ECD Prediction Model for Riser Drilling Annulus in Ultra-Deepwater Hydrate Formations

Abstract

To address the challenges of accurately predicting and controlling the annular equivalent circulating density (ECD) in ultra-deepwater gas hydrate-bearing formations of the Qiongdongnan Basin, where joint production of hydrates and shallow gas through dual horizontal wells faces a narrow safe pressure window and hydrate decomposition effects, this study develops an ECD prediction model that incorporates riser drilling operations. The model couples four sub-models, including the static equivalent density of drilling fluid, annular pressure loss, wellbore temperature–pressure field, and hydrate decomposition rate, and is solved iteratively using MatlabR2024a. The results show that hydrate cuttings begin to decompose in the upper section of the riser (at a depth of approximately 600 m), causing a reduction of about 2 °C in wellhead temperature, a decrease of 0.15 MPa in bottomhole pressure, and an 8 kg/m³ reduction in ECD at the toe of the horizontal section. Furthermore, sensitivity analysis indicates that increasing the rate of penetration (ROP), drilling fluid density, and flow rate significantly elevates annular ECD. When ROP exceeds 28 m/h, the initial drilling fluid density is greater than 1064 kg/m³, or the drilling fluid flow rate is higher than 21 L/s, the risk of formation loss becomes considerable. The model was validated against field data from China’s first hydrate trial production, achieving a prediction accuracy of 93%. This study provides theoretical support and engineering guidance for safe drilling and hydraulic parameter optimization in ultra-deepwater hydrate-bearing formations.

1. Introduction

Natural gas hydrate (NGH), as a new type of clean energy, is widely distributed in China with abundant reserves and is regarded as a potential alternative energy resource. The NGH reservoirs in the Qiongdongnan Basin are typically characterized by shallow burial depth (120–180 m below the mudline) and weakly cemented or unconsolidated formations and thus are highly prone to complex drilling problems such as kicks, losses, and borehole collapse during exploration and development [1,2,3,4,5]. In the upcoming trial production, a dual horizontal well scheme for the co-production of hydrates in the upper reservoir and shallow gas in the lower reservoir has been planned. However, the equivalent density of fracture pressure in the upper hydrate reservoir is only 1.07–1.09 g/cm³, while that in the lower shallow gas reservoir is 1.11–1.12 g/cm³, forming an extremely narrow safe pressure window [6,7,8,9]. During drilling, the annular Equivalent Circulating Density (ECD) must be precisely controlled between the collapse pressure and fracture pressure—not only to avoid wellbore instability in the upper hydrate reservoir but also to prevent fracturing of the overlying fragile hydrate formation when penetrating the shallow gas reservoir.

Furthermore, temperature and pressure perturbations induced by drilling fluid may trigger hydrate decomposition around the borehole, weakening the formation strength and aggravating borehole instability risks [10,11]. The challenge is even more severe in the Qiongdongnan Basin, where the in situ temperature of hydrate reservoirs is relatively low (7–15 °C), making them highly sensitive to thermal disturbances. Even a slight increase in temperature may easily exceed the phase equilibrium boundary, triggering hydrate dissociation, leading to pore pressure buildup and skeletal weakening of the formation. Such processes are considered potential mechanisms for catastrophic submarine landslides (e.g., Storegga Slide and Cape Fear Slide) and gas leakage [12,13,14]. Therefore, accurate prediction and control of annular ECD in ultra-deepwater hydrate-bearing formations is a key prerequisite for safe and efficient drilling.

With regard to ECD prediction, extensive research has been conducted worldwide. Hongbin Luo et al. [15] developed a deepwater ECD prediction model considering temperature, cuttings decomposition, and the riser lifting system but neglected the effects of wellbore temperature–pressure variations on drilling fluid properties. Geng Zhang et al. [16] proposed a detailed annular ECD prediction model coupling drilling fluid density, rheological parameters, and wellbore heat transfer and highlighted the significant impact of temperature–pressure effects on drilling performance. However, their regression coefficients for drilling fluid properties relied heavily on laboratory data from specific fluid formulations, thus limiting applicability. Yongde Gao et al. [17] incorporated temperature–pressure effects and riser pressurization into a deepwater high-temperature and high-pressure (HTHP) ECD prediction model but failed to consider the influences of cuttings beds and drill string eccentricity on annular pressure losses. In addition, Huangang Zhu et al. [18] developed a bottom-hole ECD prediction model for managed pressure drilling in deepwater, which considered temperature, pressure, and cuttings concentration, but its structural simplicity led to relatively low prediction accuracy.

In terms of wellbore temperature and pressure field studies, Yonghai Gao and Baojiang Sun et al. [19] established a multiphase flow and heat transfer model considering hydrate dissociation and phase change heat, analyzing temperature–pressure distribution characteristics during hydrate drilling. Deqiang Tian et al. [20] developed a transient wellbore temperature–pressure coupling model that considered heat and mass transfer induced by riser flow but overlooked radial heat conduction between annulus and drill string. Lei Wang et al. [21] proposed a wellbore temperature prediction model for hydrate horizontal well drilling, investigating the effects of drill string friction, circulation time, and drilling fluid flow rate, but without accounting for the temperature variations induced by hydrate decomposition. Mengmeng Wang et al. [22] experimentally studied temperature–pressure variations during hydrate crystallization and dissociation, but the laboratory conditions (−5 to 85 °C, ≤20 MPa) differed substantially from actual ultra-deepwater drilling environments, limiting engineering applicability.

In summary, existing studies have mainly focused on the influence of drilling fluid properties under HTHP conditions, riser pressurization, and multiphase flow heat transfer coupling on ECD prediction. However, research on annular ECD prediction under the unique drilling conditions of ultra-deepwater hydrate-bearing formations remains scarce. Moreover, no studies have been reported on annular ECD prediction in ultra-deepwater wells with risers, either domestically or internationally. Therefore, building upon previous work, this study proposes an annular ECD prediction model tailored for ultra-deepwater hydrate-bearing formations with riser drilling. The model comprehensively considers the characteristics of high pressure, low temperature, and hydrate decomposition. It is programmed and solved iteratively using Matlab to investigate the effects of hydrate cuttings decomposition and key hydraulic parameters on annular ECD. The objective is to provide theoretical guidance and technical support for annular ECD prediction and hydraulic parameter optimization in ultra-deepwater hydrate drilling.

2. Mathematical Model

The Equivalent Circulating Density (ECD) is defined as the sum of the Equivalent Static Density (ESD) and the Additional Equivalent Circulating Density (AECD) and is expressed as follows:

$$\mathit{ECD}=\mathit{ESD}+\mathit{AECD}$$

(1)

ESD represents the equivalent drilling fluid density corresponding to the hydrostatic pressure at any given depth in the wellbore. Since ESD varies with well depth and drilling fluid density, it can be calculated using the following equation:

$$ESD={\displaystyle \frac{P(H,\rho )}{gH}}={\displaystyle \frac{P_0+{\displaystyle {\int }_{H_0}^H\rho gdH}}{gH}}$$

(2)

where P₀ is the surface pressure (MPa); $\rho$ is the drilling fluid density (g/cm³); $g$ represents the gravitational acceleration (m/s²); ${\displaystyle {\int }_{H_0}^H\rho gdH}$ corresponds to the hydrostatic pressure at a true vertical depth H (MPa).

AECD quantifies the additional density equivalent resulting from the total annular pressure loss during circulation. It is computed as follows:

$$AECD={\displaystyle \frac{P_a}{gH}}$$

(3)

where P_a represents the total annular pressure loss from the surface to the specified depth (MPa).

Consequently, the accurate prediction of annular ECD hinges on the precise calculation of both ESD and the total annular pressure loss. The calculation of ESD is complex as it is significantly influenced by the downhole temperature and pressure fields, which alter the fluid’s intrinsic density. Simultaneously, the total annular pressure loss is governed by complex multiphase flow dynamics and heat transfer phenomena, particularly due to the transport and decomposition of hydrate cuttings. As illustrated in Figure 1, the pressure loss calculation must be segmented to account for the distinct hydraulic characteristics of the riser, deviated, and horizontal sections of the wellbore. To construct a comprehensive predictive framework, it is therefore necessary to develop and couple four interdependent sub-models: (1) an equivalent static density model, (2) an annular pressure loss model, (3) a wellbore temperature-pressure field model, and (4) a hydrate decomposition rate model.

2.1. Static Equivalent Density Calculation Model for Drilling Fluid

The static equivalent density of drilling fluid is highly sensitive to the downhole temperature and pressure conditions. The change in density with respect to pressure (P) and temperature (T) can be described by the following partial differential equation:

$${\displaystyle \frac{d\rho }{dh}}(P,T)={\displaystyle \frac{\partial \rho }{\partial P}}{\displaystyle \frac{dP}{dh}}+{\displaystyle \frac{\partial \rho }{\partial T}}{\displaystyle \frac{dT}{dh}}$$

(4)

As well depth increases, the concurrent rise in temperature and pressure induces two opposing effects on drilling fluid density. The elastic compression effect refers to the density increase resulting from fluid compression under elevated pressure. Conversely, the thermal expansion effect describes the density decrease caused by fluid expansion at higher temperatures. To quantify these effects, the coefficient of elastic compression is defined as follows [23]:

$$B_e={\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial \rho }{\partial P}}$$

(5)

Based on the work of Peters et al. [24], this coefficient is a function of both temperature and pressure, which can be empirically expressed as follows:

$$B_e=B_0[1+B_1(P-P_0)+B_2(T-T_0)]$$

(6)

where B₀, B₁, and B₂ are empirical constants and dimensionless.

By combining Equations (5) and (6), the following relationship is obtained:

$${\displaystyle \frac{\partial \rho }{\partial P}}=B_0\rho [1+B_1(P-P_0)+B_2(T-T_0)]$$

(7)

Similarly, the thermal expansion coefficient of the drilling fluid can be expressed as follows:

$$A_e={\displaystyle \frac{1}{\rho }}{\displaystyle \frac{\partial \rho }{\partial T}}$$

(8)

The thermal expansion coefficient is also a function of temperature and pressure and can be represented as follows:

$$A_e=A_0[1+A_1(T-T_0)+A_2(P-P_0)]$$

(9)

where A₀, A₁, and A₂ are empirical constants and dimensionless.

By combining Equations (8) and (9), the following expression is derived:

$${\displaystyle \frac{\partial \rho }{\partial T}}=A_0\rho [1+A_1(T-T_0)+A_2(P-P_0)]$$

(10)

Finally, by coupling Equations (7) and (10), the drilling fluid density under the influence of both temperature and pressure can be formulated as follows:

$$\begin{array}{l}\rho (P,T)={\rho }_0{e}^{\gamma (P,T)}\\ \gamma (P,T)={\gamma }_P(P-P_0)+{\gamma }_{PP}{(P-P_0)}^2+\\ {\gamma }_T(T-T_0)+{\gamma }_{TT}{(T-T_0)}^2+{\gamma }_{PT}(P-P_0)(T-T_0)\end{array}$$

(11)

where P₀ and T₀ represent the surface pressure and temperature, respectively; ρ₀ is the initial drilling fluid density (g/cm³); γ_P, γ_PP, γ_PT, γ_T, and γ_TT are model coefficients determined through multivariate nonlinear regression based on experimental results.

Based on the experimental data of drilling fluids in hydrate-bearing formations, part of which is presented in

Table 1. Hydrate formation drilling fluid partial experimental data.

Group	Pressure P (MPa)	Temperature T (°C)	Measured Density ρ (g/cm3)
1	12	2	1.1501
2	12	4	1.1492
3	12	7	1.1488
4	12	11	1.1481
5	12	15	1.1475
6	20	2	1.1873
7	20	4	1.1862
8	20	7	1.1869
9	20	11	1.185
10	20	15	1.1841
11	28	2	1.2255
12	28	4	1.2248
13	28	7	1.2239
14	28	11	1.2232
15	28	15	1.2221

, the expression is obtained by neglecting the second-order pressure term and the cross terms:

$$\rho \left(P,T\right)={\rho }_0{e}^{(3.38\times {10}^{-6}(P-P_0)-2.35\times {10}^{-4}(T-T_0)-4.24\times {10}^{-7}{(T-T_0)}^2)}$$

(12)

2.2. Annular Pressure Loss Calculation Model

The calculation of annular pressure loss in horizontal well drilling with a riser is divided into three wellbore sections: the horizontal section, the inclined section, and the riser section. The pressure loss calculation formulas vary across these different sections.

(1)

Vertical Section (Including the Riser Section)

The pressure loss in the annulus of the vertical section, including the riser section, is expressed as follows:

$$P_a={\displaystyle \frac{2f{L}_v{\rho }_m}{D_o-D_p}}{v}_a^2$$

(13)

where f is the Fanning friction factor (dimensionless); L_v is the well depth (m); ρ_m is the drilling fluid density (kg/m³); v_a is the drilling fluid velocity (m/s); D_o is the wellbore diameter (m); D_p is the drill pipe outer diameter (m).

In hydrate-bearing formations, the calculation of annular pressure loss in horizontal well drilling must also consider the effects of hydrate cuttings decomposition and hydrate dissociation around the wellbore. When hydrate cuttings decompose, methane gas is released, transitioning the vertical section annular flow from a liquid–solid two-phase flow to a gas–liquid–solid three-phase flow. This transition necessitates accounting for gas intrusion effects on friction factor adjustments and velocity increments [25]. As a result, for sections where hydrate cuttings decompose, the gas-phase and liquid-phase equivalent velocities replace the drilling fluid velocity, and the Joss friction factor is used instead of the Fanning friction factor [26]. The annular pressure loss in hydrate decomposition sections is calculated as follows:

$$P_a={\displaystyle \frac{2f_D{L}_v{\rho }_m}{D_o-D_p}}{(v_{sl}+v_{sg})}^2$$

(14)

where f_D is the Joss friction factor (dimensionless); v_sl is the equivalent liquid-phase velocity (m/s); v_sg is the equivalent gas-phase velocity (m/s).

(2)

Low-Inclination Section

In the low-inclination section, no cuttings bed formation occurs; thus, cuttings bed effects do not need to be considered in the annular pressure loss calculation [27]. The calculation formula is given by the following:

$$P_{an}={\displaystyle \frac{32(f_l+f_s)C_e{C}_r{\rho }_f{Q}^2}{{\pi }^2{(D_o-D_p)}^3{(D_o+D_p)}^2}}+{\rho }_{s}g{C}_s\cos \theta$$

(15)

where P_an is the annular pressure loss without a cuttings bed (MPa); f_l is the fluid friction coefficient (dimensionless); f_s is the cuttings friction coefficient (dimensionless); C_e is the pressure loss coefficient due to drill string eccentricity (dimensionless); C_r is the pressure loss coefficient due to drill string rotation (dimensionless); C_s is the annular solid-phase concentration (dimensionless); Q is the drilling fluid flow rate (m³/s); ρ_s is the cuttings density (g/cm³); $\theta$ is the well inclination angle (rad).

Based on experimental analysis and field data, Erge et al. [28] modified the Narrow Slot Theory to account for the effects of drill string eccentricity on annular pressure loss, given by the following:

$$C_e=\left\{\begin{array}{l}1-0.072k^{0.8454}{\displaystyle \frac{e}{n}}-1.5k^{0.1852}e\sqrt{n}+0.96k^{0.2527}e\sqrt[3]{n} \mathrm{Laminar}\\ 1-0.048k^{0.8454}{\displaystyle \frac{e}{n}}-0.666k^{0.1852}e\sqrt{n}+0.285k^{0.2527}e\sqrt[3]{n} \mathrm{Turbulent} \end{array}\right.$$

(16)

The impact of drill string rotation on annular pressure loss varies with the inclination angle [29]. When the wellbore inclination angle is less than 70°, the orbital motion of an eccentric drill string increases the AECD. However, for inclination angles greater than 70°, particularly when a cuttings bed is present, drill string rotation promotes the suspension of cuttings into the fluid column, thereby enhancing hole cleaning and reducing the AECD. The coefficient C_r representing the pressure loss caused by drill string rotation is given by the following:

$$C_r=\sqrt{{\displaystyle \frac{1000d_s}{Ne}}}(0.7\le C_r\le 1.3)$$

(17)

where N is the drill string rotation speed (r/min); k is the drilling fluid consistency coefficient (Pa·sⁿ); n is the flow behavior index of the drilling fluid (dimensionless); e is the eccentric distance (mm); d_s is the cuttings diameter (mm).

(3)

High-Inclination and Horizontal Sections

In high-inclination and horizontal sections, the calculation of annular pressure loss must consider not only the effects of the cuttings bed but also the influences of drill string eccentricity and rotation [30]. The primary impact of the cuttings bed on annular pressure loss is the reduction of the annular flow cross-section, leading to an increase in AECD. The height of the cuttings bed is given by the following [31]:

$$\begin{array}{ll}{H}_{ca}=& 6.489{\rho }_f^{-2.45}{\rho }_s^{-0.51}(-v_a^{1.567}+0.16v_a^{0.57}+1.62v_a^{-0.433})(-0.003{\theta }^2+0.3744\theta -1.27)\\ & (1+0.5E){(1+N)}^{-0.185}{[10d_s/(D_o-D_p)]}^{-0.15}{R}_p^{0.276}({\mu }_e^2+0.711{\mu }_e+0.0692)\end{array}$$

(18)

where H_ca is the cuttings bed height (mm); ${\rho }_{\mathrm{f}}$ is the drilling fluid density (g/cm³); ${\rho }_s$ is the cuttings density (g/cm³); v_a is the annular return velocity of the drilling fluid (m/s); μ_e is the effective viscosity of the drilling fluid (Pa·s); E is the drill string eccentricity ratio (dimensionless); R_p is the rate of penetration (m/s).

$$\begin{array}{l}E={\displaystyle \frac{2e}{D_o-D_p}} d_s={\displaystyle \frac{R_p}{0.6N}} v_a={\displaystyle \frac{Q_m}{A_a}}\\ H_c={\displaystyle \frac{H_{ca}}{D_o-D_p}} {\mu }_e=k{\left({\displaystyle \frac{12v_a}{D_o-D_p}}{\displaystyle \frac{2n+1}{3n}}\right)}^{n-1}\end{array}$$

(19)

where θ is the wellbore inclination angle (rad); A_a is the annular cross-sectional area in the horizontal section (m²); Q_m is the drilling fluid flow rate in the annular space of the horizontal section (m³/s).

By comprehensively considering the effects of the cuttings bed, drill string eccentricity, and rotation, the annular pressure loss calculation formula is expressed as follows:

$$P_a={\displaystyle \frac{0.026H_c{P}_{an}}{f}}{[{\displaystyle \frac{v_a}{g(D_o-D_p)(S-1)}}]}^{-1.25}+(1+0.0058H_c)P_{an}$$

(20)

where S is the ratio of the inner annular diameter to the outer annular diameter.

2.3. Wellbore Temperature and Pressure Field Calculation Model

In accordance with the wellbore configuration, a sectional model for the wellbore temperature field is developed. As depicted in Figure 2, the structure of a typical horizontal well targeting a deepwater shallow hydrate reservoir is partitioned into four sections. Section ① is the marine riser. Section ② is the technical cased-hole section below the mudline. Sections ③ and ④ form the horizontal open-hole section, which is distinguished by the drill string components: the drill string in Section ③ consists of drill pipes, whereas in Section ④, it consists of drill collars.

(1)

Inside the Drill String

The drilling fluid inside the drill string exchanges heat with the annular drilling fluid. Based on the principle of thermal equilibrium, the temperature of the drilling fluid inside the drill pipe is calculated as follows:

$$\begin{array}{l}2\pi r_{po}{U}_p\left(T_a-T_p\right)={\rho }_m{C}_{m}Q{\displaystyle \frac{\partial T_p}{\partial z}}\\ U_p={\left[{\displaystyle \frac{4r_{po}}{{\lambda }_m{N}_u}}+{\displaystyle \frac{r_{po}}{{\lambda }_p}}\ln \left({\displaystyle \frac{r_{po}}{r_p}}\right)\right]}^{-1}\end{array}$$

(21)

where r_po is the outer diameter of the drill string (m); r_pi is the inner diameter of the drill pipe (m); U_p is the heat transfer coefficient between the drill string and the annular fluid (W/(m²·°C)); T_a is the temperature of the annular drilling fluid (°C); T_p is the temperature of the drilling fluid inside the drill pipe (°C); ρ_m is the drilling fluid density (kg/m³); z is the length along the wellbore axis (m); C_m is the specific heat capacity of the drilling fluid (J/(kg·°C)); Q is the drilling fluid injection flow rate (m³/s); λ_m is the thermal conductivity of the drilling fluid (W/(m·°C)); N_u is the Nusselt number (dimensionless); λ_p is the thermal conductivity of the drill pipe (W/(m·°C)).

(2)

Conductor Casing Section

In the conductor casing section, the annular drilling fluid undergoes heat exchange with both the internal drilling fluid inside the drill string and the surrounding seawater. The annular drilling fluid temperature in this section is calculated as follows:

$$\begin{array}{l}2\pi r_{po}{U}_p\left(T_p-T_{a1}\right)+2\pi r_{\mathrm{ro}}{U}_1\left(T_{sea}-T_{a1}\right)={\rho }_m{C}_{m}Q{\displaystyle \frac{\partial T_{a1}}{\partial z}}-m_h\Delta H\\ U_1={\left[{\displaystyle \frac{4r_{ro}}{{\lambda }_m{N}_u}}+{\displaystyle \frac{r_{ro}}{{\lambda }_{rc}}}\ln \left({\displaystyle \frac{r_{ro}}{r_{ci}}}\right)\right]}^{-1}\end{array}$$

(22)

where U₁ is the heat transfer coefficient between the conductor casing and the annular fluid (W/(m²·°C)); T_sea is the seawater temperature (°C); r_ci is the inner diameter of the technical casing (m); r_co is the outer diameter of the conductor casing (m); λ_rc is the thermal conductivity of the conductor casing and technical casing assembly (W/(m·°C)); m_h is the hydrate dissociation rate in the conductor casing section (mol/s); ΔH is the heat of hydrate dissociation (J/mol).

(3)

Technical Casing Section

In the technical casing section, the annular drilling fluid exchanges heat with both the drilling fluid inside the drill string and the technical casing-formation composite. The annular drilling fluid temperature in this section is given by the following:

$$\begin{array}{l}2\pi r_{po}{U}_p\left(T_p-T_{a2}\right)+2\pi r_{ro}{U}_2\left(T_f-T_{a2}\right)={\rho }_m{C}_{m}Q{\displaystyle \frac{\partial T_{a2}}{\partial z}}\\ U_2={\left[{\displaystyle \frac{4r_{co}}{{\lambda }_m{N}_u}}+{\displaystyle \frac{r_{co}}{{\lambda }_c}}\ln \left({\displaystyle \frac{r_{co}}{r_{ci}}}\right)\right]}^{-1}\end{array}$$

(23)

where T_f is the formation temperature (°C); U₂ is the heat transfer coefficient between the technical casing and the annular drilling fluid (W/(m²·°C)); r_co is the outer diameter of the technical casing (m); λ_c is the thermal conductivity of the technical casing (W/(m·°C)).

(4)

Open-Hole Section

In the open-hole section, the annular drilling fluid exchanges heat with both the drilling fluid inside the drill string and the surrounding formation. The annular drilling fluid temperature in this section is calculated as follows:

$$\begin{array}{l}2\pi r_{po}{U}_p\left(T_p-T_{a3}\right)+{\displaystyle \frac{q_f}{ \mathrm{d}z}}={\rho }_m{C}_{m}Q{\displaystyle \frac{\partial T_{a3}}{\partial z}}\\ {\displaystyle \frac{q_f}{ \mathrm{d}z}}={\displaystyle \frac{2\pi {\lambda }_f}{T_D}}\left(T_f-T_w\right)=\pi {\lambda }_m{N}_u\left(T_w-T_a\right)\end{array}$$

(24)

where q_f is the heat transfer rate between the annular fluid and the formation (W); T_w is the wellbore wall temperature (°C); λ_f is the thermal conductivity of the formation (W/(m·°C)); T_D is the transient heat conduction function.

The decomposition of hydrate cuttings results in heat absorption and gas generation, both of which affect the wellbore temperature and pressure fields. Simultaneously, variations in the temperature and pressure fields alter the hydrate decomposition rate [31]. Therefore, a multiphase flow model is developed to analyze the impact of hydrate cuttings decomposition on the wellbore temperature and pressure fields.

In the annulus, taking the upward direction of annular drilling fluid return as positive, the continuity equations for the gas phase, liquid phase, hydrate phase, and rock cuttings solid phase are established based on the principle of mass conservation and hydrate phase transition:

$$\begin{array}{l}{\displaystyle \frac{\partial }{\partial t}}\left(A{\phi }_g{\rho }_g\right)+{\displaystyle \frac{\partial }{\partial z}}\left(A{\phi }_g{\rho }_g{v}_g\right)=M_{\mathrm{g}}{r}_h\\ {\displaystyle \frac{\partial }{\partial t}}\left(A{\phi }_l{\rho }_l\right)+{\displaystyle \frac{\partial }{\partial z}}\left(A{\phi }_l{\rho }_l{v}_l\right)=M_w{r}_h\\ {\displaystyle \frac{\partial }{\partial t}}\left(A{\phi }_h{\rho }_h\right)+{\displaystyle \frac{\partial }{\partial z}}\left(A{\phi }_h{\rho }_h{v}_h\right)=-M_h{r}_h\\ {\displaystyle \frac{\partial }{\partial t}}\left(A{\phi }_s{\rho }_s\right)+{\displaystyle \frac{\partial }{\partial z}}\left(A{\phi }_s{\rho }_s{v}_s\right)=0\end{array}$$

(25)

where φ is the volume fraction (dimensionless); v is the velocity (m/s); ρ is the density (kg/m³); M is the molar mass (kg/mol); r_h is the hydrate dissociation rate (mol/(m·s)); t is the time (s); z is the axial displacement (m); A is the annular cross-sectional area (m²). The subscripts g, l, h, and s correspond to dissociated gas, drilling fluid, hydrate, and rock matrix, respectively.

According to the momentum theorem, the momentum equation for the multiphase fluid mixture is expressed as follows:

$${\displaystyle \sum _{i=1}^n\left[\frac{\partial }{\partial z}\left(A{\phi }_i{\rho }_i{v}_i^2\right)dz+\frac{\partial }{\partial t}\left(A{\phi }_i{\rho }_i{v}_i\right)dz\right]}=-\left({\displaystyle \sum _{i=1}^{n}A{\phi }_i}{\rho }_i\right)g-A\left({\displaystyle \frac{d{P}_a}{dz}}+{\displaystyle \frac{d{F}_r}{dz}}\right)$$

(26)

where P_a is the annular pressure (Pa) and F_r is the annular frictional resistance (Pa).

2.4. Hydrate Decomposition Rate Model

The process of hydrate transport and decomposition in the wellbore annulus involves multiphase flow and heat transfer. As hydrates migrate upward toward the upper section of the conductor casing, the decomposition rate gradually increases. Due to the progressive decrease in wellbore pressure, the gas holdup increases from the middle section of the conductor casing to the wellhead [32]. Hydrate cuttings decompose layer by layer from the outer surface inward. During decomposition, the reaction surface area corresponds to the product of the cuttings’ surface area and the hydrate saturation. Once the outer layer of hydrate decomposes, the next inner layer is exposed and undergoes the same decomposition process until complete dissociation or transport to the wellhead [33].

Based on the experimental results of hydrate-bearing cuttings transport and decomposition tests, it was observed that when the temperature was below 8 °C, the four models—V-P, H-J, PP, and D-G—showed good agreement with the experimental data. However, at temperatures above 8 °C, the predictions of the V-P, H-J, and PP models exhibited noticeable deviations, whereas the D-G model provided the best fit with the experimental results. Therefore, the D-G model was selected in this study to determine the phase equilibrium of hydrates. The rate equation describing the decomposition kinetics of hydrate-bearing cuttings is expressed as follows [34]:

$${\left(-{\displaystyle \frac{d{n}_h}{dt}}\right)}_{T,p}=k_d^f{A}_{dyn}\left[f_e(T,p_e)-f(T,p)\right]$$

(27)

where n_h is the mole quantity of natural gas hydrate (mol); t is the decomposition time (s); k_d^f is the hydrate decomposition rate constant (mol/(s·m²·MPa)); A_dyn is the dynamic decomposition surface area of hydrate cuttings (m²); p is the wellbore pressure at the hydrate cuttings’ location (MPa); p_e is the phase equilibrium pressure at temperature T (MPa); f is the fugacity of methane at the pressure and temperature conditions of the hydrate cuttings (MPa); f_e is the fugacity of methane at equilibrium pressure and temperature T (MPa).

(1)

Dynamic Reaction Surface Area of Hydrate Cuttings

The initial reaction surface area of hydrate cuttings can be expressed as follows [35]:

$$A_{dyn0}={\displaystyle \frac{\pi d_h^2}{\psi }}={\displaystyle \frac{1}{\psi }}{\pi }^{1/3}{\left({\displaystyle \frac{6n_h{M}_h}{{\rho }_h}}\right)}^{2/3}={\displaystyle \frac{1}{\psi }}{\pi }^{1/3}{\left(6x{V}_s\right)}^{2/3}$$

(28)

where Ψ is the sphericity (%); A_dyn0 is the initial decomposition reaction surface area of hydrate cuttings (m²); $x$ denotes the hydrate saturation (%); V_s is the volume of the cuttings (m³); M_h represents the molar mass equivalent of hydrates (g/mol).

During the progressive decomposition of hydrate cuttings, both the reaction surface area and the reaction rate continuously change. To accurately determine the decomposition rate of hydrate cuttings, it is essential to derive the dynamic reaction surface area at different time intervals [36]. Given a hydrate decomposition rate of u_rec over a time interval Δt, the corresponding mass reduction of hydrate cuttings within Δt can be expressed as follows:

$$\Delta m_0={\displaystyle \frac{u_{rec}\Delta t{M}_h{\rho }_s}{x{\rho }_h}}$$

(29)

where ρ_s is the density of hydrate cuttings (kg/m³).

At time t_i, the particle diameter of hydrate cuttings, d_si, and the reaction surface area, A_dyni, can be determined as follows:

$$\begin{array}{l}{d}_{si}={\left[{\displaystyle \frac{6\left(m_0-\Delta m_0\right)}{\pi {\rho }_c}}\right]}^{1/3}\\ A_{dyni}=x\pi d_{si}^2=x{\pi }^{1/3}{\left(d_{s(i-1)}^3-{\displaystyle \frac{6u_{rec(i-1)}\Delta t{M}_h}{\pi x{\rho }_h}}\right)}^{2/3}\end{array}$$

(30)

where m₀ represents the initial mass of hydrate cuttings (kg).

(2)

Calculation of Methane Decomposition Rate Constant

The methane hydrate decomposition rate constant $k_d^f$ is determined by the intrinsic decomposition reaction rate and the mass transfer rate of methane gas [37].

$${\displaystyle \frac{1}{k_d^f}}={\displaystyle \frac{1}{k_d}}+{\displaystyle \frac{1}{k_f}}$$

(31)

where k_d is the intrinsic decomposition reaction rate of natural gas hydrate (mol/(s·m²·MPa)); k_f is the mass transfer rate of methane gas under given pressure and temperature conditions (mol/(s·m²·MPa)).

(3)

Formation Rate of Hydrate Cuttings

The formation rate of hydrate cuttings during deepwater hydrate reservoir drilling can be calculated based on the rate of penetration (ROP) as follows:

$$q_c=R_p{A}_{bit}$$

(32)

where q_c is the volume of hydrate-bearing cuttings generated per unit time (m³/s); A_bit is the cross-sectional area of the drill bit (m²).

(4)

Auxiliary Equations

Before hydrate cuttings undergo decomposition, the decomposition rate is zero, expressed as follows:

$$T<T_e,P>P_e,n_h=0$$

(33)

where $T_e$ is the critical temperature at which hydrate cuttings do not decompose (°C) and $P_e$ is the critical pressure at which hydrate cuttings do not decompose (MPa).

During the final stage of hydrate cuttings decomposition, the reaction rate gradually decreases. When the residual particle diameter is less than 0.01 mm, the hydrate cuttings are considered to be fully decomposed, and the decomposition rate becomes zero:

$$d_s<{10}^{-5}m,n_h=0$$

(34)

3. Model Solution and Validation

3.1. Initial and Boundary Conditions

At the initial time, the temperature within the annulus and the drill string is assumed to be equal to the original formation temperature, which can be expressed as follows:

$$t=0,T_p=T_a=T_{yuan}$$

(35)

The temperature boundary condition at the wellhead can be expressed as follows:

$$Z=0,T_p=T_{in}$$

(36)

The temperature boundary condition at the bottom of the well is given by the following:

$$r\to \infty ,T_f=T_{yuan}$$

(37)

where T_yuan represents the original formation and seawater temperature (°C) and T_in denotes the temperature of the injected drilling fluid (°C).

At the initial moment, the annular pressure is consistent with the single-phase flow pressure distribution in the wellbore, which can be expressed as follows:

$$t=0,P_a=P_{single}$$

(38)

The wellhead pressure boundary condition is given by the following:

$$Z=0,P_a=P_c$$

(39)

Based on the above initial and boundary conditions, the governing equations for the coupled temperature and pressure fields in the wellbore are solved using an iterative cyclic method. This approach enables the determination of the hydrate decomposition rate and the variations in ECD within the annulus. The detailed solution procedure is illustrated in Figure 3.

3.2. Model Validation

The first gas hydrate production test in the South China Sea utilized a drilling operation with a marine riser. Therefore, to validate the accuracy of the proposed ECD prediction model for riser drilling, this study utilized the relevant data collected from this production test. The specific parameters used for the validation are presented in

Table 2. Parameters related to the first gas hydrate production test in the South China Sea.

Parameter	Value	Parameter	Value
Water depth (m)	1266	Inner diameter of drill pipe (m)	0.1080
Overburden thickness (m)	201	Outer diameter of drill pipe (m)	0.1270
Hydrate-bearing layer thickness (m)	35	Inner diameter of casing (m)	0.3397
Mixed layer thickness (m)	15	Inner diameter of drill collar (m)	0.0730
Free gas layer thickness (m)	27	Outer diameter of drill collar (m)	0.1651
Seafloor temperature (°C)	3.6	Inner diameter of riser (m)	0.4820
Geothermal gradient (°C·m−1)	0.054	Rate of penetration (m·h−1)	10
Bit diameter (m)	0.3115	Drilling fluid density (g·cm−3)	1.06
Drilling fluid flow rate(L·min−1)	2200	Inlet temperature of drilling fluid (°C)	24

.

Figure 4 presents a comparison between the ECD model predictions and the field data. As the detailed drilling data from the first production test have not been publicly disclosed, only wellhead gas holdup and bottomhole pressure information were available for validation. Therefore, the model predictions were compared with the field data at the wellhead and bottomhole. The results indicate that the ECD model for riser drilling achieved a prediction accuracy of up to 93% compared to the field test results, demonstrating its capability to meet engineering design requirements.

4. Case Study

4.1. Background and Wellbore Configuration

During the drilling of two gas hydrate production test wells in the South China Sea, several significant challenges were encountered, including weakly consolidated formations, difficulty in building angle at shallow depths, and stringent requirements for drilling fluid density and properties. Although a series of technical breakthroughs were achieved, downhole complexities, primarily in the form of lost circulation, still occurred during drilling operations. This was mainly attributed to inadequate control of the Equivalent Circulating Density (ECD), highlighting the need for more in-depth research into ECD prediction and control strategies for such conditions. Therefore, this paper utilizes the second hydrate production test well in the Qiongdongnan Basin of the South China Sea as a case study to analyze the behavior of the annular ECD and the decomposition rate patterns of hydrate-bearing cuttings. The basic parameters for this case well are presented in

Table 3. Fundamental parameters of the case well.

Parameter	Value	Parameter	Value
Riser drilling fluid density (g·cm−3)	1.03~1.07	Inner diameter of drill pipe (m)	0.1080
Seafloor temperature(°C)	2.8	Bit diameter (m)	0.2159
Specific heat capacity of drilling fluid (J·kg−1·°C−1)	3930.00	Outer diameter of drill pipe (m)	0.1270
Inlet temperature of drilling fluid (°C)	20~30	Outer diameter of drill collar (m)	0.1651
Water depth (m)	1772	Inner diameter of drill collar (m)	0.0730
Primary wellbore flow rate (L·min−1)	600~1200	Inner diameter of riser (m)	0.4820
Inlet viscosity of drilling fluid (mPa·s)	10~20	Inner diameter of casing (m)	0.2245
Formation thermal conductivity (W·m−1·°C−1)	2.25	Outer diameter of casing (m)	0.2445
Thermal conductivity of drill pipe (W·m−1·°C−1)	43.75	Upper horizontal section length (m)	246
Thermal conductivity of drill collar (W·m−1·°C−1)	43.75	Lower horizontal section length (m)	329
Thermal conductivity of drilling fluid (W·m−1·°C−1)	0.60	Geothermal gradient (°C·m−1)	0.1
Length of drill collar (m)	60	Cuttings diameter/mm	8
True vertical depth of hydrate-bearing horizontal section (m)	1935	Booster line flow rate (L·s−1)	70
True vertical depth of shallow gas-bearing horizontal section (m)	2010	Rate of penetration (m·h−1)	10~30

.

4.2. Analysis of the Influence of Hydrate Cuttings Decomposition on the Wellbore Temperature and Pressure Field

4.2.1. Identification of the Hydrate Decomposition Zone

The initiation point of hydrate cuttings decomposition within the wellbore was identified by superimposing the calculated annular temperature profile onto the gas hydrate phase equilibrium curve, with pressure converted to equivalent depth. As depicted in Figure 5, the phase equilibrium curve (red line) delineates the boundary between the hydrate stability zone (left) and the decomposition zone (right). A comparison of the two profiles reveals that the annular temperature remains below the hydrate stability threshold at depths greater than the intersection point. Consequently, hydrate cuttings remain stable and do not decompose until they are transported upward to a depth of approximately 600 m, where the annular temperature profile intersects the phase equilibrium curve. This analysis confirms that hydrate cuttings are stable below the mudline and that decomposition is confined to the upper section of the riser. Since no further intersections occur above this point, only the phase transition within the riser requires consideration for its impact on drilling hydraulics.

4.2.2. Influence on Annular Temperature and Bottom-Hole Pressure

The endothermic nature of hydrate decomposition significantly influences the wellbore thermal and pressure regimes. Figure 6 compares the annular temperature distributions for scenarios with and without considering hydrate decomposition. The results show a noticeable cooling effect, with the maximum temperature deviation observed at the wellhead, where the temperature is approximately 2 °C lower when decomposition is accounted for.

This thermal effect, coupled with the release of low-density gas, also impacts the hydrostatic pressure of the fluid column. Figure 7 illustrates the transient variation of bottom-hole pressure (BHP) during a full circulation cycle. Initially, the BHP remains constant as the cuttings are transported through the stable zone, where the flow is a simple liquid-solid two-phase system. However, once the cuttings ascend to the critical decomposition depth, the generation of methane gas reduces the overall density of the annular fluid, causing a gradual decrease in BHP. By the time the fluid completes a full circulation from bottom-hole to surface, the cumulative effect results in a maximum BHP reduction of approximately 0.15 MPa.

4.2.3. Impact on Annular Pressure Profile and ECD

The decomposition-induced changes in fluid properties directly translate to alterations in the annular pressure profile and the resulting ECD. Figure 8 displays the pressure profiles within the drill string and the annulus, while Figure 9 shows the corresponding ECD variation with well depth.

In the high-inclination and horizontal sections, both drill string and annular pressures exhibit a gradual increase. Within the riser section, the frictional pressure loss is relatively low; the slight increase in ECD in this segment is primarily driven by changes in ESD due to temperature and pressure variations. In contrast, the pressure loss within the open-hole formation section is significantly higher, leading to a more pronounced rise in ECD.

Crucially, a substantial discrepancy in ECD emerges when comparing scenarios with and without hydrate decomposition. At the toe of the horizontal section (a measured depth of 246 m in the horizontal section), the calculated ECD is 1059.8 kg/m³ when decomposition is considered, compared to 1067.9 kg/m³ when it is neglected. This difference of 8.1 kg/m³ underscores the critical importance of incorporating hydrate decomposition effects for accurate ECD prediction and safe drilling in these formations.

4.3. Analysis of the Influence of Hydraulic Parameters on Hydrate Cuttings Decomposition Rate

The decomposition rate of hydrate cuttings is not only governed by the wellbore temperature–pressure profile but is also highly sensitive to operational hydraulic parameters. This section investigates the impact of the rate of penetration (ROP), drilling fluid flow rate, and drilling fluid inlet temperature on the decomposition kinetics of an individual hydrate cutting.

4.3.1. Effect of Rate of Penetration (ROP)

A sensitivity analysis was performed using three ROP values (10, 15, and 20 m/h), selected based on regional exploration data. The ROP influences the residence time of cuttings in the annulus, thereby affecting their exposure to decomposition-conducive conditions. Figure 10 presents the calculated decomposition rate profiles for a single cutting under these different ROPs. The results show that a higher ROP accelerates the decomposition process. For instance, at an ROP of 20 m/h, decomposition initiates at 3608 s and concludes at 4372 s, reaching a peak rate of 1.36 × 10⁻⁷ mol/s. When ROP increased from 10 m/h to 20 m/h, the maximum hydrate dissociation rate rose by approximately 37.92%. Generally, as ROP increases, the peak decomposition rate becomes higher, and the total decomposition duration shortens, assuming a constant initial cutting size. This is primarily because a higher ROP leads to a faster ascent of the cutting into the warmer, lower-pressure decomposition zone.

4.3.2. Effect of Drilling Fluid Flow Rate

The drilling fluid flow rate directly impacts the annular fluid velocity and the convective heat transfer to the cuttings. To analyze this effect, three flow rates (12, 14, and 16 L/s) were simulated. As shown in Figure 11, an increase in the drilling fluid flow rate significantly enhances the hydrate decomposition rate. At the highest simulated flow rate of 16 L/s, decomposition begins earlier (at 3341 s) and is completed by 4395 s, with a peak rate of 1.15 × 10⁻⁷ mol/s. The accelerated decomposition is attributed to the higher fluid velocity, which reduces the cuttings’ transit time to the decomposition zone and improves the heat transfer from the bulk fluid to the cutting surface.

4.3.3. Effect of Drilling Fluid Inlet Temperature

The inlet temperature of the drilling fluid is a critical parameter that directly controls the overall wellbore thermal profile. Figure 12 illustrates the hydrate decomposition rate under varying inlet temperatures. The results clearly indicate a positive correlation: a higher inlet temperature leads to a higher decomposition rate. Furthermore, a lower inlet temperature not only reduces the decomposition rate but also shifts the onset of decomposition to a shallower depth (upward in the wellbore). If the inlet temperature falls below a critical threshold, the cuttings may not fully decompose before reaching the surface. This scenario poses operational challenges, as the continued decomposition of hydrate cuttings at the surface would require specialized handling procedures for both the cuttings and the released gas.

4.4. Analysis of the Influence of Hydraulic Parameters on ECD

This section evaluates the sensitivity of the annular ECD profile to key hydraulic parameters, including the rate of penetration (ROP), drilling fluid density, and flow rate. A baseline scenario was established for the riser drilling simulation, with a drilling fluid inlet density of 1050 kg/m³, a flow rate of 15 L/s, an ROP of 20 m/h, and an inlet temperature of 25 °C. Other parameters were referenced from Table 2. A parametric study was then conducted by varying each parameter individually.

4.4.1. Effect of Rate of Penetration (ROP)

The ROP directly governs the concentration of cuttings in the annulus, thereby influencing both the hydrostatic (ESD) and frictional (AECD) components of the ECD [38,39,40]. A sensitivity analysis was performed using five ROP values ranging from 16 to 32 m/h. As illustrated in Figure 13, the annular ECD exhibits a clear positive correlation with ROP. This is primarily because a higher ROP leads to an increased cuttings concentration, which raises the overall density of the annular fluid column and thus the hydrostatic pressure. An interesting counter-effect is observed in the upper section of the riser near the wellhead, where a higher cuttings concentration (and associated gas from decomposition) can locally reduce the ECD.

Critically, the analysis indicates a potential operational limit. When the ROP exceeds 28 m/h, the predicted ECD at the formation depth approaches the fracture limit, indicating a heightened risk of lost circulation. This finding underscores the constraint that the narrow pressure window imposes on achieving high-efficiency drilling in this formation.

4.4.2. Effect of Drilling Fluid Density

The initial drilling fluid density is a fundamental parameter directly impacting the hydrostatic pressure. Figure 14 presents the annular ECD profiles for five different initial densities, from 1030 to 1070 kg/m³. As expected, the ECD increases almost linearly with the initial fluid density. The simulation identifies a critical operational threshold: when the initial drilling fluid density surpasses 1064 kg/m³, the corresponding bottom-hole ECD exceeds 1080 kg/m³, a value that encroaches upon the formation’s fracture gradient and poses a significant risk of inducing fluid losses.

4.4.3. Effect of Drilling Fluid Flow Rate

The drilling fluid flow rate predominantly influences the ECD through its effect on the frictional pressure loss component (AECD). A parametric analysis was conducted using five flow rates from 12 to 24 L/s. As shown in Figure 15, the annular ECD increases with the flow rate. This trend is attributed to the higher circulatory friction losses throughout the system, which directly elevate the total annular pressure. The results highlight another operational trade-off: while a higher flow rate is beneficial for hole cleaning, it must be carefully managed to prevent the ECD from exceeding the safe operating window, especially in formations with narrow pressure margins.

5. Conclusions

This study developed a comprehensive annular ECD prediction model for ultra-deepwater hydrate formations by incorporating the coupled effects of riser drilling and hydrate decomposition. A case study based on field operations in the Qiongdongnan Basin was performed to evaluate the hydraulic behavior and associated influencing factors. The key conclusions are summarized as follows:

(1)

Hydrate cuttings remain stable below the mudline, as determined by the annular hydrate phase equilibrium curve and wellbore temperature profile, while decomposition occurs only in the upper conductor casing section.

(2)

Hydrate decomposition exerts a pronounced influence on annular thermal and pressure conditions. Specifically, when decomposition is considered, the wellhead temperature decreases by about 2 °C, the bottom-hole pressure decreases by 0.15 MPa, and the ECD at the toe end of the horizontal section decreases by approximately 8 kg/m³.

(3)

Higher rate of penetration (ROP), drilling fluid flow rate, and fluid inlet temperature accelerate hydrate decomposition and increase the decomposition rate. However, increases in ROP, drilling fluid density, and flow rate also result in a substantial rise in annular ECD, highlighting the trade-off between promoting hydrate decomposition and maintaining hydraulic safety during drilling operations.