Front Movement and Sweeping Rules of CO₂ Flooding under Different Oil Displacement Patterns

Abstract

CO₂ flooding is a pivotal technique for significantly enhancing oil recovery in low-permeability reservoirs. The movement and sweeping rules at the front of CO₂ flooding play a critical role in oil recovery; yet, a comprehensive quantitative analysis remains an area in need of refinement. In this study, we developed 1-D and 2-D numerical simulation models to explore the sweeping behavior of miscible, immiscible, and partly miscible CO₂ flooding patterns. The front position and movement rules of the three CO₂ flooding patterns were determined. A novel approach to the contour area calculation method was introduced to quantitatively characterize the sweep coefficients, and the sweeping rules are discussed regarding the geological parameters, oil viscosity, and injection–production parameters. Furthermore, the Random Forest (RF) algorithm was employed to identify the controlling factor of the sweep coefficient, as determined through the use of out-of-bag (OOB) data permutation analysis. The results showed that the miscible front was located at the point of maximum CO₂ content in the oil phase. The immiscible front occurred at the point of maximum interfacial tension near the production well. Remarkably, the immiscible front moved at a faster rate compared with the miscible front. Geological parameters, including porosity, permeability, and reservoir thickness, significantly impacted the gravity segregation effect, thereby influencing the CO₂ sweep coefficient. Immiscible flooding exhibited the highest degree of gravity segregation, with a maximum gravity segregation degree (GSD) reaching 78.1. The permeability ratio was a crucial factor, with a lower limit of approximately 5.0 for reservoirs suitable for CO₂ flooding. Injection–production parameters also played a pivotal role in terms of the sweep coefficient. Decreased well spacing and increased gas injection rates were found to enhance sweep coefficients by suppressing gravity segregation. Additionally, higher gas injection rates could improve the miscibility degree of partly miscible flooding from 0.69 to 1.0. Oil viscosity proved to be a significant factor influencing the sweep coefficients, with high seepage resistance due to increasing oil viscosity dominating the miscible and partly miscible flooding patterns. Conversely, gravity segregation primarily governed the sweep coefficient in immiscible flooding. In terms of controlling factors, the permeability ratio emerged as a paramount influence, with a factor importance value (FI) reaching 1.04. The findings of this study can help for a better understanding of sweeping rules of CO₂ flooding and providing valuable insights for optimizing oil recovery strategies in the field applications of CO₂ flooding.

1. Introduction

The escalating emissions of greenhouse gases, predominantly carbon dioxide (CO₂), have led to a myriad of environmental challenges, including global climate change [1]. Statistics reveal that a staggering 64% of environmental pollution originates from the increasing concentration of CO₂ in the atmosphere [2]. In response to these concerns, China has aimed to peak carbon emissions by 2030 and achieve carbon neutrality by 2060 [3]. Carbon capture, utilization, and storage (CCUS) have emerged as pivotal strategies in addressing the global climate crisis. This technology involves the capture and separation of CO₂ from industrial emissions, followed by its beneficial utilization, ultimately contributing to a reduction in overall CO₂ emissions [4]. CCUS represents a win–win solution, fostering resource utilization and effective emission reduction. Particularly in the field of petroleum engineering, the application of CO₂ flooding holds promising prospects in terms of significantly enhancing oil recovery in low-permeability reservoirs [5].

As reservoir exploration continues, the proportion of conventional medium and high-permeability reservoir reserves is gradually decreasing, while the discovery of low-permeability reservoir reserves is steadily increasing [6,7,8,9]. In comparison with water flooding, carbon dioxide (CO₂) possesses lower density and viscosity, enabling it to penetrate even the tiny pores, improving the micro-sweep coefficient [10,11,12]. When the pressure exceeds the minimum miscible pressure (MMP), CO₂ can eliminate the interfacial tension between oil and gas through multi-contact miscibility, thus significantly enhancing the oil displacement efficiency [13,14,15,16,17]. Consequently, CO₂ flooding holds promising prospects for effectively enhancing oil recovery in low-permeability reservoirs. In addition, CO₂ can also enhance oil recovery by promoting crude oil expansion, reducing crude oil density and viscosity, changing reservoir wettability, and increasing reservoir permeability [18,19,20,21]. According to statistics, the application of CCUS technology in low-permeability oil fields in China’s Daqing and Jilin regions can enhance oil recovery rates by 10–25% [22]. In the United States, the Kelly–Snyder oil field in the Permian Basin implemented a CO₂ miscible flooding project in the SACROC block in 2002, resulting in a cumulative increase of 2456 × 10⁴ tons of crude oil and an estimated recovery rate improvement of over 26% [23].

The oil recovery within a reservoir is a product of both the sweep coefficient and the displacement efficiency [24]. In the case of miscible CO₂ flooding, the theoretical oil displacement efficiency can attain a remarkable 100%. Therefore, precise quantitative characterization of the CO₂ sweep coefficient holds immense importance in evaluating the enhanced oil recovery potential of CO₂ flooding. Furthermore, in low-permeability reservoirs, the challenges of severe heterogeneity, gravity segregation, and viscous fingering can lead to issues such as gas channeling and a low sweep coefficient [25,26]. To address these challenges effectively, conformance control technologies like WAG flooding and foam flooding become necessary [27,28,29]. A quantitative analysis of the sweep coefficient serves as the foundational basis for evaluating the efficacy of these conformance control technologies.

Characterizing the sweep coefficient involves both experimental and numerical simulation approaches [30,31,32,33]. Concerning experimental simulation, Bergit et al. [34] used high-resolution micro-positron emission tomography (μPET) to analyze the distribution of CO₂ in the core with the change of the PV number during CO₂ injection, and the sweeping effect was characterized qualitatively. Wang et al. [35] used a high-resolution nuclear magnetic resonance method and normalized MI value to distinguish the sweeping range of CO₂ in the core and studied the sweep characteristics of miscible and immiscible flooding. The results showed that the CO₂ front of immiscible flooding is more unstable, which affects the sweep coefficient of CO₂ flooding. Duraid et al. [36] used X-ray CT imaging technology to identify the distribution of oil and water in the heterogeneous core after CO₂ flooding. The results showed that the proportion of residual oil in the low-permeability part is significantly higher than that in the high-permeability part, which indirectly characterized the sweeping rules of CO₂ flooding. The visualization experiment can reflect the microscopic sweep characteristics of CO₂ flooding, and the core experiment can reflect the effect of CO₂ flooding from the macroscopy, but the numerical simulation method is helpful to analyze the sweep rules in detail. Lewis et al. [37] established a reservoir numerical model of a one-quarter five-point well pattern to study water, gas, and WAG flooding sweep coefficients. The sweep coefficients were calculated assuming that the oil displacement efficiency of gas flooding was 100%. Hao et al. [38] established a numerical simulation model of miscible flooding, delineating the contour line with oil and gas interfacial tension equal to 0.1 dyn/cm as the rear edge of the miscible zone and taking the CO₂ content in the oil phase equal to 20% as the front edge of the miscible zone, thus obtaining the sweep coefficient of CO₂ miscible flooding. Li et al. [39] established a mathematical model of miscible flooding considering CO₂ diffusion and adsorption and defined the location where a dimensionless CO₂ concentration of C/C₀ = 0.5 serves as the miscible front and the place where C/C₀ = 0.95 serves as the gas phase front to study the migration rule of the CO₂. C is the concentration of CO₂, and C₀ is the initial concentration of CO₂, which is 0.6 g·cm⁻³. When the adsorption is weak, increased porosity and initial injection rate accelerate the mass transfer and diffusion process. The stronger the diffusion effect, the larger the miscible region and the earlier the gas breakthrough. Enhanced adsorption reduces the sweeping range of the miscible zone. Li et al. [40] established a numerical simulation model of CO₂ flooding with a five-spot well pattern and an inverted nine-spot well pattern and proposed that the location where the viscosity of crude oil drops to a certain extent is defined as the miscible front, thus studying the CO₂ flooding sweeping rules of different well patterns. The results showed that the sweep coefficient of the inverted nine-spot well pattern was higher than that of the five-spot well pattern.

The factors affecting the CO₂ sweep coefficient include geological factors, fluid properties, the injection–production relationship, and so on [24,41,42]. Analyzing the main controlling factors affecting the CO₂ sweep coefficient is propitious when choosing suitable conformance control technology to improve the application effect of CO₂ flooding. Limited research has delved into identifying the main controlling factor in terms of the CO₂ sweep coefficient, with prevalent methodologies encompassing fuzzy analysis and orthogonal analysis [43,44]. Li et al. [45] evaluated the influence degrees of multiple factors on gas channeling through fuzzy analysis and concluded that fractures and heterogeneity are the most critical factors affecting gas channeling. Cui et al. [46] used orthogonal analysis to establish that the main controlling factor affecting the CO₂ sweep coefficient is well distance and established the calculation formula of the CO₂ sweep coefficient using multiple nonlinear regression methods. However, it is important to note that the selection of the weight matrix in fuzzy analysis is somewhat subjective, potentially impacting the precision of the main controlling factor analysis. Moreover, the limited data samples employed in orthogonal studies can lead to specific errors when analyzing the primary controlling factors. Consequently, there exists a need for the further exploration of methodologies for analyzing the main controlling factor influencing the CO₂ flooding sweep coefficient.

According to the relationship between reservoir pressure and minimum miscible pressure (MMP), CO₂ flooding is traditionally categorized into miscible flooding (MF) and immiscible flooding (IMF). However, throughout the reservoir development process, the continuous injection of CO₂ induces dynamic changes in the reservoir pressure distribution, leading to alterations in the miscible state of CO₂ and crude oil. Based on the pressure distribution between injection and production wells, we proposed a more nuanced classification of CO₂ flooding into three distinct displacement patterns: miscible flooding (MF), partly miscible flooding (IMF), and immiscible flooding (IMF). The position and migration law of the miscible front and the immiscible front under three displacement patterns were studied. The quantitative characterization of the sweep coefficients across these patterns was achieved through the application of the contour area method. Additionally, we elucidated the impact of geological factors, injection–production parameters, and crude oil viscosity on the sweep coefficients. Utilizing the Random Forest algorithm, we identified the main controlling factor influencing the sweep coefficient in CO₂ flooding. The findings of this study can help for providing valuable insights for optimizing oil recovery strategies in the field applications of CO₂ flooding. Section 4.1 and Section 4.2 are dedicated to the fitting of PVT (pressure–volume–temperature) and slim tube experiment results carried out in the Jilin low-permeability oil field. Based on the fitting results, 1-D and 2-D numerical simulation models of CO₂ flooding were developed. Section 4.3 focuses on pinpointing the locations of both miscible and immiscible fronts through an analysis of the fluid property variations between wells within the 1-D model. In Section 4.4, based on the contour area method, the CO₂ sweep coefficients for different flooding patterns within the 2-D model are calculated using MATLAB software. Furthermore, we introduce parameters such as GSD (gravity segregation degree) and D_m (miscible degree), investigating the impact of various factors on the sweep coefficients, gravity segregation degree, and miscible degree in the three CO₂ flooding patterns. These factors are discussed from three aspects: geology, oil viscosity, and injection–production parameters. Section 4.5 employs the out-of-bag permutation method within the Random Forest algorithm to identify the main controlling factors influencing the CO₂ sweep coefficients. Finally, our study concludes with a presentation of the findings in Section 5.

2. Materials and Methods

2.1. Materials

The crude oil and formation water used in the experiments were sampled from the Jilin oil field, and the crude oil fractions are shown in

Table 1. Crude oil composition.

Comp.	mol. (%)	Comp.	mol. (%)	Comp.	mol. (%)	Comp.	mol. (%)
sCO2	0.153	C7	3.835	C17	2.249	C27	1.062
N2	2.818	C8	5.131	C18	1.999	C28	1.024
C1	16.193	C9	4.225	C19	1.921	C29	0.936
C2	3.938	C10	3.897	C20	1.764	C30	0.905
C3	3.224	C11	3.36	C21	1.604	C31	0.7
IC4	1.675	C12	3.256	C22	1.554	C32	0.716
NC4	2.978	C13	3.271	C23	1.431	C33	0.548
IC5	0.904	C14	2.697	C24	1.385	C34	0.532
NC5	2.594	C15	2.746	C25	1.232	C35	0.476
C6	2.431	C16	2.208	C26	1.153	C36+	5.275

. CO₂ was purchased from the Beijing Analytical Instrument Factory, and the purity of the CO₂ was 99.95 mol%.

2.2. Apparatus

The PVT analyzer (purchased from DBR, Edmonton, AB, Canada) had a maximum working pressure of 103 MPa and a full operating temperature of 180 °C. The flow chart of the PVT analyzer is shown in Figure 1. The slim tube experimental device was formed in the laboratory. The tube length was 16.0 m, the inner diameter was 6.35 mm, the outer diameter was 9.60 mm, the porosity was 33%, and the permeability of the gas measurement was 3.2 mD. The flow chart of the slim tube experiment is shown in Figure 2.

2.3. Methods

2.3.1. PVT Experiments

• Constant Composition Expansion experiments (CCE)

Constant composition expansion experiments were used to determine the relationship between the volume and pressure of crude oil with a constant mass at reservoir temperature to obtain parameters such as the saturation pressure, the compression coefficient, the relative volume, and the density of the formation fluids. The steps were as follows: the PVT analyzer was evacuated at a temperature of 97.3 °C, then a certain amount of crude oil was transferred to the PVT analyzer in a single phase at a constant temperature for more than 4 h, and the crude oil was pressurized to a pressure P₁, which was higher than the reservoir pressure. Above the saturation pressure, pressurization was carried out via stepwise depressurization at 1~2 MPa per step; below the saturation pressure, volume expansion was carried out at 1~20 cm³ per step. After each depressurization step and expansion, the sample was stirred and stabilized thoroughly, and the pressure and volume were recorded. The experiment was stopped when the sample was expanded to twice the original sample.

2.

Differential Liberation experiments (DL)

Differential liberation or multi-degassing experiments involved degassing crude oil at reservoir temperature in multi-graded pressure reductions to measure the relationship between oil and gas properties and composition with pressure. The crude oil was kept in a single phase, fully stirred to equilibrate, and then stabilized at saturation pressure. The sample was depressurized in three to five pressure steps, with each depressurization recording the sample volume and the volume of gas produced.

3.

Swelling Tests (STs)

Swelling tests were used to measure the relationship between the density and viscosity of crude oil with the molar fraction of CO₂ by gradually increasing the molar fraction of the injected CO₂. First, the volume of the crude oil was tested at saturation pressure, and then a certain amount of CO₂ was injected into the crude oil at this pressure. The pressure increased until all the CO₂ was dissolved to test the saturation pressure, swelling factor, oil viscosity, and other parameters of the CO₂–crude oil system. The above experimental steps were repeated until the molar content of CO₂ in the system reached about 80%, which was when the experiment was stopped.

2.3.2. Slim Tube Experiments

The slim tube model was heated at the experimental temperature, and the slim tube was evacuated for more than 12 h. The pore volume was measured by injecting toluene into the tube model. The slim tube model was saturated with crude oil at the experimental pressure. CO₂ was injected at a constant rate of 15.00 cm³/h to displace the crude oil. Whenever a certain amount of CO₂ was injected, the output oil and gas volumes, injection pressure, and back pressure were measured. Fluid phase and color changes were observed through a high-pressure observation window. The experiment was stopped after injecting 1.2 times the pore volume of CO₂. The above experiments were repeated, and the experimental pressure was changed to determine the minimum miscible pressure for CO₂ flooding.

2.3.3. Testing the Relative Permeability Curves Based on Unsteady-State Method

• Oil–water relative permeability curve

First, the absolute permeability ka of the core was measured. The core was then vacuumed to saturate the formation water, and the effective pore volume and porosity were measured. Under the back pressure of 24.5 MPa, the irreducible water saturation Swc was established by injecting formation oil to displace formation water at the injection rate of 0.2 mL/min, and the oil phase permeability under irreducible water saturation was measured. Keeping the same back pressure, the water flooding experiment was carried out at the injection rate of 0.2 mL/min. The data relating to the water breakthrough time, pressure difference, cumulative oil production, and cumulative liquid production were recorded. When the water cut at the core outlet reached 99.5%, the experiment was stopped. The relative permeabilities of the oil phase and water phase under different water saturations were measured, and the relative permeability curve was drawn.

2.

Gas–oil relative permeability curve

The core was saturated with formation water, and the water phase permeability was measured. The formation oil was injected at an injection rate of 0.2 mL/min to displace the formation water until the water saturation reached irreducible water saturation. The oil phase permeability under irreducible water saturation was measured. CO₂ was injected to displace oil at an injection rate of 0.2 mL/min, and the displacement pressure, oil production, and gas production at each time were recorded. When only gas was produced at the outlet of the core, the experiment was stopped, the relative permeabilities of the oil phase and gas phase under different gas saturations were measured, and the gas–oil relative permeability curve was finally drawn.

3. Numerical Simulation

3.1. Simulation for Slim Tube Experiments and 1-D CO₂ Flooding

3.1.1. Simulation for Slim Tube Experiments

The 1-D numerical simulation model was based on the parameters of the slim tube experiment. The cumulative CO₂ injection volume was 1.2 PV. The fluid parameters simulated for the slim tube experiments were obtained based on the fitting results of CCE, DL, and ST experiments with the WinProp module of the CMG software. The parameters of the thin tube model are shown in

Table 2. Slim tube model parameters.

Parameters	Values
Number of grids	50 × 1 × 1
Grid size	32 cm × 5.8 mm × 5.8 mm
Porosity/%	0.33
Permeability/mD	3.2
Injection pressure constraints/MPa	35.0
Gas injection rate/(PV/d)	0.1

.

3.1.2. Simulation for 1-D CO₂ Flooding

The GEM module of CMG software was used to establish a 1-D numerical simulation model of CO₂ flooding, the EOS of which was fitted by using the WinProp module of CMG software. The values of the model parameters (porosity, permeability, saturation, and so on) were consistent with those in the Jilin oil field, and the processes of miscible flooding, immiscible flooding, and partly miscible flooding were simulated by setting different original reservoir pressures. To ensure the accuracy of the solution, the model was solved by using a fully implicit method. The relative permeability curves were obtained through the experiments, which are shown in Figure 3. The relative permeability of the oil, gas, and water phases was calculated using the Stone II method. The characterization of the miscible state was based on Coats’ component model theory, which describes the miscible state through the relationship between the relative permeability and the interfacial tension of oil and gas. The reference interfacial tension σ_og^r was set to 0.5 mN/m. When the interfacial tension σ_og was higher than 0.5 mN/m, the interfacial tension did not affect the relative permeability curves. When the interfacial tension σ_og was lower than 0.5 mN/m, oil started to be displaced in the form of miscible flooding. The relative permeability curve of miscible flooding was determined via interfacial tension interpolation. The interpolation equations are shown in Equations (1)–(3). The values of the 1-D model parameters are shown in

Table 3. The 1-D numerical simulation parameters.

Parameters	Values
Number of grids	300 × 1 × 1
Grid size	1 m × 1 m × 1 m
Porosity/%	0.13
Temperature/°C	97.3
Permeability/mD	4.5
Initial formation pressure/MPa	16.0 (immiscible flooding)
	22.0 (partly miscible flooding)
	26.0 (miscible flooding)
Gas injection rate/(m3/d)	0.00195 (reservoir condition)
Well bottom pressure constraint/Mpa	40.0 (upper limit)
	10.0 (lower limit)

.

$${\mathrm{k}}_{\mathrm{r}\mathrm{o}}{}_{\mathrm{m}}=\mathrm{m}\times {\mathrm{k}}_{\mathrm{r}\mathrm{o}}+(1-\mathrm{m})\times \frac{{\mathrm{k}}_{\mathrm{r}\mathrm{o}\mathrm{w}}({\mathrm{S}}_{\mathrm{w}})+{\mathrm{k}}_{\mathrm{r}\mathrm{g}}({\mathrm{S}}_{\mathrm{g}})}{2}\times \frac{{\mathrm{S}}_{\mathrm{o}}}{(1-{\mathrm{S}}_{\mathrm{w}})}$$

(1)

$${\mathrm{k}}_{\mathrm{r}\mathrm{g}\mathrm{m}}=\mathrm{m}\times {\mathrm{k}}_{\mathrm{r}\mathrm{g}}+(1-\mathrm{m})\times \frac{({\mathrm{k}}_{\mathrm{r}\mathrm{o}\mathrm{w}}({\mathrm{S}}_{\mathrm{W}})+{\mathrm{k}}_{\mathrm{r}\mathrm{g}}({\mathrm{S}}_{\mathrm{g}})}{2}\times \frac{{\mathrm{S}}_{\mathrm{g}}}{(1-{\mathrm{S}}_{\mathrm{w}})}$$

(2)

$$\mathrm{m}=\left\{\begin{array}{cc}1& {\mathrm{\sigma }}_{\mathrm{o}\mathrm{g}}>{\mathrm{\sigma }}_{\mathrm{o}\mathrm{g}}^{\mathrm{r}}\\ {(\frac{{\mathrm{\sigma }}_{\mathrm{o}\mathrm{g}}}{{\mathrm{\sigma }}_{\mathrm{o}\mathrm{g}}^{\mathrm{r}}})}^{\mathrm{n}}& {\mathrm{\sigma }}_{\mathrm{o}\mathrm{g}}\le {\mathrm{\sigma }}_{\mathrm{o}\mathrm{g}}^{\mathrm{r}}\end{array}\right.$$

(3)

where k_rom and k_rgm are the relative permeability of oil and gas after interpolation; k_ro and k_rg are the relative permeability of oil phase and gas before interpolation; and S_w, S_g, and S_o are the saturation of water, gas, and oil, respectively. k_row is the relative permeability of water in the oil–water relative permeability curve, which is a function of water saturation S_w; k_rg is the relative permeability of gas in the oil–gas relative permeability curve, which is a function of gas saturation, S_g; σ_og is the actual oil–gas interfacial tension in the model; σ_og^r is the reference interfacial tension, which takes the value of 0.5 mN/m; and m is the interpolated value, the value of which depends on the relationship between σ_og and σ_og^r. n is the index of the ratio of actual oil–gas interfacial tension σ_og to the reference interfacial tension σ_og^r, which characterizes the transition speed of the relative permeability curve of immiscible flooding to miscible flooding.

3.2. Simulation for 2-D CO₂ Flooding with Quarter Five-Spot Well Pattern

A 2-D numerical simulation model of CO₂ flooding components was established using the GEM module of the CMG software, the EOS equations and relative permeability curves of which were consistent with the 1-D model. The model’s porosity, permeability, and saturation were set with reference to the Jilin oil field. The miscible, immiscible, and partly miscible flooding processes were simulated by setting different original reservoir pressures. Continuous gas injection (CGI) was simulated with a constant gas injection period of 40 years. The model parameters are shown in

Table 4. The 2-D numerical simulation parameters.

Parameters	Values
Number of grids	25 × 25 × 5
Grid size	8 m × 8 m × 0.6 m
Porosity/%	0.13
Temperature/℃	97.3
Permeability/mD	4.5
Initial formation pressure/Mpa	16.0 (immiscible flooding)
	22.0 (partly miscible flooding)
	26.0 (miscible flooding)
Gas injection rate/(m3/d)	0.77 (reservoir condition)
Well bottom pressure constraint/Mpa	40.0 (upper limit)
	10.0 (lower limit)

.

Compared with the traditional numerical simulation model for CO₂ flooding, a series of improvements were made in this model: to enhance model convergence and solution accuracy, the model was solved using the fully implicit method instead of the traditional IMPSE method. In the iterative solution method, a nine-point difference format was used to suppress the grid orientation effect of CO₂ flooding instead of the conventional five-point difference format. For the general seepage equation Δu = f, the five-point differential and nine-point differential solution equations for the center point u_i,j are shown in Equations (4) and (5), respectively. In Equations (4) and (5), f is a function of (x_i,y_j), which represents the external driving force or source term at positions(i,j) in the differential equation.

$$\frac{1}{{\mathrm{h}}^2}({\mathrm{u}}_{\mathrm{i}-1,\mathrm{j}}-2{\mathrm{u}}_{\mathrm{i},\mathrm{j}}+{\mathrm{u}}_{\mathrm{i}+1,\mathrm{j}})+\frac{1}{{\mathrm{h}}^2}({\mathrm{u}}_{\mathrm{i},\mathrm{j}-1}-2{\mathrm{u}}_{\mathrm{i},\mathrm{j}}+{\mathrm{u}}_{\mathrm{i},\mathrm{j}+1})={\mathrm{f}}_{\mathrm{i}\mathrm{j}}$$

(4)

$$\frac{1}{{\mathrm{h}}^2}({\mathrm{u}}_{\mathrm{i}-1,\mathrm{j}+1}+{\mathrm{u}}_{\mathrm{i}+1,\mathrm{j}+1}+{\mathrm{u}}_{\mathrm{i}-1,\mathrm{j}-1}+{\mathrm{u}}_{\mathrm{i}+1,\mathrm{j}-1}+4({\mathrm{u}}_{\mathrm{i},\mathrm{j}+1}+{\mathrm{u}}_{\mathrm{i},\mathrm{j}-1}+{\mathrm{u}}_{\mathrm{i}-1,\mathrm{j}}+{\mathrm{u}}_{\mathrm{i}+1,\mathrm{j}})-20{\mathrm{u}}_{\mathrm{i},\mathrm{j}})={\mathrm{f}}_{\mathrm{i}\mathrm{j}}$$

(5)

3.3. Solution of Sweep Coefficient for CO₂ Flooding

Parameters such as the CO₂ content in the oil and the interfacial tension of each grid obtained from the solution of the 2-D numerical model were imported into MATLAB R2022a by programming a data reading algorithm. The discrete grid data were expanded using linear or cubic interpolation methods. Contour maps of CO₂ content in oil and interfacial tension at different moments of CO₂ flooding were drawn. The contour lines corresponding to the miscible and immiscible front of CO₂ flooding were extracted. The polygon areas surrounded by the contour lines were solved, and the sweep coefficient at the corresponding time could be obtained compared with the total grid area. The mechanism is shown in Figure 4, and the sweep coefficient E_sweep is calculated as shown in Equation (6).

$${\mathrm{E}}_{\mathrm{s}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{p}}=\frac{{\mathrm{S}}_{\mathrm{s}\mathrm{w}\mathrm{e}\mathrm{p}\mathrm{t}}}{{\mathrm{S}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}\times 100\%$$

(6)

where S_swept and S_total are the areas enclosed by the contour line of the CO₂ front and the coordinate axis and the total grid area, respectively.

3.4. Main Controlling Factor Assessment of CO₂ Flooding Based on Random Forest Algorithm

Different ranges of values were assigned to each parameter affecting the sweep coefficients of CO₂ flooding, and 1000 sets of numerical simulation models with different combinations of parameters were formed using the Latin hypercube design method, which can make the values of each parameter satisfy the normal distribution. The range of values for each parameter is shown in

Table 5. Range of values for each parameter.

Parameters	Minimum Value	Maximum Value	Unit
Permeability	0.5	100	mD
Porosity	0.05	0.2	/
Reservoir thickness	3.0	30.0	m
Permeability ratio	1.1	100	/
Well spacing	50	300	M
Injection rate	0.1	2.0	m2/d (RC)
Oil viscosity	0.74	33.52	mPa·s

. The sweep coefficients of CO₂ flooding for different parameter combinations were obtained by solving the 1000 sets of models. The Bootstrap sampling method was used to form 800 training sets and 200 prediction sets. The 800 training sets were used to construct multiple decision trees to develop a Random Forest model. Predictions were made on the prediction sets, and the ballot method was used to decide the regression or classification results. Different numbers of decision trees and leaves were set to form different Random Forest models and solve the prediction errors (MSE) of the different Random Forest models. The numbers of decision trees and leaves with minimum MSE were preferred as the parameters of the optimal Random Forest model. The principle of the Random Forest algorithm is shown in Figure 5. Based on the out-of-bag data permutation method (OOB), the optimized Random Forest model was used to evaluate the importance of each influencing factor (FI). The main steps were as follows: (1) For decision tree i, the prediction error rate e₁ of out-of-bag data was calculated. (2) After randomly replacing the observations of the influencing factor X_j, the decision tree was constructed again, and the prediction error rate e₂ of the out-of-bag data was calculated. (3) The differences between the two error rates were calculated and standardized to calculate the average MDA_j in all decision trees, which was the factor importance value (FI_j). The larger the FI_j value, the higher the importance of the parameter X_j. The calculation of FI_j is shown in Equation (7) [47].

$$\mathrm{F}{\mathrm{I}}_{\mathrm{j}}=\mathrm{M}\mathrm{D}{\mathrm{A}}_{\mathrm{j}}=\frac{1}{\mathrm{T}}{\displaystyle \sum _{\mathrm{t}}^{\mathrm{T}}\left[\frac{1}{\left|{\mathrm{D}}_{\mathrm{t}}\right|}({\displaystyle \sum _{{\mathrm{X}}_{\mathrm{i}}^{\mathrm{j}}\in {\mathrm{D}}_{\mathrm{t}}^{\mathrm{j}}}{\displaystyle \sum {({\mathrm{R}}_{\mathrm{k}}({\mathrm{X}}_{\mathrm{i}}^{\mathrm{j}})-{\mathrm{y}}_{\mathrm{i}}^{\mathrm{k}})}^2-{\displaystyle \sum _{{\mathrm{X}}_{\mathrm{i}}\in {\mathrm{D}}_{\mathrm{t}}}{\displaystyle \sum _{\mathrm{k}}{({\mathrm{R}}_{\mathrm{k}}({\mathrm{X}}_{\mathrm{i}})-{\mathrm{y}}_{\mathrm{i}}^{\mathrm{k}})}^2}}}}\right]}$$

(7)

where T is the number of decision trees; (X_i,y_i) is the training set; X_i^j is the sample after a random exchange of the j-type influence parameter of X_i; D_t is the out-of-bag sample set of the decision tree _t, and D_t^j is the sample set formed after the j-th type of influence parameter exchange; and R(X_i) is the predicted output of sample X_i. y_i^k is the regression output of the k-type influence parameter under multi-objective regression.

4. Discussion

4.1. PVT Fitting and Establishment of EOS Equation for Reservoir Fluid

The saturation pressure P_sat, relative volume, oil phase density, viscosity, and swelling factor of reservoir fluid were measured by using CCE, DL, and ST experiments. The C₁₇₊ component of the formation oil was divided into three components, C₁₇–C₂₆, C₂₇–C₃₉, and C₄₀₊, and the C₁–C₁₆ components were merged into five components, C₁, C₂, C₃+C₄, C₅+C₆, and C₇–C₁₆. By adjusting the critical pressure P_c, critical temperature T_c, binary interaction coefficient, and other parameters of the heavy components, the fluid component model was obtained based on fitting the results of the PVT experiments. The results are shown in Figure 6. Some parameters of the EOS after PVT fitting are shown in

Table 6. Parameters of EOS after PVT fitting.

Components	mol. (%)	Pc (atm)	Tc (K)	Mw (g/mol)	Vc (m3/kmol)
CO2	0.153	72.80	304.20	44.01	0.0940
N2	2.818	33.50	126.20	27.99	0.0898
C1	16.193	45.40	190.60	16.05	0.0990
C2	3.938	48.20	305.40	30.09	0.1480
C3+C4	7.877	39.02	406.11	52.38	0.2371
C5+C6	5.929	31.51	486.50	76.99	0.3335
C7-C16	31.58	19.82	624.24	148.05	0.5701
C17-C26	15.87	13.63	653.87	289.86	1.2768
C27-C39	9.478	11.76	878.05	444.69	1.8926
C40+	6.164	10.60	989.31	716.21	3.2964

. It can be seen from Figure 6 that the saturation pressure of the pure oil phase used in the experiment was 7.16 MPa, and the viscosity at saturation pressure was 1.74 mPa·s. When the mole fraction of injected CO₂ was 80%, the oil saturation pressure increased to 39.7 MPa, the viscosity decreased to 0.72 mPa·s, and the swelling factor increased to 1.8762. The swelling and viscosity reduction effects of CO₂ on crude oil were propitious to enhancing oil recovery. The experimental results were compared with the fitting results. It could be seen that the above component, the splitting and merging scheme for oil phase components, could accurately fit the results of PVT experiments, and the obtained EOS parameters could better simulate the high-temperature and high-pressure physical properties of crude oil in reservoirs.

4.2. Determination of Minimum Miscible Pressure Based on Slim Tube Experiment Simulation

The CO₂ displacement experiment was carried out with a slim tube model at the formation temperature of 97.3 °C, and the displacement pressure ranged from 18 MPa to 30 MPa. The cumulative amount of injected CO₂ was 1.2 PV. The recovery factors of CO₂ flooding under different displacement pressures were calculated, and the results are shown in Figure 7a. When the displacement pressure was less than 22.10 MPa, the recovery factor of CO₂ flooding was low, which was an immiscible displacement process, and the recovery factor increased rapidly with the increase in displacement pressure. When the displacement pressure increased from 18 MPa to 23.11 MPa, the recovery degree rose from 76.89% to 94.53%. When the displacement pressure was higher than 22.10 MPa, the CO₂ flooding pattern turned to miscible flooding, and the increase in the recovery factor slowed down. When the displacement pressure increased from 23.11 MPa to 30.0 MPa, the recovery degree only increased from 94.53% to 96.08%. The sections of immiscible and miscible displacement were fitted, and the displacement pressure corresponding to the intersection of the fitting lines was 22.10 MPa. Based on the EOS equation formed in Section 4.1, a 1-D slim tube numerical model was established to simulate the results of the tube experiment. The results are shown in Figure 7b. The maximum fitting error of the recovery factor under immiscible flooding was about 7%, and the maximum fitting error of the recovery degree under miscible flooding was about 0.8%. The simulation results showed that the minimum miscible pressure was 23.30 MPa, and the error compared with the experimental results was 5.4%, which indicated that the EOS equation formed by PVT fitting could accurately reflect the characteristics of crude oil and could be used for subsequent numerical simulation work.

4.3. Front Movement Rules of CO₂ Flooding under Different Flooding Patterns

Currently, the classification of CO₂ flooding is mainly based on the relationship between original reservoir pressure and minimum miscible pressure, which is divided into miscible flooding, immiscible flooding, and near-miscible flooding. However, in the oil field development process, the reservoir pressure field undergoes dynamic changes due to the conduction between the injection and production wells, changing the miscible degree. Therefore, according to the miscible degree, CO₂ flooding was divided into three displacement patterns: (1) In miscible flooding (MF), the pressure between the injection and production wells was higher than the minimum miscible pressure, and the miscible degree was 1.0. (2) In partly miscible flooding (PMF), the original formation pressure of the reservoir was lower than the minimum miscible pressure, but the pressure near the injection well was higher than the minimum miscible pressure due to the reservoir energy enhancement of gas injection, thus forming a miscible flooding zone. The oil production of production wells decreased the reservoir pressure, and the immiscible flooding zone was formed within a certain range near the production well. The miscible degree of partly miscible flooding was between 0 and 1.0. (3) In immiscible flooding (IMF), the pressure between injection and production wells after gas injection was lower than the minimum miscible pressure, and the displacement process maintained immiscible flooding. The miscible degree of immiscible flooding was 0. By establishing a 1-D numerical simulation model, the distribution of CO₂ composition in the oil phase, oil saturation, and oil–gas interfacial tension between the injection and production wells under different displacement patterns of CO₂ flooding was studied, and the miscible/immiscible front position and front movement rules were determined. The results are shown in Figure 8. Figure 8a also shows the distribution of fluid properties between the injection and production wells in relation to miscible flooding. The oil saturation of miscible flooding maintained a meager value with increasing distance. Then, it increased rapidly to the initial oil saturation S_oi, showing the characteristics of a piston-like displacement. The interfacial tension increased rapidly with distance and then gradually decreased to the platform value. When the distance reached a certain value, it gradually decreased to 0. The CO₂ content in the oil phase increased rapidly and reached the platform value. The CO₂ content then increased gradually to the maximum value after increasing a certain distance and finally decreased to the original CO₂ content in the oil phase. According to the distribution of the above three parameters, the inter-well phase zone of miscible flooding was divided into a pure gas zone, a two-phase zone, a miscible zone, a diffusion zone, and an unswept zone. The gas zone was near the gas injection well area, where the oil saturation and interfacial tension were zero due to continuous CO₂ injection and miscibility. In the two-phase zone, the light components gradually evaporated into the gas phase, forming a rich gas that migrated to the production wells, significantly increasing the content of heavy components in crude oil at the miscible rare edge, thus forming an oil–gas two-phase zone. The crude oil in this zone was mainly residual oil with a high heavy component content. Due to the subsequent injection and dissolution of CO₂, the CO₂ content in this zone was significantly higher than the initial level. In the miscible zone, the rich gas in the miscible front contacted the crude oil through the condensate miscible effect, so the light component and CO₂ content in the oil phase increased significantly. The difference in the component content between oil and gas decreased, and the interfacial tension, therefore, gradually decreased and finally reached zero interfacial tension. The oil saturation suddenly changed to the initial oil saturation in this zone. In the diffusion zone, CO₂ entered the crude oil mainly through diffusion. As the distance increased, the diffusion effect gradually weakened, and the CO₂ content decreased to the initial level. The unswept zone only contained the pure oil phase. The interfacial tension was zero, the oil saturation was equal to the initial oil saturation, and the CO₂ content in the oil phase was equal to the initial value. The above analysis shows that the front of the miscible zone should be located at the maximum CO₂ content in the oil phase. Figure 8b shows the distribution of fluid properties between the injection and production wells in the case of immiscible flooding. With the increased distance, the oil saturation of immiscible flooding increased slowly to the initial oil saturation, forming a wide range of two-phase zones. The interfacial tension decreased rapidly with increasing distance, then increased sharply after a certain distance, and finally decreased to zero. The content of CO₂ in the oil phase decreased slightly at first and then decreased significantly to the initial level after a certain distance. Similarly, the injection–production inter-well phase zone of immiscible flooding was divided into two-phase, diffusion, and unswept zones. In the two-phase zone, due to the dissolution of CO₂ in the oil phase, the interfacial tension was reduced to 4 mN/m, and the CO₂ content in the oil phase was increased to about 0.55, which was lower than the CO₂ content in the case of miscible flooding. In the diffusion zone, the interfacial tension increased gradually due to the formation of a CO₂ concentration diffusion gradient. The interfacial tension reached the maximum at the junction of the diffusion zone and the unswept zone, defined as the immiscible front of immiscible flooding. Figure 8c shows the distribution of the fluid properties between injection and production wells in partly miscible flooding. The oil saturation of partly miscible flooding first maintained a meager value (residual oil saturation) with increasing distance. It then gradually increased to the initial oil saturation S_oi, but the increase amplitude was less than that of miscible flooding. The interfacial tension had two extreme values with the increase in distance. The CO₂ content in the oil phase gradually increased from the platform value of about 0.63 to the maximum value of 0.75. It then gradually decreased to the original CO₂ content in the oil phase. Unlike miscible and immiscible flooding, partly miscible flooding had both miscible and immiscible zones. In the miscible zone, due to condensate miscibility, the CO₂ content in the oil phase reached the maximum value, and the interfacial tension was reduced to zero, reaching the miscible state. In the immiscible zone, as the distance increased, the pressure between the injection and production wells decreased to less than the minimum miscible pressure, and the CO₂ in the oil phase re-evaporated into the gas phase, resulting in the gradual decrease in the CO₂ content in the oil phase and the rapid increase in interfacial tension. The displacement process changed from miscible flooding to immiscible flooding. The inter-well fluid zone divisions of the three displacement patterns are summarized in Figure 9. In addition, the gas injection volume was fixed at 0.3 HCPV, and the front movement positions of miscible flooding, partly miscible flooding, and immiscible flooding were compared, as shown in Figure 7d. The front movement of immiscible flooding was the fastest to reach the production well. The front of the immiscible zone in partly miscible flooding was located at 170 m, and the front of the miscible zone was located at 134 m, which indicated that the front movement velocity of the immiscible zone in partly miscible flooding was faster than that of the miscible zone. Therefore, immiscible flooding was more likely to cause gas channeling problems than miscible and partly miscible flooding.

4.4. Front Movement Rules of CO₂ Flooding under Different Flooding Patterns

According to the fluid phase zone division results of miscible, immiscible, and partly miscible flooding proposed in Section 4.3, the reservoir numerical simulation models of three displacement patterns were established based on the quarter five-point well pattern. The distribution of oil–gas interfacial tension and CO₂ content in the oil phase under different displacement patterns were output by MATLAB, and the contour map was formed. The effective sweep coefficient of CO₂ under different displacement patterns was solved by the program. In addition, the ratio of the maximum sweep coefficient E_smax to the minimum sweep coefficient E_smin between layers was defined as the gravity overlap degree (GSD), as shown in Equation (8), to characterize the strength of the gravity overlap during CO₂ flooding. The larger the GSD value was, the stronger the gravity overlap effect of the displacement process was. The ratio of the miscible zone swept volume V_s-mis to the total swept volume V_s-total of partly miscible flooding was defined as the miscible degree (D_m), as shown in Equation (9), to characterize the strength of the miscible degree in the process of partly miscible flooding. The larger the D_m, the stronger the influence of miscibility on the sweep coefficient in the partly miscible flooding, and the range of the miscible degree D_m was 0~1.0. The effects of different factors on the sweep coefficient of CO₂ under three displacement patterns were studied from geological parameters, crude oil viscosity, and injection–production parameters.

$$\mathrm{G}\mathrm{S}\mathrm{D}=\frac{{\mathrm{E}}_{\mathrm{smax}}}{{\mathrm{E}}_{\mathrm{smin}}}$$

(8)

$${\mathrm{D}}_{\mathrm{m}}=\frac{{\mathrm{V}}_{\mathrm{s-mis}}}{{\mathrm{V}}_{\mathrm{s-total}}}$$

(9)

4.4.1. Geological Parameters

• Permeability

The relationships between permeability and sweep coefficients of miscible flooding, partly miscible flooding, and immiscible flooding are compared in Figure 10a. The sweep coefficients of CO₂ under the three flooding patterns increased first and then decreased with increased permeability. However, the sweep coefficient of miscible flooding was higher than that of partly miscible and immiscible flooding. When the permeability was low, the sweep coefficients of the three displacement patterns were low due to the high seepage resistance in the reservoir, which was the main controlling factor affecting the sweep coefficient. When the permeability increased to 2 mD, the sweep coefficient gradually increased due to decreased seepage resistance. The sweep coefficient of miscible flooding reached 74.46%, while those of the partly miscible and immiscible flooding were 73.50% and 63.62%, respectively. When the permeability further increased, the sweep coefficients of the three displacement patterns gradually decreased. This was because the viscosity and density of CO₂ were lower than that of crude oil, and it was easy to produce gravity overlap in the reservoir with low seepage resistance, move to the top of the reservoir, and produce the crude oil in the top layer. The gravity segregation degrees (GSD values) of the three displacement patterns were analyzed, and the results are shown in Figure 10a. The GSD values of the three displacement patterns increased with increased permeability. When the permeability reached 100 mD, the GSD values of miscible, immiscible, and partly miscible flooding were 12.47, 69.44, and 51.75, respectively. The gravity segregation degree of miscible flooding was the lowest, followed by partly miscible flooding, and immiscible flooding was the highest. This was because the miscible effect continuously enriched CO₂ in the displacement process, and its density and viscosity were gradually similar to those of crude oil, so gravity segregation was significantly weakened. Figure 10b shows the variation in the sweep coefficient and miscible degree of partly miscible flooding with permeability. When the permeability was 0.5 mD, due to the large seepage resistance and high gas injection pressure, the overall pressure of the reservoir was increased so that CO₂ displaced crude oil in the form of miscible flooding, and the miscible degree (D_m value) was 1.0. With the increase in permeability, the seepage resistance decreased, and CO₂ flooding began to show the characteristics of partly miscible flooding, where both miscible and immiscible zones could be observed. When the permeability increased to 20 mD, the D_m value decreased to 0.52. This was mainly because the increase in permeability led to enhanced overlap, and CO₂ easily channeled along the top of the reservoir, resulting in a continuous decrease in the formation pressure, thus reducing the miscible degree. When the permeability increased to 100 mD, the miscibility rose to 0.70. The increased permeability reduced the seepage resistance, and the migration velocity of the immiscible front was accelerated. After gas channeling, the sweeping volume of the immiscible zone decreased due to the weak ability of the immiscible zone to sweep oil in both sides of the main streamline, while the miscible front continued to move and displace the oil on both sides, thus increasing the miscible degree.

2.

Porosity

The relationships between the porosity and the sweep coefficient under three displacement patterns were compared, and the results are shown in Figure 11a. With the increase in porosity, the sweep coefficients of the three displacement patterns decreased gradually, and the sweep coefficients of miscible flooding and partly miscible flooding were higher than those of immiscible flooding. When the porosity was 0.03, the sweep coefficients of miscible, immiscible, and partly miscible flooding were 97.70%, 86.20%, and 92.13%, respectively. When the porosity increased to 0.3, the sweep coefficients of the three displacement patterns decreased to 50.46%, 42.98%, and 49.15%. The porosity affected the sweep coefficient, which was mainly attributed to the gravity segregation degree. It can be seen from Figure 10a that the GSD values of the three displacement patterns increased with the increase in porosity, and the GSD value of immiscible flooding was always greater than those of miscible flooding and partly miscible flooding. When the porosity was 0.3, the GSD value of immiscible flooding was 8.97, while the GSD values of miscible and partly miscible flooding were 1.93 and 13.57, respectively. The sweep coefficient and miscible degree of partly miscible flooding were analyzed, and the results are shown in Figure 11b. With the increase in porosity, the sweep coefficient of the immiscible zone of partly miscible flooding decreased significantly, but the sweep coefficient of the miscible zone increased slightly and then decreased slowly, and the sweep coefficient of the miscible zone decreased from 43.52% to 35.58%. The miscible degree rose from 0.47 to 0.72. On one hand, the increase in porosity accelerated the movement of the immiscible front and miscible front to production wells, but the moving velocity of the miscible front was slower. On the other hand, it was beneficial to the multi-contact miscibility in the movement of the miscible front, thus enhancing the miscible degree.

3.

Reservoir thickness

The influence of the reservoir thickness on CO₂ sweep coefficients of miscible flooding, partly miscible flooding, and immiscible flooding was studied by changing the reservoir thickness from 1.5 m to 10.0 m. The results are shown in Figure 12a. The sweep coefficients of CO₂ in the three displacement patterns decreased with the increase in reservoir thickness. When the reservoir thickness was 1.5 m, the sweep coefficients of miscible, partly miscible, and immiscible flooding were 86.85%, 82.75%, and 79.65%, respectively. When the reservoir thickness increased to 10.0 m, the sweep coefficients of the three displacement patterns decreased to 36.19%, 34.18%, and 33.01%, respectively. In addition, the GSD values of the three displacement patterns were 1.1~1.3, with a reservoir thickness of 1.5 m. When the reservoir thickness increased to 10.0 m, the GSD values of miscible flooding, partly miscible flooding, and immiscible flooding increased to 8.4, 16.4, and 78.1, respectively. The reservoir thickness had the most significant influence on immiscible flooding. Therefore, the variation in the gravity segregation degree caused by the change in the reservoir thickness was the critical factor affecting the sweep coefficient. The sweep coefficient and miscible degree of partly miscible flooding were analyzed, and the results are shown in Figure 12b. With the increase in the reservoir thickness, the sweep coefficients of miscible and immiscible zones of partly miscible flooding decreased gradually, but the miscible degree increased slightly from 0.62 to 0.74. This was mainly because the effect of the gravity segregation degree on the immiscible zone was stronger than that on the miscible zone. The increase in the reservoir thickness made the immiscible and miscible fronts move to the production well on the horizon and expand vertically simultaneously. The movement of the immiscible front was faster than that of the miscible front, so the immiscible zone quickly broke through to the production well in the high part of the reservoir. The sweeping of the miscible zone was more uniform, which ultimately improved the miscible degree.

4.

Permeability Ratio

Two-layer heterogeneous models were established to study the influence of the permeability ratio on the sweep coefficients. The permeabilities of different layers changed in an anti-rhythmic pattern, the ratio of which ranged from 2 to 100. The results are shown in Figure 13a,b. The sweep coefficients of the whole layers and low-permeable zone decreased significantly under the three displacement patterns with the increased permeability ratio. When the permeability ratio was 10, the sweep coefficient of immiscible flooding was only 0.89%. In comparison, the sweep coefficients of miscible and partial miscible flooding were 4.8% and 2.8%, respectively, which were both lower than 5%. The result indicated the influence of heterogeneity on miscible flooding, and partly miscible flooding was weaker than immiscible flooding. Under different displacement patterns, the upper limit of the anti-rhythm reservoir permeability ratio suitable for applying CO₂ flooding was about 5.0.

4.4.2. Injection–Production Parameters

• Well spacing

The influence of injection–production well spacing on the CO₂ sweep coefficients of miscible flooding, partly miscible flooding, and immiscible flooding was studied in relation to a well spacing variation range of 100~300 m. The results are shown in Figure 14a. The sweep coefficients in the three displacement patterns decreased with the increase in well spacing. The increase in well spacing delayed the movement velocity of miscible and immiscible fronts to the production well in the horizontal direction. It significantly enhanced the gravity overlap of CO₂ in the vertical direction, so the sweep coefficients were reduced considerably. However, the reduced sweep coefficients of miscible and partly miscible flooding were mainly dominated by the weakening of the front movement velocity in the horizontal direction, and the gravity segregation degree did not change. When the well spacing increased to 300 m, the GSD values of miscible and partly miscible flooding increased from 1.0 and 1.2 to 2.1 and 3.6, respectively. The decrease in the sweep coefficient of immiscible flooding was mainly affected by gravity overlap, and the GSD value increased from 1.8 to 11.0. Figure 14b shows the influence of well spacing on the sweep coefficient and miscible degree of partly miscible flooding. Although the increase in well spacing reduced the total sweep coefficient of partly miscible flooding, the sweep coefficient of the miscible zone increased first and then decreased, and the miscible degree rose from 0.44 to 0.74. This was attributed to the delay in the miscible front moving through the production well. The effect of miscible flooding could be exploited adequately. When the well spacing was further increased, the gravity overlap of the miscible front was gradually enhanced, moving to the top of the reservoir and breaking through to the production well so that crude oil at the bottom of the reservoir could not be effectively displaced. When the well spacing was 200 m, it could not only ensure a higher sweep coefficient and miscible degree but also maximize the sweep coefficient of the miscible zone, giving full play to the role of miscible flooding.

2.

Gas injection rate

The influence of the gas injection rate on the sweep coefficients of the three CO₂ flooding patterns was studied with the gas injection rate variation range of 85.98~517.5 m³/d. The results are shown in Figure 15a. The sweep coefficients of CO₂ in the three CO₂ flooding patterns increased significantly first and then decreased slightly with an increasing gas injection rate. When the gas injection rate reached 517.5 m³/d, the sweep coefficients of the three were about 70%. The GSD values of the three displacement patterns were significantly weakened with the increase in the gas injection rate. When the gas injection rate increased to 517.5 m³/d, the GSD values of the three displacement patterns were about 1.01–1.07, which could achieve uniform displacement in each layer. The gas injection rate had two effects on the increasing CO₂ sweep coefficient. On one hand, the higher gas injection rate was beneficial to recovering reservoir energy, increasing the formation pressure to above the minimum miscible pressure, which made partly miscible flooding and immiscible flooding transition to miscible flooding. On the other hand, it promoted the seepage velocity of the miscible and immiscible fronts in the horizontal direction and inhibited vertical movement. However, the overhigh gas injection rate will accelerate gas channeling in the production wells. Hence, the sweep coefficients of the three displacement patterns decreased slightly with an increasing gas injection rate. Figure 15b shows the influence of the gas injection rate on the sweep coefficient and miscible degree of partly miscible flooding. When the gas injection rate was lower than 170.81 m³/d, the sweep coefficient of the miscible zone and miscible degree were almost zero. When the gas injection rate exceeded 261.61 m³/d, the sweep coefficient of the miscible zone reached 70%, and the miscible degree increased from 0.69 to 1.0. The miscible degree and sweep coefficient could be enhanced by appropriately increasing the gas injection rate for partly miscible and immiscible flooding.

4.4.3. Crude Oil Viscosity

The influence of the crude oil viscosity on the sweep coefficients of the three CO₂ flooding patterns was studied in relation to a gas injection rate variation range of 0.74~12.18 mPa·s. The results are shown in Figure 16a. The sweep coefficients of miscible and partly miscible flooding decreased with the increase in crude oil viscosity. When the viscosity of crude oil increased to 12.18 mPa·s, the sweep coefficients of miscible flooding and partly miscible flooding decreased from 80.42% and 78.98% to 64.42% and 49.92%, respectively. However, the gravity segregation degrees of miscible and partly miscible flooding remained almost unchanged with increasing crude oil viscosity, which were 1.40 and 1.60, respectively. Therefore, the decreases in the sweep coefficients of miscible flooding and partly miscible flooding were mainly due to the high seepage resistance caused by the increase in crude oil viscosity, and the influence of gravity overlap on the sweep coefficient was relatively small. The sweep coefficient of immiscible flooding decreased first and then increased with the increase in crude oil viscosity, and the GSD value rose first and then decreased. When the viscosity of crude oil was 4.98 mPa·s, the sweep coefficient of immiscible flooding reached the minimum value of 53%, and the GSD value increased to 5.27. When the viscosity of crude oil rose to 12.18 mPa·s, the sweep coefficient of immiscible flooding increased to 61.89%, and the GSD value decreased to 2.05. The change of the sweep coefficient of immiscible flooding had an excellent corresponding relationship with the variation in the gravity segregation degree. The influence of crude oil viscosity on the sweep coefficient and miscible degree of partly miscible flooding is shown in Figure 16b. The miscible degree of partly miscible flooding decreased first and then increased with the increase in crude oil viscosity and finally dropped from 0.78 to 0.71. When the viscosity of crude oil increased by 12.18 mPa·s, the sweep coefficient of the miscible zone decreased from 61.34% to 44.45%. In contrast, the sweep coefficient of the immiscible zone first increased to 22.59% and then dropped to 17.76%. The increase in crude oil viscosity made the multi-contact miscibility between CO₂ and crude oil more difficult, decreasing the sweep coefficient of the miscible zone. In addition, increased crude oil viscosity inhibited the horizontal movement of the immiscible zone and intensified the vertical overlap, thus decreasing the miscible degree. However, the overhigh viscosity of crude oil strengthened the horizontal viscous fingering, making the immiscible zone break through the production well more easily along the horizontal direction.

4.5. Analysis of the Main Controlling Factors of CO₂ Flooding Sweep Coefficient Based on the Random Forest Algorithm

Based on the single-factor analysis of the CO₂ flooding sweep coefficient in Section 4.4, the parameter variation ranges of different influencing factors were set, and 1000 sets of CO₂ flooding numerical simulation models were formed by using a Latin hypercube design. The Bootstrap sampling method was used to create 800 training sets and 200 testing sets. The Random Forest model was established by constructing multiple decision trees using the 800 training sets. The testing sets were predicted, and the voting method determined the prediction results. The number of decision trees and the number of leaves in the Random Forest model were optimized to obtain the optimal model parameters. The optimized Random Forest model was used to calculate the decrease rate MDA of the prediction accuracy before and after the permutation of the out-of-bag data of a certain influencing factor (such as porosity, permeability, etc.), which was used as a parameter to evaluate the importance degree (FI) of the influencing factor. The larger the FI value, the greater the influence of the factors on the sweep coefficient. The parameter optimization results of Random Forest are shown in Figure 17a. Under the condition of the same number of leaves, the mean square error MSE of the prediction results decreased rapidly with the increase in the number of decision trees. However, when the number of decision trees increased to 500, MSE almost did not change. Increasing the number of decision trees will lead to overfitting the model, so the optimal number of decision trees was 500. In addition, under the same number of decision trees, MSE increased with the increase in the number of leaves. Thereby, the optimal number of leaf nodes was five. The importance degree of the influencing factors of the CO₂ flooding sweep coefficient is shown in Figure 17b. The factors affecting the sweep coefficient of CO₂ flooding were ranked in order of importance degree (FI) as follows: permeability ratio, well spacing, reservoir thickness, gas injection rate, porosity, permeability, and crude oil viscosity. The main controlling factor affecting the sweep coefficients of CO₂ flooding was the permeability ratio, the importance degree (FI) of which reached 1.04. In the field application of CO₂ flooding, attention should be paid to the problem that the low-permeability layer caused by the high-permeability ratio cannot be effectively utilized and the gravity overlap problem of CO₂ flooding in thick reservoirs.

5. Conclusions

Based on the fitting results of the PVT and slim tube experiments in the Jilin oil field, the 1-D and 2-D reservoir numerical simulation models of CO₂ flooding were developed to analyze the movement rules relating to the CO₂ front in miscible, partly miscible, and immiscible flooding, along with the influence of different factors on the sweep coefficient. The main controlling factors affecting the sweep coefficient of CO₂ flooding were determined using the out-of-bag data permutation method based on the Random Forest algorithm.

(1) The miscible front was located at the point of maximum CO₂ content in the oil phase, and the immiscible front was located at the point of maximum interfacial tension near the production well. The movement speed of the immiscible front was faster than that of the miscible front, so gas channeling was more likely to occur in immiscible flooding. Comparatively, miscible and partly miscible flooding yielded higher sweep coefficients than immiscible flooding, underscoring the advantageous effect of miscibility in achieving uniform CO₂ sweeping within the reservoir.

(2) Regarding geological factors, the increases in porosity, permeability, and reservoir thickness intensified the gravity overlap effect and reduced the sweep coefficients of CO₂ under the three displacement patterns. The increase in the permeability ratio also notably reduced the sweep coefficient, albeit to a lesser extent, in miscible and partly miscible flooding when compared with immiscible flooding. The upper limit of the reservoir permeability ratio suitable for applying CO₂ flooding under different displacement patterns was about 5. Concerning the injection–production parameters, the increase in well spacing amplified the seepage resistance in the horizontal direction, leading to reduced sweep coefficients in the cases of miscible and partly miscible flooding. In immiscible flooding, the reduction in the sweep coefficients was predominantly attributed to gravity overlap. Elevating the gas injection rate enhanced the miscibility degree in partly miscible flooding and immiscible flooding while inhabiting the gravity overlap, thus enhancing the sweep coefficient of CO₂ flooding. Crude oil viscosity primarily governed the sweep coefficients in miscible and partly miscible flooding by elevating the seepage resistance, whereas in immiscible flooding, gravity overlap took precedence in determining the sweep coefficient.

(3) The main controlling factor affecting the sweep coefficient of CO₂ flooding was the permeability difference, and the factor importance FI reached 1.04. In the field application of CO₂ flooding, attention should be paid to the problem of ineffective displacement in low-permeable zones in heterogeneous reservoirs.