Driven by the long horizontal well and multi-stage hydraulic fracture, gas has been successfully produced from the ultra-tight shale reservoirs. In the United States, dry shale gas production takes up 79% of the total dry natural gas market share in 2021 (EIA 2022). In China, the identified shale gas resources reach 402.62 billion cubic meters. Shale gas production achieved 23 billion cubic meters in 2021, but field data from different shale gas plays invariably indicated a sharp decrease in the production rate after a few years of first fracking (Baihly et al., 2010). Re-fracturing treatment has been proposed as a practicable enhancing gas recovery (EGR) approach in such reservoirs. Different studies were conducted to examine the feasibility of re-fracturing from the technical level and economic perspective (French, S et al., 2014; Eshkalak et al., 2014a; 2014b). Re-fracturing treatment is defined as the following concepts: 1) re-fracking the closed fractures and using the high-strength fractured sand to support the cracks and restore the recovery; 2) using temporary plugging additive to plug the old fractures and forcing the fracturing fluid to flow to unblocked paths to create new cracks; 3) sealing the original perforation clusters to produce new perforation clusters; and 4) reserving the original perforation clusters and adding new perforation clusters in originally fractured horizontal wells to re-stimulate low permeability reservoirs and revive gas production (Sheng et al., 2019; Huang et al., 2021; Liu et al., 2021; Xu et al., 2021; Deng et al., 2022).

In addition to re-fracturing treatment, enhancing gas recovery with CO₂ injection is also redeemed as a potential enhancing gas recovery approach. CO₂ has a preferential adsorption over CH₄ in organic-rich shale reservoirs. Experimental results show that the adsorption capacity of CO₂ is two to five times larger than that of CH₄ and one order of magnitude smaller than that in coalbed (Nuttal, 2010; Chareonsuppanimit et al., 2012; Heller and Zoback, 2014; Chen et al., 2018). CO₂ injection into shale reservoirs can not only improve natural gas production through CO₂ adsorption and CH₄ desorption but also realize the underground carbon sequestration. Shale gas formation is analogous to coalbed methane reservoirs from the perspective of methane occurring status in tight organic-rich formations (Jenkins and Boyer, 2008; Ross and Bustin, 2009). The sorbed gas content in the shale gas reservoir is relatively smaller than coalbed methane reservoirs. In the shale matrix, the gas occurs in the adsorbed status in organic nano-pores and exists in the free status in inorganic micro-pores and micro-fractures. The physio-chemical differences between the two types of formations are tabulated in Table 1 (Du and Nojabaei,2019). In the past, CO₂ injection into coalbed reservoirs has been extensively studies. Coalbed methane resources have also been commercially recovered in many countries through the gas injection technique (Marvor et al., 2004; Gunter et al., 2005; Fujioka et al., 2010). However, only a few filed pilots were performed in shale gas formations (Nuttall et al., 2005; Louk et al., 2017). Nuttall et al. (2005) conducted an in situ test of CO₂ geological sequestration in the Devonian Ohio Shale, located at eastern Kentucky. Almost 100 tons of CO₂ was planned to be injected into a vertical well. However, the injection has been forced to suspend, owing to a packer failure. Louk et al. (2017) performed a small-scale field pilot of the CO₂ huff-n-puff gas injection in the Chattanooga Shale formation, Tennessee. In this project, up to 510 tons of CO₂ was targeted injected into the formation from the depth of 777.2–1120.1 m. After shut-in for 4 months, the gas flow rate was eight times larger than before in the first month. More valuable natural gas liquid (ethane, propane, and butane) was brought out with CO₂ and methane. By the end of 17 months, more than 59% of injected CO₂ was successfully stored in the formation. This CO₂ injection test is the first successful field trial in shale gas formation.

Different simulation studies were performed to examine the effect of CO₂ injection in shale gas formation for enhancing natural gas recoveries. Yu et al. (2014) found the huff-n-puff CO₂ injection approach was unable to improve methane recovery in shale formation (matrix permeability is 500 nD). They concluded that a large amount of injected CO₂ (almost 96%) flowed back with natural gas instead of being stored in the reservoir in an adsorbed status. Huang et al. (2020) developed a multi-continuum simulation model by distinguishing the molecular transport mechanisms in organic and inorganic matter. Both the gas flooding and huff-n-puff gas injection schemes were performed in an organic-rich shale gas reservoir. The results showed that the injected CO₂ in inorganic pores were quickly being reproduced without displacing the adsorbed CH₄. Meanwhile, they also found that CO₂ flooding is not favorable for enhancing gas recovery in an ultra-tight formation, owing to the low injectivity. CO₂ huff-n-puff showed a better performance than gas flooding, and more than 50% of the injected CO₂ was successfully sequestrated in the reservoir. Du and Nojabaei (2020;2021) included the nano-confinement effect to calculate the diffusion coefficient of CO₂ in a shale gas reservoir and optimized the huff-n-puff gas injection parameters.

In the past, few attempts have been made to compare refracturing with the huff-n-puff gas injection scheme in a shale gas reservoir for EGR. Meanwhile, there is a lack of extensive investigation about the economic differences of these two well stimulation EGR approaches. The primary objective of this work was to examine and compare the re-fracturing and huff-n-puff CO₂ injection approaches to improving gas productions and economic perspectives. The CO₂ sequestration potential in shale formation is also evaluated. A fully compositional simulation approach coupled with a dual-porosity dual-permeability model is used. The differences in adsorption capacities of CO₂ and methane in the shale matrix are considered. The effects of different fracturing fluids, huff-n-puff cycles, and matrix permeabilities on shale gas recovery are also investigated.

In this study, a fully compositional simulation approach is used to study the shale gas production. Based on the mass balance equation, the governing equation is shown as follows: V Δ t Δ ( ϕ S g ρ ˜ g y i ) + V Δ t Δ M i − ∑ T ( λ g ρ ˜ g y i ΔΦ g ) − ∑ w e l l ρ ˜ g y i q g p = 0 , (1) where S g is the gas saturation, ρ ˜ g is the molar gas density, y i is the composition in the gas phase, M _i is the moles of component i stored by the adsorption isotherm in unit cell volume, T is the transmissibility between two connected cells, λ g is the mobility of the gas phase, Φ g is the potential of the gas phase, and q g p is the injection or production rate of gas in the well term.

The Peng–Robinson equation of state is used to calculate the phase compositions and gas compressibility factors, and the cubic equation is shown as follows: Z 3 + [ B − 1 ] Z 2 + [ A − B 2 − 2 B ( B + 1 ) ] Z − [ A B − B 2 ( B + 1 ) ] = 0 , (2) where A = ∑ i n c ∑ j n c c i c j A i j , (3a) A i j = ( 1 − δ i j ) ( A i A j ) 0.5 , (3b) A i = Ω a i 0 [ 1 + m i ( 1 − T r i 0.5 ) ] 2 P r i T r i 2 , (3c) B = ∑ i n c c i B i , (3d) B i = Ω b i o P r i T r i . (3e)

The classical Langmuir adsorption isotherm is used to calculate the adsorption or desorption of methane and carbon dioxide. The equation is shown as follows: q = V m b P 1 + b P , (4) where b is the Langmuir adsorption constant, and V _m is the maximal adsorbed mass. For methane and carbon dioxide, the two parameters that are used in this study are listed in Table 2.

The net present value (NPV) of a horizontal well is calculated as per Eshkalak et al. (2014): N P V = ∑ t = 1 T V r e v e n u e ( 1 + i ) t − [ F C + C w e l l + C F r a c + C R e − f r a c + C C O 2 ] , (5) where V r e v e n u e is the value of the production revenue, i is the interest rate, and t is the production time (year); F C is the fixed cost; C w e l l is the cost of drilling; C F r a c is the cost of fracturing; C F r a c is the cost of re-fracturing; and C C O 2 is the cost of carbon dioxide.

In this section, we compared re-fracturing with CO₂ huff-n-puff injection in a fractured tight shale reservoir for enhancing gas production. The shale reservoir is a 3-D cubic model with 2400 m in length, 900 m in width, and 70 m in thickness. The initial reservoir pressure is 28.7 MPa. The matrix permeability is 0.125 µD, and the porosity is 0.031. The shale reservoir properties are tabulated in Table 3. A horizontal well is located in the center with 1800 m in length.

The reservoir is initially subjected to fracking with six stages. The fracture half-length is 150 m. After gas production for 5 years, the reservoir is re-fractured. The schematic diagram is shown in Figure 1. Here, we compared two fracture fluids, i.e., supercritical carbon dioxide and water in the re-fracturing scheme. Normally, the cracks extend along a flat plane when using water as the fracture fluid. Using supercritical CO₂ as the fracture fluid generally create cracks extending three dimensions, and the breakdown pressure is lower than the hydraulic fracturing. Given that using critical the CO₂ fracture creates a more complex fracture network, we added the natural fracture in the CO₂ fracturing scheme. The effective permeabilities of the hydraulic fracture and supercritical CO₂ fracture are listed in Table 4. When using supercritical CO₂ as the fracture fluid, after generating the fractures, we injected CO₂ for 1 month prior to production to account for the remaining CO₂ during the fracturing process.

In this section, we investigated re-fracturing and gas injection methods for enhancing gas recovery and compared the production performance with the base case, i.e., initially fractured with six stages. Two simulation schemes are separately conducted, i.e., fracking with slickwater and fracking with supercritical CO₂. It should be noted that in the case of re-fracturing with supercritical CO₂, the initial fracture is also created by using supercritical CO₂ as the fracturing fluid. The fracture properties by using the two types of fracturing fluids are listed in Table 3. The simulation results of cumulative gas recovery are plotted in Figure 2.

The pressure distributions of the base case (after 15 years), prior to re-fracturing (at the 5th year), and the cases of fracturing with slickwater and supercritical CO_2, respectively, (after 15 years) are shown in Figure 3. The results showed that re-fracturing allows more gas between the previous two stages to be produced and significantly reduces the residual oil.

The results showed that re-fracturing significantly improves the gas production. After producing for 15 years, using slickwater and supercritical CO₂ as fracturing fluids can improve the gas recovery production by 43.47 and 64.17%, respectively. Using supercritical CO₂ as the fracturing fluid to frack the formation yields more gas production. This is because that CO₂ create more extended three-dimensional cracks. For a very tight formation (permeability: 0.125 nd), complex fracture networks are very important for gas migration from the tight matrix to the main fracture.

In the huff-n-puff CO₂ injection method, the reservoir is initially fractured with six stages. Two schemes are conducted, i.e., one cycle and two cycles of huff-n-puff. In one cycle of huff-n-puff, after primary production for 5 years, CO₂ is injected at 100,000 m³/d for 1 year, and then, the well is shut-in for 1 year. After 1-year soaking time, the well is re-produced for 8 years. In two cycles of huff-n-puff, CO₂ is re-injected at 100,000 m³/d for 1 year at the 10th year, followed with 1-year soaking time. Then, the well is re-producing for 3 years. The simulation results are plotted in Figure 4. The results showed that the cumulative gas production is improved by 32.85 and 14.71% corresponding to one cycle and two cycles of huff-n-puff, respectively. One cycle of gas injection performs better than two cycles. One reason is that in two cycles of the gas injection scheme, twice of injection time and soaking time occupies too much of the total production time. Given that the produced gases include not only methane but also injected CO₂, we also plotted the produced pure methane in Figure 5.

The results show that the produced pure methane is increased by 26.6 and 1.17% for one cycle and two cycles of huff-n-puff, respectively. It means that CO₂ injection indeed shows the ability to increase methane production. To investigate the CO₂ sequestration potential, we also plotted the total moles of injected CO₂ and produced CO₂ in Figure 6 and calculated the percentage of sequestrated CO₂ in the reservoir.

A total of 42.41 and 38.6% of CO₂ is successfully sequestrated in the reservoir at the end of 15 years for one cycle and two cycles of gas injection schemes, respectively. The results show that CO₂ can replace the adsorbed methane from the tight shale matrix, owing to its stronger adsorption potential. A large amount of injected CO₂ is successfully stored in the reservoir. This shows that the tight shale matrix is a huge potential geological sequestration site. A sensitivity analysis is conducted to investigate the matrix permeability on gas production and CO₂ sequestration performances. The results are plotted in Figure 7. When the matrix permeability is 500 nd, the huff-n-puff gas injection schemes yield a lower gas production than the base case. The gas recoveries are reduced by 13.33 and 26.66% for one cycle and two cycles of gas injection, respectively. Given that the produced gas contains injected CO₂, we also calculated the produced pure methane in Figure 7B. The results show that the recoveries of pure methane are decreased by 18.61 and 36.47%, respectively. It indicates that CO₂ huff-n-puff in a higher permeability reservoir is not very feasible in improving the gas production. One reason is that the Darcy’s flow plays the most important role in gas transport in a not-too-tight formation. Gas is displaced driven by the pressure gradient. The effect of adsorption-desorption becomes less crucial in a relatively high-permeable formation. We also plotted the sequestrated amount of CO₂ in Figure 7C. The sequestrated CO₂ is 20.96 and 26.48% for one cycle and two cycles of huff-n-puff gas injection, respectively. Compared to tighter formation (permeability = 125 nd), the sequestrated amount of CO₂ is much reduced. It means a lot amount of CO₂ is re-produced after shut-in time. The results show that a tighter formation is more suitable for CO₂ huff-n-puff gas injection from the view of enhancing gas recovery and CO₂ geological sequestration.

To compare re-fracturing and huff-n-puff gas injection schemes on improving gas recovery, we also tabulated the produced gas and increased gas recovery in Table 5. The matrix permeability is 125 nd. Overall, using the refracturing approach can produce more gas than the huff-n-puff gas injection method. One possible reason is that in the huff-n-puff gas injection process, the gas injection and shut-in process takes up 2 years of the total production time (10 years), leaving the production process shorter. Another finding is that re-fracturing with supercritical CO₂ shows the best performance among all the cases.

To evaluate the huff-n-puff gas injection scheme on carbon sequestration performance, we also calculated the total injected CO₂, total re-produced CO₂, and the sequestrated percentage of CO₂, as shown in Table 6. At a tighter shale matrix, more CO₂ can be stored in the reservoir instead of being re-produced. This is because the adsorption-desorption isotherm plays a more important role than the viscous flow. Meanwhile, one cycle of gas injection in a tighter formation is more favorable in a tighter shale matrix than a higher permeable matrix in terms of carbon sequestration.

The costs of drilling, fracturing, and gas prices are listed in Table 7. We calculated the NPV of cash flow for the base case, re-fracturing case, and CO₂ huff-n-puff injection case by 10 and 15 years. The results are plotted in Figure 8. The results show that after producing for 10 years, the differences of NPV among the five cases (the base case, re-fracturing with slickwater and supercritical CO₂, huff-n-puff with one and two cycles) are not very significant. However, after 15 years of production, re-fracturing with CO₂ yields the largest NPV, followed by re-fracturing with slickwater. Despite the fact that the NPV of CO₂ huff-n-puff gas injection is lower than that of the re-fracturing schemes, it is still higher than the base case. In other words, both re-fracturing treatment and huff-n-puff CO₂ injection are profitable from a long-term cash flow perspective.

In this study, we compared re-fracturing with the huff-n-puff gas injection scheme in a shale gas reservoir for EGR. A fully compositional simulation approach coupled with a dual-porosity dual-permeability model is used. EGR approaches are initiated after 5 years of first fracking. The following conclusion is addressed:

• Using refracturing approach yields a better recovery performance than the huff-n-puff gas injection method.