Research on Key Parameters of Wellbore Stability for Horizontal Drilling in Offshore Hydrate Reservoirs

Abstract

The South China Sea has abundant reserves of natural gas hydrates, and if developed effectively, it can greatly alleviate the pressure on the energy supply in China. But the hydrate reservoirs in the sea area are loose, shallow, porous, and have poor mechanical properties. During the drilling process, the invasion of drilling fluid into this kind of reservoir is likely to induce mass decomposition of gas hydrate and, in turn, a significant reduction in mechanical strength around the wellbore as well as instability of the wellbore. In this study, in light of the engineering background of exploratory wells at the South China Sea, a temperature and pressure field model in a gas hydrate reservoir at sea during open circuit drilling was established, and then, based on this model, a comprehensive model for the stability analysis of the well drilled in the hydrate reservoir at sea was constructed, both of them with errors of less than 10%. With these two models, the effects of different drilling parameters on wellbore stability were investigated. The gas and liquid produced by the decomposition of hydrates in the formation will increase the pore pressure in the formation, thereby reducing the effective stress in the formation. The closer the formation is to the wellbore, the more thorough the decomposition of hydrates in the formation and the greater the effective plastic strain. Keeping all other conditions constant, the increase in drilling fluid invasion pressure and temperature, as well as reservoir permeability, will lead to a decrease in the mechanical strength of the formation around the wellbore and an expansion of the wellbore yield zone. The results can provide a theoretical reference for the stability analysis at sea.

1. Introduction

Natural gas hydrate discovered in nature is usually white and decomposes quickly when heated [1,2,3,4,5]. During the drilling process, the drilling fluid circulating in the wellbore would exchange heat with the interface of the reservoir near the well and filter through the well wall into the formation [6,7,8]. Meanwhile, the phase transformation of hydrate would greatly weaken the original mechanical strength of the formation [9,10,11]. Moreover, hydrate reservoirs are mostly argillaceous siltstone with weak mechanical properties. These two factors coming together will make the risk of wellbore instability rise sharply in the process of hydrate reservoir drilling [12,13,14,15,16]. During the drilling process of horizontal wells in marine hydrate reservoirs, there is dynamic heat and mass transfer between the wellbore and the reservoir, as well as multiphase flow in the reservoir under fluid thermal solid coupling, which is a complex process of multi-physical field coupling. Therefore, revealing the heat and mass transfer mechanisms between the wellbore and reservoir, the degradation characteristics of formation mechanics, the coupling laws of multiple physical fields in the near wellbore zone, and conducting stability analysis of horizontal well drilling in hydrate layers are of great significance for the safe and efficient exploitation of hydrates.

During the drilling process of the horizontal well in the hydrate reservoir at sea, the drilling fluid invading the reservoir could make the solid hydrate particles decompose into gas and liquid in two phases. Consequently, the mechanical properties of the hydrate reservoir may change significantly, and the stress distribution state of the reservoir may change accordingly. So, an accurate assessment of the variations of hydrate reservoir mechanical properties during the drilling process is an important prerequisite for analyzing the wellbore stability. Yun et al. [10] (2007) investigated the effects of reservoir rock type, hydrate saturation, and effective confining pressure on the mechanical strength of hydrate reservoir by rock triaxial tests. Hyodo et al. [11] (2013) carried out stiffness experiments on samples of water and gas-saturated hydrate deposits and found that the stiffness and strength of hydrate deposits saturated with gas were significantly higher than those saturated with water. Through experiments, Lei et al. [17] reached the findings that in the formation of argillaceous siltstone, hydrate particles, when formed, would occupy the original space of the rock particles and be distributed in uneven micro-fractures in a belt or lenticular zone. This finding is very similar to the results of laboratory X-CT scanning and field logging. But in the sandy deposits with hydrate, things are completely different, either in the form of hydrate filling the pores or in the way of rock cementation. Therefore, argillaceous siltstone and sandy sediments containing gas hydrate differ widely in mechanical properties, porosity, and permeability. Hyodo et al. [18] (2014) investigated the shear strength and deformation characteristics of hydrate deposits during hydrate decomposition by depressurization and heating. Researchers at home and abroad have carried out a lot of studies on the mechanical properties of rocks containing hydrate, but few studies have covered the variation patterns of mechanical characteristics of the argillaceous siltstone reservoirs with weak cementation in the South China Sea under the disturbance by wellbore temperature and pressure in the drilling process.

In the process of drilling and mining of hydrate reservoirs, once the wellbore loses stability, many difficult problems could arise. As a result, researchers have conducted numerous studies on the stability of wellbores in hydrate formation. After simplifying the multi-phase flow caused by the hydrate, Freij-Ayoub et al. [19] established a wellbore stability evaluation model by coupling temperature, pressure, and mechanical fields. By extending the Biot consolidation model, Jin et al. [20] simulated the mechanical response characteristics of hydrate reservoirs in the process of horizontal well drilling and production, and the results provided a theoretical reference for the study of the stability of horizontal wellbores in hydrate reservoirs during drilling and production. Based on the theory of overloading and secondary loading surface, Sun et al. [21] built a mechanical constitutive model of a hydrate reservoir and simulated the formation settlement characteristics during the depressurization extraction of hydrate; moreover, they simulated the mechanical behavior of an argillaceous siltstone hydrate reservoir in the first year of depressurization extraction. Li et al. [22] considered the evolution of reservoir mechanical strength, wellbore temperature, and pressure parameters in depth; established a wellbore stability analysis model; and analyzed the stability evolution law of the wellbore area during shallow seabed drilling. Wang et al. [23] analyzed the influence of different factors on the stability of a horizontal wellbore by establishing a multi-physics coupling model between a drilling wellbore and marine natural gas hydrate reservoir. Wang et al. [24] derived analytical solutions of temperature, seepage, and mechanical parameters during hydrate reservoir drilling by coupling multiple fields. Most existent studies took vertical wells as research objects, but few studies covered the stability of horizontal wells during drilling, failing to reveal the strong coupling effect between the wellbore and hydrate reservoir in depth.

In summary, current research on the stability of hydrate wellbores is mostly focused on vertical wells, while there is relatively little research on the stability of wellbores during the drilling process of hydrate horizontal wells. Moreover, research on hydrate reservoir drilling still regards the wellbore and reservoir as two relatively independent physical models, and has not deeply revealed the strong coupling characteristics between the wellbore and hydrate reservoir. Therefore, it is necessary to establish a model coupling heat, fluid, solid, and chemical fields of the near-well zone, which takes the impact of drilling fluid loss on the reservoir into consideration in light of the drilling conditions, and to realize the analysis of wellbore stability in the drilling process by numerical simulation software-COMSOL. In this study, a model of horizontal well in the hydrate reservoir at sea during open-circuit drilling was established, and, on this basis, a comprehensive model for stability analysis was constructed, both with errors of less than 10%. This study can provide theoretical references for stability analysis of a horizontal wellbore and control of safety pressure in the wellbore during drilling at sea areas.

2. The Model of the Hydrate Reservoir at Sea Around the Horizontal Well During Drilling

Generally, shallow and hydrate reservoirs are mostly argillaceous siltstone, loose and porous, small in thickness, and average in mechanical properties. The whole horizontal well drilling process is complex, and needs to consider the influence of multi-physical fields to establish a coupled model around the wellbore.

2.1. Fluid–Solid Coupling Seepage Equation

During the drilling of a hydrate horizontal well, the drilling fluid may invade into the hydrate stratum and cause decomposition of hydrate. This is a complex coupling process of fluid and solid affected by multiple factors. The underlying assumptions are as follows:

(1)

The gas in the pores and pores in the formation were compressible, and the formation water was slightly compressible. The deformations of rock skeleton were all small in displacement.

(2)

The heat exchange in the formation only affected the decomposition of hydrate and had no effect on the properties of the rock skeleton and formation fluid.

(3)

The rock skeleton and reservoir hydrate did not change in density in the whole process.

(4)

The generalized Darcy’s law was applicable to the flow of all fluids in the formation.

2.1.1. Continuity Equation

Rock skeleton:

$$\nabla \cdot \left(1-\varphi \right)v_{\mathrm{s}}+{\displaystyle \frac{\partial \left(1-\varphi \right)}{\partial t}}=0$$

(1)

Hydrate:

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

(2)

Water phase:

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

(3)

Gas phase:

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

(4)

where φ denotes the formation porosity, dimensionless; v_g, v_w, and v_s denote the actual velocities of gas, water, and rock skeleton, respectively, m/s; S_g, S_w, and S_h denote the pore saturations of gas, water, and hydrate, respectively; ρ_g, ρ_w, and ρ_h denote the densities of gas, water, and hydrate, respectively, kg/m³; m_h denotes the decomposition rate of hydrate, kg/s; m_g denotes the formation rate of natural gas per unit volume of stratum, kg/s; and m_w denotes the formation rate of water per unit volume of stratum, kg·s⁻¹.

2.1.2. Darcy’s Law of Two-Phase Seepage

Water phase:

$$\varphi S_{\mathrm{w}}{v}_{\mathrm{rw}}=-{\displaystyle \frac{k{k}_{\mathrm{rw}}}{{\mu }_{\mathrm{w}}}}\left(\nabla P_{\mathrm{w}}-{\rho }_{\mathrm{w}}g\right)$$

(5)

Gas phase [25]:

$$\varphi S_{\mathrm{g}}{v}_{\mathrm{rg}}=-{\displaystyle \frac{k{k}_{\mathrm{rg}}}{{\mu }_{\mathrm{g}}}}\left(\nabla P_{\mathrm{g}}-{\rho }_{\mathrm{g}}g\right)$$

(6)

v_rw and v_rg denote the relative seepage velocity of water and gas to the rock skeleton, m·s⁻¹; μ_g and μ_w represent the gas phase viscosity and dynamic viscosity of the water phase, mPa·s; P_g and P_w denote the seepage pressure of the gas phase and water phase, respectively, MPa; k_rg and k_rw denote the relative permeability of the gas phase and water phase, respectively, m²; and k denotes the absolute permeability of the hydrate reservoir, m².

From the continuity equation and two-phase seepage equation, the fluid–solid coupling control equation of the hydrate reservoir was obtained:

$${\displaystyle \frac{\partial \left(\varphi {\rho }_{\mathrm{g}}{S}_{\mathrm{g}}\right)}{\partial t}}-\nabla \cdot \left(-{\displaystyle \frac{k_{\mathrm{rg}}k{\rho }_{\mathrm{g}}}{{\mu }_{\mathrm{g}}}}\left(\nabla P_{\mathrm{g}}-{\rho }_{\mathrm{g}}\mathrm{g}\right)\right)+\nabla \cdot \left(\varphi {\rho }_{\mathrm{g}}{S}_{\mathrm{g}}{v}_{\mathrm{s}}\right)=m_{\mathrm{g}}$$

(7)

$${\displaystyle \frac{\partial \left(\varphi {\rho }_{\mathrm{w}}{S}_{\mathrm{w}}\right)}{\partial t}}-\nabla \cdot \left(-{\displaystyle \frac{k_{\mathrm{rw}}k{\rho }_{\mathrm{w}}}{{\mu }_{\mathrm{w}}}}\left(\nabla P_{\mathrm{w}}-{\rho }_{\mathrm{w}}\mathrm{g}\right)\right)+\nabla \cdot \left(\varphi {\rho }_{\mathrm{w}}{S}_{\mathrm{w}}{v}_{\mathrm{s}}\right)=m_{\mathrm{w}}$$

(8)

2.2. Energy Conservation Equation

Without considering the Joule Thomson effect, the energy conservation equation is

$$\begin{array}{l}\left(\left(1-\varphi \right){\rho }_{\mathrm{s}}{C}_{\mathrm{s}}+\varphi S_{\mathrm{h}}{\rho }_{\mathrm{h}}{C}_{\mathrm{h}}+\varphi S_{\mathrm{w}}{\rho }_{\mathrm{w}}{C}_{\mathrm{w}}+\varphi S_{\mathrm{g}}{\rho }_{\mathrm{g}}{C}_{\mathrm{g}}\right){\displaystyle \frac{\partial T}{\partial t}}=\nabla \cdot \left(K_{\mathrm{e}}\nabla T\right)-\\ \nabla \cdot \left[\left(\varphi S_{\mathrm{g}}{C}_{\mathrm{g}}{\rho }_{\mathrm{g}}{v}_{\mathrm{g}}+\varphi S_{\mathrm{w}}{C}_{\mathrm{w}}{\rho }_{\mathrm{w}}{v}_{\mathrm{w}}\right)T\right]-m_{\mathrm{h}}\Delta H_{\mathrm{D}}+Q_{\mathrm{in}}\end{array}$$

(9)

where ρ_s denotes the density of the rock skeleton, kg·m⁻³; H_s denotes the enthalpy of the rock skeleton, J; H_h denotes the enthalpy of the hydrate, J; H_w denotes the enthalpy of the water, J; H_g denotes the enthalpy of the methane gas, J; ρ_h denotes the hydrate density, kg·m⁻³; K_e denotes the effective thermal conductivity of the hydrate reservoir, W·m⁻¹·K⁻¹; C_w denotes the specific heat of the water, J·kg⁻¹·K⁻¹; C_h denotes the specific heat of the hydrate, J·kg⁻¹·K⁻¹; C_s denotes the specific heat of the rock skeleton, J·kg⁻¹·K⁻¹; and ΔH_D denotes the reaction heat of the hydrate decomposition, J·mol⁻¹, calculated by the model proposed by Selim (1989) [26] in this work:

$$\Delta H_{\mathrm{D}}=\left\{\begin{array}{l}215.59\times {10}^3-394.945, 248K<T<273K\\ 446.12\times {10}^3-132.638, 273K\le T<298K\end{array}\right.$$

(10)

2.3. Equation of Solid Field of the Reservoir

2.3.1. Balance Equation of the Rock Skeleton

The balance equation of the rock skeleton solid field based on the effective stress is [27]

$${\displaystyle \frac{\partial {\sigma }_{xx}}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{xy}}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{zx}}{\partial z}}-\alpha {\displaystyle \frac{\partial P}{\partial x}}+f_x=0$$

(11)

$${\displaystyle \frac{\partial {\sigma }_{yy}}{\partial y}}+{\displaystyle \frac{\partial {\tau }_{xy}}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{yz}}{\partial z}}-\alpha {\displaystyle \frac{\partial P}{\partial y}}+f_y=0$$

(12)

$${\displaystyle \frac{\partial {\sigma }_{zz}}{\partial z}}+{\displaystyle \frac{\partial {\tau }_{xz}}{\partial x}}+{\displaystyle \frac{\partial {\tau }_{yz}}{\partial y}}-\alpha {\displaystyle \frac{\partial P}{\partial z}}+f_z=0$$

(13)

$$P=P_{\mathrm{g}}{S}_{\mathrm{g}}+P_{\mathrm{w}}{S}_{\mathrm{w}}$$

(14)

where σ_ij denotes effective stress component of the rock, MPa; α is the Biot coefficient, 1 in this study; P denotes the equivalent pore pressure, MPa; and f_i denotes the component of volume force, MPa.

The equation in tensor form is as follows:

$${\sigma }_{ij,j}+f_i-{\left(\alpha P{\delta }_{ij}\right)}_j=0$$

(15)

δ_ij, Kronecker symbol, δ_ij = [1 1 1 0 0 0]^T.

2.3.2. Geometric Equation of Reservoir Skeleton

For the hydrate reservoir, since the deformations of the rock skeleton are all small, it is expressed by the following equation [3,4]:

$$\left\{\begin{array}{c}{\epsilon }_x\\ {\epsilon }_y\\ {\epsilon }_z\\ {\gamma }_{xy}\\ {\gamma }_{yz}\\ {\gamma }_{zx}\end{array}\right\}=\left[\begin{array}{c}{\displaystyle \frac{\partial u}{\partial x}}\\ {\displaystyle \frac{\partial v}{\partial y}}\\ {\displaystyle \frac{\partial w}{\partial z}}\\ {\displaystyle \frac{\partial u}{\partial y}}+{\displaystyle \frac{\partial v}{\partial x}}\\ {\displaystyle \frac{\partial v}{\partial z}}+{\displaystyle \frac{\partial w}{\partial y}}\\ {\displaystyle \frac{\partial w}{\partial x}}+{\displaystyle \frac{\partial u}{\partial z}}\end{array}\right]=\left[\begin{array}{ccc}{\displaystyle \frac{\partial }{\partial x}}& 0& 0\\ 0& {\displaystyle \frac{\partial }{\partial y}}& 0\\ 0& 0& {\displaystyle \frac{\partial }{\partial z}}\\ {\displaystyle \frac{\partial }{\partial y}}& {\displaystyle \frac{\partial }{\partial x}}& 0\\ 0& {\displaystyle \frac{\partial }{\partial z}}& {\displaystyle \frac{\partial }{\partial y}}\\ {\displaystyle \frac{\partial }{\partial z}}& 0& {\displaystyle \frac{\partial }{\partial x}}\end{array}\right]\left\{\begin{array}{l}u\\ v\\ w\end{array}\right\}$$

(16)

It is expressed in tensor form as follows:

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

(17)

where ε_ij represents the strain tensor and u represents the displacement component, m.

2.3.3. Constitutive Equation of Reservoir Skeleton

In this study, the constitutive relation of the rock skeleton is expressed by the elastic–plastic constitutive equation [28]:

$$\mathrm{d}{\sigma }_{ij}=D_{ijkl}\mathrm{d}{\epsilon }_{kl}$$

(18)

where σ_ij denotes the stress increment; D_ijkl denotes the elastic–plastic matrix tensor; and ε_ij denotes the strain tensor.

The Mohr Coulomb criterion is commonly used in engineering to determine the yield of rocks. The Mohr Coulomb criterion holds that the shear failure of rocks on a surface is the result of the combined action of shear stress and normal stress on that surface, rather than solely the influence of shear stress. When a rock experiences the most unfavorable combination of shear stress and normal stress, it fails. The schematic diagram of rock failure is shown in Figure 1.

2.4. Kinetic Equations for Hydrate Decomposition

The chemical reaction equation of gas hydrate decomposition is [29]

$${\mathrm{CH}}_{4}n{\mathrm{H}}_2\mathrm{O}\to {\mathrm{CH}}_4+n{\mathrm{H}}_2\mathrm{O}$$

(19)

In which n denotes hydration number, dimensionless, and is taken as 5.75.

The gas production rate of the hydrate decomposition is calculated by the equations [30]

$$m_{\mathrm{g}}=k_{\mathrm{d}}{M}_{\mathrm{g}}{A}_{\mathrm{s}}\left(P_{\mathrm{e}}-P\right)$$

(20)

$$k_{\mathrm{d}}=k_0{e}^{-{\displaystyle \frac{\Delta E_{\mathrm{a}}}{RT}}}$$

(21)

$$A_{\mathrm{s}}=\varphi S_{\mathrm{h}}{\left({\displaystyle \frac{{{\varphi }_{\mathrm{wg}}}^3}{2K}}\right)}^{1/2}$$

(22)

From the rate of the gas production and chemical decomposition equation of the hydrate, the rate of hydrate decomposition and the rate of water production were derived:

$$m_{\mathrm{h}}=m_{\mathrm{g}}{\displaystyle \frac{n{M}_{\mathrm{w}}+M_{\mathrm{g}}}{M_{\mathrm{g}}}}$$

(23)

$$m_{\mathrm{w}}=m_{\mathrm{g}}{\displaystyle \frac{n{M}_{\mathrm{w}}}{M_{\mathrm{g}}}}$$

(24)

where m_h denotes the rate of the hydrate decomposition, kg·s⁻¹; k_d denotes the kinetic reaction rate of the hydrate, mol·m⁻²·Pa⁻¹·s⁻¹; A_s denotes the specific surface area of the hydrate particles, m⁻¹; ϕ denotes the absolute porosity of the hydrate reservoir, dimensionless; ϕ_wg denotes the effective porosity of the hydrate reservoir, dimensionless; P_e denotes the phase equilibrium pressure of the hydrate, MPa.

2.5. Model Definite Solution Conditions

The boundary conditions for this model are as follows.

Boundary flow continuity [31]:

$$-\stackrel{\rightharpoonup }{n}{\displaystyle \frac{{\rho }_{\mathrm{g}}k{k}_{\mathrm{rg}}}{{\mu }_{\mathrm{g}}}}\left(\nabla P_{\mathrm{g}}+{\rho }_{\mathrm{g}}\mathrm{g}\right)-q_g=0$$

(25)

$$-\stackrel{\rightharpoonup }{n}{\displaystyle \frac{{\rho }_w{k}_{\mathrm{rw}}k}{{\mu }_w}}\left(\nabla P_w+{\rho }_w\mathrm{g}\right)-q_w=0$$

(26)

where n denotes the unit normal vector at the flow boundary and q_g and q_w denote the flow rate of gas and liquid per unit area at the flow boundary, respectively, kg/m³/s.

Constant pressure boundary conditions:

$$P_{\mathrm{B}}=f_{\mathrm{p}}\left(x,y,z,t\right)$$

(27)

where f_p (x, y, z, t) is the pressure function at time t at a point (x, y, z) on boundary B, MPa.

The initial conditions of the seepage field are as follows:

$$P\left(x,y,z\right){|}_{t=0}=P_{\mathrm{l}}\left(x,y,z\right)$$

(28)

$$S{|}_{t=0}=S_{\mathrm{l}}\left(x,y,z\right)$$

(29)

P_l (x, y, z) is the pressure function, MPa and S_l (x, y, z) is the saturation function, dimensionless.

The initial conditions of the temperature field are as follows:

$$T\left(x,y,z\right){|}_{t=0}=T_{\mathrm{l}}\left(x,y,z\right)$$

(30)

T_l (x, y, z) is the temperature field function, K.

3. Numerical Solution Method and Model Validation

3.1. Mesh Division

In the process of solving the model, it is necessary to calculate the changes in fluid state at various spatial nodes inside the wellbore, so the model needs to be meshed. Divide the grid into quadrilateral grids. In order to improve the convergence, computational accuracy, and efficiency of the model, a mapping mesh partitioning model is adopted, which includes 6 vertex elements, 160 boundary elements, 1050 domain elements, and a minimum element mass of 0.9833. In addition, the grid was appropriately densified using a distribution function in the near wellbore area, as shown in Figure 2.

Length of any grid segment:

$$\Delta z_j=z_j-z_{j+1}=\Delta z$$

(31)

Total number of grids:

$$N=\mathrm{int}\left({\displaystyle \sum _{j}z/\Delta z}\right)$$

(32)

Any node location:

$$z_{j+1}=z_j+\Delta z$$

(33)

Among them, j = 1, 2, 3, 4…N.

3.2. The Numerical Solution Method

Horizontal well drilling in a hydrate reservoir at the sea is a complex coupling process. Moreover, considering the coupling between the wellbore and reservoir at the same time makes the problem more complicated. Based on the established coupling model around the horizontal well at the sea area, COMSOL software (the software version is 5.5) was used in this work to realize the simulation of stability of the horizontal wellbore in a hydrate reservoir by coupling the wellbore and reservoir conditions.

In order to better study the influence of fluid–solid coupling on wellbore stability, the following assumptions are made in this study:

(1)

The pores and gases in the formation are compressible, and the formation water is considered as a slightly compressible fluid. The deformation generated by the rock skeleton is small displacement deformation;

(2)

The heat exchange occurring in the formation only affects the decomposition of hydrates and has no effect on the rock skeleton and formation fluid properties;

(3)

The density of rock skeleton and reservoir hydrates remains unchanged throughout the entire process;

(4)

Hydrate reservoirs are uniformly isotropic;

(5)

The generalized Darcy’s law is applicable to the flow of all fluids in geological formations;

(6)

The relative velocity of hydrates to the rock skeleton is zero, and the relative velocity between the gas–liquid phases is zero.

3.3. Validation of the Model

In light of the well drilling process in the shallow gas hydrate reservoir in deep water, the stability of the horizontal well was simulated, with the horizontal section of the well assumed to be 400 m long and all the physical parameters of the simulated reservoir assumed to be isotropic. The basic parameters used in the simulations are shown in

Table 1. Basic drilling parameters.

Parameter	Unit	Value	Parameter	Unit	Value
Depth	m	1420–1464	Horizontal section length	m	400
Absolute porosity	-	0.4	Poisson’s ratio	-	0.35
Initial hydrate saturation	-	0.33	Absolute permeability	m2	4.935 × 10−14
Sea level temperature	°C	25	Pore pressure	MPa	14.508
Internal friction angle	°	12	Initial temperature of reservoir	°C	13.373
Vertical depth	m	1435.1	Minimum horizontal principal stress	MPa	15.47
Sea water depth	m	1235	Ultimate horizontal principal stress	MPa	15.47
Elastic modulus	MPa	Sh = 0:32	Vertical stress	MPa	16.36
Cohesion	MPa	Sh = 0:0.1	Temperature of injected drilling fluid	°C	25

. The two-dimensional model of the hydrate reservoir was established as a quarter circle with a radius of 4 m, where the horizontal well diameter is 0.1143 m.

The model was divided by mapping grids, which included 6 vertex units, 160 boundary units, and 1050 domain units and had a minimum unit mass of 0.9833. In addition, the grids near the wellbore were properly refined by the distribution function.

In the simulations by COMSOL Multiphysics, the boundary conditions were as follows:

(1)

AD was the boundary of the drilling fluid invading the hydrate reservoir, the temperature and pressure of the drilling fluid invading the reservoir were set, the volume fraction of the liquid phase was set at 1, and the boundary load condition of the solid field was set as the drilling fluid invading pressure.

(2)

AB and CD were both set as symmetrical boundaries, the solid field was set as roller supporting, with the normal displacement of 0.

(3)

BC was the outer boundary, which was set as the outflow boundary condition in the porous medium phase transfer and the porous medium heat transfer modules, as the boundary with the constant pressure of the initial pressure of the hydrate reservoir in the Darcy law module, and as the boundary with the load condition of the initial pressure in the solid field.

The proposed model was verified by using the drilling data of the SH2 vertical well in the hydrate reservoir of the Shenhu Sea area. In the layers at 200.1 m and 217.5 m below the mud line, the hydrate saturations calculated by the model are in good agreement with those from the field logging data, so these two reservoir layers were taken as the main research objects. The basic data are shown in

Table 2. Basic data of drilling fluid invading the hydrate reservoir.

Depth of Seabed/m	Formation Pressure/MPa	Formation Temperature/°C	Hydrate Saturation
200.1	14.508	13.357	0.33
217.5	14.689	14.178	0.27
Drilling fluid pressure/MPa	Drilling fluid temperature/°C	Horizontal stress/MPa	Vertical stress/MPa
14.771	14.35	15.47	16.36
14.975	15.2	15.74	16.70

.

The effects of drilling fluid invasion in these two layers were simulated by COMSOL software. The basic data are shown in

Table 3. Comparison of wellbore enlargement values from logging and from simulation.

Serial No.	Depth of Seabed/m	Measured Well Caliper Enlargement/mm	Simulated Well Caliper Enlargement/mm	Error/%
1	200.1	18.181	19.96	9.78
2	217.5	22.473	23.82	5.99

. The simulation results showed that the wellbore at these two layers expanded in some degrees, and the yield radii of the wellbore at these two layers after drilling fluid invasion were 0.00998 m and 0.01191 m, respectively, as shown in Figure 3. By comparing with the measured caliper data of the wellbore from logging, the errors at these two points were 9.78% and 5.99%, respectively, which verified the accuracy in simulating the horizontal well drilled in the hydrate reservoir at sea. Figure 4 shows the details.

4. Results and Discussion

This section presents the variation patterns of pressure and temperature, hydrate saturation, porosity, permeability, volume strain, and effective plastic strain of the formation at the cross-section of 200 m of the horizontal section from simulation in the drilling process.

4.1. Sensitivity Analysis of Basic Parameters

4.1.1. Distribution Pattern of Formation Pressure

The drilling fluid infiltrated into the formation constantly and the pore pressure in the formation increased gradually. When the two reached a balance, the drilling fluid stopped infiltrating. Figure 5 shows the distribution nephograms of the reservoir pressure and near-wellbore zone pressure at different moments; Figure 6 shows the distribution of the formation isobaric lines and the distribution of formation fluid streamlines 20 h after the drilling invasion; and Figure 7 shows the distribution patterns of the pressure around the well at different moments. As can be seen from the graph, with the increase in time, the wellbore pressure continues to propagate further into the formation, the pressure front continues to advance, and the pore pressure of the formation continues to increase, and in the early stage of drilling fluid invasion, due to the large pressure difference, the speed of pressure wave propagation is fast. After entering the middle and late stages of invasion, the pressure difference gradually decreases, the seepage effect weakens, and the speed of pressure propagation slows down.

4.1.2. Distribution Pattern of Formation Temperatures

High-temperature drilling fluids intrude into the formation under differential pressure, and the in situ temperature gradually increases after heat exchange with the drilling fluids. Once the temperature and pressure conditions of the hydrate phase equilibrium state are broken, the solid hydrate begins to decompose. Since heat transfer occurs throughout the drilling fluid intrusion into the hydrate reservoir, it is crucial to find out the pattern of reservoir temperature change after drilling fluid intrusion. Figure 8 shows the distribution cloud of the reservoir temperature and near-well zone temperature at different times. Figure 9 shows the distribution pattern of the temperature in the near-well zone at different times. From the graph, it can be seen that, with the continuous invasion of drilling fluid, the temperature inside the formation gradually increases. However, the propagation of temperature has a certain lag compared to pressure. The rate of temperature increase in the near wellbore zone is relatively slow, and the range of temperature changes in the formation is small. After 30 min, the pressure has already propagated to a range of 4 m around the wellbore. The temperature disturbance caused by the invasion of drilling fluid within 20 h only has a significant impact on the range of about 0.5 m around the wellbore. Therefore, the risk of wellbore instability is highest within a range of 0.5 m around the wellbore.

4.1.3. Distribution Pattern of Hydrate Saturation

As can be seen in Figure 10, Figure 11 and Figure 12, with the extension of the invasion time of the drilling fluid, the decomposition of the hydrate in the formation constantly increased in degree and range, and the hydrate decomposition front constantly advanced. The decomposition front divided the distribution of the hydrate saturation into two regions. From the decomposition front to the far end of the formation, the hydrate had not decomposed. From the wellbore to the decomposition front, the decomposition rate was faster, and the closer to the wellbore, the more sufficient the heat exchange, and the higher the degree of hydrate decomposition was. Due to the hysteresis of heat transfer of drilling fluid, the pressure front is always ahead of the hydrate decomposition front, that is, the pressure wave propagation range is always greater than the hydrate decomposition range.

4.1.4. Distribution Patterns of Porosity and Permeability

Figure 13 shows the distribution nephograms of formation-effective porosity and formation-effective permeability at different times after the drilling fluid invaded the formation. Figure 14 shows the distribution patterns of effective porosity and effective permeability in the near-wellbore zone at different times. The distribution characteristics of effective porosity and effective permeability are very similar to those of hydrate saturation of the formation.

Similarly, the distribution of effective porosity and permeability can be divided into two regions, from the wellbore to the decomposition front, as a lot of hydrate decomposed, the effective porosity and permeability rapidly increased, and from the decomposition front to the far end of the formation, they basically remained almost undisturbed. Therefore, decomposition is the main factor that affects the porosity and permeability. In the near-wellbore zone, the combination of the fluid–solid coupling effect with the hydrate decomposition effect led to the development of fractures in the reservoir massively, making the effective porosity and permeability there significantly higher than the undisturbed formation. A total of 20 h after the drilling fluid invaded the formation, the ultimate effective porosity of the formation was 0.45, about 1.13 times the absolute porosity of the formation, and the ultimate effective permeability of the formation was 5.64 × 10⁻¹⁴ m², about 1.14 times of the absolute permeability of the formation.

4.2. Sensitivity Analysis

This section presents our study of the key parameters affecting the stability of horizontal wellbores in hydrate reservoirs, and the simulation parameters are shown in

Table 4. Values of key parameters for horizontal wellbore stability analysis.

Pressure of Injected Drilling Fluid/MPa.	Temperature of Injected Drilling Fluid/°C	Absolute Porosity	Absolute Permeability/m2	Initial Hydrate Saturation
14.6	15	0.3	2.961 × 10−14	0.33
14.882	16.32	0.4	4.935 × 10−14	0.4
15	17	0.5	6.909 × 10−14	0.5
15.2	18	0.6	8.883 × 10−14	0.6

.

4.2.1. Pressure

From Figure 15 and Figure 16, with the increase in the pressure of the injected drilling fluid, the reservoir was more and more sufficient and had larger and larger ranges impacted. Therefore, the hydrate decomposition became more thorough, and the front of the hydrate decomposition enlarged. Meanwhile, the accelerated invasion of drilling fluid made the elastic modulus and cohesion of the stratum drop sharply, and the range of the elastic modulus and cohesion drop in the reservoir expanded, which together made the mechanical properties of the hydrate reservoir with weak cementation intrinsically decline further.

Therefore, for the formation of a hydrate reservoir with poor mud cake, the density of drilling fluid should be lowered as much as possible.

4.2.2. Temperature

Figure 17 and Figure 18 show that the decomposition region of hydrate gradually expands as the temperature of the injected drilling fluid increases, and the modulus of elasticity and cohesion of the formation also gradually decreases as a result of hydrate decomposition, and the range of the effective plastic strain around the well expands, with a corresponding increase in the plastic yield region of the wellbore. In addition, the expansion of the hydrate decomposition region also weakened the mechanical properties of the formation over a larger area around the wellbore and increased the extent of wellbore collapse. The final yield radius increased from 0.0527m to 0.14245 m (almost tripled) after 20 h of drilling fluid intrusion when the temperature of the injected drilling fluid was increased to 18 °C. The final diameter expansion reached 124.6%.

4.2.3. Reservoir Porosity

Figure 19 shows the variations of hydrate saturation, elastic modulus, and cohesion of the reservoir and wellbore yield area within 0.5 m of the wellbore 20 h after the drilling fluid invasion with other parameters remaining constant (assuming the reservoir porosity changed, but the formation mechanical parameters did not). Figure 20 shows the distributions of hydrate saturation and effective plastic strain around the wellbore 20 h after the drilling fluid invasion, respectively. We can see from the simulation results that the hydrate decomposition ranges at different reservoir porosities differed to some extent; with the increase in porosity of the hydrate reservoir, the hydrate decomposition range near the wellbore gradually reduced, the range of the formation with elastic modulus and cohesion drop also decreased, the range of effective plastic strain around the well also became smaller, and the region of the wellbore with plastic yield also shrunk accordingly. The increase in reservoir porosity makes the plastic yield area decrease. The risk of wellbore instability in the hydrate reservoir with higher porosity will be much greater than that in the reservoir with lower porosity after the complete decomposition of the hydrate.

4.2.4. Reservoir Permeability

Unlike the case of increasing porosity, as shown in Figure 21, with the increase in permeability, the hydrate decomposition range gradually increases, and the effective plastic strain range around the well expands. This is mainly due to the radial expansion of the hydrate decomposition range increasing the range of weakened formation mechanical properties, so the wellbore is more prone to instability.

5. Conclusions

In this study, a comprehensive model for the stability analysis of horizontal wells in hydrate reservoirs was established, the coupling of multi-physical fields in the drilling process of hydrate reservoirs was realized, the stability of horizontal wells drilled in hydrate reservoirs was examined, and relevant sensitivity analyses were carried out. The conclusions are as follows:

(1)

The intrusion of drilling fluid into the hydrate reservoir under differential pressures is the main factor leading to the decrease in the mechanical strength of the formation. Gases and liquids generated by hydrate decomposition in the formation increase the pore pressure in the formation, thereby reducing the effective stress in the formation. The combination of the two causes the risk of wellbore destabilization to rise sharply in weakly cemented, poorly diagenetic hydrate reservoirs.

(2)

Since the stress distribution around horizontal wells is different from that around vertical wells, the plastic yield zone of horizontal wells is no longer in the shape of a regular fan ring but is unevenly distributed. The closer the formation is to the wellbore, the more complete the decomposition of hydrates in the formation is, and the greater the effective plastic strain is.

(3)

All other conditions being held constant, increases in drilling fluid intrusion pressure, temperature, and reservoir permeability will lead to an expansion of the range of decline in formation mechanical strength around the wellbore and the wellbore yield area. The wellbore production area will decrease with increasing reservoir porosity, which is beneficial for wellbore stability during drilling, but the risk of wellbore destabilization may increase dramatically once prolonged production occurs and the hydrates around the wellbore are fully decomposed.

Due to limited time and energy, further in-depth research should be conducted in the following areas in the future:

(1)

Considering computational efficiency and accuracy, this article only established a two-dimensional numerical simulation model. In subsequent research, a three-dimensional physical model can be established to obtain more accurate research rules.

(2)

This article simplifies the influence of formation heat transfer, and in the future, research on the effects of formation heat transfer on rock skeleton and formation fluid properties can be considered.