Study on the Different Thermal Insulation Methods to Control the Wellbore Temperature in Deepwater Wells

Abstract

Thermal insulation is necessary for deepwater wells to achieve safe and effective production. Based on the comparison of different thermal insulation measures and the control requirements, this paper proposes two indicators to analyze thermal insulation performance. A model is established by considering the wellbore radial thermal resistance and wellbore-formation heat transfer process in order to calculate the two indicators. The analysis shows that there exists an overlapping effective range between vacuum-insulated tubing and insulation-coated tubing, and a similar overlap is observed between insulating liquid and insulated tubing. When comparable insulation performance can be achieved, insulating liquid should be prioritized, while vacuum-insulated tubing should be considered only as the final option. Under high production or a high geothermal gradient, annular temperature change is the primary control objective, whereas under low-production or low-temperature conditions, wellhead temperature becomes the dominant control target. The combination of insulated tubing and insulating liquid exhibits pronounced synergistic effects. In the case of a well under high-temperature and high-production conditions, the composite insulation reduces annular temperature change by 64.26%, and in low-temperature, low-production wells, it increases wellhead temperature by 100.43%. In practical applications, insulating fluids should be preferred, with insulated tubing employed as a supplementary measure.

1. Introduction

Deepwater oil and gas have become the primary findings for major global hydrocarbon discoveries in recent years, such as Brazil Santos Basin [1,2] and Africa Orange Basin [3]. However, deepwater oil and gas development is characterized by high risk and high cost, requiring long-term production to offset costs while maintaining strict safety to prevent catastrophic events such as blowouts, wellbore integrity failure, and hydrocarbon leakage [4]. Among the numerous technical challenges, wellbore temperature control is particularly critical. In deepwater environments, the low temperature near the mud line leads to significant heat exchange with the wellbore. As a result, the temperature of the production fluid decreases, while the temperature of the annulus and surrounding formations increases correspondingly [5,6]. The heat exchange may trigger hydrate blockage in production tubing [7,8], paraffin deposition in crude oil [9], annular pressure buildup [10,11], and even wellhead instability induced by shallow-water hydrate dissociation [12,13]. As reported, several deepwater wells in Mexico Gulf have experienced casing collapse accidents caused by annular pressure, like Pompano A-31 well [14] and Mad Dog Slot W1 well [15]. Therefore, effective control of wellbore temperature is not only essential for ensuring production, but also vital for reducing risks and achieving efficient development.

In general, the primary objectives of wellbore temperature control are to maintain the production tubing temperature and to limit the temperature rise in casing annuli. Active heating is a technique used to increase the temperature inside the production tubing, including electrical heating [16,17] and hot-fluid injection [18]. These measures are mainly suitable for low-production, low-temperature wells or heavy-oil thermal recovery wells. However, they are costly and simultaneously increase annular temperature. Thermal insulation measures can improve the wellbore temperature distribution by reducing radial heat transfer. Common approaches include insulated tubing [19,20], annular insulating fluids [21,22], thermal-insulated cement sheath [23], and nitrogen injected into the annulus [24]. In deepwater wells in Mexico Gulf, annular insulating fluids are widely used to control annular temperature and mitigate annular pressure buildup [25,26]. Ferreira et al. [27] discussed the use of insulated tubing to control annular temperature rise in Brazilian deepwater wells. Guan et al. [28] proposed a dual-layer configuration using insulated tubing and insulated casing to control annular temperature and developed a model to analyze the influence of parameters such as setting depth. Zeng et al. [29] established a model to investigate the effects of coupling-gap size at insulated tubing joints, production rate, and water cut on the wellbore temperature. Zhang et al. [30] examined the effect of nitrogen and insulating fluids on annular temperature–pressure behavior, focusing primarily on the peak value of annular pressure. Śliwa et al. [31] evaluated the application of vacuum-insulated tubing in deep well heat extraction and suggested that it has broad potential in enhancing geothermal energy utilization.

Although previous studies have analyzed insulation performance under different engineering conditions, deepwater wells require simultaneous control of both production fluid temperature and annular fluid temperature. Excessive cooling of production fluids compromises flow assurance, whereas excessive annular heating may trigger high annular pressure buildup [32], posing risks to well integrity, including potential damage to casing [33], cement sheath [34], and other safety barriers. However, available studies primarily focused on the role of thermal insulation in controlling trapped annular pressure by analyzing either insulated tubing or insulated annular liquids. Little research has made systematic comparisons of the control effectiveness and applicability of these two insulation measures. Therefore, this paper selects two key indicators to evaluate the control performance of thermal insulation on trapped annular pressure and flow assurance, including the average annular temperature rise and the temperature of the production fluid at the wellhead. A mathematical model is then developed to quantitatively compare the performance of different types of insulated tubing and thermal-insulated annular liquids. Through analysis, the applicability of various insulation strategies under different conditions is evaluated. Furthermore, a combined insulation approach is proposed to enhance control performance under both high-temperature, high-production and low-temperature, low-production scenarios, thereby providing theoretical guidance for the safe and reliable operation of deepwater wells.

2. Materials and Methods

2.1. Analysis of Typical Wellbore Thermal Insulation Measures

2.1.1. Insulated Tubing

Insulated tubing can be divided into vacuum insulation, filled insulation, and insulation coatings. These approaches increase the wellbore radial thermal resistance and thereby mitigate the temperature rise in the annulus. Vacuum-insulated tubing (VIT) typically consists of a double-walled structure (inner and outer pipes). The space between the double walls is evacuated and filled with multilayer thermal barriers—such as reflective foils, multilayer fibers, or nano-insulation material, as shown in Figure 1. The key insulation parameters of VIT include thermal conductivity, vacuum level, temperature tolerance range, and thermal behavior at the connection joints [35,36]. The typical thermal conductivity of VIT ranges from 0.01 to 0.08 W/(m·K). The main advantage of VIT is its vacuum annulus, which effectively suppresses convective heat transfer, while reflective layers and multilayer insulation materials reduce radiative and solid-phase conduction. As a result, its thermal conductivity is an order of magnitude lower than that of conventional insulated pipes. However, VIT also faces challenges, including complex structure, high cost, and a sharp increase in heat loss once the vacuum is compromised [37,38]. This type of tubing has been used for paraffin control and annular pressure management [39,40].

Filled insulated tubing typically fills the space between the inner and outer pipes with thermal insulation materials, like inert gases, insulating fluids, foamed materials, aerogels, or insulation fiber blankets. When a low-conductivity oil-based insulating fluid is used, its thermal conductivity is approximately 0.14 W/(m·K) [41]. Filling the annulus with inert gases can significantly increase annular temperature and reduce heat loss, although maintaining the gas-tight integrity of the string is essential [42]. Insulation coatings generally use low-thermal-conductivity materials—such as aerogels, hollow glass microspheres, nano-ceramic insulators, microporous silica, or polyurethane foams—sprayed or lined onto the pipe surface to form a thermal-resistance barrier. When an aerogel-based coating is applied, the thermal conductivity can be reduced to approximately 0.024 W/(m·K) (for a coating thickness of about 10 mm) [43]. For insulation coatings, thermal and mechanical endurance is crucial, including resistance to high temperatures, high pressures, and acid/alkali corrosion. In deepwater or high-temperature wells, the coating must withstand temperatures from several tens to several hundreds of degrees Celsius while resisting seawater, corrosive fluids, cyclic thermal loading, vibration, and mechanical impact [44]. Failure of the coating can drastically reduce its insulation performance. Figure 2 illustrates an insulation coating capable of withstanding 200 °C and 60 MPa.

2.1.2. Nitrogen for Thermal Insulation

As shown in Figure 3, the nitrogen gas can be injected into the tubing–casing annulus, forming a low-thermal-conductivity and low-density gas layer [45]. At 20 °C, the thermal conductivity of nitrogen is approximately 0.025 W/(m·K) and at 100 °C it is about 0.028 W/(m·K), showing low sensitivity to temperature. This makes nitrogen insulation particularly suitable for thermal steam injection wells [46]. Moreover, nitrogen does not corrode wellbore barriers such as tubing and casing. For deepwater wells, however, the liquid in the tubing–casing annulus also functions to balance the pressure across the tubing and maintain the packer setting pressure [47,48]. Replacing the annular liquid with nitrogen may lead to packer unsetting or tubing rupture [49,50]. Therefore, nitrogen injection is rarely used as a thermal insulation method in deepwater wells.

2.1.3. Annular Insulating Fluids

Annular insulating fluids work by introducing low-conductivity components such as polyols [51], cellulose nanocrystals [52], and acrylic formulations [53]. Available insulating fluids exhibit high thermal resistance, low corrosivity, and good temperature stability. They typically possess high viscosity at elevated temperatures to maintain insulation performance while retaining low viscosity during pumping at lower temperatures. Halliburton’s insulating fluids exhibit a thermal conductivity of 0.3–0.4 W/(m·K), whereas acrylic-enhanced fluids maintain conductivity as low as 0.18 W/(m·K). The development of solids-free water-based insulating fluids further eliminates sedimentation issues. For example, the solids-free insulating fluid shown in Figure 4 [54] employs nanotechnology and intermolecular associative polymers to construct a gel network, offering temperature resistance up to 260 °C with a thermal conductivity of only 0.21–0.28 W/(m·K).

2.1.4. Applicability Analysis

As summarized in

Table 1. Analysis of thermal insulation measures.

Measures	Types	Thermal Conductivity, W/(m∙K)	Analysis
Insulated tubing	Vacuum	0.012~0.14	Lowest thermal conductivity; applied in deepwater well; high cost
	Filled insulation
	Insulation coating
Nitrogen	Injection to the A annulus	0.025~0.028	Impacts the pressure file in the tubing–casing annulus; mainly applied in thermal injection heavy oil wells
Insulating fluids	Containing solids	0.18~0.40	Relatively low cost; easy to operate; widely applied in deepwater wells
	Solids-free

, insulated tubing provides the lowest thermal conductivity but is also the most expensive. To enhance insulation performance, some deepwater wells have adopted this technology. Although nitrogen-filled annuli also exhibit low thermal conductivity, such measures change the pressure distribution in the tubing–casing annulus and therefore are not used in deepwater wells. Instead, nitrogen injection is mainly applied in thermal injection wells, while in deepwater wells, nitrogen is injected into annuli primarily as a trapped-annular-pressure control method, functioning through volume compensation rather than thermal insulation [55,56]. Annular insulating fluids, by contrast, are relatively cheaper, though they offer moderate thermal conductivity. Their lower cost makes them widely used in deepwater wells. Accordingly, the insulation methods examined in this study focus primarily on insulated tubing and insulating fluids.

2.2. Determination of the Evaluation Indicators

2.2.1. Magnitude of Annular Temperature Variation

In deepwater wells, completion fluids or residual drilling fluids remain in the annulus. During production, these annular fluids receive heat transferred radially from the production tubing, resulting in an increase in annular temperature. According to the principle of volume compatibility, the ability of the confined annulus to accommodate the thermal-expanded fluid is restricted due to the differences in thermo-physical properties between the fluid and casing. This induces a compressive effect on the annular fluid volume and leads to a rise in annular pressure—commonly referred to as trapped annular pressure [57]—as expressed in Equation (1):

$$\mathrm{d}{p}_{\mathrm{a}}=\left({\displaystyle \frac{\partial p_{\mathrm{a}}}{\partial T_{\mathrm{a}}}}\right)\Delta T_{\mathrm{a}}+\left({\displaystyle \frac{\partial p_{\mathrm{a}}}{\partial V_{\mathrm{a}}}}\right)\Delta V_{\mathrm{a}}+\left({\displaystyle \frac{\partial p_{\mathrm{a}}}{\partial m}}\right)\Delta m$$

(1)

where p_a is the annular pressure, MPa; T_a is the temperature of annular fluid, °C; ΔT_a is temperature change in the annular fluid, °C; V_a is the annular volume, m³; ΔV_a is the annular volume change, m³; m is the annular fluid mass, kg/m³; and Δm is the annular fluid mass change, kg/m³.

Deepwater wells often experience rapid annular pressure buildup [58], exceeding 50 MPa within 2–3 days [15]. Excessive annular pressure can severely compromise well integrity, leading to casing collapse [59] and cement sheath failure [60], as illustrated in Figure 5 [14,15]. Moreover, deepwater wells are typically far away from land and have limited platform space, making the consequences of integrity failure extremely severe, as demonstrated by the Deepwater Horizon incident [61]. Studies show that annular temperature rise is the dominant factor contributing to trapped annular pressure, accounting for more than 80% of the pressure increase under sealed-annulus conditions [62]. Therefore, the temperature change in the annulus is a key indicator to evaluate the performance of thermal insulation measures.

2.2.2. Wellhead Temperature of Production Fluid

During production, the production fluid continuously undergoes radial heat transfer, causing a temperature decrease from the reservoir to the wellhead. Therefore, the wellhead temperature represents the lowest temperature in the entire production tubing. Low temperature can adversely affect flow assurance in three major aspects. First is hydrate formation. In the high-pressure, low-temperature deepwater environment, natural gas combines with water to form solid hydrates [63], which can plug the production tubing. Second is wax deposition. Low temperatures cause wax components in the fluid to precipitate, adhere to the tubing wall along with other solid particles, and form blockages, as shown in Figure 6 [64,65]. Third is pipeline transport risks: if the production fluid reaches excessively low temperature, hydrate or wax plugging may also occur in the pipeline. Once plugging occurs, production must be stopped, resulting in high operational costs and significant safety risks. Although it is an effective method to prevent hydrate or wax deposition by using chemicals and paraffin inhibitors, thermal insulation can strengthen the control performance and reduce the cost [66]. Therefore, the wellhead temperature of the production fluid must be considered as a key indicator for evaluating the effectiveness of thermal insulation.

2.3. Thermal Insulation Performance Analysis Model During Production

2.3.1. Characterization of Heat Transfer in Production Fluids

To simplify the calculation, the cement sheath is assumed to have a uniform thickness and the tubing is assumed to be centered in the wellbore. As illustrated in Figure 7, a micro-element of length dz is selected along the wellbore. This micro-element satisfies both momentum and energy conservation law. Momentum conservation includes friction, acceleration, and gravity terms, whereas energy conservation primarily accounts for kinetic, internal, potential, pressure, and thermal energy transfer, as expressed in Equation (2):

$$\left\{\begin{array}{l}{\displaystyle \frac{\mathrm{d}p}{\mathrm{d}z}}+{\rho }_{\mathrm{f}}g\sin \theta +f{\displaystyle \frac{{\rho }_{\mathrm{f}}{v}_{\mathrm{f}}^2}{2d_{\mathrm{tn}}}}+\rho v_{\mathrm{f}}{\displaystyle \frac{\mathrm{d}{v}_{\mathrm{f}}}{\mathrm{d}z}}=0\\ C_{\mathrm{f}}{\displaystyle \frac{\mathrm{d}{T}_{\mathrm{f}}}{\mathrm{d}z}}+v_{\mathrm{f}}{\displaystyle \frac{\mathrm{d}{v}_{\mathrm{f}}}{\mathrm{d}z}}+{\displaystyle \frac{1}{{\rho }_{\mathrm{f}}}}{\displaystyle \frac{\mathrm{d}p}{\mathrm{d}z}}+g\sin \theta +{\displaystyle \frac{1}{w_{\mathrm{f}}}}{\displaystyle \frac{\mathrm{d}Q}{\mathrm{d}z}}=0\end{array}\right.$$

(2)

where p is pressure, Pa; ρ_f is the fluid density inside the tubing, kg/m³; g is gravitational acceleration, m/s²; θ is well deviation angle, °; f is the friction factor, dimensionless; v_f is fluid velocity, m/s; C_f is fluid specific heat capacity, J/(kg·°C); T_f is fluid temperature, °C; w_f is fluid mass flow rate, kg/s; and Q is radial heat flux in the wellbore, J/s.

During production, friction caused by fluid flow leads to the conversion between kinetic and thermal energy. This process is primarily governed by flow velocity and the friction factor [67], as expressed by Equation (3):

$$f^{-0.5}=-2\log \left[{\displaystyle \frac{R_{\mathrm{a}}/d_{\mathrm{to}}}{3.7065}}-{\displaystyle \frac{5.0452}{Re}}\log \left({\displaystyle \frac{{\left(R_{\mathrm{a}}/d_{\mathrm{to}}\right)}^{1.1098}}{2.8257}}+{\displaystyle \frac{5.8506}{R{e}^{0.8981}}}\right)\right]$$

(3)

where Ra is tubing roughness, m; d_to is tubing inner diameter, m; and Re is Reynolds number, dimensionless.

Heat transfer between the wellbore and the formation follows the principle of radial heat-flow conservation. Radial heat transfer consists of two processes. First is steady-state heat transfer from the tubing center to the outer boundary of the cement sheath. Second is transient heat transfer from the cement sheath to the surrounding formation. Under the semi-steady-state assumption, radial heat-flow conservation applies to both processes. Heat transfer at the cement–formation interface follows Fourier’s law [68], as expressed in Equations (4) and (5):

$$\mathrm{d}{Q}_{\mathrm{r}\mathrm{w}}=\mathrm{d}{Q}_{\mathrm{r}\mathrm{f}}$$

(4)

$$\left\{\begin{array}{l}\mathrm{d}{Q}_{\mathrm{r}\mathrm{w}}={\displaystyle \frac{T_{\mathrm{f}}-T_{\mathrm{h}}}{R_{\mathrm{to}}}}\mathrm{d}z\\ \mathrm{d}{Q}_{\mathrm{r}\mathrm{f}}={\displaystyle \frac{2\pi \lambda \mathrm{e}\left(T_{\mathrm{h}}-T_{\mathrm{e}}\right)}{T_{\mathrm{D}}}}\mathrm{d}z\end{array}\right.$$

(5)

The dimensionless formation temperature has several formulations, among which the Hasan correlation provides high accuracy. Hasan and Kabir [69] applied this formulation to evaluate formation temperature near the wellbore. The corresponding expressions are given in Equations (6) and (7):

$$T_D=\left\{\begin{array}{ll}1.1281\sqrt{t_D}\left(1-0.3\sqrt{t_D}\right)& t_D\le 1.5\\ \left(0.4063+0.5\ln t_D\right)\left(1+0.6/t_D\right)& t_D>1.5\end{array}\right.$$

(6)

$$t_D={\displaystyle \frac{t\alpha \mathrm{e}}{r{\mathrm{w}}^2}}$$

(7)

where t is production time, s; α_e is formation thermal diffusivity, m²/s; and r_w is wellbore radius, m.

2.3.2. Calculation of Wellhead Temperature and Annular Temperature Change

The mechanisms of insulated tubing and annular insulating fluid are similar. They work by increasing the radial thermal resistance due to their low thermal conductivity, thereby reducing radial heat flux, increasing the temperature of the produced fluid, and limiting heat accumulation in the annulus. Therefore, the first step is determining the radial thermal resistance distribution. The conductive thermal resistance between the inner/outer walls of the tubing, casing, and cement sheath, as well as within the annular fluid, is calculated by Equation (8):

$$R_{\mathrm{tc}}={\displaystyle \frac{1}{2\pi {\lambda }_{\mathrm{tc}}}}\ln {\displaystyle \frac{r_2}{r_1}}$$

(8)

where R_tc is conductive thermal resistance, m·°C/W; λ_tc is thermal conductivity, W/(m·°C); and r₂ and r₁ are the outer and inner radii, m.

The total radial thermal resistance is the sum of serial resistances. Under multi-annulus conditions, the number of cement sheaths, casings, and annular fluid layers increases accordingly. Thus, the overall radial thermal resistance is as expressed by Equation (9):

$$R_{\mathrm{to}}=R_{\mathrm{cht}}+R_{\mathrm{tct}}+{\displaystyle \sum _{k=1}^m{R}_{\mathrm{tcc}k}+}{\displaystyle \sum _{j=1}^n{R}_{\mathrm{tcs}j}+}{\displaystyle \sum _{y=1}^u{R}_{\mathrm{tcf}y}}$$

(9)

where R_cht is convective thermal resistance inside the tubing, m·°C/W; R_tct is tubing conductive resistance, m·°C/W; R_tcc is casing conductive resistance, m·°C/W; k is casing number, dimensionless; m is number of casing layers, dimensionless; R_tcs is annular fluid thermal resistance, m·°C/W; j is annulus number, dimensionless; n is total number of annuli, dimensionless; R_tcf is cement sheath conductive resistance, m·°C/W; y is cement sheath number, dimensionless; and u is number of cement sheath layers, dimensionless.

Once the radial thermal resistance is determined, it can get the radial heat flux by combining Equations (4) and (5), as shown in Equation (10):

$${\displaystyle \frac{\mathrm{d}Q}{\mathrm{d}z}}={\displaystyle \frac{2\pi {\lambda }_{\mathrm{e}}\left(T_{\mathrm{e}}-T_{\mathrm{f}}\right)}{T_{\mathrm{D}}+2\pi {\lambda }_{\mathrm{e}}{R}_{\mathrm{to}}}}$$

(10)

A first-order linear nonhomogeneous differential equation can be obtained for the temperature of the production fluid by substituting Equations (10) and (3) into Equation (2), as expressed in Equation (11):

$${\displaystyle \frac{\mathrm{d}{T}_{\mathrm{f}}}{\mathrm{d}z}}={\displaystyle \frac{2\pi {\lambda }_{\mathrm{e}}\left(T_{\mathrm{e}}-T_{\mathrm{f}}\right)}{W_{\mathrm{f}}{C}_{\mathrm{f}}\left(T_{\mathrm{D}}+2\pi {\lambda }_{\mathrm{e}}{R}_{\mathrm{to}}\right)}}+f{\displaystyle \frac{v_{\mathrm{f}}^2}{2C_{\mathrm{f}}{d}_{\mathrm{tn}}}}$$

(11)

Considering that geothermal gradient, fluid temperature, and well structure vary along the wellbore, Equation (11) is solved using a spatial discretization approach. Specifically, the tubing is divided into segments of length Δz from the bottom to the wellhead, within which pressure and temperature are assumed to be constant. For each segment, Equation (11) yields Equation (12):

$$\begin{gathered} T_{\mathrm{f}}^{i+1}={\displaystyle \frac{1}{A+\Delta z}}\left(A{T}_{\mathrm{f}}^i\left(t\right)+\Delta z{T}_{\mathrm{es}}^{i+1}+A\Delta z{f}^{i+1}{\displaystyle \frac{{\left(v_{\mathrm{f}}^{i+1}\right)}^2}{2C_{\mathrm{f}}{d}_{\mathrm{tn}}}}\right) \\ A={\displaystyle \frac{w_{\mathrm{f}}{C}_{\mathrm{f}}\left[T_{\mathrm{D}}+2\pi {\lambda }_{\mathrm{e}}{R}_{\mathrm{to}}\right]}{2\pi {\lambda }_{\mathrm{e}}}} \end{gathered}$$

(12)

where i is the segment index, i = 1, 2, 3 …, and Δz is segment length, m.

The wellhead temperature of the produced fluid corresponds to the temperature at the final segment, as expressed in Equation (13):

$$T_{\mathrm{fw}}=T_{\mathrm{f}}^{N_{\mathrm{L}}}$$

(13)

where T_fw is the temperature of production fluid in the wellhead, °C, and N_L is the number of well segments at the depth of wellhead, dimensionless.

The annular temperature at any position can be obtained from radial heat-flow conservation and radial thermal resistance distribution [70], as shown in Equation (14):

$$T_{\mathrm{a}}^i=T_{\mathrm{f}}^i+{\displaystyle \frac{T_{\mathrm{h}}^i-T_{\mathrm{f}}^i}{R_{\mathrm{to}}^i}}{R}_{\mathrm{zro}}^i={\displaystyle \frac{T_{\mathrm{f}}^i\left(1+T_{\mathrm{D}}\right)+2\pi {\lambda }_{\mathrm{e}}{T}_{\mathrm{e}}^i\left(R_{\mathrm{to}}^i-R_{\mathrm{zro}}^i\right)}{T_{\mathrm{D}}+2\pi {\lambda }_{\mathrm{e}}{R}_{\mathrm{to}}^i}}$$

(14)

where T_a is the annular temperature in a segment, °C, and R_zro is thermal resistance between the annulus and the outer edge, m·K/W.

Prior to production, the wellbore temperature is typically stable and assumed equal to the formation temperature [71,72]. Therefore, the average annular temperature rise is the mean of temperature changes across all segments, as given in Equation (15):

$$\Delta T_{\mathrm{a}}={\displaystyle \sum _{i=N_{\mathrm{a}}}^{N_{\mathrm{L}}}\left(T_{\mathrm{a}}^i-T_{\mathrm{e}}^i\right)}/\left(N_{\mathrm{L}}-N_{\mathrm{a}}+1\right)$$

(15)

where N_a is the number of well segments at the depth of the annular liquid level, dimensionless.

3. Results

The insulation performance is evaluated by the case well presented in Reference [28]. The water depth of this well is 1200 m, the geothermal gradient is 4.3 °C/100 m, and the mud line temperature is 4 °C. Other key calculation parameters are listed in

Table 2. Calculation parameters.

Parameter	Value
Production rate	50 t/d
Specific heat of production fluid	3600 J/(°C·kg)
Density of production fluid	920 kg/m3
Formation specific heat	1850 J/(°C·kg)
Formation density	2100 kg/m3
Ordinary casing or tubing thermal conductivity	45.7 W/(m·°C)
Ordinary annular liquid thermal conductivity	0.6 W/(m·°C)
Cement thermal conductivity	0.72 W/(m·°C)
Formation thermal diffusivity	8 × 10−7 m2/s
Production time	900 d

. After substituting the calculation parameters, the mathematical model established in Section 2 can be solved for analysis. The wellbore is first divided into segments, and the temperature is calculated sequentially from the bottomhole to the wellhead. In this way, both the wellhead temperature and the average annular temperature can be obtained.

3.1. Analysis of Insulation Performance

3.1.1. Insulation Performance of Insulated Tubing

Figure 8 illustrates the response of wellhead temperature to tubing thermal conductivity. As shown in Figure 8a, when the tubing type shifts from insulated to ordinary, the wellhead temperature of the production fluid decreases rapidly and then becomes nearly stable. When the thermal conductivity is 0.01 W/(m·°C), the wellhead temperature reaches 125.13 °C. However, at a thermal conductivity of 45 W/(m·°C) (ordinary steel tubing), the corresponding temperature is only about 40.59 °C. This demonstrates that tubing insulation has a significant effect on wellhead temperature. Figure 8b further compares different types of insulated tubing. Vacuum-insulated tubing provides the best performance, maintaining wellhead temperatures within 110–125 °C. Meanwhile, there is an overlap between vacuum-insulated tubing and insulation-coated tubing, whereas tubing with thermal fillers shows comparatively poorer performance. Considering cost, insulation-coated tubing should be prioritized when it can achieve comparable performance, but attention must be paid to the durability of the coating.

Figure 9 shows the relationship between the temperature change in annulus B and tubing thermal conductivity. In general, the annular temperature change rises rapidly with thermal conductivity and then stabilizes. In some cases, insulated tubing and ordinary tubing exhibit similar performances—for example, at a thermal conductivity of 0.055 W/(m·°C) and 45 W/(m·°C), the temperature change is the same (40.59 °C). Moreover, a peak value of 41.70 °C appears at a thermal conductivity of 0.13 W/(m·°C). This occurs because insulated tubing elevates the temperature of the production fluid, increasing the radial temperature gradient, while the increased radial thermal resistance is insufficient to compensate for the enhanced heat transfer caused by this increased gradient. As shown in Figure 9b, the conductivity range associated with filler-insulated tubing has a very weak influence on temperature increase, whereas vacuum insulation has a more pronounced effect. These results indicate that filler-type insulated tubing is not the optimal choice for annulus temperature control, and the insulation conductivity must be properly selected to avoid ineffective or counterproductive performance.

3.1.2. Insulation Performance of Annular Insulating Fluids

As shown in Figure 10, the performance of annular insulating fluids is broadly similar to that of insulated tubing. The wellhead temperature decreases steadily as the annular fluid thermal conductivity increases. When the conductivity is 0.18 W/(m·°C), the wellhead temperature is 87.61 °C. However, replacing it with an ordinary annulus fluid with a conductivity of 0.60 W/(m·°C) reduces the wellhead temperature to 51.69 °C. Similarly, the annulus temperature variation also exhibits a peak—43.27 °C at 0.246 W/(m·°C), as shown in Figure 10b. This indicates that inappropriate selection of insulating fluid may not reduce annulus temperature and can even have the opposite effect. Overall, annular insulating fluids have weaker control capability over wellhead temperature compared with insulated tubing. The annulus temperature control must be evaluated on a case-by-case basis to achieve optimal performance.

3.2. Analysis of Key Influencing Factors

3.2.1. Influence of Production Rate on the Performance of Insulated Tubing

As shown in Figure 11, the wellhead temperature still decreases as the tubing thermal conductivity increases. However, under high-production conditions, the magnitude of this decrease becomes significantly smaller. For example, under the condition that the production rate reaches 1000 t/d, only a 2.90% reduction is obtained in wellhead temperature when the tubing thermal conductivity increases from 0.01 W/(m·°C) to 0.15 W/(m·°C). In contrast, at a production rate of 50 t/d, the reduction reaches 48.27%. This occurs because higher production rates lead to higher flow velocities of the produced fluid and lower heat loss along the wellbore. Therefore, under high-production conditions, insulated tubing is not necessary to maintain wellhead temperature, whereas under low-production conditions, attention should be focused on wellhead temperature.

As shown in Figure 12, regardless of high or low production rate, the tubing thermal conductivity has a significant impact on annular temperature change, and this influence is even more pronounced under high-production conditions. In addition, the difference in annular temperature change under different production rates becomes smaller as tubing thermal conductivity decreases. For example, when the production rate reaches 1000 t/d, increasing tubing thermal conductivity from 0.01 W/(m·°C) to 0.15 W/(m·°C) results in a 147.59% increase in annular temperature change, whereas at a production rate of 50 t/d, the increase reaches 63.04%. Considering that excessive annular temperature change leads to elevated annular pressure, annular temperature control under high-production condition is especially critical, and insulated tubing shows excellent performance in this regard.

3.2.2. Influence of Production Rate on the Performance of Insulated Liquid

As shown in Figure 13, the curves of insulated liquid under different production rates have similar changing trends to those of insulated tubing. By comparing Figure 13 and Figure 12, it can be determined that insulated liquid can provide temperature-control capabilities comparable to insulated tubing under certain conditions. For example, at a production rate of 100 t/d, when the annular liquid thermal conductivity is 0.24 W/(m·°C) and the tubing thermal conductivity is 0.0655 W/(m·°C), the wellhead temperatures are close to 118 °C for both cases. This indicates that under specific conditions, insulated liquid can serve as a cost-effective alternative to insulated tubing for maintaining wellhead temperature.

As shown in Figure 14, the curves of annular temperature change show different changing trends. In Figure 14b, under low production (50 t/d), annular temperature change initially increases and then decreases with annular liquid thermal conductivity. The remaining curves exhibit a monotonically increasing trend. Considering that low-production wells mainly prioritize maintaining wellhead temperature, this difference does not significantly affect the application of insulated annular liquid. Additionally, under high-production conditions, the annular-temperature-control performance of insulated liquid overlaps with that of insulated tubing.

3.2.3. Influence of Geothermal Gradient on the Performance of Insulated Tubing

As shown in Figure 15, geothermal gradient does not change the trend of wellhead temperature curves with tubing thermal conductivity. The impact is mainly reflected in the absolute values. A higher geothermal gradient indicates a higher formation temperature, so maintaining wellhead temperature is not the primary objective under such conditions. For example, in Figure 15b, when the geothermal gradient is 2.5 °C/(100 m), the wellhead temperature is 74.64 °C with a tubing thermal conductivity of 0.01 W/(m·°C). However, when the geothermal gradient increases to 3.5 °C/(100 m), a wellhead temperature of 74.73 °C can be achieved even when the tubing thermal conductivity is 0.037 W/(m·°C). Thus, insulated tubing is not required for high-temperature reservoirs to maintain wellhead temperature but is important for low-temperature reservoirs.

Figure 16 clearly indicates that high-temperature reservoirs require measures to control annular temperature. Overall, the trend of annular temperature change with tubing thermal conductivity remains unchanged under different geothermal gradients. The production rate in Figure 16 is 50 t/d. Combined with the analysis in Section 3.2.1, high production coupled with high geothermal gradient results in more pronounced annular temperature change. Insulated tubing can bring a greater reduction in annular temperature rise, especially under high-geothermal-gradient conditions. Therefore, vacuum-insulated tubing shows excellent potential for annular temperature control in high-temperature reservoirs.

3.2.4. Influence of Geothermal Gradient on the Performance of Insulated Fluids

As shown in Figure 17, the geothermal gradient does not change the trend of wellhead temperature curves, and annular insulated fluid exhibits a stable effect on wellhead temperature under different geothermal gradients. However, at high geothermal gradients, the enhancement effect of insulated liquid on wellhead temperature is weaker than that of insulated tubing. Similarly, wellhead temperature is not the core control target for high-temperature reservoirs, and priority should be placed on low-temperature reservoirs. When the geothermal gradient is low, insulated liquid can offer control performance comparable to insulated tubing and may be used as the preferred method.

Figure 18 shows that annular temperature change is only mildly affected by the thermal conductivity of insulated liquid, regardless of whether geothermal gradients are high or low. Combined with the analysis in Section 3.2.2, this is because Figure 17 corresponds to a low production rate (50 t/d), where radial heat flux is inherently small. Together with the conclusions in Section 3.2.3, insulated liquid provides weaker performance than insulated tubing under low-production conditions in high-temperature reservoirs. Therefore, insulated tubing should be considered for controlling annular temperature under such conditions, while the insulated liquid may be negligible.

4. Discussion

The above analysis demonstrates that annular temperature is the primary control objective under high-temperature, high-production conditions, whereas wellhead temperature is the primary focus under low-temperature, low-production conditions. As shown in Figure 19, the production rate is as high as 1000 t/d and the geothermal gradient is as high as 4.5 °C/(100 m). It can be seen that the annular temperature change increases with both tubing and annular liquid thermal conductivity, but combined insulation achieves a stronger control effect. The maximum annular temperature change is 87.99 °C, while the minimum is 31.45 °C, representing a 64.26% reduction. Considering the stability and low cost of insulated liquid, high-performance insulated liquid should be prioritized for annular temperature control in high-temperature, high-production deepwater wells. If the expected effect cannot be achieved, low-grade insulated tubing can be added to enhance insulation.

Figure 20 illustrates the wellhead temperature under low-temperature, low-production conditions, where the production rate is 50 t/d and the geothermal gradient is 2.0 °C/(100 m)). The maximum wellhead temperature reaches 64.80 °C and the minimum is 32.33 °C, representing a 100.43% increase. Combined insulation thus shows excellent performance in enhancing wellhead temperature in low-temperature, low-production deepwater wells. Similarly, for such wells, high-performance insulated liquid should be used as the primary control measure. If the expected performance cannot be achieved, low-grade insulated tubing may be used as an auxiliary measure. If both remain insufficient, active heating technologies must be considered.

5. Conclusions

(1)

Thermal insulation is critical for ensuring well integrity and flow assurance in deepwater wells. Annular temperature variation and wellhead temperature can effectively characterize insulation performance, corresponding respectively to wellbore integrity and flow assurance. Among available insulation technologies, insulated tubing and annular insulating liquid have good applicability in deepwater wells.

(2)

Vacuum-insulated tubing and insulation-coated tubing have overlapping effective ranges, and a similar overlap exists between annular insulating liquid and insulated tubing. Under certain conditions, insulation measures may bring about counterproductive effects on annular temperature control, which depend on the relative relationship between radial temperature gradients and thermal resistance. When performance is comparable, annular insulating liquid should be prioritized, whereas vacuum-insulated tubing should be considered only as a last option due to its high cost.

(3)

Under high production or high geothermal gradients, annular temperature variation is the primary control target, while under low-production or low-temperature conditions, wellhead temperature becomes the dominant objective. Insulated tubing demonstrates superior annular temperature control under high-production conditions, whereas annular insulating fluids exhibit a weaker capability for regulating annular temperature in high-temperature reservoirs at low production rates.

(4)

Composite insulation—combining insulated tubing with annular insulating liquid—shows outstanding performance. In high-temperature, high-production wells, the composite insulation reduces annular temperature change by 64.26%, and in low-temperature, low-production wells, it increases wellhead temperature by 100.43%. In practical applications, high-performance annular insulating fluids should be adopted as the primary measure, with insulated tubing used as a supplementary option to reduce cost while maintaining long-term insulation effectiveness.