The Impact of Reservoir Parameters and Fluid Properties on Seepage Characteristics and Fracture Morphology Using Water-Based Fracturing Fluid

Abstract

This study, motivated by the pronounced fluid loss characteristics of water-based fracturing fluids, developed a fluid–solid coupling model to investigate water-based fracturing in geological reservoirs. The model was further employed to analyse the effects of multiple factors on fracture propagation and the seepage capacity of water-based fracturing fluids. Moreover, the underlying mechanisms of fracture propagation and seepage enhancement were elucidated from a microscopic molecular perspective. The results obtained that the high apparent viscosity of water-based fracturing fluids not only enhances the fracturing efficiency of reservoir rocks but also results in a reduced seepage volume (−17 mL) in low-permeability reservoirs. Furthermore, the reservoir porosity (+2.5%) exhibits a clear inverse proportional relationship with fracturing efficiency (−0.9 m), while the seepage volume (+7 mL) of water-based fracturing fluids continues to increase. The strength and quantity of hydrogen bonds between molecules in water-based fracturing fluid, influenced by external factors, directly affect fluid seepage. The seepage behaviour of water-based fracturing fluids in geological reservoirs, together with the influence of reservoir conditions on fracture propagation, provides valuable reference data for rock fracturing and reservoir stimulation. However, the absence of data analysis and microscopic images of microscopic molecular dynamics constitutes a challenging problem that demands attention.

1. Introduction

The historical progression of global economic development has been predominantly propelled by the utilisation of conventional fossil fuels [1,2]. However, the escalating energy shortage has led to a deceleration in economic growth. Concomitantly, the substantial consumption of conventional energy sources has engendered the emission of considerable quantities of greenhouse gases. These gases are the primary cause of the greenhouse effect and environmental degradation [3]. Consequently, the focus of energy researchers and petroleum engineers has increasingly shifted towards new and unconventional energy sources [4]. It is expected that these alternative energy sources will not only serve as a valuable supplement to traditional energy but also contribute to a sustainable and self-reinforcing energy ecosystem [5,6]. However, new and unconventional energy sources are encumbered by a series of disadvantages that preclude their replacement of traditional energy sources, including equipment lag and defects in mining technology. (1) Despite the ecological benefits and the avoidance of the greenhouse effect that have been achieved through the use of new energy sources such as wind power and solar energy, the key to large-scale application of these sources is the stability and reliability of the energy supply [7,8]. However, the low efficiency and the lack of development in energy storage equipment means that the needs of new energy sources during peak energy supply periods cannot be met, which results in significant energy wastage and a reduction in efficiency [9,10]. (2) Although unconventional energy sources, such as shale gas and gas hydrates, exhibit a strong potential to replace traditional energy, the technological lag and mismatch in extraction methods necessitate further exploration by petroleum engineers to optimise the adaptation of conventional extraction techniques for unconventional reservoirs [11,12]. The disadvantages inherent in the utilisation of novel energy applications, consequent to the technical deficit in hardware equipment, are not readily amenable to expeditious resolution [13]. Nevertheless, reservoir transformation measures for conventional energy can be readily enhanced and applied to energy extraction in unconventional reservoirs [14].

As a measure for transforming reservoirs in the context of traditional energy, acid fracturing has demonstrated significant advantages with regard to the expansion of fractures and the enhancement of oil recovery [15,16], and the sweep coefficient of oilfield working fluid in reservoir rocks has exhibited a substantial enhancement effect. Li et al. have demonstrated the remarkable fracture expansion capacity of water-based fracturing in China’s oil reservoirs [17], resulting in the formation of 58 m reservoir fractures and the effective accumulation of reservoir oil. Moreover, Khalil et al. utilised hydrochloric acid as the acidising fluid to transform the oil reservoir in the Marcellus block, thereby exploring rock permeability. This resulted in a 39-fold increase in rock permeability and a 13% rise in porosity [18]. Despite the potential of acidizing to enhance EOR (Enhanced Oil Recovery), its numerous drawbacks, including reservoir damage and formation contamination, have led to significant challenges in subsequent reservoir treatment [19,20]. Fracturing technology, as the most widely used method for reservoir transformation, primarily encompasses water-based fracturing, oil-based fracturing, foam fracturing, and CO₂ fracturing [21,22]. Nevertheless, due to inherent limitations, including a restricted application range and suboptimal stability, conventional and unconventional reservoir exploitation is currently impeded by oil-based, foam-based, and CO₂ fracturing techniques [23,24]. In contrast, water-based fracturing fluids are presently suitable for the fracturing conditions of most reservoirs. Nevertheless, the water sensitivity and seepage behaviour of water-based fracturing fluids in low-permeability shale reservoirs hinder fracture propagation, posing a significant challenge to the efficient development of shale energy [25]. Furthermore, elevated temperatures in shale reservoirs have been shown to improve the rheological properties of water-based fracturing fluids, which decreases their thermal stability and reduces filtration control.

All the analysis contents discussed above can be summarised and analysed using Scheme 1.

Thus, this study constructed a flow model of water-based fracturing fluid in shale reservoirs based on the solid–liquid coupling equation in order to analyse the flow behaviour and seepage characteristics of water-based fracturing fluid in low-permeability reservoirs. At the same time, rock fracturing and fracture propagation criteria were used to analyse the expansion behaviour and change trend of reservoir fractures under different reservoir conditions. This helped to achieve energy convergence and efficient exploitation of unconventional low-permeability reservoirs. Furthermore, molecular dynamics models and hydrogen bond theory have been employed not only to analyse the adsorption and rheological behaviour of water-based fracturing fluid in reservoir rocks, but also to provide a satisfactory explanation for the mechanical changes in reservoir fractures.

2. Materials and Methods

2.1. Reservoir Seepage Model of Water-Based Fracturing Fluid

The reservoir seepage model of water-based fracturing fluid principally addresses the movement of oil and water within reservoir fractures, as well as the seepage of rock matrix. The pertinent models can be categorised into two distinct categories: matrix seepage (Equations (1) and (2)) and fracture seepage (Equations (3) and (4)).

$$\nabla ({\displaystyle \frac{K_m{K}_{ro}}{{\mu }_o{B}_o}}\nabla p_o)+{\stackrel{.}{{\displaystyle q}}}_{omw}+{\stackrel{.}{{\displaystyle q}}}_{omf}={\displaystyle \frac{\delta }{{\delta }_t}}({\displaystyle \frac{{\varphi }_m{s}_o}{B_o}})$$

(1)

$$\nabla ({\displaystyle \frac{K_m{K}_{rw}}{{\mu }_w{B}_w}}\nabla p_w)+{\stackrel{.}{{\displaystyle q}}}_{wmw}+{\stackrel{.}{{\displaystyle q}}}_{wmf}={\displaystyle \frac{\delta }{{\delta }_t}}({\displaystyle \frac{{\varphi }_m{s}_w}{B_w}})$$

(2)

$$\nabla ({\displaystyle \frac{K_f{K}_{ro}}{{\mu }_o{B}_o}}\nabla p_o)+{\stackrel{.}{{\displaystyle q}}}_{ofw}-{\stackrel{.}{{\displaystyle q}}}_{omf}={\displaystyle \frac{\delta }{{\delta }_t}}({\displaystyle \frac{{\varphi }_f{s}_o}{B_o}})$$

(3)

$$\nabla ({\displaystyle \frac{K_f{K}_{rw}}{{\mu }_w{B}_w}}\nabla p_w)+{\stackrel{.}{{\displaystyle q}}}_{wfw}-{\stackrel{.}{{\displaystyle q}}}_{wmf}={\displaystyle \frac{\delta }{{\delta }_t}}({\displaystyle \frac{{\varphi }_f{s}_w}{B_w}})$$

(4)

where K is the permeability of solid rock. $k$, $\mu$, $B$ and p are the relative permeability, viscosity, volume fraction and pressure of oil and water phases. $\varphi$ is the rock porosity. s is the fluid saturation. ${\stackrel{.}{{\displaystyle q}}}_{omw}$ and ${\stackrel{.}{{\displaystyle q}}}_{wmw}$ are the matrix injection strength of oil and water phases. ${\stackrel{.}{{\displaystyle q}}}_{ofw}$ and ${\stackrel{.}{{\displaystyle q}}}_{wfw}$ are fracture injection strength of oil and water phases. ${\stackrel{.}{{\displaystyle q}}}_{omf}$ and ${\stackrel{.}{{\displaystyle q}}}_{wmf}$ are Matrix-fracture cross-flow strength of oil and water phases. In addition, it is imperative to close the outer boundary of the seepage model, while the inner boundary is controlled by the well equation.

2.2. Material Damage Criterion for Low Permeability Rocks

Brittle materials, including reservoir rocks, can be characterised using the hyperbolic shape criterion to describe their fracture damage behaviour, as presented in Equation (5) [26].

$$F(\sigma )={\tau }^2-{(C-{\sigma }_n\tan \phi )}^2+{(C-{\sigma }_R\tan \phi )}^2$$

(5)

where $\sigma$_R presented the tensile strength of reservoir rock. C is the cohesion of reservoir rocks, and φ presented the maximum normal stress threshold for reservoir fracture opening. σ_n presented the shear stress. F is the force required for reservoir rock fracture.

The “cohesive fracture” model based on Equation (5) shown in Equation (6) can more effectively explore rock damage and fracture propagation in low-permeability shale reservoirs.

$$F(\sigma ,D)={\tau }^2-{\sigma }_n^2\tan {\theta }^2+2g(D){\sigma }_n{\sigma }_c-g^2(D)C^2$$

(6)

In which $\theta$ is considered as the fracture turning angle inside reservoir rock. σ_c is the hoop strength, and it could be solved be Equation (7). In addition, Figure 1a showed the relationship between $\theta$ and σ_R.

$${\sigma }_c={\displaystyle \frac{C^2+{\sigma }_R^2\tan {\theta }^2}{2{\sigma }_R}}$$

(7)

2.3. Fracture Propagation Criteria and of Low Permeability Reservoirs

The Benzeggagh-Kenane fracture criterion is utilised in the damage evolution process of water-based fracturing fluid to reservoir fractures (see Equation (8)) [27].

$$G_n^c+(G_s^c-G_n^c){({\displaystyle \frac{G_{Sn}}{G_T}})}^{\eta }=G^c$$

(8)

where $G_n$, $G_s$ and $G_T$ are considered to be the work done by the traction in the normal direction, the first shear direction and the second shear direction and their conjugate relative displacements, respectively. $G^c$ presented the mixed-mode fracture energy of reservoir fractures, and the critical energy $G_n^c$, $G_s^c$ and $G_T^c$) required for reservoir rock failure in different shear directions can be derived by LEFM [28]. $G_{Sn}$ is the actual energy release rate component, and $\eta$ is the power index.

The flow of water-based fracturing fluid in low-permeability reservoir fractures consists of tangential flow, which drives fracture expansion, and normal flow, which induces fluid leakage into the formation, as illustrated in Figure 1b. The fracturing fluid in the reservoir fracture is an incompressible non-Newtonian fluid, and that the tangential flow is principally governed by the lubrication equation, which is derived from the Poiseuille equation (Equation (9)).

$$q={\displaystyle \frac{d^2}{12\mu }}\nabla p$$

(9)

where q presented the injection rate of water-based fracturing fluid, μ and ▽p are the viscosity of water-based fracturing fluid and reservoir internal pressure. D is the fracture width.

Concurrently, the normal phase flow adheres to the parameters delineated in Equation (10) [29].

$$\begin{array}{l}{q}_t=c_t(p_i-p_t)\\ q_b=c_b(p_i-p_b)\end{array}$$

(10)

where $q_t$ and $q_b$ are the normal velocity of fracturing fluid on both sides of reservoir fracture, $c_t$ and $c_b$ are considered as the filtration coefficient on the fracture surface. $p_i$ presented the internal pressure of the fracture, $p_t$ and $p_b$ are the pore pressure at the fracture surface.

2.4. Water-Based Fracturing Model for Low Permeability Reservoirs

A two-dimensional water-based fracturing grid model comprising 32,000 CPE4P units was developed, which facilitates the analysis of the fracturing process and seepage behaviour of low-permeability shale reservoirs under varying geological structures and fluid parameters. Furthermore, an isotropic fracturing model is situated at the centre as the injection point for the water-based fracturing fluid, with opposing initial fractures surrounding the wellbore. Furthermore, the sophisticated grid surrounding the wellbore ensures stable model operation and enhances convergence. Figure 2 and

Table 1. Water-based fracturing parameters for reservoir fracturing models.

Parameter	Value	Parameter	Value
Elastic Modulus, E/GPa	26	Poisson’s ratio, ν	0.19
Minimum horizontal principal stress, σh/MPa	33	Maximum horizontal principal stress, σH/MPa	36
Tensile strength, C/MPa	6.5	Initial pore pressure, Pip/MPa	21
Initial porosity, ϕ/%	7–10	Permeability, K/m2	5.8 × 10−16
Leak-off coefficient	2.6 × 10−12	Total fracturing time, T/min	12

showed the water-based fracturing model and the characteristic parameters of low-permeability shale reservoirs are demonstrated, respectively. In addition, the boundary conditions and initial conditions of the numerical model are also placed in

Table 2. Boundary conditions and initial conditions of the numerical model.

Initial Conditions	Value	Boundary Conditions	Value
Initial fracturing length/m	0.3	Injection rate/m3/min	16
Initial fracturing width/m	0.01	Far-field pore pressure/MPa	33
Deflection angle of the fracturing/°	45	Pressure on the fracturing surface/MPa	21
Initial pressure of fluid in the fracture/MPa	33	Rock heat transfer coefficient/W/(m·K)	3.1
Initial pressure at injection point/MPa	35	Far-field displacement/m	0

, which helps the crack propagation model shown in Figure 2 to be run more accurately.

As illustrated in

Table 3. Comparative analysis of numerical models and experimental results in the reference [30].

Data Source	100s	200s	300s	400s
Simulation results of this study	17.2	25.4	32.7	36.1
Comparative Data	17.1	25.2	32.4	35.8

, the data comparison and feasibility analysis results of the fracturing numerical model constructed in this study are presented alongside those of the numerical models documented in other literature. In accordance with the conditions stipulated in the extant literature, the experimental data presented in this study demonstrated a satisfactory degree of overlap with those reported in the literature, and the numerical model employed in this study exhibited enhanced fracturing performance.

2.5. Molecular Dynamics Model

The molecular dynamics model utilises water, guar gum, and a boron-based crosslinker as its fundamental components, with the compass force field employed to optimise the three molecular structures. The Amorphous Cell module constructs an amorphous aqueous solution model of a specific fracturing fluid content, and the Forcite module performs energy-minimising geometry optimisation. In conclusion, the establishment of pertinent data, including chemical bonds, within the optimised water-based fracturing fluid model, results in the subsequent display of the corresponding chemical bond lengths. This method is employed to quantitatively describe the changing trends of chemical bond lengths and bond breakage under different conditions (defined temperature, pressure, and crosslinker content).

3. Results and Discussion

3.1. Effect of Fluid Viscosity on Reservoir Seepage and Fracture Propagation

The viscosity of water-based fracturing fluids significantly influences both fracture propagation and fluid seepage, as illustrated in Figure 3. A strong inverse proportional relationship is observed between fracturing fluid viscosity and reservoir seepage [31,32], whereas the fracture propagation parameter in low-permeability reservoirs increases with the gradual rise in fluid viscosity. Furthermore, the trends depicted in Figure 3 indicate a clear positive correlation between fracture propagation and fluid seepage, where a lower seepage capacity of the water-based fracturing fluid results in a larger fracture propagation parameter. The relationship between seepage capacity and fracture expansion may be related to the fact that smaller seepage can cause the pressure in the fracture to be quickly accumulated to the minimum fracture initiation pressure, while larger liquid seepage cannot cause the pressure in the fracture to be quickly accumulated to the minimum fracture initiation pressure that causes fracture expansion [33,34]. It is also important to note from Figure 3 that low viscosity fracturing fluid will not cause significant changes in crack expansion and liquid seepage, but high viscosity will promote a rapid increase in crack expansion rate and a decrease in liquid seepage [35].

The reduction in seepage of water-based fracturing fluids within reservoir fractures has been identified as a key factor in enhancing fracture propagation, as demonstrated through molecular dynamics simulations and mechanical analysis. At the microscopic level, polar groups in guar gum, cross-linking agents, and water molecules interact to form intermolecular hydrogen bonds, facilitating the cross-linking of molecules within the water-based fracturing fluid and leading to the formation of a microscopic grid structure. This microscopic grid [36] not only enhances the apparent viscosity of the water-based fracturing fluid but also alters its seepage behaviour within reservoir fractures (Figure 4).

The disparities in fluid percolation behaviour under varying fluid viscosities, as previously referenced, may be attributable to the formation of microscopic grids between molecules and alterations in chemical bond lengths [37]. The structured network of water-based fracturing fluid (Figure 4), formed through the interaction of free molecules via polar groups, reduces the number of free water molecules within the fluid. Consequently, only a negligible amount of free water molecules can infiltrate the reservoir rock through the fracture surface [38]. This observation is consistent with the markedly reduced seepage volume under elevated-viscosity conditions, as shown in Figure 4a. Reduced fluid seepage mitigates significant fracturing fluid seepage, thereby contributing to increased pressure within the reservoir fracture and facilitating its expansion (Equation (9)). Furthermore, the lower viscosity of water-based fracturing fluid results in a higher concentration of free molecules due to weaker intermolecular interactions [39], leading to extensive fluid seepage into the reservoir rock. This excessive seepage inhibits reservoir pressure buildup and slows the fracture propagation rate, whereas higher fluid viscosity exhibits entirely different characteristics. The ability of higher-viscosity fluids to induce rapid fracture propagation primarily stems from their extremely low seepage capacity within dense micro-grid structures, which directly facilitates the rapid buildup of water-based fracturing fluid pressure to the fracture initiation threshold of reservoir fractures [40]. Additionally, the higher micro-grid density associated with increased fluid viscosity enhances resistance to shear forces induced by fluid flow, thereby minimising the generation of free molecules due to shear-induced disruption. In contrast, the weaker micro-grid structure formed under lower fluid viscosity cannot withstand comparable shear forces, which is a key factor contributing to increased fluid seepage and reduced fracture propagation efficiency in low-viscosity conditions [41]. The preceding analysis of fluid viscosity, free molecular concentration, and fracture pressure is corroborated by the intermolecular bond lengths [42] presented in Figure 4b, which provide a clearer explanation of the relationship between fluid seepage and fracture propagation under varying viscosities, as shown in Figure 4a.

3.2. Effect of Reservoir Temperature on Reservoir Seepage and Fracture Propagation

As demonstrated in Figure 5, the effect of reservoir temperature on the flow capacity of water-based fracturing fluid in reservoir fractures is entirely distinct from that of fluid pressure. However, the fracture extension behaviour is analogous to that observed with increasing reservoir temperature and fluid viscosity [43,44]. Alterations in reservoir temperature will result in fluid seepage and fracture expansion exhibiting analogous growth trends, constituting a significant manifestation that is divergent from the influence of fluid viscosity on the aforementioned parameters [45]. The increase in reservoir temperature facilitates the infiltration of water-based fracturing fluid from the surface of reservoir fractures into the surrounding rock, with fluid flow capacity at high temperatures being significantly greater than at low temperatures [46]. Additionally, although a positive correlation between reservoir temperature and fracture propagation is observed, variations in temperature lead to distinct fracture growth patterns. Lower reservoir temperatures result in reduced fracture propagation capacity, whereas higher temperatures induce an exponential increase in fracture propagation.

The Arrhenius equation has been demonstrated to be a useful theoretical framework for understanding the impact of reservoir temperature on the seepage behaviour of water-based fracturing fluid within reservoir fractures [47]. Furthermore, the equation provides a molecular dynamics-based explanation for the mechanism of fracture expansion. It has been shown that lower reservoir temperatures result in the water-based fracturing fluid remaining in reservoir fractures being in a more stable state [48]. This is due to the fact that smaller molecular activity prevents larger irregular motions from forming. The intermolecular hydrogen bonds and microscopic grids formed between molecules will not produce significant extensions or breaks at low reservoir temperatures, thereby reducing the likelihood of microscopic grids becoming thinner at low reservoir temperatures [49,50]. Concurrently, the weaker hydrogen bond stretching or breaking at low reservoir temperatures will also impede the water-based fracturing fluid from forming too many free molecules [51,52], which will cause the water molecules to be dragged by the cross-linking agent and guar gum on a macro scale and unable to seep into the rock through the fracture surface [53,54]. Furthermore, reduced fluid seepage at low reservoir temperatures will result in the majority of water-based fracturing fluid injected into the reservoir fractures being retained. This can lead to more rapid pressure build-up in the reservoir fractures, which in turn can initiate fracture formation and cause rock damage [55,56]. Conversely, higher reservoir temperatures will not only lead to observable fluid seepage behaviour [57], but will also significantly accelerate fracture expansion due to the increasing reservoir temperature. It has been established that elevated reservoir temperatures can substantially augment the movement activity of each molecule in the water-based fracturing fluid. This can result in irregular Brownian motion between molecules. The augmented movement frequency engenders continuous stretching of the hydrogen bonds formed between molecules [58], with the molecules exhibiting greater activity also breaking the molecules to form free molecules. Furthermore, higher reservoir temperatures can increase the repulsive force between molecules of the same polarity, thereby also stretching and breaking the hydrogen bonds between molecules [29,59]. The molecules that are formed at elevated temperatures lack the pullback of guar gum and cross-linking agents in the water-based fracturing fluid [60,61]. These molecules will rapidly reach the surface pores of the reservoir rock and seep into the rock. Although more fluid seeps into the reservoir rock at higher temperatures, the molecular diffusion and exclusion caused by high temperature also increase the fluid volume of the water-based fracturing fluid [62,63]. The enhanced fluid volume at elevated temperatures can expedite the internal pressure of the reservoir fracture, which is associated with the accelerated expansion of the reservoir fracture. Consequently, while elevated reservoir temperatures can result in water-based fracturing fluid seepage, the concurrent fracture expansion can effectively mitigate the aforementioned defects [64,65].

3.3. Effects of Rock Porosity on Reservoir Seepage and Fracture Propagation

Geological parameters of reservoir rock significantly influence the seepage and filtration capacity of water-based fracturing fluids [66]. Moreover, variations in geological reservoir parameters induce substantial changes in fracture propagation behaviour [67,68]. Figure 6 illustrates the relationship between the initial porosity of the reservoir rock and the seepage and fracture propagation characteristics of water-based fracturing fluids. The seepage volume of water-based fracturing fluid gradually increases with rising rock porosity [69,70]. However, as porosity increases, fracture propagation exhibits a decreasing trend, with distinct fracture growth patterns emerging across different porosity ranges [71,72]. Lower rock porosity not only results in reduced seepage of water-based fracturing fluid but also facilitates the development of larger reservoir fractures, as weaker fluid seepage under low porosity enhances fracture expansion parameters (e.g., fracture length and width) [73,74]. Conversely, at higher rock porosity, an exponential increase in reservoir seepage is observed, inevitably leading to a rapid decline in fracture propagation [75].

The seepage of water-based fracturing fluid within the reservoir rock primarily occurs along the fracture surface where normal-phase flow dominates, directly driving the pressurised fluid into the reservoir rock through surface pores [76,77]. When flowing through low-porosity reservoir rock, water-based fracturing fluid within the fracture infiltrates the reservoir pores along the rock surface. The reduction in pore size leads to an instantaneous increase in the shear effect exerted by the fluid [78,79]. Shear-induced free molecules enhance fluid seepage, subsequently reducing pressure within the fracture. The diminished fluid pressure in the reservoir fracture fails to exceed the fracture initiation pressure of the reservoir rock [80,81], thereby decelerating fracture propagation. However, the gel state of cross-linking agents and guar in the water-based fracturing fluid progressively obstructs reservoir pores upon entering low-porosity formations, mitigating excessive fluid seepage. Simultaneously, the blockage of normal pores by the gel forces the fracturing fluid within the reservoir fracture to rapidly reach the fracture initiation pressure of the reservoir rock [82,83]. The high porosity of reservoir rock facilitates the infiltration of a substantial volume of injected water-based fracturing fluid into the formation through rock pores on the normal surface [84], leading to a significant reduction in fluid pressure within the reservoir fracture [85]. The pressure loss caused by fluid seepage prevents the fracture pressure from reaching the minimum threshold required for rock fracturing, thereby slowing the propagation rate of reservoir fractures [86,87]. Additionally, the gel present in the water-based fracturing fluid fails to accumulate in larger pores, preventing the reduction in fluid seepage that typically results from gel blockage [88,89]. The slower pressure buildup within the reservoir further limits the potential for fracture propagation. Consequently, although the rock porosity may induce gel-related formation damage, the increased fracture propagation contributes to enhanced energy recovery.

3.4. Effects of Reservoir Pressure on Reservoir Seepage and Fracture Propagation

Reservoir pressure is a critical factor influencing the physical and chemical properties of oilfield working fluids and crude oil in geological formations, as it significantly alters the rheological parameters and fracture propagation behaviour of water-based fracturing fluids, as shown in Figure 6. As demonstrated in Figure 7, reservoir pressure plays a crucial role in preventing the infiltration of water-based fracturing fluids into reservoir rocks through the normal surface of reservoir fractures. The figure also illustrates the expansion capacity of reservoir fractures as reservoir pressure gradually increases. However, it is essential to note that low reservoir pressure results in a relatively weaker reduction in fluid seepage. In contrast, higher reservoir pressure induces a more pronounced exponential decline in fluid seepage. The distinct growth trends observed under varying reservoir pressures are reflected in the behaviour of reservoir fractures, which can be primarily attributed to the effect of reservoir pressure on the hydrogen bonding between water-based fracturing fluid molecules and the pressure within fractures [90,91].

Lower reservoir pressure alters the morphology and quantity of hydrogen bonds between guar gum and water molecules in water-based fracturing fluid, exerting a decisive influence on its rheological properties and seepage behaviour [92,93]. At low reservoir pressure, a limited number of free molecules at a distance form intermolecular hydrogen bonds due to the attraction of polar groups, which slightly constrains a small fraction of free water molecules interconnected by microscopic grids and intermolecular hydrogen bonds [94,95]. The inherently low concentration of free molecules in the water-based fracturing fluid is further restricted by the drag effect of guar gum, preventing their infiltration into the reservoir rock through surface pores within the fracture [96,97]. However, the marginal enhancement in fluid seepage capacity results in only a slight improvement in fracture propagation [98,99]. Achieving optimal fracture propagation requires reduced fluid seepage under elevated reservoir pressure [100,101]. Elevated reservoir pressure gradually reduces the bond length of existing intermolecular hydrogen bonds, thereby increasing their bond energy within the water-based fracturing fluid [102,103]. Simultaneously, free molecules that remain unbonded under low reservoir pressure form new hydrogen bonds under high-pressure conditions [104,105], significantly reducing the number of free molecules in the fracturing fluid [106,107].

The continuous shortening of hydrogen bonds, along with the formation of new intermolecular hydrogen bonds, enhances the microscopic grid density within the water-based fracturing fluid [108,109]. Consequently, water molecules experience stronger drag forces from guar gum molecules, preventing their infiltration into rock pores along the normal direction of the fracture [110,111]. Reduced fluid seepage facilitates the rapid buildup of fracturing fluid pressure to the rock fracture initiation threshold, leading to an exponential increase in fracture propagation [112,113], as illustrated in the high-reservoir-pressure range of Figure 6. Thus, the influence of reservoir pressure on the seepage of water-based fracturing fluid in fractures and fracture propagation is primarily attributed to the morphological changes in microscopic hydrogen bonds [114,115]. The increased bond energy of intermolecular hydrogen bonds and the higher microscopic grid density under elevated pressure effectively promote the retention of water-based fracturing fluid within reservoir fractures [116,117,118], thereby achieving efficient pressure maintenance [119,120].

4. Conclusions

The numerical model developed in this study for evaluating the performance of water-based fracturing fluids in reservoir fractures enables a comprehensive and accurate assessment of their limitations, particularly the weak fracture propagation and severe seepage observed during reservoir stimulation. The findings further demonstrate that incorporating a cross-linking agent to enhance fluid viscosity can effectively mitigate excessive seepage and improve fracture propagation, while reservoir conditions (e.g., temperature and pressure) also exert significant influence on the effectiveness of water-based fracturing fluids in promoting fracture growth. Moreover, the identified relationships among fluid viscosity, fluid seepage, and fracture propagation under varying conditions provide new insights for elucidating the underlying mechanisms and for identifying potential improvement strategies. Finally, the three-dimensional micro-grid model constructed in this study has been validated as applicable for analysing the coupled effects of water-based fracturing fluids on fracture pressure and propagation under diverse reservoir conditions. The numerical model constructed in this study only considers simple fracture propagation in homogeneous rocks, which is inherently inadequate for fracture propagation in complex fracture networks within heterogeneous reservoirs. It is inevitable that future research will concentrate on the fracture propagation behaviour in complex fracture networks based on realistic geological parameters. This will make numerical models more practical for application.