Experimental Study of Water Displacement Rates on Remaining Oil Distribution and Oil Recovery in 2D Pore Network Model

Abstract

An amount of oil remains in oil reservoirs even at the high water-cut stage of produced liquid from oil wells. To reveal the mechanism of displacement rates to affect the remaining oil in pore scales, a two-dimensional (2D) glass etching pore network model and real-time visual system were set up to observe the characteristics of oil distribution from water flooding and study the influence of displacement rates on oil recovery. It was found that the geometry of remaining oil in the pore network is diverse and dynamically changed at the high water-cut stage. Three geometric representative parameters were defined for the classification of five types of remaining oil (contiguous, branching, film, dropwise, bar columnar type), and controlling mechanisms for each type of remaining oil were analyzed. The experimental results show that the remaining oil saturation decreases from 21.2% to 6.5% when water injection rates increase from 0.05 to 0.5 mL/min. The increase in displacement rate improves the displacement efficiency of four types of remaining oil in the range of 55.00% to 93.67% except for dropwise type. The experimental data also indicate that the reduction in continuous residual oil and branched residual oil mainly contributes to the improvement of oil recovery of the whole network model. With the increase in displacement rate (from 0.05 to 0.1, 0.2, 0.3, 0.4, and 0.5 mL/min), the areas of five types of representative local residual oil reduce step by step. This research validates that the increase in water flooding rate in porous media leads to reduction in oil saturation, and it will improve oil recovery in oil reservoirs by enhancing water injection rates.

1. Introduction

With the development of oilfield water flooding, most oilfields have entered the middle–high water-cut stage. The oil and water saturation in reservoir pore space has changed constantly, and the formation and occurrence state of the remaining oil has become more complicated, which affects the oil displacement efficiency to a certain extent. Therefore, the study of remaining micro oil is of great significance to the subsequent development of oilfields [1,2]. Its research focuses on solving the distribution characteristics, occurrence state, scale, and production possibility of micro residual oil in the reservoir [3].

In the 1950s, Fatt introduced the pore network model and visualization research into oil exploration and development and predicted the micro properties of reservoirs [4], providing an idea for the dynamic observation of the characteristics of fluid seepage in pores [5]. In the 1970s, Dullien [6,7] introduced percolation theory into the network model study on the flow rules of fluid in pores. Using simulation, scholars obtained three-phase fluid displacement of the oil, gas, and water using a displacement mechanism in porous media under water-wet conditions [8]. Under strong wetting conditions, a simple two-phase drainage mechanism completely summarizes the drainage displacement in a three-phase flow [9]. In addition, due to the groove and edge advancement of the strongly wetted phase on the solid surface between the solid and the non-wetted phase, the disconnection of the threads of the non-wetted phase at the body neck connection point and the dead corner may lead to the recapture of the non-wetted phase [10]. Comparing the microsimulation study of high and low permeability areas, micropore heterogeneity and fingering are the main factors for higher final recovery in low permeability areas [11].

Hou Jian et al. [12] verified the effectiveness of network simulation by comparing the model calculation results with the oil–water steady-state relative permeability displacement experimental results. In terms of polymer flooding, Wang Kewen et al. [13] divided the remaining oil after polymer flooding into three different distribution forms, isolated, banded, and network, and found that with the increase in pore radius, isolated residual oil increases, and the network’s remaining oil decreases. With the enhancement of connectivity, isolated residual oil increases. In terms of theoretical research, especially in micro residual oil distribution, scholars have studied the static residual oil types. Evolution laws in medium and ultra-high water-cut stages through indoor physical experiments and theoretical seepage analysis defined residual oil characteristics and influencing factors in different development stages [14,15]. Many scholars [16,17,18,19] have also conducted much research on the occurrence state of micro residual oil. According to the topological structure and other characteristics of micro residual oil, it is divided into five categories: cluster, porous, columnar, drop, and membrane, and its dynamic evolution law has been studied. Heterogeneity affects the migration of the oil phase and the distribution form of residual oil. With strong heterogeneity, the remaining oil is mainly in a clustered continuous phase with high saturation; with weak heterogeneity, the remaining oil mainly stays in the pore as a discontinuous phase. In addition, wettability affects oil displacement efficiency and residual oil distribution [11]. The comparison between water flooding and intense alkali ASP flooding shows more thin-film residual oil on the surface of rock particles after water flooding [20]. The remaining oil in the reservoir is mainly in membrane and interstitial forms. The pore structure is the critical factor affecting the distribution of remaining oil and oil displacement efficiency [21].

The imaging analysis method is a technical means to observe differences by using various imaging techniques according to the different physical and chemical properties of oil, gas, and water in rock pores. With this method, using mobile phone images and image processing, the pore structure of the reservoir core, the distribution characteristics of the remaining oil, and the relationship between remaining oil and rock position were studied [22]. As early as 1982, Wang et al. [23] tried to apply X-ray CT technology to the core displacement process and obtained the residual oil distribution image on the cross-section. Then, Hove et al. [24] used this technology to visualize the displacement process of sandstone in the North Sea. This method provided a new direction for studying residual oil’s formation mechanism, distribution, and morphology. In 1998, Coles [25] used this technology to scan and image the dry sandstone and then saturated it with oil before water flooding. After water flooding, Coles scanned the micro residual oil distribution image to realize the three-dimensional visualization of residual oil distribution. Turner et al. [26] imaged the equal diameter glass ball model and Berea sandstone after gas flooding. They described the occurrence form of remaining micro oil. Prodanovic’ et al. [27] ensured that the displacement and imbibition process reached different stages by injecting a fixed volume of wettable fluid and non-wettable fluid and performing imaging analysis. Ryazanov et al. [28,29] used different Berea sandstone samples scanned by CT to extract a three-dimensional pore network structure for displacement simulation. They quantitatively analyzed the relationship between residual oil saturation and average contact angle. Then, they studied the change of three-dimensional spatial structure of micro residual oil during displacement under different wettability conditions and obtained the configuration relationship of residual oil distribution in different pore structures. Al-Dhahli et al. [30] used the extracted pore network model to simulate the two-phase and three-phase flow of water drive, gas drive, and water–gas alternate drive with saturated oil and compared the residual oil saturation and relative permeability curves using different displacement modes. Ren Yiming et al. [31] used CT scanning technology to establish a three-dimensional mapping network model of core and simulated water drive oil. Based on the relationship between the micro displacement efficiency and the pore ratio containing residual oil with various factors, the influencing factors and mechanism of the formation of residual oil in the pores are studied. Bai Zhenqiang et al. [32] aimed at the distribution law of micro residual oil in the reservoir after polymer flooding in Daqing Oilfield using new methods of frozen film making, UV fluorescence, and CT analysis and quantitatively determined the bound state spatial distribution characteristics of 10 types of micro residual oil in two categories: semi-bound state and free state. Fan Fei et al. [33] studied the occurrence form, stock, and location of remaining oil based on nuclear magnetic resonance, CT scanning, and a micromodel. The types of remaining oil are continuous type, multi pore type, oil film type, and single pore type, and a new classification standard of remaining oil was established. Bai Zhenqiang et al. [34] studied rock samples’ micro residual oil distribution law with different degrees of water washing after polymer flooding in Daqing Oilfield using frozen production methods, UV fluorescence, and laser confocal scanning microanalysis. The analysis shows that the remaining oil in weak water-washed rock samples after polymer flooding is mainly cluster and inter-particle adsorption free oil; a thin oil film on the particle surface-bound most of the residual oil in solid water washed samples.

Ling Tong Hua et al. [35] comprehensively analyzed and determined GPR images from multiple angles by using orthogonal matching tracking and Hilbert transform (HT), which significantly improved the GPR image resolution. The imaging analysis method can accurately detect and image abnormal areas intuitively and quantitatively [36]. Tarik Saif et al. [37] used optical and scanning electron microscopy (SEM) for two-dimensional image analysis. Three-dimensional (3D) X-ray microtomography (MCT) revealed a complex and changeable fine-grained microstructure, and the volume and connectivity of pore space were visualized and quantified.

To sum up, previous studies focused more on the simulation and observation of the flow process of the remaining oil in heterogeneous porous media. Scholars systematically studied the effects of wettability, permeability, heterogeneity, and pore structure on remaining oil distribution. There are few studies on the impact of different displacement rates on micro residual oil. There is a lack of research on quantitative characterization of micro storage, storage location, and storage form of residual oil.

In this study, the glass etching model and micro image real-time acquisition system were used to observe the characteristics of oil–water two-phase seepage in the process of micro water displacement, explore the influence of oil displacement speed on the micro displacement efficiency of different forms of remaining oil, and quantitatively analyze the influence of different displacement speed on the distribution of different types of remaining oil in high water-cut stage, which provides a reference and basis for further tapping the potential of remaining oil.

2. Micro Water Flooding Remaining Oil Analysis Technology

2.1. Microscopic Visual Seepage Network Simulation Model

The glass etching model was used in the micro water flooding model, which is transparent and realizes real-time dynamic visualization of the micro displacement process. It is a powerful means to study the formation and distribution of the remaining oil. Figure 1 shows the image of the glass etching model saturated by oil; the whole model is square with four borders of 25 mm, its area is 625 mm², and the porosity of the model is 0.38. The camera continuously took pictures of the glass etching model during the experiment, and the interval between photographs was 1 s. The pictures were named as image xx-xx5 and image xx-xxx6.

2.2. Micro Remaining Oil Analysis Technology

The image processing software (imagepro-plus6.0) can identify and mark the pixels in the image (Figure 2), calculate the number of pixels occupied by crude oil in each region in the model pore, count and summarize the number of pixels occupied by crude oil in each region (Figure 3), and calculate the volume of crude oil in a region according to the ratio of the number of pixels occupied by crude oil in a region to the number of pixels occupied by summarized crude oil. The amount of remaining oil and the dispersion degree of remaining oil were quantitatively characterized.

3. Experiment

① The actual core was used to make a rock slice that meets the experimental requirements, that is, the natural sandstone micro model. Then, the micro model samples were put into a particular visual high-pressure core holder. ② Confining pressure was applied to vacuum the micro model and saturate the crude oil with a specific viscosity until the crude oil filled the whole rock slice and stood for some time until the collected image was stable. ③ The micro constant speed pump was activated, and the required initial displacement speed was set as 0.05 to start displacement. ④ Until the displacement picture was stable, i.e., the crude oil in the slice was no longer displaced at the last displacement speed, the displacement speed was increased in turn (the five displacement speeds were set as 0.1, 0.2, 0.3, 0.4, and 0.5 mL/min). ⑤ At the end of the displacement process, the photos of the micro displacement process were sorted and preserved. Figure 4 is the experimental device diagram.

3.1. Characterization of Remaining Oil

In order to classify the micro residual oil morphology, three characterization parameters were introduced (

Table 1. Characterization parameters of micro remaining oil morphology.

Characterization Parameters	Definition	Geometric Form
Residual oil connected porosity coefficient	The number of remaining oil filled in interconnected pores and throats in the selected area expressed in Cn;	example: Cn = 7
Oil hole radius ratio	The ratio of the equivalent radius of the bound oil to the equivalent radius of the water passage section of the throat, namely: $R=\frac{R_{\mathrm{oil}}}{\mathrm{Rchannel}}=\frac{Hoil}{Dchannel}$
Shape factor	The ratio of the central axis to the minor axis of remaining oil in a micro seepage channel, namely: $G=\frac{L}{W}$

). The formation mechanism of various residual oils is characterized according to the methods in

Table 2. Characterization method of microscopic residual oil formation mechanism.

Types of Remaining Oil		Geometry Under Microscope	Geometric Representation	Mechanical Characteristics
Contiguous type			The remaining oil connectivity porosity coefficient Cn > 5; Roc = 1	Axial driving pressure gradient in the center of arbitrarily connected raceway: lim(grapP)→0
Branching type			2 ≤ The remaining oil connectivity porosity coefficient Cn ≤ 5; Roc = 1	Pressure gradient at both ends of the central axis of any remaining oil channel: lim(grapP)→0. The pressure gradient around the remaining oil is greater than zero: lim(grapP)→0
Oil film type			The remaining oil connectivity porosity coefficient Cn = 1; Roc < 1/3. Adhesion to the pore surface	Axial driving pressure gradient of throat. lim(grapP) > 0 The shear stress acting on the remaining oil is less than the adhesion. lim(grapP) > 0
Isolated type	Dropwise		The remaining oil connectivity porosity coefficient: Cn = 1; Remaining shape factor ≤ 2; 1/3 ≤ Roc < 1, within the large hole	Local capillary number before remaining oil formation, Noc > 1, namely $N_{VC}=(\frac{\mu L\mathrm{t}q}{\pi R_1^3\sigma \cos \theta })=\frac{Fv}{Fc}\rangle 1$ The capillary force dominates the fluid flow in the adjacent small channels. Pressure gradient acts on remaining oil. lim(grapP)→0
	Bar columnar		The remaining oil connectivity porosity coefficient: Cn = 1; Remaining shape factor >2; Roc = 1. It is trapped in a small seepage channel	Local capillary number before remaining oil formation ≤ 1, namely $N_{VC}=(\frac{\mu L\mathrm{t}q}{\pi R_1^3\sigma \cos \theta })=\frac{Fv}{Fc}\le 1$ The viscous force dominates the fluid flow in adjacent large channels

.

The remaining contiguous oil is filled between multiple interconnected pores and throats, with the pore coefficient Cn > 5 and the oil pore ratio Roc = 1. The axial pressure gradient Lim(grapP) > 0 is also the hydrodynamic condition for forming this type of residual oil.

Branched remaining oil refers to the remaining oil stored in the pore throat with the pore coefficient of 2 < Cn < 5 and the oil pore diameter ratio of Roc = 1. Generally, the pore throat is connected. The pressure gradient is formed at both ends of the central axis of any remaining oil channel, but the pressure gradient of the surrounding pore throat is Lim(grapP) > 0, which is conducive to improving the displacement effect.

Film-like residual oil usually adheres to the surface of pore throat, with axial pressure gradient Lim(grapP) > 0 and oil pore diameter ratio Roc < 1/3. The shear stress acting on the residual oil is less than the adhesion stress τ < Fa. In order to use this kind of residual oil, it is necessary to take measures to increase the shear stress or reduce the adhesion stress.

The pore coefficient is Cn = 1, the residual shape factor is G ≤ 2, and the oil pore ratio is 1/3 ≤ Roc < 1, usually staying in the large hole. Before forming residual oil, the local capillary number is more than 1, and the capillary force dominates the fluid flow in the adjacent small channels. The pressure gradient acting on the remaining oil is lim(grapP)→0.

The remaining columnar oil pore coefficient is Cn =1, the shape factor is G > 2, and the pore size ratio is Roc = 1. The remaining oil fills the whole seepage channel, and the pressure gradient at both ends of the pore throat is lim (grapP)→0. The number of local capillary tubes before forming the remaining oil is N_vc ≤ 1.

3.2. Effect of Increasing Displacement Rate on Micro Displacement Efficiency of Different Remaining Oil Types

3.2.1. Analysis of Displacement Effect

Changing the displacement rate can significantly improve the displacement efficiency and reduce the remaining oil saturation. As shown in

Table 3. Cumulative PV numbers of water injection and remaining oil saturation calculation results.

Picture Number	Injection Time (s)	Displacement Rate (mL/min)	Cumulative PV of Water Injection	Remaining Oil Saturation (%)
Image0729	729	0.05	5.1	21.2
Image1160	1160	0.1	11.2	11.1
Image1500	1500	0.2	20.7	8.7
Image1990	1990	0.3	39.2	8.4
Image2300	2300	0.4	56.6	7.3
Image2663	2663	0.5	80.0	6.5

, the oil displacement rate increased from 0.05 to 0.5 mL/min, and the remaining oil saturation decreased from 21.2% to 6.5%. The remaining oil saturation of the above formulation is calculated as follows:

$$R\mathrm{oc}=\frac{IoilV}{IVchannel}$$

(1)

where R_OC is the remaining oil saturation; I_oil is the number of pixels of crude oil in the model; I is the number of pixels of the model; V is the total volume of the model, mm³; and Vchannel is the total volume of pores in the model, mm³.

In the oil displacement stage, the oil is displaced at the speed of 0.05 mL/min until the crude oil in the slice is no longer displaced. At this time, the time is 729 s, and then the oil displacement speed (0.1, 0.2, 0.3, 0.4, and 0.5 mL/min) is increased successively. The corresponding times were 1160, 1500, 1990, 2300, and 2663 s (Figure 5).

(a).

Relationship between displacement rate and saturation of displacement remaining oil

According to the above experimental analysis:

When the oil and water phases are displaced at the displacement rate of 0.05 mL/min until no change occurs, the final displacement effect at the displacement rate of 0.05 mL/min is a remaining oil saturation of 21.21%.

When the displacement speed is 0.1 mL/min, part of the remaining oil is swept due to the increase in displacement speed, thus having the effect of displacement. The final displacement effect is that the remaining oil saturation is 11.05% (the remaining oil displaced at this stage is mainly large continuous residual oil and branched residual oil. At the end of displacement, the straight residual oil is displaced and dispersed, a small part of which forms oil film or columnar residual oil; while most of the branched residual oil is also displaced and dispersed, a small part of which forms drop oil or columnar residual oil).

When the displacement rate is 0.2 mL/min, part of the remaining oil is swept, and the displacement effect is further increased. The final remaining oil saturation is 8.73% (the remaining oil displaced in this stage is mainly remaining oil film).

When the displacement rate increases to 0.3, 0.4, and 0.5 mL/min, the final remaining oil saturation is 8.39%, 7.26%, and 6.53%, respectively. The displacement effect increases, but the range is small. The types of residual oil displaced in the model are mainly oil film residual oil and a small amount of columnar residual oil. The drop residual oil is difficult to drive, and most of the remaining oil forms columnar or drop oil, except for a small amount of oil film residual oil. When the displacement rate increases from 0.05 to 0.5 mL/min, the remaining oil saturation decreases from 21.21% to 6.53%, and the oil displacement efficiency increases by 69.21% (see Figure 6).

(b).

Relationship between cumulative injected PV number and displacement remaining oil saturation

In the process of oil displacement, for PV numbers of 5.1, 20.7, and 80, the corresponding remaining oil saturation values are 21.21%, 8.73%, and 6.53%, and the remaining oil saturation is reduced by 14.67%. With the increase in cumulative injected PV number, the remaining oil saturation begins to decline sharply, indicating that increasing the PV number increases the sweep coefficient of water and greatly reduces the saturation of remaining oil. Then, with the increase in PV number, the remaining oil saturation decreases slowly. At this time, the sweep coefficient increases to a certain extent, the increase rate slows down, and the remaining oil saturation changes little (Figure 7).

3.2.2. Analysis of Displacement Effect of Different Types of Remaining Oil by Increasing Displacement Rate

• Total Remaining Oil Distribution of Displacement

In order to show the effect of displacement rates on the displacement efficiency of five different types of remaining oil more intuitively, the percentage of increase in displacement efficiency is defined.

$$We=\frac{As-Ae}{As}\times 100\%$$

(2)

where We is the increased percentage of displacement efficiency; As is the remaining oil area at the beginning of displacement; and Ae is the remaining oil area at the end of displacement.

When the displacement rate increases from 0.05 to 0.5 mL/min, the displacement efficiency of droplet residual oil decreases, while the displacement efficiency of remaining oil of other forms increases. This shows that in other remaining oil types, displacement processes into remaining oil droplets (see Figure 8).

When the displacement rate increases from 0.05 to 0.5 mL/min, i.e., the cumulative PV number increases from 5.1 to 80.0, the proportion of different remaining oil changes significantly. When the water drive rate is low, the remaining oil mainly exists in the contiguous type, and part of the remaining contiguous oil is displaced. Part of the remaining contiguous oil is transformed into other types of remaining oil (mainly in the form of the oil film in the early stage and mainly in the form of column and drop in the later stage). At the end of displacement, the remaining oil mainly exists in the form of drop, column, and oil film. (Figure 9 and Figure 10).

• Different Types of Residual Oil Are Produced in Each Displacement Stage

Table 4. Quantity of remaining oil produced in different displacement stages.

Displacement Rate mL/min	Displacement of Contiguous Remaining Oil/mm2	Displacement of Branched Remaining Oil/mm2	Displacement Oil film Remaining Oil/mm2	Displacement of Columnar Remaining Oil/mm2	Displacement of Dropwise Remaining Oil/mm2
0.05	20.55	7.75	11.76	8.31	2.31
0.1	5.21	4.24	8.97	5.46	2.53
0.2	2.39	3.32	4.30	7.94	2.90
0.3	1.74	2.14	5.48	7.50	3.18
0.4	1.83	0.00	5.32	4.02	6.17
0.5	1.80	0.00	3.32	3.37	7.12

shows the calculated area of different types of remaining oil produced in each displacement stage, from which we can see the main types of remaining oil with each displacement rate.

Before model displacement, almost all saturated crude oil is continuous, with an area of 50.70 mm².

(1)

V = 0.05 mL/min: Displacement of contiguous crude oil (30.153 mm²) forms branched, oil film, columnar, and dropwise residual oil;

(2)

V = 0.1 mL/min: Mainly displacement of remaining contiguous oil (15.33 mm²), followed by branched remaining oil (3.51 mm²), remaining columnar oil (2.85 mm²), oil film remaining oil (2.790 mm²), and drop remaining oil (0.21 mm²);

(3)

V = 0.2 mL/min: The primary displacement oil is film type residual oil (4.67 mm²), followed by contiguous type residual oil (2.81 mm²), branched type residual oil (0.92 mm²), column type residual oil (2.47 mm²), and drop type residual oil (0.37 mm²);

(4)

V = 0.3 mL/min: Mainly displacement of branched residual oil (1.17 mm²), followed by contiguous residual oil (0.64 mm²), columnar residual oil (0.43 mm²), oil film residual oil (1.18 mm²), and drop residual oil (0.28 mm²);

(5)

V = 0.4 mL/min: Mainly displacement of remaining columnar oil (3.48 mm²), followed by branched remaining oil (2.14 mm²), oil film remaining oil (0.16 mm²), drop remaining oil (2.98 mm²) and remaining contiguous oil (0.08 mm²);

(6)

V = 0.4 mL/min: Mainly displacement of the remaining membranous oil (1.99 mm²), followed by the remaining columnar oil (0.64 mm²), the remaining contiguous oil (0.03 mm²), and the drop remaining oil (0.94 mm²).

When the water injection rate increases from 0.05 to 0.5 mL/min, the area of five types of remaining oil (continuous, branching, film, bar column type, dropwise) decreases from 20.55, 7.75, 11.76, 8.31, and 2.31 to 1.80, 0, 3.32, 3.37, and 7.12 mm², respectively, and the remaining oil displacement efficiency increases by 91.24%, 100%, 71.70%, 59.43%, however, the displacement efficiency of drip residual oil is reduced by 207.41% (total model).

• Distribution of Local Residual Oil After Displacement

The displacement speed at the beginning of the test was 0.05 mL/min until the crude oil in the model was no longer displaced at the previous displacement speed. The displacement speed was increased by 0.1, 2, 0.3, 0.4, and 0.5 mL/min successively, and the area of different types of remaining oil in each displacement stage was calculated (

Table 5. Data of remaining oil area after displacement of five types of remaining oil by different water drive rates.

Picture Number	Displacement Rate, mL/min	Continuous Remaining Oil area/mm2	Branched Remaining Oil area/mm2	Oil Film Remaining Oil area/mm2	Area of Residual Oil in drops/mm2	Columnar Remaining Oil area/mm2
Image0729	0.050	1.325	0.661	0.611	0.220	0.098
Image1160	0.100	0.766	0.374	0.595	0.100	0.076
Image1500	0.200	0.706	0.370	0.562	0.099	0.074
Image1990	0.300	0.566	0.104	0.102	0.078	0.073
Image2300	0.400	0.543	0.040	0.095	0.035	0.044
Image2663	0.500	0.542	0.042	0.095	0.036	0.043

). The effects of different displacement rates on the displacement efficiency of different forms of residual oil were obtained (Figure 11).

It can be seen from the above results that when the displacement rate increases to 0.1 mL/min (that is, when the cumulative injected PV number is 11.2), the displacement effect increases obviously. Most of the remaining contiguous oil is displaced, and a small part forms oil film and remaining columnar oil. When the displacement rate increases, this part of the remaining oil is challenging to drive, and the displacement effect is not significant. When the displacement rate increases to 0.5 mL/min (i.e., the cumulative injected PV number is 80.0), the remaining oil area increases. This is because the surrounding remaining oil is displaced here, and the new remaining oil is formed. It can be seen that the remaining oil is mainly oil film type and has a columnar shape at the end of the total displacement, with some drops (see Figure 12). When the water injection rate increases from 0.05 to 0.5 mL/min, the remaining contiguous oil area decreases from 1.325 to 0.542 mm². The oil displacement efficiency was increased by 59.09%.

When the displacement rate increases from 0.05 mL/min (when the cumulative PV number is 5.1) to 0.1 mL/min (when the cumulative PV number is 11.2), it can be seen that the displacement efficiency increases significantly, and about half of the remaining oil is displaced. The other half of the branched remaining oil is dispersed to form the remaining columnar oil. When the displacement rate increases to 0.2 mL/min (i.e., when the cumulative PV number is 20.7), the displacement effect does not increase significantly. When the displacement rate continues to increase to 0.3 mL/min (i.e., when the cumulative PV number is 39.2), the displacement efficiency increases significantly at the end of the displacement stage, and most of the remaining columnar oil is displaced. Only a few columnar remaining oils are not driven. A small amount of drop-like remaining oil is formed in this process. When the displacement rate is increased to 0.4 mL/min (i.e., the cumulative PV number is 56.6), the displacement efficiency still increases significantly. The remaining columnar oil is displaced, and the rest is the drop-like remaining oil formed after displacement. When the displacement rate is increased to 0.5 mL/min (i.e., the cumulative PV number is 80.0), the displacement efficiency increases significantly. The displacement efficiency does not increase, which indicates that the drop-like remaining oil cannot be easily driven (see Figure 13). When the water injection rate increases from 0.05 to 0.5 mL/min, the branched remaining oil area decreases from 0.661 to 0.042 mm². The oil displacement efficiency was increased by 93.67%.

When the displacement rate increases to 0.2 mL/min (i.e., the cumulative PV number is 20.7), the displacement efficiency does not increase, although the position of the oil film remaining oil changes. When the displacement rate increases to 0.3 mL/min (i.e., the cumulative PV number is 39.2), the oil film remaining oil starts to be driven, and the original oil film remaining oil is displaced at the end of the displacement rate. A small amount of drop-like and columnar remaining oil is formed (see Figure 14). When the water injection rate increases from 0.05 to 0.5 mL/min, the film remaining oil area decreases from 0.611 to 0.059 mm². The oil displacement efficiency was increased by 84.38%.

At the end of the displacement rate of 0.1 mL/min (i.e., the cumulative PV number is 11.2), the significant initial drop-like remaining oil is swept and displaced into a small drop-like remaining oil. The displacement effect is noticeable. At the end of the displacement rate of 0.2 mL/min (i.e., the cumulative PV number is 20.7), it can be seen that the location of the drop-like remaining oil is unchanged. This shows that the displacement efficiency cannot be improved by changing the displacement rate. When the displacement rate is 0.3 mL/min (i.e., the cumulative injected PV number is 39.2), a small number of residual oil drops are displaced. However, it can be seen that the position of many small residual oil drops changes, indicating that these residual oil drops are displaced. When the displacement rate is increased to 0.4 mL/min (i.e., when the cumulative injected PV number is 56.6), most of the remaining oil drops are displaced, leaving only a few drops. When the displacement rate increases to 0.5 mL/min (i.e., when the cumulative injected PV number is 80.0), the displacement effect does not increase significantly (see Figure 15). When the water injection rate increases from 0.05 to 0.5 mL/min, the area of residual oil in drops decreases from 0.220 to 0.036 mm². The oil displacement efficiency was increased by 83.81%.

For the remaining columnar oil, at the displacement rate of 0.1 mL/min (i.e., when the cumulative PV number is 11.2), part of the remaining columnar oil is displaced at the end of displacement, but about half of the remaining oil remains in the pores. When the displacement rate is increased to 0.2 mL/min (i.e., when the cumulative PV number is 20.7), the remaining columnar oil is unchanged. This shows that this part of the remaining oil cannot be used in this displacement rate. When the displacement rate continues to increase to 0.3 mL/min (i.e., when the cumulative PV number is 39.2), the remaining columnar oil still cannot be driven. When the displacement intensity is 0.4 mL/min (i.e., the cumulative PV number was 56.6), the shape of the remaining oil pair changes significantly, and the area of the remaining oil becomes smaller. When the displacement intensity is increased to 0.5 mL/min (i.e., the cumulative PV number was 80.0), the remaining oil cannot be displaced (see Figure 16). When the water injection rate increases from 0.05 to 0.5 mL/min, the columnar remaining oil area decreases from 0.098 to 0.043 mm². The oil displacement efficiency was increased by 55.67%.

The results show that the ultimate displacement efficiency of contiguous remaining oil increased by 55.30% with the increase in displacement rate. The ultimate displacement efficiency of branched remaining oil increased by 93.67%, which shows that increasing displacement rate has a noticeable effect on the development of branched remaining oil. For oil film remaining oil, the best displacement rate was 0.3 mL/min, and the ultimate displacement efficiency was increased by 74.85%. The final displacement efficiency of the residual oil with drop shape was increased by 83.81%. The final displacement efficiency of the remaining columnar oil was increased by 55.67%. Figure 17 compares the improvement range of water drive speed on the displacement efficiency of five different types of remaining oil.

When the displacement rate is low, the axial pressure gradient in the center of the residual oil throat tends towards zero. When the displacement rate increases, the pressure gradient is formed at both ends of the pore throat so that the residual oil can be produced.

Because of the pore throat pressure gradient around the branched remaining oil, when the fluid flow direction is changed by increasing the displacement rate, the branched remaining oil can be more easily driven than the remaining contiguous oil, which is the main reason for increasing the displacement rate and the displacement effect. Of course, the branched remaining oil can also be driven by increasing the viscosity of the displacement agent.

The formation mechanism of oil film remaining oil is mainly the shear stress acting on the remaining oil being less than the adhesion stress. Increasing the displacement rate changes the direction of fluid flow and improves the displacement efficiency to a certain extent. It can also increase the shear stress acting on the remaining oil by increasing the viscosity of the oil displacement agent to improve the displacement efficiency.

For the drop-like remaining oil, increasing the displacement rate can improve the displacement efficiency, but in the formation mechanism of the remaining oil, increasing the injection rate of oil displacement agent, increasing the viscosity of oil displacement agent, and adding surfactant can reduce the surface tension of oil and water to improve the displacement efficiency.

Compared with other types of the remaining oil, the remaining columnar oil is more difficult to drive. This is mainly because the remaining columnar oil stays between the narrow pores, and it is difficult to form a pressure gradient at both ends of the pores. It can be seen that most of the remaining columnar oil begins to be driven away when the displacement rate increases to 0.4 mL/min. By adding a surfactant, the displacement efficiency can be improved by reducing the capillary effect.

• Comparison of Whole and Local Residual Oil Displacement

Total model: The percentage of improvement in displacement efficiency of contiguous, branched, oil film, and the remaining columnar oil is positive, indicating that these four types of remaining oil are displaced, while the percentage of improvement in displacement efficiency of drop remaining oil is negative, indicating that other types of remaining oil are converted into drop remaining oil.

Local: The displacement efficiency of the five types of remaining oil increases by a high percentage, which indicates that increasing the displacement speed can promote the displacement efficiency of various types of remaining oil. From the local pictures, it can be seen that the residual oil of contiguous, branched, oil film, and columnar shape is finally transformed into the residual oil of drop shape (

Table 6. Comparison data of displacement effect of whole remaining oil and local remaining oil.

Comparison Type	Percentage of Increase in Displacement Efficiency of Remaining Oil (Total Model)	Percentage of Increase in Displacement Efficiency of Remaining Oil (Local)
Contiguous residual oil	91.24%	07% (Note: after displacement, the local remaining oil is no longer continuous)
Branched residual oil	100%	93.67% (Note: after displacement, the local remaining oil is no longer contiguous)
Oil film remaining oil	71.70%	84.38%
Columnar residual oil	59.43%	55.67%
Dropwise residual oil	−207.41%	83.81%

).

4. Conclusions

(1) By increasing the displacement rate, the displacement efficiency of these different types of remaining oil can be increased, and the displacement efficiency of the remaining oil in the full mode can also be significantly increased. When the displacement rate is increased by 10 times, the displacement efficiency can increase by 69.19%.

(2) Increasing displacement intensity can improve the displacement efficiency of various forms of remaining oil to different degrees. Among them, the displacement efficiency of branched residual oil is improved most significantly, reaching 93.67%. Secondly, the displacement efficiency of drop residual oil can reach 84.25%. Thirdly, the oil film residual oil can improve the displacement efficiency by 74.85%. The displacement efficiency of continuous residual oil and the columnar residual oil is improved by about 55%.

(3) Through quantitative analysis of various types of remaining oil, it was found that the remaining contiguous oil is basically dispersed in the later stage of displacement, and most of it is displaced, but some is still converted into oil film remaining oil, columnar remaining oil, and drop remaining oil. Although the branched remaining oil is the most easily driven, it cannot be entirely displaced, and a small part of the remaining oil is still converted into drop-like remaining oil in the final stage of displacement. At the end of displacement, a small part of the oil film remaining oil still adheres to the pore surface and becomes small quantities of oil film remaining oil and drop remaining oil. The final remaining oil is a tiny amount of small oil film, column remaining oil, and drop remaining oil.

(4) Although the displacement efficiency of the remaining contiguous oil increases only by about 55% with the increase in displacement rate, most of the remaining oil is contiguous and branched at the beginning of displacement, so it is the remaining contiguous oil and branch remaining oil that contribute to the improvement of displacement efficiency.

(5) In the displacement process, continuous crude oil continues to form branched, oil film, column, and drop residual oil. The main types of residual oil displaced in each increasing displacement speed are also different. With the increase in displacement speed, the main types of residual oil displaced in the model are continuous residual oil, oil film residual oil, branch residual oil, column residual oil, and film residual oil.