Horizontal Wellbore Stability in the Production of Offshore Natural Gas Hydrates via Depressurization

Abstract

Wellbore stability is a crucial factor affecting the safe exploitation of offshore natural gas hydrates. As a sustainable energy source, natural gas hydrate has significant reserves, high energy density, and low environmental impact, making it an important candidate for alternative energy. Although research on the stability of screen pipes during horizontal-well hydrate production is currently limited, its importance in sustainable energy extraction is growing. This study therefore considers the effects of hydrate phase change, gas–water seepage, energy and mass exchange, reservoir deformation, and screen pipe influence and develops a coupled thermal–fluid–solid–chemical field model for horizontal-well natural gas hydrate production. The model results were validated using experimental data and standard test cases from the literature. The results obtained by applying this model in COMSOL Multiphysics 6.1 showed that the errors in all simulations were less than 2%, with errors of 12% and 6% observed at effective stresses of 0.5 MPa and 3 MPa, respectively. The simulation results indicate that the presence of the screen pipe in the hydrate reservoir exerts little effect on the decomposition of gas hydrates, but it effectively mitigates stress concentration in the near-wellbore region, redistributing the effective stress and significantly reducing the instability risk of the hydrate reservoir. Furthermore, the distribution of mechanical parameters around the screen pipe is uneven, with maximum values of equivalent Mises stress, volumetric strain, and displacement generally occurring on the inner side of the screen pipe in the horizontal crustal stress direction, making plastic instability most likely to occur in this area. With other basic parameters held constant, the maximum equivalent Mises stress and the instability area within the screen increase with the rise in the production pressure drop and wellbore size, and the decrease in screen pipe thickness. The results of this study lay the foundation for wellbore instability control in the production of offshore natural gas hydrates via depressurization. The study provides new insights into sustainable energy extraction, as improving wellbore stability during the extraction process can enhance resource utilization, reduce environmental impact, and promote sustainable development in energy exploitation.

1. Introduction

As energy supplies become increasingly constrained, natural gas hydrate has gradually attracted the attention of countries due to its vast reserves, high energy density, and environmental friendliness. As a sustainable energy source, natural gas hydrate not only has significant reserves but also a low environmental impact, making it an ideal candidate for replacing traditional fossil fuels. Natural gas hydrate is a crystalline compound formed by natural gas and water under low temperatures and high pressures [1]. Existing research shows that more than 97% of natural gas hydrates are distributed at the margins of maritime continents [2], and it is expected to become an alternative clean energy source [3,4,5,6].

To date, countries represented by the United States, Japan, China, South Korea, and India have formulated research plans for the exploration of offshore natural gas hydrate [7]. In line with the physical and chemical characteristics of gas hydrate, various hydrate production methods have been proposed, including depressurization, thermal stimulation, chemical injection, CO₂ replacement, and solid fluidization [8,9,10,11,12]. Among them, the depressurization method is mainly employed to reduce the hydrate reservoir pressure through engineering means, so that the hydrate in the reservoir can reach the phase equilibrium condition for decomposition. This method, not needing continuous stimulation, and being low in cost and suitable for large-scale exploitation, is the most promising among the traditional production methods and the most widely used in existing trial production projects [2,13].

In the production of hydrates via depressurization, as the solid hydrate in the porous media decomposes into gas and water, the cementation between the sand grains of the reservoir weakens, so the mechanical strength of the formation reduces accordingly, and wellbore instability is likely to occur. To increase the decomposition area of the hydrate reservoir and improve the production of hydrates, the depressurization-induced production through horizontal wells has been widely studied. For example, the feasibility of horizontal-well production in the South China Sea was tested from 2019 to 2020, and the well produced gas continuously for 30 days, with an average daily gas production of 2.87 × 10⁴ m³/d [14]. However, as the hydrate decomposition is faster during the depressurization-induced production through the horizontal well, the mechanical strength of the hydrate reservoir will diminish faster, and the wellbore instability risk of the horizontal well will be more serious.

In recent years, the problem of wellbore instability in hydrate drilling and production has gradually attracted the attention of many scholars. Ref. [15] proposed a multi-field coupling model considering fluid–solid coupling and solved the model to analyze the stability of reservoir and wellbore wall during drilling. They found that besides the fluid column pressure in the well, the wellbore stability was also related to the wall building property, filtration loss, and low temperature stability of the drilling fluid. Ref. [16] analyzed the plastic yield characteristics of the formation near the well by using the Mohr–Coulomb criterion within the FLAC3D 3.0 software framework. Ref. [17] developed fluid–solid coupling numerical simulation software based on the FEPG platform and studied reservoir and wellbore stability during hydrate production via depressurization. They found that the decomposition part of the reservoir in the minimum horizontal principal stress direction of the wellbore exhibited the poorest stability, being the position likely to first show instability and sand production in the entire reservoir. In addition, the authors also determined that the “hydrate decomposition effect”, production pressure difference, fluid–solid coupling effect, and horizontal stress heterogeneity all had a considerable effect on the stability of a near-wellbore reservoir. By combining TOUGH + Hydrate with FLAC3D 3.0, Refs. [18,19] found that overbalanced drilling could effectively reduce the stress yield zone of the formation around the wellbore, which was positive for maintaining wellbore stability. Ref. [20] established a three-dimensional solid finite element model of a hydrate reservoir’s cement sheath/casing using the ABAQUS 6.16 finite element software package to explore the effects of initial hydrate saturation, casing wall thickness, production pressure differences, and production time on the stability of the wellbore during hydrate production.

To avoid or mitigate sand plugging in the process of hydrate production, a screen pipe is often installed at the bottom of the well, but measuring the wellbore stability under these conditions has been challenging. To date, the mechanical stability of the screen pipe has been studied extensively. Ref. [21] deduced a formula to calculate screen pipe collapsing strength by establishing a screen pipe plastic hinge model to explore the influences of screen pipe phase angle, perforation diameter, perforation density, initial ovality, and diameter/thickness ratio on screen pipe collapsing strength. Ref. [22] examined the effects of perforation parameters on casing strength using the ANSYS 17.0 finite element software package and found that the stress concentration near the perforation noticeably reduced the casing collapsing strength, and damage to the perforated casing was most likely to develop along spiral lines. Refs. [23,24] developed finite element numerical models of screen pipe crushing strength and combined load via ABAQUS 6.16 to analyze the influences of parameters and screen pipe hole arrangement patterns, and the authors derived a simplified formula for calculating the crushing strength.

Ref. [25] suggested that for standalone screen completions, sand control precision should be designed at different levels based on the uneven degree of screen pipe plugging. The sand control precision of screen pipes within the gravel packing layer should be designed according to the sand particle size to ensure long-term stable hydrate production. Ref. [26] explored how to reduce the impact of mudcake plugging on the permeability of sand control screens. Ref. [27] analyzed the characteristics and performance of six types of sand control screens and proposed a clear design for sand control screens in clayey fine silt hydrate reservoirs. The newly designed screens exhibited excellent flow performance and were capable of meeting certain gas production requirements. Ref. [28] designed an experiment to evaluate the skin factor of the completion column with a combination of blank and screen pipes. By calculating the skin factor, they obtained the variation patterns of the skin factor for completion columns with blank and screen pipes under different conditions, which were then applied to production evaluation. Ref. [29] supported the development of multi-layer combination wire-wound screen pipes and anti-clogging filling gravel technology. However, hydrate-bearing sediments face more complex challenges during extraction compared to conventional reservoirs. The permeability of hydrate reservoirs is lower, and their pore structure is generally denser, which leads to slower hydrate decomposition. Furthermore, the release of gas and water during hydrate decomposition significantly impacts the reservoir’s stress state, thereby increasing the risk of wellbore instability. In addition, sand particles within the hydrate sediments continue to accumulate, increasing the risk of screen pipe plugging. The complex dynamic changes in external loads on the screen pipe mean that existing research findings cannot be directly applied to the actual hydrate production process.

In summary, the literature on wellbore stability in hydrate production is rich, but the stability of wellbores with a screen pipe has rarely been studied. In this work, the stability of a wellbore with a screen pipe during hydrate production was examined. Specifically, the stability and factors influencing the stability of the wellbore with a screen pipe were analyzed by establishing a model coupling heat–fluid–solid–chemical fields of a horizontal well with a screen pipe.

2. Coupling Model of Heat–Fluid–Solid–Chemical Fields for Horizontal Well Producing Natural Gas Hydrates

2.1. Constitutive Relationship of Natural Gas Hydrate Sediments

2.1.1. Overview of the Model

There are abundant studies on the constitutive models of hydrate sediments so far, and researchers have proposed many models to characterize the constitutive relationship of hydrate sediments, which can be divided into the elastic, elastic-plastic, nonlinear elastic, statistical damage theory, and critical state models. Among the many rock and soil mechanical models, the Duncan–Chang model [30] can accurately characterize the nonlinear elastic stress–strain relationship of hydrate-bearing sediments, and given its clearly defined parameters, it has been widely used [31]. The relationship between deviatoric stress and axial strain can be expressed as follows:

$$q={\displaystyle \frac{{\epsilon }_{\mathrm{a}}}{a+b\cdot {\epsilon }_{\mathrm{a}}}}$$

(1)

where q is the deviatoric stress, MPa; ε_a is the axial strain (dimensionless); and a and b are experimental constants (dimensionless).

In the equation above, a and b are the reciprocals of the initial tangent modulus of elasticity and the ultimate deviatoric stress, respectively, and substituting a and b into Equation (1), the equation is transformed into

$$q={\displaystyle \frac{{\epsilon }_{\mathrm{a}}}{\frac{1}{E_{\mathrm{i}}}+\frac{{\epsilon }_{\mathrm{a}}}{q_{\mathrm{ult}}}}}$$

(2)

where E_i is the initial tangent modulus of elasticity, MPa, and q_ult is the parameter that describes the maximum bearing capacity of a material before any plastic deformation occurs, MPa.

The breakdown ratio can be expressed as the ratio of the breakdown strength to the ultimate deviatoric stress:

$$R_{\mathrm{f}}={\displaystyle \frac{q_{\mathrm{f}}}{q_{\mathrm{ult}}}}$$

(3)

Equation (1) can therefore be further transformed into

$$q={\displaystyle \frac{{\epsilon }_{\mathrm{a}}}{\frac{1}{E_{\mathrm{i}}}+\frac{R_{\mathrm{f}}\cdot {\epsilon }_{\mathrm{a}}}{q_{\mathrm{f}}}}}$$

(4)

where R_f is the breakdown ratio, 0.82 [32], and q_f refers to the stress value at which material failure occurs, MPa.

Miyazaki [32] obtained a nonlinear elastic constitutive model of hydrate-bearing sediments by introducing the relationships between mechanical parameters E_i and q_f and between hydrate saturation and effective confining pressure, and the expressions are as follows:

$$E_{\mathrm{i}}=(1+\gamma \cdot S_{\mathrm{h}}^{\delta })\cdot {\sigma }_3^{\prime n}\cdot E_{\mathrm{i}0}$$

(5)

$$q_{\mathrm{f}}={\displaystyle \frac{2\cdot \cos {\phi }_{\mathrm{n}}}{1-\sin {\phi }_{\mathrm{n}}}}{c}_0+\alpha \cdot S_{\mathrm{h}}^{\beta }+{\displaystyle \frac{2\cdot \sin {\phi }_{\mathrm{n}}}{1-\sin {\phi }_{\mathrm{n}}}}{\sigma }_3^{\prime }$$

(6)

where σ₃′ is the effective confining pressure, MPa; E_i0 is the initial elastic modulus of the sedimentary medium with a hydrate saturation of zero, MPa; c₀ is the initial cohesion of the sedimentary medium with a hydrate saturation of zero, MPa; φ_n is the internal friction angle, °; and γ, δ, n, α, and β are parameters from fitting the experimental data of Toyoura sand by Miyazaki [32].

2.1.2. Breakdown Criteria

In the process of hydrate production, owing to the presence of wellbore, there is stress concentration near the wellbore wall. Once the wellbore pressure is lower than a critical value, the stress on the sediment around the wellbore will exceed its shear strength, and the wellbore wall will suffer shear damage, leading to a series of production problems such as sand production via hydrate formation. In this study, the Mohr–Coulomb criterion was used to identify the shear failure of hydrate sediments. Based on this theory, only the maximum principal stress, σ₁, and the minimum principal stress, σ₃, have an influence on the failure of the rock, which would fracture along a certain plane where the shear stress and the normal stress combine most critically [15]. The shear force resisting failure in homogeneous materials is equal to the sum of the frictional resistance and the cohesion C along the potential failure plane. This criterion is expressed using the following equation:

$${\tau }_{\mathrm{n}}=\tan {\phi }_{\mathrm{n}}{\sigma }_{\mathrm{n}}+C$$

(7)

where C is the rock cohesion [15], MPa.

The normal stress σ_n and shear stress τ_n can be expressed as follows:

$${\sigma }_{\mathrm{n}}={\displaystyle \frac{{\sigma }_1+{\sigma }_3}{2}}-{\displaystyle \frac{{\sigma }_1-{\sigma }_3}{2}}\sin {\phi }_{\mathrm{n}}$$

(8)

$${\tau }_{\mathrm{n}}={\displaystyle \frac{{\sigma }_1-{\sigma }_3}{2}}\cos {\phi }_{\mathrm{n}}$$

(9)

The Mohr–Coulomb criterion can therefore be further transformed into

$${\sigma }_1^{\prime }={\displaystyle \frac{1+\sin {\phi }_{\mathrm{n}}}{1-\sin {\phi }_{\mathrm{n}}}}{\sigma }_3^{\prime }+{\displaystyle \frac{2C\cos {\phi }_{\mathrm{n}}}{1-\sin {\phi }_{\mathrm{n}}}}$$

(10)

where σ₁′ and σ₃′ are the maximum and minimum principal stresses with pore pressure counted, MPa, respectively.

2.2. Governing Equation of Horizontal Well Producing Natural Gas Hydrate

2.2.1. Fluid–Solid Coupling Equation

(1)

The continuity equation

To simplify the calculation for large-scale hydrate production, some reasonable assumptions were made for the model in this study: ① the hydrate sediment reservoir was homogeneous and isotropic; ② the pore gas was compressible; ③ the rock skeleton, hydrate, and water had a constant density. On this basis, the continuity equation of offshore horizontal well producing natural gas hydrate was established as follows:

Sediment skeleton:

$${\displaystyle \frac{\partial [(1-\phi ){\rho }_{\mathrm{s}}]}{\partial t}}+\nabla \cdot [(1-\phi ){\rho }_{\mathrm{s}}{v}_{\mathrm{s}}]=0$$

(11)

Hydrate:

$${\displaystyle \frac{\partial (\phi S_{\mathrm{h}}{\rho }_{\mathrm{h}})}{\partial t}}+\nabla \cdot (\phi S_{\mathrm{h}}{\rho }_{\mathrm{h}}{v}_{\mathrm{h}})=-m_{\mathrm{h}}$$

(12)

Gas:

$${\displaystyle \frac{\partial (\phi S_{\mathrm{g}}{\rho }_{\mathrm{g}})}{\partial t}}+\nabla \cdot (\phi S_{\mathrm{g}}{\rho }_{\mathrm{g}}{v}_{\mathrm{g}})=m_{\mathrm{g}}$$

(13)

Water:

$${\displaystyle \frac{\partial (\phi S_{\mathrm{w}}{\rho }_{\mathrm{w}})}{\partial t}}+\nabla \cdot (\phi S_{\mathrm{w}}{\rho }_{\mathrm{w}}{v}_{\mathrm{w}})=m_{\mathrm{w}}$$

(14)

where ρ_s, ρ_h, ρ_g, and ρ_w are the densities of the sediment skeleton, hydrate, gas, and water, respectively, kg·m⁻³; v_s, v_h, v_g, and v_w are the actual velocities of the sediment skeleton, hydrate, gas, and water, respectively, m·s⁻¹; m_h is the hydrate decomposition rate, kg·s⁻¹; m_g is the gas production rate, kg·s⁻¹; and m_w is the water production rate, kg·s⁻¹.

In the equations above, v_s = v_h, ρ_s, ρ_h, and ρ_w were assumed to be constants, and ρ_g was calculated using

$${\rho }_{\mathrm{g}}={\displaystyle \frac{P_{\mathrm{g}}{M}_{\mathrm{g}}}{RT}}$$

(15)

where T is the system temperature, K; M_g is the molar mass of the gas, g·mol⁻¹; P_g is the percolation pressure of the gas, MPa; and R is the universal gas constant, J·mol⁻¹·K⁻¹.

(2)

Fluid–solid coupling seepage equation

During the production of natural gas hydrate, due to the flow of fluids in sediments and the decomposition of hydrate, the sediment skeleton will deform under the effect of stresses, and this deformation will influence the seepage behavior of fluids in pores. Gas–liquid two-phase flow exists in hydrate sediments, and its migration in porous media meets Darcy’s law. If the influence of gravity is ignored, it can be expressed as follows:

$$\phi S_{\mathrm{w}}{v}_{\mathrm{rw}}=-{\displaystyle \frac{K{K}_{\mathrm{rw}}}{{\mu }_{\mathrm{w}}}}\nabla P_{\mathrm{w}}$$

(16)

$$\phi S_{\mathrm{g}}{v}_{\mathrm{rg}}=-{\displaystyle \frac{K{K}_{\mathrm{rg}}}{{\mu }_{\mathrm{g}}}}\nabla P_{\mathrm{g}}$$

(17)

where v_rw and v_rg are the seepage velocity components of water and gas relative to the sediment skeleton, respectively, m·s⁻¹; K_rw and K_rg are the relative permeability of water and gas, respectively, m²; µ_w and µ_g are the dynamic viscosities of water and gas, respectively, mPa·s; Pw is the seepage pressure of water, MPa; and K is the permeability of the hydrate reservoir, m².

v_rw and v_rg were relative to the sediment skeleton, which can be calculated using

$$v_{\mathrm{rw}}=v_{\mathrm{w}}-v_{\mathrm{s}}$$

(18)

$$v_{\mathrm{rg}}=v_{\mathrm{g}}-v_{\mathrm{s}}$$

(19)

where v_s is the seepage velocity of the rock skeleton, m·s⁻¹.

The influence of rock skeleton deformation on gas–liquid flow can be obtained by substituting the relative flow velocity calculation equation and Darcy’s law equation into the continuity equation established above:

$${\displaystyle \frac{\partial (\phi S_{\mathrm{g}}{\rho }_{\mathrm{g}})}{\partial t}}+\nabla \cdot (-{\displaystyle \frac{{\rho }_{\mathrm{g}}K{K}_{\mathrm{rg}}}{{\mu }_{\mathrm{g}}}}\nabla P_{\mathrm{g}})+\nabla \cdot (\phi S_{\mathrm{g}}{\rho }_{\mathrm{g}}{v}_{\mathrm{s}})=m_{\mathrm{g}}$$

(20)

$${\displaystyle \frac{\partial (\phi S_{\mathrm{w}}{\rho }_{\mathrm{w}})}{\partial t}}+\nabla \cdot (-{\displaystyle \frac{{\rho }_{\mathrm{w}}K{K}_{\mathrm{rw}}}{{\mu }_{\mathrm{w}}}}\nabla P_{\mathrm{w}})+\nabla \cdot (\phi S_{\mathrm{w}}{\rho }_{\mathrm{w}}{v}_{\mathrm{s}})=m_{\mathrm{w}}$$

(21)

In the above formulas, the two terms $\nabla \cdot (\phi S_{\mathrm{g}}{\rho }_{\mathrm{g}}{v}_{\mathrm{s}})$ and $\nabla \cdot (\phi S_{\mathrm{w}}{\rho }_{\mathrm{w}}{v}_{\mathrm{s}})$ reflect the influence of the rock skeleton deformation on the seepage.

2.2.2. Solid Field Equation

To study the deformation of hydrate sediments, a solid field equation should be established. The solid field equation mainly includes the equilibrium equation and the geometric equation of the sediment skeleton. Neglecting the variation in momentum, the static equilibrium equation of the sediment skeleton can be expressed as follows:

$${\sigma }_{ij,j}-{({\alpha }_{\mathrm{B}}{\delta }_{ij}{P}_{\mathrm{p}})}_{,j}+f_i=0$$

(22)

where σ_ij is the stress tensor of the sediment skeleton; α_B is the pore pressure coefficient (dimensionless); P_p is the pressure of formation pore fluid, MPa; δ_ij is the Kronecker function; and f_i is the body force.

The geometric equation represents the relationship between strain and displacement, which can be expressed in tensor form as follows:

$${\epsilon }_{ij}={\displaystyle \frac{1}{2}}\left(u_{i,j}+u_{j,i}\right)$$

(23)

where ε_ij is the sediment skeleton strain tensor; and u is the displacement component.

2.2.3. Energy Conservation Equation

In the initial hydrate reservoir, due to the depressurization-induced production, the original equilibrium condition is broken, and as there is a temperature difference between the wellbore and the reservoir, heat transmission will take place; meanwhile, the decomposition and regeneration of hydrate will also cause changes in the reservoir temperature. Considering heat conduction, heat convection, external energy supply, and hydrate phase change heat, and neglecting kinetic energy, thermal radiation, and the Joule–Thomson effect, the energy conservation equation can be expressed as follows:

$$\begin{array}{l}[(1-\phi ){\rho }_{\mathrm{s}}{C}_{\mathrm{s}}+\phi S_{\mathrm{h}}{\rho }_{\mathrm{h}}{C}_{\mathrm{h}}+\phi S_{\mathrm{g}}{\rho }_{\mathrm{g}}{C}_{\mathrm{g}}+\phi S_{\mathrm{w}}{\rho }_{\mathrm{w}}{C}_{\mathrm{w}}]{\displaystyle \frac{\partial T}{\partial t}}\\ =\nabla \cdot \left[(n_{\mathrm{s}}{K}_{\mathrm{s}}+n_{\mathrm{h}}{K}_{\mathrm{h}}+n_{\mathrm{g}}{K}_{\mathrm{g}}+n_{\mathrm{w}}{K}_{\mathrm{w}})\nabla T\right]\\ -\nabla \cdot \left[(\phi S_{\mathrm{g}}{C}_{\mathrm{g}}{\rho }_{\mathrm{g}}{\nu }_{\mathrm{g}}\right.+\phi S_{\mathrm{w}}{C}_{\mathrm{w}}{\rho }_{\mathrm{w}}{v}_{\mathrm{w}})T]-m_{\mathrm{h}}\mathsf{\Delta }{H}_{\mathrm{h}}+Q_{\mathrm{in}}\end{array}$$

(24)

$$\mathsf{\Delta }{H}_{\mathrm{h}}=c_1+c_{2}T$$

(25)

where C_s, C_h, C_g, and C_w are the specific heat of the sediment skeleton, hydrate, gas, and water, respectively, J·m⁻³·s⁻¹; K_s, K_h, K_g, and K_w are the thermal conductivities of the sediment skeleton, hydrate, gas, and water, respectively, W·m⁻¹·K⁻¹; ΔH_h is the reaction heat of hydrate decomposition, kJ·mol⁻¹; Q_in is external heat source, J·m⁻³·s⁻¹; and c₁ and c₂ are the regression coefficients, at 56.599 kJ·mol⁻¹ and 0.016744 kJ·mol⁻¹·K⁻¹, respectively [33].

In addition, auxiliary equations with hydrate sediment reservoir characteristics are needed to accurately calculate the variations in reservoir parameters in hydrate production, for example, the hydrate decomposition kinetic, capillary force, permeability response, and porosity response equations.

2.2.4. Characterization Method of Screen Strength and Permeability

(1)

Characterization method for screen strength

According to their structure, screens can be divided into single-, double-, and three-layer screens, and regardless of screen type, a screen’s strength mainly depends on its base pipe [34,35]. Due to perforation, the casing reduces in integrity and whole strength, so before establishing the formation–screen coupling model, it is necessary to determine the characterization method of screen strength. Ref. [24] explored the effects of different hole arrangement patterns (Figure 1) and parameters on the crushing strength of the screen, and found that there were close relationships between the crushing strength of the screen and the hole arrangement patterns and parameters, which can be expressed mathematically as follows:

Parallel hole arrangement:

$$S_1={\displaystyle \frac{P_{\mathrm{b}1}}{P_{\mathrm{n}}}}=1-1.1391{({\displaystyle \frac{d}{L_1}})}^{1.12176}{({\displaystyle \frac{d}{C_1}})}^{0.36679}$$

(26)

Staggered hole arrangement:

$$S_2={\displaystyle \frac{P_{\mathrm{b}2}}{P_{\mathrm{n}}}}=1-0.92253{({\displaystyle \frac{d}{L_2}})}^{0.9657}{({\displaystyle \frac{d}{C_2}})}^{0.36834}$$

(27)

Spiral hole arrangement:

$$S_3={\displaystyle \frac{P_{\mathrm{b}3}}{P_{\mathrm{n}}}}=1-1.1535{({\displaystyle \frac{d}{L_3}})}^{1.28502}{({\displaystyle \frac{d}{C_3}})}^{0.13004}$$

(28)

where S₁, S₂, and S₃ are the crushing strength coefficients for the three hole arrangement patterns, respectively (dimensionless); P_b1, P_b2, and P_b3 are the crushing strengths of the screen pipes with the three hole arrangement patterns, respectively, MPa; L₁, L₂, and L₃ are, respectively, the axial spacings of holes in the three arrangement patterns, mm; C₁, C₂, and C₃ are, respectively, the circumferential spacings of holes in the three arrangement patterns, mm; P_n is the crushing strength of the casing before perforation, MPa; and d is the hole diameter, mm.

Equations (26)–(28) show that the crushing strength of the screen is inversely proportional to the hole diameter and hole density; that is, the larger the hole diameter and hole density of the screen are, the more significant the stress concentration caused by perforation is, and the easier the screen is crushed. In this study, the von Mises yield failure criterion was used to tell whether the screen would fail: after perforation, the screen would have stress concentration near the holes when subjected to external pressure, and when the Mises stress at a point in the screen was greater than the yield strength of the screen, local deformation would occur and lead to the instability of the screen. A stress concentration factor k was introduced, which is expressed as follows:

$$k={\displaystyle \frac{{\sigma }_i}{{\sigma }_0}}$$

(29)

where k is the stress concentration factor (dimensionless); σ_i is the Mises stress at a certain position after perforation, MPa; and σ₀ is the Mises stress at a position before perforation, MPa.

The authors of Ref. [20] demonstrated the following: the distribution of the stress concentration factor in the casing varied under different hole arrangement parameters and sizes of produced sand particles; the stress concentration factor was positively correlated with the hole diameter, hole density, and size of the produced sand particles in general; and the maximum stress concentration factor appeared near the hole inside the screen, reaching nearly 4.25 in their research range. In this study, since the established model was a two-dimensional equivalent screen pipe model unable to directly simulate the stress concentration caused by the presence of holes in the screen pipe, the equivalent Mises stress was approximately taken as the dependent variable of the yield failure standard, and the calculation method of the equivalent Mises stress based on Equation (29) is as follows:

$$\left[{\sigma }_{\mathrm{Mises}}\right]=k\cdot {\sigma }_{\mathrm{Mises}}$$

(30)

where $\left[{\sigma }_{\mathrm{Mises}}\right]$ is the equivalent Mises stress, MPa; and σ_Mises is the Mises stress, MPa.

(2)

Characterization method of screen permeability

In the actual production process, as the formation produces sand continuously, the sand accumulated outside the screen varies in amount and accumulation pattern constantly; accordingly, the screen’s sand retention can be divided into the beginning, the increasing retention, and the balance retention stages. Ref. [36] showed that for sand retention precision in the range of 20–60 µm, the time for different types of screens to reach the balance retention stage after sand production was 800–3600 s, which is almost negligible compared with the long period (one year) of hydrate production. In this study, to model performance, the balance retention permeabilities were therefore taken as the permeability values for the screens of different sand retention precisions.

To meet the requirement of appropriate sand control, the ratio of screen sand retention precision to the median grain size of formation sand should be kept in the optimal range between 3.8 and 4.2 [37]. The argillaceous fine silt in the hydrate reservoirs of the South China Sea has a median particle size of 10–15 µm, so the optimal range of the sand retention precision of the screen is 38–63 µm. After examining the balance retention permeabilities of various screens with different sand retaining precisions, Ref. [36] concluded that the balance retention permeabilities of various screens were in the order of magnitude of 100 µm² under the sand retaining precisions of 40 µm and 60 µm. Based on this conclusion, the permeability of the equivalent screen in the model was taken as 1 µm².

2.3. Model Validation

2.3.1. Validation of Solid Mechanical Model

To accurately calculate the dynamic evolution laws of mechanical parameters of the hydrate reservoir, verifying the accuracy of the constitutive model is particularly important. In this work, the accuracy of introducing the nonlinear constitutive model into COMSOL was validated by reproducing the triaxial compression experiments on hydrate-bearing sediment samples performed by Refs. [32,38] in COMSOL.

The device used in the experiments was a triaxial compression digital servo control system. The core preparation and triaxial compression experiments were all performed in the system. The core samples of hydrate sediments used in the experiments were prepared using Toyoura sand via the water saturation method, with a diameter of 50 mm, a height of 100 mm, an average porosity of 0.378, an average density of 1.64 g·cm⁻³, and a pore pressure of 8 MPa. The experiments were performed at a constant temperature of 278 K. Twelve groups of axial loading tests were conducted on core samples with gas hydrate saturations of 0, 0.3, and 0.4 at an axial strain rate of 0.1%/min⁻¹ under confining pressures of 8.5, 9, 10, and 11 MPa. The detailed conditions of each group of tests can be found in reference [38]. According to the above test conditions, a two-dimensional axisymmetric model was built in COMSOL. Different confining pressures were applied on the model, and the deviatoric stress–axial strain curves obtained from the simulations were compared with the experimental values.

Figure 2a–c show the deviatoric stress–axial strain curves calculated by the model at hydrate saturations of 0, 0.3, and 0.4, respectively. The solid lines in the figure plots represent the calculated values of the model in COMSOL; the dotted lines show the calculated values in the related literature; and the dash–dot lines show the fitted curves from the experimental data. With the rise in hydrate saturation, the fitted values from experimental data showed a more noticeable stress-softening characteristic, with the initial tangent elastic modulus and failure strength increasing accordingly; the rise in confining pressure also increased the initial tangent elastic modulus and failure strength to some extent. Compared with the calculated values given by Ref. [33], the calculated values obtained by applying the model of this study to COMSOL yielded errors of less than 2% in all of the simulations, except under the hydrate saturation of 0.3 and effective stresses of 0.5 MPa and 3 MPa (with errors of 12% and 6%, respectively). It is therefore deemed that simulation by applying the model to COMSOL is viable.

2.3.2. Verification by Simulating the Standard Test Question

In 2005, the National Energy Calculation Laboratory (NETL) of the United States began conducting many numerical simulations to investigate the impact of hydrate decomposition, and they established some standard test questions (based on the simulation results) for verifying simulation results via different software programs [39]. In this study, we combined experimental data and theoretical analysis to ensure that the simulation parameters reflect the conditions likely encountered in actual production processes, particularly in the selection of parameters such as pressure, temperature, and hydrate saturation. To verify the thermal–fluid–chemical portion of the established model, we selected Standard Question 3 for validation. In Standard Question 3, the simulation area is 1.5 mm × 1 m, with the initial conditions of the simulation area shown in

Table 1. Basic parameters of the verification model using the standard test question.

T0/°C	P0/MPa	S0	Ks/(10−3 µm2)	φ
6	8	0.5	300	0.3

. One side of the model is the depressurization end. Under hydrate production conditions, hydrate decomposition in the simulation area occurs at a pressure of 2.8 MPa and a temperature of 6 °C.

Based on this, a two-dimensional simulation area was established in COMSOL. The two-dimensional verification model was 1.5 m long and 1 m wide, and the initial conditions are shown in

Table 2. Basic parameters of the hydrate reservoir at SH2 station in Shenhu sea area.

Parameter	Unit	Value	Parameter	Unit	Value
Initial hydrate saturation	—	0.33	Horizontal ground stress	MPa	15.77
Formation porosity	—	0.4	Initial gas saturation	—	0.05
Initial temperature	°C	13.373	Initial liquid phase saturation	—	0.62
Initial pressure	MPa	14.508	Residual gas saturation	—	0.05
Initial permeability	10−3 µm2	2.38	Residual liquid phase saturation	—	0.1
Poisson’s ratio	—	0.35	Initial tangent modulus of elasticity	MPa	398
Vertical ground stress	MPa	16.86	Initial cohesion	MPa	0.3

. The boundary conditions of the model were set as follows: the pressure-dropping production end was set at a pressure of 2.8 MPa and temperature of 6 °C, while the other boundaries were set as having no-flow and thermal insulation constraints.

After the simulation started, the pressure-dropping end was kept at 2.8 MPa and 6 °C for 3 days, and the hydrate saturations, pressures, and temperatures in the horizontal axis direction obtained are shown in Figure 3. As clearly shown, the pressure in the simulation area gradually dropped to below the phase equilibrium pressure due to the decrease in pressure at the depressurization end after the depressurization began, and the hydrate started to decompose. As the decomposition of the hydrate is endothermic, the temperature in the simulation area fell, and the decomposition rate of the hydrate gradually slowed down. Finally, the simulation area more than 0.4 m away from the decompression end had a hydrate saturation stabilizing at about 0.4 and a temperature stabilizing at about 1.2 °C due to insufficient heat supply. The simulation area less than 0. 4 m from the depressurization end had higher temperatures all the way due to sufficient heat supply, driving the decomposition of the hydrate; as a result, the hydrate in the area 0–0.28 m from the depressurization end decomposed completely. After 3 days of depressurization, the calculated distributions of the hydrate saturation and temperature along the horizontal axis were basically consistent with the simulation results from other simulation software. However, the pressure in the simulation area showed minimal difference from the pressure at the depressurization end and was lower than the radial pressure distribution established using other numerical simulation software packages. Upon analysis, it is believed that the main reason for this discrepancy is the use of different permeability models, which leads to variations in pressure propagation speeds. Under different permeability models, there are certain differences in pressure distribution and propagation speeds. The two-phase gas–liquid seepage in sediments is primarily influenced by the absolute permeability of the hydrate sediment and the relative permeability of the gas–liquid phases. The basic hydrate sediment permeability models mainly include the parallel capillary, Kozeny particle, LBNL, and Tokyo models, from which many complex dynamic permeability models have been derived, incorporating the presence of hydrate in the pore space. However, these new models generally involve many complex parameters that require experimental fitting, which creates significant challenges for their application in numerical simulations. Ref. [40] used nuclear magnetic resonance (NMR) to measure hydrate-bearing sandstone samples from the Shenhu area in the South China Sea and studied the impact of natural gas hydrates on the permeability of hydrate sediments based on the Tokyo model. The permeability model used in their study is based on the Tokyo model, which considers the two-phase flow phenomenon (gas–liquid flow) in hydrate sediments. Error analysis indicates that under different permeability models, there are certain differences in pressure distribution and propagation speeds.

3. Wellbore Stability Analysis During Natural Gas Hydrate Production via Depressurization

3.1. Hydrate Reservoir–Screen Coupling Simulation Model

Based on the basic reservoir data of the SH2 station in the South China Sea, a square two-dimensional model with a side length of 10 m was established. The wellbore with a radius of 0.13 m was located at a corner of the square and represented by a quarter circle obtained from the difference set. It was assumed that the reservoir was isotropic in physical properties and had a uniform initial temperature and pressure within 10 m around the wellbore. The basic parameters of the simulation are shown in Table 2, and the basic parameters of the screen referred to the API casing standard and are shown in

Table 3. Basic parameters of the screen pipe.

Parameter	Unit	Value	Parameter	Unit	Value
Modulus of elasticity	GPa	210	Poisson’s ratio	—	0.3
Density	kg·m−3	7850	Yield strength	MPa	552
Permeability	µm2	1	Stress concentration factor	—	3

.

In Figure 4, part II represents the hydrate formation, and part I represents the screen, with a thickness set at 7.62 mm. Parts I and II constitute the formation–screen coupling model. To ensure the convergence and calculation speed of the model, the model was divided by a free triangular mesh. The complete mesh of the model included 2090 domain elements and 157 boundary elements. The mesh of the screen part was properly refined, where the minimum element size was 0.00075, the maximum element size was 0.2, and the maximum element growth rate was 1.2.

3.2. Influence of Screen on Physical Property Parameters of the Near-Wellbore Zone

The hydrate production at a pressure difference of 3 MPa in one year was simulated by the above model to obtain the distributions of reservoir effective stress and stability index. Figure 5 shows the distributions of effective stress and volumetric strain in the near-wellbore zone in the cases with and without the screen. It is shown that there was an area of stress concentration near the wellbore before installation of the screen pipe, which made the effective stress near the wellbore about 3.7 MPa higher than that inside the reservoir and uneven in distribution (Figure 6); meanwhile, the effective stress in the horizontal crustal stress direction was greater than that in the vertical crustal stress direction. In both cases, the volume strains near the wellbore were negative, indicating that the formation was compressed under the effects of crustal stresses and the wellbore, and the formation also showed certain inhomogeneity with the difference in crustal stresses in two directions, and had a larger volume strain in the horizontal crustal stress direction.

After the screen pipe was added, the effective stress inside the reservoir increased and became more uniform, while the stress concentration near the borehole weakened. The effective stress near the wellbore was only about 1.5 MPa higher than that inside the reservoir, as shown in Figure 6, and the maximum effective stress was no longer in the horizontal crustal stress direction but in the 42° direction, as shown in Figure 7a. This might be related to the squeezing effect of the deformed screen on the wellbore wall; the volumetric strain of the hydrate reservoir increased due to the squeezing effect of the deformed screen, and the volumetric strain in the horizontal crustal stress direction was larger, and the deformation in this direction was thus more significant, as shown in Figure 7b.

Figure 8 shows the distributions of the reservoir stability index and possible area of instability in the near-wellbore zone before and after the addition of the screen. Before adding the screen pipe, the reservoir had a stability index increasing locally near the wellbore and also greater heterogeneity in the horizontal crustal stress direction. Under this condition, part of the reservoir near the wellbore had a stability index greater than 0, indicating the risk of instability. After the screen was put in, the stability index near the wellbore dropped considerably, with a maximum value of only −0.56 MPa, and the maximum value occurred at the 42° direction instead of the horizontal crustal stress direction, which might be related to the squeezing effect of the screen after deformation on the wellbore wall of the hydrate reservoir. After the screen was added, the hydrate reservoir no longer exhibited a risk of instability.

3.3. Distributions of Screen Pipe Mechanical Parameters

Figure 9 shows the distributions of equivalent Mises stress, volumetric strain, and displacement around the screen pipe, and Figure 10 shows the distributions of equivalent Mises stress, volumetric strain, and displacement on the AB and CD sides of Figure 9, where 0° represents the horizontal crustal stress direction, and 90° represents the vertical crustal stress direction. Obviously, the equivalent Mises stress around the screen exhibited an uneven distribution, showing a trend of first decreasing and then increasing along the AB side, and an increasing trend along the CD side. It also showed an uneven distribution in the radial direction of the wellbore; in the horizontal crustal stress direction, the equivalent stress decreased gradually from point A to C, while in the vertical crustal stress direction, it increased from point B to D. Under the condition of a 3 MPa production pressure drop, there were therefore two positions with higher equivalent Mises stress values in the quarter model: the maximum value, 395.6 MPa, in the vertical crustal stress direction was located in the outer side of the wellbore, and plastic yield would not occur at this position, while the maximum value in the horizontal crustal stress direction, 570 MPa, was present at the inner side of the wellbore. As this was higher than the yield strength of the screen, the screen would have yield deformation and lose stability.

3.4. Sensitivity Analysis of Stress Distribution Around the Screen

3.4.1. Influence of Production Pressure Difference

The influence of the production pressure difference (dP) on the stability of the screen was explored by simulating the hydrate production in 1 year under the dP of 1, 2, 3, and 4 MPa, respectively. Figure 11 shows the distributions of equivalent Mises stress and volumetric strain around the screen. It is shown that with the rise in pressure difference, the equivalent Mises stress around the screen became more uneven in distribution, with the minimum value remaining basically constant, while the maximum value increased gradually. Specifically, as the dP increased from 1 MPa to 4 MPa, the maximum equivalent Mises stress on the screen increased from 387 MPa to 648 MPa (Figure 12). When the dP reached 3 MPa, the maximum equivalent Mises stress on the screen was greater than the yield strength of the screen, so wellbore instability would occur mainly inside the screen along the horizontal crustal stress direction; moreover, the instability area increased as the dP increased from 3 MPa to 4 MPa, while the proportion of screen instability area increased from 0.32% to 2.75% (Figure 13). At the same time, the distribution of volumetric strain became more significant too, and the position of maximum volumetric strain in the screen was located at point A. With the increase in pressure difference from 1 MPa to 4 MPa, the volumetric strain rose from −0.423 × 10^–3 to −0.651 × 10^–3, indicating a more noticeable deformation. Reducing the dP can therefore effectively improve the wellbore stability.

3.4.2. Influence of Wellbore Size

The cases with wellbore radii of 0.06, 0.10, 0.13, and 0.17 m were simulated in light of the API casing standard. Figure 14 shows the distributions of equivalent Mises stress and volumetric strain around the screen under different dPs. Apparently, with the increase in wellbore size, the part with a low equivalent Mises stress in the screen gradually reduced, and the part with a high equivalent Mises stress gradually expanded. When the wellbore had a smaller radius of 0.06 m, the maximum equivalent Mises stress in the screen was only 501 MPa, and the wellbore would not lose stability. As the wellbore radius increased to 0.10 m, the maximum equivalent Mises stress of the screen reached 573 MPa, which was greater than the yield strength of the screen, and wellbore instability would occur (Figure 15). However, as the wellbore size increased further, the rate of increase in maximum equivalent Mises stress on the screen reduced, and the area of wellbore instability increased further. As the wellbore radius increased from 0.06 m to 0.17 m, the proportion of unstable area rose from 0 to 0.78% (Figure 16). For the volumetric strain, when the wellbore had a smaller radius of 0.06 m, the volumetric strains near points B and C in the screen were greater than 0, indicating tensile deformation, while the volumetric strains at other positions were all negative, representing compressive deformation. With the increase in wellbore size, the strains at points B and C decreased and gradually transformed into compressive deformation, and the maximum deformation occurred at point A. With the increase in wellbore size, the maximum volumetric strain increased first, and remained stable after the wellbore radius reached 0.10 m (Figure 15). Reducing the wellbore size can therefore improve the wellbore stability to some extent.

3.4.3. Influence of Screen Thickness

Considering the API casing standard, the cases with screen thicknesses of 7.62, 10.92, 15.11, and 19.05 mm were simulated. Figure 17 shows the distributions of equivalent Mises stress and volumetric strain around the screen under different dPs. It is shown that with the increase in screen thickness, the low-stress region in the screen increased, while the high-stress region decreased in proportion. When the screen thickness increased from 7.62 mm to 15.11 mm, the equivalent Mises stress decreased from 569 MPa to 533 MPa, and the proportion of instability area decreased from 0.31% to 0. When the screen thickness reached 19.05 mm, the maximum equivalent Mises stress dropped to 455 MPa (see Figure 18). For the volumetric strain, when the thickness of the screen was 7.62 mm, the volumetric strain was negative in most parts except for the area near point B; that is, most regions in the screen were compressed, and the maximum volumetric strain was −0.583 × 10⁻³. With the increase in screen thickness, the volumetric strain at point C gradually shifted to tensile deformation, and the maximum volumetric strain remained basically unchanged; when the thickness of the screen reached 15.11 mm, the volumetric strain at point C transformed into tensile deformation; and with a further increase in screen thickness, the maximum volumetric strain decreased to −0.476 × 10⁻³ (Figure 19). The wellbore stability can therefore be improved to some extent by increasing the screen thickness.

4. Conclusions

(1)

Based on the basic reservoir data of the SH2 station in the South China Sea, considering the hydrate phase change, gas–water seepage, energy and mass exchange, reservoir deformation, and their mutual influence in the reservoir during the production of natural gas hydrate offshore, a model coupling thermal, fluid, solid, and chemical fields for a horizontal well producing natural gas hydrate was established. In addition, the model was verified via Miyazaki’s experimental data and a standard test question for hydrate production numerical simulation established by the NETL. The comparison results show that it is feasible to apply the model to analyze the stability of horizontal wellbores producing natural gas hydrates offshore.

(2)

The effects of screen pipes on the physical parameters of hydrate reservoirs near wellbores, the distributions of mechanical parameters around the screen pipe, and the sensitivity of related production parameters were analyzed. Installing the screen pipe hardly affects the decomposition of hydrate in the reservoir, but it can weaken the stress concentration in the near-wellbore zone of the reservoir, causing a redistribution of its effective stress and a significant reduction in the instability risk of the hydrate reservoir. The mechanical properties of the screen are not even in distribution; for example, the maximum values of equivalent Mises stress, volumetric strain, and displacement all generally appear in the inner side of the screen pipe in the horizontal crustal stress direction, so plastic instability is most likely to develop there. With the other basic parameters remaining identical, the maximum equivalent Mises stress and the instability area in the screen increased with the increase in dP, wellbore size, and stress concentration factor and with the decrease in screen thickness; meanwhile, the screen permeability has hardly any effect on the distribution of equivalent Mises stress and instability area of the screen.