A New Numerical Solution To Predict the Temperature ... - OnePetro

J160160 DOI: 10.2118/160160-PA Date: 18-July-17

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Total Pages: 12

A New Numerical Solution To Predict the Temperature Profile of Gas-Hydrate-Well Drilling Ben Li, China University of Petroleum, Beijing; and Hui Li, Boyun Guo, Xiao Cai, and Mas lwan Konggidinata, University of Louisiana at Lafayette

Summary Gas-hydrate cuttings are conveyed upward by the drilling fluid through the outer drillpipe/wellbore annulus during the gashydrate-well-drilling process. The temperature profile along the wellbore during the drilling process has not been thoroughly investigated because the gas-hydrate cuttings could affect the temperature of the drilling fluid along the wellbore. As the mixture of drilling fluid and gas hydrates flows from the bottom to the surface, the methane and other hydrocarbons present in the gas hydrates would change from liquid to gas phase and further cause well-control issues. Furthermore, the bottomhole pressure would decrease and could not provide sufficient balance to the formation pressure, which could significantly increase the risk of well blowout. A numerical solution is presented in this paper to predict the temperature profile of the gas-hydrate well during the drilling process. The main considerations were the following: • Hydrate cuttings entrained in the bottom of the hole would affect the temperature of the fluid in the annulus space. • The entrained hydrate cuttings could affect the fluid thermal properties in the drillstring and in the annulus. • Because of the Joule-Thomson cooling effect at the outlet of the nozzles, the fluid temperature at the bottom of the hole was lower than that above the drill-bit nozzles. Hence, the gas-hydrate-dissociation characteristics were considered and integrated in the proposed numerical model. The numerical model was validated by comparing the obtained data with the Shan et al. (2016) analytical model. In addition, the obtained data were also compared with the measured temperature data of a conventional well drilled in China and a gas-hydratewell drilling record in India. Sensitivity analysis was used to evaluate the effects of the pumping rate, Joule-Thomson effect, and injection drilling-mud temperature on the annulus temperatureprofile distribution. It was found that the injection drilling-mud temperature and pumping rate could affect the temperature profile in the annulus, whereas the Joule-Thomson effect could decrease the annulus temperature of the drilling mud near the bottom. Introduction Gas hydrates are considered one of the potential promising energy sources primarily found in cold environments. Gas hydrates are ice-like crystalline compounds and can be found in permafrost continental environments and in shallow marine sediments beneath deepwater around the world. Gas hydrates were first discovered in 1810 by Sir Humphry Davy, a British chemist. Since then, many studies focusing on gas hydrates have been conducted. Interest was further fueled by the blockages that occurred in the gas-transmission pipelines back in the 1930s. The blockage was initially thought to be ice. However, it was later proposed that the blockages were caused by the gas hydrates (Hammerschmidt 1934). Many new research interests were generated to understand how to avoid or delay the formation of gas hydrates. C 2017 Society of Petroleum Engineers Copyright V

Original SPE manuscript received for review 27 January 2016. Revised manuscript received for review 24 November 2016. Paper (SPE 185177) peer approved 29 November 2016.

Studies indicated that the volume of methane trapped in the hydrates is approximately 20 1015 m3, two orders of magnitude more than the estimated 25 1013 m3 of conventional methane (Collett 2000; Collett et al. 2000). Because of this huge amount of natural gas stored, the gas hydrates have been considered to be future clean-energy resources (Makogon 2010). However, production of natural gas from the gas hydrates is confronted with a series of challenges, uncertainties, and specific issues (Moridis et al. 2009, 2011). One of the problems that may occur is the uncontrolled release of gas from hydrates during the drilling process. The structure of solid-gas-hydrate crystals is dependent on the pressure and temperature. The reduction in pressure and increase in temperature because of the circulation of drilling fluid in the wellbore could cause the in-situ decomposition of gas hydrates and wellbore instability (Khabibullin et al. 2011). The decomposed gas could lead to hole enlargement and wellbore collapse because of the gasification of the drilling fluid. In addition, it could also have an effect on the mechanical and petrophysical properties of the sediments, such as the increase in permeability and the reduction in strength. Therefore, it is critical to predict the temperature in the wellbore in drilling gas-hydrates wells. Several analytical solutions and numerical algorithms to predict the temperature distribution have been applied. Ramey (1962) conducted a pioneering work that created a solution to the wellbore-heat-transmission problem for a single-phase fluid flowing through a single conduit in a line-source well. The study assumed a steady-state heat flowed in the wellbore while an unsteady heat flowed to the formation. However, this solution is only limited to the ideal gas and incompressible fluid. Edwardson et al. (1962) developed an analytical model to determine the formation-temperature distribution caused by fluid circulation. The model showed that the temperature at points removed from the drill bit are constant. Tragesser et al. (1967) developed a modified model of the Edwardson et al. (1962) work to calculate the bottomhole circulating temperature. The study applied a numerical solution for the transient-heat transfer at a given depth. However, further study revealed that neither the Edwardson et al. (1962) model nor the Tragesser et al. (1967) model could be used as a generalized predictive tool (Chen and Novotny 2003). Raymond (1969) derived the first numerical model to calculate the temperature of circulating fluid for both pseudosteady-state and transient conditions. The model showed that the temperature of fluid in hole bottom changed continually over time and a steady-state condition was never attained. In addition, the result suggested that circulation lowered the temperature of both the hole bottom fluid and the temperature of the rock. The model also predicted that the maximum temperature occurred at a certain portion of the way up the annulus. Holmes and Swift (1970) presented a steady-state analytical model to rapidly predict the mud-temperature distribution in drillpipe and in annulus. The model suggested that the total heat transfers between the fluids in the annulus and the fluids in the drillpipe were much greater than the heat transfers between the annulus fluid and the formation. This could be because of the low thermal conductivity of the formation and the film-thermal resistance formed at the interface of the mud and the rock. The model was applied to predict the mud temperature in the drillpipe and in the annulus at any depth. Sump and Williams (1973)

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J160160 DOI: 10.2118/160160-PA Date: 18-July-17

applied a mathematical model to compute wellbore temperature during mud circulation and cementing operations. The model was derived from the improved Raymond (1969) model by modifying the heat-transfer correlations. Keller et al. (1973) provided a 2D transient-heat-transfer model for predicting temperature distributions of the circulating mud columns in and around the wellbore. This model accounted for the presence of multiple casing strings that the Raymond (1969) method ignored. Wooley (1980) developed a computer model for predicting downhole wellbore temperatures for different flow options by applying the finite-difference method. In addition, three key variables (fluid-inlet temperature, fluid-flow rate and depth) have strong effects on the wellbore temperatures tested. Marshall and Bentsen (1982) claimed that the past computer models required to solve the finite-difference equations were time-consuming and had problems in accuracy and stability. A more-efficient computer model to calculate the temperature distribution was developed by use of a direct-solution technique. Because of the high efficiency, this model could be easily applied at the wellsite to continuously monitor the temperature in the wellbore. Sagar et al. (1991) improved the Ramey (1962) model and calculated temperature profiles in two-phase wells. A simplified model suitable for hand calculation was also developed. In the simplified model, a correlation developed from the field data was used to replace the Joule-Thomson and kinetic-energy terms. Alves et al. (1992) proposed a general model to predict the flow-temperature distribution in pipes and wellbores under single- or two-phase flow and over all inclination angles. Their work was dependent on the simplified Ramey (1962) method. The calculations of the overall heat-transfer coefficient and the transient-heat flow to the formation were ignored. This temperature model can be simplified into the Ramey (1962) model with the specific assumptions. Kabir at al. (1996) derived an analytical model to determine the temperature of the circulating fluid in drilling, workover, and well-control operations. This model was presented by brief equations that can be adopted into different formation-temperature distribution functions. The reverse-fluid-circulation condition, which means the fluid flows downward in the annulus and upward in the pipe, was also concerned. Chen and Novotny (2003) described the complete transient-heat behavior between the wellbore and reservoir dependent on the finite-difference method. Their model was applicable to any onshore well and riserless offshore well that has mud return to the seafloor. Nguyen et al. (2010) demonstrated a model to represent the temperature distribution in the fluid during drilling and estimated the influence of the temperature on the stability of the wellbore. The model also accounted for the effect of mechanical friction. However, it was found that the temperature of the drilling fluid could exceed the geothermal-formation temperature in some specific cases when the mechanical friction was taken into consideration. Wu et al. (2012) developed a pseudo-3D model to calculate the heat transfer between the wellbore and the reservoir during fluid circulation in the annulus. The model also considered the mechanical response of the system and predicted the stress changes under the same condition. Hasan and Kabir (2012) derived a unified method that presented the heat behavior under different conditions. The model is applicable for both single- and multipleflow conduits. In addition, it is also suitable for both steady- and unsteady-state-flow models during production. For decades, many studies have been conducted to predict the fluid temperature in the wellbore region. Analytical and numerical approaches have been used to compute the fluid temperature under steady- and unsteady-heat-flow conditions. The existing works had been widely applied in industrial practices, and great successes had been achieved. However, those works were not suitable for the following specific situations of hydrate drilling: • Hydrate cuttings entrained in the hole bottom would affect the temperature of the fluid in the annulus space. • The entrained hydrate cuttings could have an effect on the fluid-thermal properties in the drillstring and in the annulus. • Because of the Joule-Thomson cooling effect at the outlet of the nozzles, the fluid temperature at the hole bottom was lower than that above the drill-bit nozzles.

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The present work developed a numerical solution to describe the temperature profiles in the drillpipe and annulus, taking the effect of gas-hydrate cuttings entrained at the hole bottom and the Joule-Thomson cooling effect into consideration. Because the formation-temperature gradient and wellbore geometry change with different depths, the numerical solution has more advantages in describing the formation-temperature distribution along the wellbore compared with the analytical models. Numerical Solution of Temperature Profile This section describes the new numerical model developed to predict the temperature profile of the drilling fluid on the inside and outside of the drillstring during the gas-hydrate-drilling process. Details of the model derivation are provided in Appendix A; Matlab (2012) was used to develop the numerical solution. The drilling-fluid temperatures inside the drillstring Tp and in the annulus Ta are represented by the following equations: Tp;LþDL ¼ Tp;L þ

M2 DLDtðTa;L Tp;L Þ ; . . . . . . . . . . . . ð1Þ M1 Dt þ M3 DL

and Ta;L ¼ Ta;LþDL N2 ðTa;LþDL Tp;LþDL Þ N3 ðTg;LþDL Ta;LþDL Þ ; N1 Dt þ N4 DL ð2Þ where M1 ¼ Cp m_ p ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð3Þ M2 ¼

pdp Kp ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð4Þ tp

M3 ¼ qp Cp Ap ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð5Þ N1 ¼ Ca m_ a ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ð6Þ N2 ¼

pdp Kp DLDt ; . . . . . . . . . . . . . . . . . . . . . . . . . . ð7Þ tp

N3 ¼

pdc Kwellwall DLDt ; . . . . . . . . . . . . . . . . . . . . . . ð8Þ tdrainage

N4 ¼ qa Ca Aa : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð9Þ This numerical model has a unique advantage over the existing models because the mass and heat of gas hydrates entrained to the fluid stream at the hole bottom were considered. The equation to calculate the average mass-flow rate in the annulus m_ a is expressed as m_ a ¼

Cp m_ p þ Cs m_ s ; . . . . . . . . . . . . . . . . . . . . . . . . ð10Þ Ca

where the mass-flow rate inside the drillstring is expressed as m_ p ¼ qp Qp : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð11Þ The product of heat capacity and mass-flow rate of solid Cs m_ s is further expressed in two terms: Cs m_ s ¼ Ch m_ h þ Cr m_ r ; . . . . . . . . . . . . . . . . . . . . .

ð12Þ

where p m_ h ¼ D2b Rp /qh ; . . . . . . . . . . . . . . . . . . . . . . . . . . ð13Þ 4 and p m_ h ¼ D2b Rp ð1 /Þqr : . . . . . . . . . . . . . . . . . . . . . ð14Þ 4

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120

120 110

Etolerance 3.0

110

100

Etolerance 3.5

100

Etolerance 4.0

90

90

Etolerance 4.5

80

Etolerance 5.0

70

Etolerance 5.5

80

Ta (°C)

Tp (°C)

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60

Etolerance 3.0

70

Etolerance 3.5

60

Etolerance 4.0

50

50

40

40

30

30

Etolerance 4.5 Etolerance 5.0 Etolerance 5.5

20

20 0

1000

2000

3000

4000

5000

6000

Depth (m) Fig. 1—Effect of Etolerance on the accuracy of the Tp. Etolerance can affect the accuracy of the drilling-mud temperature inside the drillpipe. The Etolerance value must be higher than 4.0 to achieve the numerical-model accuracy for the temperature profile inside the drillpipe.

The values of tp , dp , Ap , and Aa are dependent on well geometry and would change along the wellbore. The heat capacity of the drilling fluid is dependent on temperature, and for a wide temperature interval, the temperature-dependent-heat capacity CðTÞ can be expressed as CðTÞ ¼ CðTi Þ þ bc ðT Ti Þ; . . . . . . . . . . . . . . . . . . ð15Þ where T is the reference temperature ( C); bc is the coefficient of the specific heat capacity [J/(kg C2)]; and Tp and Ta along the well trajectory can be solved by the following steps: 0 ¼ Tg;L and use Eq. 1 to calculate • Step 1: Assume initial Ta;L i from surface to bottom. Tp;L i i and Eq. 2 to calculate Ta;L from bottom to • Step 2: Use Tp;L surface. iþ1 i and Eq. 1 to calculate the new Tp;L from • Step 3: Use Ta;L surface to bottom. iþ1 iþ1 and Eq. 2 to calculate Ta;L from bottom to • Step 4: Use Tp;L surface. • Step 5: Repeat Steps 3 and 4 until the following convergence criterion is achieved: X D=DL iþ1 T a; j j 1 < 10Etolerance : . . . . . . . . . . . . . . . ð16Þ XD=DL i Ta; j j The accuracy of the numerical model is indicated by the Etolerance . The larger the Etolerance value, the higher the accuracy of the numerical solution. However, the convergence time of the numerical model will also increase as the value of Etolerance increases. Sensitivity analysis is performed to evaluate the effect of Etolerance on the accuracy of the numerical model. Figs. 1 and 2 showed the effects of Etolerance on the accuracy of the drilling-mud temperature in the drillpipe Tp and in the annulus Ta , respectively. The Etolerance is varied from 3.0 to 5.5. It was observed that the Etolerance greater than 4.0 achieved stable accuracy without causing any instability issues. Sensitivity analysis could also be conducted to optimize the Etolerance value by use of the specific features of the well geometry and drilling-fluid/formation properties. Model Comparison The new numerical solution derived was programed and compared with other models to ensure that no error is made in the mathematical equations in the solution and computer modeling. A number of numerical models to predict the fluid temperature have

0

1000

2000

3000

4000

5000

6000

Depth (m) Fig. 2—Effect of Etolerance on the accuracy of the Ta. Etolerance can affect the accuracy of the drilling-mud temperature in the annulus. The Etolerance value must be higher than 4.0 to achieve the numerical-model accuracy for the temperature profile in the annulus.

been published (Keller et al. 1973; Wooley 1980; Marshall and Bentsen 1982; Hasan and Kabir 1994; Kabir at al. 1996; PooladiDarvish 2004). However, all these models did not take the features of gas-hydrate drilling into consideration and could not be used for gas-hydrate drilling. A new analytical model was created by Shan et al. (2016) to investigate the temperature profiles of gas-hydrate drilling. This model was used as the comparison model. The Shan et al. (2016) analytical model was derived with the same concept as this paper but was analytically solved. The advantage of using the Shan et al. (2016) analytical model as the comparison model was because derivations of the analytical and the numerical model were dependent on the same concepts and assumptions. The results of these two models have a good correlation, which indicated the validity of the mathematical derivation. Although the results of these two models matched well with each other, only the validity of the mathematical derivation of the numerical model was proved. Further comparison must be conducted to verify the proposed numerical model. Results from the numerical model and the Shan et al. (2016) analytical model were compared with a typical data set. The data used in the models are provided in Table 1, and the temperature profiles given by the two models are presented in Fig. 3. The results showed good agreement, with an average difference of less than 0.1%. The wellbore-geometry parameters, such as tp , dp , Ap , and Aa , would vary along the wellbore, and the properties of drilling fluid, such as Cp and Ca , are dependent on temperature. The proposed numerical model has the advantage and the capacities to simulate these conditions, whereas some analytical models just use constant values for the simplified estimation. Table 2 presents the specific drillstring data and well-schematic data for further model comparison. Fig. 4 compares the temperature profiles generated from the numerical model by considering the specific drillstring and wellgeometry data, the numerical model without considering the specific drillstring and well-geometry data, and the Shan et al. (2016) analytical model. The same constant geothermal-gradient value (Table 1) was used in the proposed numerical model and the Shan et al. (2016) analytical model. The results suggested that the Shan et al. (2016) analytical model and the numerical model without considering the specific drillstring and well-geometry data generated similar temperature profiles. The results were lower than the temperature profiles generated by the numerical model considering the specific drillstring and well-geometry data. It could be concluded that the combination of well-geometry and drillstring data could affect the temperature-profile prediction. Both Ta and Tp would be underestimated if these factors were simplified.



J160160 DOI: 10.2118/160160-PA Date: 18-July-17

2300

m

Bit diameter

0.201

m

Inner diameter of cement

0.340

m

Outer diameter of cement

0.445

m

Inner diameter of drillstring

0.109

m

Outer diameter of drillstring

0.127

m

20

°C

0.0245

°C/m

Thermal conductivity of drillpipe

43

W/(m·°C)

Thermal conductivity of cement

1.7

W/(m·°C)

Injection rate

0.03

m /s

30

°C

Heat capacity of fluid inside pipe

4180

J/(kg·°C)

Heat capacity of rock

920

J/(kg·°C)

Heat capacity of formation fluid

1880

J/(kg·°C)

Porosity

0.27

–

Rate of penetration

1.8

m/h

2

°C

Density of rock

2650

kg/m

3

Density of formation fluid

910

kg/m

3

Density of injected fluid

1127

kg/m

3

0

m /s

Geothermal gradient

Temperature of injected fluid

Temperature drop at the drill bit (Joule-Thomson effect)

Formation-fluid influx rate

Total Pages: 12

Inside drillstring - Numerical solution Annulus - Numerical solution Geothermal temperature

Temperature (°C)

70

Inside drillstring - Analytical solution Annulus - Analytical solution

60 50 40 30 20 10 0

500

3

Field Verification Traditional Well Drilling. A traditional well-drilling example was used to evaluate the performance of the numerical model. The Nanpu oil field is in the Nanpu County of Hebei Province, China. Well N23 was drilled as an oil-production well in the sandstone at a depth of approximately 4050 m in 2009. Table 3 presents the well-schematic and completion data of Well N23 in the Nanpu Field. The well was drilled to 4050 m and the temperature profile was recorded during the well drilling. The drillingmud temperature was 20 C at the surface and the surface-geothermal temperature was 15 C. The formation pressure and the bottom pressure with the drilling fluid were approximately 41.8 and 42.5 Mpa, respectively. The pH value of the drilling mud was 9.0. Table 4 shows the well-operation parameters of Well N23. The thermal and physical properties of rock and drilling fluid is presented in Table 5. Water is the major component of the drilling mud, and heat capacity of water is a function of temperature and pressure (Abbott and van Ness 1989). Considering the extreme

1000

1500

2000

2500

Depth (m)

3

Table 1—Data used in model comparison.

Well Data

Page: 1204

80

Depth

Geothermal temperature at surface

Stage:

Fig. 3—Comparison of temperature profile of the proposed numerical solution with the Shan et al. (2016) analytical model by use of the same data set. Results of the numerical model and the Shan et al. (2016) analytical model are almost the same, which indicates that the numerical algorithm is reliable.

condition of 4 C at 0.9 kPa and 160 C at 618 kPa, the heat capacity of water varies between 4205 and 4350 J/kgoC, or approximately 3.4%. When calculating the temperature profiles, the numerical model first assumed constant-heat-capacity value at the start of the iteration. Then, the values of the heat capacity were adjusted by use of Eq. 15 and the temperature profiles in both the annulus and in the drillpipe. Results of the newly developed numerical model were compared with field-measurement temperature data of Well N23. A comparative plot, as shown in Fig. 5, illustrates that the temperature profile of the drilling mud inside the drillstring would increase while flowing down the drillstring. This could be because of the heat transfer from the formation rock. The temperature in the annulus between outer drillpipe and formation was a little higher than that in the drillpipe at the same depth because the annulus was relatively closer to the formation than the drilling mud in the drillpipe. Because the heat transfer is a function of time and distance, the temperature in the annulus would be a little higher than that in the drillpipe. The real wellbore temperature was measured and shown in Fig. 5. The temperature profile determined by the numerical model had a good match with the measured temperature data. However, some of the differences observed could be because of two main reasons. First, the temperature profile calculated by the numerical model represented the temperatures during the drilling process, whereas the real temperatures were measured after the drilling process. The different time intervals allowed more of the heat-transfer process to occur. Besides that, the formation between 2665 and 3300 m was composed of the combination of basaltic mud rock and the interbedded sandstone. Hence, the density of the drilling fluid was increased from 1.03 to 1.38 g/cm3 to maintain the wellbore stability. However, the increase of drilling-fluid density had caused more fluid leaking to the formation, especially to the porous sandstone layers. Reduced formation temperatures near the wellbore were observed. The same reasoning could also be used to explain the lower drilling-fluid temperature observed.

Inner Diameter (m)

Outer Diameter (m)

Length (m)

Surface casing

0.318

0.340

1500

Drillpipe

0.109

0.127

1884

Heavy water drillpipe

0.101

0.127

142

Drill collar

0.076

0.203

274

Table 2—Well-geometry data used in model comparison. 1204


J160160 DOI: 10.2118/160160-PA Date: 18-July-17

60 55

Temperature (°C)

50 45 40 35 30 Tp Shan et al. (2016) model Ta Shan et al. (2016) model Tp Numerical model with the same data as Shan et al. (2016) model Ta Numerical model with the same data as Shan et al. (2016) model Tp Numerical model considering well geometry Ta Numerical model considering well geometry

25 20 15 10 0

500

1000

1500

2000

2500

Depth (m) Fig. 4—Effect of well geometry on the temperature profiles of the numerical solution. The numerical solution that considers the specific well-geometry data generates higher temperature profiles than the numerical model and the Shan et al. (2016) analytical model, which do not take these factors into consideration. The temperature profiles would be underestimated if the specific well-geometry data are simplified.

Gas-Hydrate-Well Drilling. Gas-hydrate-well drilling has its own distinguished characteristics that are different from traditional well drilling. One of the major differences is the reduction of well hole bottom pressure when gas-hydrate cuttings entered the wellbore annulus and migrated upward to the surface. This is more related to well-control scope and similar applied theories than to traditional well control. The gas hydrates would not dissociate until the temperature reaches the gas-hydrate-dissociation temperature. The major gas-phase components of the gas hydrates are methane and traces of carbon dioxide, hydrogen sulfide, or nitrogen. The risk of well blowout would increase as the gashydrates cuttings migrated upward to the surface. As the temperature and pressure change, it could be a potential threat to drilling operations. To mitigate the gas kicks in the upper section of borehole, the temperature along the wellbore must be predicted and monitored properly, especially for the gas-hydrate-well drilling. A gas-hydrate-well-drilling case was further used to validate the numerical solution. The National Gas Hydrate Expedition Programme (NGHP-01) of India found the occurrence of natural-gas hydrates along the passive continental margins of the Indian peninsula and in the Andaman convergent margin (Collett et al. 2014). Drilling results from Well NGHP-01-17A in the Andaman Islands indicated gas-hydrate saturations to be 10 and 20% in two zones at intervals of 547 to 570 m and 586 to 602 m below the seafloor, respectively. The formation temperature of the hydratebearing layer was approximately 10.6 C (Winters 2011; Shankar and Riedel 2013). Table 6 summarized the well-configuration data and the operation parameters of Well NGHP-01-17A. Estimated material properties are given in Table 7. Fig. 6 shows the temperature profiles calculated from the numerical model. The profile indicated that the temperature of the drilling fluid inside the drillpipe would increase as the fluid flowed down the annulus. However, the drilling-mud temperature would not rise close to the geothermal temperature at the hole botType of Casing

Stage:

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tom. The temperature of the upward-fluid mixture (mixed with drilling fluid, rock cuttings, and gas hydrates) in the annulus would increase to the formation temperature in a short distance above the hole bottom and then it would go beyond the geothermal temperature at the same depth, not far from the seafloor. Because the measured annulus temperature of Well NGHP-0117A was not published by the authors, the gas-hydrate-dissociation-temperature curve of Well NGHP-01-17A was used for comparison. The formation pressure at the top of hydrate-bearing layer (1891 m) was approximately 18.9 MPa. The hydrate-dissociation temperature at this pressure was approximately 18.3 C. The geothermal temperature of the hydrate-bearing layer was only 10.6 C, and at the depth of seafloor, the calculated annulus temperature was 2.3 C. Because of the slightly higher geothermal temperature at the same seabed, the mud temperature at the hydrate depth would never reach the hydrate-dissociation temperature while migrating upward in the annulus. Because this annulus temperature was much lower than the gas-hydrate-dissociation temperature of 18.3 C, the hydrates in the drill cuttings would not dissociate at the depth of seafloor and there should be no free gas in the drilling mud while circulating upward the annulus. Further investigation on the gas-hydrates dissociation will be discussed in the next subsection. The calculation results agreed well with the fact that Well NGHP-01-17A was drilled successfully without any well-control issues reported. On the basis of the case studies of traditional well drilling (Well N23, China) and gas-hydratewell drilling (Well NGHP-01-17A, India), the proposed numerical solution has the potential to be further used to predict the annulus temperature of the gas-hydrate-well drilling. Gas-Hydrate Dissociation. The numerical solution also integrated the heat transfer during gas-hydrate dissociation and pressure-dependent gas-hydrate-dissociation-temperature profiles that can be used to simulate the features of gas-hydrate drilling. Gashydrate enthalpy of fusion, or the heat of formation, is a parameter that describes the amount of heat required to melt a hydrate. It also represents the formation of a hydrate from liquid water and a gaseous guest molecule (Carroll 2003). Table 8 summarizes the physical properties of the typical gas hydrates (Keenan et al. 1978; Sloan 1998). The enthalpy of fusion of the pure water is 0.333 kJ/g, which is significantly less than that of the gas hydrate. This could be because when a gas hydrate melts, it forms a liquid phase and a gas phase, and the gas is a more highly energetic state. The gas-hydrate dissociation is an endothermic process, and the temperature of the drilling fluid would decrease during the dissociation process of gas hydrates. However, during the dissociation of gas hydrates, free-gas bubbles or gas slugs would appear in the drilling mud. The decrease in the bottomhole pressure could not provide sufficient balance to the formation pressure. Hence, gas kicks in the wellbore annulus would appear, and the risk of well flow or even well blowout would increase. The major factor that describes the appearance of gas-hydrate dissociation is the dissociation temperature of gas hydrates, which is functions of pressure and compositions of gas hydrates. Carroll (2003) presented the relationship between pressure and temperature for gas-hydrate dissociation in the temperature range of 0–25 C, as shown in Eq. 17. The relationship is modified from the original expression published by Makogon (1981): 2 1: . . . . . . . . . . . ð17Þ logPdis ¼ b þ 0:0497 Tdis þ kTdis

Conductor

Surface Casing

Intermediate Casing

Production Casing

Bit diameter (mm)

660.4

444.5

311.1

215.9

Casing length (m)

36

250

2000

4050

Casing outer diameter (mm)

762

508

339.7

244.5

–

J-55

J-55

J-55

0–36

0–250

0–2000

1950–4200

Casing grade Cement interval (m)

Table 3—Well schematic of Well N23 in the Nanpu oil field, China. August 2017 SPE Journal


J160160 DOI: 10.2118/160160-PA Date: 18-July-17

160

Page: 1206

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Thermal conductivity of drillpipe Inside drillstring temperature Annular temperature Well N23 measured temperature

140

Temperature (°C)

Stage:

120

43

W/(m·°C)

Heat capacity of mud inside drillpipe

4210

J/(kg·°C)


930

J/(kg·°C)

Rock porosity

0.26

–

Density of rock

2700

kg/m

100 80

Table 5—Estimated material properties of Well N23 in Nanpu oil field, China.

60 40 20

3

Total depth below seafloor 500

602

m

Bit diameter

0.201

m

Outer diameter of drillpipe

0.127

m

Inner diameter of drillpipe

0.109

m

1.5

°C

Geothermal gradient

0.015

°C/m

Mud-injection rate

0.025

m /s

1070

kg/m

2

°C

0.008

m/s

1000 1500 2000 2500 3000 3500 4000 4500

Well Depth (m) Fig. 5—Comparison of temperature profile of numerical solution with field-measurement results. The predicted temperature profile of drilling mud inside the drillpipe is slightly lower than that of the drilling mud in the annulus. The temperature profiles matched well with the measured data of Well N23.

Geothermal temperature at seafloor

Outer diameter of drillpipe

0.127

m

Mud density

Inner diameter of drillpipe

0.111

m

Mud temperature inside drillpipe at seafloor

15

°C

Rate of penetration

Geothermal gradient

0.032

°C/m

Mud-injection rate

0.0278

m /s

1070

kg/m

20

°C

0.0075

m/s

Geothermal temperature at surface

Mud density Mud temperature at surface Rate of penetration

3

3

Table 4—Well-operation parameters of Well N23 in the Nanpu oil field, China.

b and k can be obtained graphically or calculated as a function of gas specific gravity (SG), expressed by Eqs. 18 and 19:

3

3

Table 6—Well- and operation-parameter values in drilling Well NGHP-01-17A.

ature of gas hydrates would increase nonlinearly as the pressure increases. As the gas-hydrate cuttings circulated upward along the wellbore annulus, the annulus pressure would decrease. This would result in the dissociation temperature of gas hydrates decreasing accordingly. In addition, the components of gas hydrates could also affect the dissociation temperature. The dissociation temperature of pure methane (SG ¼ 0.55) is lower than that of the typical natural gas (SG ¼ 0.81) at the same pressure as shown in Fig. 7. The dissociation temperature of methane could be considered as a strict-limitation dissociation temperature of the gas hydrates if the SG of the gas hydrates is not available during

b ¼ 2:681 3:811c þ 1:679c2 ; . . . . . . . . . . . . . . . . ð18Þ 18

k ¼ 0:006 þ 0:011c þ 0:011c2 ; . . . . . . . . . . . . . . . ð19Þ

Thermal conductivity of drillpipe

43

W/(m·°C)

Heat capacity of mud inside drillpipe

4210

J/(kg·°C)


920

J/(kg·°C)

Heat capacity of hydrates

2050

J/(kg·°C)

Rock porosity

0.27

16 14

Temperature (°C)

where Pdis is dissociation pressure of gas hydrates (MPa); Tdis is dissociation temperature of gas hydrates ( C); and c is the gas gravity. The relationship between typical gas-hydrate-dissociation temperature and pressure is shown in Fig. 7. The dissociation temper-

12 10 8 6 4

Inside drillpipe temperature Annular temperature Geothermal temperature Dissociation temperature

2 0

–

0

100

200

300

400

500

600

700

Depth Below Seafloor (m) Density of rock

2650

kg/m

3

Density of hydrates

985

kg/m

3

Table 7—Estimated material properties in drilling Well NGHP-0117A.

Fig. 6—Model-predicted temperature profile of Well NGHP-0117A. The temperature of drilling fluid in the annulus was always lower than the dissociation temperature of the gas-hydrate cuttings, which indicated that no gas-hydrate-dissociation process would appear while drilling.

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J160160 DOI: 10.2118/160160-PA Date: 18-July-17

Density (g/cm )

Enthalpy of Fusion (kJ/g)

Methane

I

0.913

3.06

Ethane

I

0.967

3.7

Propane

II

0.899

6.64

Isobutene

II

0.934

6.58

drilling. Because the annulus pressure along the wellbore is dependent on depth, the dissociation temperature of gas hydrates can be calculated by the pressure along the annulus. The seafloor depth below the rig of Well NGHP-01-17A was approximately 1356 m and the total well depth below the rig was 2047 m. The annulus-circulation pressure could be calculated while considering the hydraulic pressure and annulus-pressure loss along the wellbore annulus. The annulus pressure of Well NGHP01-17A is shown in Fig. 8, and the results indicated that the annulus temperature of the drilling mud with gas-hydrate cuttings would not reach the dissociation temperature of gas hydrates. Sensitivity Analysis For well control, it was desirable to explore major factors affecting the annulus temperature profile during gas-hydrate drilling and to further optimize the gas-hydrate-well-drilling design. The annulus temperatures were dependent on the injection drillingmud temperature at the surface and drilling-mud-pumping rate. These two parameters determine the heat that the drilling mud brought to the wellbore and the heat-conduction time during the circulation, respectively. The Joule-Thomson cooling effect below the drill-bit nozzles could also affect the temperature profile of the annulus. All these factors were investigated with the proposed numerical model by use of the same data presented in Tables 6 and 7, with one parameter varied at a time. Sensitivity analysis was performed to identify the key factors that could affect the drilling-mud temperature. The analysis would provide the guidelines for the design and operation of the gas-hydratewell drilling. Effect of the Drilling-Mud Pumping Rate on the Annulus Temperature Profile. Fig. 9 illustrates the temperature profiles calculated by the numerical model with the drilling-mud-pumping rate varied from 0.022 to 0.05 m3/s. It indicated that the fast pumping of cold drilling mud could reduce the drilling-mud temperature near the hole bottom. The temperature of the upwardflowing fluid mixture in the annulus was slightly elevated because 20

0

15

0

100

200

300

400

500

600

Annular Pressure (MPa)

Temperature (°C)

Annular temperature Dissociation temperature of gas hydrates Annular pressure

20

Total Pages: 12

Dissociation Curve of Gas Hydrates

25

Table 8—Physical properties of different types of gas hydrates.

40

Page: 1207

30

10 700

Depth Below Seabed (m) Fig. 8—The dissociation-temperature profile of gas hydrates. The annulus temperature is always lower than the dissociation temperature of gas hydrates, which indicates that the gashydrate cuttings will not dissociate along the wellbore.

Temperature (°C)

3

Hydrate Type

Stage:

20

Typical natural gas Methane

15

10

5

0

0

5

10

15

20

25

30

35

40

45

Pressure (MPa) Fig. 7—The relationship between dissociation temperature and pressure of typical gas hydrates. The dissociation temperature of gas hydrates will increase nonlinearly as the pressure increases. The dissociation temperature is also dependent on the components of the gas hydrates. The dissociation temperature of pure-methane (SG 5 0.55) gas hydrates is lower than that of typical natural gas (SG 5 0.81).

of the fast convection of heat from the deeper section. The upward flowing fluid mixture (mud and rock cuttings with hydrates) in the annulus was heated to the formation temperature at various pumping rates. This indicated that the formation-thermal energy was a key factor that could affect the annulus temperature profile. By use of the pumping-rate-sensitivity analysis, higher pumping rate could reduce the annulus temperature of drilling mud near the hole bottom and increase the outlet annulus temperature at the surface. Gas-hydrate cutting can also influence the annulus temperature profiles. The annular temperature without gas-hydrate cuttings was found to be higher than that with gas-hydrate cuttings. This indicated that the gas-hydrate cuttings could lower the annular temperature, to some extent. For Well NGHP-01-17A, the pumping rate was not a sensitive parameter for the gas-hydratewell drilling. However, for other wells with different geological conditions, it is recommended that the drilling-mud-pumping rate be designed and optimized thoroughly before drilling to avoid the gas-hydrate dissociation. Joule-Thomson Effect and the Annulus Temperature Profile. Fig. 10 demonstrates the annulus temperature profiles calculated by the proposed numerical solution for 0 to 5 C, dependent on the Joule-Thomson cooling effect at the drill-bit nozzles. Fig. 10 shows that the Joule-Thomson cooling effect rapidly diminished because of the effect of heating from the formation geothermal energy in a short interval above the hole bottom. The temperature variation at the outlet annulus, caused by the Joule-Thomson effect, could be ignored. Although the Joule-Thomson cooling effect could reduce the temperature at a certain distance of the drill-bit depth, formation thermal energy could compensate for this effect in a short time. Because it is better to use lower-temperature drilling mud to drill gas-hydrate wells, the Joule-Thomson cooling effect can further reduce the drilling-mud temperature around the drill bit. The combined effect of low drilling-mud temperature and Joule-Thomson cooling effect could result in ice-like drilling mud that would be a threat to the gas-hydrate-well drilling. In this case, the Joule-Thomson cooling effect must be considered while designing the surface-drilling-mud temperature for the gas-hydrate-well drilling. Effect of the Initial Drilling-Mud Temperature On the Annulus Temperature Profile. Fig. 11 presents the effect of drilling-mud temperature at the surface before pumping. The



J160160 DOI: 10.2118/160160-PA Date: 18-July-17

10

8

Page: 1208

Total Pages: 12

10

0.022, no hydrate cuttings 0.022 0.028 0.033 0.039 0.044 0.050

0°C 1°C 2°C 3°C 4°C 5°C

9

Annular Temperature (°C)


12

Stage:

6

4

8 7 6 5 4 3

2

2 0

100

200

300

400

500

600

700

Depth (m) Fig. 9—Effect of drilling-mud pumping rate on the annulus temperature profile. The surface drilling-mud temperature after circulating is higher than the surface drilling-mud temperature (28C) before pumping, which indicates that the geothermal energy can heat the pumping mud to some extent while circulating upward along the annulus. Because the geothermal temperature will decrease from the bottom to the surface, less thermal energy would be transferred during the circulating out along the annulus. The drilling mud will be heated up while circulating below the balance-temperature point, and the drillingmud temperature will be cooled down while traveling above the balance-temperature point. By use of the theory of heat transfer, heat-transfer time will also affect the temperature of the drilling mud. The circulating time of the lower pumping rate is longer than that of the faster pumping rate. If the drilling mud is pumped in a relatively slow rate, the pumped mud will be exposed to the wellbore for a relatively longer time, which means the heat-exchange period in the wellbore is longer than that of the faster pumping rate and more energy will be transferred from the formation to the drilling mud in the annulus. First, the drilling-mud temperature will be decreased because of the Joule-Thomson effect at the outlet of the drill-bit nozzles. Then the drilling mud will be heated up by the geothermal energy below the balance-temperature point, whereas the drilling mud will be cooled down above the balance-temperature point. For the slow-pumping drilling mud, the annulus temperature will be higher than that of the fast-pumping drilling mud below the balance-temperature point. The annulus temperature of the slow-pumping rate will be lower than that of the fastpumping drilling mud above the balance-temperature point. Both circulating time and geothermal energy will affect the temperature profile along the annulus. The annular temperature without gas-hydrate cuttings is higher than that with gashydrate cuttings, which indicates the gas-hydrate cuttings can lower the annular temperature to some extent. To lower the drilling-mud temperature along the annulus, a faster pumping rate in a reasonable range is preferred.

surface temperature of the drilling mud was varied from 2 to 14 C. As the surface temperature of the drilling mud increased, the temperature along the annulus increased accordingly. The highest value of the annulus temperature existed at the well hole bottom, whereas the lowest value of the annulus temperature occurred at the annulus outlet. Fig. 12 illustrates that the annulus temperature at the hole bottom and at the annulus outlet would increase as the surface injection drilling-mud temperature increases. However, the degree of increment at the annulus outlet was observed to be higher than that at the hole bottom. A temperature threshold must be carefully studied before drilling gashydrate wells. Conclusions A numerical model was developed and programmed to investigate and predict the temperature profiles along the wellbore for gashydrate-well drilling. The characteristics of the gas-hydrate dissociation were also discussed and integrated in the proposed numeri-

0

100

200

300

400

500

600

700

Depth (m) Fig. 10—Effect of Joule-Thomson cooling on the annulus temperature profile. The Joule-Thomson effect describes the temperature change of a real gas or liquid when it is forced through a valve or porous plug while kept insulated so that no heat is exchanged with the environment, which will exist while drilling mud jets out of the nozzles of the drill bit. The drilling-mud temperature will be decreased because of the Joule-Thomson cooling effect. However, the drilling-mud temperature would be heated up and finally has the same temperature while circulating out. This indicates that the Joule-Thomson cooling effect can be compensated by the geothermal energy of the formation. Even the Joule-Thomson cooling effect will be compensated by the geothermal energy of the formation, it must be carefully evaluated to avoid the ice-like drilling mud, which would further threaten the gas-hydrate drilling.

cal model. The numerical model was validated by comparing the results with the Shan et al. (2016) analytical model and further verified with the measured temperature data of conventional-welldrilling records (China) and a gas-hydrate-well-drilling records (India). Sensitivity analysis was conducted to evaluate the effects of the mass-pumping rate, Joule-Thomson effect, and injection drilling-mud temperature on the annulus temperature-profile distribution. The following conclusions were drawn. 1. The comparison between field-measurement temperature data of Well N23 in China and the drilling record of Well NGHP01-17A in India with the temperature profile determined by the proposed numerical model indicated good correlations between field observations and model implications. 2. The bottomhole temperature could be affected by the surface temperature of the drilling mud and mass-pumping rate of the drilling mud. The drilling-mud temperature near the hole bottom was lower than the geothermal temperature at the same depth. 3. The pumped drilling mud was rapidly heated by the geothermal energy after entering the annulus space. The temperature of the drilling mud in the annulus could become higher than the formation temperature at the same depth. This was dependent on the mass pumping rate of drilling mud. 4. The Joule-Thomson cooling effect below the drill-bit nozzles rapidly diminished in a short interval above the hole bottom because of the heating effect of geothermal energy. The JouleThomson cooling effect must be considered in the design of the surface drilling-mud temperature of the gas-hydrate-well drilling to avoid the appearance of ice-like drilling mud around the drill bit. 5. The surface drilling-mud temperature must be lower than the gas-hydrate-dissociation temperature. A temperature threshold must be carefully studied before drilling gas-hydrate wells. Nomenclature Aa ¼ cross-sectional area of annulus open for fluid flow, m2

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J160160 DOI: 10.2118/160160-PA Date: 18-July-17

Stage:

Page: 1209

16

15

Surface annular temperature Bottom annular temperature

2°C 6°C 8°C 10°C

9

12°C 14°C 6

3


4°C

12


Total Pages: 12

12

8

4

0

0 0

200

400

600

800

0

Depth (m) Fig. 11—Effect of initial drilling-mud temperature on the annulus temperature profile. The annulus temperature would increase as the surface drilling-mud temperature increases. If the surface temperature of the drilling mud is in a relatively lower range (0–8 C), the drilling mud will be cooled down while circulating from bottom to surface. If the surface temperature of the drilling mud is in a relative higher range, the drilling mud will be heated up while circulating from the bottom to the surface. Although the geothermal energy is a dominant factor that could affect the temperature of the annulus, lowering the surface drilling-mud temperature could lower the temperature along the annulus, which could help to prevent the gas-hydrate cuttings from dissociating. The lower surface drilling-mud temperature could be considered a potential way to conquer the dissociation effect of gas-hydrate cuttings. The proposed numerical solution can be used to evaluate and design the surface drilling-mud temperature for the gas-hydrate-well drilling.

Ap ¼ cross-sectional area of drillpipe open for fluid flow, m2 Ca ¼ heat capacity of fluid in the annulus, J/kg C Ch ¼ heat capacity of gas hydrates, J/kg C Cp ¼ heat capacity of fluid inside drillpipe, J/kg C Cr ¼ heat capacity of rock cuttings in the annulus, J/ kg C D ¼ well depth, m Db ¼ bit diameter, m Dcasingshoe ¼ casing-shoe depth, m Kp ¼ thermal conductivity of drillpipe, W/m C Kwellwall ¼ equivalent thermal conductivity of well wall, W/ m C m_ a ¼ mass-flow rate in the annulus, kg/s m_ h ¼ mass-flow rate of hydrates, kg/s m_ p ¼ mass-flow rate inside the drillpipe, kg/s m_ r ¼ mass-flow rate of rock cuttings in the annulus, kg/s Qp ¼ fluid-pumping rate, m3/s RP ¼ rate of penetration, m/s tdrainage ¼ the interval between the wellbore and the nearest position to the wellbore at which the temperature is Tg;L while drilling, m tp ¼ drillpipe thickness, m Ta ¼ temperature of annulus fluid, C Tg ¼ geothermal temperature at depth, C Tp ¼ temperature of fluid inside drillpipe at depth, C Tpipe ¼ temperature of the drillpipe, C Twellwall ¼ the well-wall temperature between the wellbore and the nearest position to the wellbore at which the temperature is Tg;L while drilling, C bc ¼ coefficient of the specific heat capacity, J/(kg C2) qa ¼ fluid density in the annulus, kg/m3 qh ¼ density of hydrates, kg/m3 qp ¼ fluid density inside drillpipe, kg/m3

4

8

12

16

Initial Drilling-Fluid Temperature (°C) Fig. 12—Effect of initial drilling-mud temperature on the annulus temperature at the hole bottom and at surface. Lowering the surface drilling-mud temperature could decrease the drillingmud temperature in the annulus to some extent, but the cooling effect caused by the surface drilling-mud temperature would be reduced by the geothermal energy.

qr ¼ density of dry rock, kg/m3 / ¼ porosity of rock Acknowledgments This research was supported by the China State Key Laboratory of Petroleum Resources and Prospecting Foundation (PRP/indep04-1608), the Science Foundation of China University of Petroleum (Beijing) Grant (2462016YJRC033), the National Science and Technology Major Project of China (2016ZX05051), and the China National Natural Science Foundation (51134004, 51274220, 51334003). Any opinions, findings and conclusions, or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of these organizations. References Abbott, M. M. and van Ness, H. C. 1989. Thermodynamics, second edition. New York City: McGraw-Hill. Alves, I. N., Alhanatl, F. J. S., and Shoham, O. 1992. A Unified Model for Predicting Flowing Temperature Distribution in Wellbores and Pipelines. SPE Res Eng 7 (4): 363–367. SPE-20632-PA. https://doi.org/ 10.2118/20632-PA. Carroll, J. J. 2003. Natural Gas Hydrates – A Guide for Engineers. Amsterdam: Elsevier. Chen, Z. and Novotny, R. J. 2003. Accurate Prediction Wellbore Transient Temperature Profile under Multiple Temperature Gradients: Finite Difference Approach and Case History. Presented at the SPE Annual Technical Conference and Exhibition, Denver, 5–8 October. SPE84583-MS. https://doi.org/10.2118/84583-MS. Collett, T. S. 2000. Natural Gas Hydrates: Resource of the 21st Century? Presented at the AAPG Foundation Pratt Conference: Petroleum Provinces, 21st Century, San Diego, 1215 January. Collett, T. S., Lewis, R., and Uchida, T. 2000. Growing Interest in Gas Hydrates. Oilfield Rev. Summer 2000: 42–57. Collett, T. S., Ray B., James, R. C. et al. 2014. Geologic Implications of Gas Hydrates in the Offshore of India: Results of the National Gas Hydrate Program Expedition 01. Mar. Petrol. Geol. 58A (December): 3–28. https://doi.org/10.1016/j.marpetgeo.2014.07.021. Edwardson, M. J., Girner, H. M., Parkison, H. R. et al. 1962. Calculation of Formation Temperature Disturbances Caused by Mud Circulation. J Pet Technol 14 (4): 416–426. SPE-124-PA. https://doi.org/10.2118/ 124-PA. Hammerschmidt, E. G. 1934. Formation of Gas Hydrates in Natural Gas Transmission Lines. Ind. Eng. Chem. 26 (8): 851–855. https://doi.org/ 10.1021/ie50296a010.



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Hasan, A. R. and Kabir, C. S. 1994. Aspects of Wellbore Heat Transfer During Two-Phase Flow. SPE Prod & Fac 9 (3): 211–216. SPE22948-PA. https://doi.org/10.2118/22948-PA. Hasan, A. R. and Kabir, C. S. 2012. Wellbore Heat-Transfer Modeling and Applications. J. Pet. Sci. Eng. 86–87 (May): 127–136. https:// doi.org/10.1016/j.petrol.2012.03.021. Holmes, C. S. and Swift, S. C. 1970. Calculation of Circulating Mud Temperatures. J. Pet Technol 22 (6): 670–674. SPE-2318-PA. https:// doi.org/10.2118/2318-PA. Kabir, C. S., Hasan, A. R., Kouba, G. E. et al. 1996. Determining Circulating Fluid Temperature in Drilling, Workover, and Well-Control Operations. SPE Drill & Compl 11 (2): 74–79. SPE-24581-PA. https:// doi.org/10.2118/24581-PA. Keenan, J. H., Keyes, F. G., Hill, P. G. et al. 1978. Steam Tables. New York City: John Wiley & Sons. Keller, H. H., Couch, E. J., and Berry, P. M. 1973. Temperature Distribution in Circulating Mud Columns. SPE J. 13 (1): 23–30. SPE-3605PA. https://doi.org/10.2118/3605-PA. Khabibullin, T., Falcone, G., and Teodoriu, C. 2011. Drilling Through Gas-Hydrate Sediments: Managing Wellbore-Stability Risks. SPE Drill & Compl 26 (2): 287–294. SPE-131332-PA. https://doi.org/ 10.2118/131332-PA. Makogon, Y. F. 1981. Hydrates of Natural Gas. Tulsa: PennWell Publishing Company. Makogon, Y. F. 2010. Natural Gas Hydrates–A Promising Source of Energy. J. Nat. Gas. Sci. Eng. 2 (1): 49–59. https://doi.org/10.1016/ j.jngse.2009.12.004. Marshall, D. W. and Bentsen, R. G. 1982. A Computer Model to Determine the Temperature Distributions in A Wellbore. J Can Pet Technol 21 (1): 63–75. PETSOC-82-01-05. https://doi.org/10.2118/82-01-05. Matlab R2012b. 2012. Natick, Massachusetts: The MathWorks, Inc. Moridis, G. J., Collett, T. S., Boswell, R. et al. 2009. Toward Production from Gas Hydrates: Current Status, Assessment of Resources, and Simulation-Based Evaluation of Technology and Potential. SPE J. 12 (5): 745–771. SPE-114163-PA. https://doi.org/10.2118/114163-PA. Moridis, G. J., Collett, T. S., Pooladi-Darvish, M. et al. 2011. Challenges, Uncertainties, and Issues Facing Gas Production from Gas-Hydrate Deposits. SPE Res Eval & Eng 14 (1): 76–112. SPE-131792-PA. https://doi.org/10.2118/131792-PA. Nguyen, D. A., Miska, S. Z., Yu, M. et al. 2010. Modeling Thermal Effects on Wellbore Stability. Presented at the Trinidad and Tobago Energy Resources Conference, Port of Spain, Trinidad, 27–30 June. SPE-133428-MS. https://doi.org/10.2118/133428-MS. Pooladi-Darvish, M. 2004. Gas Production from Hydrate Reservoirs and Its Modeling. J Pet Technol 56 (6): 65–71. SPE-86827-JPT. https:// doi.org/10.2118/86827-JPT. Ramey, H. J. Jr. 1962. Wellbore Heat Transmission. J Pet Technol 14 (4): 427–435. SPE-96-PA. https://doi.org/10.2118/96-PA. Raymond, L. R. 1969. Temperature Distribution in A Circulating Drilling Fluid. J Pet Technol 21 (3): 333–342. SPE-2320-PA. https://doi.org/ 10.2118/2320-PA. Sagar, R., Doty, D. R., and Schmidt, Z. 1991. Predicting Temperature Profiles in a Flowing Well. SPE Prod Eng 6 (4): 441–448. SPE-19702PA. https://doi.org/10.2118/19702-PA. Shan, L., Guo, B., and Cai, X. 2016. Development of an Analytical Model for Predicting the Fluid Temperature Profile in Drilling Gas Hydrates Reservoirs. J. Sustain. Energ. Eng. 3 (3): 254–269. https://doi.org/ 10.7569/JSEE.2015.629516. Shankar, U. and Riedel, M. 2013. Heat Flow and Gas Hydrate Saturation Estimates from Andaman Sea, India. Mar. Petrol. Geol. 43 (May): 434–449. https://doi.org/10.1016/j.marpetgeo.2012.12.004. Sloan, E. D. Jr. 1998. Clathrate Hydrates of Hydrocarbons, second edition. New York City: Marcel Dekker. Sump, G. D. and Williams, B. B. 1973. Prediction of Wellbore Temperature during Mud Circulation and Cementing Operations. J. Eng. Ind. 95 (4): 1083–1092. https://doi.org/10.1115/1.3438255. Tragesser, A. F., Crawford, P. B., and Crawford, H. R. 1967. A Method for Calculating Circulating Temperature. J Pet Technol 19 (11): 1507–1512. SPE-1484-PA. https://doi.org/10.2118/1484-PA. Winters, W. J. 2011. Physical and Geotechnical Properties of Gas Hydrate Bearing Sediment from Offshore India and Northern Cascadia Margin Com-

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Appendix A—Derivation of Mathematical Model for Heat Transfer in Gas-Hydrate-Drilling System Assumptions. The following assumptions were made in the model formulation: • Temperatures in the drillpipe and in the annulus were constant in the radial direction. • The geothermal gradient behind the annulus was not affected by well fluid. • Friction-induced heat was negligible. Governing Equation. Fig. A-1 depicts a small element of a borehole section with a drillstring at the center. The heat flow inside the drillpipe was considered for a time period of Dt. Heat balance was given by Qp;in Qp;out qp ¼ Qp;chng ; . . . . . . . . . . . . . . . . . ðA-1Þ where Qp,in is the heat energy brought into the drillpipe element by fluid because of convection (J); Qp,out is the heat energy carried away from the drillpipe element by fluid because of convection (J); qp is heat transfer through the drillpipe because of conduction (J); and Qp,chng is the change of heat energy in the fluid (J). These terms could be further formulated as Qp;in ¼ Cp m_ p Tp;L Dt; . . . . . . . . . . . . . . . . . . . . . . . ðA-2Þ Qp;out ¼ Cp m_ p Tp;LþDt Dt; . . . . . . . . . . . . . . . . . . . . . ðA-3Þ @Tpipe qp ¼ pdp Kp DL Dt; . . . . . . . . . . . . . . . . . ðA-4Þ @r Qp;chng ¼ Cp qp Ap DLDTp : . . . . . . . . . . . . . . . . . . . . ðA-5Þ Substituting Eqs. A-2 through A-5 into Eq. A-1 creates @Tpipe Cp m_ p DtðTp;L Tp;LþDL Þ þ pdp Kp DL Dt @r ¼ Cp qp Ap DLDTp : . . . . . . . . . . . . . . . . . . . . . . . ðA-6Þ The radial temperature gradient in the drillpipe wall could be formulated as @Tpipe Ta;L Tp;L ; . . . . . . . . . . . . . . . . . . . . . . . ðA-7Þ ¼ @r tp where tp is the drillpipe thickness (m) and Tpipe is the temperature of the drillpipe ( C). Substituting Eq. A-7 into Eq. A-6 gives Ta;L Tp;L Cp m_ p DtðTp;L Tp;LþDL Þ þ pdp Kp DLDt tp ¼ qp Cp Ap DLDTp : . . . . . . . . . . . . . . . . . . . . . . . ðA-8Þ The temperature difference, DTp , can be formulated as DTp ¼ Tp;LþDL Tp;L : . . . . . . . . . . . . . . . . . . . . . . . ðA-9Þ Substituting Eq. A-9 into Eq. A-8 gives Tp;LþDL ¼ Tp;L þ

M2 DLDtðTa;L Tp;L Þ ; . . . . . . . . . .ðA-10Þ M1 Dt þ M2 DL

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Qp,in

Cement

Casing

Qa,out

Drillpipe

Drillpipe

Inside Drillpipe

Annulus

ΔL

Total Pages: 12

Casing

Annulus

Cement

J160160 DOI: 10.2118/160160-PA Date: 18-July-17

qp

Qp,out

qa

Qa,in

Fig. A-1—Sketch illustrating convection and conduction heat transfer in a borehole section.

where M1 ¼ Cp m_ p ; . . . . . . . . . . . . . . . . . . . . . . . . . . M2 ¼

ðA-11Þ

pdp Kp ; . . . . . . . . . . . . . . . . . . . . . . . . . . ðA-12Þ tp

M3 ¼ qp Cp Ap : . . . . . . . . . . . . . . . . . . . . . . . . . . ðA-13Þ We now consider the heat flow in the annulus during a time period of Dt. The heat balance was given by Qa;in Qa;out þ qp qa ¼ Qp;chng ; . . . . . . . . . . . . . ðA-14Þ where Qa,in is the heat energy brought into the drillpipe element by fluid because of convection (J); Qa,out is the heat energy carried away from the drillpipe element by fluid because of convection (J); qa is the heat transfer through casing and cement caused by conduction (J); and Qa,chng is the change of heat energy in the fluid (J). These terms can be further formulated as Qa;in ¼ Ca m_ a Ta;LþDL Dt; . . . . . . . . . . . . . . . . . . . . ðA-15Þ Qa;out ¼ Ca m_ a Ta;L Dt; . . . . . . . . . . . . . . . . . . . . . . ðA-16Þ @Tcsg qa ¼ pdc Kwellwall DL Dt; . . . . . . . . . . . . . ðA-17Þ @r Qa;chng ¼ Ca qa Aa DLDTa : . . . . . . . . . . . . . . . . . . . ðA-18Þ Substituting Eqs. A-15 through A-18 into Eq. A-14 gives @Tpipe Ca m_ a DtðTaþLþDL Ta;L Þ pdp Kp DLDt @r @Twellwall ¼ qa Ca Aa DLDta : þ pdc Kwellbore DLDt @r ðA-19Þ The radial temperature gradient in the casing can be formulated as

@Twellwall Tg;L Ta;L ; . . . . . . . . . . . . . . . . . . . . . ðA-20Þ ¼ @r tdrainage where tdrainage is the interval between the wellbore and the nearest position to the wellbore at which the temperature is Tg;L while drilling (m), and Twellwall is the well-wall temperature between the wellbore and the nearest position to the wellbore at which the temperature is Tg;L while drilling ( C). The thermal conductivity Twellwall;L at the interval of tdrainage can be calculated by use of the following: Kwellwall;L ¼

½Kcsg tcsg þ Kc tc þ Kf ;L ðtwellwall tcsg tc Þ ; twellwall L < Dcasingshoe ; ðA-21Þ

Kwellwall;L ¼ Kf ;L ; L > Dcasingshoe ; . . . . . . . . . . . . . . ðA-22Þ where Dcasingshoe is the casing-shoe depth (m). Substituting Eqs. A-7 and A-20 into Eq. A-19 gives Ta;L Tp;L Ca m_ a DtðTa;L Ta;LþDL Þ pdp Kp DLDt tp Tg;L Ta;L ¼ qa Ca Aa DLDta : þ pdc Kwellwall DLDt tdrainage ðA-23Þ The temperature difference DTa can be formulated as DTa ¼ Ta;L Ta;LþDL : . . . . . . . . . . . . . . . . . . . . . ðA-24Þ Substituting Eq. A-24 into Eq. A-23 gives Ta;L ¼ Ta;LþDL N2 ðTa;LþDL Tp;LþDL Þ N3 ðTg;LþDL Ta;LþDL Þ ; N1 Dt þ N4 DL ðA-25Þ where N1 ¼ Ca m_ a ; . . . . . . . . . . . . . . . . . . . . . . . . . . . ðA-26Þ



J160160 DOI: 10.2118/160160-PA Date: 18-July-17

N2 ¼

pdp Kp DLDt ; . . . . . . . . . . . . . . . . . . . . . . . ðA-27Þ tp

N3 ¼

pdc Kwellwall DLDt ; . . . . . . . . . . . . . . . . . . . . ðA-28Þ tdrainage

N4 ¼ qa Ca Aa : . . . . . . . . . . . . . . . . . . . . . . . . . . ðA-29Þ The formation temperature can be expressed as Tg;L ¼ Tg;0 þ GL; . . . . . . . . . . . . . . . . . . . . . . . . ðA-30Þ where G is the geothermal gradient ( C/m). The temperatures Tp and Ta at any given depth can be solved numerically by use of Eqs. A-10 and A-25. Boundary Conditions. The boundary conditions for solving Eqs. A-10 and A-25 are expressed as Tp;L ¼ Tp;0 at L ¼ 0;

. . . . . . . . . . . . . . . . . . . . . . ðA-31Þ

Ta;L ¼ Tp;L at L ¼ D:

. . . . . . . . . . . . . . . . . . . . . ðA-32Þ

The tp , dp , Ap , and Aa values are dependent on well geometry, which would change along the wellbore. The heat capacity of the drilling fluid is dependent on temperature. For a wide temperature interval, the temperature-dependent heat capacity CðTÞ could be expressed as CðTÞ ¼ CðTi Þ þ bc ðT Ti Þ; . . . . . . . . . . . . . . . . . ðA-33Þ where Ti is the reference temperature ( C) and bc is the coefficient of the specific heat capacity [J/(kg C2)].

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For the numerical iteration, the heat capacity of the drilling mud would be adjusted as the temperature changes along the wellbore by use of Eq. A-33. Ben Li is an assistant professor at the China University of Petroleum (Beijing). His research interests include hydraulic fracturing, rock mechanics, and reservoir simulation. Li holds a PhD degree in petroleum engineering from the University of Louisiana at Lafayette. Hui Li is a PhD degree student at the University of Louisiana at Lafayette. Her research interests include rock mechanics and reservoir simulation. Previously, Li was a petroleum engineer with China National Petroleum Corporation from 2010 to 2013. She holds a master’s degree in petroleum engineering from China University of Petroleum, Beijing, and a bachelor’s degree from Northeast Petroleum University, China. Boyun Guo is a professor at the University of Louisiana at Lafayette. His research interest is productivity enhancement of oil and gas wells. Guo holds a PhD degree in petroleum engineering from New Mexico Institute of Mining and Technology. Xiao Cai is a PhD degree student at the University of Louisiana at Lafayette. His research interests include parameter optimization for preventing screenout in hydraulic fracturing and temperature prediction during drilling in gas-hydrate reservoirs. Cai holds a master’s degree in petroleum engineering from the University of Louisiana at Lafayette and a bachelor’s degree from Northeast Petroleum University, China. Mas Iwan Konggidinata is a master’s degree student at the University of Louisiana at Lafayette. His research is focused on the adsorption of organics from waste water by use of ordered mesoporous carbons. Previously, Konggidinata was an application and sales engineer at Sulzer Chemtech, Singapore, from 2013 to 2015. He holds a bachelor’s degree in chemical engineering from the University of Minnesota.

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