## Abstract:

Gas injection is one of the most effective enhanced oil recovery methods for the unconventional reservoirs. Recently, CH_{4} has been widely used; however, few studies exist to accurately evaluate the cyclic CH_{4} injection in the Eagle Ford Shale considering molecular diffusion and nanopore effects. Additionally, the effects of operation parameters are still not systematically understood. Therefore, the objective of this work is to build an efficient numerical model to investigate the impacts of molecular diffusion, capillary pressure, and operation parameters.

#### Authors:

#### Yuan Zhang^{1}, Yuan Di^{2}, Yang Shi^{3} and Jinghong Hu^{1}

^{1}Beijing Key Laboratory of Unconventional Natural Gas Geology Evaluation and Development Engineering, China University of Geosciences (Beijing), China. ^{2}College of Engineering, Peking University, China. ^{3}Research Institute of Petroleum Exploration and Development, PetroChina, China

Received: 24 October 2018 / Accepted: 7 November 2018

The confined phase behavior was incorporated in the model considering the critical property shifts and capillary pressure.

Subsequently, we built a field-scale simulation model of the Eagle Ford shale reservoir. The fluid properties under different pore sizes were evaluated. Finally, a series of studies were conducted to examine the contributions of each key parameter on the well production. Results of sensitivity analysis indicate that the effect of confinement and molecular diffusion significantly influence CH_{4} injection effectiveness, followed by matrix permeability, injection rate, injection time, and number of cycles. Primary depletion period and soaking time are less noticeable for the well performance in the selected case.

Considering the effect of confinement and molecular diffusion leads to the increase in the well performance during the CH_{4} injection process. This work, for the first time, evaluates the nanopore effects and molecular diffusion on the CH_{4} injection. It provides an efficient numerical method to predict the well production in the EOR process. Additionally, it presents useful insights into the prediction of cyclic CH_{4} injection effectiveness and helps operators to optimize the EOR process in the shale reservoirs.

## Introduction

As reported, around 40% of the natural gas reserves are contained in the unconventional reservoirs all over the world [1]. The Eagle Ford shale is one of the productive oil shale reservoirs in the North America, which is located in the northwest of Texas. The main thickness of production varies from 50 to 300 feet [2,3]. The technologies of horizontal drilling and multistage hydraulic fracturing have attracted much attention, especially for the micro- and nano-pores in the unconventional reservoirs [4,5].

The combination of these technologies is extensively used to exploit the reserves in the tight and shale reservoirs [6,7]. However, Dejam et al. [8,9] pointed out that low permeability may increase the threshold pressure gradient, and large amount of oil still reserves in the formations, which requires gas injection for the production enhancement [10,11,12].

Due to the low permeability of shale rocks, waterflooding cannot perform as effective as that in the conventional resources. Hence, the attention has been attracted to gas injection in the unconventional reservoirs. Recent theoretical and experimental studies have shown that CH_{4} injection is more impressive than CO_{2} because it has high compressibility and the sources are rich [13,14].

Therefore, CH_{4} can take the place of CO_{2} in some situations. Alfarge et al. [15] pointed out that extending soaking period and increasing injection volume are benefit to improve the well production. Meng and Sheng [16] conducted the experiment of CH_{4} Huff-n-Puff injection in the core samples, confirming that condensate recovery increase by 6% in the Huff-n-Puff injection operation. However, most studies focus on the primary depletion production; the physical mechanisms on the effectiveness of cyclic CH_{4} injection are still limited.

Literatures have reported the evaluation of gas injection in shale oil reservoirs [15,17,18,19]. Sigmund et al. [20] and Brusilovsky [21] have conducted experiments in the porous media. They concluded that the phase behavior in the porous media deviates from the bulk phase. Recent studies have shown that nanopore confinement is an important factor since the nanopores cause high capillary pressure, affecting the properties of components as well as phase behavior further theoretically and experimentally [22,23,24,25].

Wang et al. [26] and Nojabaei et al. [23] modified the vapor-liquid phase equilibrium model based on Young-Laplace equation and Leverett J-function. They then incorporated the phase equilibrium model into the reservoir simulator to predict the well production in the tight oil reservoirs. Yang et al. [27] modified the Peng-Robison equation of state and introduced a new term representing the molecule-wall interaction.

They reproduced the collected data with an overall error of 7.64% compared to the molecular simulation results. Nanofluidic devices were applied to investigate the nanopore effects. Luo et al. [28] and Alfi et al. [29] conducted the nanofluidic experiment and they all concluded that the bubble point shifts with the effect of confinement. Salahshoor et al. [1] reviewed the mathematical models and experimental studies to compare the phase behavior in conventional reservoirs and tiny pores.

Molecular diffusion is another key mechanism affecting the gas injection effectiveness. Yu et al. [30] has investigated that molecular diffusivity should be correctly included in the simulation model. In the process of CO_{2}-CH_{4} displacement, diffusion is also an important mechanism [31]. Zhang et al. [32] compared the oil recovery of CO_{2}-EOR process and concluded that considering molecular diffusion is beneficial to improve the oil recovery. However, these investigations only focus on the CO_{2} injection process; the impact on the CH_{4} injection was not well understood. Recent studies have concluded that the diffusion coefficient of CH_{4} is on the same order of CO_{2} [33,34]; hence, the effect of molecular diffusion needs to be well examined.

*Figure 1.** The sketch of CH _{4} injection process in the fractured horizontal well (CH_{4} molecules diffuse into different nanopores).*

Figure 1 shows the sketch of CH_{4} injection process in the fractured horizontal well. As CH_{4} is injected, the molecules will move into the fractures and diffuse into the matrix. The fluid phase behavior in nanopores should be determined. Due to the nanopore effects, the injected components will not distribute homogenous among different sizes of pores. Additionally, it will result in different swelling effect in the gas injection from conventional reservoirs because of the confined phase behavior in nanopores.

From the literature survey, there are still some limitations behind the previous studies. Although the EOR process is efficient in the tight oil reservoirs, few studies focus on the effect of confinement on the EOR effectiveness, especially for the CH_{4} injection. Additionally, most of previous studies analyzed the operation parameters and the investigation of physical mechanisms affecting the CH_{4} injection is limited.

In order to fill this gap, we proposed a useful method incorporating the phase behavior model into the compositional simulator, which can accurately and efficiently evaluate the effect of key parameters on the CH_{4} injection effectiveness. This work systematically analyzes the physical mechanisms and operation parameters; it can be easily used in the operations of EOR process.

In this work, we evaluated the effect of confinement and CH_{4} molecular diffusion on the cyclic CH4 injection in the Eagle Ford shale reservoir. First, the methodology and detailed procedure were explained. Then, we built a reservoir model based on the fluid properties from the published Eagle Ford data [35]. The pore size distribution was obtained from the Eagle Ford rock samples [24]. Afterwards, a series of sensitivity analysis were performed to identify the impacts of the physical mechanisms on the effectiveness of cyclic CH_{4} injection. Finally, we conducted the sensitivity analysis including operation parameters and physical mechanisms. This work provides a better analysis and optimization of CH_{4} injection in the Eagle Ford shale reservoir.

## Methodology

### Shifts of Critical Properties

The nanopore effect on the critical temperatures and pressures has been reported in the literatures [24,36,37]. The interaction between the molecules and the pore walls is significant when the pore size is less than 10 nm [38,39]. In our study, the correlations published by Singh et al. [36] were applied to describe the critical property shifts [40]:

where r_{p} represents the pore-throat radius, ΔT^{∗}_{c} and ΔP^{∗}_{c} express the relative critical temperature and pressure shift, respectively. T_{cb} and P_{cb} are the bulk critical temperature and pressure, respectively. T_{cp} and P_{cp} are the critical temperature and critical pressure in the confined space, respectively. σ_{LJ }is the Lennard-Jones size parameter (collision diameter).

### Phase Equilibrium Calculation Considering Nanopore Confinement

In order to include the effect of confinement in the phase equilibrium model, the criterion of phase equilibrium can be rewritten as:

where f_{iL} and f_{iV} express the fugacity of component i in the liquid and vapor phases, respectively. T is the reservoir temperature. P_{V} and P_{L} represent the pressures of the vapor and liquid phase, respectively. P_{cap} is the capillary pressure in the confined space, which is calculated using the Young-Laplace equation [41], defining as:

where θ represents the contact angle. In this model, the contact angle is assumed as zero and the angle between organic and inorganic pores was neglected. The interfacial tension, σ is calculated using the following equation:

where ρ^{¯}_{L} and ρ^{¯}_{V} denote density of the liquid and vapor phases, respectively. [P]_{i} is the parachor of component i. Parachor of pure component and mixture can be obtained from the work by Pedersen and Christensen [42].

The Peng-Robinson equation of state [43] is modified as Equation (8) considering the effect of confinement:

where V_{m} and R represent the mole volume of component i and the universal gas constant, respectively. a and b are the parameters obtained by van der Waals mixing rules.

When the confinement is included, Equation (8) should be solved separately for liquid and vapor phases:

Where

Z_{L} and Z_{V} are the compressibility of liquid and vapor phases, respectively. The non-linear equations are solved by Newton-Raphson method. The roots of Equations (9) and (10) are determined with the criterion of Gibbs free energy minimization in the liquid and vapor phases.

In the following section, we first built a reservoir model based on the typical fluid and fracture properties, and then performed sensitivity analysis of different parameters in the cyclic CH_{4} injection. The fluid properties considering the nanopore effects were calculated through the phase equilibrium model. Afterwards, the properties were implemented into the reservoir simulator of CMG to evaluate the cyclic CH_{4} injection effectiveness [44]. The detailed workflow of this work is presented in Figure 2.

*Figure 2.** The workflow of evaluation of CH4 injection effectiveness.*

## Base Case

In the simulation study, we set up the reservoir model using the CMG-GEM simulator [44]. The domain of the model is: 7785 ft in x direction, 1300 ft in y direction, and 40 ft in z direction. A horizontal well was set in the middle of the reservoir model, along with 76 hydraulic fractures. The fracture spacing is 80 ft and the fracture half-length is 210 ft.

*Figure 3.** The reservoir simulation model in the cyclic CH _{4} injection.*

As reported, the reservoir temperature is 270 °F, the matrix porosity is 12%, and the initial reservoir pressure is 8125 psi. Table 1 summarizes the reasonable rock and fluid properties in the Eagle Ford shale reservoir [45]. The reservoir model is shown in Figure 3. Mohebbinia and Wong [46] have pointed out that molecular diffusion would be dominated in the low-permeability fractured reservoirs when gravitational drainage is inefficient. Hence, only diffusion mechanism was included in this work. The relative permeability curves are shown in Figure 4.

*Figure 4.** Relative permeability curves: (a) Water-oil relative permeability curve; (b) Liquid-gas relative permeability curve [38].*

* *

*Table 1.** Rock and fluid properties used in the reservoir model.*