Xiolong Zho ,Yizhong Zho ,Zenglin Wng ,Gng Chen ,Peng Li ,Wei Ling ,Xuefeng Go ,Hnming Xu ,Lin Jing ,*,N Wei ,d

a Research Institute of Petroleum Engineering,Shengli Oilfield,SINOPEC,Dongying,257000,China

b Shengli Oilfield Company,SINOPEC,Dongying,257000,China

c State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,Southwest Petroleum University,Chengdu,610500,China

d State Key Laboratory of Natural Gas Hydrate,Beijing,10027,China

ABSTRACT The natural gas hydrate resources in the South China Sea alone are about 85 trillion cubic meters.In the drilling process of marine gas hydrate,the natural gas hydrate will decompose and produce gas,as the rising of temperature and dropping of the pressure in the annulus.This process will have a significant impact on drilling safety.Therefore,it is necessary to study the wellbore temperature distribution during the drilling of marine hydrate layer.In this paper,the wellbore temperature distribution of safe drilling in hydrated formation is taken as the research goal,and the research status of relevant domestic and international wellbore temperatures was investigated.According to the characteristics of the marine environment and reservoir-forming characteristics of hydrate reservoirs in the South China Sea,the wellbore temperature distribution model of offshore drilling wellbore under the condition of hydrate decomposition was established.The temperature distribution curve of drilling straight wellbore in hydrate layer of South China Sea was obtained.When drilling the hydrate reservoir,the distribution regularity of the wellbore temperature is similar to that of the conventional offshore drilling wellbore.However,the temperature of the wellbore annulus near the hydrate decomposition site is lower than the ambient temperature,mainly due to the hydrate decomposition endothermic.In this paper,the sensitivity analysis of several main parameters of the wellbore temperature distribution of drilling straight wellbore in hydrate layer of South China Sea was carried out.Through the conduction of experiment and numerical simulation,we have get some new findings:(1)The hydrate saturation has little effect on the wellbore temperature;(2)As the drilling fluid displacement increases,the annulus temperature of the wellbore above the mudline increases,and the temperature of the wellbore below the mudline decreases continuously;(3)As the density of the drilling fluid increases,the temperature at the wellhead decreases,and the temperature at the bottom of the well increases slightly;(4)The greater the rate of penetration of the well,the temperature at the upper part of the wellbore decreases,and the temperature at the bottom of the wellbore increases;Among them,the penetration rate has the most obvious effect on the annular temperature.The results are expected to be helpful to guide the drilling process of marine gas hydrate and offer some references.

Keywords:Wellbore temperature Natural gas hydrate South China Sea Numerical simulation Sensitivity analysis

1.Introduction

Natural gas hydrate attracts people's attention as a new type of clean energy at present.The reserves of marine gas hydrate are about 100 times that of land,and the total amount is conservatively estimated to be 2.83×1015m3,which is 1.56 times that of known natural gas reserves[1,2].The Ministry of Land and Resources and other exploration preliminarily delineated 11 potential hydrate occurrence areas in the South China Sea,with prospective resources of about 680×108t.In the face of such a huge amount of resources,speeding up the safe and efficient development of gas hydrate reservoirs is of great strategic significance to alleviate the contradiction between energy supply and demand and ensure national energy security.When drilling the marine hydrate layer,the hydrate enters the annulus,which will bring new problems and challenges to the drilling and production process parameter design,wellbore safety control,riser design and so on[3-5].When drilling hydrate layer,the change of external environment can easily cause the decomposition of natural gas hydrate to produce gas.The decomposition of hydrate will also lead to the decrease of the cementation between the formation particles and the sharp change of the submarine formation pressure,which will lead to the structural destruction and severe deformation of the formation.The decomposition gas of hydrate will also lead to a sharp increase in the content of dangerous gases in the drilling area,which will do great harm to the marine environment.

Scholars at home and abroad have carried out related research from different perspectives.In 1961,Edwardson[6]put forward an approximate model for estimating formation temperature distribution after mud circulation.By using heat conduction difference equation,the temperature distribution of different formation radius under various mud displacements was obtained in the form of chart.In 1962,Ramey[7]combined the heat transfer mechanism in the wellbore with the transient heat conduction in the surrounding formation,regarded the fluid temperature as a function of well depth and time,and deduced a formula for predicting the temperature of incompressible fluid in the wellbore.In 1965,the method proposed by Satter[8]improved the work of Ramey,taking into account the effect of fluid phase transition in steam injection wells.In 1967,Willhite[9]derived the classical expression for calculating the comprehensive heat transfer coefficient.In 1970,Holmes and Swift[10]ignored the heat generated by the bit and the axial and radial heat conduction of the fluid,and assumed the linear variation of the ground temperature profile,established an onedimensional steady-state mathematical analysis model,and proposed the analytical solution of the borehole heat exchange equation in the steady state.In 1980,Wooly first developed a transient model computer software for predicting wellbore temperature during drilling of geothermal wells or oil wells[11].In 1990,Arnold viewed that when the drilling fluid circulates in the wellbore,the wellbore temperature distribution was determined by the heat exchange between the formation and the wellbore drilling fluid,and the heat exchange process was described by the differential equation under steady condition[12].In 2005,Harris studied the influence of temperature distribution and well pressure change of drilling fluid on the equivalent density of drilling fluid[13].In 2009,Gilberto and Espinosa applied feedback control theory to establish a method to obtain static formation temperature using temperature measurement data,and at the same time correct the calculation results according to the obtained static formation temperature[14,15].However,there are few studies focusing on wellbore temperature distribution in gas hydrate layer during drilling.

In order to implement the drilling construction design of marine gas hydrate layer safely and smoothly,we need to have a more detailed grasp of the data in the drilling process.Wellbore temperature is one of the most important parameters in the process of drilling.Understanding the temperature change during drilling is of great significance to the safe and efficient drilling of marine gas hydrate layer.It is also of great significance to the safe and efficient drilling and production of gas hydrate in the South China Sea.

2.Physical model of wellbore heat transfer

The physical model of heat transfer during the offshore drilling process is established as shown in the Fig.1.

3.Mathematical model of wellbore temperature

Based on the basic theory of heat transfer,combined with the actual working conditions in the process of offshore drilling,the wellbore temperature mathematical model of offshore drilling hydrate layer is established according to the law of conservation of energy.We have set up the following assumption to make it convenient for calculation and simulation.

(1)The drilling fluid and other liquids in the wellbore are singlephase incompressible fluids.

(2)There is only radial and axial heat conduction in and around the wellbore,and the thermal convection in the formation hole is not taken into account.

(3)The decomposition rate of natural gas hydrate in the annulus is the same under the same environment(temperature,pressure and migration velocity).

(4)The fluid in the wellbore takes into account the influence of heat source term and axial and radial forced thermal convection heat transfer.

(5)The geothermal gradient and sea water temperature are constant,and the distribution is always stable in the process of drilling.

In the actual situation of the offshore drilling site,the drilling fluid is pumped into the wellbore and circulates out of the wellbore through the bit annulus.We set this process as a complete system.The wellbore and the surrounding formation system are comprehensively considered,and the fluid in the wellbore is taken as the main research target.The system satisfies the law of conservation of energy.The change of the energy of the system in a certain period of time is equal to the difference between the energy entering the system and the energy leaving the system.Establish the following equation:

wheredEis the energy that enters the system;dWis the total work done by the external environment to the system;dUis total energy change of the system.

3.1.Seawater temperature distribution model

According to the database of Levitus in 1994[16],the water temperature in the region of 200 m-3500 m was obtained by taking a value of longitude and latitude at every interval in the area of latitude 7°-12°N and longitude 111°-118°E.the data were compared with the data obtained by the Chinese Academy of Sciences,and the data were accurate[17].According to the water temperature data obtained by Levitus,the sea water temperature equation of the South China Sea is fitted as follows.

where a=39.398,b=37.091,c=130.137,d= 402.732;Tseais sea water temperature,°C;his sea water depth,m.

The mixed layer in the South China Sea is not obvious in spring and summer,but respectively reaches 50 m and 100 m in autumn and winter.Assuming that the thermocline has a fixed temperature gradient,that is,the temperature in this region decreases with the depth,the following fitting equations are obtained.

whereTseais seawater temperature,°C;Tsis sea surface temperature,°C;his sea water depth,m.

3.2.Phase equilibrium and decomposition model of natural gas hydrate

In the production of offshore water-producing gas wells,based on the phase equilibrium model of natural gas hydrate,combined with wellbore temperature and pressure,it can be judged whether hydrate is formed or decomposed in the wellbore.In order to analyze the law of non-equilibrium formation and decomposition of gas hydrate in offshore water-producing gas wells,a phase equilibrium and decomposition model of gas hydrate was established considering the continuous variation of wellbore temperature and pressure with well depth.

(1)Phase equilibrium of natural gas hydrate

Hydrate phase equilibrium equation:

whereTis system temperature,K;viis number of type I holes per unit water molecule in hydrate phase;Cijis Langmuir constant of component j in type I hole is fugacity of component j in equilibrium phases,Pa;NCis the number of components in the mixture that can form hydrate;Δμ0is chemical potential difference between empty hydrate lattice and pure water in standard state;T0andP0are the temperature and pressure in the standard state,T0is 273.15K andP0is 0.1 MPa under the standard condition.ΔH0,ΔVand ΔCPare specific enthalpy difference,specific tolerance difference and specific heat difference between empty hydrate lattice and pure water.

The Langmuir constant can be solved by the following correlation[18]:

whereBijis Empirical constant.

(2)Decomposition model of natural gas hydrate

Based on the Englezos model[19],the kinetic model of nonequilibrium hydrate formation was established.

Based on the Kim model[20],the kinetic model of nonequilibrium decomposition of hydrate was established.

wherenfandndare the amount of substance in the process of nonequilibrium formation and decomposition of gas hydrate in wellbore,mol;tfandtdare formation and decomposition time of natural gas hydrate,s;KfareKdreaction rate constant of formation and decomposition of natural gas hydrate,mol/(s·m2·Pa);AfandAdare effective area of formation and decomposition of natural gas hydrate,m2;fm(Tm,Pm)is methane fugacity under wellbore temperatureTmand wellbore pressurePm,Pa;feq(Tm,Peq)is methane fugacity under wellbore temperatureTmand hydrate phase equilibrium pressurePeq,Pa;The parameters are solved as follows.

The calculation model of reaction rate constant of gas hydrate formation and decomposition is as follows:

whereKis reaction rate constant of formation and decomposition of natural gas hydrate,mol/(s·m2·Pa);Kcis reaction rate of hydrate self-formation or decomposition;Kmis mass transfer rate of methane at a certain temperature and pressure,mol/(s·m2·Pa).

In order to simplify the calculation and more clearly analyze the law of non-equilibrium formation and decomposition of hydrate in the wellbore,it's assumed that all the hydrate generated are homogeneous spherical particles and rise continuously along the wellbore at the same velocity as the air flow.The hydrate begins to decompose when a critical decomposition condition is reached at a certain position.Based on this,a model for calculating the effective area of gas hydrate formation and decomposition is established.

whereAis effective area of formation or decomposition of natural gas hydrate,m2;nhis the amount of substance in the process of formation or decomposition of natural gas hydrate,mol;Dhis hydrate particle diameter,m;Vhis hydrate particle volume,m3;Mhis molar mass of hydrate,kg/mol;ρhis hydrate density,kg/m3.

According to the definition of gas fugacity,the calculation model of methane fugacity is as follows.

Therefore:

wherefx(Tx,Px)is methane fugacity at a certain temperatureTxand pressurePx,Pa;Txis a certain temperature,K;Pxis a certain pressure,Pa;P*is reference state pressure,Pa;Ris general gas constant,m3·Pa/(mol·K);Vxis the Molar volume of methane underTxandPx,L/mol;aandbare R-K gas equation of state constant,Dimensionless.

(3)Decomposition heat of natural gas hydrate

The decomposition heat of hydrate above 0°C is calculated by Clausius- Clapeyron equation[21].

wherePandTare pressure and temperature of hydrate formation/decomposition,MPa,K;ΔHis decomposition heat,kJ/mol;Zis gas compression factor.

3.3.Mathematical model of wellbore temperature in drilling hydrate layer

(1)Mathematical model of drilling fluid temperature in drill string

Fig.2 is a schematic diagram of heat transfer of microplasma in drilling fluid inside the drill string.Through the analysis of the heating microplasma of the drilling fluid inside the drill string,it is mainly affected by flowing four aspects[22,23].

1)The heat carried by the drilling fluid in the axial drill pipe as it moves downward along the wellbore

2)Heat transfer of drilling fluid and drill pipe inner wall facing flow

3)Heat generated by the change of drilling fluid's own energy

4)The work done by other factors to the microplasma of the drilling fluid includes the heat produced by friction,the heat generated by the drilling fluid through the bit nozzle,the work done by the bit breaking rock,and so on.

According to the principle of conservation of energy,the following equations are established:

Inside the drill string:

where ρais drilling fluid density,kg/m3;cais specific heat capacity of drilling fluid,J/(kg·°C);Tais drilling fluid temperature in drill string,°C;Tsis temperature of drill string inner wall,°C;h′a1is convective heat transfer coefficient on the inner surface of drill string,J/(m2·s·°C);qis drilling fluid displacement,m3/s;Edis power per unit length of heat source in drill string,J/s;r1is drill string inner diameter,m.

(2)Temperature mathematical model of wellbore annulus fluid

Fig.3 is a schematic diagram of fluid microplasma heat transfer in wellbore annulus.The thermal analysis of fluid microplasma in the riser annulus is mainly affected by four aspects:

1)The amount of heat carried by a fluid in an axial annulus as it moves upward along the annulus.

2)Heat transfer of annular fluid and heat transfer between the outer wall of the drill string and the inner wall of the wellbore

3)Heat generated by the change of the energy of the annular fluid itself

4)The work done by other factors to the microplasma of the drilling fluid includes the heat produced by friction,the heat generated by the drilling fluid through the bit nozzle,the heat absorbed by hydrate decomposition,and so on.

According to the principle of conservation of energy,the following equations are established:

In Annulus:

where ρbis fluid density in wellbore annulus,kg/m3;cbspecific heat capacity of fluid in wellbore annulus,J/(kg·°C);Tbis annular fluid temperature,°C;Tris wellbore inner wall temperature,°C;ha1is convective heat transfer coefficient of wellbore inner wall,J/(m2·s·°C);qmis fluid displacement in wellbore annulus,m3/s;Eais the work done by the outside world on the annular fluid,J/s;r3is wellbore inner diameter,m.

4.Mathematical model solving method

The temperature variables required in the mathematical model are merged radially from the wellbore to the formation,longitudinally from the wellhead to the bottom of the well and in time from the smallest to the largest,to form a set of algebraic equations to be solved[24].For each node,the system of finite difference equations can be expressed in the following general format:

The finite difference equations of all nodes are expressed in matrix form:

The solution can be realized by the fast successive over relaxation iterative method(SOR),and the general form of the expression is as follows:

where:when ω = 1,the SOR method is the Gauss-Seidel iterative method.When ω ＞1,it is called over relaxation method.When ω ＜1,it is called low relaxation method.The calculation process is shown in Fig.4.

5.Sensitivity analysis

In order to obtain the wellbore temperature distribution of the drilled gas hydrate layer,the simplified wellbore structure shown in Fig.1 is set.Total well depth is 2000 m,water depth is 1500 m,wellbore diameter is 215.90 mm,drill pipe size is 127.00 mm,outer diameter of riser is 533.40 mm,sea surface temperature is 25°C,displacement is 20L/s,geothermal gradient is 0.041°C/m,drilling fluid density is 1.2 g/cm3.The thermodynamic parameters of each substance are shown in Table 1.

There are many factors affecting wellbore temperature distribution in marine hydrate layer.The main factors studied in this paper are as follows:hydrate abundance,drilling fluid density,drilling fluid displacement,mechanical penetration rate and so on.

5.1.Hydrate abundance

According to the well depth structure and the basic parameters of drilling fluid,the mechanical penetration rate is 10 m/h and the circulationtime is 2h.According totheabovewellbore structureparameters and data,the hydrate phase equilibrium diagram in the wellbore in Fig.5 can be calculated by the hydrate phase equilibrium condition formula.From the following figures,we can see that the hydrate phase equilibrium curve and the wellbore annulus temperature curve intersect at the well depth of 500 m,and the region where the wellbore annulus is less than 500 m can maintain the stable state of hydrate,and the hydrate in the annulus begins to decompose above 500 m.

Fig.6 shows the temperature distribution in the wellbore under different hydrate abundance,and the hydrate abundance is 10%,30%and 50%,respectively.From the above Figure,we can see that the effect of hydrate abundance on wellbore temperature is very small,only the wellbore temperature below the mud line changes very little,with the increase of hydrate abundance,the wellbore temperature belowthe mud line is slightly lower.The main reason is that the hydrate decomposition rate is mainly affected by temperature and pressure conditions,and the increase of abundance has a limited effect on the hydrate decomposition rate.The amount of hydrate decomposition does not increase,and the heat absorption of hydrate decomposition does not change,so the change of temperature in the wellbore is not obvious.Only the annular density decreases,and the annular temperature increasesslightly due totheincreaseof hydrate abundance in the well below the mud line.

Fig.7 shows the comparison of temperature difference between wellbore annulus and drill string under different hydrate abundance.From the above picture,we can see that with the increase of hydrate abundance,the temperature difference in the wellbore drill string and annulus does not change obviously,only below the mud line,the temperature difference decreases with the increase of the abundance,but the decrease is very small.This is mainly due to the increase of hydrate abundance,which reduces the density of liquid in the annulus,which leads to the increase of annular temperature and the decrease of temperature difference.

5.2.Drilling fluid displacement

According to the well depth structure and the related basic parameters of drilling fluid,the mechanical penetration rate is 10 m/h and the circulation time is 2h.Through the hydrate phase equilibrium condition formula,the phase equilibrium diagram of hydrate in the wellbore with different drilling fluid displacement can be calculated.From Fig.8,we can see that with the increase of drilling fluid discharge,the hydrate decomposition position increases gradually,and the temperature of the decomposition point decreases.When the drilling fluid displacement is 30L/s,the decomposition point is at the well depth of 490 m,when the drilling fluid displacement is 20L/s,the decomposition point is at the well depth of 500 m,and when the drilling fluid displacement is 10L/s,the decomposition point is at the well depth of 510 m.

Fig.9 shows the temperature distribution in the wellbore under different drilling fluid displacement.From the figure,we can see that with the increase of drilling fluid discharge,the wellbore annulus temperature above the mud line also increases,and the wellbore temperature below the mud line continues to decrease,but the extent of the decrease is becoming smaller.The increase of the temperature in the upper annulus is mainly due to the increase of heat carried into the wellbore from the outside,and the temperature in the upper annulus is affected by the temperature in the drill string and increases gradually.Because the wellbore below the mud line is the first contact between the formation and the annulus fluid,the formation heat is first transferred into the annulus,the displacement increases and the annular liquid velocity increases,which shortens the convective heat transfer time between the annulus liquid and the formation and reduces the heat absorbed.Therefore,with the increase of discharge,the annulus temperature in the lower part of the wellbore decreases gradually.

Fig.10 shows the comparison of temperature difference between wellbore annulus and drill string under different drilling fluid displacement.With the increase of drilling fluid discharge,the range of temperature difference between drill string and annulus in wellbore gradually decreases.In the section below the mud line,the wellbore temperature is mainly affected by the formation ambient temperature.the larger the discharge,the greater the velocity,the shorter the convective heat transfer time between the liquid in the annulus and the formation,so the temperature difference between the liquid in the annulus and the liquid in the drill string decreases,and the temperature in the annulus and the drill string is closer.

5.3.Drilling fluid density

According to the well depth structure and the basic parameters of drilling fluid,the mechanical penetration rate is 10 m/h and the circulation time is 2h.Through the hydrate phase equilibrium condition formula,the phase equilibrium diagram of hydrate in the wellbore under different drilling fluid density can be calculated.From Fig.11 below,we can see that with the increase of drilling fluid density,the hydrate decomposition position increases gradually,and the temperature of the decomposition point decreases.When the density of drilling fluid is 1400 kg/m3,the decomposition point is at the depth of 450 m,when the density of drilling fluid is 1200 kg/m3,the decomposition point is at the depth of 500 m,and when the density of drilling fluid is 1050 kg/m3,the decomposition point is at the depth of 530 m.

Fig.12 shows the temperature distribution in the wellbore under different drilling fluid densities.As shown in the figure,with the increase of drilling fluid density,the wellbore temperature decreases slightly in the upper section of the mud line,and the annulus temperature increases slightly in the lower part of the mud line.However,the change of temperature is not obvious,and the increase of bottom hole temperature is mainly due to the increase of density,the increase of wellbore annulus,the influence of hydrate decomposition rate and the decrease of hydrate decomposition heat,so the bottom hole annulus temperature increases slightly.

Fig.13 shows the comparison of the temperature difference between the wellbore annulus and the drill string under different drilling fluid densities.It can be seen from the above diagram that the temperature difference between the wellbore annulus and the drill string increases gradually with the increase of the density,but the increase is small.

5.4.Mechanical penetration rate

According to the well depth structure and the related basic parameters of drilling fluid,under the conditions of 10 m percussion rate,20 m stroke h and 30 m/h respectively,the phase equilibrium diagram of hydrate in the wellbore under different mechanical penetration rates can be calculated by the hydrate phase equilibrium condition formula.From Fig.14,we can see that the effect of the increase of mechanical penetration rate on the hydrate decomposition position is negligible.

Fig.15 shows the comparison of the temperature difference between the wellbore annulus and the drill string before and after drilling hydrate.From the figure,we can see that with the increase of mechanical penetration rate,the wellbore temperature decreases gradually in the well section above the mud line,and the temperature in the wellbore increases gradually below the mud line.In the well section above the mud line,due to the increase of drilling mechanical penetration rate,the increase of hydrate cuttings and the increase of hydrate decomposition,the required decomposition heat increases,which leads to the gradual decrease of annulus temperature.In the section below the mud line,the friction heat generation between the bit and the formation increases with the increase of the mechanical penetration rate,which leads to the increase of the temperature at the bottom of the wellbore.

Fig.16 shows the comparison of the temperature difference between the wellbore annulus and the drill string at different penetration rates.It can be seen from the temperature curve in the figure that near the decomposition position,the temperature difference between the annulus and the drill string increases gradually with the increase of the mechanical penetration rate,and at the upper 200 m of the decomposition position,the temperature difference between the annulus and drill string is also gradually affected by the heat absorption of hydrate decomposition.The greater the amount of hydrate decomposition,the more heat needed for decomposition,and the lower the annular temperature.Therefore,it will cause the temperature difference to increase with the increase of mechanical penetration rate.

6.Conclusions

(1)Based on the phase equilibrium and decomposition theory of natural gas hydrate,the decomposition position of gas hydrate in wellbore is studied,and the wellbore temperature distribution model under hydrate decomposition is established.According to the relevant conditions and the physical parameters of hydrate,the wellbore temperature distribution curve of drilling vertical well in marine hydrate layer is calculated.At first,the wellbore temperature decreases gradually,and then due to the influence of ground temperature,the wellbore temperature begins to increase.The temperature of the wellbore annulus near the hydrate decomposition position is lower than the ambient temperature,which is mainly caused by the heat absorption of hydrate decomposition.

(2)This paper makes a sensitivity analysis of wellbore temperature distribution in vertical wells drilled in marine hydrate layer,and mainly analyzes the effects of hydrate abundance,drilling fluid displacement,density and mechanical penetration rate on wellbore temperature distribution.The main conclusions are as follows:①Hydrate abundance has little effect on wellbore temperature.②With the increase of drilling fluid discharge,the wellbore annulus temperature above the mud line also increases,and the wellbore temperature below the mud line decreases continuously.③With the increase of drilling fluid density,the wellhead temperature decreases,and the bottom hole temperature increases slightly.④When the mechanical penetration rate increases,the temperature in the upper part of the wellbore decreases and the temperature at the bottom of the wellbore increases,and the mechanical penetration rate has the most obvious effect on the annular temperature.

(3)In the process of marine gas hydrate drilling,in order to ensure safe drilling,it is necessary to select the appropriate drilling fluid displacement and density,and control the mechanical penetration rate,so as to reduce the impact of hydrate decomposition on drilling safety.

Declaration of competing interest

All the authors of this work declare that we have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The work described in this paper is supported by the prospective research project of petroleum and gas development foundation of science and technology department of Sinopec(P20040-3),Postdoctoral program of Shengli Oilfield,Sinopec(YKB2107),National Key Research and Development Program of China(2019YFC0312302 and 2019YFC0312303),National Natural Science Foundation of China(U20B6005 and 51874252),and 111 Project(D21025).