In recent years, tight oil has become another hot spot of global unconventional oil and gas exploration and development after shale gas^[1,2,3]. Tight oil reservoirs have a surface air permeability of less than 1×10^-3 μm² or permeability under overburden pressure of less than 0.1×10^-3 μm^2[4], and are characterized by poor physical properties, large distribution area and low resource abundance^[5,6]. At present, the initial development of tight oil reservoirs relies on large-scale volume fracturing of horizontal well, and depletion development of tight oil reservoir features high initial production, rapid middle term production decline, and low overall recovery^[7]. How to further supplement formation energy to realize secondary oil recovery after depletion development has become a problem to improve the development effect of tight oil reservoir^[8]. As an efficient development method to further improve oil recovery after depletion development for tight oil reservoir, CO₂ huff and puff has the advantage of effectively storing CO₂ while improving oil recovery^[9,10], and can achieve a win-win situation of economic benefits and environmental protection, so it is increasingly valued by the industry^{[11,12,13,14,15,16,17]}.

The CO₂ huff and puff is characterized by nonlinear seepage, and there is an interaction between CO₂ and crude oil, so its seepage law is very complicated^[18,19]. In 1991, some researchers abroad demonstrated the feasibility of CO₂ huff and puff in improving oil recovery of light oil reservoirs based on field data, laboratory experiments and numerical simulation^[20,21]. In 2013, Hawthorne, et al.^[22] pointed out that CO₂ huff and puff was an important means of tight oil development, and the scale of fracture network was the key factor affecting huff and puff effect. In 2016, Pu, et al.^[23] studied the effects of soaking time, huff and puff cycle and production pressure difference on CO₂ huff and puff outcome through lab cylindrical core experiments. In 2019, Li, et al.^[24] pointed out that the molecular diffusion of CO₂ resulted in a large amount of CO₂ existing in the reservoir in the form of dissolved gas, which was conducive to the enhancement of oil recovery. However, limited by model size, experimental device and experimental method, the lab physical modeling of CO₂ huff and puff in tight oil reservoir mainly uses cylindrical cores^[25,26,27], and can not accurately reveal the complex seepage law in tight oil reservoir after volume fracturing^{[28,29,30,31]}. Although some researchers carried out huff and puff experiments on large-scale models^[32,33], there is hardly systematic research on dynamic variations of parameters, influencing factors and oil-displacement mechanisms in the process of CO₂ huff and puff.

Based on a large-scale outcrop core and the self-developed high temperature and high pressure physical experimental system, a large-scale physical modeling experimental method of CO₂ huff and puff was established. By physical modeling experiments, a variety of schemes of CO₂ huff and puff were tested to analyze the dynamic characteristics of CO₂ huff and puff, the influencing factors and injection-production parameters.

1.1.1. Model making

The model used in this work was designed and manufactured from a large-scale outcrop core. The outcrop core had a permeability of 0.98×10^-3 μm² and porosity of 10.94%. The model making steps are as follows: (1) A 30 cm×30 cm×3.5 cm square core was cut from the large tight sandstone outcrop. (2) An empty slot (0.2 cm wide) was cut through the pressure monitoring hole 1^# and pressure monitoring hole 2^# (the distance between 1^# and 2^# is 26 cm) on one side of the core to simulate a horizontal well with infinite conductivity. (3) Two 15 cm long and 0.2 cm wide gaps were cut at 1/3 and 2/3 of the core side length to simulate hydraulic fractures perpendicular to the horizontal well. To make the gaps have stable conductivity, two core slices taken from a core with a higher permeability of 2000×10^-3 μm² were embedded into the two gaps of the model. At the same time, to ensure that there was no more gap between the slice and matrix, a mixture of fine sand and epoxy resin was coated on the surface of the slices so that the slices and the matrix were cemented to form a whole after heating and aging, and two fractures with a permeability of 2000×10^-3 μm² were formed finally. (4) An injection-production well and multiple pressure monitoring wells were arranged on the surface of the model (1^# was the injection-production well, 2^#-15^# were the pressure monitoring wells, of which 13^#, 14^#, 15^# were spare injection-production wells during the period of saturating water and saturating oil), and then the model was integrally poured and sealed with epoxy resin (Fig. 1).

1.1.2. High temperature and high pressure physical experimental system

The high temperature and high pressure physical model experimental system (Fig. 2) mainly includes square core model, high temperature and high pressure experimental chamber, multi-point pressure acquisition system, temperature acquisition and control system, throttle valve, oil-gas-water separating-metering device, and constant pressure and speed pump, etc. Among them, the high temperature and high pressure experimental chamber is a sealable cylindrical steel chamber with a door on one side that can be opened. When sealed, the chamber is filled with transformer oil. Together with the temperature acquisition and control system and the confining pressure pump, it can provide a high temperature and high pressure external environment for the square core model. The multi-point pressure acquisition system is mainly based on multiple pressure monitoring holes arranged on the core model, which is connected to the external pressure sensor through a pipeline to realize the real-time monitoring of the multi-point pressure in the model. The throttle valve is used to control the production rate during development.

1.1.3. Experimental design

Experimental conditions: the experiments were conducted at the temperature of 35 °C and confining pressure outside the model of 15 MPa.

The materials: the viscosity of simulated oil was 4.1 mPa•s at 35 °C; the water used was simulated formation water with a salinity of 25 000 mg/L and viscosity of 0.73 mPa•s at 35 °C; the purity of CO₂ used in the experiment was 99.9%.

The schemes: according to the experimental requirements, a total of 16 experimental schemes were designed according to different CO₂ injection quantity, soaking time and injection rates (Table 1).

The steps: (1) The square core model was put in the high temperature and high pressure experimental chamber and vacuumized for more than 24 hours until the vacuum gauge showed vacuum state. (2) Water was injected at the constant pressure of 0.1 MPa from 1^# wellbore to the model for 3 days to saturate the model, then the injection pressure was gradually increased, and when the pressure of the remote monitoring wells started to rise, the outlet of the remote wells (13^#, 14^#, 15^#) were opened and the waterflooding was started by increasing the pressure to 13.8MPa. After 2 PV (pore volume) of water was injected, the waterflooding was ended, and the saturated water volume and porosity of the model were calculated based on the water injection and production volume. (3) The core was saturated with oil by injecting oil in the horizontal well and producing from the remote well, and the injection pressure was gradually increased to the original formation pressure (13.8 MPa), when the cumulative oil injection volume reached 3 PV and there was no more water produced at the outlet, the outlet was closed, and then oil was injected in the horizontal well continuously until the pressure in the model was evenly distributed (13.8 MPa), then the model was set aside to age for 3 days, after that the initial oil saturation was calculated. (4) The backpressure valve of 1^# well was opened and the well was put on production by depletion at the constant outlet pressure of 5MPa. In the course, pressures at the monitoring points and produced liquid volume were monitored in real time until no more liquid was produced at the outlet. (5) After the depletion production, the throttle valve was closed and CO₂ was injected into 1^# well at a constant rate to reach the design volume. Then, 1^# was closed and soaked, and the pressures of the model at the monitoring points were monitored during the huff period in real time. (6) After the huff period, the 1^# well was opened for the puff production at the constant outlet pressure of 5 MPa. During the puff period, pressures at monitoring points, and produced liquid and gas volumes were monitored in real time, and the puff production was stopped when no more liquid or gas was produced at the outlet. (7) The wellhead pressure of 1^# well was kept at 5MPa, while oil was injected from 13^#, 14^#, 15^# wells at a constant pressure of 13.8 MPa, after more than 2 PV of oil was injected and no water or gas was produced at the outlet, the injection was stopped. When no liquid was produced from 1^# well, the model was deemed back to the state after depletion production. (8) According to the experimental schemes (Table 1), steps (5)-(7) were repeated to complete all the CO₂ huff and puff experiments.

To ensure that the huff and puff experiments on the columnar core are similar to the huff and puff experiments on the square core, both the columnar core and the square core were taken from the same large outcrop, and the experimental conditions were all the same. Also, the injection-production pressure difference was maintained at 8.8 MPa. The experimental columnar core was 2.5 cm in diameter and 30 cm in length. As the columnar core has small pore volume and relatively small volume of oil produced by huff and puff, the calculation of recovery factor based on oil volume data obtained by traditional measurement methods would have large errors. Therefore, the weighing method was used to calculate the huff and puff recovery factor of the columnar core, specifically, the core was weighed before and after the experiment, and the produced oil was calculated by the weight difference. The columnar core experiment schemes are shown in Table 2, and the experimental apparatus is shown in Fig. 3.

The columnar core huff and puff experiments can be divided into two injection types: CO₂ injection pressurization and oil injection pressurization. The experimental steps were: (1) After the core was vacuumed, saturated with oil, and then weighed, the core was placed into the holder. (2) For experiments No. 17 and 18, CO₂ was injected from the injection valve at a constant pressure of 8.8 MPa, and the core was soaked for the time designed in the schemes. (3) For experiments No.19 and 20, oil was injected from the injection valve, after the internal pressure of the core was stable at 8.8 MPa for more than 30 minutes, the injection was stopped; then, the outlet valve was opened (the outlet pressure was set at 8.8 MPa), and CO₂ was injected at a constant pressure of 8.9 MPa (slightly greater than 8.8 MPa) to remove excess oil at the inlet end of the holder and the periphery of the core quickly. After that, the outlet valve was closed and the inlet pressure was kept stable at 8.8 MPa for the whole soaking period. (4) The inlet valve was closed and the outlet valve opened for puff development. When the pressure at the outlet end dropped to atmospheric pressure and no fluid or gas was produced, the puff development was ended, and the core was taken out and weighed to calculate the recovery factor.

During the depletion development, the square core had internal pressure gradually dropping from 13.8 MPa to 5 MPa and a final recovery factor of 8.13%. The Arps production decline model^[34] was used to fit the depletion production data (Fig. 4). It is found that the decline rate has a good correlation with the output, with a multiple correlation coefficient R² of 0.844 0, and a decline index of 0.739 2, representing hyperbolic decline. This is consistent with the field research results^[35], indicating that the experimental design is reasonable.

Taking experiment No. 1 in Table 1 as an example, the dynamic characteristics of the soaking period and development period in the process of CO₂ huff and puff were analyzed.

2.2.1. Soaking period

Fig. 5 shows the bottom hole pressure curve in the soaking period. It can be seen that the bottom hole pressure dropped relatively quickly at the beginning of the soaking period (within 2 h), and the bottom hole pressure decreased linearly in the middle stage of the soaking period (2-14 h). In the latter stage of the soaking period (after 14 h), the bottom hole pressure was stable.

Fig. 6 shows the pressure field distribution in the model at four different times in the soaking period. It can be seen from Fig. 6a-b that there was a significant pressure difference between the near-well zone and the distal-well zone (approximately 0.6 MPa and 0.2 MPa). Due to the pressure difference, the fluids flowed, and the CO₂ diffused and dissolved in the oil phase, as a result, the bottom hole pressure dropped rapidly in this period. After soaking for 8 hours (Fig. 6c), the pressure in the model gradually balanced (with a pressure difference of less than 0.1 MPa), hence, the fluid flow caused by the pressure difference significantly weakened and the diffusion and dissolution of CO₂ in the oil phase played a major role. After soaking for 24 hours (Fig. 6d), the overall pressure of the model stabilized at about 12.8 MPa, and the flow caused by the pressure difference generally stopped. The subsequent pressure drop was mainly related to the diffusion and dissolution of CO₂ in the oil phase.

2.2.2. Development period

Fig. 7 shows the curves of bottom hole pressure, cumulative oil production, and cumulative gas production (standard condition) over time during the puff period. It can be seen that the bottom hole pressure drops first fast and then slowly, the gas production rate is first high and then low, and the oil production rate is first low and then high and then low during the puff period.

Fig. 8 shows the curves of gas-oil ratio and oil production rate with time. According to this figure, the puff period can be divided into 4 stages: (1) CO₂ backflow stage (0-1 min): This stage is relatively short and is mainly affected by the rapid backflow of CO₂ left in the horizontal well and fractures. This stage has the characteristics of large gas production and generally no oil production, and the bottom hole pressure dropped rapidly due to the high gas production rate. (2) Gas production with some oil stage (1-29 min): With adequate free CO₂ in the matrix near the well, the remaining oil in the matrix near the well was in contact with free CO₂ for a long time and swelled due to dissolution of CO₂. As the bottom hole pressure decreased, the swelling oil was reversely displaced by the free CO₂. At this stage, a large amount of gas and a small amount of oil were produced, and the oil production rate and gas-oil ratio fluctuated greatly at different times. Meanwhile, the expansion effect of free gas slowed down the decrease rate of bottom hole pressure, and the bottom hole pressure was relatively stable. But with the rapid decrease of free gas, the overall gas-oil ratio went down rapidly on the whole. (3) High-speed oil production stage (29-35 min): With the production of free gas, the free gas in the matrix significantly reduced, and the displacement mode changed from free gas displacement to dissolved gas displacement. Therefore, the oil phase production rate at this stage greatly increased, and the gas-oil ratio was relatively stable at a low level. Due to the significant reduction of free gas, the expansion effect of free gas weakened and the bottom hole pressure dropped slightly faster. (4) Low oil production stage (35-44 min): As the dissolved gas displacement entered the later stage, the drainage capacity of the square core obviously declined, the production pressure difference gradually tended to zero, and the oil production rate and gas production rate gradually approached zero too.

Fig. 9 shows the pressure field distribution in the model at four different times during the puff period. It can be seen from Fig. 9a that at the CO₂ backflow stage, the internal pressure drop is relatively small, and there is a large pressure difference (about 1.4 MPa) between the distal-well zone of the model and the bottom hole, which leads to the rapid backflow of gas; At the production stage of gas with some oil, the internal pressure drops overall (Fig. 9b), and some oil is carried out by the gas phase. Meanwhile, the distal-well zone obliviously supplies fluid to the near-well zone, leading to the drop of pressure difference (about 0.7 MPa); At the high-speed oil production stage, the pressure in the core is generally low (Fig. 9c), and the pressure difference further reduces (about 0.2 MPa). The dissolved CO₂ releases from the oil and expands, driving oil production. At the low oil production stage, the internal pressure is close to the outlet back pressure (5 MPa), and the pressure difference between the distal end of the model and the well bottom is very small. Also, almost all CO₂ dissolved in oil has released, and the displacement energy almost exhausts, and the production is nearly over.

Fig. 10 shows the relationship between the recovery and bottom hole pressure. It can be seen that the curve has a "two-stage" characteristic, that is, when the bottom hole pressure is greater than 7.95 MPa at the initial stage of development, the recovery rises slowly with the drop of bottom hole pressure, and when the bottom hole pressure is lower than 7.95 MPa, the rise of recovery accelerates obviously.

The volume expansion coefficient of CO₂ can be calculated by equation (2)^[5].

Assuming that the initial pressure is 12.8 MPa, the volume expansion coefficient of CO₂ during the depressurization process can be calculated (Fig. 11). It can be seen that Fig. 1 and Fig. 2 are basically the same in shape, indicating that either in the free CO₂ or the dissolved CO₂ displacement of oil, the main driving power comes from the expansion of CO₂. The CO₂ puff period shows the characteristics of elastic gas drive.

2.3.1. Quantity of injected CO₂

The quantity of injected CO₂ has a great impact on the development effect. The relationship curve of recovery factor with quantity of injected CO₂ of experiments No. 1-5 (Fig. 12) show that with the increase of injected CO₂ quantity, the recovery increased from 1.55% to 3.13 %, but the oil/gas replacement rate decreased from 1.93 g/g to 0.42 g/g. From the trend of the curve, with the increase of the injected CO₂, the increase of recovery gradually slowed down, and the drop of the oil/gas replacement rate also slowed down. Therefore, it is necessary to combine economic evaluation to determine the appropriate quantity of injected CO₂.

2.3.2. Soaking time

Based on the results of experiments No. 6-10 in Table 1, the relationship between recovery and soaking time was plotted (Fig. 13). It can be seen that the longer the soaking time, the higher the recovery rate, but the increase rate gradually slows down, and the soaking time of 14 hours is an obvious turning point. Meanwhile, it can be seen from Fig. 5 that after 14 hours of soaking, the bottom hole pressure tended to be stable, the pressure difference was almost zero, and the fluid almost stopped flowing, the sweeping range of CO₂ diffusion dissolution was almost stable, and longer soaking time had little contribution to recovery. Whether the soaking time is sufficient can be judged by whether the bottom hole pressure is stable in the oilfield.

2.3.3. Production rate

Based on the results of experiments No. 1, and 11-14 in Table 1, the relationship curve between recovery and development time was plotted (Fig. 14). It can be seen that as the development duration shortens and the production rate increases, the recovery reduces from 3.85% to 1.18%. Obliviously, the production rate has a greater impact on the recovery, and a lower production rate is conducive to the improvement of recovery.

2.3.4. CO₂ injection rate

The recovery of experiments No. 1, 15 and 16 are 3.13%, 3.27% and 3.18%, respectively. That means the CO₂ injection rate has little effect on the recovery. This is because the core used in the experiment was homogeneous and had closed boundaries, flow range of CO₂ was limited, the injection rate had little impact on the gas front. In oilfield practice, the reservoirs are often strongly heterogenous, and the flow range of CO₂ is large, these factors would affect the advancing mode and working distance of CO₂ at different injection rates, and in turn the development effect.

Based on the difference in CO₂ spreading mode, the sweeping mode of CO₂ huff and puff can be divided into flow sweep and diffusion sweep^[22,36], in which flow sweep refers to CO₂ entering into matrix under the action of pressure difference, and diffusion sweep refers to the CO₂ entering into the matrix under the action of diffusion (Fig. 15). The main oil production mechanisms of flow sweep are dissolution, expansion and extraction of CO₂, in other words, after fully contacting with CO₂, some oil expands or is extracted, and is discharged with the free gas. The main oil production mechanism of diffusion sweep is the driving of dissolved CO₂, namely, the CO₂ further diffuses into the oil from the CO₂ front due to molecule diffusion, some CO₂ dissolves in oil, with the pressure drop in the development process, the CO₂ releases from the oil gradually, forming dissolved gas displacement.

The experiments No. 17 and 18 were conventional CO₂ huff and puff experiments, the recovery included the contributions of both flow sweep and diffusion sweep. In comparison, in the experiments No. 19 and 20, oil was first injected into the core to increase pressure to 8.8 MPa so that there was no difference between CO₂ injection pressure and the core. In this case, the CO₂ was in contact with the core end under no pressure difference, avoiding the flow sweep caused by pressure difference, so the recovery of experiments No. 19 and 20 was only caused by diffusion sweep.

The experimental results (Fig. 16) show that with the increase of soaking time, the recovery (including flow sweep and diffusion sweep) of CO₂ injection pressurization experiments increased from 2.53% to 5.42%, and the recovery (diffusion sweep) of oil injection pressurization experiments increased from 1.26% to 4.03%. At the same soaking time, the difference in recovery between the two different injection modes is just the contribution of flow sweep. Apparently, the recovery rates of flow sweep at 0.25 h and 48.00 h were 1.27% and 1.39%, respectively, while those of diffusion sweep were 1.26% and 4.03%. It can be seen that with the increase of the soaking time, the recovery from flow sweep didn’t change significantly, while the recovery from diffusion sweep increased by 2.77%, indicating diffusion plays a major role in the improving oil recovery when the soaking time is long enough.

The puff period can be divided into four stages: CO₂ backflow stage, production of gas with some oil stage, high-speed oil production stage, and low oil production stage. The stage of gas production with some oil is dominated by free gas drive, and the high-speed oil production stage is dominated by dissolved gas drive.

Quantity of injected CO₂ and production rate are the main factors affecting the development effect. The larger the quantity of injected CO₂, and the lower the production rate, the higher the oil recovery will be. Reasonable quantity of injected CO₂ and injection rate need to be worked out in conjunction with on-site demand and economic evaluation. There is an appropriate soaking time for the huff period, and longer soaking time than this will not contribute much to the improvement of oil recovery. Whether the soaking time is sufficient can be judged by whether the bottom hole pressure is stable in oilfield practice.

In CO₂ huff and puff development, the contribution to recovery mainly comes from flow sweep and diffusion sweep. When the soaking time is long enough, the contribution of recovery mainly comes from diffusion sweep and the dissolved gas flooding plays a major role.

D—production decline rate, s^-1;

E—increased times of CO₂ volume expansion, dimensionless;

Q—production rate, mL/min;

V₀—CO₂ volume at the initial pressure, m³;

V_i—CO₂ volume under a certain pressure, m³;

ρ₀—CO₂ density at initial pressure, kg/m³;

ρ_i—CO₂ density under a certain pressure, kg/m³.