Transient gas–liquid–solid flow model with heat and mass transfer for hydrate reservoir drilling

International Journal of Heat and Mass Transfer 141 (2019) 476–486

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Transient gas–liquid–solid flow model with heat and mass transfer for hydrate reservoir drilling Youqiang Liao a, Xiaohui Sun a, Baojiang Sun a,⇑, Yonghai Gao a,b, Zhiyuan Wang b,⇑⇑ a b

Key Laboratory of Unconventional Oil & Gas Development (China University of Petroleum (East China)), Ministry of Education, Qingdao 266580, PR China School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266555, PR China

a r t i c l e

i n f o

Article history: Received 22 February 2019 Received in revised form 24 May 2019 Accepted 27 June 2019 Available online 3 July 2019 Keywords: Hydrate reservoir drilling Gas–liquid–solid flow model Hydrate dynamic decomposition Cuttings transport Heat and mass transfer

a b s t r a c t The three–phase gas–liquid–solid flow, caused by hydrate decomposition in cuttings is a main concern during drilling through gas–hydrate reservoir. In this study, a transient gas–liquid–solid flow model is developed considering the coupling interactions between hydrate dynamic decomposition, cuttings transport and heat transfer in multiphase flow. Using this model, the transient gas–liquid–solid flow behaviors are investigated. Numerical simulations show that the decomposition rate of hydrate in formation is only 1/140 of that in annular cuttings for a unit depth, therefore, the influences of hydrate decomposition in hydrate layers can be neglected. Hydrate particles undergo three processes from bottom hole to wellhead in annulus: non–decomposition, slow decomposition and rapid decomposition. In annulus where the depth is more than 400 m, hydrates decompose slowly and the decomposed gas hardly expands due to the high pressure. While, if the hydrates and decomposed gas return upwards to the position where the depth less than 400 m, the gas void fraction increases significantly, not only due to the faster decomposition rate of hydrates but also due to the more intense expansion of decomposed gas. After the hydrate particles return upwards to the wellhead, the behaviors of gas–liquid–solid flow tend to be a quasi–stable state. If there is no backpressure device at the wellhead, that is, the wellhead backpressure is 0 MPa, the gas void fraction at the wellhead can reach 0.68, which is enough to cause blowout accident. Increasing wellhead backpressure to 2 MPa through managed pressure devices and lowering the inlet temperature of drilling fluid to 17.5 °C except adjusting drilling fluid density can manage the gas void fraction within 10%. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Gas hydrates, as a potential environmentally friendly and widely distributed resource, have gradually become the research focus of countries and oil companies all over the world [1,2]. The methods of developing hydrate reservoirs primarily include depressurization, thermal stimulation, CO2 replacement and inhibitor injection [3–5]. All of the above methods need to open the hydrate layers through drilling technology. Meanwhile, the hydrate layers are sometimes drilled in deep water drilling due to the low temperature and high pressure conditions [6,7]. Therefore, safely and efficiently drilling in hydrate reservoirs is a great significance for the development and utilization of hydrate resources [8,9].

⇑ Corresponding author. ⇑⇑ Corresponding author. E-mail addresses: [email protected] (B. Sun), [email protected] (Z. Wang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.06.097 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

The existing studies on hydrate mainly focus on the development of hydrate reservoirs and the prevention of hydrates in flow assurance [10,11]. Meanwhile, most studies on the multiphase flow in the wellbore are focusing on hydrate formation during deep water drilling. Wang et al. [6,12] studied the hydrate formation region and analyzed the influence of hydrate formation on annulus multiphase flow behaviors during deep water drilling. Sun et al. [13,14] studied the overflow process coupled with hydrates phase transformation and presented a unified gas–liquid flow mechanistic model. While, few studies have researched the hydrate dynamic decomposition coupling the heat and mass transfer in wellbore during drilling through hydrate reservoir in–depth. For hydrate reservoir drilling, Hao [15], Fereidounpour et al. [16] and Sun et al. [17] presented experimental and numerical analysis of wellbore stability focusing on the stability of hydrate bearing formations and drilling fluid systems. Yu et al. [9] investigated hydrate dissociation and gas flow into wellbore induced by circulation of drilling fluid during drilling through hydrate bearing formations. While, few studies on multiphase flow in wellbore

Y. Liao et al. / International Journal of Heat and Mass Transfer 141 (2019) 476–486

477

Nomenclature Aa Ah Ap CD Cf Cg C0 Ct Cw D Dc E Fc FG Fb FD Fw g hci hhole hpi hpo hri hro Hcas Hsea Hwell kc keh kcem kr 0 kd Mh _ gw m _ gf m _ ww m _ wf m _ hw m _ hf m nh Nu

cross–sectional area of annulus, m2 the superficial area of hydrate, m2 cross–sectional area of drill pipe, m2 drag coefficient, dimensionless specific heat of drilling fluid, J=ðkg
 CÞ specific heat of gas, J=ðkg
 CÞ distribution parameter, dimensionless temperature revised coefficient, dimensionless specific heat of water, J=ðkg
 CÞ wellbore diameter, m cuttings diameter, m volume fraction The resultant force of cuttings, N gravity force of cuttings, N buoyancy force of cuttings, N drag force of cuttings, N frictional force, N gravitational acceleration, m=s2 convection heat
 transfer coefficient of inner wall of casing, w= m2
 C convection
 heat transfer coefficient of inner wall of hole, w= m2
 C convection
heat transfer coefficient of inner wall of drill pipe, w= m2
 C convection
heat transfer coefficient of outer wall of drill pipe, w= m2
 C convection heat
 transfer coefficient of inner wall of riser, w= m2
 C convection heat
 transfer coefficient of outer wall of riser, w= m2
 C depth of casing, m depth of sea, m depth of well, m heat conductivity of cuttings, w=ðm
 CÞ the effective thermal conductivity of the gas hydrate formation, w=ðm
 CÞ heat conductivity of cement sheath, w=ðm
 CÞ heat conductivity of formation, w=ðm
 CÞ hydrate decomposition rate constant,
 mol= MPa
m2
s the molar mass of hydrate, kg=mol gas production
rate due to hydrate decomposition in wellbore, kg= m3
s gas production
rate due to hydrate decomposition in formation, kg= m3
s water production rate
 due to hydrate decomposition in wellbore, kg= m3
s water production
rate due to hydrate decomposition in formation, kg= m3
s
 decomposition rate of hydrate in wellbore, kg=
m3
s  3 decomposition rate of hydrate in formation, kg= m
s the number of moles of the hydrate, mol Nussels number

caused by hydrate particles decomposition were introduced in the literatures. Coupling with the wellbore and reservoir heat transfer process, Gao et al. [18,19] first proposed a multiphase flow model to study the variation of bottom hole pressure and temperature field in hydrates drilling process for two conditions: with riser and without riser. And then, Wei et al. [20] proposed a multiphase flow model preliminarily considering the interactions of pressure, hydrate decomposition, phase contents and velocities in the wellbore. While, Multiphase flow in wellbore during drilling through

p r r ce re r ci r co r pi r po r ri r ro rw Re Rec Sh

pressure, Pa distance from the wellbore, m radius of the wellbore, m radius of the hydrate formation, m inner diameter of casing, m outer diameter of casing, m inner diameter of drill pipe, m outer diameter of drill pipe, m inner diameter of riser, m outer diameter of riser, m inner diameter of wellbore, m three phase Reynolds number, dimensionless Reynolds number of cuttings, dimensionless hydrate saturation

Sk1 h

hydrate saturation at last time

Skh t Ta Te Tp ulc Ua

hydrate saturation at this time drilling time, s annulus temperature, °C formation temperature, °C drill pipe temperature, °C relative velocity of cuttings and drilling fluid, m/s overall heat transfer coefficient in the annulus,
 w= m2
 C overall heat transfer coefficient in the drill pipe,
 w= m2
 C velocity, m/s velocity of drilling fluid in annulus, m/s slippage speed, m/s velocity of drilling fluid in drill pipe, m/s volume, m3 distance from the wellhead, m the difference in the fugacity of methane gas, MPa the sphericity, dimensionless density, kg=m3 the effective product of the density
and specific heat capacity of the fluid in annulus, J= m3
 C the effective product of the density and
specific  heat capacity of the gas-hydrate formation, J= m3
 C deviation angle liquid surface tension, N/m viscosity, Pa
s Porosity Heat of gas hydrate dissociation, J=kg

Up

v va v gr vp

V z Df g w

q ðqC Þefh ðqC Þeh

h

r l

/ DH

Subscripts f drilling mud g gas l liquid c cuttings h hydrate m mixture

hydrate reservoir is a complex phenomenon, for which the interactions between different factors can be summarized as follows (As shown in Fig. 1): (1) The dynamic decomposition rate of hydrates depends on its temperature and pressure. Cuttings transport will affect the return upwards speed and decomposition position of hydrates in wellbore. Heat transfer in wellbore will affect the decomposition rate of hydrates.

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Fig. 1. The inter–coupling of hydrate decomposition, cuttings transport and heat transfer.

(2) Hydrate in cuttings particles decomposition will reduce the mass of the whole cuttings, accordingly, the forces such as gravity, buoyancy and drag force, etc. will change, which will affect its transport speed. The complex gas–liquid–solid multiphase flow in the wellbore will be formed due to hydrate dynamic decomposition [20] which will also affect cuttings transport in annulus [21]. (3) Hydrates decomposition is an endothermic process. The decomposed gas not only reduces annular pressure, but also reduces the comprehensive heat transfer coefficient between drilling fluid and formation, resulting in the reduce of the energy loss and increase of the temperature in annulus [22,23]. In turn, the temperature field changes will affect the dynamic decomposition of hydrates in the annulus [8,24]. Therefore, the flow in annulus can be summarized as a complex three–phase gas–liquid–solid flow coupled with hydrate dynamic decomposition, cuttings transport and heat transfer. In this study, the coupling interactions between hydrate dynamic decomposition, cuttings transport and heat transfer are considered, and a fully coupled transient gas–liquid–solid flow mechanism model is developed. Then, the complex model is solved numerically by pressure based method [25]. Furthermore, the three–phase gas–liquid–solid flow and the effects of wellhead backpressure, drilling fluid density and injection temperature are thoroughly analyzed. This proposed mathematical model is a more in-depth extension of the conventional multiphase flow model, it can present some important implications for drilling through gas–hydrate formation for practical projects.

2. Transient gas–liquid–solid flow model To appropriately establish a transient gas–liquid–solid flow model in annulus during drilling through hydrate formation, it is necessary to analyze the flow mechanism coupling hydrate decomposition. As shown in Fig. 2, in the process of drilling, the cuttings carrying hydrate particles return upwards continuously during drilling through hydrate layers. In this upwards process, the phase equilibrium condition of hydrate is broken down due to the pressure decreasing and temperature increasing, resulting in the decomposition of hydrate and the generation of a large number of gases, furthermore, forming a complex gas–liquid–solid three– phase flow in the wellbore. The gas rapidly expands since the decomposed gas moving to the upper part of the wellbore, resulting in a large increase in volume void fraction. It not only reduces the pressure distribution in wellbore, caused by the decrease of hydrostatic column pressure,

Fig. 2. Mechanisms decomposition.

of

solid–liquid–gas

flow

coupling

hydrate

dynamic

but also reduces the energy loss due to the decrease of comprehensive heat transfer coefficient in annulus. Thereby, the decomposition of hydrate is further promoted. To solve this complex gas–liquid–solid flow problem, the following assumptions are made: (1) Gas hydrate formation is isotropic. (2) Drilling mud and cuttings are incompressible in annulus. (3) Ignoring the influence of adiabatic cooling and JouleThomson effects on wellbore temperature field [18–20]. 2.1. Gas–liquid–solid flow model During drilling through hydrate formation, hydrate particles are adhered to the pore of cuttings. With the pressure decreasing and temperature increasing in the process of cuttings returning upwards [26], the flow in wellbore becomes complex three–phase gas–liquid–solid flow due to the decomposition of hydrates [27]. 2.1.1. Mass–balance equations During drilling through hydrate formation, gas in annulus mainly includes the gas generated by hydrate decomposition in cuttings and hydrate formation. According to the conservation of mass, the continuity equation of gas phase can be obtained as follows.

  @ Aa E g q g @t

¼

  @ Aa E g q g v g @z

_ gw þ þ Aa Ec m

Z

re

r ce

_ gf dr 2p r m

ð1Þ

The left–hand side of Eq. (3) represents the change in the gas mass in the annulus unit. The right–hand side represents the gas mass of the inflows and outflows of the annulus unit, mass increased from the hydrate decomposition in cuttings and hydrate formation, respectively. In addition to the difference between inflow and outflow, the mass increment of liquid phase in annulus unit also includes the produced water from hydrate decomposition. On the basis of mass conservation, the continuity equation of liquid phase can be obtained as follows.

@ ðAa El ql Þ @ ðAa El ql v l Þ _ ww ¼ þ Aa E c m @t @z

ð2Þ

The decomposition of hydrate in cuttings will reduce the quality of cuttings particles, resulting in the change of their force, and furthermore, affecting their transport speed [21]. On the basis of mass conservation, the continuity equation of solid phase can be obtained as follows.

Y. Liao et al. / International Journal of Heat and Mass Transfer 141 (2019) 476–486

@ ðAa Ec qc Þ @ ðAa Ec v c qc Þ _ gw ¼  Aa Ec m @t @z

ð3Þ

2.1.2. Momentum–balance equation The momentum conservation equation in the annulus can be written as [28] @ ðAa Eg qg v g þAa El ql v l þAa Ec qc v c Þ @t

þ

  ¼ Aa F w  Aa Eg qg þ Aa El ql gcosh

ð4Þ

2.1.3. Cuttings transport model As shown in Fig. 3, under the critical decomposition depth of hydrate, the flow in annulus is liquid–solid two–phase flow, which is the same as that in conventional drilling. For cuttings transport, Mohammadzadeh et al. [29], GhasemiKafrudi et al. [30] and Pang et al. [31] studied the transport rate in wellbore considering the effects of drill string rotation, drilling fluid properties and well deviation by CFD simulations. While, those models are so complex that it is difficult to apply them directly in field engineering. Therefore, empirical correlated cuttings transport equation is often used in research and engineering practice. The empirical correlation of cuttings slip velocity is presented as follows [29]

q ðq  qm ÞD2c ðg  v m
rv m Þ ulc ¼ l c 18ll ql C D

ð5Þ

When the cuttings move above the critical decomposition depth, the flow in the wellbore changes from liquid–solid two– phase flow to gas–liquid–solid three–phase flow. With the decomposition of hydrate in the cuttings, the cuttings quality decreasing, and the force of cuttings will change accordingly, resulting in the change of the transport velocity of cuttings. Additionally, the complicated gas–liquid–solid flow will also affect cuttings transport in wellbore [21]. On the basis of momentum conservation, the formulas of force and velocity can be expressed as follows.

Z t

tþDt

  _ th Dt v ctþDt  mtc v tc F c dt ¼ mtc  m

(1) Gravity

F G ¼ ½qe ð1  /Þ þ qh /Eh þ qw /ð1  Eh ÞgV c

ð7Þ

(2) Buoyancy

  F b ¼ qg Eg þ ql El gV c

ð8Þ

(3) Drag force

@ ðAa Eg qg v 2g þAa El ql v 2l þAa Ec qc v 2c þAa pÞ @z

479

ð6Þ

Here, Fc denotes the resultant force of cuttings in drilling fluid, N. In addition to its own gravity, cuttings are also subjected to the buoyancy and dragging force. The calculation method of the component force of cuttings is as follows.

FD ¼

1 C D ql Ac ðv l  v c Þ2 2

ð9Þ

CD is drag function and taken from Schillere–Nauman relation as [29]

(

CD ¼

1 þ 0:15Re0:687 c 0:0183Rec

Rec 6 1000 Rec > 1000

ð10Þ

where the Reynolds number for cuttings phase is defined as:

Rec ¼

Dc El ql jv l  v c j

ll

ð11Þ

2.2. Heat transfer model Accurate prediction of annulus temperature field is also important for the simulation of hydrate dynamic decomposition [11]. Ramey [32] pioneered a numerical model to calculate the wellbore temperature for incompressible fluids and ideal gases. Hasan et al. [33,34] carried out extensive studies to develop wellbore temperature calculation models, which became the basis for other models and their applications. Gao et al. [35] presented new expressions for the heat transfer coefficient in different flow patterns based on experimental data, and improved the prediction accuracy of temperature field for multiphase flow. 2.2.1. Heat transfer model in drill pipe The drilling fluid in the drill pipe continuously transfers heat to the annulus during its downward movement along the well. On the basis of energy conservation, the heat transfer model in drill pipe can be presented as follows [7].

 @T p @T p 2pr pi U p
Ta  Tp þ vp ¼ @t @z C f qf Ap

ð12Þ

2.2.2. Heat transfer model in annulus During hydrate formation drilling, drilling fluid in annulus, carrying cuttings and hydrates returns upwards to wellhead with heat transfer with hydrate formation and drill pipe. Meanwhile, the hydrate in annulus is decomposed by absorbing heat during its transport upwards. Furthermore, the heat transfer mode in annulus is changed into gas–liquid–solid multiphase heat transfer. On the basis of energy conservation, the heat transfer model in annulus can be presented as follows.


 @T a @T a ¼ va  A T a  T p þ BðT e;0  T a Þ @t @z _ hw DH=ðqC Þefh  Ec /Sh m

ð13Þ

where,

8 h i > < A ¼ 2pr pi U p = ðqC Þefh Aa h i > : B ¼ 2pr ci U a = ðqC Þefh Aa

Fig. 3. Transport of cuttings containing hydrate particles in wellbore.

ð14Þ

Sh is hydrate saturation which varies with time and space. The same as liquid and gas, hydrate is a component of pore, so the calculation method is as follows.

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 Skh ¼

 _ hw k1 m Sh 1

qh

ð15Þ

Ua is overall heat transfer coefficient in the annulus and Up is overall heat transfer coefficient in the drill pipe. The calculation method is as follows [7].

U 1 p ¼


 1 r pi ln r po =rpi rpi þ þ kp hpi r po hpo

8 > ð0 6 h 6 Hsea Þ U 1 ¼ h1ri þ rri lnðkrror =rri Þ þ rrorrihro > > < a 1 r ln ð r =r Þ r ln ð r =r Þ co co w co U a ¼ h1ci þ ci kc ci þ kcem ðHsea < h 6 Hcas Þ > > > : U 1 ¼ 1 ðHcas < h 6 Hwell Þ a h

ð16Þ

ð17Þ

hole

Compared with pure liquid heat transfer in wellbore, hydrate decomposition in cuttings not only absorbs a lot of heat, but also greatly reduces the comprehensive convective heat transfer coefficient due to the forming of gas–liquid–solid multiphase flow in annulus. The key to the calculation of convective heat transfer coefficient lies in the calculation of Nusselt number. Gao et al. [35] presented new expressions for the heat transfer coefficient in different flow patterns based on experimental data.

  ðforbubbleflowÞ Nu ¼ 0:01215Re0:7922 Pr0:3 C t 1  0:30577E0:16578 g

Fig. 4. The numerical simulation flow diagram.

ð18Þ   Nu ¼ 0:46359Re0:7922 Pr0:3 C t 1  0:97599E0:01314 ðfor slug flowÞ g ð19Þ

2.2.3. Heat transfer model in gas–hydrate formation During drilling through hydrate formation, the higher temperature drilling fluid circulates in annulus and exchanges heat with hydrate formation, which increases formation temperature and promotes the decomposition of hydrates in pore. In the region where the gas hydrates decompose, the energy obtained is used to heat the hydrate formation, provide decomposition heat for the hydrates, heat the hydrate decomposition products [36]. On the basis of energy conservation, the heat transfer model in gas– hydrate formation can be presented as follows.

!  @ ðqC Þeh T e @ 2 T e 1 @T e _ hf DH  /Sh m þ ¼ K eh r @r @t @r 2
 _ gf þ C w m _ wf DT  Cg m

3.2. Model verification Although the United States, Russia, Japan and China have carried out hydrate production test [37–39], currently, the gas–liquid–solid three–phase flow in annulus during drilling through hydrate formation has not been sufficiently studied and lack of field and laboratory simulation data. Therefore, it is difficult to directly verify the accuracy of this model. While, the heat transfer models without hydrate decomposition have already been verified by experimental and field data in previous works [34]. So, we indirectly verify the accuracy of the model by comparing the wellbore temperature data found in literature. Fig. 5 shows the numerical results compared with mechanistic model of Gao et al. [19] and the model without hydrate decomposition. The variation trends in the temperatures of the three methods are the same, with a difference of less than 10%.

ð20Þ

3. Numerical solution and verification 3.1. Solution method The flow in wellbore during drilling through hydrate formation can be regarded as a complex gas–liquid–solid three–phase flow coupling hydrate decomposition with heat and mass transfer. Therefore, for this complex coupling model, it is extremely difficult to directly solve it. Wang et al. [25] proposed a Pressure Based Method for calculating gas–liquid two–phase flow in wellbore which has been proved a good accuracy and convergence. On the basis of this method, the numerical solution in this study is coupled with hydrate dynamic decomposition and cuttings transport, as shown in Fig. 4. The detailed solution process is shown in Appendix C.

Fig. 5. Comparison for the temperature profile between the mechanistic model of Gao et al. (2016), the model without hydrate decomposition and the present transient gas–liquid–solid flow model.

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In addition, it should be noted that under the consideration of multiphase flow in wellbore caused by hydrate decomposition, the heat transfer coefficient is lower, therefore, the simulation results in this study are higher than the other two models. This further prove the accuracy of the model. 4. Results and discussions To determine the effects of the gas–hydrate decomposition and multiphase flow behaviors in annulus, a series of numerical simulations were performed using the proposed model. Studies of hydrates in the South China Sea show that the burial depth of hydrate layer is about 900 m, the thickness is about several meters to hundreds of meters, and the hydrate saturation can be as high as 70% [9,18,40]. So, based on those data above and related study of hydrates, the following fundamental parameters, shown in Tables 1 and 2, are used for these simulations. Table 1 lists the basic parameters used in the simulation, Table 2 lists the thermal physical parameters.

Fig. 6. Decomposition rate of hydrate in cuttings and formation for a unit depth.

4.1. Results A series of numerical simulations were performed to research the gas–hydrate decomposition rules and multiphase flow behaviors in annulus at different times, where the time t = 0 refers to the time when drilling into hydrate layer. 4.1.1. Hydrate decomposition rate in annulus and hydrate layers Fig. 6 shows the decomposition rate curves of hydrates in wellbore and hydrate layers. It can be seen that the rate of hydrate decomposition in hydrate layers is only 1/140 of that in annular cuttings particles. The reason is that the pressure in the hydrate layer is higher and the temperature increasing is limited by the relatively low thermal conductivity of the hydrate layer [9,41], resulting in the low decomposition rate of the hydrate. Therefore, the influences of gas hydrate decomposition in hydrate layers can be neglected in the drilling process of hydrate reservoir. Fig. 7. Hydrate decomposition rate along the annulus at times of 1, 2, 3, and 4 h. Table 1 Basic parameters used in the simulation [9,18]. Parameter

Value

Parameter

Value

Depth of seawater (m) Depth of casing (m) Depth of hydrate formation (m) Drill pipe outer diameter (m) Drill pipe inner diameter (m) Riser outer diameter (m)

900 1000 1200

Injection rate (m3/s) Injection temperature (°C) Porosity

0.05 25 0.45

0.1397

Hydrate saturation

0.63

0.121

Water saturation

0.37

0.5334

15

Riser inner diameter (m) Casing outer diameter (m) Casing inner diameter (m) Wellbore diameter (m)

0.502 0.508 0.4757 0.445

Temperature of sea surface (°C) Geothermal gradient (°C/m) Rate of penetration, m/h Cuttings diameter (m) Wellhead backpressure (MPa)

0.02 40 0.003 1

Table 2 Thermal parameters [40]. Item

Density (kg/m3)

Specific heat capacity (J=ðkg
 CÞ)

Heat conductivity (J=ðs
m
 CÞ)

Drilling fluid Hydrate Formation rock Drill pipe/casing Cement sheath

1150 919 2650 7810 2000

4000 3000 999 880 500

0.72 0.5 2.09 43.2 0.71

Additionally, as shown in Fig. 7, Hydrate particles undergo three processes from bottom hole to wellhead in annulus: non–decomposition, slow decomposition and rapid decomposition. In annulus where the position is under mud line, hydrate hardly decompose due to the high pressure low temperature. Then, with the upwards of hydrate particles, the temperature increases and pressure decreases gradually, the hydrates begin to decompose slowly. While, if the hydrates and decomposed gas return upwards to the position where the depth less than 400 m, the decomposition rate of hydrates will increase significantly. 4.1.2. Pressure and temperature distributions along the annulus It is important to accurately simulate the distributions of annular temperature and pressure fields for the safely and efficiently drilling in hydrate formation. Fig. 8 shows the pressure distribution along the annulus at times of 1, 2, 3, and 4 h. As shown in the figure, wellbore pressure tends to decrease slightly with time which is due to the gas generated by hydrate decomposition and the reduction of hydrostatic column pressure in annulus. In addition, it can be seen from the bottom hole pressure curve that when drilling in hydrate layer for 0.528 h, cuttings carrying hydrate particles return upwards to the hydrate decomposition area, and the hydrate begins to decompose, resulting in the bottom hole pressure gradually decreases. Fig. 9 shows the temperature distribution along the annulus at times of 1, 2, 3, and 4 h. As shown in the figure, the temperature in

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Fig. 8. Pressure distribution along the annulus at times of 1, 2, 3, and 4 h.

Fig. 9. Temperature distribution along the annulus at times of 1, 2, 3, and 4 h.

annulus increasing with time. This is due to the continuous circulation of high–temperature drilling fluid in the drill pipe and annulus, which makes the temperature of hydrate formation near the wellbore will increase continuously, and further leads to an increase in the temperature of the whole wellbore. Hydrate decomposition will absorb amount of heat, while, due to the very small amount of hydrate and the decrease of heat transfer coefficient for gas–liquid–solid multiphase flow caused by hydrate decomposition in annulus. Therefore, as shown in Fig. 5, the decomposition effect of hydrate will make the annular temperature field relatively higher. This is because the decrease of heat transfer coefficient caused by hydrate decomposition plays a dominant role in the temperature field. 4.1.3. Three–phase gas–liquid–solid volume fraction distributions Fig. 10(a), (b) and (c) show the volume fraction distributions of gas, liquid and solid in annulus, respectively. It can be found that hydrates do not decompose under the critical decomposition position of hydrate, the behaviors of liquid–solid two–phase flow in the wellbore is basically the same as that in conventional formation. While, when the cuttings carrying hydrate particles return upwards to the hydrate decomposition area, the hydrate begins to decompose, forming gas–liquid–solid three–phase flow in the annulus. However, the gas expansion is small in this area, and

Fig. 10. Gas, liquid and cuttings volume fraction distributions at times of 1, 2, 3, and 4 h.

the volume fraction of cuttings and liquid phase decreases slightly. The gas void fraction increases significantly in the wellbore where the depth is less than 400 m, which is not only due to the faster decomposition rate of hydrates (as shown in Fig. 7) caused by the higher temperature and lower pressure in this area, but also due to the more intense expansion of decomposed gas. In particular, for the solid content distribution at 1 h (black line), the cuttings of hydrate particles have not yet been transported to the wellhead (as shown in Fig. 7). In the area where hydrates have reached, the cuttings content tends to decrease gradually, while in the area where hydrate has not reached, the distribution of cuttings concentration shows a gradual increase rule without the hydrate decomposition effects.

Y. Liao et al. / International Journal of Heat and Mass Transfer 141 (2019) 476–486

For the gas–liquid–solid three–phase volume fraction distributions in the whole wellbore, with the passage of time, the gas volume fraction in the wellbore increases gradually while the volume fraction of liquid phase and cuttings decreases. But after the hydrate particles return upwards to the wellhead (2 h in this case), the three–phase volume fraction distributions tend to be a quasi– stable state. 4.1.4. Three–phase gas–liquid–solid velocity distributions Fig. 11(a), (b) and (c) shows the velocity distributions of gas, liquid and solid in annulus, respectively. As shown in Fig. 11, in the casing and open hole section below the mudline, the hydrate decomposition rate is very slow or zero, and the decomposed gas

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hardly expands, so the gas–liquid–solid three–phase velocity distributions are basically stable. While, when the hydrates and gas return upwards into the riser, especially the position where the depth is less than 400 m, the gas velocity increases rapidly due to acceleration of hydrate decomposition and the rapid expansion of gas. The gas expansion and the increase of gas velocity will also cause the increase of liquid velocity. For cuttings, on the one hand, the decomposition of hydrate particles in cuttings will cause the total mass of cuttings decrease. On the other hand, the increase of liquid velocity will increase the drag force on cuttings. Therefore, the velocity of cuttings particles in the upper riser will increase. 4.2. Discussions For hydrate formation drilling, a detailed understanding of the distribution rules of gas void fraction in annulus under different conditions is a great significance for fine control of wellbore pressure and safely and efficiently drilling. Fig. 12 shows the effect of wellhead backpressure on gas void fraction in annulus. It can be found that the gas void fraction decreases with the increase of wellhead backpressure. This is because the increase of wellhead backpressure indirectly increases wellbore pressure, which will reduce the decomposition rate of hydrates and also inhibit the rapid expansion of decomposed gas in the upper part of the riser section. If there is no backpressure device at the wellhead, that is, the wellhead backpressure is 0 MPa, the gas void fraction at the wellhead can reach 0.68, which is enough to cause blowout accident. However, when the wellhead backpressure increases to 0.5 MPa, the wellhead gas void fraction decreases rapidly to 0.28. Therefore, in order to control the gas void fraction within 10% [42], thereby ensure the safely and efficiently drilling of hydrate reservoirs, the wellhead backpressure of 2 MPa can be applied through managed pressure devices. Fig. 13 shows the effect of drilling fluid density on gas void fraction in annulus. It can be found that the influence of drilling fluid density on gas void fraction distribution in annulus is very small. Although increasing the density of drilling fluid can increase the pressure field distribution in annulus, and then make the critical decomposition position of hydrate move up, it is difficult to inhibit the rapid decomposition rate of hydrate and the rapid expansion of decomposed gas in the upper riser. Fig. 14 shows the effect of drilling fluid inlet temperature on gas void fraction in annulus. We find that the gas void fraction in annulus gradually increases with the inlet temperature of drilling fluid.

Fig. 11. Gas, liquid and cuttings velocity distributions at times of 1, 2, 3, and 4 h.

Fig. 12. Effect of wellhead backpressure on gas void fraction in annulus.

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Fig. 13. Effect of drilling fluid density on gas void fraction in annulus.

(1) During drilling through hydrate layers, the influences of hydrate decomposition in hydrate layers can be neglected, because the decomposition rate of hydrate in formation is only 1/140 of that in annular cuttings for a unit depth. (2) Hydrate particles undergo three processes from bottom hole to wellhead in annulus: non–decomposition, slow decomposition and rapid decomposition. In annulus where the depth is more than 400 m, hydrates decompose slowly and the decomposed gas hardly expands due to the high pressure. While, if the hydrates and decomposed gas return upwards to the position where the depth less than 400 m, the gas void fraction increases significantly, not only due to the faster decomposition rate of hydrates but also due to the more intense expansion of decomposed gas. (3) The decomposition of hydrate in cuttings and the increase of liquid velocity will result in the increase of cuttings transport velocity and decrease of the solid volume content. (4) After the hydrate particles return upwards to the wellhead (2 h in this case), the behaviors of gas–liquid–solid flow such as volume fraction and velocity distributions tend to be a quasi–stable state. (5) If there is no backpressure device at the wellhead, that is, the wellhead backpressure is 0 MPa, the gas void fraction at the wellhead can reach 0.68, which is enough to cause blowout accident. Increasing wellhead backpressure to 2 MPa through managed pressure devices and lowering the inlet temperature of drilling fluid to 17.5 °C except adjusting drilling fluid density can manage the gas void fraction within 10%.

Declaration of Competing Interest None. Acknowledgments Fig. 14. Effect of drilling fluid inlet temperature on gas void fraction in annulus.

The temperature field of the wellbore can be reduced by lowering the inlet temperature of drilling fluid, which can not only make the critical decomposition position of hydrate move upwards, but also reduces the decomposition rate of hydrates. Therefore, the wellhead gas void fraction can be controlled in a safe and controllable range if the temperature of drilling fluid is controlled below 17.5 °C. In conclusion, increasing wellhead backpressure to 2 MPa through managed pressure devices and lowering the inlet temperature of drilling fluid to 17.5 °C except adjusting drilling fluid density can effectively inhibit the rapid decomposition of hydrate and the expansion of decomposed gas in the upper riser, thereby achieving the gas fraction at wellhead less than 10%, finally, preventing the occurrence of blowout and other malignant accidents. 5. Conclusions In this study, considering the coupling interactions between hydrate dynamic decomposition, cuttings transport and heat transfer, a fully coupled transient gas–liquid–solid flow mechanism model is developed. The gas–liquid–solid three–phase flow rules and the effects of wellhead backpressure, drilling fluid density and injection temperature were thoroughly analyzed by conducting numerical simulations. The following are the main conclusions of this study:

The work was supported by the National Natural Science Foundation of China (No. 51890914). the National Natural Science Foundation–Outstanding Youth Foundation (51622405), the Shandong Natural Science funds for Distinguished Young Scholar (JQ201716), National Key Basic Research Program of China (973 Program, 2015CB251200), the National Natural Science Foundation of China (No. 51876222). Appendix A. Hydrate kinetics model Jamaluddin et al. [43] proposed a hydrate decomposition kinetic model considering heat and mass transfer and intrinsic kinetics which can be used to calculate the rate of hydrate decomposition.

dnh 0 ¼ kd Ah Df g dt

ðA:1Þ

The decomposition rate of hydrate particles in cuttings is determined by the temperature and pressure conditions and the contact area between liquid phase and hydrate particles. Under the local temperature and pressure in annulus, once the fugacity of methane exceeds its phase equilibrium fugacity, the hydrate at the gas–liquid interface will decompose to gas and water. Assuming that the hydrate particles are spherical, the effective decomposition area of hydrate in the cuttings is obtained as follows [20]:

Ah ¼

 2=3 1 1=3 6nh Mh p w qh

ðA:2Þ

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Combining the Eqs. (A.1) and (A.2), the mass decomposition rate of hydrate can be given as follows.

_ hw ¼ Mh _ hf ¼ m m



dnh 6nh M h 0 1 ¼ Mh kd p1=3 w dt qh

Df g

ðA:3Þ

v gr

1þ

1000

1:2  0:2E4g
Re 2 1 þ 1000

ðB:1Þ

30:25 2  g r ql  qg 5 ¼ 1:534 þ 0:35 2

ql

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  u  ugD q  q
0:25 l g t Eg 1  Eg 

ðB:2Þ

ql

Appendix C. Solution method Firstly, assuming the distribution of pressure and temperature fields in wellbore, the three–phase mass conservation equation is solved. The mass conservation equations for discretizing is as follows. k1 k1 Aj Ekgj qkgj  Aj Egj qgj

Dt

¼

k1 k1 k1 Ajþ1 Ekgjþ1 qkgjþ1 v kgjþ1  Ajþ1 Egjþ1 qgjþ1 v gjþ1

ðC:7Þ

Eklj

v kgj ¼ C 0 Ekcj ¼

Drift flux model, first proposed by Zuber and Findlay [44], has been widely used to describe the phenomenon of gas–liquid two phase flow in wellbores. On the basis of ensuring the accuracy of calculation, the flow pattern independent drift flux correlation presented by Wang et al. [25] which can avoid calculating flow pattern transition boundary, is used to calculate gas slip velocity.

C0 ¼

K l  bl Eklj

2=3

Appendix B. Drift flux correlation

2
Re 2 þ

v klj ¼




 K g þ K l  bg þ v gr

ðC:8Þ

bc Aj Ecjk1 þ Ajþ1 Ekcjþ1 v kcjþ1  M khj Dz bc Aj þ Aj v kcj

v kcj ¼ v klj  v lc

ðC:9Þ

ðC:10Þ

where

8 > > Kg ¼ > > > <

Ajþ1 Ekgjþ1 qkgjþ1 v kgjþ1 Aj qkgj

Ajþ1 Ekljþ1 qkljþ1 v kljþ1

þ

Kl ¼ þ > > Aj qk > lj > > : Dx bg ¼ bl ¼ bc ¼ Dt

Ek1 qk1 gj gj

qkgj

Eljk1 qk1 lj

qklj

bg þ ADqhk M g j gj

bl þ ADqhk M l

ðC:11Þ

j lj

Using the guess pressure, gas physical properties can be calculated using the gas state equation proposed by Peng and Robinson [45], and then the gas velocity, liquid velocity, cuttings velocity, gas void fraction, liquid holdup and solid concentration can be calculated. Next, use the momentum equation to correct the guess pressure. Combining the Eqs. (12)–(19) in the heat transfer model, the temperature fields in wellbore can be solved after the solution of the gas–liquid–solid three–phase flow model. Then, the new temperature and pressure distributions can be used to correct the gas physical properties and decomposition rate of hydrate. Finally, the iteration is repeated until the gas velocity, liquid velocity, cuttings velocity, void fraction, liquid holdup and solid concentration satisfy the given convergence conditions.

Dz þ M kgj

Appendix D. Supplementary material

ðC:1Þ k1 Aj Eklj qklj  Aj Ek1 lj qlj

Dt

¼

Dz þ M klj

Aj Ekcj qkcj  Aj Ecjk1 qk1 cj

Dt

¼

Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.06.097.

k1 k1 Ajþ1 Ekljþ1 qkljþ1 v kljþ1  Ajþ1 Ek1 ljþ1 qljþ1 v ljþ1

ðC:2Þ

k1 k1 Ajþ1 Ekcjþ1 qkcjþ1 v kcjþ1  Ajþ1 Ek1 cjþ1 qcjþ1 v cjþ1

Dz  M kcj ðC:3Þ

where

8  k R > > _ gf dr  _ gw þ rre 2pr m M kgj ¼ AEc m > > ce < j k k _ m M ¼ ð AE Þj c w > gj j > > > : _ Þjk M k ¼ ðAE m gj

c

h

ðC:4Þ

j

Combining the Eqs. (A.1)–(A.3), Eqs. (B.1)–(B.2) and Eqs. (5)– (11) described in the hydrate kinetics model, drift flux correlation and cuttings transport model, respectively, the gas velocity, liquid velocity, cuttings velocity, void fraction, liquid holdup and solid concentration are given by

Ekgj ¼

Kg

v kgj þ bg

Eklj ¼ 1  Ekgj  Ekcj

ðC:5Þ ðC:6Þ

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