The oil sample used in the experiment is anhydrous kerosene, exhibiting a density of 0.8 g/cm³ and a viscosity of 2.5 mPa s at 25 °C and 0.1 MPa. The water sample used in the experiment is high-purity deuterium oxide (D₂O) with a density of 1.105 g/cm³ and a viscosity of 1.095 mPa s under the same conditions of 25 °C and 0.1 MPa. In this experiment, three tight cores from the Y District of the HuaQing Oilfield, located in the Ordos Basin, are used, and the physical properties of the cores are shown in Table 1.

We used anhydrous kerosene as a surrogate for light crude oil for three reasons: (i) reproducibility and safety—kerosene has a stable, well-characterized composition and physical properties, reducing variability due to crude compositional changes and minimizing hazards; (ii) NMR compatibility—kerosene’s hydrogen signal is strong and consistent, while deuterium oxide (D₂O) suppresses water signals, enabling clean separation of oil-phase responses without interference from paramagnetic species occasionally present in crude; (iii) wettability and flow similarity—kerosene closely approximates the behavior of light tight oils under laboratory conditions, allowing us to isolate the effects of pressure gradient and pore-scale geometry on waterflooding performance. Accordingly, we refer to the oil phase as “kerosene” throughout the manuscript, and all NMR and simulation analyses are based on kerosene–water systems.

The experimental setup comprises three primary components: the core displacement device, the nuclear magnetic resonance monitoring system, and the metering apparatus. Figure 1 illustrates the configuration of the experimental device. The displacement system consists of an ISCO constant-speed, constant-pressure pump and an intermediate container. The core experimental equipment features a self-developed online nuclear magnetic resonance monitoring system, which includes a low-field nuclear magnetic resonance device (Macro12-150H-I, Suzhou Niumai), a core holder, and a constant-pressure circulating control pump. In this experiment, the Q-CPMG sequence was employed to collect the core throat signals, operating at a resonance frequency of 12.79 MHz with a coil diameter of 25 mm. The echo time (TE) was set to 0.5 m, with a waiting time of 6 s and a total of 1024 echoes recorded. Additionally, the HSE sequence was utilized to scan the nuclear magnetic resonance imaging signals. During the experimental process, data measurement occurs through two means: one involves the metering system, which records the pressures at the inlet and outlet ends of the core and the flow rate at the outlet, while the other employs the nuclear magnetic resonance monitoring system to observe the distribution patterns of oil and water throughout the experiment.

To compare the effects of varying scales of advanced fracturing-flooding water injection, three experimental sets were designed, simulating both conventional water flooding and advanced fracturing-flooding water injection. The first set of conventional water flooding experiments involved a total injection volume of 3 PV (pore volumes). For the second set of advanced fracturing-flooding water injection experiments, the total volume injected was also 3 PV, with the pre-injection volumes (the pre-injection volume when production is terminated and the injection pressure approaches the fracture initiation pressure.) set at 0.3 PV and 0.6 PV, corresponding to multiplicative factors in the near-wellbore region. The experimental design details are summarized in Table 2. The experimental steps are as follows:

Basic preparations: The materials for the experiment, such as the oil sample, water sample, core, etc., are prepared in accordance with the experimental designs, and the central device is connected and its airtightness is verified.

Under the influence of a static magnetic field and an externally applied low magnetic field, the hydrogen nuclei in the pore throats of kerosene (oil phase) resonate (Yuan et al., 2023; Liu et al., 2022). During the relaxation process, radiofrequency signals are emitted. By receiving these signals and conducting mathematical inversion, we can generate an amplitude-relaxation time curve. The expression of relaxation time is shown in Equation 1 (Li et al., 2022b): 1 T 2 = 1 T 2 B + 1 T 2 S + 1 T 2 D (1)

Where T₂ is the total relaxation time, ms; T _2B is the transverse relaxation time of the filling fluid, ms; T _2S is the surface transverse relaxation time, ms; T _2D is the transverse relaxation time caused by fluid diffusion in the magnetic field gradient, ms.

Due to the significant interaction between fluids and the surface of the rock within dense cores, the bulk relaxation time (T _2B) is considerably greater than the relaxation time (T ₂). Additionally, because the echo time (T _E) is relatively small, the diffusion relaxation time (T _2D) also greatly exceeds T ₂. Consequently, these two terms can be disregarded, allowing the relaxation time to be expressed as follows (Equations 2–4): T 2 = T 2 S = 1 ρ δ r = C r (2) δ = S V r (3) C = 1 ρ δ (4)

Where ρ is the relaxation strength constant of the rock surface; δ is the pore shape factor; S is the surface area of rock particles, cm²; V is the pore volume, cm³; r is the average pore radius, cm; C is the conversion coefficient, μm/ms.

From Equation 2, it is evident that the relaxation time (T ₂) is directly proportional to the pore radius of the rock, meaning that larger pores correspond to longer relaxation times, while smaller pores are associated with shorter relaxation times. After obtaining the conversion factor (C), the T₂ spectrum’s horizontal axis can be translated into pore radius, thereby allowing the T2 spectrum to effectively reflect the distribution of pore sizes within tight sandstone reservoirs.

By calibrating the T ₂ curve obtained from NMR scanning of the saturated core with mercury intrusion experiments, we can derive the pore size conversion factor (C), enabling the translation of the relaxation time on the original T ₂ spectrum into pore throat radius. Following the approach proposed by Li et al., we accumulate the intensity of hydrogen signals from kerosene (oil phase) to generate a cumulative distribution map of the hydrogen signal strength in the core. Based on the T ₂ spectrum of the core used in the experiments, pore throats are categorized into three distinct groups: small pore throats (0.01 μm < r < 0.1 μm), medium pore throats (0.1 μm < r < 0.5 μm), and large pore throats (r > 0.5 μm).

During the experimental process, the simulated water used for saturation was a composite deuterium oxide, and the NMR monitoring system was only capable of detecting the hydrogen signal from kerosene (oil phase). Consequently, the nuclear magnetic resonance signals obtained throughout the displacement experiment solely reflect changes in the oil. The formula for calculating oil recovery efficiency is shown in Equation 5: E = A 0 − A 1 A 0 × 100 % (5)

Where E is the oil recovery efficiency, %; A ₀ is the area enclosed by the T ₂ spectrum and the horizontal axis over a specific pore radius range after saturation, cm²; A ₁ is the area enclosed by the T ₂ spectrum and the horizontal axis over a specific pore radius range after displacement, cm².

A comparison of the results of three groups of different-scale advanced fracturing-flooding water injection experiments shows that the initial displacement pressure differentials at the onset of waterflooding were recorded as 6.34 MPa, 7.56 MPa, and 8.45 MPa, respectively. This indicates that the advanced fracturing-flooding water injection significantly enhances the displacement pressure differential compared to conventional water injection. As the injection scale increases, the pressure gradient becomes greater, thereby facilitating the establishment of an effective displacement pressure system between the oil and water wells.

Figure 2 depicts the final oil recovery efficiencies after the displacement was completed in the three experimental groups. The ultimate oil recovery efficiencies for the three experiments were recorded at 35.5%, 40.5%, and 43.5%, respectively. These results demonstrate that, compared to conventional water injection, AFWI enhances oil recovery efficiency by 5%. Furthermore, increasing the scale of AFWI further augments the oil recovery efficiency.

The comparative results of the kerosene (oil phase) signal intensity along the core at the conclusion of the advanced fracturing-flooding water injection experiment are illustrated in Figure 3. This method enables the utilization of the oil phase at the injection end of the core. For the 0.3 PV advanced fracturing-flooding water injection, the advancement distance of the waterflood front was measured at 1.5 cm, while for the 0.6 PV advanced fracturing-flooding water injection, the advancement distance reached 2.6 cm. As the scale of the advanced fracturing-flooding water injection increases, the extent of utilization at the injection end of the core also intensifies, resulting in an expanded advancement distance of the waterflood front.

The comparative results of the kerosene (oil phase) signal intensity along the core at the conclusion of the waterflood displacement following the advanced fracturing-flooding water injection are illustrated in Figure 4. During the pre-injection phase, a certain displacement pressure differential and pressure gradient were established, allowing the fluid within the core to be “activated in advance.” The subsequent continuous water injection further established the displacement pressure differential, facilitating the extraction of this prematurely mobilized fluid. Upon the completion of the displacement, advanced fracturing-flooding water injection exhibited a superior ability to utilize the throat of the core at the injection end. Overall, advanced fracturing-flooding water injection demonstrates a greater extent of utilization compared to synchronous water injection; consequently, increasing the scale of advanced fracturing-flooding water injection can further enhance the utilization of the oil phase within the core.

Nuclear magnetic resonance (NMR) scans of the core were conducted after initial saturation, at the conclusion of synchronous water displacement, and after advanced fracturing-flooding water injection of 0.3 PV and 0.6 PV, yielding the corresponding T₂ spectra. These spectra were then transformed into probability distribution curves of the oil phase within pores of varying radii, as depicted in Figure 5. Upon completion of the displacement, the hydrogen signal intensity of kerosene (oil phase) in the small pore throats experienced a modest decline, while the signal intensity in the large pore throats exhibited a significant reduction. Moreover, as the volume of advanced fracturing-flooding water injection increased, the utilization extent within the core correspondingly intensified. Based on the T₂ spectra from the experimental cores, pore throat radii were categorized as small, medium and large.

Figure 6 illustrates the extent to which different pore throats in the core are mobilized after the completion of displacement following advanced fracturing-flooding water injection. Synchronous water injection primarily mobilizes large pore throats along with a portion of small pore throats. In contrast, advanced fracturing-flooding water injection not only primarily mobilizes large pore throats but also enhances the utilization extent of small pore throats. Both 0.3 PV and 0.6 PV g advanced fracturing-flooding water injection effectively mobilize pore throats of various sizes, predominantly focusing on large throats. However, as the volume of advanced fracturing-flooding water injection increases, the utilization extent of small pore throats also rises. This phenomenon is largely attributed to the fact that a greater volume of advanced fracturing-flooding water injection generates an increased displacement pressure differential and pressure gradient, thereby facilitating the further utilization of the oil phase within the small pore throats.

The model underwent a binarization process through threshold segmentation of the scanned image of the cast specimen (Figure 7a), followed by the application of MATLAB code to smooth the boundaries and eliminate noise, resulting in the pore throat structure distribution portrayed in Figure 7b. The model dimensions were 30 μm × 30 μm. Subsequently, the obtained point-line formatted image was imported into COMSOL software, where the geometric model was subjected to mesh partitioning using Delaunay’s free triangular meshing, yielding the model displayed in Figure 7c with a total of 105,624 elements and a minimum element mass of 0.1169. The initial fluid distribution within the model is depicted in Figure 7d, where blue represents the aqueous phase and red represents the oil phase. The simulation parameters of the model are shown in Table 3.

The pore-scale numerical model is based on the following assumptions.

The whole simulation process encompasses solely the two phases of oil and water.

In this simulation, the phase-field method was employed to couple the Cahn-Hilliard equation with the Navier-Stokes equations via surface tension. This approach allows for an accurate description of the fluid flow processes of two-phase fluids while ensuring mass conservation. The Cahn-Hilliard equation primarily describes the phase separation process, which includes the separation of two-phase or multiphase fluids, expressed as follows (Equation 6): ∂ φ ∂ t + u · ∇ φ = γ λ ε 2 Δ ψ ψ = − ε 2 Δ φ + φ φ 2 − 1 (6)

Where u is the fluid flow velocity, m/s; γ is the mobility, m³·s/kg; λ is the mixed energy density, N; ε is the interfacial thickness, m; ψ is the phase field auxiliary variable; φ is the dimensionless phase field variable. In the oil-water two-phase flow, φ = 1 represents the oil phase, and φ = 1 represents the water phase. In the oil-water transition region, the phase field variable φ varies continuously between 1 and 1. The fluid properties corresponding to the phase-field variable can be expressed as follows (Equation 7): n φ = 1 + φ 2 n 1 + 1 − φ 2 n 2 (7)

Where n ₁ and n ₂ are the physical properties of the oil and water phases, thereby achieving a smooth transition of fluid properties at the interface.

The Navier-Stokes equations are primarily employed to delineate the variations of mass and momentum in steady-state fluid flow. By incorporating interfacial tension as a body force within the Navier-Stokes equations, it becomes possible to characterize the flow processes of two-phase fluids. The corresponding expression is as follows (Equation 8): ρ ∂ u ∂ t + ρ u · ∇ u = − ∇ p I + ∇ · μ ∇ u + ∇ u T + F st ∇ · u = 0 (8)

Where ρ is the density, kg/s³; p is the pressure, Pa; I is the unit vector; μ is the viscosity, mPa·s; F st is the interfacial tension force term.

Combined with the Cahn-Hilliard equation, a two-phase Cahn-Hilliard-Navier-Stokes flow system can be obtained as Equation 9. ∂ φ ∂ t + u · ∇ φ = γ λ ε 2 Δ ψ ψ = − ε 2 Δ φ + φ φ 2 − 1 ρ ∂ u ∂ t + ρ u · ∇ u = − ∇ p I + ∇ · μ ∇ u + ∇ u T + F st ∇ · u = 0 (9)

For the surface of rock particles, the boundary conditions considering the contact angle of oil and water are shown in Equations 10–12 (Yue et al., 2006; Zhou et al., 2010): u = 0 (10) m · ε 2 ∇ ϑ = ε 2 ⁡ cos θ c ∇ ϑ (11) m · γ λ ε 2 Δ ψ = 0 (12)

Where θ c is the contact angle, °.

COMSOL Multiphysics is a powerful software tool for multi-physics simulation. This software is used to mesh and solve the finite element problem. The backward difference method is used to discretize time, and the MUMPS direct solver is used to solve the problem. The utilization characteristics of pore throats during advanced fracturing-flooding water injection at various scales are simulated.

To validate the applicability of the phase field method in simulating oil-water two-phase flow, a simulation was conducted using this approach on a horizontal channel measuring 1 μm × 10 μm, following the validation methodology proposed by Wang et al. (Wang et al., 2024). The channel was initially filled with oil, while the water phase entered from the left side. The model disregarded the effects of gravity and inertial forces. The simulation results were then compared with the theoretical equations put forth (Equation 13) by Lucas (Lucas, 1918) and Washburn (Washburn, 1921). x t = r σ ⁡ cos ⁡ θ 2 μ t (13)

Where μ is the viscosity of the wetting liquid, Pa·s; θ is the contact angle, °; r is the tube radius, m; σ is the surface tension of the wetting liquid, N/m.

The comparative results are illustrated in Figure 8, where the viscosities of oil and water were set at 0.005 Pa s and 0.001 Pa s, respectively, and the contact angle was established at 60°. The simulation results align closely with the calculated outcomes of the theoretical equations, thereby verifying that the phase field method can accurately model the migration behavior of oil and water at pore-throat scales.

Based on the established simulation plan, micro-simulations of advanced fracturing-flooding water injection at varying scales have been completed, resulting in pressure fields of different scales of advanced injection, as depicted in Figure 9. As the scale of pre-injection increases, the pressure at the inlet gradually rises, which is consistent with the findings from the core experiments.

Figure 10 illustrates the oil saturation fields for different scales of advanced fracturing-flooding water injection. Due to the relatively small pressure gradient at both ends of conventional water injection, in Figure 10a, the injected water primarily displaces crude oil along the main flow path, mainly mobilizing the oil within larger pore throats, while the crude oil trapped in the smaller throats remains largely inaccessible, resulting in a high residual oil saturation and a low overall recovery rate. However, as the scale of advanced fracturing-flooding water injection increases, the pressure gradient at both the injection and production ends progressively intensifies. In Figures 10b,c, the crude oil in smaller pore throats becomes mobilized, leading to a gradual decrease in residual oil saturation, an expanded range of water displacement, and an overall enhancement in recovery efficiency.

Figure 11 depicts the streamline fields of pore throats at varying scales of advanced fracturing-flooding water injection. In contrast to the oil saturation fields, it is evident that during conventional water injection, the main streamlines are primarily distributed along the larger pore throats, forming dominant pathways, while the number of streamlines within the smaller throats is nearly nonexistent. Consequently, with a relatively low pressure gradient, the utilization predominantly occurs within the larger throats, rendering the smaller throats largely ineffective. However, as the scale of advanced fracturing-flooding water injection increases, the pressure gradient is gradually amplified, resulting in an increase in the number of streamlines within the smaller pores. The enhanced pressure differentials enable both large and small pore throats to be mobilized, leading to an overall increase in the degree of utilization (Figure 12).