Figure S2, η_app increased from 223 to 569 mPa·s with f_i rising from 0.06% to 0.18%, and then declined to 424 mPa·s when f_i was further increased to 0.24%.

Subsequently, the influence of terpolymer composition on rheological properties was evaluated by measuring the apparent viscosity (η_app) of the polymerizing solution after 6 h at 80 °C. The concentration of each monomer (f_am, f_ams, and f_ae9) was varied individually across three experimental groups, while maintaining a baseline molar ratio of AM:AMS:AEG:I at 10:2:1.4:0.18. The effects of f_am, f_ams, and f_ae9 on η_app are presented in Figure 1b. The results reveal a dual dependence of η_app on each monomer concentration. Specifically, η_app reaches a maximum at f_am = 30%, f_ams = 3%, and f_ae9 = 3.6%, respectively. The non-monotonic behavior observed with varying f_am or f_ams is attributed to ionic hydrogen bonding between -SO₃⁻ and -NH₂ groups, which is sensitive to the molar ratio of sulfonic to amide groups (Scheme 1). On the other hand, the dual trend in η_app with f_ae9 is ascribed to changes in topological conformation resulting from optimal steric repulsion among interpenetrating side chains [37].

Based on the above analysis, the theoretically optimal feed molar ratio of AM:AMS:AEG was determined to be 10:1:1.2, with an optimal AM concentration of 30 mol%. To identify a practical feed ratio that ensures both high monomer conversion and favorable rheological properties, free-radical copolymerization was carried out under five different monomer and surfactant compositions. Each polymerization was conducted at 80 °C for 6 h with an initiator concentration (f_i) of 0.18 mol%, using TBAC as a surfactant. The tested molar ratios AM:AMS:AEG:TBAC were as follows: 9:1:2.7:0.2, 9:1:1.7:0.2, 9:2:2.4:0.1, 10:2:0.7:0.2, and 10:2:1.4:0.1. The monomer conversion (conv.) and apparent viscosity (η_app) of the resulting terpolymers are presented in Figure S3a,b. Among these, the system with the molar ratio of 10:2:1.4:0.1 exhibited the highest comprehensive performance, achieving a conversion of 96% and an apparent viscosity of 582 mPa·s. For simplicity, this terpolymer is denoted as P(AM₁₀-AMS₂-AEG_1.4)/TBAC_0.1.

The representative ¹H NMR spectrum of P(AM₁₀-AMS₂-AEG_1.4) in D₂O is given in Figure 1c to clarify the chemical structure of the resulting P(AM-AMS-AEG) polymers. The signal assignments of the ¹H NMR spectrum has been reported in the literature [18]. In detail, signals a and b at 1.54 and 2.10 ppm are assigned to H atoms on polymer chains (-CH_a2-CRH_b-), respectively, in which the integral ratio of a to b (I_a/I_b) equals 2. Signals c and d at 1.07 and 3.54 ppm are assigned to H atoms on the side groups of AMS (-NH-C(CH_c3)₂-CH_d2-SO₃H), respectively, in which the integral ratio of a to b (I_a/I_b) equals 3. Signal f at 3.61 ppm is assigned to H atoms on PEG side chains (-O-CH_f2-CH_f2-). The chemical constitution of P(AM₁₀-AMS₂-AEG_1.4) can be calculated according to Equations (1) and (2):

$$F_{AMS}={\displaystyle \frac{I_d}{I_a}}\times 100\%={\displaystyle \frac{1.84}{13.92}}\times 100\%=13.22mol\%$$

(1)

$$F_{AEG}={\displaystyle \frac{I_f÷23÷2}{I_a}}\times 100\%={\displaystyle \frac{70.9÷44}{13.92}}=11.09mol\%$$

(2)

where F_AMS and F_AEG indicate the molar content of AMS and AEG units on the terpolymer chains.

GPC characterization was performed on the five terpolymers mentioned above to quantify the number-average molecular weight (M_n) and molecular weight distribution (MWD) of terpolymers. All the GPC traces shown in Figure 1d present unimodal molecular weight distributions in the MWD range of 1.7 to 2.54, and the terpolymers with higher conversions were obviously shifted toward the higher-M_n region from 152 to 250 kg·mol⁻¹. In brief, the chemical constitution, M_n, and polydispersity (PDI) of these terpolymers are listed in

Table 1. Brief illustration of the structural characterization of P(AM-AMS-AEG), including F_AMS, F_AEG, M_n, and PDI, according to ¹H NMR and GPC analysis.

Sample	FAMS (%)	FAEG (%)	Mn (kg·mol−1)	PDI
P(AM10-AMS2-AEG1.4)	13.22	11.09	250.2	1.71
P(AM10-AMS2-AEG0.7)	15.03	5.84	205.3	1.88
P(AM9-AMS2-AEG2.4)	22.42	17.96	202.1	1.92
P(AM9-AMS1-AEG1.7)	21.27	13.65	200.7	2.07
P(AM9-AMS1-AEG2.7)	20.80	20.31	152.6	2.54

.

P(AM-AMS-AEG) can be easily synthesized in aqueous solution with the Na₂SO₃-K₂S₂O₈ initiating system at 80 °C for 6 h. The conv. and M_n of P(AM₁₀-AMS₂-AEG_1.4) can reach 96% and 250 kg·mol⁻¹, respectively, in which the M_w of P(AM₁₀-AMS₂-AEG_1.4) is far less than that of guar gum with a typical M_w of 2000 kg·mol⁻¹.

3.1.2. Cross-Linking Process of Terpolymer Solution

The terpolymer solution containing surfactant cannot be directly used as a fracture fluid, due to its still unsatisfactory rheological performance. To further enhance the viscosity of the terpolymer solution, a chemical cross-linking process was introduced in subsequent investigations. Commercial cross-linkers for fracture fluids typically rely on coordination between Zr⁴⁺ ions and polar functional groups—such as carboxylate, amine, and amide—and are available in both organic and inorganic zirconium-based formulations. To evaluate the compatibility of these cross-linkers with the representative terpolymer solution P(AM₁₀-AMS₂-AEG_1.4)/TBAC_0.1, comparative tests were conducted (Figure S4). It was observed that the solution turned into a white emulsion immediately after the addition of just 0.3 mol% of the inorganic zirconium reagent. In contrast, the solution remained transparent even after the introduction of up to 1 mol% of the organic zirconium reagent.

Considering the apparent compatibility of the organic Zr-reagent (hereafter denoted as [Zr]), the effect of cross-linking temperature (T_xl) or the dosage of [Zr] on the rheological characteristics of this solution is further investigated. To prevent the irreversible gelation during the cross-linking process, the P(AM₁₀-AMS₂-AEG_1.4)/TBAC_0.1 solution was diluted 10 times to a concentration of 0.55 wt% and mixed with [Zr] at various cross-linking temperatures (T_xl). With increments in T_xl, the cross-linking time (t_xl) decreases from 600 to 100 s, and the η_app of the dilute solution increases from 60 to 130 mPa·s (Figure 2a). The plot of t_xl vs. T_xl is in accordance with Boltzmann growth, and the plot of η_app vs. T_xl is in accordance with exponential growth. As the t_xl or η_app of the resulting solutions barely changes with T_xl ranging from 80 to ~90 °C, the practical T_xl is set to 80 °C for continuous synthesizing operation. On the other hand, t_xl decreases from 1200 to 300 s with the molar ratio of [Zr] to AM (f_[Zr]) increasing from 0.1% to 0.45%, and the η_app of the dilute solution increases from 320 to 650 mPa·s in the process after cooling down (Figure 2a). The plot of t_xl vs. f_[Zr] is in accordance with linear growth, and the plot of η_app vs. f_[Zr] is in accordance with exponential growth. The products with various f_[Zr] exhibiting various rheological characteristics can be utilized under different operating conditions, which is described in Section 3.2.2.

The chemical structure of the cross-linked terpolymer, P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35/TBAC_0.1, was analyzed by FTIR characterization, as shown in Figure 2b. For comparison, the FTIR spectra of P and [Zr] are also given in Figure 2b. The absorbance peaks at 1048, 1132, and 1152 cm⁻¹ are assigned to vibration of S-O (ν_S-O) and symmetric and asymmetric vibration of O-S-O (ν_s,O-S-O and ν_s,O-S-O), indicating the existence of AMS units in the terpolymer. The absorbance peaks at 1122 and 954 cm⁻¹ are assigned to vibration of C-O (ν_S-O) and C-O-C (ν_C-O-C), indicating the existence of AEG units in the terpolymer. After cross-linking with [Zr], the absorbance peaks assigned to the amide group coordinated with Zr⁴⁺ can be observed at 1558 and 3352 cm⁻¹. In addition, the absorbance assigned to ionic hydrogen bonds between -NH₂ and -SO₃H can be detected at 3207 cm⁻¹, indicating that the multiple networks with covalent cross-linking sites ([Zr] groups) and noncovalent cross-linking sites (ionic hydrogen bonds) can in situ generate in aqueous solution.

3.1.3. Formula of Fracture Fluid

The infiltration of polymer-based fracture fluids into formation cracks can cause significant formation damage due to their rheological properties. To mitigate this risk and enable controllable viscosity reduction, the inclusion of a gel breaker is essential in fracture fluid formulations. In this study, ammonium persulfate ((NH₄)₂S₂O₈) was selected as the gel breaker. Its effect on the rheological and surface characteristics was evaluated by adding varying molar ratios of (NH₄)₂S₂O₈ to AM (denoted as f_breaker) into a 0.55 wt% aqueous solution of P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35/TBAC_0.1.

As shown in Figure 2c, the apparent viscosity (η_app) decreases sharply from 100 to 10 mPa·s as f_breaker increases from 0.01% to 0.04%, and then declines gradually to 5 mPa·s when f_breaker reaches 0.06%. Similarly, the surface tension (γ_s) drops markedly from 40 to 20 mN·m⁻¹ over the same initial range of f_breaker (0.01% to 0.04%), and stabilizes between 10 and 20 mN·m⁻¹ with the further increase to 0.06%. These results indicate that the effective adjustment range for f_breaker lies between 0.01% and 0.04%, with the optimal dosage dependent on specific operational requirements.

In addition to viscosity control, surfactants play a crucial role in fracture fluids by enhancing surface activity, which is vital for effective proppant transport. To investigate the influence of TBAC concentration on interfacial behavior, the surface tension (γ_s) and sand–fluid interfacial tension (γ_i) of the P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35 solution were measured across a range of TBAC-to-AM molar ratios (f_s) from 0.2% to 1.0% (Figure S5a,b). Both γ_s and γ_i decrease consistently with increasing f_s: γ_s declines from 34.65 to 27.13 mN·m⁻¹, and γ_i decreases from 7.30 to 1.39 mN·m⁻¹. These results suggest excellent compatibility between TBAC and sand when f_s ≥ 0.8%.

Furthermore, the surfactant content also affects the apparent viscosity of the fracture fluid. As f_s increases, η_app rises slightly from 610 to 685 mPa·s, which can be attributed to enhanced phase interactions induced by the surfactant.

The P(AM-AMS-AEG)/[Zr]/TBAC/[(NH₄)₂S₂O₈] fracture fluid can be in situ synthesized via free-radical polymerization for 6 h and subsequent cross-linking reaction with [Zr] at 80 °C. The effect of the feeding ratio of the terpolymer to the cross-linking reagent, gel breaker, and surfactant on the rheological characteristics was investigated, in which the P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35/TBAC_0.1 aqueous solution reveals the best comprehensive performance.

3.2. Rheological Behavior of Fracture Fluid Under Various Conditions

3.2.1. Associating Behavior and Segmental Motion in P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35/TBAC_0.1 Aqueous Solution

The polymer solution has a general transition process from dissociating status to associating status with increasing concentration, as shown in Figure 3a. The associating polymer in aqueous solution reveals remarkable non-Newtonian characteristics, whereas the dissociating sample can be regarded as a Newtonian fluid. In order to clarify the critical associating concentration (CAC) of samples, the increase in η_app with increments in c_terpolymer was analyzed first (Figure 3b). η_app enhances from 120 to 150 mPa·s with a linear slope of 375 in the c_terpolymer range of 0.08~0.16 wt%, and then dramatically enhances to 420 mPa·s with a linear slope of 1688 in the c_terpolymer range of 0.16~0.32 wt%. The c_terpolymer of 0.16 wt% at the inflection point can be recognized as the CAC.

To analyze in-depth the CAC and corresponding rheological behavior, the variations in shearing stress (τ) with shearing rate ($\dot{\mathsf{\gamma }}$) were recorded for terpolymer solutions with various concentrations. The plots of lnτ vs. ln$\dot{\mathsf{\gamma }}$ are given in Figure S6 and the relationships between the consistency coefficient (K) or flow index (n) and c_terpolymer are shown in Figure 3c, according to Equation (3).

$$ln\mathsf{\tau }=nln\dot{\mathsf{\gamma }}+lnK$$

(3)

Figure 3c shows that K increases from 0.35 to 0.95 and n decreases from 0.44 to 0.39 with increasing c_terpolymer. The CAC can be determined by the inflection point at 0.15 wt%, which is basically in accordance with the value according to the η_app-c_terpolymer plot.

Furthermore, the special pseudoplastic characteristic of the branched terpolymer has been proved due to the topological structure, which can adjust the rheological behavior of fracture fluid. In order to study the effect of f_AEG on the sol–gel transition process, the solation time (t_sol) of terpolymer solution with various f_AEG values of P(AM₁₀-AMS₂-AEG) under the $\dot{\mathsf{\gamma }}$ of 1000 s⁻¹ at 20 °C was recorded, as shown in Figure S7. The t_sol of terpolymer solution increases from 15 to 60 min, in which the relationship between t_sol and f_AEG is in accordance with exponential growth. The increase in t_sol has a dramatic transition point at an f_AEG of 0.8%, indicating that the topological structure has a remarkable effect when f_AEG > 0.8%.

According to the above analysis, c_terpolymer is selected as 0.27 wt% for a stable associating structure in a static state in the fracture fluid. The dynamic stability of the fracture fluid was studied by the variation in storage (G′) and loss modulus (G″). The modulus comparison of P(AM₁₀-AMS₂-AEG_1.4) and guar gum aqueous solutions (0.27 wt%) with increasing shearing stress is shown in Figure 3d. It is shown in Figure 3d that the edge of the linear viscoelastic zone (LVZ) of guar gum is at a stress of 0.1 Pa, whereas that of P is at a stress of 0.17 Pa. Compared with guar gum solution, the higher G′ and G″ of P(AM₁₀-AMS₂-AEG_1.4) solution have no section point in the testing range, indicating that the P(AM₁₀-AMS₂-AEG_1.4) solution is more robust than guar gum solution. Ultimately, the G′ and G″ can be further improved by cross-linking, leading to a steady associator in P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35/TBAC_0.1 (hereinafter denoted as PASG/[Zr]) solution. The oscillation frequency results of P(AM₁₀-AMS₂-AEG_1.4) in the absence or presence of [Zr] and guar gum are given in Figure 3e. The steep decreases in G′ and G″ during the shearing process of guar gum with decreasing frequency are noticed, in which a section point is found at a frequency of 0.2 Hz. In contrast, the G′ of PASG/[Zr] solution is higher than the corresponding G″ from beginning to end, in which the modulus values are still higher than the corresponding values of guar gum. Moreover, the G′ and G″ of PASG/[Zr] solution with a gentle decrease are higher than those of P(AM₁₀-AMS₂-AEG_1.4) solution due to the cross-linking sites. Meanwhile, the loss factor (tanδ) of PASG/[Zr] solution is lower than those of P(AM₁₀-AMS₂-AEG_1.4) and guar gum solutions, since the multiple cross-linking networks can inhibit the segmental motion of polymers.

The PASG/[Zr] solution with the CAC of 0.15 wt% at 20 °C exhibits a fast disassociation–reassociation process, leading to a steadier associator in PASG/[Zr] solution compared to the guar gum solution.

3.2.2. Effect of Temperature on the Rheological Performance of Fracture Fluid

The associating affinity of PASG/[Zr] solution is dominated by the environmental temperature and oscillating strength. Fracture fluid with strong affinity exhibits excellent performances under extreme conditions. In order to evaluate the affinity of the PASG/[Zr] solution, the relationships between η_app of PASG/[Zr] solution (0.27 wt%) and $\dot{\mathsf{\gamma }}$ at various temperatures are recorded in Figure 4a. According to the linear relationships, the effect of temperature on K plotted in Figure 4a is in accordance with the Arrhenius Function shown in Equation (4).

$${\eta }_{app}=A{e}^{-{\displaystyle \frac{E_a}{RT}}}$$

(4)

where A, R, and E_a indicate the pre-exponential factor, universal gas constant, and disassociating active energy during the damage process. E_a is 304.96 kJ·mol⁻¹ according to Equation (4).

The affinity of the associating solution is also dependent on the dosage of [Zr], in which a higher f_[Zr] can lead to a higher resistance to high temperature. The effect of f_[Zr] on the temperature resistance of PASG/[Zr] solution is given in Figure 4c,d to describe the importance of f_[Zr]. The plots of η_app and oscillating temperature (T_os) can be fitted by the Boltzmann Function according to Equation (5).

$${\eta }_{app}={\displaystyle \frac{{\eta }_{app,max}}{1+e^{\frac{T_{os}-T_{os,d}}{{dT}_{os}}}}}$$

(5)

where η_app,max indicates the maximum η_app in the process. T_os,d and dT_os indicate the disassociating temperature and the disassociating rate at the disassociating temperature in the process. T_os,d according to Equation (5) increases from 38 to 101 °C with the increase in f_[Zr] from 0.1% to 0.35%, indicating that the temperature resistance can be remarkably improved by increments in f_[Zr] (Figure 4c–d).

On the basis of the above analysis, the fracture fluid with various f_[Zr] values can be utilized under various conditions. The disassociation of P(AM₁₀-AMS₂-AEG_1.4)/[Zr]/TBAC_0.1 solution with f_[Zr] values of 0.25%, 0.35%, and 0.45% at 60, 90, and 120 °C, respectively, is shown in Figure S8. The associators in the P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.25/TBAC_0.1 solution are totally broken after shearing for 8 h at 60 °C, whereas the associators in P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35/TBAC_0.1 and P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.45/TBAC_0.1 solutions are broken after shearing for 6 h at 90 °C and shearing for 4 h at 120 °C. This indicates that the f_[Zr] of fracture fluid can be adjusted according to practical application.

The remarkable temperature resistance of PASG/[Zr] solution is due to the high disassociating active energy (E_a) of 304.96 kJ·mol⁻¹. Meanwhile, the higher f_[Zr] results in a higher affinity of the associating solution and higher rheological performance at high temperature.

3.2.3. Thixotropy and Self-Recovery Ability of Fracture Fluid

The thixotropic and self-recovery properties of the associative networks are critical for practical applications, as they rely on the dynamic reformation of cross-linked structures under shear. In the PASG/[Zr] system, abundant ionic hydrogen bonds (iHBs) between sulfonic and amine groups enable a rapid response to shear, whereas the Zr⁴⁺ coordination responds more slowly. To clarify the role of iHBs in balancing association and dissociation, density functional theory (DFT) analysis was performed (Figure 4b). The average bond length of N···H or O···H in these iHBs is 1.46 Å, significantly shorter than that of conventional hydrogen bonds. Moreover, the total bond energy reaches 92.6 kJ·mol⁻¹, exceeding typical hydrogen bond strengths. These results indicate that the iHBs are both strong and highly dynamic, facilitating rapid breakdown and reformation under shear. Consequently, the presence of active iHBs supports the construction of stable yet responsive associative networks, ensuring efficient self-recovery and robust thixotropic behavior.

To study the recovery process of associators in PASG/[Zr] solution (0.27 wt%), the recovery rate of η_app (η/η₀) of PASG/[Zr] solution was recorded in Figure 4c,d under strong shearing ($\dot{\mathsf{\gamma }}$ = 1000 s⁻¹) and weak shearing ($\dot{\mathsf{\gamma }}$ = 500 s⁻¹) for increasing duration. The damage of strong shearing is always stronger than that of weak shearing, leading to low η/η₀ in each of the three groups. However, the increment in concentration results in an increase in η/η₀ from 83% to 92% after 100 min even under strong shearing. Considering that f_[Zr] is settled as 0.35% in solution, the increases in η/η₀ are mainly attributed to the greater amount of iHBs in concentrated solution. In addition, Figure S9 shows that the interfacial tension can be recovered under shearing conditions, which is also not sensitive to temperature.

The thermal relaxing characteristic endows the polymer network with the ability of rapidly balancing disassociation and reassociation. Identical to the above analysis, the contribution of [Zr] to the recovery ability can also be quantified by investigating the effect of f_[Zr] on the shearing balance of P(AM₁₀-AMS₂-AEG_1.4)/[Zr]/TBAC_0.1 solution given in Figure 4e. The plots of η_app and t_os can also be fitted by the Boltzmann Function according to Equation (5).

$${\eta }_{app}={\displaystyle \frac{{\eta }_{app,max}}{1+e^{\frac{t_{os}-t_{os,d}}{{dt}_{os}}}}}$$

(6)

where t_os,d and dt_os indicate the relaxing time and the disassociating rate at the relaxing time in the process. t_os,d according to Equation (5) increases from 11 to 130 min with the increase in f_[Zr] from 0.1% to 0.35%. This indicates that the shearing resistance can be remarkably improved by increments in f_[Zr], whereas the recovery ability is inhibited in the process. Therefore, the robustness of the polymer associator is decided by f_[Zr], but the recovery and thixotropy ability are decided by iHBs. The multiple networks have synergetic effects, resulting in different applications under various conditions.

In addition, the thixotropy of PASG/[Zr] solution (0.27 wt%) can be evaluated by the cyclic thixotropic test (Figure 4f). The maximum stress of the PASG/[Zr] solution (0.27 wt%) of 22.96 Pa is higher than that of guar gum solution (0.27 wt%) of 18.18 in the $\dot{\mathsf{\gamma }}$ range of 100~500 s⁻¹. Meanwhile, the area of the thixotropic ring (hysteresis) of PASG/[Zr] solution (0.27 wt%) is 14.08 kPa·s⁻¹ in a $\dot{\mathsf{\gamma }}$ range of 100~500 s⁻¹. For comparison, the value of guar gum solution (0.27 wt%) is 10.89 Pa·s⁻¹, which is smaller than that of the PASG/[Zr] solution. This confirms that the thixotropic ability of PASG/[Zr] solution fracture fluid is superior to traditional guar gum fracture fluid.

The PASG/[Zr] solution, with its stable network structure, exhibits excellent disassociation–reassociation behavior under shear, owing to its branched topological architecture, intrinsic hydrogen bonds (iHBs), and Zr⁴⁺ coordination. The Zr⁴⁺ coordination provides strong associative strength, while the iHBs contribute to rapid recovery and thixotropic properties. By adjusting the formulation, the operational parameters of the fracturing fluid can be finely tuned, making it suitable for application under extreme conditions.

The abundant iHBs between sulfonic and amine groups in the PASG/[Zr] system respond rapidly during thixotropic processes, promoting stable interactions and fast reconstruction of multiple networks through the synergistic effect of iHBs and Zr⁴⁺ coordination. Furthermore, increasing the Zr⁴⁺ content enhances the network reconstruction activity and improves the frequency resistance of the P(AM₁₀-AMS₂-AEG_1.4)/[Zr]/TBAC_0.1 solution. The outstanding thixotropic performance of the PASG/[Zr] solution—characterized by rapid recovery and low hysteresis—is crucial for thickening agents to prevent circulation loss and extend thickening time.

3.3. Fracturing Fluid as Thickening Agent Protecting Cores

3.3.1. Sand-Carrying Ability of PASG/[Zr]-Based Fracturing Fluid

To protect the stratum from the corrosion by natural fluid, a kind of non-Newtonian fluid with high compatibility and good impact resistance should be applied as the thickening reagent for shale gas extraction. To reduce the damage caused by precipitated sands, the sand-carrying ability of the above fracture fluid is investigated. The increases in settling volume (V_s) of sand from the surface at various settling durations (t_s) in the static mixture of PASG/[Zr] solution (0.27 wt%) and sand with various particle sizes at 20 °C are plotted in Figure 5a. For comparison, the increases in V_s in guar gum are also given in Figure 5a under corresponding conditions, with larger particle sizes and faster settling rates. The V_s of sand with constant particle size in PASG/[Zr] solution is always lower than that in guar gum solution. The V_s-t_s plots can be fitted by the Boltzmann Function according to Equation (6).

$$V_s={\displaystyle \frac{V_{s,max}}{1+e^{\frac{t_s-t_{s,semi}}{{dt}_s}}}}$$

(7)

where V_s,max indicates the maximum V_s in the process. t_s,semi and dt_s indicate the semi-settling time and the settling rate at the semi-settling time in the process. The t_s,semi of sand in the PASG/[Zr] solution decreases from 28.24 to 24.90 h with the increase in average particle size from 30 to 70 mesh, which is always higher than each t_s,semi of the sand in guar gum solution (Figure 5b).

Meanwhile, the effect of temperature is also noticed, due to the possible disassociation and sand aggregation. The sand-carrying ability of the above fracture fluid at various temperatures is analyzed. The increase in V_s with increasing t_s in the static mixture of PASG/[Zr] solution (0.27 wt%) and sand (30 mesh) at various temperatures is plotted in Figure 5a. For comparison, the increasing V_s in guar gum is also given in Figure 5a under corresponding conditions, with higher temperature and faster settling rate. Identical to the above analysis, the V_s of sand in PASG/[Zr] solution is always lower than that in guar gum solution at the same temperature. The V_s-t_s plots can also be fitted by the Boltzmann Function according to Equation (6). The t_s,semi of sand in PASG/[Zr] solution decreases from 19.54 to 8.74 h with the increase in temperature from 30 to 90 °C, which is always higher than each t_s,semi of sand in the guar gum solution (Figure 5b).

The sand-carrying ability of flowing PASG/[Zr] solution can be further studied by carrying experiments in a horizontal pipe (d_pipe = 2.5 cm, Scheme 2). The pressure gradient (∇×P) and flow velocity (v) of the mixture with solute and sand concentrations (C_solute, C_sand) of 0.27 and 30 wt%, respectively, were recorded with increasing experimental duration at 20 °C, as shown in Figure 5c. Initially, the sand suspended in the fluid can smoothly move through the pipe in 2 min with a slight change in ∇×P and decrease in v. ∇×P sharply increases from 0.1 to 2.9 kPa·s⁻¹ and v decreases from 0.24 to 0.02 m·s⁻¹ in 2~13 min with the sand gradually settling on the bottom of the pipe, due to the reduction in actual internal area. Subsequently, the sand begins to be recarried in the fluid because of the high ∇×P, leading to an enhancement of the fluid. When v reaches 0.26 m·s⁻¹ at 24 min, the sand is totally suspended in the fluid without any settlement on the bottom. The v of fluid beginning to settle is denoted as the settling velocity (v_c,settle), and the v of sand totally suspended in fluid is denoted as the suspending velocity (v_c,suspend). The v_c,settle and v_c,suspend of the above experiment are 0.24 and 0.26 m·s⁻¹.

In order to clarify the dynamic sand-carrying ability of PASG/[Zr] fracturing fluid during the flowing process at 20 °C, the relationships between the diameter of the pipe (d_pipe) or C_sand and v_c,settle or v_c,suspend of PASG/[Zr] fluid are given in Figure 5d. For comparison, the corresponding relationships of guar gum fluid are also given in Figure 5d. v_c,suspend is always higher than v_c,settle as the driving force of sand suspension is always higher than that of sand settlement. All of the velocity values reveal increases with an increase in d_pipe or C_sand, according to the Bernoulli Principle. Significantly, the v_c,settle or v_c,suspend of guar gum fluid is always higher than that of PASG/[Zr] fracturing fluid, whether the variable is d_pipe or C_sand, indicating that the sand-carrying ability of PASG/[Zr] fracturing fluid is much better than that of guar gum fluid during the flowing process.

Consequently, the PASG/[Zr] fracturing fluid exhibits a good sand-carrying ability due to its great rheological performance and interfacial activity, leading to low V_s during the static sand-carrying test and low v_c,suspend during the dynamic sand-carrying test.

3.3.2. Filtration System Based on PASG/[Zr] Fracturing Fluid

The filtration performance is a critical factor in evaluating the applicability of fracturing fluids, as it reflects the degree of core damage caused by fluid leakage. To quantify the filtration loss of rock with the fracture fluid through the core, the filtration loss volume (V_f) of the artificial core was measured at 20 °C during the flowing process with various $\dot{\mathsf{\gamma }}$ and a constant filtration differential pressure (Δp_f) of 3.5 MPa by using the filtration experimental device shown in Figure S10. The plots of V_f vs. t^0.5 of PASG/[Zr] and guar gum solutions with various $\dot{\mathsf{\gamma }}$ are given in Figure 6a. The filtration coefficient (c_f) and core damage rate can be calculated according to Equation (8).

$$c_f=0.005\times {\displaystyle \frac{m}{A}}$$

(8)

where m indicates the slope of the linear stage of the V_f vs. t^0.5 plot. A indicates the cross-sectional area of the flowing pipe. c_f reveals a low increase from 2 × 10⁻⁴ to 4.2 × 10⁻⁴ m·min^−0.5 by using PASG/[Zr] fracturing fluid, which is lower than the increase from 8 × 10⁻⁴ to 16 × 10⁻⁴ m·min^−0.5 by using guar gum fracturing fluid. On the other hand, the increase c_f from 2.8 × 10⁻⁴ to 30.6 × 10⁻⁴ m·min^−0.5 is gentler than the increase in c_f from 7.6 × 10⁻⁴ to 59.4 × 10⁻⁴ m·min^−0.5 with an increment in core permeability from 5 to 96 mD. This indicates that the PASG/[Zr] fracturing fluid exhibits better filtration performance than guar gum fracturing fluid due to the good compatibility and rheological performance of PASG/[Zr] fracturing fluid. In addition, the core permeability has a more prominent effect on c_f than $\dot{\mathsf{\gamma }}$. Δp_f is another vital practical parameter in the field of stratum protection, which determines the filtration and damaging process of cores (Figure S12). c_f slightly increases from 2.2 × 10⁻⁴ to 2.3 × 10⁻⁴ m·min^−0.5 with an increment in Δp_f from 3.5 to 11.0 MPa by using PASG/[Zr] fracturing fluid, and R_d also slightly increases from 15.4% to 21.1% in the process. For comparison, the increase in c_f from 8.2 × 10⁻⁴ to 8.6 × 10⁻⁴ m·min^−0.5 and increase in R_d from 30.5% to 37.7% in the filtration system with guar gum fracturing fluid can lead to severe damage to cores. It also indicates that the PASG/[Zr] fracture fluid can also serve well in drilling operations and as cement slurry because of its low filtration and active thixotropy, which also exhibits a high displacement efficiency of 68.74%, calculated according to references [6,7,8,9].

In addition, the fracture fluid with various f_[Zr] can exhibit exceptional filtration performance at various temperatures. To illustrate the filtration performance of fracture fluid at various temperatures, the relationships between the change in η_app (Δη_app) of P(AM₁₀-AMS₂-AEG_1.4)/[Zr]/TBAC_0.1 solution (0.27%) with an f_[Zr] of 0.25%, 0.35%, and 0.45% at 60, 90, and 120 °C, respectively, and t^0.5 are shown in Figure S11. The Δη_app in P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.25/TBAC_0.1 solution increases from 8.5 to 17.8 mPa·s at 60 °C from 9 to 36 min, that of P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35/TBAC_0.1 increases from 10.2 to 19.7 mPa·s at 90 °C from 9 to 36 min, and that of P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.45/TBAC_0.1 solutions increases from 10.9 to 20.3 mPa·s at 120 °C from 9 to 36 min. A high f_[Zr] leads to high-temperature resistance during the filtration process, confirming that the f_[Zr] of fracture fluid mediates the filtration performance for practical application.

LF-NMR analysis was performed on artificial cores treated with different fluids to evaluate formation damage under various conditions. Two groups of identical artificial cores were first saturated with standard brine (2.0% KCl + 5.5% NaCl + 0.45% MgCl₂ + 0.55% CaCl₂) to measure initial water permeability. After 100 min of exposure to the fracturing fluids, the cores were subjected to LF-NMR analysis (Figure 6c). The transverse relaxation time (T₂) reflects the mobility of hydrogen atoms in hydrogen-bearing components within the filtration system: a longer T₂ indicates higher mobility and stronger associative or absorptive interactions [43,44,45,46]. In the T₂ spectra of cores saturated with standard brine, three signal groups were observed at 2.42 ms, 13.92 ms, and 177.7 ms, corresponding to small pores, large pores, and free water, respectively, based on previous studies [47,48,49,50]. After treatment with the PASG/[Zr] fracturing fluid, the T₂ values were detected at 2.96 ms, 13.99 ms, and 177.8 ms for small pores, large pores, and free water, respectively (Figure 6d). The integral area ratios of these three signals showed negligible changes. In contrast, after exposure to guar gum fracturing fluid, the T₂ values shifted to 2.96 ms, 21.23 ms, and 239.1 ms (Figure 6d), indicating an increase in pore size and a reduction in core–fluid affinity. The integral ratio of the small-pore signal increased from 15.1% to 18.9%, while those of large pores and free water decreased from 21.4% and 63.5% to 20.6% and 60.5%, respectively. These results suggest that the guar gum fracturing fluid causes structural loosening within the core and impairs fluid–core interactions, ultimately leading to formation damage.

The PASG/[Zr] solution with admirable viscosity, rheological characteristics, and affinity between the core and fluid reduces the damage from high pressure and leads to low filtration loss of the artificial cores during the filtration process. The filtration performance of PASG/[Zr] fracture fluid is better than that of traditional fluid (guar gum), which can be used as a novel thickening agent for stratum protection and shale gas extraction.

4. Conclusions

A novel fracturing fluid based on the graft copolymer P(AM-AMS-AEG), cross-linked by an organic zirconium reagent, was successfully developed via free-radical polymerization followed by in situ cross-linking. The P(AM-AMS-AEG) polymer, with a molecular weight (M_w) lower than that of typical guar gum (2000 kg·mol⁻¹), was readily synthesized in aqueous solution using a Na₂SO₃-K₂S₂O₈ initiating system at 80 °C for 6 h. Under these conditions, the conversion rate and number-average molecular weight (Mn) of P(AM₁₀-AMS₂-AEG_1.4) reached 96% and 250 kg·mol⁻¹, respectively. The P(AM-AMS-AEG)/[Zr]/TBAC/[(NH₄)₂S₂O₈] fracturing fluid was subsequently prepared through in situ cross-linking by adding zirconium reagent at 80 °C for 1200 to 300 s, with the zirconium mass fraction (f_[Zr]) varying from 0.1% to 0.45%. The effects of the feed ratios of f_[Zr], the breaker (f_b), and salt (f_s) on rheological properties were systematically investigated. Among the formulations, the P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.35/TBAC_0.1 aqueous solution demonstrated the most comprehensive performance. At concentrations exceeding 0.15 wt% and 20 °C, the PASG/[Zr] solution exhibited faster and more stable disassociation–reassociation behavior compared to guar gum. Its high activation energy (E_a) of 304.96 kJ·mol⁻¹ contributes to exceptional temperature resistance. The abundant intrinsic hydrogen bonds (iHBs) between sulfonic and amine groups enable a rapid response during thixotropic processes, promoting stable interactions and rapid reconstruction of multiple networks through synergistic effects with Zr⁴⁺ coordination. Increasing f_[Zr] enhanced the associative affinity and high-temperature rheological performance. Notably, the cross-linked structures in the P(AM₁₀-AMS₂-AEG_1.4)/[Zr]_0.45/TBAC_0.1 solution remained unbroken even after 4 h of shearing at 120 °C. Higher f_[Zr] also improved the network reconstitution activity and frequency resistance, resulting in a higher hysteresis area of 14.08 kPa·s⁻¹ for the PASG/[Zr] solution. Owing to its pseudoplasticity, thixotropy, and good sand compatibility, the PASG/[Zr] fluid effectively minimizes formation damage under high pressure and shows low filtration loss in artificial cores. It also exhibits excellent sand-carrying capacity, attributed to its superior rheological properties and interfacial activity. In static sand-suspension tests, the settling velocity (V_s) increased only slowly between 30 and 90 °C, while in dynamic tests conducted in a horizontal pipe (d = 2.5 cm), the critical settling velocity (v_c,suspend) was as low as 0.26 m·s⁻¹. The filtration coefficient (c_f) of the PASG/[Zr] fracturing fluid ranged from 2.2 × 10⁻⁴ to 2.5 × 10⁻⁴ m·min^−0.5, showing low sensitivity to shear rate ($\dot{\mathsf{\gamma }}$), core permeability, and differential pressure (Δp_f). This indicates significantly improved filtration performance compared to conventional guar gum-based fluids. With its combination of robust rheological properties, minimal formation damage, and effective suspension characteristics, the PASG/[Zr] fracturing fluid demonstrates strong potential as a novel thickening agent for applications in reservoir protection and shale gas extraction.