Simulation and Sensitivity Analysis of CO₂ Migration and Pressure Propagation Considering Molecular Diffusion and Geochemical Reactions in Shale Oil Reservoirs

Abstract

Unconventional shale oil reservoirs, characterized by ultra-low porosity and permeability, severely constrain oil recovery. CO₂-enhanced oil recovery (CO₂-EOR) following hydraulic fracturing is an effective approach that combines incremental oil recovery with long-term CO₂ storage. However, CO₂ transport in the fracture–matrix system is complex, especially when molecular diffusion and geochemical reactions are coupled. This study conducts numerical simulations on a representative shale reservoir in the Ordos Basin, incorporating both mechanisms under post-fracturing injection–soaking conditions. The results show that molecular diffusion enhances CO₂ mass transfer across the fracture–matrix interface, increasing the final CO₂ sweep efficiency by 0.17 percentage points relative to convection alone, whereas geochemical reactions reduce it by about 0.3 percentage points. When both mechanisms coexist, the net effect is a decrease of approximately 0.2 percentage points in CO₂ sweep efficiency. In contrast, pressure sweep efficiency differs by less than 0.5 percentage points among all cases and stabilizes near 47%, suggesting that pressure propagation is only weakly affected by diffusion and reactions. Sensitivity analysis reveals that, among operational parameters, injection pressure and injection rate strongly affect CO₂ sweep efficiency, whereas soaking time governs pressure propagation. Among reservoir parameters, permeability has the most pronounced influence on both CO₂ and pressure sweep efficiencies, followed by temperature, while initial reservoir pressure has minimal impact. This work quantitatively elucidates the coupled roles of molecular diffusion and geochemical reactions in shale reservoirs and provides practical guidance for optimizing post-fracturing CO₂-EOR operations.

1. Introduction

Driven by the “dual carbon” goals aimed at transforming the global energy structure and combating climate change, Carbon Capture, Utilization, and Storage (CCUS) has emerged as a pivotal technology for achieving carbon neutrality [1,2]. With the continuous growth in global energy demand and the progressive depletion of conventional oil and gas resources, unconventional resources, particularly shale oil, have become a strategic priority for ensuring national energy security [3]. However, shale reservoirs are typically characterized by ultra-low porosity, nano-scale permeability, and complex natural fracture systems [4,5,6,7]. Even with the application of the technology of multi-stage hydraulic fracturing in horizontal wells, the primary recovery factor often remains below 10% [8]. This leaves a substantial amount of oil trapped within the dense matrix, necessitating effective EOR techniques to unlock these valuable resources. Injecting captured CO₂ into deep saline aquifers or depleted oil and gas reservoirs is an effective method for its geological sequestration [9]. Notably, injecting CO₂ into oil reservoirs not only achieves carbon sequestration but also yields significant economic benefits by enhancing oil recovery, thereby creating a win–win situation for both the environment and the economy [10]. Against this backdrop, CO₂-EOR technology is widely considered one of the most promising techniques for the development of shale oil reservoirs. At the broader industrial scale, CO₂-EOR and associated geological storage also fit within emerging green-economy frameworks, where carbon-management and sustainability indicators are increasingly used to assess the development prospects of raw-materials companies [11].

Unlike conventional reservoirs, however, shale reservoirs are typically stimulated by multistage hydraulic fracturing of horizontal wells, where the induced fracture networks serve as the primary pathways for rapid CO₂ migration, often resulting in faster production decline rates compared with conventional systems [12,13,14]. To mobilize the majority of oil stored in the matrix, CO₂ must traverse the fracture-matrix interface and penetrate into nanoscale pores, where direct interactions with the resident hydrocarbons occur [15]. In tight and naturally fractured reservoirs, molecular diffusion across the fracture-matrix interface has been recognized as a dominant mechanism governing the incremental oil recovery during the soaking stage [16,17]. This interfacial mass transfer process plays a crucial role in enhancing hydrocarbon mobilization under limited permeability conditions. Additionally, the transient adsorption of CO₂ on the rock surface, while initially reducing displacement efficiency, contributes to maintaining a more stable displacement front over successive injection–soaking cycles, thereby promoting sustained recovery performance. Beyond mechanistic interpretations of injection and soaking dynamics, studies have demonstrated that CO₂ injection in fractured shale reservoirs preferentially mobilizes hydrocarbons from meso- and macropore systems [18,19]. During the initial stages of the huff-and-puff process, oil recovery is primarily driven by interfacial tension reduction and oil swelling effects. As the soaking period progresses and the pressure path is optimized, molecular diffusion gradually becomes the dominant recovery mechanism, highlighting the evolving interplay between physical and mass-transfer processes throughout the injection cycle. It has been demonstrated that the effective radius of CO₂ influence and the associated sequestration ratio are strongly dependent on reservoir permeability [20]. Specifically, reservoirs with lower permeability tend to exhibit a more limited CO₂ penetration zone yet achieve a higher proportion of CO₂ retention, reflecting the coupled effects of flow resistance and trapping efficiency within tight formations. The displacement and spontaneous imbibition behavior of CO₂ in porous media have been shown to be strongly influenced by injection pressure and matrix permeability [21,22]. Higher pressure differentials and enhanced permeability promote faster imbibition and improved mass transfer between the fracture and matrix systems. However, excessive fracture connectivity may accelerate gas channeling and cause premature breakthrough, highlighting the necessity of optimizing injection-production strategies to maintain displacement front stability and ensure effective reservoir sweep. Compared with conventional hydraulic fracturing, CO₂ fracturing has been shown to generate fractures that are generally longer and narrower, while simultaneously enhancing the connectivity of pre-existing natural fracture networks [23]. In reservoirs characterized by high water saturation, the efficiency of CO₂ injection is largely governed by operational parameters such as the injected slug volume, water alternating gas (WAG) ratio, and injection pressure, which together determine the extent of gas channeling and the overall enhanced oil recovery performance [24]. The incorporation of surfactants, polymers, or nanocolloids into the injection fluid has been shown to enhance the stability of the CO₂ displacement process by reducing the relative permeability and mobility of the CO₂ phase, thereby improving both vertical and areal sweep efficiencies [25]. Moreover, the behavior of CO₂ foam within fractured media is strongly influenced by fracture geometry, which governs foam strength and the progression of the displacement front [26]. The interaction between fracture network density and reservoir pore structure fundamentally governs the evolution of viscous fingering and defines the dissolution flux threshold that controls large-scale mass transport within the formation [27]. Furthermore, accounting for non-Darcy flow behavior of CO₂ across multiple scales is essential, as factors such as threshold pressure gradients, gas slippage, and inertial effects critically influence the coupled flow dynamics between the fracture and matrix systems [28]. In tight oil reservoirs, such as those in the Ordos Basin, increasing the CO₂ injection rate can initially enhance both displacement efficiency and sweep effectiveness; however, the incremental recovery benefit declines sharply once gas breakthrough occurs [29]. This behavior highlights the importance of optimizing injection strategies to balance displacement performance and CO₂ utilization efficiency under reservoir-specific conditions. Existing research has clarified the fundamental mechanisms governing CO₂ mass transfer, displacement behavior, and sequestration potential under diverse geological and operational conditions. The performance of CO₂ injection processes is strongly influenced by fracture geometry, matrix permeability, and key operational parameters. Moreover, insights derived from multi-scale investigations ranging from the pore scale to the reservoir scale have established an essential theoretical framework for the design and optimization of CO₂ injection strategies aimed at maximizing recovery efficiency and storage security. In recent years, a number of studies have emphasized that geochemical reactions during CO₂ injection play a critical role in porosity–permeability evolution, mineral trapping and long-term storage security in CCUS reservoirs [30,31]. In shale systems, experimental and reactive-transport investigations have shown that CO₂–brine–shale interactions can significantly modify pore structure and mineralogy and thus affect both injectivity and trapping behaviour [32,33]. Although several recent studies have started to couple molecular diffusion with geochemical reactions in tight and shale systems, most of them focus on long-term storage behaviour or generic fractured media and do not explicitly analyse short-term huff-n-puff sequences after hydraulic fracturing in a specific continental shale reservoir. In particular, the competing effects between diffusion-driven mass transfer from fractures into the matrix and geochemical consumption of CO₂ on sweep behaviour remain poorly quantified. There is also a lack of studies that simultaneously quantify both CO₂ and pressure sweep efficiencies based on pressure-threshold affected volumes and systematically evaluate the roles of key operational and reservoir parameters under field-representative conditions of the Ordos Basin.

Therefore, this study employs numerical simulation to investigate the impact of molecular diffusion and geochemical reactions on the diffusion extent and pressure propagation of CO₂ from hydraulic fractures into the matrix of a shale reservoir. Furthermore, a sensitivity analysis of key reservoir and operational parameters is conducted. First, a reservoir model and a corresponding fluid model are constructed based on the characteristics of the Chang 7 shale in the Ordos Basin. Subsequently, a series of CO₂ injection scenarios incorporating different mechanisms are simulated, with each scenario consisting of a one-month injection period followed by a one-month soaking period. Through a comparative analysis of these scenarios, the effects of molecular diffusion and geochemical reactions on the propagation fronts of CO₂ and pressure during the injection and soaking stages are evaluated. The sensitivity study systematically assesses the influence of reservoir parameters including temperature, initial reservoir pressure, and permeability, as well as operational parameters such as injection pressure, injection rate, and soaking duration, on CO₂ sweep efficiency and formation pressure variation. The findings are expected to provide fundamental theoretical support and operational design guidance for the development of continental shale oil in the Ordos Basin.

2. Methodology and Simulation

2.1. Flow Governing Equation

A reservoir numerical simulation model was developed using CMG-GEM (2023, Computer Modelling Group Ltd., Calgary, AB, Canada) based on the typical properties of the Chang 7 Member of the Upper Triassic Yanchang Formation shale oil reservoir in the Ordos Basin [34]. The differential form for the mass conservation of any component i distributed among the aqueous (w), oleic (o), and gaseous (g) phases is expressed as:

$${\displaystyle \frac{\partial }{\partial t}}\left[\varphi {\displaystyle \sum _{p=w,o,g}(S_p}{\rho }_p{X}_{ip})\right]+\nabla \cdot \left[{\displaystyle \sum _{p=w,o,g}({\rho }_p{X}_{ip}{v}_p-\varphi S_p{\rho }_p{D}_{ip}\nabla X_{ip})}\right]=q_i+q_r$$

(1)

where phase $p$ represents the set of fluid phases, encompassing the aqueous, oleic, and gaseous states. $\varphi$ is the porosity; $S_p$ is the saturation; ${\rho }_p$ is the mass density; $v_p$ is the velocity of each phase in Darcy’s flow; $X_{ip}$ is the mole fraction of component i in phase $p$; $D_{ip}$ is the molecular diffusion coefficient of component i in phase $p$; $q_i$ is external sources or sinks in injection or production, quantifying the mass rate of component i added or removed per unit bulk volume; $q_r$ signifies internal sources or sinks resulting from homogeneous and heterogeneous geochemical reactions.

$v_p$ is described as

$$v_p=-{\displaystyle \frac{K{K}_{rp}}{{\mu }_p}}\left(\nabla P_p-{\rho }_{p}g\right)$$

(2)

where $K$ is the absolute permeability; $K_{rp}$ is the relative permeability; $\mu$ is the viscosity; $g$ is the gravity constant.

In this study, the molecular diffusion coefficients of CO₂ in the oil and aqueous phases are calculated using the Sigmund [35] and Wilke-Chang [36] correlations, respectively. For the oleic phases, the Sigmund correlation is employed to calculate the binary molecular diffusion coefficient $D_{ij}$ between components. The correlation is expressed as a function of the mixture’s density and pseudo-reduced molar density. The Sigmund correlation is given by:

$$D_{ij}={\displaystyle \frac{{\rho }_k^0{D}_{ij}^0}{{\rho }_k}}\cdot \left(0.99589+0.096016{\rho }_{kr}-0.22035{\rho }_{kr}^2+0.032874{\rho }_{kr}^3\right)$$

(3)

where $D_{ij}$ is the binary molecular diffusion coefficient between components i and j; ${\rho }_k$ is the molar density of the phase (oil or gas); ${\rho }_k^0{D}_{ij}^0$ is the low-pressure gas-density-diffusion product; ${\rho }_{kr}$ is the pseudo-reduced molar density of the mixture.

The effective diffusion coefficient of a specific component i within the multi-component mixture is then calculated using the following relationship:

$$D_{ik}^{*}={\displaystyle \frac{1-y_{ik}}{{\displaystyle \sum _{j\ne i}{y}_{ik}}{D}_{ij}^{-1}}}$$

(4)

where $y_{ik}$ and $y_{jk}$ are the mole fractions of components i and j in phase k

For the diffusion of CO₂ in the aqueous phase, the Wilke and Chang correlation is adopted. this correlation is specifically suited for determining the diffusion of gaseous components dissolved in a liquid solvent. The Wilke and Chang correlation is formulated as:

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

(5)

where $D_{ik}^{*}$ is the molecular diffusion coefficient of solute i in solvent k; $M_{ik}^{\prime }$ is the molecular weight of the solvent; $T$ is the absolute temperature; ${\mu }_k$ is the viscosity of the solvent; ${\nu }_{bi}$ is the molar volume of the solute at its boiling point.

2.2. Reservoir and Fluid Characterization

The numerical simulations in this study were conducted using the commercial compositional simulator CMG-GEM, which is well recognized for its robust capability in handling complex fluid phase behavior, molecular diffusion, and coupled geochemical reactions. A field-scale two-dimensional reservoir model was constructed with dimensions of 110 m, 350 m, and 20 m in the x, y, and z directions, respectively, and discretized using a grid system of 2 m × 2 m × 20 m. To reduce computational cost while maintaining model representativeness, a symmetric element was established to represent the stimulated reservoir volume (SRV) controlled by a single hydraulic fracture around the horizontal well. The fracture height was assumed to be equal to the reservoir thickness. To accurately capture the fluid exchange between fracture and matrix, a logarithmically spaced, locally refined (LS-LR) grid was employed. The key reservoir and fracture parameters were determined based on the geological characteristics of the target formation, as summarized in

Table 1. Key parameters of the reservoir and hydraulic fracture system.

Parameters	Value	Unit
Model dimensions	110 × 350 × 20	m
Initial reservoir pressure	18	MPa
Reservoir temperature	69	°C
Initial water saturation	45.90	%
Matrix porosity	8	%
Matrix permeability	0.02	mD
Total compressibility	6.3 × 10−4	1/MPa
Fracture height	20	m
Fracture width	0.003	m
Fracture half-length	100	m
Fracture conductivity	60	mD·m
Model dimensions	110 × 350 × 20	m
Initial reservoir pressure	18	MPa

.

The fluid model was developed based on compositional analysis of a representative Chang 7 crude oil sample. The Peng–Robinson equation of state (PR-EOS) was employed to characterize the fluid phase behavior, and the model was constructed and calibrated using Winprop module. For computational efficiency, the crude oil components were lumped into nine pseudo-components: CO₂, C₁, N₂-C₂, C₃, C₄-C₆, C₇-C₁₀, C₁₁-C₁₄, C₁₅-C₁₉, and C₂₀₊. The mole fractions, critical properties, and binary interaction coefficients (BICs) of these pseudo-components are summarized in

Table 2. Compositional properties of reservoir fluid.

Component	mol. (%)	Pc (atm)	Tc (K)	Acentric Factor	Mw (g/mol)
CO2	0.09	72.80	304.20	0.2250	44.010
C1	25.72	45.40	190.60	0.0080	16.043
N2-C2	10.54	47.36	264.76	0.0905	29.803
C3	12.14	41.90	369.80	0.1520	44.097
C4-C6	12.08	40.00	447.97	0.2164	67.278
C7-C10	7.24	24.38	630.61	0.3812	116.961
C11-C14	8.96	18.86	634.90	0.5464	169.979
C15-C19	7.23	12.00	700.00	0.6358	233.372
C20+	16.00	14.99	737.31	0.7680	378.757

and

Table 3. Binary Interaction Coefficients Between Reservoir Fluid Components.

Component	CO2	C1	N2-C2	C3	C4-C6	C7-C10	C11-C14	C15-C19	C20+
CO2	0
C1	1.13 × 10−1	0
N2-C2	1.05 × 10−1	1.06 × 10−3	0
C3	1.25 × 10−1	1.24 × 10−3	4.58 × 10−3	0
C4-C6	1.16 × 10−1	4.64 × 10−3	1.01 × 10−2	1.09 × 10−3	0
C7-C10	2.00 × 10−1	1.23 × 10−2	2.04 × 10−2	5.83 × 10−3	1.89 × 10−3	0
C11-C14	1.95 × 10−1	2.08 × 10−2	3.09 × 10−2	1.21 × 10−2	5.98 × 10−3	1.15 × 10−3	0
C15-C19	1.40 × 10−1	2.90 × 10−2	4.05 × 10−2	1.86 × 10−2	1.08 × 10−2	3.71 × 10−3	7.29 × 10−4	0
C20+	9.86 × 10−2	4.39 × 10−2	5.75 × 10−2	3.11 × 10−2	2.09 × 10−2	1.04 × 10−2	4.69 × 10−3	1.73 × 10−3	0

. The accuracy of the fluid model was validated against laboratory PVT data, including constant composition expansion (CCE), differential liberation (DL), and CO₂ swelling tests.

As shown in Figure 1, the maximum deviations between the EOS-calculated and experimental PVT data for solution gas–oil ratio, oil formation volume factor, saturation pressure and CO₂ swelling factor are all within 5%, with most data points showing deviations below 3%, indicating that the calibrated EOS provides a satisfactory representation of the fluid behavior for this study.

In this study, geochemical reactions were coupled within the multiphase flow-compositional transport framework. Considering that the Chang 7 shale samples from the study area contain a relatively high carbonate content and exhibit the fastest kinetic response to CO₂-water interactions over a short time scale, calcite can be regarded as one of the most sensitive and representative reactive minerals under CO₂ exposure. Therefore, only the dissolution and precipitation of calcite are considered in the numerical simulations conducted in this study. (see

Table 4. Geochemical reactions.

	Reactions
Intra-aqueous reactions	$\mathrm{C}{\mathrm{O}}_2+{\mathrm{H}}_2\mathrm{O}\leftrightarrow {\mathrm{H}}^{+}+\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}$
	$\mathrm{C}{\mathrm{O}}_3^{2-}+{\mathrm{H}}^{+}\leftrightarrow \mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}$
	${\mathrm{H}}^{+}+\mathrm{O}{\mathrm{H}}^{-}\leftrightarrow {\mathrm{H}}_2\mathrm{O}$
Mineral reactions	$\mathrm{C}\mathrm{a}\mathrm{C}{\mathrm{O}}_3+{\mathrm{H}}^{+}\leftrightarrow \mathrm{C}{\mathrm{a}}^{2+}+\mathrm{H}\mathrm{C}{\mathrm{O}}_3^{-}$

). The intra-aqueous reactions occur rapidly and are modeled as equilibrium-controlled reactions. In contrast, the dissolution and precipitation of calcite are relatively slow processes and are modeled as kinetically controlled reactions based on the Transition State Theory. The geochemical reaction database was constructed based on the work of Wolery and Daveler [37]. The dissolution and precipitation of minerals alter the pore volume of the rock and thus affect the evolution of porosity. The change in porosity can be calculated based on the variation in the number of moles of minerals, and the relationship is expressed as follows:

$${\varphi }^{*}\equiv {\varphi }^0-{\displaystyle \sum _{\alpha =1}^{n_{\alpha }}\left(\frac{N_{\alpha }}{{\rho }_{\alpha }}-\frac{N_{\alpha }^0}{{\rho }_{\alpha }}\right)}$$

(6)

where ${\varphi }^{*}$ is the porosity after mineral reaction; ${\varphi }^0$ is the porosity before mineral reaction; $N_{\alpha }$ is the total moles of mineral $\alpha$ per bulk volume at the current time; $N_{\alpha }^0$ is the total moles of mineral $\alpha$ per bulk volume at time 0; ${\rho }_{\alpha }$ is the mineral molar density and $n_{\alpha }$ is the number of reactive mineral species. The Kozeny–Carman equation is used to describe the relationship between porosity and permeability:

$$k=k_0{\left({\displaystyle \frac{\varphi }{{\varphi }_0}}\right)}^3{\left({\displaystyle \frac{1-{\varphi }_0}{1-\varphi }}\right)}^2$$

(7)

where $k$ and $k_0$ are the permeabilities after and before the mineral reaction.

2.3. Simulation Schedule

The numerical simulations in this study were initialized after one year of natural depletion production, aiming to reproduce the reservoir pressure depletion caused by the primary recovery stage (see Figure 2). During this production period, the minimum bottom-hole flowing pressure of the production well was set at 10 MPa to maintain the reservoir pressure above the bubble point, thereby preventing the liberation of dissolved gas from the crude oil. Upon completion of this stage, hydraulic fractures were introduced into the model, followed by a one-month period of continuous CO₂ injection. After injection, the well was shut in for an additional one-month soaking period.

A series of four simulation scenarios were designed to systematically investigate the mass transfer and pressure propagation behavior of CO₂ in hydraulically fractured shale reservoirs during the injection–shut-in process, and to evaluate the respective roles of molecular diffusion and geochemical reactions. All cases were modeled under closed boundary conditions, i.e., no-flow boundaries. Case A considered only convection driven by pressure gradients. Case B incorporated geochemical reactions in addition to convection. Case C introduced CO₂ molecular diffusion in oil and water phases on top of convection. Case D accounted for the coupled effects of convection, molecular diffusion, and geochemical reactions.

3. Results

In this study, two types of normalized propagation factors are employed to quantitatively describe the extent of pressure disturbance and CO₂ distribution during the injection and soaking processes. To characterize the propagation of the pressure field, a pressure propagation factor is defined based on a pressure threshold. When the pressure increase in a grid block exceeds a predefined threshold, $\Delta P^{*}$, the block is identified as part of the affected zone. The pressure propagation factor is then calculated as the ratio of the total area of all grid blocks satisfying this condition to the total area of the model. In this study, a pressure threshold of 0.1 MPa is chosen to identify the region experiencing effective perturbation, consistent with the detectable limit for pressure propagation [38]. This indicator reflects the energy propagation during the injection and soaking processes, capturing the spatiotemporal characteristics of pressure transmission during these phases.

A similar approach is used to quantify the diffusion extent of CO₂ in the reservoir during injection and soaking. Regarding compositional distribution, the sweep zone is defined by a CO₂ mole fraction of 1%, a threshold selected to exclude regions with negligible phase behavior effects. The definitions of these objective parameters are detailed below. First, for any given grid block, if its pressure increase, $\Delta P$, satisfies:

$$\Delta P(x,y,t)=P(x,y,t)-P(x,y,0)\ge \Delta P^{*}$$

(8)

then the grid block is considered to be within the pressure-affected zone. The total area covered by such grid blocks is denoted as $A_{\Delta P}\left(t\right)$, and the total area of the model is $A_{\mathrm{model}}$. Based on this, the definition of pressure sweep efficiency is given as follows:

$$E_p(t)={\displaystyle \frac{A_{\Delta P}(t)}{A_{\mathrm{model}}}}$$

(9)

For each case, the pressure increase is determined relative to the initial reservoir pressure prior to CO₂ injection.

3.1. Effect of Molecular Diffusion and Geochemical Reactions

The evaluation of different scenarios of CO₂ injection and soaking in hydraulically fractured reservoirs is presented in terms of CO₂ sweep efficiency and pressure sweep efficiency at the end of each process (Figure 3 and Figure 4). The results indicate that when molecular diffusion is considered (Case C), the final CO₂ sweep efficiency increases from 1.95% (Case A) to 2.12%, i.e., by 0.17 percentage points. For Case A, the slope of the sweep efficiency curve decreases significantly as the pressure gradient weakens, leading to only a minor increase in sweep efficiency from 1.55% to 1.95%. By comparison, in Case C the decline in slope is less pronounced, and the sweep efficiency increases from 1.59% to 2.12%.

As shown in Figure 5B, the CO₂ sweep efficiency of Case B remains consistently lower than that of Case A, with the gap gradually widening during the injection period and further increasing throughout the soaking stage. By the end of the simulation, the sweep efficiency of Case B is only 1.62%, indicating that geochemical reactions exert a pronounced negative effect on the extent of CO₂ diffusion from fractures into the matrix. While the slope of the sweep efficiency curves of Case A and Case B are nearly identical during injection, Case A maintains moderate growth during the soaking stage, whereas Case B exhibits an almost stagnant trend. For Case D, after the shut-in stage, the CO₂ sweep efficiency lies between those of Case A and Case B, at approximately 1.8%. This result indicates that geochemical mineralization reactions partially weaken the molecular diffusion capacity of CO₂, thereby limiting its diffusion range within the reservoir.

Figure 4 illustrates the temporal evolution of pressure sweep efficiency under different cases. The results indicate that, under the same injection scheme, the differences in pressure sweep efficiency among the four cases are minor, all remaining around 47%, exhibiting similar pressure propagation characteristics. At the early stage of injection, the pressure sweep efficiency increases rapidly. However, as the injection continues and the process enters the shut-in stage, pressure propagation gradually stabilizes, and its growth rate decreases significantly. This finding suggests that the influence of molecular diffusion driven by concentration gradients and short-term geochemical reactions on the extent of pressure propagation is negligible.

3.2. Effect of Reservoir and Operational Parameters

The controlling effects of operational and reservoir parameters on CO₂ diffusion and pressure propagation during the injection–soaking process following hydraulic fracturing in shale reservoirs were examined through a sensitivity analysis based on a model incorporating both molecular diffusion and geochemical reactions (Case D). The sensitivity analysis primarily evaluated the effects of operational and reservoir parameters on CO₂ sweep efficiency and pressure sweep efficiency. The operational parameters considered include injection rate, injection pressure, and soaking time, while the reservoir parameters encompass initial reservoir pressure, reservoir permeability, and reservoir temperature. The baseline case corresponds to an injection rate of 3000 m³/day, an injection pressure of 30 MPa, a soaking time of 30 days, a matrix permeability of 0.05 mD, a reservoir temperature of 70 °C, and an initial reservoir pressure of 18 MPa.

The parameter ranges used in the sensitivity analysis are chosen to represent the main sources of uncertainty under representative conditions of the Chang 7 shale. In particular, the matrix permeability range spans the measured core permeability values for the target reservoir, and the base-case PVT/EOS description is calibrated against available laboratory data for the reservoir oil and brine.

3.2.1. Injection Rate

The effect of injection rate on CO₂ sweep efficiency and pressure sweep efficiency was evaluated. The sensitivity of CO₂ and pressure sweep efficiencies to the injection rate is shown in Figure 6. As the injection rate increases from 2000 m³/day to 4000 m³/day, the CO₂ sweep efficiency rises from 1.35% to 2.13%, i.e., by 0.78 percentage points. Meanwhile, the pressure sweep efficiency increases from 43.71% to 48.28%, i.e., by 4.57 percentage points. With increasing injection rate, both CO₂ sweep efficiency and pressure sweep efficiency show noticeable improvement, allowing more CO₂ to diffuse from fractures into the deeper matrix and come into contact with a greater volume of crude oil, thereby reducing oil viscosity and causing oil expansion. In addition, the pressure propagation range expands with higher injection rates, replenishing and maintaining reservoir pressure, which provides additional driving energy for oil flow and ultimately enhances oil recovery.

3.2.2. Injection Pressure

Figure 7 illustrates the effect of injection pressure on CO₂ sweep efficiency and pressure sweep efficiency. Both indicators increase significantly with rising injection pressure. When the injection pressure increases from 24 MPa to 36 MPa, the CO₂ sweep efficiency rises from approximately 1.52% to 2.78%, and the pressure sweep efficiency increases from 46.61% to 50.83%. A clear positive correlation is observed within the investigated pressure range, with the most pronounced improvement occurring when the injection pressure is below 30 MPa. These results indicate that increasing injection pressure effectively expands the CO₂ sweep range and enhances pressure propagation within the studied range.

3.2.3. Shut-In Time

Figure 8 illustrates the effect of soaking time on CO₂ sweep efficiency and pressure sweep efficiency. Both indicators gradually increase with the extension of soaking time, showing a continuous upward trend within the range of 20 to 40 days. When the soaking time is extended from 20 days to 40 days, the CO₂ sweep efficiency increases from approximately 1.71% to 1.90%, while the pressure sweep efficiency rises from 42.38% to 49.10%. Extending the soaking period allows CO₂ to achieve a wider sweep range and has a positive effect on the extent of pressure propagation.

3.2.4. Permeability

The effect of permeability on CO₂ sweep efficiency and pressure sweep efficiency after CO₂ injection and soaking following hydraulic fracturing is reported in Figure 9. As permeability increased from 0.01 mD to 0.03 mD, the CO₂ sweep efficiency rose sharply from 1.48% to 1.99%, while the pressure sweep efficiency increased from 34.12% to 56.31%. With further increases in permeability to 0.05 mD, these values reached 2.17% and 70.3%, respectively. Beyond 0.07 mD, both efficiencies continued to rise but at a slower rate, with the CO₂ sweep efficiency reaching 2.34% and the pressure sweep efficiency stabilizing near 76% at 0.09 mD. The most significant improvements were observed in the low-permeability regime, where small increases in permeability resulted in disproportionately large enhancements in both CO₂ migration and pressure propagation.

3.2.5. Temperature

Figure 10 shows the influence of reservoir temperature on CO₂ sweep efficiency and pressure sweep efficiency. At reservoir temperatures ranging from 59 °C to 79 °C, the CO₂ sweep efficiency increased from 1.65% to 2.06%, while the pressure sweep efficiency rose from 45.10% to 47.93%. The overall improvement in pressure sweep efficiency was relatively small, with an increase of 2.83 percentage points. Both indicators exhibited an approximately linear growth trend with increasing temperature.

3.2.6. Initial Reservoir Pressure

Figure 11 illustrates the effect of initial reservoir pressure on CO₂ sweep efficiency and pressure sweep efficiency. As the initial reservoir pressure decreases, both the CO₂ sweep range and the pressure propagation range decline. Specifically, the CO₂ sweep efficiency decreases from 1.87% to 1.79%, and the pressure sweep efficiency drops from 48.45% to 44.95%. The variations in both indicators under different reservoir pressure conditions are relatively minor.

4. Discussion

This section investigates the variations in CO₂ diffusion range and pressure propagation range in the reservoir under the effects of molecular diffusion and geochemical reactions. Subsequently, the main controlling factors of operational and reservoir parameters, including injection rate, injection pressure, soaking time, permeability, reservoir temperature, and initial reservoir pressure, on the CO₂ diffusion range and pressure influence range are analyzed.

The characteristics and behaviors of CO₂ injection and soaking processes in the fractured reservoir were studied under different mechanisms. During the injection stage, the sweep efficiency curves of Case A and Case C almost overlap. Under the convection-dominated regime driven by high injection pressure gradients, the effect of molecular diffusion on the CO₂ migration range is negligible, and the extent of CO₂ penetration from the fractures into the matrix is primarily controlled by the pressure gradient. In contrast, during the soaking stage, the reservoir system tends to reach a new pressure equilibrium. This behavior demonstrates that the concentration gradient between the CO₂-rich zone formed near fractures during injection and the zero-concentration zone in the matrix drives molecular diffusion, which becomes the dominant mechanism for CO₂ migration into the deeper matrix during soaking. This finding is further illustrated in Figure 5. As shown in Figure 5A, when only convection is considered, CO₂ penetration into the surrounding matrix is limited, restricting further migration into the deeper matrix and reducing the extent of CO₂-oil contact, thereby diminishing the displacement efficiency. In contrast, when molecular diffusion induced by concentration gradients is included (Figure 5C), diffusion gradually emerges as the primary driving mechanism for CO₂ transport into the matrix during soaking. As a result, more CO₂ dissolves into the oil, promoting oil swelling and viscosity reduction, and enhancing recovery. Molecular diffusion, as a slow but persistent process, proves to be the critical mechanism for enlarging the sweep volume, improving CO₂-oil interactions, and ultimately achieving effective sequestration.

During the injection stage, part of the injected CO₂ dissolves into the formation water, causing a reduction in pH (Figure 12). Under such acidic conditions, minerals such as calcite undergo dissolution, which increases porosity. However, even though the pH in the near-fracture aqueous phase changes significantly, the total amount of calcite dissolved and CO₂ converted into bicarbonate represents only a small fraction of the overall CO₂ inventory, causing only minor changes in porosity and permeability over the short simulation period, so that the net reduction in CO₂ sweep efficiency remains on the order of 0.3 percentage points. It is noteworthy that the porosity–permeability relationship described by the Kozeny–Carman equation is only a simplified approximation for representing the influence of porosity changes on permeability, and it cannot fully capture the nanoscale pore structure and pronounced heterogeneity characteristic of unconventional reservoirs. During the soaking stage, when molecular diffusion attempts to transport CO₂ deeper into the matrix, geochemical reactions continuously convert dissolved CO₂ into bicarbonate ions in the aqueous phase. This process markedly decreases the concentration of free CO₂ available for diffusion and weakens the concentration gradient that drives the entire diffusion process. Consequently, despite the slight improvement in porosity, the reduction in CO₂ diffusion potential leads to a smaller amount of CO₂ penetrating into the deeper matrix, thereby lowering the overall sweep extent, as illustrated in Figure 5C,D. These findings clearly demonstrate that the negative influence of geochemical reactions is particularly pronounced during the diffusion-dominated soaking stage. Given that the overall CO₂ sweep efficiency in this extremely tight shale system accounts for only about ~2% of the matrix volume within the 60-day injection–soaking window, absolute differences of 0.2–0.3 percentage points among the mechanistic scenarios still correspond to relative variations of approximately 10–15%.

Pressure sweep efficiency is primarily governed by hydraulic diffusivity, which is determined by reservoir permeability, fluid viscosity, system compressibility, as well as boundary conditions and time scales. Consequently, during both CO₂ injection and soaking following hydraulic fracturing, the pressure diffusion extent exhibits no significant variations among the cases [39]. This weak sensitivity arises because pressure propagation is primarily controlled by hydraulic diffusivity, which depends on permeability, porosity, fluid viscosity and overall compressibility, all of which are only marginally affected by molecular diffusion and geochemical reactions over the short simulation period. Overall, the extent of pressure propagation is more strongly influenced by factors such as injection intensity, duration, and reservoir permeability. Within the spatial and temporal scale considered in this study, the inclusion of molecular diffusion or the coupling of geochemical reactions exerts a negligible effect on pressure diffusion.

This study fills an important knowledge gap by examining the interplay between molecular diffusion and geochemical reactions in tight shale reservoirs, particularly during the soaking stage when fluid flow is extremely slow. The results reveal a key counterbalancing mechanism: although geochemical reactions lead to limited mineral dissolution and a slight increase in pore volume, these reactions simultaneously consume CO₂ dissolved in the aqueous phase. Such CO₂ consumption reduces the concentration gradient between the fracture and the matrix, which is the primary driving force for CO₂ diffusion from the fracture system into the matrix. Consequently, geochemical reactions actually slow the expansion of the CO₂ diffusion front. In addition, we found that the pressure differences among the mechanistic scenarios are all less than 0.5%. This outcome is scientifically significant, as it indicates that pressure propagates through the reservoir much more rapidly than the chemical reactions proceed and is essentially unaffected by them. For field applications, this implies that pressure monitoring during the soaking stage does not require explicit or highly detailed resolution of the accompanying chemical reactions.

A higher injection rate or pressure directly intensifies convective transport during the injection stage. A higher injection rate facilitated the migration of CO₂ within the fracture-matrix system, thereby enhancing matrix displacement and improving overall sweep efficiency. However, excessive injection rates may induce fluid fingering and accentuate heterogeneity-related channeling, leaving low-permeability zones unswept; this effect was particularly evident in pressure sweep efficiency [40]. Injection pressure governed the driving force for CO₂ penetration into the matrix by controlling the pressure differential across fractures and the matrix. With increasing pressure, CO₂ more readily entered nanopores and enhanced the dissolution-swelling effect, thereby improving sweep efficiency. Conversely, excessively high pressures could strengthen fracture channeling, resulting in premature breakthrough and reduced pressure sweep efficiency. Therefore, an optimal balance in injection pressure must be achieved to enhance CO₂ displacement while maintaining efficient pressure propagation.

The extended soaking period significantly enhanced pressure sweep efficiency, primarily because, under no-flow conditions, the pressure gradient was allowed to diffuse further into the matrix over a longer period, thereby expanding the pressure-affected region. In addition, the prolonged pressure equilibration provided more time for CO₂ molecular diffusion and dissolution, which contributed to a moderate improvement in the sweep efficiency within the matrix.

As shown in Figure 13 and Figure 14, injection pressure serves as the dominant factor governing CO₂ sweep efficiency, with injection rate ranking second, while shut-in time exerts a more significant influence on pressure sweep efficiency. Compared with the injection rate, CO₂ sweep efficiency is more sensitive to changes in injection pressure. In contrast, soaking time has only a limited impact on CO₂ sweep efficiency but exhibits a pronounced influence on pressure sweep efficiency. Overall, the contribution of soaking time to CO₂ sweep efficiency is considerably smaller than that of injection rate and pressure, indicating that under the shale reservoir conditions considered in this study, the effect of molecular diffusion, though present, remains constrained by permeability and pore-throat structure.

The enhancement in permeability reduces viscous resistance and broadens the domain of convective flow, enabling pressure disturbances to propagate more rapidly and extensively, which in turn leads to a marked increase in pressure sweep efficiency. Meanwhile, permeability controls the effective transmissibility of the fracture-matrix system, allowing more CO₂ to penetrate into the matrix and thereby expanding the overall sweep region. In contrast, under low-permeability conditions, convective effects are significantly weakened, and the system becomes predominantly diffusion-controlled, resulting in a notable decline in CO₂ sweep efficiency. Furthermore, permeability is closely associated with pore-throat size: larger throats correspond to lower capillary entry pressures, facilitating CO₂ penetration into nanopores. Conversely, mineral precipitation at the advancing front may constrict pore throats, reduce effective permeability, hinder front propagation, and ultimately diminish CO₂ sweep efficiency.

The increase in temperature significantly elevates the effective diffusion coefficient of CO₂ in oil, water, and nanopores while simultaneously reducing fluid viscosity, thereby intensifying the diffusive flux across the fracture-matrix interface and enabling greater CO₂ penetration into the matrix. In addition, higher temperatures accelerate the kinetics of dissolution and precipitation, where mineral dissolution in the near-fracture zone slightly enhances local porosity and effective permeability, further facilitating pressure transmission and mass transfer. It is noteworthy that temperature also influences the solubility and phase behavior of CO₂ in oil-water systems; however, compared with the effects of enhanced diffusion and viscosity reduction, its contribution to sweep efficiency is relatively minor and does not alter the overall upward trend [41].

As the initial reservoir pressure increases, the injection pressure differential and corresponding pressure gradient are directly reduced, slowing down pressure propagation and leading to a decline in pressure sweep efficiency. At the same time, elevated initial pressure enhances CO₂ solubility and swelling effects in oil-water systems, thereby increasing the dissolved CO₂ content in the near-fracture region; however, the reduced pressure differential weakens convective exchange between fractures and the matrix, shortening the penetration distance of CO₂ into the matrix. Consequently, CO₂ sweep efficiency manifests as a weak, non-monotonic response. Furthermore, Figure 15 and Figure 16 clearly show that matrix permeability is the dominant factor influencing CO₂ sweep efficiency, followed by temperature, while permeability also plays the most critical role in controlling pressure sweep efficiency. This is mainly because the tested permeability range spans almost one order of magnitude and directly scales both advective fluxes and hydraulic diffusivity, whereas the temperature range only induces moderate changes in diffusion coefficients and fluid viscosity, leading to a secondary impact on sweep efficiencies. In contrast, initial reservoir pressure exerts only a minor effect, being weakly negatively correlated with pressure sweep efficiency, and its contribution to CO₂ sweep efficiency is negligible compared with permeability and temperature.

Finally, several limitations of the present study should be acknowledged. The simulations were performed in a two-dimensional symmetric element representing a single hydraulic fracture and SRV. This configuration is suitable for resolving near-fracture CO₂ migration and pressure diffusion, but it does not fully capture the three-dimensional connectivity of complex fracture networks, vertical and lateral heterogeneity, or multi-fracture and multi-well interference in real shale reservoirs. In addition, the total simulation window of 60 days, covering one month of CO₂ injection followed by one month of soaking, is representative of a single short-term huff-n-puff cycle rather than long-term operations, so cumulative pressure dissipation and progressive geochemical effects over multiple cycles or geological time scales are not fully addressed. Moreover, the geochemical model accounts only for calcite dissolution-precipitation, while other minerals such as clays, quartz and feldspars are treated as inert and do not participate in reactions. This simplification does not fully represent the complex multi-mineral reaction networks and pore-structure evolution in real shale formations. These simplifications imply that the predicted CO₂ and pressure sweep efficiencies should be interpreted as local, short-term responses around an isolated stimulated volume under representative shale reservoir conditions. Future work should be extended to three-dimensional multi-fracture systems and incorporate multi-mineral reactive transport as well as longer simulation periods, in order to more accurately quantify reservoir-scale spatial heterogeneity, fracture interference, and the cumulative effects of geochemical reactions.

From a broader perspective, the large-scale deployment of CCUS and post-fracturing CO₂-EOR is influenced not only by reservoir-scale technical performance but also by broader innovation and governance frameworks. Cooperation among universities, industry and policy makers has been identified as a key enabler for aligning technological advances with regulatory requirements and decarbonization targets through mechanisms such as industrial symbiosis and innovation networks [42]. The quantitative insights obtained in this study on the controls of injection strategy and reservoir properties on CO₂ and pressure sweep efficiencies can therefore provide technical input to such collaborative decision-making for the design of post-fracturing CO₂-EOR projects.

5. Conclusions

In this study, the Chang 7 shale oil reservoir of the Ordos Basin was selected as a representative case to establish a numerical simulation framework for investigating the effects of molecular diffusion and geochemical reactions on CO₂ migration and pressure propagation during the post-fracturing injection–soaking process. Four simulation cases were designed to compare the individual and coupled contributions of molecular diffusion and geochemical reactions. A sensitivity analysis was further conducted to evaluate the influence of key reservoir and operational parameters. The principal conclusions of this study are as follows:

• Compared with convection alone, molecular diffusion increases the final CO₂ sweep efficiency by approximately 1.7%, whereas geochemical reactions consistently suppress the CO₂ sweep efficiency, reducing it by about 0.3% and further widening the gap during the soaking stage. When diffusion and reactions coexist, the positive effect of molecular diffusion is partially offset, resulting in a reduction of approximately 0.2% in the final CO₂ sweep efficiency compared with the diffusion-only case.
• At the scale of this study, the simulation results show that after 60 days of CO₂ injection and soaking following hydraulic fracturing, the maximum difference among the four mechanisms is only 0.5%. This indicates that the effects of molecular diffusion and geochemical reactions on pressure propagation are negligible.
• The results indicate that, for CO₂-EOR following hydraulic fracturing, injection pressure and reservoir permeability constitute the primary controlling factors governing CO₂ sweep efficiency and energy utilization, whereas shut-in duration and reservoir temperature play secondary roles and should be considered as auxiliary parameters in adaptive design. The specific optimal values of these parameters are reservoir-dependent and require site-specific calibration.

These findings are derived from a two-dimensional, single-fracture symmetric element with a short injection–soaking window and a simplified geochemical model that explicitly considers only calcite, and thus are most representative of local, short-term behavior around a single stimulated volume; the detailed model limitations and directions for future 3D, multi-fracture and multi-mineral extensions are discussed in the Section 4.