Optimization of CO₂ Huff-n-Puff in Unconventional Reservoirs with a Focus on Pore Confinement Effects, Fluid Types, and Completion Parameters

Abstract

The cyclic injection of CO₂, referred to as the huff-n-puff (HnP) method, is an attractive option to improve oil recovery from unconventional reservoirs. This study evaluates the optimization of the CO₂ HnP method and provides insight into the aspects of CO₂ sequestration for unconventional reservoirs. Furthermore, this study also examines the impact of nanopore confinement, fluid composition, injection solvent, diffusivity parameters, and fracture properties on the long-term recovery factor. The results from over 500 independent simulations showed that the optimal recovery is obtained for the puff-to-huff ratio of around 2.73 with a soak period of fewer than 2.7 days. After numerous HnP cycles, an optimized CO₂ HnP process resulted in about 970-to-1067-ton CO₂ storage per fracture and over 32% recovery, compared to 22% recovery for natural depletion over the 30 years. The optimized CO₂ HnP process also showed higher effectiveness compared to the N₂ HnP scenario. Additionally, for reservoirs with significant pore confinement (pore size ≤ 10 nm), the oil recovery improved by over 3% compared to the unconfined bulk phase properties. We also observed over 300% improvement in recovery factor for a fluid with a significant fraction of light hydrocarbons (C₁–C₆), compared to just a 50% improvement in recovery for a fluid with a substantial fraction of heavy hydrocarbons (C₇⁺). Finally, the results also showed that fracture properties are much more important for CO₂ HnP than natural depletion. This study provides critical insights to optimize and improve CO₂ HnP operations for different fluid phases and fracture properties encountered in unconventional reservoirs.

1. Introduction

The global oil demand is expected to grow from 97 million barrels per day in 2021 to 120 million barrels per day by 2050, according to estimates from the US EIA [1]. This increase in global energy demand will be mainly supported by developing unconventional reservoirs, made possible due to technological advancements in horizontal drilling and hydraulic fracturing. Horizontal wells and hydraulic fractures increase the effective permeability of the tight reservoirs, resulting in improved productivity from previously uneconomic formations. However, unconventional reservoirs suffer from rapid production decline despite technological improvements. The primary recovery only accounts for less than 10% of oil in place [2,3]. Approximately 90% of reserves remain in the reservoirs by the end of primary depletion [4], making them good candidates for enhanced oil recovery (EOR). For instance, an estimated 1.6–9 billion barrels of oil can be recovered from the Bakken reservoir with a 1% improvement in the oil recovery factor [5]. Water flooding is generally the preferred choice for enhanced oil recovery after the primary depletion of conventional reservoirs. However, water flooding is not the best option for unconventional reservoirs due to the low injectivity caused by ultra-low permeability. Water flooding in unconventional reservoirs may also lead to clay swelling, further degrading the formation permeability. In addition, poor sweep efficiency in induced fracture networks makes waterflooding unsuitable for unconventional reservoirs [6,7]. EOR through CO₂ injection, first commercially used in 1972 in West Texas, is more suitable for low permeability reservoirs due to its various advantages over other EOR techniques. Although the injection of other gases, such as nitrogen (N₂), and lean and intermediate-weight hydrocarbons, is just as effective as EOR solvents in some cases, CO₂ injection is desirable as it can also be used as one of the facets of a multi-pronged greenhouse gas reduction strategy. Although more than 70% of the current CO₂ EOR projects in the United States use naturally occurring underground sources of CO₂, captured anthropogenic sources can be permanently stored or sequestered in depleted underground formations. Some projects, such as Petra Nova and the Century plant, have successfully utilized captured CO₂ produced in power generation and industrial fertilizer production for EOR in West Texas [8,9]. The carbon captured from the Century plant allowed Occidental Petroleum to economically develop approximately 500 million barrels of oil in 2016 [10]. After oil production, a large percentage of the injected CO₂ remains securely trapped within the dead-end pores/channels and adsorbed to the rock surfaces. The CO₂ produced with the oil is economically separated back out, recompressed, and combined with CO₂ from other sources for further re-injection into the reservoir. The initial trapping and the closed-loop system result in 90–95% sequestration of the injected CO₂ in deep geologic formations [8,9,10].

There are two kinds of CO₂ EOR, miscible or immiscible. The miscible CO₂ EOR results in better residual oil recovery efficiency than the immiscible one due to the improvement in the overall mobility of the residual oil by viscosity reduction and oil swelling. However, a miscible EOR is only possible when all the conditions required for the miscibility of oil and CO₂ are satisfied. The primary condition required for miscibility is that the pressure has to be greater than the minimum miscibility pressure (MMP) of the CO₂ and oil. CO₂ injection processes are usually multiple contact miscibility. Achieving first-contact miscibility is often impossible, especially in light and medium oil reservoirs [11]. There are many approaches to implementing CO₂ EOR, including continuous, intermittent/cyclic (HnP injection), and water-alternating injection strategies. In the continuous injection process (Figure 1a), a CO₂ injector is used to pump pressured CO₂ continuously to produce the residual oil from a connected producer well. For the CO₂ HnP strategy (Figure 1b), the producer well is temporarily converted into an injector well after a certain period of primary production, where CO₂ is injected until the desired downhole pressure is achieved. After the injection period, the well is shut-in for some time so that the injected gas soaks into the formation. Finally, the well is reopened for production.

Numerous studies have concluded that the HnP method suits unconventional reservoirs with low permeability and many natural fractures more than the continuous gas injection method. The injected fluid (CO₂) also reopens the natural fractures around the wellbore, enhancing the formation’s permeability. The success of the CO₂ HnP process depends on several factors, such as the injection rate and injection time of CO₂, the soaking time, and the number of cycles performed. Song and Yang [12] performed the numerical and experimental evaluation of the CO₂ huff and puff process in the Bakken Formation. They concluded that miscibility and soaking time were the key parameters to optimize CO₂ HnP. They highlighted that the main mechanics underlying the CO₂ HnP method were oil swelling, interfacial tension (IFT) decrease, viscosity reduction, and solution gas drive. Alharthy et al. [13] showed that long soaking periods reduced cumulative oil recovery, and fracture spacing affected the efficiency of the soaking time. Kanfar et al. [14] performed an optimization study for the injection time and length alongside the soaking time to improve productivity. Their work also recommended fine gridding for simulating hydraulic fractures to prevent convergence and dispersion problems. Chen et al. [15] showed that reservoir heterogeneity significantly impacts oil recovery during CO₂ HnP. Enab and Emami-Meybodi [16] evaluated the HnP performance in ultra-tight reservoirs with different fluid types and injection gases. Their study showed that the CO₂ HnP provides the highest recovery for retrograde condensate fluid type, whereas C₂H₆ was more suitable for black oil and volatile oil systems. They also evaluated other phenomena like diffusion, adsorption, and hysteresis. Min et al. [17] evaluated the critical parameters of the CO₂ HnP affecting the recovery accuracy and recovery process in preserved liquid-rich shale core samples. They concluded that the residence time (summation of soaking and production time) controls the recovery. Their work also recommended that, for higher recovery, the injection pressure needs to be at or above MMP. Although the CO₂ HnP has been shown to be effective in improving productivity after natural depletion, its implementation remains challenging due to the numerous complexities related to the rock properties, fluid flow, and phase behavior in unconventional shale reservoirs. One such complexity is introduced due to multiple complex hydrocarbon-bearing nanopores. The nanopores restrict the movement of the fluid particles, resulting in phase behavior that is different from that of unconfined fluid. Pressure, volume, and temperature (PVT) conditions affect how the fluid behaves in the hydrocarbon phase, and each PVT condition results in a distinct behavior. Numerous authors have extensively studied the impact of nanopore confinement on hydrocarbons in unconventional shale reservoirs [18,19]. Their studies have shown that nanopore confinement should be carefully accounted for in numerical and modeling studies as it can significantly impact hydrocarbon recovery and reserves estimation.

The nanopores also have a significant impact on CO₂ EOR [2,11,20]. The change in phase behavior results in a substantial change in the interaction between the injected CO₂ and in situ hydrocarbons. Mohammad et al. [11] confirmed this finding by experimentally calculating the MMP with the vanishing interfacial tension method (VIT) in a tight reservoir with nanopores of different sizes. Furthermore, Li et al. [20] performed an experimental investigation of the CO₂ HnP method using shale core samples from the Eagle Ford formation and studied the oil recovery. Their study revealed that oil recovery increased when conditions for miscibility were changed from immiscible to miscible due to the presence of nanopores. The MMP required for miscibility decreased when the number of nanopores increased. Later work by Yu et al. [7] showed the importance of molecular diffusion during CO₂ EOR. They observed a recovery of up to 9.4% in the Bakken field over 30 years. Zhang and Zhang [21] studied the effects of nanopores on CO₂ EOR processes. Their study indicated that nanopore confinement significantly reduces key parameters, such as the gas–oil interfacial tension and CO₂ minimum miscibility pressure. This reduction cumulatively led to an increase in recovery.

Numerous simulation, experimental, and pilot-scale studies have been conducted on miscible CO₂ HnP in unconventional reservoirs. However, there have been few studies considering the effect of nanopores on the CO₂ HnP process [15,22]. Furthermore, to the best of our knowledge, the effect of pore confinement on different fluid samples has not received much attention. Thus, there is a further need for combined studies that evaluate the effect of nanopore confinement and fluid property. This study performs a rigorous compositional simulation to understand these impacts on the production performance of a CO₂ HnP process. The remainder of the paper is organized as follows. Section 2 describes the base case model, including the study region. We start with arbitrarily selected critical HnP decision parameters (injection, soaking, and production time) to demonstrate the importance of optimized operating conditions on the production performance of a well subjected to CO₂ HnP. Section 3 presents the optimization of the base case model by simulating multiple plausible realizations of the CO₂ HnP process. Section 4 presents the effect of different uncertain parameters on the HnP process. A brief insight into the aspects of CO₂ storage during the HnP process is presented in Section 5. Finally, Section 6 provides the main conclusions of this study. This study provides improved insight into the influence of key parameters on CO₂ HnP in unconventional shale reservoirs with nanopores and other underlying uncertainties.

2. Base Case Model

This study uses a modified version of a previously history-matched model set in the Eagle Ford shale [23]. A compositional unconventional reservoir simulator CMG-GEM was used for the simulation. The Eagle Ford is stratigraphically positioned above the Buda Limestone and below the Austin Chalk [24]. The landing zone for the well in this study is near the base of the lower Eagle Ford, above the top of Buda limestone. Around 24 months of historical production data available for a horizontal well (well H1, Figure 2) drilled in Brazos County for the history match.

Most of the well and fracture properties, such as the number of fracture stages (and fractures), well spacing, well length, and monthly oil production history, were known before the simulation. However, the geological properties, such as the permeability, porosity, and fracture conductivity, were unknown and estimated from the history match. A model with all the reported 131 fractures was used for the history match. We used over 20,000 grid blocks to create the base case model, including the logarithmically refined grids (LGR) close to the fractures. The LGR reduces the total number of grid blocks needed for simulation by only using small grid blocks close to the fracture, which are needed to capture the drastic change in fluid saturations and pressures near the hydraulic fractures. Furthermore, we used black oil PVT properties provided by the operator during the history match to reduce the computational time. However, it is critical to emphasize that after the history match, the simulations in this study use a compositional model. The drainage was assumed to occur at constant bottom-hole pressure of 1,000 psi. The relative permeability curves are generated from modified Brooks–Corey correlations with typical Eagle Ford values from the literature [18,26,27,28,29], as shown in Figure 3.

The same relative permeability curve was applied to both the fracture and the matrix as a simplification. As history matching is an inverse problem, multiple plausible iterations of the unknown parameters are possible. Further details on history matching can be found in Khanal and Weijermars [23].

Although the history match assumed a black oil PVT model, this study uses a compositional model, which was needed to account for the compositional changes during CO₂ EOR combined with the pore confinement effect. We also use a fracture half-length of 625 ft so that it touches the neighboring horizontal wells. The parameters used for this study are listed in

Table 1. Reservoir parameters used for this study.

Parameters	Values	Units
Well Length	6550	ft
Initial Reservoir Pressure	4891	psia
Reservoir Temperature	220	°F
Total Compressibility	3 × 10−6	psi−1
Permeability	600	nD
Fracture Half-length	625	ft
Number of Fractures	131
Fracture Spacing	50	ft
Fracture Stages	22
Fracture Width	0.01	ft
Fracture Permeability	300	mD
Fracture Height	60	ft
Fluid Properties	Table 2
Net Pay	60	Ft
Porosity	4.5%
Initial Oil Saturation	0.85

.

Table 2. Extended PVT properties of the representative base case reservoir fluid.

Component	Mole. Frac	Pc (atm)	Tc (K)	Acentric Factor	Mol. Wt	Vc (L/mol)	S.G	Parachor
CH4	38.52	45.4	190.6	0.008	16.0	0.099	0.3	77
C2H6	4.93	48.2	305.4	0.098	30.1	0.148	0.356	108
C3H8	2.75	41.9	369.8	0.152	44.1	0.203	0.507	150.3
IC4	0.63	36	408.1	0.176	58.1	0.263	0.563	181.5
NC4	1.09	37.5	425.2	0.193	58.1	0.255	0.584	189.9
IC5	0.50	33.4	460.4	0.227	72.2	0.306	0.625	225
NC5	0.53	33.3	469.6	0.251	72.2	0.304	0.631	231.5
FC6	0.75	32.46	507.5	0.275	86	0.344	0.69	250.1
C07–C11	26.98	28.71	545.1	0.307	103.9	0.409	0.711	300.6
C12–C16	7.33	18.19	684.7	0.553	192.7	0.740	0.788	529.3
C17–C23	6.56	13.94	767.3	0.733	274.7	1.014	0.832	709.9
C24–C29	3.43	11.15	838.2	0.941	367.0	1.291	0.867	877.7
C30	0.44	10.05	872.5	1.036	419.2	1.434	0.884	956.0
C31+	5.56	7.41	981	1.288	612.2	1.882	0.933	1141.5

shows the extended PVT properties of the representative reservoir fluid for the Eagle Ford liquid fluids considered for the base case [28,29]. The heavy fraction (C₇₊) of the original fluid has a molecular weight, mole fraction, and standard gravity of 216 g/mole, 41.49%, and 0.82, respectively. The C₇₊ fraction is further split into additional pseudo-components and tuned by changing the binary interaction coefficients to match the reported saturation pressure, GOR, and °API of 2260 psi, 500 scf/STB, and 37.7 °API, respectively.

In order to further reduce the computational time, we only simulated a single fracture, with symmetrical no-flow boundaries at 25 ft in either direction. The vertical no-flow boundary is located at 625 ft, symmetrical to the neighboring wells (Figure 4). We again used the logarithmic grid refinement, where the grid is more refined around the region of interest, i.e., around fractures. It should be noted that differences in grid sizing may result in slightly different results; however, the difference is usually minimal [16].

For the base case, we also do not include the effect of diffusion of CO₂ into the oil during the HnP process. As the diffusivity of CO₂ in oil is an uncertain parameter, we evaluate this later to understand its impact on the recovery factor. The reservoir was produced with natural depletion for the first two years, after which CO₂ HnP cycles were initiated. For both production schemes, we use an appropriate minimum BHP of 1000 psia, similar to several other studies [30,31,32]. The injection, soaking, and production duration were chosen as 60 days, 7 days, and 120 days, respectively, which is close to the values used in the work of Kurtoglu [33], who used 60 days of injection, 10 days of soaking, and 120 days of the production period. It is worth noting that different studies in literature study the HnP performance for very different injection, soaking, and production periods. For example, Wang et al. [34] used an injection period of 10 years, followed by 5 years of soaking and 5 years of production time. In contrast, Shoaib and Hoffman [22] used a uniform three-month duration for each injection, soaking, and production period. The duration for each step considered in this study will be optimized later by using sensitivity analysis. The CO₂ injection was controlled by ensuring that the injector BHP was greater than the reservoir fluid’s minimum miscibility pressure (MMP). The MMP for the base case fluid sample was calculated as 3375 psia using the cell-to-cell method [35].

Figure 5 shows the oil rate and cumulative oil for natural depletion (ND) and the HnP scheme. The HnP scheme is implemented after two years of natural depletion for 10,957 days, or about 30 years. As only one symmetric element is simulated, the total production rates and rates must be multiplied by the total number of fractures. This well’s initial production (IP) was over 900 bbl/day, making it a highly productive well, as the mean IP for the Eagle Ford shale is around 500 bbl/day. However, the well declined to over 80% of the initial rates after three years of production, necessitating EOR techniques. As shown in Figure 5, the HnP method results in significantly lower production than natural depletion. The recovery factor for natural depletion is 21.9% compared to 18.0% for the HnP method. The cumulative oil for the ND and HnP were 3987 bbl/fracture and 3277 bbl/fracture, respectively. This result is consistent with the results from other studies [14]. Although the CO₂ injection improves the flow properties of the in situ oil, the injection and soaking period prevents the well from producing for a significant period. The combined injection and soaking period accounts for over ten years, during which the well cannot produce any hydrocarbons.

If the well produces for a more extended period, accounting for the loss in production time, the HnP method should yield improved production compared to the natural depletion. However, the NPV of the HnP method will be significantly lower than the natural depletion due to the deferred production.

Figure 6 shows the average reservoir pressure for both production scenarios. As the gas injection rate in HnP is controlled by the well constraint of a maximum BHP of 3375 psia, the average reservoir pressure bounces around 3000 psia. This reduces production as the miscibility is not reached throughout the reservoir. Furthermore, the production time after injection is insufficient to reach the minimum BHP of 1000 psia set for the reservoir. Therefore, the production can be improved by optimizing the injection pressure to keep the reservoir pressure above the estimated MMP, the soaking time to improve the mobility of the residual oil, and the injection time so that the drawdown is close to the minimum BHP.

3. Optimization of the HnP Process

The base case results show that optimizing the injection, soaking, and production period of the HnP process is critical. The valid objective function for a field case depends on numerous constraints, such as availability of solvent (CO₂), compression costs, safety/operational constraints, and economic parameters (e.g., NPV). An objective function that captures all of these variables requires numerous assumptions outside this study’s scope. Furthermore, as most of the other variables will be similar across each run, our objective function is to maximize the recovery factor.

To optimize the recovery (%), we change the injection (huff) and production (puff) time between 30 and 360 days. We use this range to evaluate a wide range of production scenarios. Furthermore, the soaking period is varied between 0 days and 28 days. The well constraint is changed to a maximum BHP of 4872 psia, which is the initial pressure of the reservoir to keep the average reservoir pressure above the MMP. We ran over 500 simulations with different injection combinations, soaking, and production times to generate multiple scenarios with multiple recovery factors (Figure 7). The highest recovery of 32.0% was obtained for 30 days of a huff, 2.8 days of soak, and 85 days of puff time, corresponding to about 87 HnP cycles, as shown in Figure 8a. This recovery was higher than the ND recovery by 10.4%. This increase is equivalent to 1893 bbl/fracture (248 MStb/well) over the 30-year interval. In contrast, the lowest recovery of 12.9% was observed for 360 days of huff, 28 days of soak, and 30 days of puff time. The well stays non-producing for a significant amount of time for the least optimal case, which significantly hinders the overall production over 30 years. Such extremely suboptimal operating conditions lead to reduced drawdown and a loss of 9% recovery compared to ND, which amounts to 1635 bbl/fracture (214 MStb/well) over the 30 years of operation. Although the extreme suboptimal case presented in Figure 8b is unlikely, this result illustrates the importance of careful huff-soak-puff time needed to optimize the gas injection process.

Next, we performed a variance-based sensitivity analysis using the Sobol method to identify the parameters that significantly impact the % recovery factor. Figure 9a shows that both huff (injection) and puff (production) have significant total effects (main and interaction), whereas the soaking period has negligible impact on the objective function. Further evaluation of the 500 independent simulations also illustrated that for the optimal cases (cases with %Recovery > 30), the soak time is less than or close to 7 days. As the effect of soak time is negligible compared to the huff and puff time, we screened the 450 runs that had a % recovery greater than that of natural depletion (21.9%) to further evaluate the relationship between the huff and puff times to the % recovery. A quadratic fit with an adjusted R² of 0.78 was observed when the ratio of puff and huff time was plotted against the recovery (%), as shown in Figure 9b. The global maximum for the ratio (huff/puff) for the maximum % recovery for the selected range of inputs was observed to be 2.73. We will use the optimal case for sensitivity analysis and evaluation of uncertain parameters for the remainder of the paper.

4. Effect of Different Parameters in the HnP Process

4.1. Effect of Pore Confinement

In conventional reservoirs, pore throat sizes are large, the effect of capillary pressure and other forces (like Van der Waals, adsorption) on phase behavior is negligible [36], and PVT properties are close to lab PVT cell measurements. However, phase property deviates from the measured PVT cell measurement in reservoirs with a significant fraction of nanopores. The phase property deviation due to the presence of nanopores has been verified and estimated by using different methods such as adsorption–desorption experiments, differential scanning calorimetry experiments, diffusion experiments, nanochannel chip experiments, molecular dynamics simulation, equation of state, and numerous other techniques [37,38]. Although the different methods have their own strengths and weaknesses, this study uses the modification of critical properties for the equation of state models due to its relative ease of implementation into a compositional reservoir simulation model. Therefore, we will use the previously developed correlations based on the rigorous molecular dynamics simulation to calculate the critical properties needed for the equation of state models [18]. The critical temperature and pressure shift correlation used in this study are:

$$Ln\left(\Delta T_n\right)=-3.007Ln\left(r_p\right)+0.869$$

(1)

$$\Delta P_n=\frac{2.63}{r_p}$$

(2)

where $\Delta T_n$ is normalized deviated temperature, $\Delta P_n$ is normalized deviated pressure, and r_p is the pore radius. The confined critical properties can then be calculated from Equations (3) and (4) as follows:

$$T_{cc}=T_c\left(1-2.38.r_p{}^{-3.007}\right)$$

(3)

$$P_{cc}=P_c\left(1-2.63/r_p\right)$$

(4)

where T_cc, and P_cc are the pore-confined critical temperature and critical pressure calculated from the respective critical temperature (T_c) and pressure (P_c). For the large pore radius (r_p) value, the confined critical properties equal the bulk critical properties. We use the Peng–Robinson (PR) EOS [39] to calculate the phase properties using the correlations Equations (3) and (4). The substance-specific constants that account for the attractive and repulsive forces are directly calculated from the critical properties and acentric factor [40].

In order to evaluate the effect of nanopore confinement, we changed the critical properties of the fluid sample in the base case after tuning the PVT parameter to match the reported saturation pressure, GOR, and °API. The rationale is that these measurements are taken for bulk samples and do not represent the fluid behavior in the confined state. Therefore, the critical property was shifted by assuming pore sizes ranging from 5 nm to 200 nm. The actual phase behavior would be between the two extreme pore sizes and require an accurate pore-size distribution, which is not considered here. Figure 10 shows the base case fluid sample’s pressure–temperature (PT) phase diagram obtained from the rigorous multi-component flash calculation based on Peng–Robinson EOS using the modified T_c and P_c. As the reservoir temperature is 250 °F, the reservoir behaves like black oil regardless of the assumed pore sizes. Figure 10 also shows that the critical properties of the fluid mixture are significantly depressed because of nanopore confinement. However, the effect of nanopore confinement on T_c was negligible for fluids confined in pore sizes greater than 10 nm. The impact of pore confinement was much more significant on combined fluid P_c, which was reduced by over 53% (for 5 nm). In summary, the combined fluids T_c and P_c change due to pore confinement, which is clearly observed in Figure 10 for P_c but is not very apparent for T_c due to a relatively minor change.

Next, we evaluate the effect of pore confinement on the MMP of the base case fluid. The miscible CO₂ injection results in up to three times higher oil recovery than immiscible injection [41]. The MMP of a reservoir depends on several factors, including the phase properties of the in situ fluid. Since the nanopore confinement effect affects the critical properties of reservoir fluids, the MMP for CO₂ miscibility is also impacted. This effect causes tight reservoirs such as shale to have a lower MMP when compared to conventional reservoirs like sandstone. In order to evaluate the impact of nanopore confinement on MMP, we calculated the MMP using cell-to-cell simulation, which is shown in Figure 11 [35]. We used oil properties that are shifted due to the confinement effect, as shown in Figure 10.

We evaluate the optimized base case’s recovery factor for each pore size. Figure 12 shows that the oil recovery factor increases due to the pore confinement effect. For the reservoir with pore sizes of 5 nm and 10 nm, there are 8.0% and 8.5% increases in recovery compared to the unconfined optimized base case model (from 32.0% for the base case recovery, Figure 12). Thus, proper characterization of reservoirs is critical to account for the presence of nanopores which leads to pore confinement.

4.2. Effect of Fluid Composition

The fluid composition has one of the most significant impacts on production from unconventional reservoirs. Accurate characterization of the reservoir fluids is essential for successful EOR operations, including the CO₂ HnP. The selection of injection pressure, the number of HnP cycles, the time for huff-soak-puff cycles, and other decision parameters may also depend on the reservoir fluid properties. For a compositional simulation, the fluid composition data for the reservoir fluid needs to be appropriately tuned to match the experimental data obtained from various laboratory experiments, such as constant composition expansion, differential liberation, separator test, and others. We use two additional oil samples from the Eagle Ford shale with different fluid compositions in addition to the base case oil (Sample 1). The fluid composition and reported properties for Samples 2 and 3 are given in

Table 3. Properties of Sample 2 and Sample 3 fluid ((a): composition; (b): tuning parameters).

(a)
Sample 2		Sample 3
Component	Mole Frac.	Component	Mole Frac.
CH4	49.9	CH4	67.44
C2H6	6.4	C2H6	8.27
C3H8	3.6	C3H8	4.63
IC4	0.8	IC4	1.07
NC4	1.4	NC4	1.82
IC5	0.6	IC5	0.83
NC5	0.7	NC5	0.89
FC6	1.0	FC6	1.27
C7+	35.5	C7+	13.79
(b)
Properties	Sample 2	Sample 3
Sat. Pressure (psi)	3265	4754
GOR, scf/STB	1000	4000
° API	40	44.5
C7+ Mol. Wt.	195	164
C7+ Mol%	34.88	13.78
Std. Gravity C7+	0.81	0.79

. The individual hydrocarbons heavier than C₇⁺ are lumped together to define several pseudo-components. The fluid properties were tuned to match the reported saturation pressure and API for each sample, as presented in Table 3.

The PT diagram for Samples 2 and 3 is shown in Figure 13, including the effect of pore confinement. Moreover, the MMP for Sample 2 and Sample 3 fluid are presented in Figure 14.

Examination of Figure 10 and Figure 13 reveals that the pore confinement effect significantly suppresses the critical properties (P_c and T_c). However, as observed in Sample 1, the critical pressure shift (P_c) is much more significant than the critical temperature shift (T_c). Therefore, we further evaluated the critical property shift for smaller-sized pores (3 nm) and observed a similar trend.

Table 4. The deviation in critical properties due to the pore confinement effect.

	Sample 1				Sample 2				Sample 3
Pore Size (nm)	Pc (bar)	$\mathbf{\Delta }$	Tc (°F)	$\mathbf{\Delta }$	Pc (bar)	$\mathbf{\Delta }$	Tc (°F)	$\mathbf{\Delta }$	Pc (bar)	$\mathbf{\Delta }$	Tc (°F)	$\mathbf{\Delta }$
3	230	88.0	751	−13.4	326	88.0	618	−14.3	540	88.0	300	−19.6
5	901	52.8	842	−2.89	1281	52.8	699	−3.09	2121	52.8	357	−4.21
10	1405	26.4	867	0.00	1996	26.4	719	−0.38	3306	26.4	371	−0.51
30	1741	8.8	867	0.00	2473	8.8	721	−0.01	4097	8.8	373	−0.02
100	1858	2.6	867	0.00	2640	2.6	721	0.00	4373	2.6	373	0.00
200	1883	1.3	867	0.00	2676	1.3	721	0.00	4432	1.3	373	0.00
Bulk *	1908	0.0	867	0.00	2712	0.0	721	0.00	4492	0.0	373	0.00

* Bulk properties calculated with original fluid properties.

summarizes the critical property deviation for all the fluid samples considered in this study, including the 3 nm case, which is not used for simulations.

We used the optimized HnP model to simulate recovery for both fluid samples (2 and 3). Figure 15 compares the cumulative oil and recovery factor for different fluids after 30 years of simulation. As expected, the fluid sample with a higher fraction of heavy hydrocarbons results in the highest per fracture cumulative oil recovery of 5870 bbl, compared to 3987 bbl from natural depletion over the 30-year period when the bulk phase fluid behavior is considered. As the phase behavior deviates from the pore confinement, the cumulative oil increases for each case.

The recovery factor plot shows that for fluid Sample 3, which has significantly lower fractions of C₇⁺ hydrocarbons, the increase in recovery factor due to the HnP process is noticeably higher than that for Samples 1 and 2, which have a higher amount of C₇⁺ hydrocarbons. The recovery factor for Sample 3 jumps from 9.1% using natural depletion to 30.7% (~300% increase) using the HnP process when bulk PVT properties are used over 30 years of production. However, for the base case (Sample 1), the recovery factor only increases from 21.9% to 32.2% (~50% increase) for the same scenario (Figure 15a,b). For Sample 2, which has a moderate amount of C₇⁺ components, the recovery factor increases from 18.4% for natural depletion to 34.4% (~100% increase) for the HnP process.

4.3. Effect of Injection Solvent

Due to the poor injectivity condition for water flooding—requiring high injection pressure in ultra-low permeability conditions—HnP scenarios using gas-based solvents are recognized to be the preferred method in several studies. N₂ and CO₂ are the most common gas used during HnP injection [42,43]. Considering these two gases, CO₂ has a higher sweep efficiency and lower minimum miscibility pressure, thus making it the better choice for HnP scenarios [44,45]. However, employing CO₂ in HnP scenarios can come with obstacles due to high production costs and considerable corrosion on the wellbore and pipeline. N₂ HnP injection can become an economical alternative due to its cost-effectiveness and non-corrosive nature [43]. For CO₂ injection, maintaining the reservoir pressure above the minimum miscibility pressure of CO₂ is essential, ensuring higher oil recovery due to CO₂ swelling and viscosity reduction at miscible conditions [44,45].

After six injection cycles, Li et al. [31] observed a cumulative oil recovery factor of 61.49% for CO₂ HnP and 34.85% for N₂ HnP. Moreover, compared to N₂ injection, CO₂ has better injectivity in ultra-low permeability shale cores. Higher oil recovery potential for CO₂ HnP (33 to 85%) was observed in the work of Gamadi et al. [6] when compared to N₂ HnP oil recovery (10 to 50%). However, it should be noted that the results cannot be fully comparable due to inconsistent experimental parameters in terms of core samples and injection factors used for CO₂ and N₂ HnP.

Figure 16 features the recovery (%) for N₂ and CO₂ HnP scenarios, after 87 huff-n-cycles, at different pore confinement for the three fluid samples considered in this study. As shown in Figure 16, CO₂ HnP is more effective than N₂ for all fluid types and pore confinement scenarios. For both HnP scenarios, the recovery percentage increases as the pore size decreases for all the fluid samples. Moreover, for the N₂ HnP scenario, Sample 1 (base case fluid) and Sample 2 fluid (higher fraction of heavy hydrocarbon fluid) correspond to a higher recovery percentage, compared to Sample 3 fluid, with the only exception being for 5 nm pore confinement. Furthermore, a contrasting trend can be observed while comparing the recovery for Sample 1 and Sample 2 fluid. While CO₂ HnP recovery is higher in the case of Sample 2 fluid compared to Sample 1 fluid, for all pore confinement, N₂ HnP recovery is higher in the case of Sample 1 fluid.

4.4. Effect of Diffusivity

Oil–gas diffusion is another parameter of consideration in HnP EOR. Injected gas molecules diffuse into in situ oil due to the concentration gradient, causing the oil to swell, thus facilitating oil moving out of nanopores into different micro- and macro-fractures [30,46]. It should be noted that the diffusion efficiency in any porous media is also dictated by matrix tortuosity, which varies on the reservoir’s geographic formation and is higher in tight reservoirs. For a porous medium, Equation (5) can explain the displacement of one fluid by another in miscibility conditions [46].

$$\mathrm{Dispersion}\mathrm{Coefficient}=\frac{{\mathrm{D}}_{\mathrm{c}}}{\mathrm{F}\mathsf{\Phi }}+0.5{\mathrm{vd}}_{\mathrm{p}}\mathsf{\sigma }$$

(5)

where the bulk-diffusion coefficient (cm²/s) is D_c and matrix tortuosity is $\mathrm{F}\mathsf{\Phi }$. The average displacement velocity dictated by the matrix permeability is represented as v (cm/sec). Moreover, d_p represents the particle diameter-controlling pore-throat size (cm), and the media heterogeneity is expressed by $\mathsf{\sigma }$. The second term ($0.5{\mathrm{vd}}_{\mathrm{p}}\mathsf{\sigma }$) in Equation (5) represents the advection or mechanical mixing and is considered the dominating factor in conventional rocks at high porosity and permeability conditions. However, in tight rock formations at reduced permeability and pore-throat size, the advection factor can decrease by six to nine orders of magnitude, making the first term ($\frac{{\mathrm{D}}_{\mathrm{c}}}{\mathrm{F}\mathsf{\Phi }}$) in Equation (5), or the diffusive phenomenon, the dominant factor in controlling the dispersion [46].

The mechanism and effects of CO₂ diffusion during the HnP process need a substantial study to accurately predict the effectiveness of the CO₂ HnP. Despite observing a significant effect of molecular diffusion on incremental oil recovery during CO₂ solvent-soaking experiments using the Bakken core, Alharthy et al. [19] found negligible molecular diffusion effect on the incremental oil recovery in a history-matched field scale model, whereas Sun et al. [47] stated that CO₂ diffusivity is the primary contributing factor in optimizing cumulative oil production for the CO₂ HnP process. Their work considered a diffusion coefficient range of 0.01 cm²/s to 0.001 cm²/s for optimization scenarios. Using a similar range, the effect of CO₂ diffusivity in oil production was also verified by the work of Yu et al. [48]. In addition, using a CO₂ diffusion coefficient range of 0.0001 to 0.01 cm²/s for a CO₂ HnP sensitivity study, Yu et al. [49] concluded that CO₂ molecular diffusion has lower effects than parameters like CO₂ injection rate, injection time, soaking time, and the number of HnP cycles. The different ranges used in the literature necessitates finding accurate CO₂ diffusivity values for different reservoir formations.

This study uses a diffusivity coefficient of 0.0001 cm²/s and a tortuosity factor of 1 to compare the diffusion and no diffusion scenario effects for fluid samples at different pore confinement, as shown in Figure 17. It should be noted that tortuosity can vary based on the rock formation and must be accounted for in order to accurately estimate diffusivity effects during production. As seen in Figure 17, the production scenario and corresponding recovery can increase when diffusivity is considered, which is in agreement with the work of Yu et al. [49]. The cumulative oil production is highest for both diffusive and non-diffusive cases for Sample 1 fluid and lowest for Sample 3 fluid for all pore confinement scenarios.

4.5. Effect of Fracture Conductivity

For an unconventional reservoir, hydraulic fracturing is one of the most important operations needed for the commercial recovery of hydrocarbons [50,51,52]. The hydraulic fractures increase the fluid flow path needed for the hydrocarbons to move from the pores to the wellbore. In addition, the fractures also provide a pathway for injected solvent (CO₂) to come in contact with the residual oil, leading to improved recovery from the reservoir. The fracture properties, such as the fracture half-length and fracture conductivity, are uncertain parameters determined from the history-matching process. Fracture conductivity determines the flow capacity of the induced fractures and is determined from the product of fracture width and fracture permeability. Both fracture conductivity and fracture half-length can vary significantly from the designed parameter due to several factors such as proppant properties, injection rate and volume of the proppant, proppant embedment/crushing, stress-induced compaction, fracture hits, and numerous other uncertainties [53]. Dimensionless fracture conductivity (F_CD) is useful to account for the impact of fracture half-length and fracture conductivity for a reservoir with a particular permeability. The F_CD is defined as the ratio of the product of the fracture permeability and fracture width over the product of the formation permeability and fracture half-length. The value of F_CD is also critical in determining whether the hydraulic fracture has finite or infinite conductivity. There is no pressure drop in the fractures during production for infinitely conductive fractures. Therefore, further increases in conductivity, which require additional material and operational costs, will not positively impact productivity. For an infinitely conductive fracture, different threshold values for F_CD are greater than 30 [54,55]. In some studies, a value of F_CD greater than 50 is defined as the threshold for an infinitely conductive fracture [55]. We perform sensitivity analysis by varying the fracture permeability from 60 mD to 6000 mD, keeping all other parameters constant, which covers a wide range of F_CD.

Figure 18 shows the recovery factor for different F_CD ranging from 1.6 to 160 for natural depletion and optimized HnP EOR. For natural depletion (Figure 18a), the enhanced F_CD results in faster recovery initially, but the final recovery % does not appreciably change between each case. The recovery % for F_CD of 1.6 and 160 is 20.9% and 21.9%, respectively. However, Figure 18b shows that the fracture properties significantly impact the recovery factor from HnP EOR. For the F_CD of 1.6, the recovery % is lower than the natural depletion at 14.9%. However, the recovery % improves significantly when the F_CD increases to 80 (35.8%). The recovery% does not increase when the F_CD is doubled to 160 (Figure 18b, inset). This shows that we can significantly improve recovery from a HnP EOR by improving the fracture conductivity (and F_CD). However, it also shows a risk of lower recovery due to deterioration of fracture parameters due to proppant crushing, embedment, fracture closure, and other processes. This result also directly translates to other parameters needed for calculating F_CD, such as reservoir permeability and fracture half-length.

5. CO₂ Storage during HnP

Considered to be one of the key issues in global warming, CO₂ emissions into the atmosphere are increasingly the focus in different studies [56,57,58]. Among the CO₂-based EOR processes, the CO₂ HnP process has better potential to reduce climate change [59]. A significant portion of the CO₂ used for enhanced hydrocarbon extraction from reservoirs can become trapped, aiding in CO₂ sequestration [60]. Due to the CO₂ adsorption ability of organic matter, unconventional organic-rich reservoirs possess good CO₂ sequestration potential, despite most of the current CO₂ storage sites being conventional reservoirs [60,61,62]. After conducting a CO₂ storage assessment study during a, enhanced recovery operation, Liu et al. [63] concluded that more than 90% of injected CO₂ is instantaneously trapped through gas adsorption upon entering the reservoir.

The trapped CO₂ during the HnP process can be stored in four ways: (i) free CO₂ gas phase storage in available reservoir space where oil is produced, (ii) CO₂ dissolving as a solution gas into the remaining oil, (iii) CO₂ dissolving into the brine left in the reservoir, and (iv) CO₂ reacting with minerals presents in the reservoir and forming carbonaceous minerals like calcium carbonate, magnesium carbonate, ferrous carbonate, etc. [57]. Despite the potential high CO₂-storage capabilities during the CO₂ HnP scenario, the EOR process is usually optimized to minimize the amount of CO₂ injection and maximum oil recovery due to the high-cost nature of the procedure. Thus, to co-optimize both the oil recovery and the CO₂ storage, different objective functions along with weight factors are assigned to the CO₂ storage factor and oil recovery factor, based on the primary goal of the EOR-storage project, in several studies [57,63]. A mathematical approach adopted in the work of Zhou et al. [57] stated that free gas phase in available reservoir space and CO₂ dissolution into remaining heavy oil are the primary CO₂ storage aspects in the HnP process. It should be noted that CO₂ storage optimization is outside the scope of this study. Therefore, the stored CO₂ amount in this study does not reflect an optimized CO₂ storage scenario during HnP.

Figure 19 presents the CO₂ storage percentage after 87 CO₂ HnP cycles for fluid samples at different pore confinement. About 970 to 1067 ton CO₂ is stored per fracture during the HnP period considered in this study, corresponding to a total of 125,130 to 137,643 tons of CO₂ stored over the entire region. As seen in Figure 19, Sample 1 and Sample 2 fluid types have slightly higher CO₂ storage potential at smaller pore size, whereas the pore confinement effect on CO₂ storage is insignificant for Sample 3 fluid. Furthermore, it can be concluded that fluid type and pore confinement do not significantly affect CO₂ storage, as the difference in storage percentage is relatively small. We did not model any adsorption effect in the current study, which may further enhance the amount of CO₂ stored in the reservoir.

6. Discussion

This study optimized the CO₂ HnP process in maximizing the recovery factor for unconventional reservoirs, focusing on different fluid types, pore confinement effects, and other crucial completion parameters. By using variance-based sensitivity analysis, huff and puff time were identified as the significant parameters impacting the recovery parameters, whereas soaking time had minimal effect.

This study used critical property shift to evaluate the effect of pore confinement in phase behavior of hydrocarbons confined in nanopores. However, it should be noted that factors like high capillary pressure and component adsorption/desorption can also impact the phase behavior of hydrocarbons in nanopores. In addition, other fluid properties, including density, viscosity, and others, also deviate from the bulk properties, which can significantly affect the phase behavior of hydrocarbons confined in nanopores. These deviations are not explicitly modeled in this study, which may further affect the fluid phase behavior. However, critical property shift is also a commonly accepted method of modeling pore-confinement in nanopores, which is grounded in experimental and simulated data [19,38,64]. Jin et al. [38] compared the effect of using just the phase property shift and both capillary pressure and phase property shift. They observed that the maximum relative error between the methods compared to the experimental data was less than 5%, which means both approaches are appropriate for studying the effect of pore proximity on phase behavior and fluid properties. Furthermore, Teklu et al. [64] also observed that these effects are synergistic, resulting in bubble point depression due to both capillary pressure and critical property shift. The correlations used in this study (Equations (1)–(4)) are based on robust grand-canonical Monte Carlo (GCMC) and molecular dynamics simulations (MDSs) [65], which are easier to implement with critical property shifts in a compositional simulation.

We observed a significant reduction in the critical fluid mixture properties caused due to nanopore confinement (Table 4). However, the change due to pore confinement was mostly observable for critical pressure shift (P_c) and comparatively small for critical temperature shift (T_c)_. Although 3 nm pore size was not considered in this study, a similar P_c and T_c trend was also observable for 3 nm. Apart from critical pressure and temperature shift, the effect of factors like high capillary pressure and component adsorption/desorption will be considered in our future study for more in-depth analysis.

Another possible line of future work may include a detailed investigation of the effect of diffusivity and tortuosity factors in HnP production scenarios. Although the tortuosity factor changes based on the reservoir formation, accounting for tortuosity will yield accurate predictions for the HnP process. Furthermore, CO₂ sequestration aspects are also worth investigating during the HnP optimization process.

7. Conclusions

This study presents a numerical study to optimize the CO₂ HnP model in the Eagle Ford shale and understand the impact of nanopore confinement on the recovery factor. Based on the results of this study, the following conclusions can be obtained:

(1)

As the well loses productive time during the injection and soaking period, the recovery factor may be lower than natural depletion if the injection, soaking, and production period are not optimized. For example, compared to 21.9% recovery for natural depletion, a non-optimal HnP cycle had only 18% recovery, which is counterproductive to the desired goal of improving recovery (Figure 5).

(2)

The optimized CO₂ HnP process resulted in 32.03% recovery over 30 years, significantly higher than 21.9% from natural depletion (Figure 8).

(3)

The injection and production time are the two most important parameters to optimize a CO₂ HnP process. However, the soaking period had the least impact on the overall recovery. The ratio of around 2.7 for puff (production) and huff (injection) with a soaking period of fewer than 2.7 days resulted in the most optimal recovery for the base case fluid and reservoir conditions (Figure 9).

(4)

The confinement effect of nanopores enhances recovery compared to cases with bulk-phase PVT properties. Significant pore confinement (pore sizes ≤ 10 nm) results in around 3.4% additional recovery compared to the case without pore confinement. Hence, reservoir simulators need to include probable pore-size distribution to account for any uncertainty due to the change in PVT properties (Figure 12).

(5)

CO₂ EOR results in significantly improved recovery for a reservoir with a significant fraction of light hydrocarbons, with an over 300% increase in recovery compared to around 50% increase in recovery for a sample with a significant fraction of heavy hydrocarbons (C₇⁺) (Figure 15).

(6)

CO₂ showed higher effectiveness as an injection solvent than N₂ during the HnP process, as CO₂ HnP had a higher recovery % than N₂ for all the fluid samples at different pore confinement considered in this study (Figure 16).

(7)

Including diffusion resulted in a 40–60% recovery compared to a 30 to 40% recovery when no diffusion was considered. However, it was noteworthy that a lack of accurate diffusivity data can cause inaccuracy in prediction and must be accounted for in calculations (Figure 17).

(8)

The increase in dimensionless fracture conductivity (F_CD) can significantly improve the recovery from the CO₂ HnP process (Figure 18). However, if the F_CD is suboptimal due to fracture deterioration, the recovery can be lower than what is observed from natural depletion.

(9)

Although higher oil recovery is the primary optimization factor considered in this study, the considerable amount of CO₂ stored (970 to 1067 ton CO₂ per fracture) shows that CO₂ HnP could be an effective strategy for managing anthropogenic CO₂. Therefore, selecting both CO₂ storage and oil recovery as optimization parameters, and prioritizing CO₂ storage over oil production could be used if carbon sequestration is the main goal of the project.