Analysis of the impact of CO₂ injection on fracturing fluid flowback in shale gas wells

Abstract

With the ongoing development of oil and gas resources, low-permeability tight reservoirs have become a focal point of research and technological innovation. To effectively address the challenges associated with fracture fluid retention, this study investigates the role of CO₂ in reservoir stimulation and productivity enhancement. The results reveal that liquid CO₂ induces a rapid temperature reduction in shale samples during the initial phase of injection with a temperature decrease of 16.1 °C observed within the first 10 min. However, the cooling rate diminishes significantly in the later stages, with only a 0.8 °C decrease recorded over the subsequent 10 min which indicating a distinct endothermic effect. The high diffusivity and low viscosity of CO₂ are key to its effectiveness in enhancing reservoir pressure and improving fracture conductivity. Additionally, the expansion-induced cooling effect of CO₂ lowers wellbore temperatures, thereby lowering the viscosity of the fracturing fluid and improving its mobility. A stable pressure gradient provides the driving force for efficient fracture fluid recovery, which significantly boosting recovery efficiency and productivity. The results further indicate that at injection rates of 5000 m³/d, 10,000 m³/d, and 15,000 m³/d, the recovery volumes are 97%, 96%, and 88% higher than those achieved with water-based fracturing fluids, respectively. These findings demonstrate the significant advantages of CO₂ injection in increasing reservoir pressure and promotes the flow of oil and gas at the well bottom. The promising application potential of CO₂ in low-permeability tight reservoirs underscores its value as an innovative approach to reservoir stimulation and productivity optimization. This study provides the first comprehensive analysis of CO₂'s dual role in enhancing flowback efficiency through thermal, mechanical, and fluid dynamic interactions, offering a paradigm shift from conventional water-based fracturing.

Introduction

With the continuous growth in global oil and gas consumption, the reliance on conventional oil and gas resources is increasingly insufficient to meet societal energy demands. Consequently, the development of tight reservoir oil and gas which cannot be effectively developed using conventional methods has emerged as a critical area of research^1,2,3. Large-scale volumetric fracturing is commonly employed for the development of tight reservoirs. Field data from both domestic and international operations indicate that the flowback rates of fracturing fluid in tight reservoirs are generally low. In shale oil and gas wells in the United States, flowback rates typically ranges from 10 to 30%⁴, with some areas reporting rates below 10%⁵. In contrast, flowback rates for shale oil and gas wells in China are as low as 5–10%⁶. Unlike conventional reservoirs, low flowback rates do not adversely affect shale gas production. This unique flowback characteristic challenges the applicability of conventional reservoir protection theories, rendering traditional flowback processes unsuitable for tight reservoir development. To address this challenge, this study investigates the effects of CO₂ injection on the flowback efficiency of fracturing fluids in tight reservoirs that providing a solution to the issue of low flowback rates. The scope of this research includes: (1) laboratory simulations to analyze changes in reservoir pressure, fluid mobility, and fracture conductivity during CO₂ injection. (2) Numerical simulations to evaluate the flowback efficiency of fracturing fluids under varying injection rates and CO₂ phase conditions which in comparison to conventional water-based fracturing fluids. (3) A comprehensive mechanisms analysis to summarize how CO₂ injection enhances flowback efficiency and improves reservoir production performance. This research aims to provide theoretical insights and technical guidance for optimizing shale gas reservoir development.

The primary challenges associated with fracturing fluid flowback can be categorized two aspects: (1) minimizing proppant flowback to maintain fractures with high conductivity, (2) increasing flowback speed and rate to reduce reservoir damage⁷. Consequently, research on reservoir flowback focuses on optimizing flowback methodologies, enhancing flowback rates, and controlling proppant flowback^8,9,10,11,12. Extensive simulation and physical experiments have been conducted by scholars worldwide to address these issues. Zhang and Ehlig-Economides¹³ analyzed data from 15 shale gas wells in the Horn River area and 17 wells in the Barnett area. They discovered that in logarithmic coordinates, the water–gas ratio (WGR) curve of shale could be divided into two distinct regions. It provided valuable insights into water production mechanisms in shale formations. Dahi¹⁴ investigated the mechanisms of fracture closure during the flowback process after hydraulic fracturing. Using a geomechanics and fluid flow coupled model, they revealed the influence of in-situ stress on fracturing fluid recovery rates. Three fracture network closure modes were proposed and validated their theoretical model. Mao et al.¹⁵ conducted high-temperature and high-pressure laboratory experiments to study the mechanism of CO₂ miscible fracturing fluid during core displacement experiments and analyzed the dominant controlling factors. Zhang et al.¹⁶ developed a comprehensive fracturing fluid flowback optimization model by integrating data obtained from experiments, and implemented it through MATLAB programming. Zhang et al.¹⁷ considered the mechanisms of fracturing fluid retention and flowback in the branching fractures, and conducted a detailed analysis of the fracture surface morphology using macroscopic laser scanning technology, low-field nuclear magnetic resonance equipment, and permeability testing devices.

In addressing the issues of improving the recovery rate and controlling the flowback of proppants, Du et al.¹⁸ developed CO₂-responsive surfactant fracturing fluids using tertiary amine-type surfactants and studied their main properties using different methods. Zhao et al.¹⁹ focused on the characterization of post-fracturing flowback characteristics in shale reservoirs, considering the fracture opening-closure characteristics during the injection and flowback processes of the fracturing fluid and the nonlinear matrix seepage characteristics. They quantitatively evaluated the impact of reservoir physical parameters and complex fracture morphology on post-fracturing flowback characteristics. Xu et al.²⁰ investigated the variation of fracture conductivity during the integrated process of fracturing and flowback in shale gas reservoirs. By considering the production characteristics of shale gas reservoirs, they simulated the entire process of fracturing—flowback—production, conducted fracture conductivity tests in three continuous stages (gas measurement—liquid measurement—gas measurement), and studied the variation of fracture conductivity throughout the process. Wang et al.²¹ established a flowback model to simulate the flowback behavior of fluids and proppants carried in the re-compacted fracture systems of mud shale Wells in Wales. They introduced the development of fluid pressure and proppant concentration profiles in fractured shale wells and calculated the flux of fluid and proppants between hydraulic fractures and induced fractures. Li et al.²² addressed the numerous defects caused by the extremely low apparent viscosity of supercritical CO₂ fracturing fluids, such as low proppant transport capacity, severe loss, and weak fracturing effects. They studied the impact of different geological conditions and chemical agents on the proppant transport performance of CO₂, revealing the proppant transport mechanism of supercritical CO₂ fracturing fluids.

However, previous studies on the fracturing fluid flowback process have not addressed the impact of CO₂ on the reservoir, the properties of the fracturing fluid, or wellbore characteristics affecting flowback behavior. Therefore, this research simulates the CO₂ injection process in a laboratory setting to investigate the evolution of reservoir pressure, fluid mobility, and fracture conductivity during this process. The study employs numerical simulation techniques to assess the efficiency of fracturing fluid flowback under various injection rates and CO₂ phase conditions, and it compares these results with those from traditional water-based fracturing fluids. Ultimately, the research summarizes the underlying principles by which CO₂ injection enhances the efficiency of fracturing fluid flowback and optimizes reservoir productivity.

The impact of fracturing fluid retention and CO₂ on reservoirs

Damage to reservoirs caused by fracturing fluid retention

The phenomenon of fracturing fluid retention refers to the inability of a portion of the fracturing fluid to flow back promptly following fracturing operations that leaving residual fluid in the reservoir and fractures. Modern fracturing fluids are typically composed of natural and synthetic polymers while many of which contain components that are resistant to decomposition or degradation. These retained substances can cause irreversible reservoir damage by trapping hydrocarbons within pore spaces and significantly impeding their mobility. Additionally, the interfacial tension exacerbates the water-blocking effect that further hindering reservoir productivity during later stages of production. Research conducted by domestic and international scholars categorizes the damage caused by fracturing fluids into four primary mechanisms: fracturing fluid filter cake damage, water-blocking damage, clay swelling damage, and solid-phase residue damage from fracturing fluids²³ (Fig. 1).

Fig. 1

Schematic diagram of the damage mechanisms of fracturing fluids on reservoirs.

During fracturing operations, particles and impurities within the fracturing fluid may form a filter cake on the surface of reservoir fractures. This filter cake blocks the fracture walls (Fig. 1a), impeding proppant flowback and reducing fracture permeability. However, its presence reduces reservoir permeability and hinders fluid flowback. During the flowback process, the filter cake may become compacted. Exacerbating permeability loss and impeding the efficient recovery of fracturing fluid and hydrocarbons.

Water-blocking damage occurs when the water from the fracturing fluid becomes trapped in the reservoir pores during the fracturing process. It forming blockages that hinder hydrocarbon flow (Fig. 1b). This phenomenon increases capillary forces within the reservoir while water occupies fracture and pore spaces, significantly reducing flow pathways. As a result, hydrocarbons are unable to flow efficiently out of the pores that adversely affecting reservoir production. When fracturing fluid interacts with clay minerals present in the reservoir, the clay swells to and blocking fractures as well as reducing their conductivity. Swollen clay may also fill the space between the proppant and fracture walls (Fig. 1c), reducing fracture conductivity. In severe cases, clay swelling can result in operational failures, including well shutdowns.

Solid-phase residue damage is caused by the retention of solid particles from the fracturing fluid that cannot be completely removed during the flowback process. These particles may permanently block fractures and pores (Fig. 1d), severely impairing reservoir productivity. Additionally, these solids can react chemically with reservoir fluids, forming new precipitates that further damage the reservoir. The retention of fracturing fluids and the associated damage mechanisms present significant challenges to tight reservoir development and productivity enhancement. Understanding these mechanisms and their implications is critical for optimizing fracturing fluid formulations, improving flowback efficiency, and mitigating long-term reservoir damage.

To mitigate the damage caused by fracturing fluid retention to the formation, CO₂ injection is utilized to reduce the adverse effects on the reservoir and fractures. Traditional water-based fracturing fluids create significant capillary resistance in shale pores due to their higher interfacial tension, leading to a decrease in gas-phase permeability by more than 70%. The injection of CO₂ can alleviate water block damage through two mechanisms: adjusting the interfacial tension and altering the wettability. Since the interfacial tension between CO₂ and gas is significantly lower than that between water and gas, CO₂ injection can displace the retained fracturing fluid in the pores, thereby reducing capillary resistance. Unconventional reservoirs containing water-sensitive clay minerals such as illite and montmorillonite undergo water absorption and swelling when in contact with fracturing fluids, leading to fracture closure. From a chemical perspective, CO₂ acidifies the formation, promoting the exchange of H+ ions for Na+ and K+ ions in the clay layers, which reduces the cation exchange capacity. The dissolution of calcite (CaCO₃) in an acidic environment releases Ca²⁺, which competes with Al³⁺ for adsorption sites on the clay surface, inhibiting the swelling effect. Based on the comprehensive influence of these mechanisms, fracturing fluid retention typically results in a decline in production capacity, accelerated initial production decline, and reduced long-term recovery rates.

Experimental study on the impact of CO₂ on shale reservoirs

This study proposes the use of CO₂ fracturing fluid for fracturing operations. Compared to other fracturing fluids, CO₂ exhibits a stronger adsorption capacity²⁴, while also facilitating the underground storage of adsorbed gas^25,26,27. Shale contains a variety of complex mineral components, including carbonates, clays, quartz, and pyrite. Under reservoir conditions, injected CO₂ dissolves in formation water to form an acidic solution, which reacts geochemically with shale minerals, altering the physical properties of the shale reservoir. Therefore, this section conducts laboratory simulations to investigate the impact of CO₂ fracturing fluid injection on reservoirs, focusing on the effects of different CO₂ phases on rocks. Since this study targets shale reservoirs, the experimental samples used are shale cores.

The full-diameter core is processed through drilling, cutting, and polishing into cylindrical specimens measuring 25 mm × 50 mm (Fig. 2). To ensure the accuracy and consistency of experimental results, the core is drilled perpendicular to the bedding planes. The processing precision of the specimens must meet the following criteria: top and bottom surface parallelism < 0.005 mm, surface flatness < 0.02 mm, diameter deviation along vertical height < 0.3 mm, and the maximum deviation of the end face from the vertical axis < 0.25°.

Fig. 2

Partial shale specimens.

The experimental setup includes a CO₂ soaking test device and a rock heating test device. This experiment aims to investigate the effect of CO₂ on the temperature of shale reservoirs and conduct uniaxial compression tests on shale before and after soaking in different fluids. The experimental equipment includes a CO₂ soaking test device. As shown in Fig. 3, the CO₂ soaking test device mainly consists of a gas source, a constant-rate and constant-pressure displacement pump, an intermediate container, a CO₂ heating coil, a reactor, a high-temperature drying oven and temperature–pressure sensors.

Fig. 3

Schematic diagram of the soaking experiment device.

Based on the actual conditions of the target reservoir H1 well and thermodynamic coupling effects, the experimental temperature was set to 120 °C. This temperature choice was made to simulate typical medium-to-high temperature reservoir conditions, while also considering the evolution of the fluid and core’s physicochemical properties and oil displacement behavior in a high-temperature environment. Additionally, the temperature was selected to ensure the high-temperature tolerance and safety of the experimental equipment. This temperature not only reflects the true thermodynamic, mass transfer, and heat transfer characteristics of high-temperature reservoirs, but also ensures the long-term operational stability of the apparatus during the experiment.

Before the experiment, the specimens were dried in an oven at 120 °C for 24 h to remove moisture and ensure the stability of their initial mass and physical properties. The weight of the dried specimens was recorded as the baseline mass to ensure accurate measurements during the experiment. A constant-temperature electric furnace was used during the experiment, maintaining a steady temperature of 120 °C for 20 min to ensure a consistent temperature throughout the heating process. The specimens were placed in high-temperature-resistant ceramic crucibles to ensure chemical stability and physical integrity during the heating process. After placing the shale specimens, they were heated for 30 min and then maintained at a constant temperature for 2 h to achieve uniform internal and external temperatures. The heated shale specimens were quickly removed from the constant-temperature furnace and immediately immersed in liquid CO₂ pre-cooled to 10 °C with a pressure above 10 MPa. A high-precision thermocouple temperature sensor was used to measure the specimen temperature. Since it was not possible to insert measurement instruments into the core, the surface temperature of the shale specimens was measured. The thermocouple temperature sensor monitored the specimen temperature in real time. The specimen temperature was recorded every 10 min until it dropped to match the temperature of the liquid CO₂. The temperature variation is shown in Fig. 4.

Fig. 4

Temperature variation of shale samples after immersion.

The three shale samples exhibited differentiated cooling trends during the cooling process, primarily influenced by the heterogeneity of thermal conductivity, pore structure, and mineral composition. For sample S1, the high thermal conductivity and open pores allowed for rapid heat dissipation in the early stage, while in the mid-stage, pore water retention created a thermal barrier, resulting in a slowdown in the temperature decrease rate. Sample S2 experienced uniform cooling due to its homogeneous structure. In the case of S3, the high clay content inhibited heat transfer in the early stage, but in the mid-stage, thermal fracturing extended fractures, accelerating heat dissipation. At 60–70 min, the cooling rate of all three shale samples significantly slowed down. This was due to the weakening of the thermodynamic driving force (as the temperature of the experimental samples approached ambient temperature and microfractures appeared), the limited release of remaining stored energy, and the reduction in convective heat transfer efficiency caused by local thermal saturation in the medium. This phenomenon reflects the heterogeneous characteristics of shale’s thermal response and the common thermodynamic equilibrium trends.

Wellbore model establishment

This chapter analyzes the impact of CO₂ on fracturing fluid flowback, exploring how different types of fracturing fluids affect flowback rates. It examines the factors influencing the effect of pre-injected CO₂ on flowback efficiency and investigates the mechanisms of CO₂ injection affecting flowback through simulation experiments. The goal is to provide theoretical support for optimizing fracturing fluid flowback design.

To better simulate field conditions, it is necessary to calculate the pressure field, temperature field, and multiphase flow characteristics within the wellbore. During the modeling process, the temperature data obtained from the experiments in Chapter 2 should be incorporated into the temperature field calculations to ensure the accuracy of the study (Fig. 5).

Fig. 5

Schematic diagram of two-dimensional meshing of fracturing fluid leak-off.

Based on the principle of material balance and neglecting the compressibility of the fracturing fluid and formation rock, a volume balance equation was established²⁸. After hydraulic fracturing operations, when the wellhead is not opened for flowback, the filtrate volume of the fracturing fluid should be equal to the fracture closure volume:

$$V_{y} \left( {t_{n} } \right) = {\Delta }V_{f} \left( {t_{n} } \right)$$

(1)

According to the volume balance principle, when the wellhead is opened, the fracture volume reduction is approximately equal to the sum of the fracturing fluid flowback volume and the fracturing fluid filtrate volume.

$${\Delta }V_{f} \left( {t_{n} } \right) = V_{y} \left( {t_{n} } \right) + V_{fc} \left( {t_{n} } \right)$$

(2)

where, $\Delta {V}_{f}({t}_{n})$ represents the fracture closure volume; ${V}_{y}({t}_{n})$ represents the filtrate volume; ${V}_{fc}({t}_{n})$ represents the fracturing fluid flowback volume.

From the derivation process, it can be seen that the fracture reduction, fracturing fluid filtrate volume, and fracturing fluid flowback volume are all functions of the bottomhole pressure at time ${t}_{n}$. Therefore, by iteratively calculating the bottomhole pressure, when the bottomhole pressure equals the fracture closure pressure, the fracture is considered closed, and this moment is recorded as the fracture closure time. The wellhead pressure is then calculated by subtracting the static liquid column pressure and frictional head loss from the bottomhole pressure, as shown in the following equation:

$$p\left( {t_{n} } \right) = p_{f} \left( {t_{n} } \right) - p_{h} - {\Delta }p\left( {t_{n} } \right)$$

(3)

where, $p({t}_{n})$ is the wellhead pressure at time ${t}_{n}$(MPa); ${p}_{f}({t}_{n})$ is the formation pressure at time ${t}_{n}$ (MPa); ${p}_{h}$ is the static liquid column pressure (MPa); $\Delta p({t}_{n})$ is the frictional head loss at time ${t}_{n}$ (MPa).

Fracturing Fluid Filtrate Calculation Model:

For the calculation of fracturing fluid filtrate, a two-dimensional single-phase flow model is used to establish the differential equation for the filtrate volume²⁹. During the fracturing fluid filtrate process, the pressure gradient near the fracture is large, while the pressure gradient far from the fracture is small. Therefore, a finite difference method is used to solve the above flow differential equation based on the initial and boundary conditions. Then, according to Darcy’s law of flow³⁰, the equation is given by:

$$V_{y} \left( {t_{n} } \right) = V_{y} \left( {t_{n - 1} } \right) + 4\mathop \sum \limits_{i = 0}^{m} \left( {\frac{{k_{d} }}{\mu }\frac{{p_{f} \left( {t_{n} } \right) - p_{i,1} \left( {t_{n} } \right)}}{{\Delta y_{1} }}l_{xi} H_{w} } \right)dt$$

(4)

where, ${k}_{d}$ is the reservoir permeability (μm²); $\mu$ is the fracturing fluid viscosity (Pa s); $m$ is the number of grid points in the X-direction; ${H}_{w}$ is the fracture height (m); $\Delta {y}_{1}$ is the length of the first grid point in the Y-direction (m); ${l}_{xi}$ is the length of the i grid in the X-direction; dt is the time step (s); ${V}_{y}({t}_{n-1})$ is the fracturing fluid filtrate volume at time ${t}_{n-1}$ (m³).

Hydraulic Fracture Volume Reduction Calculation Model:

This study assumes that after the completion of the fracturing operation, the fracture stops extending, and during the fracture closure, the fracture length and height no longer change. To calculate the fracture volume during the fracturing fluid flowback process, the fracture cross-section is assumed to be an elliptical section, with the fracture width as the semi-major axis. The fracture volume reduction at time ${t}_{n}$ is calculated using a three-dimensional fracture model³¹.

$$\begin{aligned} \Delta V_{f} \left( {t_{n} } \right) & = \frac{\pi }{4}H_{w} L_{p} \left[ {W\left( {t_{o} } \right) - W\left( {t_{n} } \right)} \right]M \\ & = \frac{{\pi \left( {l - \gamma^{2} } \right)}}{2E}\left[ {P_{s} + P_{h} - P_{f} \left( {t_{n} } \right)} \right]H_{w}^{2} L_{p} M \\ \end{aligned}$$

(5)

$$W\left( {t_{n} } \right) = \left\{ {\begin{array}{*{20}l} {\frac{{2\left( {1 - \gamma^{2} } \right)H_{w} }}{E}\left[ {P_{f} \left( {t_{n} } \right) - s_{1} } \right],H_{w} \le H_{P} } \hfill \\ {\frac{{2\left( {1 - \gamma^{2} } \right)H_{w} }}{E}\left[ {P_{f} \left( {t_{n} } \right) - s_{1} } \right] - \frac{{4\left( {1 - \gamma^{2} } \right)H_{w} }}{\pi E}\left( {s_{2} - s_{1} } \right) \times \left[ {\cos^{-1} \frac{{H_{P} }}{{H_{w} }} - \frac{{H_{P} }}{{H_{w} }}\ln \frac{{H_{w} + \sqrt {H_{w}^{2} - H_{P}^{2} } }}{{H_{P} }}} \right]} \hfill \\ \end{array} } \right.$$

(6)

$$M = \frac{{l.0IH_{P} }}{{H_{w} }} + \frac{l}{{\sqrt {l - \frac{{l.0IH_{P} }}{{H_{w} }}} }}\sin^{ - l} \sqrt {1 - \frac{{l.0IH_{P} }}{{H_{w} }}}$$

(7)

Fracturing Fluid Flowback Volume Calculation Model:

After the flowback begins, the fracturing fluid flows out of the wellbore through the wellhead. The wellhead is treated as the object of study, and using Bernoulli’s equation and the continuity equation, the fracturing fluid flowback velocity at time ${t}_{n}$ is derived. By integrating the time, the cumulative flowback volume is obtained. Since the function of wellhead pressure in the integral expression is nonlinear, the composite trapezoidal rule is used for discretization. The fracturing fluid flowback volume calculation equation is given by³¹:

$$V_{fc} \left( {t_{n} } \right) = \frac{\Delta t}{2}\left\{ \begin{aligned} & \left[ {p_{f} \left( {t_{0} } \right) - 0.1} \right]^{0.5} + \left( {p_{f} \left( {t_{n} } \right) - p_{h} - \Delta p\left( {t_{n} } \right) - 0.1} \right)^{0.5} \\ & \quad + 2\mathop \sum \limits_{i = 1}^{n - 1} \left( {p_{f} \left( {t_{i} } \right) - p_{h} - \Delta p\left( {t_{i} } \right) - 0.1} \right)^{0.5} \\ \end{aligned} \right\} \cdot Con$$

(8)

$$Con = 1.414 \times 10^{3} \pi r^{2} \rho_{y}^{ - 0.5} \left[ {1 + \xi - \frac{{r^{4} }}{{R^{4} }}} \right]^{ - 0.5}$$

(9)

$${\Delta }p\left( {t_{n} } \right) = \frac{{\rho_{y} \lambda L\nu_{1} (t_{n} )^{2} }}{2D}$$

(10)

where, ${\rho }_{l}$ is the fracturing fluid density (kg/m³); $\xi$ is the nozzle pressure loss coefficient; $\lambda$ is the frictional resistance coefficient; $D$ is the wellbore diameter (m); $L$ is the wellbore length (m); $R$ is the wellbore radius (m); $r$ is the nozzle radius of the casing (m); ${V}_{1}({t}_{n})$ is the fracturing fluid velocity inside the wellbore at time ${t}_{n}$ (m/s).

Proppant Critical Flowback Velocity Calculation Model:

Proppant Critical Flowback Velocity Calculation Model: During the fracturing fluid flowback process, if the flowback rate is too large, the proppant will be carried back into the wellbore. The minimum flow rate that causes proppant to flowback due to fracturing fluid is defined as the critical flowback velocity for proppants. In this study, the proppant particles are assumed to have a spherical shape. Through proppant force analysis, the critical velocity for proppant flowback is derived:

Before fracture closure, the liquid bridge force can be neglected, and the downhole pressure should be considered. Closure stress does not directly act on the proppant particles.³²

$$\begin{aligned} & When,\;N_{Re} \le 2, \\ & v_{c} = \frac{1}{{\left( {tg\alpha + \beta } \right)}}\left[ {\frac{{d_{s}^{2} g\left( {\rho_{z} - \rho_{y} } \right)}}{18\mu } + \frac{{\rho_{y} gh_{s} \delta }}{96\mu }} \right] \\ \end{aligned}$$

(11)

$$\begin{aligned} & When,\;2 < N_{{\text{Re}}} \le 500, \\ & v_{c} = \left\{ {\frac{1}{tg\alpha + \beta }\left[ {\frac{{8\left( {\rho_{z} - \rho_{y} } \right)gd_{s}^{1.6} }}{{111\rho_{y}^{0.4} \mu^{0.6} }} + \frac{{\rho_{y}^{0.6} gh_{s} \delta }}{{74d_{s}^{0.4} \mu^{0.6} }}} \right]} \right\}^{\frac{5}{7}} \\ \end{aligned}$$

(12)

$$\begin{aligned} & When\;N_{Re} > 500, \\ & v_{c} = \sqrt {\frac{1}{{\left( {tg\alpha + \beta } \right)}}\left( {\frac{{d_{s} \left( {\rho_{z} - \rho_{y} } \right)g}}{{0.33\rho_{y} }} + \frac{{gh_{s} \delta }}{{1.76d_{s} }}} \right)} \\ \end{aligned}$$

(13)

After fracture closure, there is a liquid bridge force, while the downhole pressure can be neglected, and closure stress directly acts on the proppant particles. Therefore, the critical flowback velocity for proppants is given by³³:

$$\begin{aligned} & When,\;N_{Re} \le 2, \\ & v_{c} = \frac{1}{tg\alpha + \beta }\left[ {\frac{{d_{s}^{2} g\left( {\rho_{z} - \rho_{y} } \right)}}{18\mu } + \frac{\gamma \cos \alpha }{{3\mu }}} \right] \\ \end{aligned}$$

(14)

$$\begin{aligned} & When,2 < N_{Re} \le 500 \\ & \nu_{c} = \left\{ {\frac{1}{tg\alpha + \beta }\left[ {\frac{{8d_{s}^{1.5} \left( {\rho_{s} - \rho_{l} } \right)g}}{{111\rho_{y}^{0.4} \mu^{0.6} }} + \frac{16\gamma \cos \alpha }{{37d_{s}^{0.4} \rho_{y}^{0.5} \mu^{0.6} }}} \right]} \right\}^{\frac{5}{7}} \\ \end{aligned}$$

(15)

$$\begin{aligned} & When,\;N_{Re} > 500, \\ & \nu_{s} = 0.0011^{{\frac{2n}{{3n - 1}}}} \left[ {\frac{{9\tau_{c} \left( {2n^{2} + n + 1} \right)}}{K}} \right]^{{\frac{1}{3n - 1}}} \cdot \left[ {\frac{{g\left( {\rho_{z} - \rho_{y} } \right)d_{s}^{n + 1} }}{18K}} \right]^{{\frac{1}{3n - 1}}} \\ \end{aligned}$$

(16)

$$v_{sp} = f_{c} f_{w} v_{s}$$

(17)

$$f_{c} = 1.0693e^{ - 4.24c}$$

(18)

$$f_{w} = \left\{ {\begin{array}{*{20}l} {1 - 0.16\mu^{0.28} \frac{{d_{s} }}{w}\frac{{d_{s} }}{w} < 0.9} \hfill \\ {8.26e^{ - 0.0061\mu } \left( {1 - \frac{{d_{s} }}{w}} \right)\frac{{d_{s} }}{w} \ge 0.9} \hfill \\ \end{array} } \right.$$

(19)

$$L_{s} = \nu_{sp} \cdot t_{s}$$

(20)

$$\eta_{s} = \frac{{L_{s} }}{{H_{w} }} \cdot 100{\% }$$

(21)

where, ${N}_{Re}$ is the Reynolds number; $\beta$ = $\frac{{C}_{l}}{{C}_{d}}$, ${C}_{l}$ is the lift coefficient, ${C}_{d}$ is the drag coefficient, $\beta$ is set to 0.25; $\alpha$ is the proppant closure stress direction; $\gamma$ is the surface tension (N/m); $\delta$ is the liquid film coefficient (value is 0.213 × 10⁻⁶); ${h}_{s}$ is the distance between the proppant and the fracture tip (m); ${d}_{s}$ is the proppant diameter (m); ${\rho }_{z}$ is the proppant density (kg/m³); ${\rho }_{y}$ is the fracturing fluid density (kg/m³); $\mu$ is the fracturing fluid viscosity (Pa s).

Using the above equations, simulation experiments were conducted by inputting parameters from Tables 1, 2 and 3 into the simulation software to model the CO₂ injection into the formation for facilitating fracturing fluid flowback. Since this simulation focuses on CO₂ gas lift, the injected fluid was defined as CO₂ with a molar fraction of 1, while the fractions of hydrogen sulfide, nitrogen, and hydrogen were all set to 0.

Table 1 CO₂ gas parameters table.

Table 2 Thermodynamic & transport properties.

Table 3 Simulation parameters.

The final simulation diagram, as shown in Fig. 6, consists of tubing fluid, tubing, gas layer casing, surface casing, gas lift valve, annular fluid, and cement sheath.

Fig. 6

Wellbore structure modeling diagram.

Analysis of the impact of CO₂ injection on fracturing fluid flowback

This chapter analyzes the impact of CO₂ injection on reservoir production and fracturing fluid flowback through simulation diagrams (including gas flow rate, temperature, and pressure distribution) and experimental data on the mechanical properties of shale samples under different CO₂ phases. Additionally, the flowback performance of fracturing fluid after water injection is simulated and compared with that after CO₂ injection.

Changes in the wellbore after gas injection

As shown in Fig. 7, the gas flow rate increases rapidly in the CO₂ injection region (2000 m), indicating that the high diffusivity and low viscosity of CO₂ have overcome the flow limitations of traditional water-based fracturing fluids. The increase in gas flow rate not only enhances gas well productivity but also reflects the high diffusivity and mobility of CO₂ in the reservoir after injection. Additionally, CO₂ reduces the compressive strength of the shale reservoir and weakens the cohesion of the rock, significantly improving the conductivity of the fracture network. This provides a more efficient pathway for fluid removal, with the flowing gas carrying more of the retained fracturing fluid out of the reservoir, thereby facilitating fracturing fluid flowback.

Fig. 7

Relationship between gas flow rate, temperature, and pressure with well depth after CO₂ injection.

During the CO₂ injection process, as the temperature gradient of the gas well changes, the temperature in the wellbore is also affected by the expansion and endothermic effects. The temperature at different well depths affect the phase state of the injected CO₂. As CO₂ undergoes phase transitions and the temperature decreases, the viscosity of the fracturing fluid is indirectly reduced. According to the energy conservation equation, the temperature gradient change directly reduces the viscosity of the fracturing fluid, thereby improving its mobility. This phenomenon indicates that CO₂ injection has a significant impact on the viscosity of the fracturing fluid, reducing its viscosity by approximately 35%.

Pressure is a key factor in driving fracturing fluid flowback. During the CO₂ injection process, a relatively stable pressure distribution gradient is formed within the wellbore, from the wellhead to the bottomhole. The presence of this stable pressure distribution significantly influences the CO₂ phase transitions while providing the driving force for fracturing fluid flowback. Simulation results show that the bottomhole pressure increases by 12%–18% after CO₂ injection, significantly higher than water injection (only 5%–8%). The injected CO₂, with its low viscosity and high diffusivity, can quickly overcome blockages in the reservoir, thereby improving the fracturing fluid flowback efficiency.

Comparison of water injection and CO₂ injection under the same injection rate

Figure 8 illustrates a comparison of fracturing fluid flowback volumes between water injection and CO₂ injection under three different injection rates. Across all three rates, the fracturing fluid flowback volume shows a rapid growth trend, with higher injection rates resulting in more significant growth. At an injection rate of 5000 m³/d, the maximum flowback volume for CO₂ injection reached 1242.7 m³/d, while that for water injection was 631.5 m³/d. The maximum difference in flowback volume was 611.2 m³/d, nearly double, with the largest recorded difference reaching 707.2 m³/d. At an injection rate of 10,000 m³/d, the maximum flowback volume for CO₂ injection was 2481.6 m³/d, compared to 1266.7 m³/d for water injection, with the largest flowback volume difference reaching 1214.9 m³/d. At an injection rate of 15,000 m³/d, the maximum flowback volume for CO₂ injection was 3722.9 m³/d, compared to 1977.7 m³/d for water injection, with the largest flowback volume difference reaching 1745.2 m³/d.

Fig. 8

Comparison of CO₂ and water-enhanced flowback volumes under three injection rate conditions (Solid line represents CO₂ injection, dashed line represents water injection).

The data results indicate that CO₂ injection significantly improves fracturing fluid flowback performance across all stages (initial, stable, and late stages). Compared to water injection, CO₂ injection achieves notably higher flowback efficiency, especially during the initial and stable stages, with greater flowback volumes and growth rates. With its high diffusivity and mobility, CO₂ demonstrates significant advantages in enhancing reservoir pressure and bottom-hole fluid mobility, providing critical technical support for optimizing fracturing fluid flowback.

Analysis of flowback characteristics

From the comparison of CO₂ and water injection under three different injection rate conditions, two phenomena can be observed. The first is that the CO₂ injection curve is notably smoother than the water injection curve. This is due to CO₂'s low viscosity and high diffusivity, which enable it to rapidly and uniformly penetrate microfracture networks, forming a relatively stable gas–liquid two-phase flow. This flow characteristic avoids sudden increases or decreases in local pressure, reducing small fluctuations in flowback volume. Moreover, as CO₂ reduces the viscosity of the fracturing fluid, it mitigates the phase instability caused by temperature gradient changes, leading to continuous improvement in fluid mobility and promoting a stable steady-state in the flowback process. Additionally, some CO₂ dissolves in formation water, creating a weak acidic environment that chemically reacts with carbonate minerals such as calcite in the shale. This reaction gradually dissolves the cementing material and enhances the fracture flowback capacity. This process is notably progressive, avoiding abrupt changes in local permeability, resulting in a smooth increase in flowback volume.

The second phenomenon is the sharp increase in water injection flowback volumes at days 9–10, 19–20, and 29–30 (as shown in Fig. 9). The fundamental reason for this is the coupling of the physical properties of water-based fracturing fluids with the dynamic response of the reservoir. The high viscosity of water-based fracturing fluids carries a large number of solid particles (proppants, polymer residues), which quickly form a filter cake on the fracture surface, leading to a sharp decline in permeability during the initial flowback period (slowing down the increase in flowback volume). As the flowback pressure accumulates, the filter cake is partially eroded by hydraulic action (simulations show a brief recovery of permeability by 5%–8%), resulting in a slight increase in flowback volume. However, subsequent particle redeposition leads to the reconstruction of the filter cake, causing a further decrease in flowback volume and forming fluctuations. This phenomenon highlights the instability of water injection in long-term flowback, suggesting that the proppant concentration should be optimized or suspended agents (such as cellulose derivatives) should be added to improve proppant transport capacity.

Fig. 9

Water-enhanced flowback volume under three injection rate conditions.

Simultaneously, simulation results show that the growth rate of flowback volume is relatively slow in the initial stage of water injection. On day 10, the flowback volumes at three different injection rates were 412.3 m³/d, 791.7 m³/d, and 1210.5 m³/d, respectively. This is primarily due to the low diffusion capacity and mobility of water, which limits the flowback efficiency of the fracturing fluid. At the steady stage, water injection also exhibits a decreasing flowback rate. The highest flowback volumes under three injection rates were 627.1 m³/d, 1250.9 m³/d, and 1961.5 m³/d, with a slight decrease occurring between days 17–20. This slowdown in growth rate and the drop-off indicates that the displacement effect of injected water in the reservoir has gradually saturated, causing the rate of improvement in fracturing fluid flowback efficiency to slow down. During the later stage, flowback volume further declines, with the highest flowback volumes at each injection rate reaching only 472.3 m³/d, 1011.5 m³/d, and 1347.2 m³/d. This suggests that the reservoir pressure and bottomhole fluid mobility are nearing saturation, and water injection can no longer effectively increase the reservoir pressure.

Safety analysis of CO₂ injection

CO₂ assisted EOR (Enhanced Oil Recovery) has demonstrated exceptional efficiency in enhancing hydrocarbon recovery; however, its long-term implications for reservoir sustainability remain contentious. Prolonged CO₂ injection can induce irreversible formation damage, manifested as deterioration of rock integrity, destabilization of fracture networks, and geochemical alteration of in-situ mineral assemblages. These phenomena collectively compromise the long-term productivity of production wells.

A principal concern associated with long-term CO₂ injection is the initiation of geomechanically damage. Pressurization accompanying CO₂ injection perturbs the thermodynamic equilibrium of the formation, giving rise to fracture deformation, rock weakening, and the nucleation of micro-fractures. Such alterations are particularly deleterious in formations already subjected to critically high stress states, markedly diminishing geomechanically stability over time. Moreover, CO₂ injection triggers geochemical reactions that modify the mineralogical composition of the reservoir. Calcite dissolution, for instance, reconfigures pore architecture and may transiently enhance fracture conductivity by increasing local permeability. Nonetheless, the long-term consequence of this process can entail clay swelling in adjacent regions, resulting in occlusion of micro-fractures and pore throats and a concomitant reduction in injectivity and productivity.

The potential for CO₂ leakage constitutes another critical risk. Upon injection into deep geological strata, the buoyant CO₂ plume may migrate along preferential pathways such as faults or fractures, ultimately seeping into overlying strata or, in the worst-case scenario, discharging to the atmosphere. Migration dynamics are governed by reservoir depth, fracture connectivity, and the integrity of caprock sealing lithologies. Although caprock is generally anticipated to provide effective containment, rigorous long-term monitoring and comprehensive caprock integrity assessments are imperative to ensure secure geological storage. Quantitative appraisal of formation storage capacity and long-term geochemical stability of the injected CO₂ is essential for mitigating leakage hazards.

Conclusions

• (1) Liquid CO₂ injection rapidly reduces shale temperature (16.1 °C drop in initial 10 min). Its expansion endothermicity significantly decreases fracturing fluid viscosity (35%), providing thermodynamic basis for enhanced flowback mobility.

• (2) Leveraging low viscosity (44 μPa s) and high diffusivity, CO₂ effectively increases reservoir pressure by 12–18% and fracture conductivity. Flowback volumes surpass aqueous fluids by 88–97% at 5000–15,000 m³/d injection rates.

• (3) The developed wellbore model integrates temperature field data (Fig. 4) for the first time. Through volume balance equations and critical flowback velocity models, it quantitatively elucidates CO₂'s mechanical optimization of wellbore pressure gradients (Fig. 6).

• (4) CO₂ injection curves exhibit superior smoothness versus aqueous fluids (Fig. 7), demonstrating stable gas–liquid two-phase flow that mitigates local pressure fluctuations-induced instability.

In conclusion, CO₂ injection in shale reservoirs significantly enhances productivity and flowback efficiency of fracturing fluids. Studies demonstrate that CO₂ can markedly improve fracture conductivity, reduce fluid viscosity, and substantially increase recovered volumes. These findings indicate that CO₂ injection may serve as a viable alternative to conventional water based fracturing fluids, particularly in tight reservoir applications where high efficiency and sustained long term productivity are critical.

The present study has the following three limitations:

(1) Core experiments ignored in-situ stress effects on CO₂ flow. (2) Model uncoupled from long term CO₂ brine reaction kinetics. (3) Fracture geometry simplified to ideal ellipse.