Study on the Startup Mechanism and Quantitative Characterization of Multiple Oil-Phase Morphologies During the Ultra-High Water-Cut Stage

Abstract

After long-term waterflooding in offshore oilfields, the remaining oil becomes highly dispersed and discontinuous. To address the limitations of classical waterflooding theory in describing the effects of microscopic oil occurrence and stress differences on oil-phase flow, this study investigated oil–water two-phase flow during heavy-oil waterflooding using core samples from the Bohai Oilfield. The evolution of the oil-phase starting pressure gradient at different water-cut stages was measured through core two-phase steady-state displacement experiments. By combining in situ core CT scanning with pore-scale phase-field simulations, the multi-form start-up mechanisms and microscopic causes of the oil phase were clarified. The fractal characteristics of the reservoir pore structure were further incorporated to establish a calculation method for the multi-form start-up resistance of the oil phase. The results show that, as the water cut increases, the starting pressure gradient of the oil phase exhibits a nonlinear increasing trend. At a water cut of 90%, the oil-phase starting pressure gradient is approximately 7–8 times that of the pure oil phase. Meanwhile, the oil phase gradually transforms from a continuous phase to a discontinuous phase, with a smaller pore radius and a larger surface area per unit volume. Owing to the Jamin effect, capillary force exerts a stronger influence on oil-phase flow, resulting in a significant increase in the starting pressure gradient during the ultra-high water-cut stage. These findings provide a pore-scale explanation for the increase in oil-phase starting pressure gradient during ultra-high water-cut waterflooding and offer a theoretical basis for the sustainable development of mature offshore oilfields.

1. Introduction

Waterflooding remains the principal development method for offshore oilfields in China. Taking the Bohai Oilfield as an example, both the production and reserves associated with waterflooding account for more than 90%. Offshore waterflooded reservoirs are characterized by high injection–production intensity per well. After long-term water injection, the water cut of the major producing fields has now reached 90%, indicating entry into the ultra-high water-cut stage. At this stage, the degree of remaining-oil dispersion increases markedly. After extensive waterflood scouring, both reservoir structure and fluid properties undergo complex changes, which increase the difficulty of remaining-oil prediction and pose major challenges to precise potential tapping [1,2,3,4].

During the Fifteenth Five-Year Plan period, in-depth potential tapping in mature oilfields will constitute the most important production foundation as well as a key technical challenge. Accurate understanding of the oil–water seepage mechanism during the ultra-high water-cut stage is therefore essential for further improving the precision of remaining-oil exploitation. With advances in experimental techniques and methods, research on waterflooding seepage mechanisms has generally progressed from the macroscopic scale to the microscopic scale. Early pore-network models and glass-etched micromodels revealed the controlling effects of displacement pressure difference, capillary force, interfacial tension, and pore-throat size on oil-phase mobilization and trapping. These studies demonstrated that microscopic remaining oil is not governed simply by the macroscopic pressure gradient, but is jointly constrained by local pore-throat geometry and the stability of the oil–water interface [5]. On this basis, micromodels, scanning electron microscopy, fluorescence thin sections, and CT imaging have been widely used to identify the types and spatial distribution characteristics of remaining oil. Previous studies have shown that remaining oil after waterflooding may occur in various forms, including clustered, columnar, droplet, film-like, and patchy oil. Its formation is commonly associated with fingering, bypassing, snap-off, pore-throat shielding, and wetting-film retention [6,7,8,9,10]. In recent years, Micro-CT and digital rock technologies have further promoted the study of remaining oil from two-dimensional observation toward three-dimensional quantitative characterization. Pore-scale experiments based on 4D X-ray Micro-CT have shown that wettability differences significantly affect the spatial distribution, cluster morphology, and trapping behavior of remaining oil during waterflooding. In water-wet, mixed-wet, and oil-wet sandstone, remaining oil may occur as isolated oil droplets, pore refilling, and corner-trapped oil or surface oil films, respectively [11]. Meanwhile, studies on the relationship between sandstone pore structure and remaining oil distribution have indicated that complex pore geometry can significantly influence fluid distribution and residual oil trapping locations during waterflooding, suggesting that remaining oil mobilization should be understood from both pore-throat structural constraints and local flow-field evolution [12].

From the perspective of flow mechanisms, the oil–water two-phase distribution during waterflooding is jointly controlled by capillary force, viscous force, wettability, displacement rate, and pore-scale heterogeneity. When a low-viscosity water phase displaces a high-viscosity oil phase, the oil–water interface is prone to instability and viscous fingering, causing injected water to preferentially break through along dominant flow channels, while oil in low-permeability pore throats, dead-end pores, and complexly connected regions remains poorly swept [13,14,15,16]. Differences in pore-throat radius and wettability further alter the local capillary pressure distribution, causing the oil phase to break up, become trapped, or form thin films along solid surfaces during waterflooding. 4D X-ray Micro-CT experiments have also shown that the number, size distribution, and occurrence locations of remaining oil clusters vary significantly under different wettability conditions [11]. As displacement proceeds, large connected oil clusters gradually break into multiple small-scale discontinuous oil ganglia. Their mobilization and migration are no longer governed by a single pressure gradient, but instead depend on whether the local pressure gradient can overcome capillary trapping, interfacial deformation resistance, viscous shear, and the additional resistance associated with discontinuous oil phases [17,18,19,20]. Therefore, remaining oil mobilization in the extra-high water-cut stage is essentially a multiscale problem jointly controlled by pore-throat structure, oil–water interfacial interactions, and the local flow field.

From the perspective of field development, previous studies have proposed the concept of an additional resistance gradient for discontinuous oil phases to explain oil-phase mobilization difficulty and ineffective water circulation in the high water-cut stage. Zhang Daiyan et al. [21] pointed out that, for heavy-oil reservoirs, the oil phase can start to move only when the reservoir pressure gradient exceeds the additional resistance gradient; this critical condition is further affected by reservoir properties, fluid properties, and oil-phase occurrence state [22,23]. This understanding partly compensates for the limitations of conventional Darcy flow theory. Traditional Darcy flow theory generally assumes that both oil and water phases are continuous phases. However, in the extra-high water-cut stage, remaining oil at the microscopic pore-throat scale exhibits obvious characteristics of dispersion, discontinuity, and local confinement. The average flow capacity reflected by macroscopic relative permeability curves is therefore insufficient to fully characterize the initiation, deformation, migration, and re-trapping of isolated oil ganglia at the pore-throat scale. In recent years, pore-scale numerical simulations based on Micro-CT-reconstructed pore structures have further demonstrated that injection rate, oil–water viscosity ratio, wettability, and capillary number all affect oil–water two-phase flow behavior and remaining-oil mobilization during waterflooding [24,25]. In particular, the volume-of-fluid method can directly simulate oil–water interfacial evolution in three-dimensional pore space and reveal remaining-oil trapping, intra-phase circulation, and enhanced viscous dissipation induced by complex pore structures. These findings indicate that explaining the difficulty of remaining-oil mobilization in the extra-high water-cut stage cannot rely solely on a single core flooding experiment or microscopic observation. Instead, it is necessary to integrate core-scale seepage behavior, real pore-throat spatial characterization, and pore-scale flow simulation.

2. Steady-State Oil–Water Two-Phase Core Flooding Experimental

2.1. Experimental Samples

The core samples used in the experiments were collected from the SZ Oilfield, a major waterflooded oilfield in Bohai Bay. The oil sample used for saturation was prepared from degassed crude oil produced at the wellhead of this oilfield and diluted with kerosene to obtain a viscosity of 150 mPa·s (see

Table 1. Basic parameters of the experimental samples.

Length (cm)	Diameter (cm)	Porosity (%)	Permeability (mD)	Crude Oil Viscosity (mPa·s)
5	2.5	30.5	2996.5	150

).

2.2. Experimental Procedures

(1)

Procedure for the Steady-State Two-Phase Core Flooding Experiment

Figure 1 shows the experimental apparatus used to measure the starting pressure gradient for heavy-oil flow under two-phase conditions, including an ISCO pump, an intermediate container, a core holder, and a pressure acquisition system.

① Pre-displacement procedures: these included cleaning the oil from the core, drying, weighing, measuring the core permeability and porosity, and saturating the core with the experimental oil.

② Two-phase core flooding: during displacement, oil and water were injected simultaneously at a constant rate and at a specified ratio using an oil pump and a water pump, respectively, while the stabilized pressure differential across the core was recorded. For example, at a water cut of 10%, oil and water were injected at a ratio of 9:1. By varying the oil−water ratio, the displacement behavior at different water-cut stages was investigated.

③ Measurements at each water-cut stage: at each water-cut stage, the total oil−water flow rate was varied as 0.05, 0.1, 0.15, 0.2, 0.3, 0.5, 0.7, 1, 1.5, 2, and 3 mL/min, and the displacement rate and pressure gradient across the core were measured to plot their relationship curve.

(2)

Procedure for the Core Flooding CT Scanning Experiment

① Dry core scanning: the core sample was cleaned to remove oil, dried, weighed to obtain its dry weight, and measured for core diameter, after which it was placed in the core holder for the first in situ CT scan.

② Simulation of reservoir formation: after water saturation, a second in situ CT scan was performed; the core was then saturated with oil, followed by a third in situ CT scan.

③ One-dimensional displacement: simulated formation water was injected in the forward direction at a constant rate. When the cumulative injected volume reached 0.5 PV, 1 PV, 5 PV, 10 PV, 30 PV, and 70 PV, respectively, the pump was stopped and the valves were closed for scanning; the experimental parameters were recorded.

2.3. Experimental Program

Due to the small size of the core samples, in conventional one-dimensional waterflooding experiments the water cut rises rapidly after water breakthrough, making it impossible to carry out stable measurements at a specific water-cut stage. In this study, a steady-state oil−water two-phase flooding scheme was adopted, in which a fixed oil–water ratio was maintained and the injection rate was varied. The pressure differential across the core was monitored at different injection rates, and the relationship curve between injection rate and pressure gradient was plotted. By performing linear regression on the linear segment under steady-state conditions, the oil-phase starting pressure gradient at the corresponding oil–water ratio was determined. For heavy oil, owing to the large viscosity difference between oil and water, the water phase does not exhibit a starting pressure gradient; therefore, the measured starting pressure gradient reflects that of the heavy-oil phase. By varying the oil–water ratio and repeating the above procedure, the starting pressure gradient of heavy oil at different water cuts can be obtained.

The steady-state oil−water co-injection method used in this study should be regarded as a controlled experimental approximation rather than a complete reproduction of the transient waterflooding process in real reservoirs. This method was adopted to obtain stable pressure responses under prescribed oil–water injection ratios and to compare the oil-phase threshold pressure gradient under different water-cut conditions. In conventional unsteady waterflooding of small core samples, the water cut rises rapidly after water breakthrough, making it difficult to maintain a stable state at a specific water-cut stage.

The same experimental procedure was repeated on several core samples with similar reservoir properties, and the nonlinear increase in the oil-phase threshold pressure gradient with increasing water cut was consistently observed. The absolute values may vary slightly because of core heterogeneity, pressure measurement accuracy, pump-rate stability, oil–water ratio control, end effects, and the selection of the fitting interval. To reduce these uncertainties, pressure data were recorded after stabilization at each injection rate, and multiple flow-rate points were used for linear fitting. It should also be recognized that transient effects in real reservoirs, such as saturation history, capillary hysteresis, fluid redistribution, oil-droplet breakup and re-trapping, and reservoir-scale heterogeneity, cannot be fully captured by the steady-state approximation. Therefore, the steady-state results are mainly used to characterize the relative variation trend of oil-phase threshold pressure gradient, with the microscopic mechanism further supported by in situ CT scanning and pore-scale phase-field simulation.

2.4. Experimental Results and Analysis

Figure 2 presents the variation curves of pressure gradient versus injection rate for the steady-state two-phase flooding system at different water cuts. Under the pure-oil condition, as shown in Figure 2a, the displacement-rate curve is still a straight line that does not pass through the origin, and its intercept on the x-axis represents the starting pressure gradient under the pure-oil condition. For heavy oil, because of its high content of heavy components such as resins and asphaltenes, viscous resistance is stronger; therefore, a starting pressure gradient still exists even under the pure-oil condition. As the water cut continues to increase, the characteristic curve of injection rate exhibits obvious nonlinear behavior. This is because the oil phase gradually becomes discontinuous, and under slug-flow conditions the flow resistance of the oil phase becomes greater, showing nonlinear flow characteristics at low flow rates. Therefore, it is necessary to fit the linear segment corresponding to the normal-flow stage, as shown in Figure 2c,d.

The oil-phase starting pressure gradients obtained by fitting at different water cuts are plotted in Figure 3. It can be seen that, as the water cut increases, the oil-phase starting pressure gradient shows a nonlinear increasing trend. At the low water-cut stage, the oil-phase starting pressure gradient changes relatively slowly with increasing water cut. Once the water cut exceeds 70%, however, the variation in the oil-phase starting pressure gradient becomes significantly greater at different water-cut stages. At a water cut of 90%, the oil-phase starting pressure gradient is approximately 7–8 times that under the pure-oil condition. Therefore, for waterflooded oilfields, characterization of oil-phase flow during the ultra-high water-cut stage must consider the effect of the additional starting pressure gradient of the oil phase.

The results shown in Figure 2 and Figure 3 are representative results obtained from repeated steady-state flooding experiments on core samples with similar reservoir properties. Although slight differences in absolute threshold pressure gradients were observed among different cores, the nonlinear increasing trend with water cut was consistent.

3. Analysis of the Startup Mechanism and Microscopic Causes of Multiple Oil-Phase Morphologies

Further investigation and analysis of the observed increase in the additional starting pressure gradient of the oil phase with increasing water cut, as well as the underlying seepage mechanisms, require the use of in situ CT and microscopic pore-scale simulation methods.

3.1. Description of Oil-Phase Morphological Differences at Different Displacement Stage

Using the in situ CT scanning method, three-dimensional renderings under different states were obtained after segmentation of the pore space and fluid distribution space. The voxel size of the CT images was 4 μm × 4 μm × 4 μm. Features smaller than several voxels could not be reliably identified. In these images, blue represents the water phase and red represents the oil phase. The oil–water distribution states in the core pore space at different injected pore volumes (PV) are shown in Figure 4.

Based on the CT scanning results, the proportions of remaining oil in pores of different sizes at different displacement stages were statistically analyzed, as shown in Figure 5. Under the irreducible-water condition, the oil phase fills the entire rock pore space and exists as a continuous phase. As displacement proceeds, the oil phase in large pores is mobilized first. Owing to the Jamin effect, the dispersed remaining oil trapped in medium and small pores gradually becomes the dominant portion of the remaining oil. Therefore, at different stages of waterflooding, the remaining oil not only becomes increasingly dispersed, but also becomes trapped in pores with progressively smaller radii.

Because of the interfacial force between oil and water, the additional resistance experienced by an oil droplet due to deformation when passing through small pores is referred to as the Jamin effect. In actual reservoir pores, however, the influence of the Jamin effect is almost negligible at the low water-cut stage, because the oil phase is continuous and the effect of capillary force can be ignored, as shown in Figure 6a. Under waterflood scouring, with increasing water cut, the continuous oil phase gradually disperses into isolated oil droplets. At the ultra-high water-cut stage, the oil phase changes from a continuous phase to a discontinuous phase, as shown in Figure 6b. According to the formulas for the volume and surface area of cylinders and spheres, assuming the same oil-phase volume, the surface area of droplet-shaped remaining oil at the high water-cut stage is 1.33 times that of slug-shaped remaining oil at the low water-cut stage. A larger surface area makes the oil phase more susceptible to the Jamin effect and therefore more likely to be trapped during pore-scale flow. The surface area of oil phase per unit volume at different displacement stages is shown in Figure 7. As the injected pore volume (PV) during waterflooding increases, the oil-phase surface area per unit volume also increases. At 70 PV, the surface area per unit oil-phase volume is approximately 1.32 times that under the irreducible-water condition.

3.2. Construction of the Porous Media Model

To verify that the variation in the additional threshold resistance of the oil phase at different water-cut stages is caused by changes in oil-phase morphology and differences in the size of the pores and throats through which it flows, two types of pore-flow models were established using the phase-field simulation method in COMSOL Multiphysics 6.3, as shown in Figure 8.

To ensure the reliability of the phase-field simulation, the numerical settings, mesh convergence, and validation procedure were further clarified. The computational domain was discretized using an unstructured mesh, with local mesh refinement applied near narrow pore throats and regions with strong oil–water interfacial deformation. The minimum and maximum mesh sizes were 8.97 × 10⁻⁴ mm and 7.78 × 10⁻² mm. During the calculation, the relative residual and the variation in pressure gradient between successive iterations were used as convergence criteria. The simulation was considered to be converged when the relative tolerance of the time-dependent solver was set to 0.005.

Figure 8a shows the microscopic photograph of the actual oilfield core thin section, while Figure 8b shows the homogeneous core model and the heterogeneous core model constructed based on the microscopic photograph of the actual core thin section. In the models, the gray region represents the pore–throat space, and the white region represents the solid rock particles. In the homogeneous core model, the solid rock particles are uniformly sized spheres evenly distributed throughout the model, and pores and throats of identical size are formed between the solid spheres. In this homogeneous model, the pore-throat radius in which the oil phase is dispersed does not change at different water-cut stages. Its pore–throat structure can represent the oil–water flow paths in a homogeneous packed-sand tube, as shown in Figure 8b. The heterogeneous model is based on thin sections from actual oilfield cores, and its pore–throat structure more closely reflects the oil–water flow paths in real reservoir formations. By analyzing the oil-phase distribution state and the pressure differential across the model at different water-cut stages, the extent to which oil-phase flow is hindered by differences in pore–throat structure can be quantitatively evaluated.

The displacement pressure gradients across the two sides of the models at different water-cut stages were statistically analyzed, as shown in Figure 9a. As displacement proceeds, the water cut of the model continuously increases. Because the water phase has low viscosity and low seepage resistance, the overall displacement pressure gradient of the model gradually decreases under constant-rate displacement conditions. In the homogeneous core model, the pore–throat structure is relatively simple, and the overall pressure gradient is lower than that of the real-core-based model.

The displacement pressure gradient across the two sides per unit oil-phase volume is shown in Figure 9b. This parameter reflects the magnitude of the force directly acting on the oil phase at different water-cut stages and corresponds to the displacement pressure gradient required for normal oil-phase flow. For the homogeneous model, after the water cut increases, the radius of the pores and throats in which the oil phase is dispersed does not change significantly; therefore, the displacement pressure gradient per unit oil-phase volume shows no obvious change compared with that at the low water-cut stage. In contrast, for the real-core model, as the water cut increases, the oil phase gradually accumulates in medium and small pores, and the pore structure in which it is trapped becomes more complex. As a result, the displacement pressure gradient across the two sides per unit oil-phase volume increases significantly compared with that at the low water-cut stage. This phenomenon is also consistent with the understanding obtained from the CT scans.

4. Calculation Method for the Startup Resistance of Multiple Oil-Phase Morphologies Based on Fractal Theory

Changes in the morphology of remaining oil and in the pore-throat radius of the seepage space at different water-cut stages lead to differential seepage behavior of the oil phase under different water-cut conditions. In the ultra-high water-cut stage, the oil phase is no longer continuously distributed in the pore space, but gradually breaks up into discontinuous oil droplets or oil ganglia. These discontinuous oil phases are more easily trapped in medium and small pores, where capillary resistance and the Jamin effect become increasingly significant. Therefore, the startup pressure gradient of the oil phase cannot be accurately described—only by conventional Darcy flow theory or by traditional fractal models that consider pore structure alone.

Conventional fractal capillary-bundle models usually describe porous media by considering pore-size distribution, capillary tortuosity, and pore-throat connectivity. These models are useful for characterizing the influence of complex pore structure on seepage flow. However, they generally assume that the flowing phase is continuously distributed or do not explicitly consider the morphological evolution of the residual oil phase. During the ultra-high water-cut stage, the startup resistance of the oil phase is controlled not only by the fractal characteristics of the pore structure, but also by the pore-radius distribution, dispersion degree, and capillary resistance of multiple oil-phase morphologies.

To overcome this limitation, a modified fractal model is proposed in this study. The novelty of the model lies in coupling the fractal description of reservoir pore structure with the morphology evolution of the oil phase observed by in situ CT scanning. In the proposed model, the CT-derived pore-radius distribution of residual oil is used to describe the spatial occurrence of different oil-phase morphologies; the Jamin-effect-induced capillary resistance is introduced to characterize the additional startup resistance of discontinuous oil droplets; and a dispersion correction factor based on the oil-phase specific surface area is further incorporated to quantify the influence of oil-phase fragmentation during waterflooding. Therefore, the model can quantitatively characterize the water-cut-dependent startup resistance of multiple oil-phase morphologies in the ultra-high water-cut stage.

The fundamental cause of this phenomenon lies in the complex composition of the reservoir pore structure. Reservoir pore structure can be characterized using fractal theory, which considers the effects of irregular pore distribution and complex connectivity caused by the disordered arrangement of rock detrital particles on seepage flow. By introducing fractal theory, the reservoir rock is treated as a cluster of tortuous capillaries that conform to fractal laws, as shown in Figure 10.

The fractal capillary length of the porous medium is given by:

$$L_{\mathrm{e}}=L^{\delta }{r}^{1-\delta }$$

(1)

Taking a single capillary tube as an example, and neglecting the gravity and buoyancy acting on the oil droplet, the maximum pore radius at which the oil droplet remains trapped under different pressure gradients can be determined. When the oil droplet is trapped, the critical capillary force and the displacement pressure difference satisfy Equations (2) and (3):

$$\mathsf{\Delta }p={\displaystyle \frac{2\sigma {\mu }_{\mathrm{s}}\left(\cos \theta -0.5\right)}{r}}$$

(2)

$$\mathsf{\Delta }p=L_{\mathrm{e}}\times \nabla p=L^{\delta }{r}^{1-\delta }\times \nabla p$$

(3)

Therefore, the critical pressure gradient required to mobilize an oil droplet with radius r is:

$$\nabla p={\displaystyle \frac{2\sigma {\mu }_{\mathrm{s}}\left(\cos \theta -0.5\right)}{r^{2-\delta }{L}^{\delta }}}$$

(4)

$$\delta =1+{\displaystyle \frac{\ln \left(T_{av}\right)}{\ln \left(L_m/2r_{av}\right)}}$$

(5)

$$T_{av}={\displaystyle \frac{1}{2}}\left[1+{\displaystyle \frac{1}{2}}\sqrt{1-\phi }+\sqrt{1-\phi }\sqrt{{\left({\displaystyle \frac{1}{\sqrt{1-\phi }}}-1\right)}^2+{\displaystyle \frac{1}{4}}}/\left(1-\sqrt{1-\phi }\right)\right]$$

(6)

Based on nuclear magnetic resonance (NMR) experiments or micron-scale CT experiments, the distribution range of remaining oil droplets in pores at different stages of waterflooding can be obtained. For the oil phase, the condition required for flow initiation is to overcome the resistance caused by the Jamin effect in medium and small pores. Therefore, according to the principle of volume-weighted averaging, the starting pressure gradient of the oil phase at different water-cut stages can be calculated as follows:

$$\nabla p\left(t\right)={\displaystyle \sum _{r=r\min }^{r\max }\left(\frac{2\sigma {\mu }_{\mathrm{s}}\left(\cos \theta -0.5\right)}{r^{2-\delta }{L}^{\delta }}\right)}\times S_{\mathrm{o}}\left(r\right)$$

(7)

At the initial stage, when the pores are saturated with oil, the oil phase exists as a continuous phase and the influence of the Jamin effect is essentially negligible. Therefore, it is necessary to further correct the starting pressure gradient of the oil phase by considering the degree of oil-phase dispersion at different water-cut stages. The correction factor is defined as shown in Equation (6):

$$\lambda =\left({\displaystyle \frac{a\left(t\right)/V_{\mathrm{o}}\left(t\right)}{a\left(0\right)/V_{\mathrm{o}}\left(0\right)}}-1\right)$$

(8)

Therefore, the corrected starting pressure gradient of the oil phase can be expressed as follows. At the initial stage of waterflooding, the pore space is essentially filled with the oil phase, and $\lambda$ = 0. At this time, the oil phase flows as a continuous phase, and no starting pressure gradient exists. As displacement proceeds, the oil phase is continuously dispersed into small oil droplets, and the specific surface area per unit volume increases, resulting in $\lambda$ > 0. Moreover, a larger value of $\lambda$ indicates a higher degree of oil-phase dispersion and a more pronounced threshold-pressure-gradient effect for the oil phase.

$$\nabla p\left(t\right)=\lambda \times \left[{\displaystyle \sum _{r=r\min }^{r\max }\left(\frac{2\sigma {\mu }_{\mathrm{s}}\left(\cos \theta -0.5\right)}{r^{2-\delta }{L}^{\delta }}\right)}\times S_{\mathrm{o}}\left(r\right)\right]$$

(9)

Taking a typical cored core sample from a coring well in the Bohai SZ Oilfield as an example, and based on the micron-scale in situ CT flooding results shown in Figure 5, the variation in the pore-radius distribution proportion of cluster-like and porous constrained oil at different displacement stages was statistically analyzed. Using the experimental data and the calculation formula for the oil-phase starting pressure gradient, the oil-phase starting pressure gradients at different displacement multiples were calculated, as shown in Figure 11.

5. Conclusions

(1)

Using the steady-state oil–water two-phase flooding method, the variation law of the oil-phase starting pressure gradient at different water-cut stages was determined. As the water cut increased, the oil-phase starting pressure gradient showed a nonlinear increasing trend. At the low water-cut stage, the oil-phase starting pressure gradient changed relatively slowly with increasing water cut. When the water cut exceeded 70%, however, the variation in the oil-phase starting pressure gradient became significantly greater at different water-cut stages. At a water cut of 90%, the oil-phase starting pressure gradient was approximately 7–8 times that under the pure-oil condition.

(2)

Using in situ CT scanning and microscopic pore-scale phase-field simulation, the causes and influencing factors of the oil-phase starting pressure gradient at the high water-cut stage were clarified. As water saturation increased, the oil phase gradually changed from a continuous phase to a discontinuous phase, the degree of oil-phase dispersion increased, and the radius of the pores in which the oil phase was trapped became significantly smaller. The greater the injected waterflooding PV, the larger the oil-phase surface area per unit volume; at 70 PV, the surface area per unit oil-phase volume was approximately 1.32 times that under the irreducible-water condition. Under the influence of the Jamin effect, capillary force exerted an increasingly strong control on oil-phase flow, resulting in a pronounced starting pressure gradient of the oil phase during the ultra-high water-cut stage.

(3)

Based on the startup mechanism and microscopic causes of multiple oil-phase morphologies, and considering the fractal characteristics of reservoir pore structure, a calculation method for the startup resistance of multiple oil-phase morphologies at different water-cut stages was established, realizing the quantitative characterization of the oil-phase starting pressure gradient at different displacement stages.