Prediction of natural gas hydrate formation region in wellbore during deep- water gas well testing

Availableonlineatwww.sciencedirect.co. ScienceDirectJournal of HydrodynamicsELSEVIER2014,26(4):568-576www.sciencedirect.comDOI:10.1016/S1001-6058(14)600640science/journal/10016058Prediction of natural gas hydrate formatiwater gas well testingWANG Zhi-yuan(王志远), SUN Bao-jiang(孙宝江), WANG XUe-rui(王雪瑞), ZHANG Zhen-nan(张振楠)School of Petroleum Engineering, China University of Petroleum(East China), Qingdao 266580, ChinaEmail:wangzy1209@126.com(Received November 1, 2013, Revised February 26, 2014)Abstract: Wellbore temperature field equations are established with considerations of the enthalpy changes of the natural gas duringthe deep-water gas well testing. A prediction method for the natural gas hydrate formation region during the deep-water gas wellsting is proposed, which combines the wellbore temperature field equations, the phase equilibrium conditions of the natural gashydrate formation and the calculation methods for the pressure field. Through the sensitivity analysis of the parameters that affect thehydrate formation region, it can be concluded that during the deep-water gas well testing, with the reduction of the gas productionrate and the decrease of the geothermal gradient, along with the increase of the depth of water, the hydrate formation region in theellbore enlarges, the hydrate formation regions differ with different component contents of natural gases, as compared with the purenethane gas, with the increase of ethane and propane, the hydrate formation region expands, the admixture of inhibitors, the type andthe concentrations of which can be optimized through the method proposed in the paper, will reduce the hydrate formation region,the throttling effect will lead to the abrupt changes of temperature and pressure, which results in a variation of the hydrate formationregion, if the throttling occurs in the shallow part of the wellbore, the temperature will drop too much, which enlarges the hydrateformation region, otherwise, if the throttling occurs in the deep part of the wellbore, the hydrate formation region will be reduced dueto the decrease of the pressureKey words: deep-water gas well testing, temperature and pressure fields, hydrate, throttling effectIntroductionphase state of the hydrate is a focus. Vandelwalls andDuring the deep-water gas well testing, there is Platteeuw (1959) proposed the method of VDw-Pnormally a certain amount of water in the gas produ- which was used to predict the phase state of the hyed andely to form the natural gas hydrate in drate and laid the foundations for the subsequent me-the environment of low temperature and high pressure thods of hydrate predictions. Parrish and Prausnitzin the wellbore. After the hydrate is formed, it will oc- (1972) proposed the constant Langmuir Equation, andclude the circulation channel of the natural gas, resu- applied the VDW-P in multiple gas components. Nglting in serious accidentsIl-31. Therefore, during the Robinson et al. (1976)made corrections on Langmurideep-water gas well testing, it is important to pay at- constants, which further improved the prediction accttention to the formation of the hydrate and to take racy of the hydrate phase state. Ng and robinsonmeasures for the prevention of the hydrate forming(985) measured the main components of the naturalFor the prediction of the hydrate formation, the gas and the phase equilibrium conditions of mixtureswith methanol: Englezos et al.(1987) put forward anew formation model of the natural gas hydrate, SongProject supported by the National Natural Science Foun- and Kobayashi(1989)studied the inhibitory effect ofdation of China( Grant Nos. 51104172,U1262202), the Pro- methanol and glycol on the hydrate of methane andgram for Changjiang Scholars and Innovative Research Team ethane mixture, Dholabhai et al. (1991), Dholabhain University( Grant No. IRT1086)Biography: WANG Zhi-yuan(1981-), Male, Ph Dand Bishnoi(1994) studied the phase equilibrium conAssociate Professorditions of the hydratining an electrolyte system,Ebeltoft et al中国煤化工 r of the hydrate in the deCNMHG(999)stu569died the difference of the natural gas hydrate forma- of the total heat transfer coefficient is introducedtion conditions between the seawater-methane two- Willhite(1967) proposed a calculation method for thehase system and the pure water-methane two-phase total heat transfer coefficient, which found a widesystem, Majumadar et al. studied the phase equili- application. Wu and Pruess(1990)obtained an analybrium of hydrogen sulfide, carbon dioxide and propy- tical solution of the temperature field model of the welene in ethylene glycol and electrolyte. JafarJavanma- lore based on the consideration of the thermal para-di et alDaImazzone and Herzhaft Nasrifar 8meters of various formations. Romero(1998)put forYang and Xu studied the phase equilibrium condi- ward a method for the temperature prediction in deeptions of the hydrate with inhibitors. These studies laid water drilling. Hasan et al. 12-14 carried out an enogood foundations for the prediction of the hydrate for- rmous amount of work in a series of papers on themation region during the deep-water gas well testing temperature field calculation of the wellbore, and theand for engineering calculations, the calculation mo- methods for the wellbore temperature calculation weredels of hydrate phase state can achieve a good accura- well accepted and with a good accuracyDuring the deep-water gas well testing, one mayHowever, during the deep-water gas well testing, find throttling problems in the testing pipe of variablebesides the formation phase state of the hydrate, the diameter, due to the high flowing velocity of gas. Bformation region is also an important factor in the de- cause of the compressibility of gas, the work done bysign of the injection position and the determination of the volume variation will lead to changes of enthalpy,the required concentrations of the inhibitors. Wang et therefore, this paper takes up the issue of the enthalpypredicted the formation region of the natural changes, to deal with the throttling problems as wellgas hydrate during the deep-water drilling and the as the work done by the volume variation, and sets upwell control process. But so far, the prediction of the the temperature field equation of the wellbore duringhydrate formation region during the deep-water well the decell testinstesting has not been much studied. Three aspects areIn the temperature field calculation model, thenvolved in the prediction of the hydrate formation re- following assumptions are madegion in the wellbore during the deep-water well tes1)Gas is in a one-dimensional steady flow in theting: the temperature field distribution, the pressure wellborefield distribution, and the phase state conditions of the(2)The heat transfer is steady in the wellborenatural gas hydrate formation. In this paper, conside- when the gas production rate is stable during the deepring the throttling effect (Joule-Thomson effect)in the water gas well testin in u direction of the wellboretesting pipe of variable diameter, as well as the work(3) The heat lossdone by the volume variation during the gas flowing, can be ignored, only the radial heat loss is considereusing the concept of enthalpy, the temperature field(4)The relationship between the formation temluation of the wellbore during the deep-water gas perature and the depth is linear, and this ratio coeffi-well testing is established. A method for the prediction cient(the temperature gradient)is knownof the natural gas hydrate formation region during thedeep-water gas well testing is proposed, combiningAnnulthe phase state conditions of the natural gas hydratemantleformation and the calculation of the pressure fieldFurthermore, a sensitivity analysis of the parametersthat affect the hydrate formation region is made in thispaper.1. Models of natural gas hydrate formation regionprediction1. 1 Temperature field equationsThe solutions for the temperature and the presre of the wellbore are the basis of a precise prediction Fig. I Heat transfer in the wellboof the natural gas hydrate formation region. Ramey(1962)established a temperature prediction model forFigure 1 shows the heat transfer in the wellboreincompressible fluid or ideal gas, which has a far-rea- According to the above assumptions, the enthalpyching influence on solving the wellbore temperature change is considered when the gas flows, to establishfield, and in which the wellbore temperature and the the temperatureformation temperature are combined, and the conceptH中国煤化工CNMHG570d ph pgzsin0+pv t pvin theof Equation(1)should be adjusted correspondingly,and the expression of the temperature field should beUk +trU(n-T)=0d ph6+where H is the enthalpy of the gas, g is the accele-ration of gravity, 6 is the included angle between the 2r Uwellbore axis and the horizontal direction(T-T,)gas velocity, z is the well depth, w is the mass flow,r is the outer radius of the pipe, r is the inner rawhere r is the external diameter of the riser Udius of the pipe, Ut is the overall heat transfer coe- the overall heat transfer coefficient with the outer surfficient. k is the formation heat conduction coeffiface of the riser as the datum plane,is the tempe-cient, To is the dimensionless temperature(Kabir et rature of the sea wateral. 1996), Tei is the formation temperature, T, isThe first term on the left side of Eg. (1)is theoverall energy change of the gas, which includes fourin the pipe, pparts: the enthalpy, the kinetic energy, the potentialfriction coefficient. dimensionlessenergy, and the work done by the external force (i.eUo depends on the thermal resistance from the term of friction), the second term is the heat exchangefluid in the pipe to the surrounding formation, inclu- between the fluids in and outside the wellbore. Theding the thermal resistance of the forced convection heat exchange between the gas in the wellbore and theheat transfer of the inner wall, the thermal resistance surrounding environment is equal to the overall eneof the pipe wall, the convection and radiation heat rgy change, hence, the sum of these two terms is zerotransfer resistance of the annular liquid or gas, alongIn Eq (1), H is the enthalpy of the gas duringwith the thermal resistance of the casing wall as wellits flow movement, which includes the internal energyas the cement ring. It is expressed as(Willhite 1967)and the flow work and can be expressed as5lno(P, T)=C,dT, +eva-T:)dPrhwhere V is the specific volume, To, Po are the tem-T, Pthe present temperature and pressure, C, is the specific heat capacity, B is the thermal expansion coefficient,P is the pressure of the gas in the pipewhere h. is the heat convection coefficient, k, isThe first term on the right side of eq. 4)is the inthe heat conduction coefficient of the pipe, h is the ternal energy, which mainly represents the effect ofthe temperature change during the flow movement ofheat transfer coefficient of the annulus convection, hthe natural gas on the enthalpy of the system, the seis the heat transfer coefficient of the annulus radiation, cond term is the flow work, which mainly representsro is the outer radius of the casing, r is the inner the effects of the pressure and volume changes on theradius of the casing, k is the heat conduction coeffienthalpy of the system during the flow movement ofthe natural gas. However, when the fluid in the wellcient of the casing, wb is the external diameter of the bore is liquid the effect of the fluid volume chankcem is the heat conduction coefficient of the the enthalpy is usually ignoredcement ringEquation(4)is rewritten in the differential formEquation (I)is for the formation environmentfollowsbelow the mud line. however in the sea water environment. the process of the heat loss is different fromthat in the formation. therefore, the overall heat tran- dH=C dT中国煤化工sfer coefficient in the sea water is different from thatYHCNMHG571The enthalpy of the gas changes all the time in hydrate, the formation conditions of the hydrate shou-the whole wellbore. While at the position where the ld be known, which include the temperature and thenternal diameter of the testing pipe varies, the gas pressure in the testing pipe when the hydrate is beingflow is regarded as an adiabatic process within the re- formed. The hydrate is formed when the pressure at alatively shorter distance of the variable diameter be- certain position in the testing pipe is higher than thatfore and after the variation point. Therefore, the entha- of the hydrate formation and the temperature is lowerlpy values before and after the throttling position are than that of the hydrate formation. A chemical balanceequal, that is to say, dH=0.The expression of the is reached between the water phase, the gas phase, andadiabatic throttle coefficient can be derived from the lattice in the hydrate lattice system. The equationsEq (5)asfor the phase equilibrium are obtained based on thethermodynamic equilibrium theory(Van delwalls andPlatteeuw(1959))△A△Hn+△CA(Tn-o)an+mBDn=P△VRT JToRTwhere A is the adiabatic throttle coefficient JouleThomson coefficient)Another expression of the enthalpy can be de-rived from Eqs. (5)and(6)()∑Mm-∑dh=C dTe-C u dP(i=1,2,,1),(=1,2,L)When the expression of the enthalpy in Eq (7)issubstituted into Eq. I)and the friction term npv/fIn x(10)4r in Eq (1)is ignored, the wellbore temperatureffield equation is obtained, which is the same as theequation established by Hasan and Kabir(1994where Auo is the difference between the chemicalpotential in the unoccupied lattice and the pure water1.2 Pressure field equationsat the reference state, R is the gas constant, TH isThe pressure is obtained by solving simultaneously the steady equations of the gas, the expression ofthe hydrate-formation temperature, AHo is the diffethe gas flow velocity, and the expression of the gasrence between the enthalpy in the unoccupied latticethe heat capacity in the unoccupied lattice and thedP+5×10-39x×3484.8×10rd7is the hydrate-formationAy is the difference between the molar volume in theunoccupied lattice and the pure water, f is484.8×10in edz+city of the water in the solution, fwr is the fugacity27of the water at the reference state (TH, PH), I is thetotal number of hydrate species, M, is the ratio of thenumber of cavities of type i to the number of wate|5×103×34848×103Zdz=0 gas types, B, is the fraction of the cavities of typemolecules in the hydrate phase, Le totai occupied by a gas molecule of type j, x is themole fraction of the water, y is the water activitywhere q. is the gas flow in the standard state, Zcoefficient in the solutionthe gas compressibility factor, 'g is the relative densi- 1.4 Model verificationThe prediction accuracy of the hydrate formationregion in the wellbore during the deep-water gas well1.3 Equations for prediction of natural gas hydrate testing dependperature and中国煤化 Iy of the temphase stateTo predict the formation region of the natural gasohase state. InTHCNMHGare used for572Table I Basic parametersLocationX Block in South Sea of chinaDepth of the water(m)1350Depth of testing layer(m)3170Type of wellsVertical WellPore Pressure(MPa)32.97Geothermal gradient(C/100 m)Table 2 Comparisons of the calculated and measured valuesasPressure(MPa)rate(10" m/d)MeasurementCalculationRelative Error MeasurementCalculation Relative error44,45732.7834.404.94%25.Il1258642.7843.521.73%24.6424.790.61%148.6655.0056.743.16%20.6420.87the hydrate phase state prediction and these two equa-It is a well in the south sea, and the well structuretions have been verified by experiments. Now our as well as the data related to the testing pipe isfocus is on the accuracy of the temperature and the shown in Fig.2pressure in the wellboreThe temperature and pressure fields of the gaswells in the South Sea of China during the gas testingalculated, and the results are compared with themeasured values. and it is shown that the agreement is20-12×10mgood. Take one of the wells as an example. The basicparameters of the well are shown in Table l, and thecomparisons of the calculation and measured valuesare shown in Table 22. Sensitivity analysis of hydrate formation regionin the wellbore during deep-water gas well tesngFig 3 Predictions of hydrate formation region with various gasAccording to the calculation methods of the well-duction rates(@)bore temperature and pressure fields as well as theprediction methods of the hydrate phase state, a sensi- 2. 1 The influence of gas output on hydrate formationtivity analysis of the factors affecting the hydrate formation region is made through a software developedFigure 3 shows the prediction of the hydrate forfor the prediction of the hydrate formation region in mation region in the wellbore under the conditionsthe wellbore during deep-water gas well testinggiven by Table 3, and different gas production rates(Q.). The x axis represents temperature (T)andDepthSea surfacethe y axis represents depth (D). The area surrou0.6604nded by the hydrate phase curve and the temperatureMud li768mcurve is the hydrate formation region. The temper8365mture gradually decreases from the well bottom to the0. 114 3 m tuberwellhead, when @. is low, the temperature in the0.33970.4445 m open holewellbore drops rapidly due to the complete heat exhange between the slowly flowing fluid and the su-rrounding environment, on the other hand, the large0. 0889 m tubingthe 2. is, the less slowly the temperature drops, and0.24445 m casin0.3175 m open holethe temperatuthe wellhead would rise with theFig. 2 The sketch diagram of well structure中国煤化工CNMHG573Table 3 basic data related to calculationsTemperature Geothermal Depth Formation Density Pressure GasFormation Outpuof the seagradientheat conof theof thespecificsurface(C) (C/100 m) seaduction formationell duction wellborem) coefficient (kg/m) bottom rate (m) (J/(K Kg)w/(m k))(MPa) (m/d)1.777682.264×1034×10194259MethaneWith the increase of @, the temperature at larger for the case of propane, that is to say, it is easieevery position in the wellbore rises gradually. The in- Tor propane to produce hydrate than for ethane. As acrease of the temperature is unfavorable for the hydrmatter of fact, with the increase of the hydrocarbon ofte formation, therefore, for a same well, the hydrate a large molecular weight in the generated gas, the hydrate formation region will increase graduallyformation region is smaller with a higher 2.. Underthese conditions in this case, the hydrate formation re- 2.3 Influence of geothermal gradient on hydrate forgIon Is0m-1675 m when Q。is5×10m/d, the hymation regiondrate formation region is 0 m-1 335 m when Qon of the hydrate for-mation region under the conditions given by Table 310 m/d, and there is no longer hydrate being formedand various geothermal gradients, in which the dottedwhen the output is 6x10 m/d. Hence, the hydrate line is the curve for the hydrate phase state, and theformation should be paid more attention to during the rests are the wellbore temperature field curves withtestingss of lowvarious geothermal gradients (1.0C/100100m,2.0°C/100m,2.5°C/l00mand3.0°C/100m250020001.0c/100mg0% methane+1% ethanmethane-+20% ethan100 mHydrate phase1822263034384246Fig 4 Prediction of hydrate formation region with various gasFig5 Prediction of hydrate formation region with various geo-thermal gra2.2 Effect of gas components on hydrate formation re-Under these conditions, the hydrate formationFigure 4 shows the prediction of the hydrate for- region is 0 m-2 100 m when the geothermal gradientmation region under the conditions given by Table 3 is 1.0"C/100 m, when the geothermal gradient isand various gas components, as shown in Fig.5. When 1. 5C/100 m, the hydrate formation region is reducedthe gas is pure methane (100% Methane), the hydrate to 0 m-1 010 m, and there is no longer hydrate foformation region is 0 m-612 m, when the gas contains mation produced if the geothermal gradient is higher10% ethane(90% Methane +10% Ethane), the hydrate than 2.0C/100 m. With the increase of the geothermalformation region is 0 m-845 m, when the gas contains gradient, the temperature difference between the well20% ethane(80% Methane +20% Ethane), the hydrate bottom and the wellhead increases as well, and the hy-formation region is expanded to 0 m-899 m. Therefore, drate formation region decreases gradually, this is bethe hydrate formation region will expand when the gas cause the temperature of the formation rises, whichgenerated contains ethane, and the higher the percent- makes the temperature of the wellbore rise as well,age of ethane is contained, the larger the hydrate for- and it is unfavorable for the hydrate formation. Hence,mation region will be. Likewise, when the gas con- during the deep-water gas well testing, if the geothetains propane, the hydrate formation region will expa- rmal gradient中国煤化工 the hydrated. When the gas contains ethane or propane with the should be paidsame mole fraction, the hydrate formation region isCNMHG5742.4 Influence of water depth on hydrate formation re- rate is 2x10 m/d, and other data are shown in Table3. Figure 7 and Fig 8 present the predictions of theFigure 6 shows the prediction of the hydrate for- hydrate formation region with different concentrationsmation region under the conditions given by Table 3 of NaCl or methanol, respectively. With the increaseand various sea water depths, in which the double of the concentration for NaCl or methanol, the hydratepoint lines are the curves for the hydrate phase state, formation region reduces gradually, and there is noand the rests are the curves for the wellbore tempera- more hydrate formed in the wellbore when the con-ture with different sea water depths(250 m, 500 m, centration of NaCl and methanol reduces under 20%750mand1000m)and 15%, respectively.E1500Temperature curvea-75-Hydrate phase1 s%o methanolcurveFig 6 Prediction of hydrate formation region with various sea Fig 8 Predictions of hydrate formation region with variouswater depthsmass fractions of methanolUnder these conditions, when the water depth is1 000 m, the hydrate formation region is 0 m-1 224 m,when the water depth is 750 m, the hydrate formationregion is 0 m-623 m, and there is no hydrate formewith the water depth of 500 m and 250 m with the in回crease of the sea water depth, the hydrate formationregion expands gradually. This is because with the inTemperature curvecrease of the water depth, the temperature near thesubmarine mud line becomes low in the meantimeoP CaCIthe cooling of the sea water in the wellbore takelonger time, which makes the temperature in the wellbore drop, which is favorable for the hydrate forma-ereforeh the increase of the water depthFig 9 Predictions of hydrate formation region with various saltinhibitorshe hydrate formation becomes more active25002000ture curve-C--Temperature curve#+ 20%NaCl0152025T°CFig 7 Predictions of hydrate formation region with variousFig 10 Predictions of hydrate formation region with various alcohol inhibitorsmass fractions of NaclFi2.5 Effect of inhibitors on hydrate formation regionstrate the predictionsof the hydrate f中国煤化工 ect to variousThe effect of different inhibitors on the hydrateformation region is analyzed when the gas production salt and alcoheYHCNMHG Fig9, withthe same mass concentration, the hydrate formationt the same depth, with the increase of the variaegion is the smallest for the inhibitor of Nacl, follo- ble diameter ratio, the curves for the temperature inwed by that for the inhibitor of KCl, and that for the the wellbore and for the hydrate phase state both movenhibitor of CaCl2 is the largest, which demonstrates to the left, which demonstrates that the temperaturethat among these three common salt inhibitors, the and pressure values in the wellbore decrease becauseeffect of NaCl is the best. As shown in Fig. 10, the hy- of the throttling effect. However, the hydrate formadrate formation region for the inhibitor of glycol is tion region is reduced when the throttle devices withsmaller than that for the inhibitor of methanol with a the same variable diameter ratio are set at the deep posmall difference. With the methodology in this paper, sition near the wellbore bottom, and the hydrate forthe types and the concentrations of hydrate inhibitors mation region will expand otherwiseduring the deep-water gas well testing can be chosens shown in Fig. 11. when the down hole threttling device is located at the depth of 768m, with the2.6 Influence of throttling effect on hydrate formation variable diameter ratio of 1: I(which means not variable), the hydrate formation region is 0 m-610 m, whenDuring the deep-water gas well testing, the th- the variable diameter ratio is 15: 1, the hydrate formarotting can be observed in the testing pipe of variable tion region in the wellbore expands to 0 m-768 m. Asdiameter, and it is shown that the pressure and the shown in Fig. 12, when the down hole throttling devicetemperature at positions where the diameter varies is located at the depth of 2 500 m, with the variablechange abruptly, which can lead to a change of the diameter ratio of 1: 1, the hydrate formation regionhydrate formation region in the wellborealso 0 m-610 m. however when the variable diameterratio is 15: 1. the wellbore will not create the conditions for the formation of the hydrateTherefore, the hydrate formation region is expa2000nded when the variable diameter of the testing pipe isat the shallow position; otherwise, the hydrate formation region is reduced,. This phenomenon can be used15 I temperature curveto prevent the formation of the hydrate. The variable-O- 12: 1 temperature curvediameter at a shallow position of the testing pipe should be avoided during the deep-water gas well testing5101520253035404550553. Conclusions1)a prediction method for the natural gas hyFig. I I Prediction curves for hydrate with downhole throttling drate formation region, during the deep-water gas welldevice located at 768 m(mud line)testing is proposed, which combines the temperaturefield equations established with considerations of the2500enthalpy changes of the natural gas, the phase stateconditions for the natural gas hydrate formation as2000well as the calculation equation for the pressure field(2)With the increase of the gas production rate,the hydrate formation region decreases gradually. The-H 15: 1 temperature curvehydrate formation region disappears when the gas pro15: 1 hydrate phase curveduction rate is over 6x10m'/d under the condition: I temperature curvedescribed in this paper(3)Different components of the natural gas have2530354045TCdifferent abilities to form the hydrate, if other com-ponents with large molecular weight are mixed withFig 12 Prediction curves for hydrate with downhole throttling methane, it will be much easier to generate the hydevice located at 2 500 mdrate(4) Different inhibitors have different inhibitoryFigures 11 and Fig 12 show the hydrate forma- effects, and the higher the concentration of the inhibition region under the conditions of Table 3, with di- tor is, the better effect it will produce. In a practicalfferent depths of throttling devices, and diameterwell testing, the types and the concentration of hydratetios of 15: 1, 14: 1, 12: 1 and 1: 1,. 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