Compared with other gas flooding technologies, air flooding has the unique advantage of low-temperature oxidation (LTO) with crude oil, but the sweep efficiency of air flooding is low, the contact range between crude oil and the air is small, and the low-temperature oxidation is reduced^[1]. In addition, light oil reservoirs air flooding has the risk of explosion, which affects the popularization and application of air flooding to some extent. In order to prevent detonation and ensure safe and controllable air flooding technology, oxygen-reduced air is usually used for oil displacement in light oil reservoirs, but the reduction of oxygen concentration further weakens the role of LTO and seriously affects the development effect^[2].

Gas assisted gravity drainage (GAGD) technology utilizes gravity differentiation generated by the density difference between injected gas and the fluid in the reservoir to drive the oil and gas interface to move down steadily, which can inhibit the viscous fingering and expand the swept volume, improve the microscopic oil displacement efficiency, and significantly increase the recovery. On the one hand, the combination of GAGD and oxygen reduced air flooding in the light oil reservoir can expand the oil and gas contact area and effectively accelerate the low-temperature oxidation reaction. On the other hand, the viscosity reduction effect of low- temperature oxidation reaction can reduce the displacement resistance of stable gravity flooding. The synergistic effect of the two has the potential to significantly enhance recovery^[3].

Having a stable oil and gas front is the key to the success of GAGD. Gravity, viscous force and capillary force are the main forces controlling the GAGD process. Dimensionless numbers (bond number, capillary number and gravity number) are mainly used to characterize the effects of gravity, viscosity force and capillary force in the GAGD process. Kulkarni^[4] found that the higher bond number, gravity number and capillary number, the higher the recovery, indicating that gravity drive is the primary production mechanism. However, this conclusion only considers the combined influence of the three forces on recovery without considering the inherent influence of the interaction of three forces during displacement. Bautista et al.^[5] used numerical simulation to study the relationship between various dimensionless numbers and recovery in the GAGD displacement process and obtained a conclusion that was not the same as Kulkarni's.

Since the dimensionless number is intrinsically related to GAGD, it can be used to predict the recovery of GAGD. Kulkarni et al.^[6] defined a new dimensionless number of gravity drainage number by combining capillary number, bond number and gravity number, and obtained the relationship between immiscible flooding recovery and gravity drainage number. Considering the contact angle and oil-gas viscosity ratio, Wu et al.^[7] revised the gravity drainage number and reworked the prediction formula. Rostami et al.^[8] thoroughly considered the influence of reservoir parameters and heterogeneity on the recovery, and gave relevant predictions through reservoir numerical simulation and nonlinear fitting. With the help of the machine learning method, Chen et al.^[9] fully considered the influence of various parameters on development and proposed a recovery prediction model for GAGD immiscible flooding development reservoir.

It can be seen that there are many research results related to GAGD, but there are few reports on the microscopic mechanism of oxygen-reduced air gravity flooding. In this paper, through the two-dimensional visualization of oxygen-reduced air gravity flooding (OAGD) experiment and long core displacement experiment, the internal relationship between oil and gas front shape and gravity, capillary force and viscous force was studied. The relationship between gravity number, capillary number and recovery before and after the breakthrough of OAGD was analyzed, and the mechanism of gravity, capillary force and viscous force in the process of OAGD was revealed. At the same time, considering the influence of the degree of low-temperature oxidation reaction on the recovery, a new dimensionless combination number was proposed and its relationship with the recovery was established for the prediction of the OAGD recovery.

The experimental model (Fig. 1) has an internal sand filling size of 230 mm×106 mm×1.4 mm and the inside is filled with glass beads with a diameter of 800 μm to form a consolidated porous medium structure. The upper and lower parts of the model are set with a horizontal groove, and the groove is filled with a sieve to simulate the horizontal well. The white oil dyed with Sudan red was used in the experiment, and the viscosity was 12.3 mPa•s at room temperature. The experimental gas is oxygen-reduced air (oxygen content of 15%).

The porosity of the model was 0.69, and the permeability was 10 810 μm². Due to the model’s limited bearing pressure capacity, the experiment was conducted at room temperature and pressure without considering the effect of low-temperature oxidation. The research focuses on the influence of the relative magnitude between gravity, viscous force and capillary force on the oil and gas front during gravity drainage. By adjusting the gas injection velocity and model inclination, the viscous force and gravity in the experimental process was changed to realize the change of the driving force. A total of 32 experimental schemes are designed (Table 1). The experimental steps are as follows: (1) vacuumize the model and saturate it with crude oil, and the material balance method was used to calculate the model porosity; (2) place for 12 h to balance the fluid distribution in the model; (3) experiments were carried out according to the schemes. The high-precision camera was used to record the changes of the oil and gas front in the model, and the changes of oil production with time in the experiment were recorded. End the experiment after the gas breakthrough; (4) to ensure the consistency of the experimental model, the same model was used in each scheme. After the previous experiment, the model was cleaned with an organic solvent and dried for the next experiment.

The experimental oil was taken from Jilin Oil Field. The basic parameters are shown in Table 2. The composition of simulated water ions for experiments is shown in Table 3. The experimental gases include pure nitrogen and a mixture of oxygen and nitrogen (oxygen content was 22%, 15%, 10% and 5% respectively).

It is difficult to obtain long enough natural cores, so the long cores used in the experiment are spliced with two 30 cm cores. To avoid the influence of the difference of capillary force on the contact surface of the two core sections on the experimental results, filter paper was inserted between the two core sections’ contact surfaces. The schematic diagram of the experimental setup was shown in Fig. 2.

A total of 9 experimental schemes were designed according to the experimental purpose (Table 4). Experiments ①—⑤ were used to study the influence of gas injection velocity on OAGD recovery and the influence of dimensionless number changes on recovery during displacement. Experiments ⑤—⑨ was used to study the relationship between oxygen concentration in injected gas and OAGD recovery.

Experimental steps: (1) vacuum the combined core and saturate the water, calculate the porosity and determine the permeability; (2) fix the core holder after saturated with oil, keep it at 60° to the horizontal, and put it in a 90 ℃ thermostat; (3) inject the gas at the designed gas injection velocity, increase the pressure to 15 MPa (experimental back pressure), record the time of pressure increase; (4) start the experiment, record the produced oil and gas data and end the experiment after 1 PV injection; (5) change the experimental parameters, and repeat steps (1)-(4).

In the process of gas intrusion, the shape of the oil and gas front is controlled by the interaction of gravity, capillary force and viscous force. It is difficult to directly characterize the interaction between these three forces, so the dimensionless number is used to characterize the relative relationship of any two forces. Keep the dimensionless number unchanged, change the third force for single factor analysis, study the influence of gravity, capillary force and viscous force on OAGD. Fig. 3 is the relationship between capillary number and recovery when the gravity is constant (the experimental model inclination is 90°, the bond number is 4.52×10^-4). The points a, b and c in the figure correspond to the displacement situation under different capillary number conditions in Fig. 4.

The bond number is the ratio of gravity to capillary force. When the gravity remains constant and the bond number doesn't change, the capillary force is constant. It can be seen from Fig. 3 that the bigger the capillary number (the ratio of viscous force to capillary force), the smaller the recovery. It shows that when the bond number remains constant (the interaction between gravity and capillary force reaches a dynamic equilibrium), the viscous force is main driving force for controlling the change of the oil and gas front. When the gas injection velocity is changed to make the capillary number less than 1.68×10^-3, the displacement process is in the equilibrium region of gravity, capillary force and viscous force, and the oil and gas front can basically remain stable during the displacement process. At this time, with the change of capillary number, the recovery fluctuates slightly (about 1%) and remains basically stable. In this region, the capillary number is small, and the viscous force is low. The viscous force is balanced with gravity and capillary force to inhibit the occurrence of fingering. The displacement process is similar to piston-like displacement, and gas can enter most of the tiny pores and maintain the stability of the oil and gas front (Fig. 4a). There are no oil clusters in the gas swept area, and the macro swept volume and micro flooding efficiency are very high. It should be noted that the three-force equilibrium does not mean the instantaneous equilibrium at each position of the oil and gas front, but the dynamic equilibrium along with the displacement process. In the experiment, it was found that even with the stable displacement, there would be obvious local fingering on the front. When fingering reached a certain degree, the pressure of the hydrostatic column formed by the height difference between the front and rear ends of fingering drove the back end to overcome the capillary force and started the migration. Finally, the part of the back end that was not fingering would catch up with the front end of fingering and form a stable oil-gas front again^[10].

Increasing the gas injection velocity, when the capillary number is between 1.68×10^-3 and 2.69×10^-2, the displacement process is in the capillary force dominant region, and the recovery decreases greatly with the increase of the capillary number. In this stage, the viscous force increased, which broke the equilibrium state among the three forces, and the oil and gas front began to lose stability, showing obvious local fingering, trapping and bypass flow (Fig. 4b). Compared with the stable region, the part of the back end that was not fingering would be hard to catch up with the front end of fingering. The capillary force at the rear ends without fingering of this region controlled the subsequent oil and gas flow state. The greater the capillary force, the easier it is to form traps and bypass flow.

To further increase the gas injection velocity, when the capillary number is higher than 2.69×10^-2, the recovery hardly changes with the change of the capillary number. The oil and gas front in this region shows a clear viscous fingering state (Fig. 4c) and it is entirely dominated by the viscous force. The airflow dominant channel is basically formed, and the recovery is hardly affected by the change of capillary number.

Fig. 5 shows the relationship between the gravity number and the recovery when the viscous force is constant (the corresponding gas injection velocity for each curve is the same). Since the gravity number is 0 when the model inclination angle is 0°, the experimental results with 0° inclination angle are not included in the figure. When the capillary number keeps constant (the interaction between viscous force and capillary force reaches a dynamic balance), the larger the inclination of the model, the greater the gravity driving effect and the higher the recovery. The reason is that the difference in gravity caused by the density inhibits the local fingering of the oil and gas front, which reduces traps and bypass flow phenomena. The greater the gravity effect, the better the inhibition, the more conducive to the stability of the oil and gas front, and the greater the swept range of gas drive^[11] (Fig. 6). Under the same inclination angle condition, the larger the capillary number, the worse the stability of the oil and gas front. Under the same capillary number condition, the greater the inclination angle, the better the stability of the oil and gas front. In actual oilfield development, gravity is basically constant, and the capillary force is controlled by the microscopic physical properties of the reservoir, which is basically uncontrollable. Reducing the gas injection velocity is the only way to obtain a low capillary number and improve the development effect.

2.2.1. OAGD influence factors

2.2.1.1. Oxygen concentration

Oxygen concentration is of great significance to the safety and efficient development of OAGD. (1) Oxygen concentration is an important factor that affects the degree of LTO. Under the same temperature and pressure conditions, the higher the oxygen concentration, the greater the oxygen partial pressure, the more intense the LTO reaction. (2) The higher the injected oxygen concentration, the higher the residual oxygen consumption, and the higher the probability that the oxygen concentration at the production end exceeds the explosion critical oxygen content. It can be seen from Fig. 7 that when the oxygen concentration is low (5%), the LTO reaction intensity is low, the oxygen consumption is only 0.8%, there is almost no carbon monoxide or carbon dioxide in the gas product. Compared with pure nitrogen flooding without considering LTO, the recovery increase is less than 2%. As the oxygen concentration increases, the LTO reaction intensity increases, the system's oxygen consumption capacity increases, and carbon monoxide and carbon dioxide begin to appear in the gas product. The higher the oxygen concentration, the greater the increase in recovery, and the content of carbon monoxide and carbon dioxide in the gas product will also increase. Through physical and numerical simulations, Jiang^[12] confirmed that the EOR of air flooding is accomplished by nitrogen flooding, heating and viscosity reduction, and carbon dioxide flooding. Among them, nitrogen flooding is dominant, followed by heating and viscosity reduction, with the smallest contribution of carbon dioxide. Limited by the experiment’s constant temperature environment, the heat generated by the oxidation reaction cannot be accumulated. In this case, the heating and viscosity reduction has little effect on the recovery. OAGD recovery increases with the increase of oxygen concentration, mainly because the amount of carbon dioxide produced by oxidation increases with the increase of oxygen injection concentration, contributing to the improvement of recovery. Simultaneously, the oxidation reaction consumes some light components, the density of oil increases, and the gravity differentiation becomes stronger. To some extent, the gas fingering can be inhibited, and a stable gas displacement front is more likely to form in the core. The stronger the LTO, the more obvious the effect of improving oil recovery.

2.2.1.2. Gas injection velocity

Gas injection velocity is the main control factor that affects the stability of the gas-oil interface. The stability of the gas-oil interface has a significant impact on the development effect of OAGD. Mudhafar^[13] found a critical value for the effect of gas injection velocity on the recovery. When it is lower than the critical value, the displacement process is stable and the OAGD recovery is high. When it is higher than the critical value, the process is unstable and the OAGD recovery is low. Fig. 8 shows the relationship between gas injection volume and recovery at five gas injection velocities. It can be seen that the critical value of gas injection velocity is 0.05-0.10 mL/min. When the gas injection velocity is higher than the critical value, the higher the gas injection velocity, the greater the viscous force. When the viscous force is much greater than the capillary force, the fingering phenomenon is serious, the oil-gas interface is unstable, and the oil-gas contact time becomes shorter with small contact area. On the one hand, the gas breakthrough time is significantly shortened and the sweeping effect of gas flooding is poor; on the other hand, the LTO reaction is suppressed with low recovery. When the gas injection velocity is lower than the critical value, the capillary force, viscous force and gravity can maintain a dynamic balance. The oil and gas front can continue to advance in a relatively stable state, similar to piston-like displacement, with high sweep efficiency, large oil and gas contact area, strong LTO reaction and high recovery. The maximum velocity of stable flooding is defined as the upper limit velocity of efficient stable flooding^[4]. However, the injection velocity is not necessarily as low as possible. When the injection velocity is too low (such as 0.01 mL/min in Fig. 8), although the oil and gas have sufficient contact reaction time, which is conducive to the LTO reaction, the low flow velocity will lead to the fact that the viscous force can't overcome the capillary force of most pore throats, and the capillary retention phenomenon is serious, and the final recovery is not high. This velocity is called the lower limit velocity of stable flooding. Rostami et al.^[14] also discovered this phenomenon in the gravity flooding experiment of other gases.

It can be seen that for OAGD, the choice of injection velocity needs to pay attention to two aspects: (1) ensure that the gas injection velocity is lower than the upper limit of the efficient stable flooding to ensure the steady advance of the displacement front, increase the oil and gas contact area, and extend the LTO time; (2) ensure that the gas injection rate is higher than the lower limit of efficient and stable flooding, and the viscous force is sufficient to overcome the capillary force in most small pore throats to achieve the purpose of replacing the crude oil in the small pores with injected gas.

2.2.2. The effect of dimensionless number on OAGD

The bond number in the long core displacement experiment has no order of magnitude change, so the gravity and capillary numbers are used to describe the gravity flooding process of OAGD. During the experiment, the dynamic dimensionless number is difficult to calculate, and the pressure change during each group of experiments is not obvious, which has little effect on the properties of oil and gas. Therefore, the initial dimensionless data of the experiment was selected to approximately replace the whole process for analysis.

2.2.2.1. The effect of gravity number on OAGD

The results of long core displacement showed that the upper limit velocity of stable flooding is 0.05-0.10 mL/min, and the lower limit of interval 0.05 mL/min is taken as the boundary between stable flooding and unstable flooding to ensure that it will not affect the subsequent analysis results.

The gravity number is the ratio of gravity to viscous force. In the core experiment, the core holder was kept at 60° from the horizontal direction, so the gravity can be basically regarded as a fixed value. Therefore the gravity number is mainly affected by the viscous force, which is influenced by the gas injection velocity, the higher the gas injection velocity, the smaller the gravity number. Calculate the gravity number of the core experiment ①-experiment ⑤, and make the relation curve between the gravity number and the stage recovery under different injection gas pore volumes (Fig. 9). The black dashed line in the figure is the boundary line for the gas breakthrough, with the breakthrough area at the top and the non-breakthrough area at the bottom. It can be seen that in the stable flooding area, before the gas breakthrough, under the same injection pore volume, as the gas injection velocity decreases, the gravity number increases, and the recovery increases slightly, indicating that before the gas breakthrough, compared with viscous force, gravity displacement oil dominated. By reducing the gas injection velocity, the viscous force can be reduced and the development effect of OAGD can be improved. However, the viscous force is not as low as possible. If the viscous force is too small, capillary retention will increase. Bautista et al.^[5] also verified this conclusion by numerical simulation. After the gas breakthrough, under the condition of the same injection pore volume, the larger the gravity number, the lower the recovery, indicating that compared with gravity, viscous force is dominant in oil displacement after gas breakthrough. At this time, the remaining oil is mainly produced by oil film flow^[14]. The higher the gas flow velocity, the stronger the viscous force carrying capacity, and the more favorable the oil film flow. Therefore, increasing the gas injection velocity can improve the development effect of OAGD in this stage.

Before gas breakthrough in unstable flooding stage, the dynamic characteristics are similar to the stable flooding. After the gas breakthrough, the dynamic characteristics are reversed. The main reason is that the higher the gas injection velocity, the more serious the viscosity fingering phenomenon, the smaller the gas swept volume, and the lower the stage recovery. Although the higher the gas velocity after the breakthrough, the stronger the ability to carry oil film flow, but the oil film flow has limited oil displacement potential^[15], which is far less than the contribution of gas sweep to recovery.

2.2.2.2 The effect of capillary number on OAGD

The physical meaning of the capillary number is the ratio of viscous force to capillary force. With the same core and same fluid, the capillary force is stable. In the core displacement experiment, the capillary number is mainly affected by the viscous force, that is, by the gas injection velocity. The larger the injection velocity, the larger the capillary number will be. Fig. 10 is the relationship between the capillary number and the stage recovery under different injection gas pore volumes. The black dashed line in the figure is the boundary line for gas breakthrough, with the breakthrough area at the top and the non-breakthrough area at the bottom. In the stable flooding area before gas breakthrough, under the same injection pore volume, the stage recovery decreases slightly with the increase of the capillary number, indicating that before gas breakthrough, capillary force is dominant in enhancing oil recovery compared with the viscous force. At this stage, the contribution of macro oil displacement to oil recovery is greater than that of micro oil displacement^[5]. The larger the capillary number, the larger the viscous force, and the smaller the capillary force is, and the oil and gas front is easy to lose stabilization and form local fingering, which reduces the macroscopic displacement efficiency. At the same time, as the displacement process is stable, the oil and gas front has a certain self-stabilizing ability, so the recovery decreases slightly in the stage. After the gas breakthrough, under the condition of the same injection pore volume, the larger the capillary number, the larger the injection velocity, the higher the stage recovery, indicating that after gas breakthrough, viscous force is dominant in enhancing oil recovery compared with the viscous. At this stage, the contribution of micro oil displacement to oil recovery is greater than that of macro oil displacement^[5], high viscous force is more conducive to resist the trapping effect of capillary and mobilizing the residual oil in small pores.

Before the unstable displacement gas breakthrough, the oil-gas interface is unstable, and the effect of reducing the gas injection velocity to expand swept volume is not obvious. Although increasing the gas injection velocity can improve the micro oil displacement efficiency in the affected area, it also reduces the gas macro sweep efficiency. Therefore, the increase of capillary number has little effect on recovery. The larger the capillary number after gas breakthrough, the lower the macroscopic sweep efficiency and the smaller the stage recovery.

In summary, the stable GAGD reduces the gas injection velocity before the gas breakthrough, which can expand the gas swept volume and obtain a high recovery. After the gas breakthrough, increasing the gas injection velocity is more conducive to improving the micro oil displacement efficiency and obtain a high recovery.

Gravity number, bond number, and capillary number have a certain influence on OAGD recovery, so the combination of these dimensionless parameters and OAGD recovery must be correlated. Kulkami et al.^[16] analyzed the results of visualization experiments and found that the recovery of GAGD has a linear relationship with the logarithm of gravity number, capillary number and bond number. The logarithmic scatter diagram of the long core displacement experimental data (Fig. 11) shows that the correlation between recovery and gravity number, capillary number and bond number is very poor, among which the correlation with capillary number is the worst, which is consistent with the research results of Rezaveisi et al.^[17]. The OAGD process is complex, and the recovery is affected by many factors. It is difficult for a single factor variable to establish a correlation with the OAGD recovery.

Kulkarni et al.^[6] considered the effect of oil-gas density difference on recovery, and defined the combination of capillary number, bond number and gravity number as gravity drainage number. Rostami et al.^[14] considered the influence of oil gas viscosity ratio on the oil displacement process, and defined the dimensionless combinatorial number (Ros combination number for short), so as to improve the prediction accuracy of GAGD recovery. Using the above two parameters to analyze the results of the long core displacement experiment (Figs. 12 and 13), it can be seen that although the gravity drainage number and Ros combination number take into account the influence of oil and gas density, viscosity and other factors, the correlation with OAGD recovery is not ideal, and it is challenging to predict OAGD recovery.

According to the analysis, the gravity drainage number and Ros combination number do not consider the chemical reaction between oxygen and oil. The crude oil properties are set to be constant. The long core displacement experiment results confirmed that the LTO reaction has a significant effect on the recovery during air flooding. This factor must be considered to predict the recovery of OAGD. Therefore, it is proposed to consider the dimensionless combination number of LTO reaction and analyze its relationship with recovery. LTO reaction mainly affects the viscosity of oil, so the change of crude oil viscosity before and after the LTO reaction is selected to characterize the effect of LTO, and the oil produced within a time after the gas breakthrough is used to determine the oil viscosity after the LTO reaction. The low-temperature oxidation number is defined as:

Levenberg marquardt method^[18] was used for regression analysis of sample data to determine that A₁, A₂ and A₃ were 1.00, 0.06 and 0.02, respectively. The coefficients in the LTO number indicate that when predicting the OAGD recovery, the bond number has the largest weight, followed by the capillary number, and the viscosity ratio of crude oil before and after the reaction characterizing LTO is the least weighted, indicating that the main displacement mechanism of OAGD is gravity flooding, and LTO reaction only plays a supporting role. The calculated LTO number and recovery were plotted in a scatter diagram (Fig. 14). It can be seen that they have a reasonable correlation, and the complex correlation coefficient was increased to 0.966 8. The LTO number considers the combined effects of bond number, capillary number, and LTO reaction, which has a good correlation with the recovery, and can be used to predict the OAGD recovery. What needs to be explained is that the results are only experimental results, and the field application needs to be modified according to specific conditions.

The shape and change law of the oil and gas front are mainly affected by the combined effects of gravity, capillary force and viscous force. When the bond number is constant (4.52×10^-4), the shape of the oil and gas front is controlled by the capillary number. When the capillary number is less than 1.68×10^-3, the oil and gas front is stable; when the capillary number is greater than 2.69×10^-2, the oil and gas front is viscous fingering; when the capillary number is 1.68×10^-3-2.69× 10^-2, the oil and gas front is capillary fingering

Before gas breakthrough of stable OAGD, the higher the gravity number and the lower the capillary number, the higher the recovery. The recovery is mainly affected by gravity. The recovery can be increased by reducing the injection velocity; after gas breakthrough, the lower the gravity number and the higher the capillary number, the higher the recovery. The recovery mainly depends on the viscous force and the recovery can be improved by increasing the gas injection velocity.

The LTO number comprehensively considers the combined effects of bond number, capillary number, and LTO reaction, and has a good correlation with the recovery, which can be used to predict the OAGD recovery.

A₁, A₂, A₃—correction coefficient, represents the importance of the corresponding dimensionless number, which is determined by data fitting and sensitivity analysis, dimensionless;

E_R—enhanced oil recovery, %;

N_B—bond number, dimensionless;

N_C—capillary number, dimensionless;

N_GD—gravity drainage number, dimensionless;

N_CO—Ros combination number, dimensionless;

N_G—gravity number, dimensionless;

N_LTO—LTO number, dimensionless;

R²—complex-correlation coefficient, dimensionless;

μ_R—viscosity ratio of crude oil before and after LTO reaction, dimensionless.