Numerical Simulation of CO₂ Injection and Production in Shale Oil Reservoirs with Radial Borehole Fracturing

Abstract

Shale oil is a vital strategic resource in China. Developing shale oil using CO₂ not only enhances oil recovery but also contributes to achieving Chinese “dual carbon” goals. Given the challenges of insufficient number of fractures, inadequate vertical stimulation volume, and poor reservoir mobility associated with horizontal well fracturing, this study proposes a method for CO₂ flooding based on radial borehole fracturing in a single well to achieve long-term carbon sequestration. To this end, a multi-component numerical model is built to analyze the production capacity of radial borehole fracturing. This study analyzed the impacts of non-Darcy flow, diffusion, and adsorption mechanisms on CO₂ migration and sequestration. It also compared the applicability of continuous CO₂ flooding and CO₂ huff-and-puff under different matrix permeabilities. The results indicate that (1) CO₂ flooding using radial borehole fracturing can achieve long-term oil production and carbon sequestration. (2) Under low permeability conditions, the liquid non-Darcy effect retards the flow of oil and CO₂, while diffusion and adsorption facilitate CO₂ sequestration in the reservoir. The impact on carbon sequestration is ranked as follows: non-Darcy effect > adsorption > diffusion. (3) High-permeability reservoirs are more suitable for carbon sequestration and should utilize continuous CO₂ flooding. For low-permeability reservoirs (<0.001 mD), huff-and-puff should be employed to mobilize the reservoir around fractures and achieve carbon sequestration. The findings of this study are expected to provide new methods and a theoretical basis for efficient and economical carbon sequestration in shale oil reservoirs.

1. Introduction

The goal proposed by China to achieve peak carbon dioxide emissions by 2030 and strive for carbon neutrality by 2060 is a key measure in promoting ecological civilization construction. Carbon capture, utilization, and storage (CCUS) technology is widely regarded as a key solution to achieving large-scale greenhouse gas emission reductions and meeting long-term carbon neutrality targets. Over the past two decades, CCUS has been successfully demonstrated in multiple deep geological formations, including saline aquifers, depleted oil and gas reservoirs, and coal seams. Notably, the Mount Simon Sandstone Formation in the Illinois Basin (USA) has been a major site for CO₂ injection at depths exceeding 2100–2200 m, where the thick, laterally continuous saline aquifer and overlying shale caprock provide favorable conditions for long-term storage [1]. In China, field-scale CO₂ sequestration pilot projects have been conducted in the Ordos Basin and Junggar Basin, with injection depths reaching 2500 to over 3000 m [2]. These sites feature low-permeability formations and multi-layered caprock systems, making them suitable analogs for evaluating CO₂ behavior in deeply buried, heterogeneous reservoirs.

These examples highlight the geological feasibility and practical success of deep CO₂ sequestration under varying lithological and structural conditions, and they serve as important references for the reservoir setting and injection strategy adopted in this study [3,4].

With advances in geological understanding and technological progress, the focus of oil and gas exploration and development has gradually shifted to unconventional resources such as tight oil and shale oil and gas [5]. China possesses shale oil resources with significant development potential [6]. The widespread distribution of shale oil reservoirs provides vast storage space for CO₂ geological sequestration [7]. However, shale oil resources vary significantly across different regions and types, posing substantial challenges [8]. Under reservoir conditions, CO₂ exhibits unique properties such as high density, low viscosity, and high diffusivity [9], enabling it to penetrate shale micro- and nanopores and mobilize the oil stored within. Therefore, CO₂-enhanced shale oil recovery has the potential to improve shale oil recovery rates while achieving CO₂ geological sequestration, addressing the critical needs of Chinese “dual carbon” goals.

The tight pores in shale oil reservoirs not only lead to rapid reservoir depletion but also cause fluid flow behavior to deviate from conventional reservoirs, transitioning from Darcy to non-Darcy flow [10]. In shale reservoirs with pore throat radii ranging from 1 to 200 nm, the continuum theory of fluid flow fails, and gas molecules move along random paths while still maintaining the general flow direction controlled by the pressure gradient. Molecules collide with pore walls and tend to slide along them [11]. Consequently, the measured gas permeability was observed by Klinkenberg in 1941 to be higher than the values predicted by Darcy’s law [12]. To correct for non-Darcy flow in different flow regimes within nanopore spaces and to fully account for slip flow and Knudsen diffusion in gas non-Darcy flow, previous studies have proposed two types of gas apparent permeability models: the dusty gas model and the Knudsen number-based model. The dusty gas model incorporates Knudsen diffusion and slip flow effects to account for the interaction between gas molecules and solid walls, integrating the three primary transport mechanisms of viscous flow, Knudsen diffusion, and molecular diffusion. This enables the description of gas flow behavior in porous media, including gas non-Darcy effects [13,14,15]. The Knudsen number-based model primarily focuses on gas flow at micro- and nano-scales, especially when flow is influenced by the Knudsen effect (i.e., when the mean free path of gas molecules is comparable to the pore size). This is achieved by adjusting the slip factor or apparent permeability based on a function of the Knudsen number [16,17,18,19,20], effectively multiplying the permeability by a gas non-Darcy coefficient greater than 1.

Horizontal wells with multi-stage hydraulic fracturing represent the primary application scenario for CO₂-enhanced oil recovery (EOR) in shale oil reservoirs [21,22,23,24]. CO₂ injection in shale oil reservoirs can be implemented in two main modes: continuous injection and huff-and-puff. Generally, huff-and-puff is considered more suitable for low-permeability reservoirs [25]. The fracture network created by hydraulic fracturing in horizontal wells effectively reduces flow resistance and creates pathways for shale oil and CO₂ flow [26]. In 2023, Chinese exploration and development of shale oil advanced steadily [27,28,29]. However, Chinese lacustrine shale oil deposits are characterized by thick sedimentary layers, rapid changes in lithology and oil saturation both vertically and laterally. Shale oil reservoirs exhibit well-developed bedding fractures and poor vertical penetration capability of hydraulic fracturing, resulting in limited reservoir modification in the vertical direction after horizontal well fracturing [30]. This makes it difficult to form complex fracture networks, and vertical flowing is limited. Consequently, vertical CO₂ migration, oil displacement, and sequestration effects are limited when based on horizontal well fracturing [31]. In summary, horizontal well hydraulic fracturing technology cannot meet all the development needs of CO₂ EOR in shale oil reservoirs [32,33,34], and there is a need to explore a new technology that can enable long-term, efficient CO₂ injection for shale oil reservoir development.

This study proposes a method for CO₂ flooding in fractured shale oil reservoirs based on radial borehole fracturing. Focusing on the three-dimensional fracture network of radial boreholes, a multi-component compositional model was employed to predict the productivity and carbon sequestration capacity. The impacts of non-Darcy flow, diffusion, and adsorption on reservoir fluid flow, oil production, and carbon sequestration were analyzed. Additionally, the adaptability of continuous CO₂ injection and CO₂ huff-n-puff production modes was compared. The research findings are expected to provide a novel method and theoretical foundation for the efficient development of shale oil and carbon sequestration.

2. Radial Borehole Fracturing in Shale Oil Reservoirs

Increasing stimulated reservoir volume is crucial for shale oil reservoirs. The United States has achieved a revolution in shale oil and gas by employing three-dimensional development technologies, transitioning from an energy importer to an exporter [35]. In 2014, Li et al. first proposed the method of radial borehole fracturing. This technique involves drilling one or more radial horizontal holes along the vertical wellbore using hydraulic jetting, followed by fracturing [36,37]. Radial boreholes guide hydraulic fracturing, allowing for flexible deployment of radial boreholes and hydraulic fractures underground to form multi-layer three-dimensional fractures in shale oil reservoirs [38]. However, due to the tight nature of shale oil reservoirs, depletion development after fracturing fails to maintain stable production. Nevertheless, due to the inherently tight and low-permeability nature of shale formations, depletion development after fracturing often fails to sustain long-term production. Furthermore, in deep shale formations, elevated horizontal stresses pose additional challenges for borehole stability. Stress anisotropy may induce localized casing deformation, shear failure, or collapse-especially near radial outlets where stress concentrations are high [39]. The coupling between in situ stress fields and natural fracture systems must therefore be carefully considered in both fracture design and operational planning to ensure mechanical integrity and field applicability.

In addition to these mechanical challenges, induced geohazards such as microseismicity, fault reactivation, and uncontrolled fracture propagation are also more likely to occur in deep unconventional reservoirs [40]. These phenomena are linked to higher energy release potential and complex stress redistribution patterns, especially when CO₂ injection disturbs pre-existing fracture networks [41]. Field-scale monitoring has documented microseismic events associated with both CO₂ sequestration and hydraulic stimulation, raising concerns over caprock disturbance or fluid migration through compromised sealing zones [42]. Therefore, it is essential to incorporate these depth-related dynamic risks into reservoir modeling and injection planning to ensure long-term storage safety and operational reliability.

Therefore, CO₂ flooding based on multi-layer radial borehole fracturing is proposed to economically and efficiently achieve oil displacement and carbon sequestration [43]. One continuous flooding implementation is shown in Figure 1. After hydraulic fracturing forms fractures in a vertical well with radial boreholes deployed at two depths in a shale oil reservoir, CO₂ is injected into the upper radial boreholes through the annulus, driving shale oil to flow into the lower radial boreholes, from which oil is produced to the surface through the tubing. Another implementation involves CO₂ huff-and-puff, where the upper and lower radial boreholes serve simultaneously as injection and production wells, alternating between production, injection, and soaking operations. In horizontal well fracturing, it is generally believed that CO₂ continuous flooding and CO₂ huff-and-puff methods should be selectively applied according to reservoir conditions in well-pattern development, with CO₂ huff-and-puff being preferred for low-permeability reservoirs [44]. Therefore, it is necessary to analyze the reservoir adaptability of this method in the context of radial borehole fracturing. The novelty of this method lies in the vertical movement of CO₂, which enables long-term carbon sequestration in a single vertical well.

In previous studies, reservoir dynamics and production predictions of CO₂ flooding after radial borehole fracturing are analyzed under different fractures and radial borehole parameters. However, the black-oil model used did not account for mechanisms such as adsorption and diffusion. Therefore, further research is needed based on a compositional model.

3. Numerical Model and Solution

3.1. Compositional Model

During CO₂-enhanced oil recovery (EOR) in shale oil reservoirs, the adsorption and diffusion of CO₂, the miscible/non-miscible displacement between CO₂ and oil, and non-Darcy flow are key mechanisms that cannot be ignored. Compared to the black-oil model, the compositional model can more accurately describe the multi-phase, multi-component kinetics during CO₂ flooding, especially the diffusion and adsorption of various components. Therefore, this study employs a compositional model to simulate the CO₂ flooding process. To optimize simulation convergence, the reservoir temperature is assumed to remain isothermal throughout the process, unaffected by the injection of CO₂; the non-stimulated reservoir volume (non-SRV) region forms an effectively closed reservoir boundary due to extremely low permeability; the diffusion and solubility of CO₂ in water are neglected, as are capillary pressure, relative permeability hysteresis, threshold pressure effects, and the influence of asphaltene and hydrate formation. For the oil and gas phases, the mass balance equation considering diffusion and adsorption can be expressed as [46]

$${\partial }_t[\varphi {\displaystyle \sum _{\alpha =o,g}{\rho }_{\alpha }{S}_{\alpha }{X}_{\alpha }^i}+{\delta }_s\left(1-\varphi \right){\rho }_s^i]+{\displaystyle \sum _{\alpha =l,v}\nabla \cdot ({\rho }_{\alpha }{X}_{\alpha }^i{\overrightarrow{v}}_{\alpha }+J_{\alpha }^i)}={\displaystyle \sum _{\alpha =o,g}{\rho }_{\alpha }{X}_{\alpha }^i{q}_{\alpha }/V}$$

(1)

where the superscript i represents the component; the subscript α represents the phase (liquid or vapor); ρ represents density (kg/m³); S represents saturation (dimensionless); X represents mass fraction (dimensionless); V is the Darcy velocity (m/s); δ_s is a discrimination coefficient, equal to 1 for shale matrix elements and 0 for non-matrix elements; J is the diffusion intensity (kg/s), expressed by Fick’s diffusion law [47] as

$$J_{\alpha }^i=-{\displaystyle \frac{\phi S_{\alpha }}{\tau }}{D}_{\alpha }^i\nabla ({\rho }_{\alpha }{X}_{\alpha }^i)$$

(2)

where φ is the matrix porosity (dimensionless); D represents the diffusion coefficient (m²/s). The diffusion coefficient in this study is calculated using the empirical formula proposed by Wilke and Chang [48]:

$$D_{ik}={\displaystyle \frac{7.4\times {10}^{-8}{\left(M_{ik}^{\prime }\right)}^{1/2}T}{{\mu }_k{V}_{bi}^{0.6}}}$$

(3)

where the subscript k represents the solvent component into which component i diffuses; M represents the solvent molecular weight; T represents temperature (K); μ represents the solute viscosity (cp); V_b represents the molar volume of the solute at boiling point.

The term involving ρ_s represents the adsorbed component mass (kg), where ρ_s is the adsorption density at pressure P (kg/m³). When multiple components are present, this can be expressed using the extended Langmuir equation [49]:

$${\rho }_s^i={\rho }_{sL}^i{\displaystyle \frac{y_i\frac{P}{P_L^i}}{1+{\displaystyle {\sum }_{j=1}^n{y}_i\frac{P}{P_L^j}}}}$$

(4)

where ρ_SL represents the maximum adsorption capacity (kg/m³), P_L represents the minimum pressure required to reach maximum adsorption (Pa), and y represents the molar fraction of each component in the gas phase. It should be noted that using the extended Langmuir equation to describe adsorption phenomena in shale oil is a relatively simplified approach. Currently, the theory of shale oil adsorption is still incomplete, lacking appropriate models to accurately describe the competitive adsorption interactions between CO₂ and other components within shale oil. Future research will further investigate component-based competitive adsorption theories for shale oil.

For the liquid phase non-Darcy law, this study employs the exponential non-Darcy equation proposed by Wang and Sheng [50], based on coreflood waterflooding experimental data [51]:

$$v_{\alpha }=-{\lambda }_{\alpha }{\rho }_{\alpha }({\displaystyle \frac{1}{1+a_{\alpha }{e}^{-b_{\alpha }|\nabla P_{\alpha }|}}})\nabla \mathsf{\Phi }$$

(5)

where Φ represents the potential energy, and the dimensionless non-Darcy coefficients a_α and b_α in the non-Darcy term can be expressed as functions of phase mobility λ_α:

$$a_{\alpha }=-0.6095{{\lambda }_{\alpha }}^3+2.5821{{\lambda }_{\alpha }}^2-3.4594{\lambda }_{\alpha }+1.5836$$

(6)

$$a_{\alpha }=e^{-1.176{\lambda }_{\alpha }}$$

(7)

$$b_{\alpha }=0.3603{{\lambda }_{\alpha }}^2-0.1049{\lambda }_{\alpha }+1.0935$$

(8)

In the equation, the value may become negative when the mobility is excessively high. Therefore, when a negative value occurs, the value of a_α is calculated using the equation.

For gases in shale reservoirs, gas transport mechanisms vary with the Knudsen number. When the Knudsen number is below 0.001, intermolecular collisions are prevalent, and the continuum flow mechanism dominates. When the Knudsen number is between 0.001 and 0.1, collisions between molecules and walls increase in frequency, leading to slip flow phenomena where slip effects become significant. When the Knudsen number is between 0.1 and 10, the frequency of molecular-wall collisions and intermolecular collisions is comparable, forming a transition flow state. When the Knudsen number exceeds 10, molecular-wall collisions dominate, and gas transport is primarily driven by Knudsen diffusion. This reflects the transition from continuum flow to Knudsen diffusion, highlighting the dynamic changes in gas transport mechanisms. According to the Beskok and Karniadakis (BK) model [52], the non-Darcy law for gases can be expressed as

$$v_{\alpha }=-{\lambda }_{\alpha }{\rho }_{\alpha }\left(1+{\displaystyle \frac{4Kn}{1+4Kn}}\right)\left(1+{\displaystyle \frac{128}{15{\pi }^2}}Kn\cdot {\tan }^{-1}\left(4K{n}^{0.4}\right)\right)\nabla \mathsf{\Phi }$$

(9)

where K_n is the Knudsen number, defined as

$$Kn={\displaystyle \frac{\lambda }{d}}$$

(10)

where d represents the pore diameter (m); λ represents the mean free path of molecules (m), defined as [53]

$$\mathsf{\lambda }={\displaystyle \frac{{\mu }_v}{P_v}}\sqrt{{\displaystyle \frac{\pi RT}{2M}}}$$

(11)

where μ_v is the dynamic viscosity of the gas phase (Pa·s). R is the universal gas constant, i.e., 8.314 J/(mol·K). M is the molecular molar mass (kg/mol).

The relationship between pore diameter, permeability, and porosity can be expressed as [54]

$$d=2\sqrt{2\tau }\sqrt{{\displaystyle \frac{K}{\phi }}}$$

(12)

where τ is the tortuosity.

Flash vaporization is solved using the Rachford–Rice method to determine gas–liquid equilibrium, and the physical properties of each phase (including the supercritical phase) are determined based on the Peng–Robinson equation of state. The hydraulic fractures and natural fractures in this study are coupled through the embedded discrete fracture method. This study is based on the MATLAB Reservoir Simulation Toolkit (MRST) platform (version: 2024b) provided by SINTEF (Trondheim, Norway), which runs on the basis of MATLAB R2024b (Beijing, China).

The Newton–Raphson method is employed to solve the discretized equation system [55]. Diffusion and adsorption are implemented through secondary modifications of the mass conservation equation, and the non-Darcy law is realized by multiplying the mobility with a coefficient. The detailed modifications to the formation code can be found in reference [56].

3.2. Model Description

The fluid properties and relative permeability characteristics employed in this study are detailed in reference [57]. The reservoir fluid is composed of six components: CO₂, N₂, C₁, C₂-C₅, C₆-C₁₀, and C₁₁₊. A three-dimensional reservoir model was constructed with dimensions of 250 m × 250 m × 90 m. The model domain reflects a conceptual structure in which radial fracturing generates a high-permeability stimulated reservoir volume (SRV) surrounded by tight shale matrix that serves as a hydraulic barrier. This configuration supports the use of quasi-closed boundaries and aligns with existing practices in shale CO₂ injection modeling [45].

Previous studies have shown that when the domain radius exceeds twice the fracture half-length (e.g., >200 m), boundary effects are negligible under low-permeability conditions [48]. With a fracture half-length of 50 m, the 250 m lateral extent used in this study ensures containment of pressure and saturation changes within the active region.

As shown in Figure 2, the reservoir features two layers of radial boreholes, located at depths of 15 m and 75 m, respectively. In the CO₂ continuous injection process, the upper radial boreholes serve as the CO₂ injection well, while the lower radial boreholes function as the production well. Physical experiments and numerical simulations have demonstrated that radial boreholes can induce fracture propagation. When radial boreholes are symmetrically distributed along the direction of the maximum horizontal principal stress, the fractures in the horizontal radial boreholes propagate a certain distance before gradually turning in the direction of the maximum horizontal principal stress under its influence [37]. In addition to governing fracture propagation, horizontal in situ stresses exert a direct influence on the mechanical stability of radial boreholes [41]. High differential stress between the maximum and minimum horizontal principal stresses may cause asymmetric deformation of the borehole wall, leading to localized ovalization, shear failure, or even collapse at radial junctions [39]. These risks are particularly pronounced in deep shale formations, where the energy stored in the stress field is higher and the presence of bedding planes or natural fractures further weakens structural integrity.

To address these challenges, the numerical model incorporated stress-related constraints during borehole layout and fracture simulation. The orientation of the radial boreholes was aligned with the σH direction to minimize shear concentration, and boundary conditions were applied to mimic the realistic stress envelope surrounding the wellbore [58]. These settings ensure that both the predicted fracture paths and borehole integrity remain geomechanically feasible throughout injection and production stages.

The fracture geometry is assumed as depicted in Figure 2, based on the previously established understanding of the influence of stress changes on fracture morphology. The solid black lines in the figure indicate the positions of the simulated fractures, while the dashed red lines represent the direction of hydraulic fracture propagation. Vertical fractures were selected as the primary configuration, reflecting the prevailing fracture orientation in shale reservoirs, where the minimum principal stress is horizontal, favoring vertical propagation. While horizontal fractures may form under special stratigraphic or structural conditions, they are uncommon in most shale gas reservoirs [37].

The fracture half-length of 50 m (total length 100 m) was chosen to match practical constraints in radial borehole fracturing, including limited injection energy, restricted well spacing, and reservoir model dimensions (250 m × 250 m). This design is consistent with prior radial fracturing simulations and field data [59], where fracture extensions typically range from 40 to 100 m.

Moreover, the focus of this study is on vertical CO₂ migration between injection and production layers, and horizontal fracture growth plays a secondary role in transport efficiency under these conditions. Although fracture geometry can affect fluid behavior, dynamic fracture propagation and longer-length sensitivity were not included in the current model and are identified in Section 5 as important directions for future work. As the fracture length increases, the fracture will continue to extend along the direction of the dashed red lines, i.e., parallel to the maximum horizontal principal stress.

The radial boreholes are arranged around a vertical main well at the center of the reservoir, with each layer comprising four mutually perpendicular radial boreholes, having a phase angle of 0°. CO₂ is injected, and the produced fluids are transported through the main well via the radial boreholes. However, since the main well is cased and cemented and does not directly contact the reservoir, it is not considered in the model.

Table 1. Basic reservoir characteristics.

Parameter	Value	Unit
Reservoir dimensions (length × width × height)	250 × 250 × 90	m
Grid discretization (length × width × height)	21 × 21 × 31	Unit
Reservoir permeability	10−3 to 0.1	mD
Porosity	10	%
Tortuosity	2
Initial reservoir pressure	48.26	MPa
Reservoir temperature	450	K

lists the basic properties of the reservoir. The specific formulas describing the geometry of the radial borehole fractures can be found in reference [38]. To simplify the model, Jia et al. [59,60] adopted a model with constant fracture conductivity in the drainage area. Therefore, the width, height, and conductivity of the hydraulic fractures are assumed to be constant and independent of their positions. The specific parameters are listed in

Table 2. Basic characteristics of radial borehole fracturing.

Parameter	Value	Unit
Number of main wells	1	Unit
Number of radial boreholes	4	Unit
Angle between radial borehole and maximum principal stress	45	°
Diameter of radial borehole	50	mm
Length of radial borehole	15 (Li et al., 2017 [63])	m
Induced length	25	m
dβ	1	°/m
Total length of a single fracture	50	m
Fracture height	9	m
Fracture conductivity	426.72	md-m

. The model is validated in our previous study [61,62,63]. In addition,

Table 3. Initial and boundary conditions used in the simulation.

Parameter	Value	Description
Initial Pressure	32 MPa	Reservoir initial pressure
Initial Temperature	78 °C	Reservoir initial temperature
Initial Oil Saturation	0.65	Oil saturation at initial state
Initial Gas Saturation	0.05	Gas saturation at initial state
Lateral Boundary	Constant-pressure	Allows fluid communication
Top Boundary	No-flow	Represents caprock sealing
Bottom Boundary	No-flow	Represents base sealing

presents the initial and boundary conditions applied in the simulation, including pressure, temperature, saturation, and boundary type definitions for each reservoir face.

3.3. Model Validation

The simulation model was validated using production data from a hydraulically fractured well in the Eagle Ford shale condensate reservoir [45], covering the period from January 2010 to July 2012. The validation focused on the sixth stage of a nine-stage horizontal well, with the reservoir model dimensions set at 67 m (length) × 137 m (width) × 27.4 m (height) and discretized into 2210 grid cells. Key reservoir parameters included a top depth of 3048 m, initial pressure of 48.3 MPa, temperature of 175 °C, matrix porosity of 10%, and permeability of 0.64 mD, with initial fluid saturations of 65% gas and 35% water. The hydraulic fractures were characterized by a half-length of 41.1 m, height of 15.2 m, and initial conductivity of 140 mD·ft (~42.7 mD·m). A constant bottomhole pressure of 20.7 MPa was maintained during production. As shown in Figure 3, the simulated production closely matches field data, confirming the model’s reliability for subsequent analysis.

4. Results and Discussion

4.1. Influence of Non-Darcy Flow

When the matrix permeability is 0.1 mD, non-Darcy flow is a key factor influencing low-permeability oil reservoirs. The bottomhole pressure of the injection radial borehole and the production radial borehole are maintained at 49.26 MPa and 47.26 MPa, respectively, as shown in Figure 4.

As shown in Figure 5, the non-Darcy flow characteristics of liquids and gases in the matrix are distinct, manifesting as a retarding effect with a value less than 1 and a slip effect with a value greater than 1, respectively. According to Equation (5), the smaller the pressure gradient, the stronger the liquid non-Darcy coefficient, which is why the liquid non-Darcy coefficient is only 0.53 near the boundary. Conversely, the higher the mobility, the closer the value of a is to 0, indicating a weaker non-Darcy effect. Therefore, around the interface between CO₂ and oil, the viscosity of oil decreases, resulting in a liquid non-Darcy coefficient of approximately 0.92. The low non-Darcy coefficient near the injection radial borehole is due to low liquid saturation, which leads to low relative permeability and, consequently, low mobility. However, since this region does not contain oil, it does not affect oil flow. Compared to the liquid non-Darcy effect, the gas non-Darcy effect is influenced only by viscosity under a given permeability condition. Thus, in regions with low viscosity, the gas non-Darcy coefficient is relatively low.

As shown in Figure 6, when the matrix permeability is 0.001 mD, CO₂ injection into the reservoir is impeded, and the viscosity of the reservoir fluid remains essentially unchanged. Under the same bottomhole pressure conditions, the matrix non-Darcy coefficient is below 0.39, while the gas non-Darcy coefficient exceeds 1.1. Therefore, the lower the permeability, the more difficult it is for oil to flow.

Although the gas non-Darcy effect increases the apparent permeability of CO₂, it is insufficient to offset the decline in carbon sequestration capacity due to low permeability, as shown in Figure 7 and Figure 8.

4.2. Influence of Diffusion

Diffusion is an important fluid driving force in addition to the pressure gradient, and its intensity is influenced by both the concentration gradient of the substance and its inherent diffusivity. As shown in Figure 9. Diffusion has a relatively high intensity only around the interface between oil and CO₂, which is in line with the understanding that diffusion is driven by the concentration difference in substances. The area where the diffusion intensity alternates between positive and negative is the oil–CO₂ interface, representing that CO₂ diffuses from the inside out and C1 diffuses from the outside in. The strong dispersion intensity of CO₂ is approximately ten times that of C1, indicating the strong migration ability of CO₂ molecules.

Diffusion is relatively weaker compared to the driving force of pressure gradients. As shown in Figure 10, the rate of CO₂ sequestration is relatively high at the beginning of production, but it rapidly decreases due to the release of elastic energy (0–1 h). Once the reservoir pressure gradient stabilizes, the oil production rate gradually increases (1 h–2700 days). Subsequently, CO₂ begins to gas-breakthrough in the production well, eventually leading to a gradual decline in both the oil production rate and the rate of carbon sequestration (>2700 days). The overall weak influence of diffusion observed in Figure 7 can be attributed to two key factors. First, the matrix permeability is extremely low (0.001 mD), resulting in fracture-dominated flow where pressure-driven advection overwhelms molecular diffusion. Second, the diffusion coefficient used in this simulation is 10⁻¹⁰ m²/s, which, as confirmed in previous studies (Dai et al., 2025 [45]), lies below the threshold (~10⁻⁸ m²/s) required for diffusion to exert a significant impact. Parameter sensitivity analysis in that study showed that only when the diffusion coefficient increases by at least two orders of magnitude does it substantially redistribute CO₂, delay breakthrough, or enhance oil production.

Therefore, the similarity between the diffusion and non-diffusion scenarios in Figure 7 is consistent with both physical expectations and prior simulation findings under low-permeability, fracture-dominated conditions.

Furthermore, the impact of diffusion on productivity and carbon sequestration capacity is relatively minor, whether diffusion is considered or not. However, when diffusion is taken into account, CO₂ is not only driven downward by the pressure gradient but also migrates laterally into the surrounding reservoir. As a result, less CO₂ enters the production well compared to when diffusion is neglected, meaning that diffusion is more favorable for carbon sequestration. Future research will further investigate the impact of diffusion on CO₂ sequestration over longer timescales following the cessation of gas injection.

To amplify the effect of CO₂ displacement, multiply it by a multiplier before the CO₂ diffusion coefficient. The cumulative oil production and cumulative CO₂ sequestration were plotted against the diffusion coefficient, as shown in Figure 11. Both the cumulative oil production and CO₂ sequestration increased slightly with the increase in the diffusion coefficient multiplier (from 1 to 5 times) but then decreased significantly (from 5 to 40 times). As the diffusion coefficient multiplier increased, the mobility of CO₂ within the reservoir was enhanced. Due to its higher diffusion capacity, gas breakthrough occurred earlier in the production well, ultimately leading to a gradual decline in both oil production and CO₂ sequestration.

4.3. The Impact of Adsorption

Shale oil matrices are characterized by well-developed micro- and nanopores. The adsorption of multiple components is a significant factor influencing both shale oil production and CO₂ sequestration. As shown in Figure 12, when the matrix permeability is 0.1 mD, with the upper radial boreholes injecting CO₂ at a constant rate of 5 m³/day and the lower radial borehole maintaining a bottomhole pressure of 38.26 MPa, the distribution of CO₂ and C₁ adsorption reveals that CO₂ adsorption is higher in the regions through which CO₂ flows, and it displaces some of the adsorbed C₁. Therefore, under the same CO₂ injection rate, when the adsorption of CO₂ is considered, a portion of the injected CO₂ is adsorbed by the matrix, reducing the amount of CO₂ flowing towards the production well. This results in a greater amount of CO₂ being sequestered when adsorption is taken into account. The adsorption of CO₂ displaces light hydrocarbons, and the decrease in reservoir pressure also causes some of the adsorbed oil to desorb, thereby increasing oil production. For example, as shown in Figure 13, the breakthrough time of CO₂, i.e., the time when the CO₂ production rate significantly increases, is nearly 500 days earlier when adsorption is not considered compared to when it is considered. On Day 4000, the cumulative oil production and carbon sequestration with adsorption considered are 1.047 and 1.312 times those without considering adsorption, respectively. This indicates that carbon sequestration capacity is more sensitive to adsorption.

To amplify the effect of adsorption, multiply it by a multiplier before the adsorption density. As shown in Figure 14, the cumulative oil production increases continuously with the increase in the adsorption density multiplier, while the carbon sequestration capacity decreases with the increase in the adsorption density multiplier. This is because as the adsorption density multiplier increases, the adsorption capacity of shale oil is enhanced. The adsorption of CO₂ can displace more light hydrocarbons, but it becomes more difficult to displace the adsorbed oil. As a result, the sequestration capacity of CO₂ in the reservoir is slightly reduced. This trend is consistent with previous findings [64,65,66], which showed that fracture connectivity and injection duration significantly influence both hydrocarbon mobilization and gas trapping behavior. A highly connected fracture network enhances early-stage production by creating dominant flow channels, but it can also accelerate CO₂ breakthrough, reducing long-term storage effectiveness. Conversely, limited connectivity or shorter injection duration may suppress CO₂ migration but compromise oil displacement efficiency. These trade-offs underscore the need for balanced injection strategies that match the physical structure of the reservoir.

Geological heterogeneity has also been shown to increase CO₂ storage uncertainty [67,68,69], particularly when small-scale variations in permeability and capillarity influence CO₂ phase behavior. Such heterogeneity can lead to uneven plume distribution, bypassed oil zones, and inconsistent trapping efficiency across the reservoir. Therefore, the spatial variability of formation properties must be carefully integrated into simulation workflows and injection design. Our results reaffirm these observations, indicating that adsorption-enhanced trapping in some regions may limit dynamic sweep efficiency elsewhere, and that tailoring injection parameters to local rock characteristics is essential for optimizing both recovery and sequestration outcomes.

4.4. Comparison of Continuous Flooding and Huff-n-Puff

Both CO₂ continuous injection and CO₂ huff-n-puff are commonly used in shale oil development and carbon sequestration. However, the productivity and carbon sequestration capacity of these two methods vary under different matrix permeabilities. Therefore, three matrix permeabilities—0.001 mD, 0.01 mD, and 0.1 mD—were set. When radial boreholes serve as injection and production wells, the bottomhole pressures are maintained at 38.26 MPa and 58.26 MPa, respectively. Within one cycle of huff-n-puff, oil production, CO₂ injection, and shut-in are carried out sequentially, with durations of 36 days, 7.2 days, and 1.8 days, respectively.

The lower the permeability, the poorer the injection capacity of CO₂ and the mobility of shale oil. Figure 15 and Figure 16 show the distribution of CO₂ mole fraction under continuous injection and huff-n-puff at different permeabilities, respectively. When the permeability is 0.1 mD, CO₂ can flow through the majority of the area between the upper and lower radial boreholes under continuous injection, while under huff-n-puff, CO₂ affects a spindle-shaped region symmetrically above and below, with a significantly smaller high-concentration CO₂ area compared to continuous injection. The results reflect the disadvantages of huff-n-puff at higher permeabilities, namely, discontinuous production and partial early breakthrough of injected CO₂. As shown in Figure 17, both the oil production rate and CO₂ production rate of huff-n-puff exhibit a saw-tooth pattern, with cumulative oil production and CO₂ sequestration at Day 4000 being only 2.23 and 2.55 times that of continuous injection, respectively.

When the permeability is 0.01 mD, CO₂ can sweep the upper half of the reservoir under continuous injection, while under huff-n-puff, CO₂ affects the upper and lower 1/4 regions. Therefore, the productivity and carbon sequestration capacity of the two methods are relatively close. As shown in Figure 18, at Day 4000, the cumulative oil production of huff-n-puff is 1.55 times that of continuous injection. Although huff-n-puff has a higher initial carbon sequestration capacity than continuous injection, the significant CO₂ breakthrough in the later stage reduces the CO₂ sequestration efficiency, resulting in lower cumulative carbon sequestration than continuous injection.

When the permeability is 0.001 mD, CO₂ under both continuous and huff-n-puff can only sweep a small area around the hydraulic fractures. Therefore, the advantage of huff-n-puff is demonstrated, as it can mobilize the reservoir in multiple layers simultaneously and leverage the diffusion of CO₂. For example, as shown in Figure 19, the cumulative oil production and carbon sequestration of huff-n-puff are 4.72 and 2.32 times that of continuous injection, respectively.

4.5. Influence of Model Boundary and Fracture Length on Simulation Results

To evaluate whether simulation outcomes are sensitive to model scale and fracture length assumptions, we conducted a comparative analysis using extended model boundaries and longer fractures. Specifically, we doubled the lateral domain size from 250 m × 250 m to 500 m × 500 m and simultaneously increased the fracture half-length from 50 m to 100 m. Figure 20 presents the cumulative oil production results under four configurations.

The results indicate that while the absolute oil production and CO₂ storage values are affected by boundary and fracture size-particularly under ultra-low permeability conditions—the relative performance trends between injection modes remain consistent. For instance, huff-n-puff consistently outperforms continuous injection in 0.001 mD permeability settings, regardless of fracture size or model boundary. The cumulative production of continuous gas injection conditions and huff-and-puff steam injection conditions increased to about 2.18 and 2.20 times, respectively, after the boundaries and fractures extension.

This suggests that although domain and fracture dimensions influence flow volume and injectivity as evidenced by the observation that scaling both the fracture network and domain boundary dimensions by a factor of two results in a proportional doubling of production volume, they do not alter the fundamental comparative insights derived from the simulation. This supports the robustness of the conclusions and confirms that the simplified base case is sufficient for identifying dominant flow patterns and injection strategy suitability.

5. Conclusions

To address the limitations of vertical reservoir stimulation and the rapid decline in shale oil production in fractured horizontal wells, and in conjunction with the concept of CO₂-driven shale oil recovery for carbon sequestration, an innovative method of CO₂-enhanced shale oil recovery and carbon sequestration using radial borehole multistage fracturing networks based on single-well foundations is proposed. A compositional model was established to analyze the impacts of different mechanisms on reservoir fluid flow, oil production, and carbon sequestration. The adaptability of continuous CO₂ injection and CO₂ huff-n-puff production modes was compared. The main conclusions of this study are as follows:

(1)

CO₂ injection using radial borehole multistage fracturing requires only a single vertical well to achieve long-term oil recovery and carbon sequestration, providing a reference method for efficient carbon sequestration.

(2)

Non-Darcy flow, diffusion, and adsorption are important factors influencing the CO₂ injection process in radial borehole fracturing. The liquid-phase non-Darcy effect not only retards oil flow but also counteracts the acceleration of CO₂ flow by the gas-phase non-Darcy effect. Both diffusion and adsorption facilitate the retention of CO₂ in the reservoir, with the impact order being non-Darcy > adsorption > diffusion.

(3)

For reservoirs with higher permeability (>0.01 mD), continuous CO₂ injection can effectively mobilize and sequester carbon in the majority of the reservoir. For reservoirs with lower permeability (<0.001 mD), huff-n-puff development should be employed to mobilize and sequester carbon in the vicinity of the fractures.

(4)

The simulated CO₂ injection pressure and rate are within the safe operating limits of conventional injection systems. While technically feasible, the method may still pose risks such as casing corrosion, wellbore instability, and near-well mechanical failure. Future studies should include wellbore integrity modeling and pilot testing to ensure safe field implementation.

(5)

While the compositional model captures key fluid flow and retention mechanisms, it does not explicitly represent fracture-scale leakage, caprock integrity, or heterogeneity in fracture connectivity. In complex field scenarios, these factors can influence both storage security and injectivity. Future improvements should include geomechanical coupling, sealing capacity evaluation, and site-specific calibration to enhance the model’s reliability under field conditions.