Compositional Simulation of CO₂ Huff-n-Puff Processes in Tight Oil Reservoirs with Complex Fractures Based on EDFM Technology Considering the Threshold Pressure Gradient

Abstract

Although tight oil reservoirs have abundant resources, their recovery efficiency is generally low. In recent years, CO₂ injection huff-n-puff has become an effective method for improving oil recovery on the basis of depleted production of volume-fracturing horizontal wells in tight oil reservoirs. In order to study the effects of CO₂ huff-n-puff (CO₂-HnP) on production, a compositional numerical simulation study of CO₂ huff-n-puff (CO₂-HnP) was conducted in tight oil reservoirs with complex fractures. Embedded discrete fracture model technology was used in the simulations to characterize complex fractures. The process of CO₂ huff-n-puff (CO₂-HnP) was simulated, which consists of CO₂ injection, CO₂ soaking, and CO₂ production. Taking into account the threshold pressure gradient and stress sensitivity in the model, we conducted a series of numerical simulations with different production condition parameters, such as bottom-hole pressure, CO₂ injection rate, injection time, soaking time, and the number of cycles of CO₂ huff-n-puff (CO₂-HnP). Then, the effects of these sensitivity parameters on the cumulative oil production (COP) were studied. The results indicate that the threshold pressure gradient and rock stress sensitivity factors greatly affect the pressure field of tight reservoirs and the cumulative oil production (COP) of multistage-fracturing horizontal wells. The production parameters all have an impact on the COP. The injection rate and circulation number both have optimal values, and the injection time and soak time tend to have less significant effects on the growth of cumulative oil production over time. According to the numerical simulation, the optimal solution is 5 × 10⁴ m³/day injection rate per cycle, 25 days of injection time, 35 days of soaking time, three cycles, and production for 5 years, which can obtain the optimal cumulative oil production.

1. Introduction

Tight oil reservoirs are becoming a global hotspot in oil resource exploration and development. Although tight oil reservoirs have abundant resources, their recovery efficiency is generally low. The global average recovery rate of natural depletion development in tight oil reservoirs is only 3 to 10% [1,2,3]. How to improve the recovery efficiency in tight oil reservoirs has become a difficult problem that needs to be continuously addressed.

Improving the recovery rate of tight oil reservoirs requires reservoir densification and reservoir energy enhancement to enhance the fluid mobility in tight formations. Reservoir densification is a reservoir transformation method that benefits from the technology of volume fracturing and horizontal wells, which are used to increase the movable oil area and improve the permeability of tight reservoirs. Multistage hydraulic fracturing has become the main technology for extracting tight oil and has achieved significant results [4]. Many tight formation outcrops, cores, and image logs have confirmed the existence of natural fractures or fracture traces [5,6]. Hydraulic fracturing establishes fracture fairways, which interact with natural fracture systems [7]. Because the presence of fractures and the geometry of the fracture networks significantly affect the flow behavior, it is crucial to accurately simulate realistic fractures with complex geometric shapes, as well as the influence of fractures on well productivity [8]. Due to the complexity of fracture geometry, several approaches have been proposed to simulate fracture networks. There are generally two types of models to simulate complex fractures, i.e., dual-continuum and discrete fracture models (DFMs) [9].

Dual-continuum models are the conventional method, first introduced by Barenblat et al. (1960) and Warren and Root (1963) [10,11]. Later, dual-porosity models as well as dual-porosity and dual-permeability models have been developed, and these have been applied to many field-scale fractured reservoir simulators [12,13,14,15,16,17,18,19]. However, dual-continuum models fail to solve fluid flow problems in large-scale complex fractured reservoirs [20]. Fortunately, discrete fracture models (DFMs) have been developed to overcome the above issues. Unstructured grids are used in DFMs to capture more of the actual geometry of fractures and the location of fracture networks. Moreover, they consider the influence of every single fracture on the fluid flow. However, advantages often turn into disadvantages. Due to their computational cost, putting unstructured grids to use in real field studies is a substantial challenge [21,22,23,24,25,26,27].

Considering these disadvantages of DFMs, a novel discrete fracture model was proposed by Li and Lee (2008) [28], called the embedded discrete fracture model (EDFM). Structured grids are employed to represent the matrix in the EDFM, which entirely bypasses challenges associated with unstructured gridding. The EDFM allows for fractures with any orientation, considering the heterogeneity and complexity of a fractured reservoir. Moreover, it does not require refining the grid near fractures. Thus, it provides a more computationally efficient method to accurately model fluid transport in the stimulated zone compared to other discrete fracture models [29,30,31]. However, compared to dual-continuum models and discrete fracture models (DFMs), EDFMs also have their limitations. The accuracy of EDFMs needs to be improved when conducting infinite flow. The accuracy of EDFMs depends on the refinement of the grid near fractures. Some grid encryption technologies are being developed, but there are currently few appropriate technologies applied in EDFMs [32]. Nonetheless, the EDFM provides an effective solution for modeling complex fracture geometries with more flexible, reliable, and scalable methods [33]. In this paper, we implement the EDFM approach to a compositional reservoir simulator to model the complex fracture networks with any orientation.

Reservoir energy enhancement generally refers to the injection of external fluids to supplement formation energy. Fluid injection mainly includes gas injection, water injection, thermal, chemical, hybrid, and some other innovative approaches [34,35,36,37,38,39,40]. The traditional method of increasing reservoir energy through water injection is no longer efficient in tight reservoirs [41,42]. The thermal method is also a good method of EOR [37]. Thermal methods inject a heating medium to oxidize and decompose immature kerogen [35,43]. The injection of superheated steam can cause changes in thermal properties such as the viscosity and density of the formation fluids, as well as changes in reservoir porosity and permeability [44]. This leads to the complexity of the simulations [43]. Aysylu et al. have devoted efforts to the research of thermal simulation and have achieved significant results [35]. Anas et al. investigated a new intelligent water-assisted foam flooding (SWAF) technology [45], which is a combination of intelligent water and foam flooding. Robert et al. proposed a method of injecting solvent liquid using a three-cylinder pump and then recovering the injection agent on the surface for reinjection into shale reservoirs in wells, but this method is currently in the testing stage [46]. Mojtaba et al. studied thermal–gas–chemical technology; through in situ modification, high-temperature gas and acid were released, thereby improving the fracture conductivity and increasing the fracture network [47].

Gas injection can further reduce crude oil’s viscosity, expand it, and increase its fluidity [48]. Therefore, gas injection has more advantages. A wide range of gases can be used for injection, but CO₂ has aroused great interest among researchers, as it is one of the most plentiful compounds on this planet [49]. Low-carbon and green development technologies have become a consensus for future oil development. CO₂-EOR technology mainly includes CO₂-HnP, CO₂ flooding, utilizing the effective diffusion of CO₂ in the formation, and reducing the crude oil’s viscosity, while achieving large-scale CO₂ storage and reducing carbon emissions. This not only develops resources economically but also protects the environment and solves the problem of climate change [1,50,51]. Among them, CO₂ injection for huff-n-puff oil recovery is the most widely used method. By injecting CO₂ into the formation, the energy of the formation is replenished, and CO₂ storage and displacement of oil are achieved [52].

CO₂ injection technology has been proven to be implementable at the oilfield site scale [53]. Recent experimental studies have shown that circulating CO₂ injection into tight reservoirs can improve crude oil recovery and achieve CO₂ storage [42,54]. Zhao et al. studied the impacts of different operating parameters on EOR during CO₂-HnP using NMR technology [54]. Sun et al. investigated the effects of injection parameters such as CO₂ injection amount, injection rate, and time on EOR through experimental methods [55,56]. Simultaneously, experiments can effectively reflect the process and mechanism of CO₂ injection, providing a foundation for numerical simulation [54,57,58]. But the experiments are all at the core scale and have certain limitations. Some scholars have also conducted numerical simulations of CO₂ injection into condensate gas reservoirs [59]. The results show that compared to continuous injection of CO₂, CO₂-HnP can improve condensate oil recovery to 25%, which is much higher than with the continuous injection of CO₂ [60]. Some numerical simulation studies focus on the impact of engineering parameters such as half-length of fracture or fracture conductivity on CO₂-EOR. Zhang et al. conducted numerical simulations on the effects of molecular diffusion and minimum miscibility pressure on CO₂-EOR in tight reservoirs [42,61].

The CO₂-HnP in tight fractured reservoirs is comprehensively influenced by factors such as reservoir geological factors and injection production parameters. Currently, CO₂-HnP construction design is mostly based on experience, with few factors considered and vague understanding. There is a lack of quantitative understanding of the controlling factors of CO₂-HnP production and insufficient consideration of low-permeability reservoir characteristics such as start-up pressure gradient and stress sensitivity. Therefore, an effective yield is difficult to guarantee.

In this article, a component numerical model of volume-fracturing horizontal wells in fractured tight oil reservoirs is established to simulate the CO₂-HnP process. In this model, threshold pressure gradients and rock stress sensitivity are considered, which affect oil production and recovery. The fracture model was established using the EDFM technique, and a complex fracture network was coupled with the flow field. Then, we performed a series of sensitivity analyses for a single well to weight the main control factors affecting oil recovery, such as CO₂ injection rate, injection time, soaking time, and the number of cycles of CO₂-HnP. The purpose of this article is to set up a universal framework for CO₂ huff-n-puff in unconventional fractured reservoirs and conduct parameter optimization. The component numerical simulation technology provides a better understanding of the main parameters controlling the CO₂-HnP process in hydraulically fractured tight reservoirs. The innovation of this article is the integration of nonlinear seepage with the starting pressure gradient, stress sensitivity, and EDFM technology.

2. Materials and Methods

2.1. Model Parameter Settings

The reservoir numerical simulation approach provides an effective way to evaluate CO₂-HnP for enhanced oil recovery (EOR). The CO₂-HnP process, as shown in Figure 1, consists of CO₂ injection, CO₂ soaking, and production [62,63,64]. In Figure 1, the blue line represents discrete fractures, the long red line in the middle represents a horizontal well, the yellow endpoint on the left side of the red line represents the wellhead of the horizontal well, and the red arrow represents the injection direction. In Figure 1a, the red arrow points towards the yellow wellhead, indicating that the horizontal well is an injection well, injecting CO₂ into the well. In Figure 1b, the absence of a red arrow indicates that the horizontal well is neither injected nor produced and is in a soaking state. In Figure 1c, the red arrow deviates from the wellhead, indicating that the horizontal well is a production well, and at this time, the well produces oil from the formation to the surface. In this article, CO₂ huff-n-puff is abbreviated as CO₂-HnP.

In this research, we used the Unconventional Oil and Gas Simulator (UNCONG) for component numerical simulation. A tight fractured reservoir was selected as the targeted reservoir. The reservoir thickness was 40 m. The matrix permeability of the formation was 0.01 mD, and its porosity was set as 15%. The rock’s compressibility was set as 9.72 × 10⁻⁵. A 3-dimensional compositional model was used to establish the corresponding tight oil reservoir model. The model size was set to 2000 m (length) × 1000 m (width) × 40 m (thickness). The grid blocks were set as 50 (in the x-direction) × 25 (in the y-direction) × 5 (in the z-direction). One horizontal tight oil well with a hydraulic fracture located in the middle of the reservoir was taken as the production well or the injection well during the CO₂-HnP process. In order to explore and stimulate the process of CO₂-HnP in fractured reservoirs, we randomly generated some connected and disconnected natural fractures and hydraulic fractures. The length of the fractured horizontal well was set to 1200 m, while the half-length of the fractures was 150 m and the number of fractures was 13. The hydraulic fractures were set to be evenly spaced and equal in length. The EDFM technology was applied to characterize the hydraulic fractures and the complex fracture system. The numerical simulation model and EDFM are shown in Figure 2. The blue line (blue rectangle) in Figure 2 represents discrete fractures, and the red tubular line in the middle of the model represents a horizontal well, named W1. W1 is a horizontal well. The 13 blue rectangles perpendicular to the horizontal well represent hydraulic fractures, while the blue rectangles distributed at any angle around the periphery of the horizontal well represent natural fractures. The essential data of the reservoir model and important hydraulic fracture data are listed in

Table 1. Basic parameters of the reservoir and fractures.

Parameter	Value	Unit
Model size (x × y × z)	2000 × 1000 × 40	m
Number of grid blocks (x × y × z)	50 × 25 × 5	–
Reservoir permeability	0.01	mD
Reservoir porosity	15%	–
Rock compressibility	9.72 × 10−5	bar−1
Reservoir thickness	40	m
Well length	1200	m
Fracture half-length	150	m
Fracture height	40	m
Fracture permeability	2000	mD

.

For the tight oil fluid model, eight components were assumed in this article, including CO₂, N₂, C₁, C₂, C₃–C₅, C₆, C₇, and C₈, and their molar fractions were set as 1.72%, 1.4%, 19.58%, 7.36%, 13.02%, 26.06%, 23%, and 7.86%, respectively.

Table 2. Compositional data of the fluid components.

Component	Molar Fraction	Critical Pressure (Bar)	Critical Temperature (K)	Critical Volume (m3/kg⸱mol)	Molecular Weigh	Acentric Factor	Parachor Coefficient
CO2	0.0172	73.866	304.7	0.094000661	44.01	0.225	78
N2	0.014	33.944	126.2	0.089999236	28.013	0.04	41
C1	0.1958	46.042	190.6	0.098000352	16.043	0.013	77
C2	0.0736	48.839	305.43	0.14799645	30.07	0.0986	108
C3–C5	0.1302	42.455	369.8	0.19999748	44.097	0.1524	150.3
C6	0.2606	30.104	507.5	0.35099954	84	0.299	271
C7	0.23	29.384	548	0.39200317	96	0.3	312.5
C8	0.0786	28.797	575	0.43299929	107	0.312	351.5

lists the detailed compositional data of the fluid model.

Table 3. Binary interaction parameters for the components.

Component	CO2	N2	C1	C2	C3–C5	C6	C7	C8
CO2	0	−0.012	0.1	0.1	0.1	0.1	0.1	0.1
N2	−0.012	0	0.1	0.1	0.1	0.1	0.1	0.1
C1	0.1	0.1	0	0	0	0.0279	0.03308	0.0363
C2	0.1	0.1	0	0	0	0.01	0.01	0.01
C3–C5	0.1	0.1	0	0	0	0.01	0.01	0.01
C6	0.1	0.1	0.0279	0.01	0.01	0	0	0
C7	0.1	0.1	0.03308	0.01	0.01	0	0	0
C8	0.1	0.1	0.0363	0.01	0.01	0	0	0

shows the binary interaction parameters for the components. The relative permeability curves are shown in Figure 3.

2.2. Threshold Pressure Gradient and Stress Sensitivity

In tight oil reservoirs, due to the porosity of the formation being extremely low, the fluid will not flow immediately under the action of force, and the minimum starting pressure needs to be overcome. Therefore, the flow of fluids in porous media is nonlinear seepage with a minimum threshold pressure gradient. The starting pressure gradient can affect the flow calculation of “matrix–matrix”, as well as the flow calculation of “matrix-crack” and “embedded crack-matrix”. So, it is necessary to consider the impact of the threshold pressure gradient on production capacity when conducting numerical simulations.

Previously, we have established component simulations. In the development process of low-permeability reservoirs, the flow of oil is affected by the starting pressure. However, many studies on the numerical simulation of CO₂-HnP in tight oil reservoirs have not considered the starting pressure gradient [63,65,66]. This greatly reduces the accuracy of the simulation results. Therefore, the percolation law containing the starting pressure gradient was presented in the article. When considering the starting pressure gradient, the equation has strong nonlinearity. The equation below was introduced into the simulator to enable it to consider the influence of the starting pressure gradient [67].

When considering the starting pressure gradient, the expression for the flow rate of phase P can be written as follows:

$$q_{P,ji}=\frac{{\rho }_P{k}_{rP}}{{\mu }_P}{T}_{ij}\left({\Phi }_{P,j}-{\Phi }_{P,i}\right)\left[1-\frac{\lambda }{\left(\left|\right|\nabla \Phi {\left|\right|}_{ij}-{\lambda }_0\right)+\lambda }\right]$$

where q represents the flow rate, P represents the gas phase or oil phase, λ represents the pressure gradient, λ₀ represents the threshold value, ${\Phi }_{P,j}$ and ${\Phi }_{P,i}$ represent the pressure potential of grids j and i, respectively, $\left|\right|\nabla \Phi {\left|\right|}_{ij}$ represents the pressure gradient between grids i and j, k_rP represents the relative permeability, and μ_P represents the P phase viscosity.

We set an example to examine the impact of the starting pressure gradient on the formation pressure field and the cumulative oil production of the well. We selected a well in the formation and conducted a one-year depleted development, followed by CO₂-HnP development. After four rounds of CO₂-HnP cycles, a total of 5 years of production was achieved. We set two scenarios: one considering the starting pressure gradient, and the other not considering it. Comparing the numerical simulations of CO₂-HnP with and without considering the threshold pressure gradient, the results of the pressure field changes after four rounds of huff-n-puff are shown in Figure 4. It can be seen that the variation in formation pressure when considering the threshold pressure gradient is relatively smaller than that when not considering it, after the same production time.

The COP curve is shown in Figure 5. It can be seen that, considering the impact of the starting pressure gradient, the cumulative oil production is significantly lower than that without considering it after production for 5 years. This suggests that the effect of the starting pressure gradient cannot be ignored in simulations.

Rock stress sensitivity is another important factor affecting the development effectiveness of tight formations. For more accurate simulations, stress sensitivity is considered in the CO₂-HnP model. Using the stress-related permeability correlation model, the production decline caused by the change in permeability in tight reservoirs can be simulated. In this article, we assume that the porosity does not vary with stress. The expression for stress-related permeability can be written as follows:

$$k=k_0{e}^{-A({\sigma }^{\prime }-\sigma 0)}$$

(1)

where σ’ represents the effective stress, A represents the experimental coefficient, and σ₀ represents the initial state. The coefficient used is obtained experimentally. Figure 6 illustrates the stress-sensitivity curves for the fractures and matrix in the model.

Similarly, we can take a comparative example. Based on the previous example of starting pressure, one scenario considers stress sensitivity and the other does not consider it. We investigated the impact of rock stress sensitivity on the formation pressure field and cumulative oil production of wells in two scenarios. Figure 7 shows the effect of stress sensitivity on the formation pressure field after a one-year depletion development, four cycles of CO₂-HnP development, and a total of five years of production. Figure 7a shows the pressure field distribution without considering stress sensitivity. Figure 7b shows the distribution of the formation pressure field considering stress sensitivity. In Figure 7a, it can be seen that the color of the formation pressure field is darker. This indicates that the pressure field changes more significantly and that the range of changes is larger without considering stress sensitivity. Under the same production situation, the pressure field changes less without considering stress sensitivity, as shown in Figure 7b. There are obvious differences in the formation pressure field between the two situations.

The COP curve is shown in Figure 8. The blue line in Figure 8 represents the COP without considering stress sensitivity, while the orange line represents the COP when considering stress sensitivity in the model. We can see that the blue line is significantly higher than the orange line, and the value of the blue line is almost twice that of the orange line. This indicates that, without considering stress sensitivity, the cumulative oil production is abnormally high, which does not comply with the actual situation of unconventional reservoirs. So, when conducting numerical simulations, stress sensitivity is a factor that cannot be ignored.

3. Results and Discussion

Based on the reservoir model parameters and fluid characteristics set above, numerical simulations of CO₂-HnP were conducted, and the effects of different CO₂ injection conditions on the cumulative oil production were compared. The CO₂-HnP process in a multistage-fracturing horizontal tight oil well consists of three main stages, as shown in Figure 1: CO₂ injection, CO₂ soaking, and production. In the compositional numerical simulation research, we conducted a series of simulations to determine the reasonable ranges and values of the uncertainty parameters that affect the CO₂-HnP process, such as bottom-hole pressure, CO₂ injection rate, CO₂ injection time period, soaking time, and the number of cycles of CO₂-HnP. Only one variable was changed at a time, while the other parameters remained unchanged. When comparing the results, the cumulative oil production was used as the measurement standard.

Here, we briefly describe the entire the CO₂-HnP process in the basic case. Initially, as a production well, the horizontal well produces through depletion development for one year, and then it is switched to an injection well that injects CO₂ at a rate of 50,000 cubic meters per day and maintains a bottom-hole pressure of 100 bar. After 30 days of CO₂ injection, the well is shut down and kept soaking for another 30 days. After 30 days of soaking, the well is converted to a production well to resume production. This is one cycle of the CO₂-HnP process. Each cycle lasts for 360 days, with one cycle ending and the other cycle starting. In this simulation study, the well was developed for a total of five years. The well experienced four cycles after one year of primary depletion development during the total production time.

3.1. Sensitivity Parameter Analysis for CO₂ Huff-n-Puff

3.1.1. Effect of Bottom-Hole Pressure

In order to find a suitable bottom-hole pressure, numerical simulation calculations were carried out for six bottom-hole pressure values of 200 bar, 180 bar, 150 bar, 100 bar, 80 bar, and 75 bar, while keeping the other huff-n-puff parameters the same as in the basic case mentioned above. The bottom-hole pressure optimization plan is listed in

Table 4. Bottom-hole pressure (BHP) optimization plan.

Bottom-Hole Pressure (Bar)	Injection Rate (m3/day)	Injection Time Period (Day)	Soaking Time Period (Day)
200	50,000	30	30
180	50,000	30	30
150	50,000	30	30
100	50,000	30	30
80	50,000	30	30
75	50,000	30	30

. Simulation results for the effect of bottom-hole pressure on cumulative oil production are shown in Figure 9. The cumulative oil production is abbreviated as COP and the bottom-hole pressure is abbreviated as BHP in the following text.

Figure 9 is a histogram of cumulative oil production (COP) and bottom-hole pressure (BHP). The higher the blue bar in the graph, the higher the COP. From Figure 9, it can be seen that as the BHP decreases, the COP gradually increases. The results indicate that BHP has a significant influence on the COP. The lower the bottom-hole pressure, the higher the cumulative oil production. However, when the BHP drops to 100 bar, the increase in COP is not significant. That is, the BHP has an optimal value. This is because the lower the BHP, the greater the pressure gradient between the bottom hole and the formation. The greater the displacement energy in the formation, the higher the cumulative production of the well. However, when the BHP drops to a certain value, due to the stress sensitivity of the rock, the porosity and permeability of the rock decrease, making it difficult for oil to flow from the formation into the wellbore, resulting in a slower increase in well production. Because the increase in COP is already very small when the BHP reaches 100 bar, and the growth rate of COP essentially does not change, it is necessary to avoid excessive development of the formation due to low BHP, leading to a decrease in the reservoir’s porosity and permeability, while also obtaining the best cumulative oil production. Therefore, 100 bar is the optimal value. In the following case, the BHP value was set to 100 bar in order to obtain the most efficient COP.

3.1.2. Effect of CO₂ Injection Rate

In order to find the best CO₂ injection rate, numerical simulation calculations were carried out for four injection rates: 40,000 cubic meters per day, 50,000 cubic meters per day, 60,000 cubic meters per day, and 100,000 cubic meters per day, while maintaining the total injection volume of 600,000 cubic meters for each cycle and keeping the other huff-n-puff parameters constant. The parameters of the CO₂ injection rate optimization scheme are shown in

Table 5. Injection rate optimization scheme.

Injection Rate (m3/day)	Injection Time Period (Day)	Soaking Time Period (Day)	Number of CO2 Huff-n-Puff Cycles
40,000	15	30	4
50,000	12	30	4
60,000	10	30	4
100,000	6	30	4

. Figure 10 shows the effect of the injection rate on COP.

In this case, we kept the total CO₂ injection volume constant and chose different CO₂ injection rates to simulate. When the CO₂ injection rate was high, the corresponding injection time would decrease. We tried to find the optimal combination of injection rate and injection time through multiple scenario simulations. As shown in Figure 10, when the total gas injection volume remained unchanged, as the CO₂ injection rate increased, the COP first increased and then gradually decreased, reaching a maximum value when the CO₂ injection rate reached 50,000 cubic meters per day. This may be because the initial injection of CO₂ takes a relatively long time and CO₂ undergoes sufficient exchange with the original oil in the formation under the CO₂ diffusion effect, resulting in more crude oil flowing into the well. However, when the injection rate increases to a certain value and the total injection amount is constant, the injection time becomes shorter, and CO₂ does not have sufficient opportunities to be effectively replaced with crude oil. In the following simulation, we set the CO₂ injection rate to 50,000 cubic meters per day.

3.1.3. Effect of Injection Time

In order to find the optimal CO₂ injection time period, we set the CO₂ injection time period as 10 days, 20 days, 30 days, 60 days, 90 days, and 120 days, while keeping the other huff-n-puff parameters constant. That is, in each simulation case, the injection rate was set to the same 50000 cubic meters per day, the same soaking time, the same production time, and the same number of cycles, with the only difference being the injection time. The parameters of the CO₂ injection time optimization scheme are shown in

Table 6. Injection time period optimization scheme.

Injection Rate (m3/day)	Injection Time Period (Day)	Soaking Time Period (Day)	Number of Huff-n-Puff Cycles
50,000	10	30	4
50,000	20	30	4
50,000	30	30	4
50,000	60	30	4
50,000	90	30	4
50,000	120	30	4

. Figure 11 shows the simulation results of the effect of the injection time period on COP.

In Figure 11, the blue bar represents the COP, while the orange line represents the trend of COP growth. The higher the blue bar, the higher the COP; the larger the slope of the orange line, the higher the COP growth; and the smaller the slope, the slower the COP growth. The injection time ranged from 10 days to 30 days, with a slow increase in cumulative production; from 30 days to 90 days, the COP increased rapidly, but from 90 days to 120 days, the growth rate of COP slowed down and gradually stabilized in the region. The results indicate that COP gradually increases with the extension of the injection time period. However, the COP growth rate slowed down from 3 months to 4 months. After 4 months of injection, the growth effect of COP was no longer significant. Therefore, there is a reasonable range of injection time. Due to the short duration of this simulation, in the following simulation cases, we will take an injection time of 20 days per cycle.

3.1.4. Effect of Soaking Time

The soaking time directly impacts the utilization rate of the injected CO₂ during the huff-n-puff process. Based on the previously optimized injection rate and injection time, we optimized the soaking time of the well. Six different soaking times were set: 10 days, 15 days, 20 days, 30 days, 35 days, and 40 days. The injection rate was set to 50,000 cubic meters per day, the injection time was set to 20 days, the production time was set to 360 days, and there were four cycles. The other parameters remain unchanged.

Table 7. Soaking time optimization scheme.

Injection Rate (m3/day)	Injection Time Period (Day)	Soaking Time Period (Day)	Number of Huff-n-Puff Cycles
50,000	20	10	4
50,000	20	15	4
50,000	20	20	4
50,000	20	30	4
50,000	20	35	4
50,000	20	40	4

shows the parameters of the soaking time optimization scheme. Figure 12 shows the effect of soaking time on cumulative oil production (COP).

Similarly, the blue bars in Figure 12 represent cumulative oil production (COP), while the orange line represents the trend of cumulative oil production (COP) growth. It can be seen from Figure 12 that when the soaking time ranges from 10 days to 20 days, the COP slowly increases. When the soaking time increases from 20 days to 35 days, the COP increases rapidly, but when the soaking time is greater than 35 days, the COP essentially does not increase. This implies that as the soaking time increases, the COP also gradually increases, but when the soaking time extends to a certain value, the COP growth is not significant. So, there is an optimal soaking time for the well. The optimal final soaking time is 35 days. In the following simulation case, the soak time was set to 35 days per cycle.

3.1.5. Effect of the Number of CO₂ Huff-n-Puff Cycles

In order to find a suitable number of CO₂-HnP cycles, the number of cycles was set to 1, 2, 3, and 4, while the other HnP parameters were kept constant. In order to compare the impact of the number of CO₂-HnP cycles on the well’s production efficiency, a simulation case of depleted development without cycles was carried out. The injection rate was set to 50,000 cubic meters per day, the injection time was set to 20 days, the soaking time was set to 35 days, and the production time was set to 360 days. All of the other parameters remained unchanged, with only the number of cycles changing.

Table 8. Number of CO₂ huff-n-puff cycles optimization scheme.

Injection Rate (m3/day)	Injection Time Period (Day)	Soaking Time Period (Day)	Number of Huff-n-Puff Cycles
50,000	20	35	0
50,000	20	35	1
50,000	20	35	2
50,000	20	35	3
50,000	20	35	4

shows the parameter list for the number of CO₂-HnP cycles optimization scheme in simulations, while Figure 13 shows the effect of the number of CO₂-HnP cycles on COP.

In Figure 13, the orange bars represent depleted development without external energy supplementation, while the blue bars represent different numbers of CO₂-HnP cycles. From Figure 13, it can be seen that all of the blue bars are significantly higher than the orange bar, which indicates that CO₂-HnP can indeed significantly increase oil production and improve oil recovery. Next, we take a look at the impact of the number of cycles on the COP. After increasing the number of cycles from one to three, the COP gradually increases. After three cycles, the COP begins to decrease. At the time of three cycles of huff-n-puff, the COP reaches its maximum. The optimal final number of CO₂-HnP cycles is three.

3.1.6. Comprehensive Analysis of Multiple Factors Affecting COP

In order to understand and estimate the effects of the above sensitivity parameters on COP, we need to analyze the weight of each parameter’s impact on the COP. After numerical simulation, the COP under each variable parameter can be obtained. The decision tree method was applied to calculate the contribution of each parameter to COP, and then the impact degree values calculated by machine learning were drawn into bar charts (Figure 14) and pie charts (Figure 15). Figure 14 and Figure 15 represent the contribution of all sensitivity parameters to COP. In Figure 14, the blue bars represent the percentage of impact of the parameters on COP. The longer the blue bar, the greater the impact of this parameter on COP. From Figure 14, it can be seen that the number of cycles has the greatest impact on COP, followed by the injection time and soak time, while the injection rate has the smallest impact on COP. Similarly, in Figure 15, the size of the sector and the percentage in the sector represent the degree of influence of the parameters on COP. The larger the sector, the greater the impact of the parameter on COP. The larger the percentage value, the greater the impact of the parameter on COP. From Figure 15, it can be seen that the degree of influence of the number of cycles accounts for 38.04%, the degree of influence of injection time accounts for 29.41%, the soaking time accounts for 24.10%, and the injection rate accounts for 8.45%. The number of cycles contributes the most to COP, followed by the injection time and soak time, with the injection rate contributing the least.

4. Conclusions

In this study, a component numerical simulation model based on discrete fracture model technology was established to simulate the CO₂-HnP process of multistage fractured horizontal wells in tight reservoirs with complex fractures. This model can serve as a universal framework for CO₂-HnP in unconventional fractured reservoirs. Taking into account the starting pressure gradient and stress sensitivity, a series of sensitive parameters affecting CO₂-HnP efficiency were simulated, and their impacts on cumulative production were analyzed. The following conclusions can be drawn:

(1)

The latest embedded discrete fracture technology (EDFM) was applied in the model, making the simulation of CO₂ huff-n-puff in complex fractured reservoirs faster and more efficient.

(2)

The starting pressure gradient and rock stress sensitivity factors greatly affect the pressure field of tight reservoirs and the cumulative production of multistage-fracturing horizontal wells. The rock stress sensitivity influences the reservoir’s permeability and porosity, and the starting pressure gradient can interfere with the flow calculation of “matrix–matrix”, as well as the flow calculation of “matrix-fracture” and “embedded fracture–matrix”, which cannot be ignored in component numerical simulations.

(3)

In CO₂ huff-n-puff simulations, production parameters such as injection rate, injection time, soak time, and the number of cycles all have an impact on COP. The degree of influence of the number of cycle accounts for 38.04%, the injection time accounts for 29.41%, the soaking time accounts for 24.10%, and the injection rate accounts for 8.45%. So, the number of cycles contributes the most to COP, followed by injection time and soak time, with the injection rate contributing the least. The injection rate and the number of cycles both have optimal values, while the injection time and soak time tend to have less significant effects on the growth of COP over time. Based on the results of our numerical simulations, the plan of injecting CO₂ at a daily injection rate of 50,000 cubic meters for 20 days, soaking for 35 days, circulating for three rounds, and producing for 5 years can achieve the highest cumulative production.

(4)

This study provides a universal and more efficient numerical simulation method for CO₂ huff-n-puff in multistage-fracturing horizontal wells of complex fractured tight oil reservoirs. The innovation of this study is the integration of nonlinear seepage with the starting pressure gradient, stress sensitivity, and EDFM technology.