Transient Pressure and Temperature Analysis of a Deepwater Gas Well during a Blowout Test

Abstract

On one hand, a blowout test can clean the bottom of the well, and on the other, it can learn the productivity of the well, which is important work before putting the well into production and also the main basis for production allocation of the well. The accurate prediction of the blowout test process provides a theoretical basis for the design of a reasonable blowout test system and the determination of well cleaning time. During deepwater blowout tests, gas and liquid flows are unsteady in pipes, and flow parameters change over time. At present, accurately predicting changes in fluid temperature, pressure, liquid holdup, and other parameters in a wellbore during an actual blowout process using the commonly used steady-state prediction methods is difficult, and determining whether a test scheme is reasonable is impossible. Therefore, based on the conservation of mass, momentum, and energy during the blowout test process, in this study, formation, wellbore, and nozzle flows were coupled for the first time, and a time and space of unsteady pressure drop and a heat transfer differential equation system was established; furthermore, using the Newton–Raphson method, the equations were solved. Finally, the simulation of the transient flow of the blowout test was completed. Considering a measured deepwater gas well A as an example, the blowout test process was simulated, and the variations in the wellbore flow parameters were analyzed. Comparing the simulation result with the test data, we concluded the following. (1) During the blowout process, the wellbore temperature gradually increased; pressure at the bottom of the wellbore decreased; and pressure at the wellhead increased; and (2) the established model agreed well with the actual production data, and the average error of the wellhead pressure and temperature was less than 5%. Considering the high production capacity of deepwater gas wells, the use of large-sized tubing and nozzles to spray is recommended, which can improve the speed of clearing wells and prevent the formation of hydrate.

1. Introduction

At present, deepwater is one of the focuses of oil and gas resource development and has broad prospects, but deepwater oil and gas exploitation has been handicapped by the complexity of the environment. Due to environmental complexities in deepwater gas wells, fluid flow parameters change with time during a two-phase flow (i.e., from the formation to the wellbore and in the wellbore), thereby making the flow complicated. Therefore, accurately predicting changes in flow parameters such as wellbore fluid temperature, pressure, and liquid holdup during an actual blowout process is difficult, and researching the two-phase transient flow during blowouts is necessary.

Deepwater well testing is characterized by high technology, investment, and risk. Moreover, gas well testing is crucial in the development potential evaluation of deepwater wells [1,2]. Wellbore storage effect is obvious during a shut-in period of a deepwater gas well [3]. The maximum test flow of the test string, ground process, and test system affect the test, and the influence of the test system is the greatest [4]. Therefore, Wu et al. designed a work system based on a critical test flow and proposed a test program of “one-open and one-close” [5].

At present, the research on wellbore temperature and pressure is relatively perfected. Churchill and Chu studied the convective heat transfer coefficient of seawater, and Mathews conducted a similar study [6,7]. Chin and Wang studied thermodynamic losses in the risers of top test trees [8]. Based on the first principle of transient gas well production, Hasan et al. established a wellbore temperature model [9]. Stiles and Trigg developed a temperature mathematical simulator for deepwater drilling [10]. Izgec et al. and Ismadi used nodal analysis methods to study temperature distribution [11,12,13,14].

Spindler explicitly gave the initial and boundary conditions for a calculated transient temperature distribution [15]. Hasan and Kabir unified different situations of heat transfer models, and Kabir used transient measured temperature to calculate static temperature as well as established flow temperature gradient to accurately estimate geothermal gradient and gas flow [16,17]. Chen derived a set of borehole-formation heat transfer differential equations [18]. The difference between seawater and production pipe temperatures was large, and thermal radiation could not be ignored, there was a large difference between the flow of the formation and seawater sections in deepwater wells, and heat loss mainly occurred in the seawater section [19,20].

Liu et al. established a transient temperature and pressure model for gas well testing to explain the reason of abnormal wellhead pressure [21]. Zhang et al. reported that the pressure at the bottom decreased to a certain extent, whereas the pressure at the wellhead gradually increased and finally remained relatively stable. and Kabir et al. studied the production logging of natural gas wells [22]. These studies were based on heat transfer models and recorded well-logging fluid flows along boreholes to determine regional contributions.

With an increase in production, the Joule–Thomson effect increases. On this basis, Li et al. obtained the relationship between temperature and flow rate, and Xu established a coupling model of the transient multiphase flow between the formation and wellbore. He et al. studied the induced transient flow of deepwater gas wells and established a transient model of multiphase flow, reproducing the flow in a wellbore under actual working conditions [23,24,25,26].

At present, the commonly used prediction methods do not consider the transient flow process response of formation inflow, wellbore flow rule, and surface nozzle flow. Moreover, the prediction of the blowout test temperature, pressure, and liquid holdup of the actual blowout test wellbore fluid has poor accuracy. Therefore, in a first, herein, the formation, wellbore, and surface nozzle flows are coupled to establish a deepwater wellbore transient flow model of the blowout test to improve the accuracy of the calculation results.

2. Mathematics Model

The wellbore flow is an unsteady two-phase flow in the test. The model is assumed as follows:

(1)

the gas–liquid flow in the pipe is one-dimensional and unsteady;

(2)

the gas is compressible, whereas the liquid is incompressible;

(3)

a high production and homogeneous flow during the blowout test; and

(4)

the downward direction of the wellbore flow is defined as the positive direction of the z-axis.

According to the principles of the conservations of mass, momentum, and energy, the control equations are

$$\frac{\partial {\rho }_m}{\partial t}+\frac{\partial G_m^{}}{\partial z}=0$$

(1)

$$\frac{\partial G_m}{\partial t}+\frac{\partial }{\partial z}\left(\frac{\partial G_m^2}{{\rho }_m}\right)+\frac{\partial P}{\partial z}+{\rho }_{m}g\sin \theta +\frac{f_m{G}_m\left|G_m\right|}{2d_{ti}{\rho }_m}=0$$

(2)

$$Q=\frac{\partial {(mE)}_{cv}}{\partial t}+\frac{\partial {(m\prime E\prime )}_w}{\partial t}+\frac{\partial }{\partial z}\left[w_m\left(H_f+\frac{1}{2}{v}^2+gz\cos \theta \right)\right]$$

(3)

Considering the high gas production in the test, the transient simulation of the gas–liquid flow is simplified to a homogeneous flow. Rendeiro and Kelso (1988) modified the correction of the gas relative density, and the mixture relative density and mixture density are expressed as follows:

$${\gamma }_m=\frac{{\gamma }_g+817.7{\gamma }_L/GLR}{1+200GLR}$$

(4)

$${\rho }_m=\frac{28.96{\gamma }_{m}P}{Z_{m}RT}$$

(5)

where the natural gas deviation coefficient, Z_m, can be calculated using the Dranchuk–Abu–Kassem relation:

$$\begin{array}{l}{Z}_m=1+\left(A_1+A_2/T_{pr}+A_3/T_{pr}^3+A_4/T_{pr}^4+A_5/T_{pr}^5\right){\rho }_{mr}+\left(A_6+A_7/T_{pr}+A_8/T_{pr}^2\right){\rho }_{mr}^2\\ -A_9\left(A_7/T_{pr}+A_8/T_{pr}^2\right){\rho }_{mr}^5+A_{10}\left(1+A_{11}{\rho }_{mr}^2\right)\left({\rho }_{mr}^2/T_{pr}^3\right)\exp \left(-A_{11}{\rho }_{mr}^2\right)\end{array}$$

(6)

2.1. Steady-State Heat Transfer

Heat transfer in deepwater wells comprises two sections: seawater and formation sections. The heat transfer in the wellbore is steady, and the heat transfer during the formation is unsteady and can be described via a transfer heat-conduction time function. The wellbore structure and length of the differential cell, dz, are shown in Figure 1.

According to the law of heat conduction from the wellbore to formation and unsteady heat dissipation, the radial heat gradient equation of formation can be established. Moreover, according to the law of convection heat transfer from the wellbore to seawater, the radial heat gradient equation of seawater can also be established. Combining the conservation of energy and enthalpy gradient equations, a general formula to calculate the wellbore temperature gradient of offshore oil and gas wells is formed:

$$\frac{dT}{dz}=-L_r(T-T_{ei})-\frac{g\cos \theta }{C_{pm}}-\frac{v_m}{C_{pm}}\frac{d{v}_m}{dz}+C_{Jm}\frac{dp}{dz}$$

(7)

For the formation section:

$$L_r=\frac{2\pi r_{to}{U}_{to1}{K}_e}{C_{pm}{w}_t\left[K_e+f\left(t_D\right)r_{to}{U}_{to1}\right]}$$

If the fluid heat-transfer coefficient in tubing, the heat conductivity of tubing and casing offer negligible resistance to heat flow, U_to1 can be approximated by

$$U_{to2}={\left[\frac{1}{h_c+h_r}+\frac{r_{to}}{K_{cem}}\ln \frac{r_w}{r_{co}}\right]}^{-1}$$

For the seawater section:

$$L_r=\frac{2\pi r_{to}{U}_{to2}}{C_{Pm}{w}_t}$$

Similarly, where U_to2 can be approximated by

$$U_{to2}={\left[\frac{1}{h_c+h_r}+\frac{r_{to}}{r_{co}{h}_w}\right]}^{-1}$$

2.2. Transient Heat Transfer

During the test, the output fluid dissipates heat to the wellbore, and the temperature decreases gradually from the bottom to wellhead. Furthermore, the cement and string are continuously heated by the high-temperature fluid so that the temperature difference between the fluid and wellbore constantly decreases, and the fluid temperature continuously changes with time. Therefore, the heat loss of the wellbore fluid during the test blowout is a transient process (Figure 2).

We introduced the Hasan and Kabir heat storage coefficient into Equation (3) and combined it with the wellbore steady-state heat transfer, Equation (7); an explicit equation for calculating the transient temperature of the wellbore fluid is obtained as follows:

Partial differential equation:

$$Q=\frac{\partial {\left(mE\right)}_{cv}}{\partial T}+\frac{\partial {\left(m^{\prime }{E}^{\prime }\right)}_w}{\partial T}+\frac{\partial }{\partial z}\left[w_m\left(H_f+\frac{1}{2}{v}^2+gz\cos \theta \right)\right]$$

Introduced heat storage coefficient:

$$C_T=\frac{m^{\prime }{E}^{\prime }}{mE},\frac{d{T}_f}{dz}=g_T\cos \theta -e^{\left(z-L\right)L_R}\psi$$

Explicit equation:

$$T_f(z,t)=T_{ebh}-g_{T}z\cos \theta +\frac{1-e^{-bt}}{L_R}\left[1-e^{(z-L)L_R}\right]\psi$$

For different wells, the heat storage coefficient can be fitted using test data. Combined with the conservations of mass and momentum in the transient process, the wellbore pressure and temperature coupling model is obtained as follows:

$$\{\begin{array}{l}\frac{\partial P}{\partial z}=-\frac{\partial G_m}{\partial t}-\frac{\partial }{\partial z}\left(\frac{\partial G_m^2}{{\rho }_m}\right)-{\rho }_{m}g\sin \theta -\frac{f_m{G}_m\left|G_m\right|}{2d_{ti}{\rho }_m}\\ T_f(z,t)=T_{ebh}-g_{T}z\cos \theta +\frac{1-e^{-bt}}{L_R}\left[1-e^{(z-L)L_R}\right]\psi \end{array}$$

(8)

2.3. Temperature during Production Adjustment

Because production is often unstable, it requires frequent production adjustment. In this case, using an ordinary temperature transient model cannot predict the temperature change accurately, which leads to a large pressure deviation. To improve the prediction accuracy of the real blowout test process, developing the transient superposition correlation of the wellbore temperature is necessary.

Assuming a virtual initial temperature rise time, the temperature is calculated through the steady-state heat transfer model in the period of an increasing production. The temperature change is divided into a superposition of the well shut-in and opening processes in the period of a decreasing production. The corresponding transient superposition is shown in Figure 3.

(1) Increasing production

The temperature T₁ can be calculated as follows:

$$\frac{T_1-T_{ei}}{T_{2,stable}-T_{ei}}=1-e^{-a\mathrm{\Delta }{t}_1}$$

(9)

The virtual time Δt₁ can be calculated as follows:

$$\mathrm{\Delta }{t}_1=-\frac{1}{a}\ln \frac{T_{2,stable}-T_1}{T_{2,stable}-T_{ei}}$$

Therefore, the temperature T₂ at time t₂ can be calculated as follows:

$$\frac{T_2-T_{ei}}{T_{2,stable}-T_{ei}}=1-e^{-a(t_2-t_1+\mathrm{\Delta }{t}_1)}$$

(10)

(2) Decreasing production

Temperature changes ΔT_2,close at t₂ time shut-in process can be calculated as follows:

$$\frac{\mathrm{\Delta }{T}_{2,close}}{T_1-T_{ei}}=e^{-a(t_2-t_1)}-1$$

(11)

Temperature changes ΔT_2,open in the well opening process can be calculated as follows:

$$\frac{T_{2,open}}{T_{2,stable}-T_{ei}}=1-e^{-a(t_2-t_1)}$$

(12)

Finally, the temperature T₂ at time t₂ can be calculated as follows:

$$T_2=T_1+\mathrm{\Delta }{T}_{2,open}+\mathrm{\Delta }{T}_{2,stable}=T_{2,stable}-(T_{2,stable}-T_1)e^{-a(t_2-t_1)}$$

(13)

3. Blowout Test Process and Model Solution

(1) Blowout test process

When the well is closed, the induced fluid is on the top of the test fluid in the wellbore. However, when the gas well is open, the upper induced fluid relieved pressure; wellhead fluid flowed first; and bottom fluid flowed later, leading to a two-phase variable mass flow in the wellbore, the blowout test process is shown in Figure 4. During the upstream period, the gas–liquid fluid flowed from the formation into the wellbore and continuously released heat to the formation and seawater sections. When blown out for a while, a steady flow stage was developed. Therefore, the transient flow model was coupled by “wellhead nozzle flow + induced fluid pipe flow + well fluid pipe flow + formation seepage.”

In summary, based on the above-mentioned phenomena, the two-phase flow transient model comprises the transient conservations of mass, momentum, and energy, and the coupling of the wellbore flow, wellhead throttling, and formation productivity is considered. The influence of the heat transfer difference between the formation and seawater is involved in the calculation of the fluid density in the wellbore using a pseudo single-phase model.

Deliverability equation:

$$q_{gsc}=C{\left(P_r^2-P_{wf}^2\right)}^n$$

(14)

The flow rate in the blowout was high, and the wellhead nozzle flow was suitable for the multiphase flow formula (i.e., the Sachdeva-Model of subcritical flow).

The critical pressure ratio of gas–liquid two phases passing through the nozzle:

$$p_r={\left\{\frac{\frac{k}{k-1}+\frac{(1-x_g){\upsilon }_L(1-p_r)}{x_g{\upsilon }_{g1}}}{\frac{k}{k-1}+\frac{n}{2}+\frac{n(1-x_g){\upsilon }_L}{x_g{\upsilon }_{g2}}+\frac{n}{2}{\left[\frac{(1-x_g){\upsilon }_L}{x_g{\upsilon }_{g2}}\right]}^2}\right\}}^{\frac{k}{k-1}}$$

(15)

$$n=1+\frac{x_{g1}(c_p-c_v)}{x_{g2}{c}_v+(1-x_{g1})c_l}$$

Total mass flow rate:

$$G_m=C{A}_2{\left[2p_1{\rho }_{m2}\left(\frac{(1-x_g)(1-p_{rcal})}{{\rho }_L}+\frac{x_{g}k}{k-1}({\upsilon }_{g1}-p_{rcal}{\upsilon }_{g2})\right)\right]}^{0.5}$$

(16)

(2) Model solution

The transient model of the gas well contains partial differential equations, Equations (1)–(3), which need to be solved numerically. First, divide the well depth H into N sections (the well depth step is Δz = H/N), and determine the time step Δt and difference grid (Figure 5). The implicit central finite difference method is used to express the difference equations of each grid:

$$f_i\left(\mathsf{\rho },\mathrm{G}\right)=\left({\rho }_{i,j+1}+{\rho }_{i+1,j+1}-{\rho }_{i,j}-{\rho }_{i+1,j}\right)+\frac{\mathrm{\Delta }t}{\mathrm{\Delta }z}\left(G_{i+1,j}+G_{i+1,j+1}-G_{i,j}-G_{i,j+1}\right)=0$$

(17)

$$\begin{array}{l}{f}_{N+i}\left(\mathsf{\rho },\mathrm{G}\right)=\left(G_{i,j+1}+G_{i+1,j+1}-G_{i,j}-G_{i+1,j}\right)+\frac{\mathrm{\Delta }t}{\mathrm{\Delta }z}\left(\frac{G_{i+1,j}^2}{{\rho }_{i+1,j}}+\frac{G_{i+1,j+1}^2}{{\rho }_{i+1,j+1}}-\frac{G_{i,j}^2}{{\rho }_{i,j}}-\frac{G_{i,j+1}^2}{{\rho }_{i,j+1}}+p_{i+1,j}+p_{i+1,j+1}-p_{i,j}-p_{i,j+1}\right)\\ +\frac{\mathrm{\Delta }tg\sin \theta }{2}\left({\rho }_{i,j}+{\rho }_{i+1,j}+{\rho }_{i,j+1}+{\rho }_{i+1,j+1}\right)+\frac{\lambda \mathrm{\Delta }t}{4D}\frac{\left(G_{i,j}+G_{i+1,j}+G_{i,j+1}+G_{i+1,j+1}\right)\left|G_{i,j}+G_{i+1,j}+G_{i,j+1}+G_{i+1,j+1}\right|}{{\rho }_{i,j}+{\rho }_{i+1,j}+{\rho }_{i,j+1}+{\rho }_{i+1,j+1}}=0\end{array}$$

(18)

where $\mathsf{\rho }=\left({\rho }_{1,j+1},{\rho }_{2,j+1},\cdots ,{\rho }_{N,j+1},{\rho }_{N+1,j+1}\right)$, $\mathrm{G}=\left(G_{1,j+1},G_{2,j+1},\cdots ,G_{N,j+1},G_{N+1,j+1}\right)$, and i = 1, 2,…, N; i = 1 represent a wellhead node, and i = N + 1 represents a bottom node.

The wellbore pressure at any moment can be solved using the Newton–Raphson method, where the Jacobian matrix J, residual vector R, and independent variable change vector V are, respectively, as follows:

$$J={\left[\begin{array}{cccccccccccc}1& 1& 0& \cdots & 0& 0& -\mathrm{\Delta }t/\mathrm{\Delta }z& \mathrm{\Delta }t/\mathrm{\Delta }z& 0& \cdots & 0& 0\\ 0& 1& 1& 0& \cdots & 0& 0& -\mathrm{\Delta }t/\mathrm{\Delta }z& \mathrm{\Delta }t/\mathrm{\Delta }z& 0& \cdots & 0\\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ 0& \cdots & 0& 1& 1& 0& \cdots & 0& 0& -\mathrm{\Delta }t/\mathrm{\Delta }z& \mathrm{\Delta }t/\mathrm{\Delta }z& 0\\ 0& 0& \cdots & 0& 1& 1& 0& \cdots & 0& 0& -\mathrm{\Delta }t/\mathrm{\Delta }z& \mathrm{\Delta }t/\mathrm{\Delta }z\\ a_{\left(N+1\right)1}& a_{\left(N+1\right)2}& 0& \cdots & 0& 0& a_{\left(N+1\right)\left(N+2\right)}& a_{\left(N+1\right)\left(N+3\right)}& 0& \cdots & 0& 0\\ 0& a_{\left(N+2\right)2}& a_{\left(N+2\right)3}& 0& \cdots & 0& 0& a_{\left(N+2\right)\left(N+3\right)}& a_{\left(N+2\right)\left(N+4\right)}& 0& \cdots & 0\\ \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots & \cdots \\ 0& \cdots & 0& a_{\left(2N-1\right)\left(N-1\right)}& a_{\left(2N-1\right)N}& 0& \cdots & 0& 0& a_{\left(2N-1\right)\left(2N\right)}& a_{\left(2N-1\right)\left(2N+1\right)}& 0\\ 0& 0& \cdots & 0& a_{\left(2N\right)N}& a_{\left(2N\right)\left(N+1\right)}& 0& \cdots & 0& 0& a_{\left(2N\right)\left(2N+1\right)}& a_{\left(2N\right)\left(2N+2\right)}\\ a_{\left(2N+1\right)1}& 0& 0& \cdots & 0& 0& 1& 0& \cdots & \cdots & 0& 0\\ 0& 0& 0& \cdots & 0& a_{\left(2N+2\right)\left(N+1\right)}& 0& 0& \cdots & \cdots & 0& 1\end{array}\right]}_{\left(2N+2\right)\times \left(2N+2\right)}$$

(19)

$$-f_1\left(\mathsf{\rho },\mathrm{G}\right),-f_2\left(\mathsf{\rho },\mathrm{G}\right)\cdots \cdots -f_{2N+1}\left(\mathsf{\rho },\mathrm{G}\right),-f_{2N+2}\left(\mathsf{\rho },\mathrm{G}\right)$$

(20)

$$V={\left[\mathrm{\Delta }{\rho }_{1,j+1}^{},\mathrm{\Delta }{\rho }_{2,j+1}^{}\cdots \cdots \mathrm{\Delta }{\rho }_{N,j+1}^{},\mathrm{\Delta }{\rho }_{N+1,j+1}^{},\mathrm{\Delta }{G}_{1,j+1}^{},\mathrm{\Delta }{G}_{2,j+1}^{}\cdots \cdots \mathrm{\Delta }{G}_{N,j+1}^{},\mathrm{\Delta }{G}_{N+1,j+1}^{}\right]}^T$$

(21)

The Newton–Raphson iterative and Gaussian elimination methods are used to solve the difference equation iteratively. The procedure can be described as follows.

(1)

Input basic parameters: well depth H, tubing diameter dti, formation pressure p_r, fluid extraction index I_L, average wellbore temperature T_ave, external pressure P₀, nozzle size d_chock, test fluid level L_h, and time interval dt.

(2)

Calculate the initial values at t = 0: bottomhole pressure p_wf(0), liquid depth L_h(0), pressure at the liquid level p_h(0), wellhead pressure p_t(0), and liquid column mass m_L(0).

(3)

Sort the well structure; determine the calculation step length of the formation and seawater sections; and calculate the position, temperature, and pressure of the interpolation point.

(4)

Set the calculation time and calculate the step length; perform the transient flow simulation calculation; and obtain the transient temperature and pressure profiles of the deepwater wellbore.

A simple flowchart of the model solution process is shown in Figure 6.

4. Application and Analysis Discussion

We selected deepwater well A to verify the applicability of the established model. The basic parameters corresponding to well A are shown in

Table 1. Basic parameters of well A.

Parameter	Value	Unit
Well depth	3350.7	m
Water depth	1447	m
Production pressure	40	MPa
Shut-in wellhead pressure	1.5	MPa
Production temperature	95	°C
Mudline temperature	4	°C
Surface seawater temperature	15	°C
Geothermal gradient	3.87	°C/100 m
Outer diameter of testing pipe	114.3	mm
Inner diameter of testing pipe	76.2	mm
Outer diameter of cement	317.5	mm
Inner diameter of cement	244.5	mm
Heat transfer coefficients of formation section	20	W/(m2·°C)
Heat transfer coefficients of seawater section	45	W/(m2·°C)
Formation thermal conductivity	4.2	W/(m·°C)
Dimensionless heat storage coefficient	5	-
Induced fluid specific density	1.16	-
Gas specific weight	0.6	-
Hole drift angle	0	rad

.

Before the blowout, the wellbore was filled with the test and induced fluid. We assumed that the density of the induced fluid was equal to that of the test fluid to simplify the calculation. The gas well productivity is described using an exponential equation; select the coefficient n = 0.75 and C = 1.2 × 10⁴ m³/d·MPa⁻²ⁿ. The results of the interpolation temperature and initial pressure profile are shown in Figure 7.

4.1. Transient Flow Prediction

According to the actual test conditions, the wellbore pressure, temperature, gas production, liquid holdup, hydrate formation temperature, and other parameters were simulated during the blowout (Figure 8). After opening the well for approximately 2 h (8640 s), the formation started producing gas; the working fluid in the wellbore began to be displaced by the gas; the gas–liquid two-phase interface kept moving up; and the wellhead pressure started to increase. At approximately 14,400 s, the wellhead liquid holdup changed to 0 and working fluid was completely displaced, which agreed with the actual situation. The average error in the wellhead pressure and temperature calculations and measured parameters was less than 5%. The simulations agreed well with the measured values, which showed that the established model met the requirements of computational accuracy. The simulation results were verified via field temperature measurements. The simulation results showed that the mudline temperature was slightly lower than the hydrate formation temperature at the end of the cleanup, and the hydrate inhibitor was injected in the field operation.

The wellbore pressure, temperature, liquid holdup, and mixture density distribution at different times were predicted; the results are shown in Figure 9. After the well opening, the test fluid was replaced by airflow and wellbore pressure gradient decreased, whereas the wellhead pressure increased gradually. The gas production and wellbore temperature increased gradually. The liquid holdup and mixture density decreased gradually and finally formed as an annular flow.

4.2. Sensitivity Analysis of the Key Parameters of the Test

(1) Nozzle size

In the blowout design, the nozzle size is an essential technological parameter. The nozzle size significantly influences the clearance time, surface equipment, and flow path. We selected 3-, 6-, 9-, 12-, and 15-mm nozzles for the sensitivity analysis (Figure 10). The larger the nozzle size, the higher the gas production, the faster the clearance speed, and higher the mudline temperature. When selecting the nozzle size, it should be larger than 10 mm to improve the cleaning speed and mudline temperature as well as prevent hydration.

(2) Influence of tubing sizes

Based on the basic data of well A, 62-, 76-, 88.3-, and 100.5-mm inner diameter tubing were selected for the sensitivity analysis (Figure 11). The larger the tubing, the lower the friction resistance, the higher the gas production, and faster the cleaning speed. However, affected by the decrease in the flow rate, the rising speed of the mudline temperature would be slower. To improve the cleaning speed, choosing tubing with a size of 76 or 88.3 mm is recommended.

5. Conclusions

(1)

Coupling formation, wellbore, and surface nozzle flows as well as combining a two-phase nozzle flow model, two-phase fluid holdup model, formation productivity equation, and deepwater transient heat transfer model, a deepwater blowout wellbore transient flow model was established, which considered the characteristics of the transient flow and determines the reliable blowout test time and test system.

(2)

As the blowout test continued, the bottomhole pressure decreased slightly and the wellhead pressure increased gradually. Moreover, the wellbore temperature increased gradually; however, the mudline temperature was low. The mudline temperature may be lower than the hydrate formation temperature in the cleaning process, so corresponding measures should be taken to prevent and control the hydrate formation.

(3)

The new model can be used to simulate the variation in the wellbore fluid level, pressure, temperature, gas production, liquid holdup, and hydrate formation temperature with time and well depth changing during the blowout period. The simulation result of gas well A showed that the calculated data agreed well with the measured values in the test, with an average error in the wellhead pressure and temperature of less than 5%, and the established model had a high calculation accuracy.

(4)

The sizes of the nozzles and tubing are the essential parameters in the blowout design. They significantly influence the clearance time, surface equipment, and blowout process. The transient model of the blowout test in this paper could effectively determine the nozzle regulation system during a blowout test as well as determine the reasonable injection time of the inhibitor and tubing string size. Application analysis and discussion showed that under the condition of satisfying the requirements of the test operation, choosing large nozzle and tubing sizes is necessary to accelerate the discharge of the wellbore working fluid, increase the wellbore temperature, and prevent hydrate formation.