## 1. Introduction

Gas hydrates are solid crystalline compounds which consist of water and guest molecules [

1]. Gas hydrates are formed under certain sets of high pressure and low temperature conditions, outside of which the gas and water species typically remain in separate phases [

2]. The guest molecules are gas molecules such as methane, ethane, propane, or carbon dioxide. These guest molecules are combined by hydrogen-bonded water. This natural gas is a premium fuel because it burns cleanly and produces less carbon dioxide [

3]. According to the latest research, approximately 230 natural gas hydrate deposits have been investigated globally, with reserves of about 1.5 × 10

^{15} m

^{3} of natural gas [

4]. Most natural gas hydrate deposits appears to be in the form of ‘structure I’, with methane as the trapped guest molecule, and its fraction is more than 90% [

5,

6].

Methane hydrate is also an important future energy resource for South Korea. The national projects, Ulleung Basin gas hydrate expeditions 1 and 2 (UBGH1 in 2007 and UBGH2 in 2010), were conducted to investigate the hydrate reserves and characteristics of gas hydrate-bearing sediments of the Ulleung Basin in the East sea of Korea [

7,

8,

9]. Based on the data of UBGH2, the estimated amount of natural gas-hydrate deposits in Ulleung Basin ranged from 4.4 × 10

^{6} to 9.2 × 10

^{9} m

^{3} [

10,

11,

12]. Recently, Bo et al. [

13] suggested deterministic estimation from rock physics modeling and pre-stack inversion, and estimated the total gas-hydrate and gas resource volume in Ulleung Basin as about 8.43 × 10

^{8} m

^{3} and 1.38 × 10

^{11} m

^{3}, respectively. These amounts can provide usable energy for more than thirty years to the whole nation.

Several methods of dissociating the gas hydrate from the hydrate-bearing sediment (HBS) have been suggested; thermal or inhibitor injection, depressurization, CO

_{2}/CH

_{4} exchange and combinations of these are representative production methods [

14,

15]. The main mechanisms of production methods are to dissociate the hydrate in the form of ice-crystals to a gaseous or liquid state by increasing the temperature or lowering the pressure. Among other methods, depressurization is the most common method, and has been applied as a major method of production for the field test (e.g., Mallik site in 2002, Nankai Trough in 2013) for gas hydrate production in the reservoir [

16,

17].

During depressurization to dissociate the methane gas from HBSs, significant ground settlement occurs. This is because of the strength and stiffness reduction induced by the phase change of hydrate (e.g., the state of hydrate converts from ice crystal state to liquid or gaseous state), and the increase of effective stress, which is the stress carried by the soil. Field test for gas hydrate production has several technical problem according to the complexity of mechanism aforementioned, and needs huge budget. Thus, it is essential to perform the numerical analysis to ensure the productivity of gas hydrate and stability of production facilities before the field test. Thermal-hydraulic-mechanical (THM) coupled numerical analysis should be performed to simulate the mechanism of gas hydrate production [

18]. Several numerical coupled simulators based on kinetic and equilibrium model have been developed (e.g., TOUGH+Hydrate [

19], HydrateResSim [

20], MH21 [

21], and STOMP-HYD-KE [

22]). Kim et al. [

23,

24] also developed the THM coupled simulator using FLAC3D, and verified with cylindrical core experimental data [

25]. The input parameters (e.g., boundary condition, intrinsic hydrate reaction rate, intrinsic permeability, initial hydrate saturation, overall heat conductivity, wellbore heating temperature, bottom hole pressure, etc.) and constitutive models (e.g., permeability model, stiffness model, and heat transfer model) for numerical analysis significantly affects both the energy recovery potential and geological hazards prevention [

26,

27,

28]. Kim et al. [

26] provided a comprehensive estimation for model parameters and properties based on vast data from field seismic surveys in Ulleung basin and laboratory experimental results. Numerical studies on the efficiency and productivity of gas hydrate production have been carried out continuously, while stability analysis for the hydrate-bearing sediments or wellbore has not been much considered, although stability analysis is essential to field production [

29,

30,

31,

32,

33,

34].

As depressurization is applied in a sediment, frictional forces are evolved at the interface between the production wellbore and the soil layer due to the stiffness differences of materials. These frictional forces result in axial stresses induced on the production wellbore [

35,

36,

37]. For this reason, soil–structure interaction (SSI) analysis should be conducted before the field test to properly evaluate the stability of the wellbore and HBS. The concepts of shear and normal coupling stiffness (also called interface stiffness) based on the linear Coulomb shear strength criterion are widely used to simulate interfacial stress behavior in numerical analysis [

38]. The non-linear behavior of the soil–structure interface and the displacement behavior were investigated according to the interface models [

39]. However, there is not much research on the stability analysis of the interface between the production wellbore and HBSs, which is related to the complex mechanism of gas hydrate production in the oceanic environment. Only a few studies have considered the wellbore stability during gas hydrate production [

24]. Geological stability was assessed for vertical and horizontal well production scenarios from a displacement perspective [

40]. Numerical analyses were performed to investigate the geomechanical behavior of HBS (e.g., pressure, temperature, hydrate saturation, and volumetric stain) and wellbore stability during methane production [

24,

41]. Kim et al. [

24] also restrictively considered the interface properties related to the interaction behavior between the sediment and wellbore. Previous studies have conducted the numerical analysis using the interface model, which considers mainly stiffness of sediments ignoring the confining stress change. The stability analysis during gas hydrate production has to consider the variation of confining stress according to depressurization. However, the research which conducted the stability analysis considering confining stress on interface model has not been published yet.

In this study, the authors investigated the effects of coupling stiffness and slippage phenomena on the stability of the wellbore under gas hydrate production. The present paper describes the concept of coupling stiffness, and the limitation of coupling stiffness model used in FLAC3D. The coupling stiffness models considering the confining stress were derived from the results of experimental tests using artificial Ulleung basin specimen, and applied to the T-H-M simulator developed in previous research [

24]. Qualitative numerical analyses were performed to investigate the effects of coupling stiffness and slippage phenomena on the stability of wellbore under depressurization. More specifically, parametric analysis was conducted to investigate the trend of the development of axial stress according to the shear and normal coupling stiffness, and effects of slippage phenomena on the evolution of axial stress of wellbore. Additionally, the relationship between the development of axial stress on wellbore and geotechnical behavior of hydrate bearing sediments under depressurization was investigated.

## 5. Conclusions

The aim of the present study was to evaluate the stability of a production wellbore under the depressurization method for gas hydrate production from hydrate bearing sediments. In order to evaluate the stability of the wellbore, it is essential to consider the interface behavior between the wellbore and hydrate bearing sediments. In this paper, an algorithm for wellbore stability analysis was suggested. The effects of the shear and normal coupling stiffness were investigated and coupling stiffness models, which considered confining stress and slippage phenomena, were suggested and applied to the algorithm. The key findings from this study are as follows:

The shear and normal coupling stiffness have to be considered to simulate the interface between the wellbore and the ground. From the parametric analysis relating coupling stiffness to wellbore stability, shear coupling stiffness has a significant effect on the development of axial stress of the wellbore while normal coupling stiffness does not affect the development of axial stress on the wellbore.

The shear and normal coupling stiffness are the function of confining stress. This study derived a coupling stiffness model considering confining stress by performing the direct shear test and consolidation test.

The shear coupling stiffness has to be considered differently from the depth of the wellbore to estimate the actual development of axial stress on the wellbore.

The compressive stress is induced at the wellbore due to the subsidence and heave of the ground.

As the effective stress with depressurization for gas hydrate production increases, slippage occurs between the wellbore and the ground because of shear failure. After shear failure, additional axial stress on the wellbore is not developed. For this reason, the maximum generated axial stress converges to a whole range during gas hydrate production.

Preferentially, the maximum axial stress occurs at the neutral point where displacement is zero, and gradually converges to the whole range of the wellbore. The final conclusion based on the key findings is that the coupling stiffness has to be considered differently from the depth of the wellbore, and the slippage phenomena also has to be considered to performed accurate stability analysis.

This study contains limitation and the authors suggest further work. In this study, the coupling stiffness models are valid only for Ulleung basin because the models were derived from the experimental results using Ulleung basin sediment. In order to improve the applicability of the models, it is necessary to develop them including factors (e.g., bulk and shear modulus) that can consider the characteristics of the soil type.