Determination of Structure and Formation Conditions of Gas Hydrate by Using TPD Method and Flash Calculations

Transcription

1 nd atonal Iranan Conference on Gas Hydrate (ICGH) Semnan Unersty Determnaton of Structure and Formaton Condtons of Gas Hydrate by Usng TPD Method and Flash Calculatons H. Behat Rad, F. Varamnan* Department of Chemcal Engneerng, Gas and Petroleum, Semnan Unersty, Iran *Correspondng Author s E-mal: faramnan@semnan.ac.r Abstract In ths wor, satblty calculatons and determnaton of gas hydrate structure n equlbrum condtons by usng mnmzaton of TPD functon for methane-water system (SI), propane-water system (SII) and methane-methyl cyclo pentane-water system (SH) were performed. Based on results, at 74 and 75 temperatures, the lqud phase of methane-water system at 7 bar and 3 bar pressures, propane-water system at.7 bar and.5 bar pressures and methane-methyl cyclo pentane-water system at 9.6 bar and. bar pressures was decomposed. As a result of decomposton of lqud phase for these systems, two new phases, a new lqud phase and hydrate phase were formed. Subsequently, multphase flash calculatons n order to determne the amount and composton of stable phases n equlbrum state were performed. For mnmzaton of TPD functon, Algorthm Genetc was used. The results Show good accuracy wth data of Herot Watt unersty hydrate model (HWHYD). eywords: Tangent plane dstance, Multphase flash calculaton, Gbbs energy mnmzaton, Gas Hydrate. Research Hghlghts Determnaton of thermodynamc condtons of gas hydrate formaton by usng mnmzaton of tangent plane dstance from Gbbs energy surface (TPD method). Determnaton of numbers and type of stable phases n equlbrum state n order to performng multphase flash calculatons. Calculaton of amount and composton of stable phases n equlbrum state.

2 Determnaton of Structure and Formaton Condtons of Gas Hydrate. Introducton Gas hydrates are ce-le crystallne structures that forms n the presence of lght gases such as methane and ethane or non-hydrocarbons gases such as ntrogen and carbon doxde wth water. These gases are trapped n seeral dfferent cages that forms dfferent crystallne structures le si, sii or sh. Stablty of gas hydrate crystallne s the result of hydrogen bonds between water molecules and an der waals forces between water and gas molecules n structure lattce of hydrate. After desgnng the frst gas transfer ppelne, blocage of ppelnes wth gas hydrate by Hammerschmdt [] n Unted State was ntroduced. Subsequent to ths phenomenon, methods of preenton of gas hydrate formaton n ppelnes were studed. For the frst tme, thermodynamc prncples of gas hydrate by Van der waals and Platteeuw [] were studed. Because of the problems that were the result of gas hydrate formaton, many studes about predcton of gas hydrate formaton condtons and stablty of gas hydrate were performed. Mchelsen [3] proposed a method for stablty analyss calculatons at certan temperature and pressure. Ths method s based on mnmzaton of tangent plane dstance from Gbbs energy surface (TPD method).. TPD Method The dstance between tangent hyperplane to Gbbs energy of system at ntal composton (z) and system at another composton le (x) can be wrtten as follow: TPD C x x x z where, s the chemcal potental of component n the mxture and C s the total number of components. Also we hae a constrant for Eq. as: C x, x () When the TPD functon for arables x (,..., C ) wth consderng Eq. to be mnmzed; the amount of mnmzed functon ( ) s the stablty analyss of the prmary mxture at composton x * *. Subsequently f TPD, the system s stable and f TPD, the system s unstable. Snce all mnma of TPD (x) are located n the nteror of the permssble regon n Eq. (), TPD (x) wll be non-negate, f t s non-negate at all statonary pont, that s, ponts where the derates wth respect to all ndependent arables equal zero. By dfferentaton of Eq. respect to the C ndependent mole fractons yeld the statonary condton [3] x z (3) Where s ndependent of the component ndex. For equatons of state calculatons, t s more conenent to wor n terms of fugacty coeffcents, thus stablty crteron can be wrtten as: lnx ln,..., RT x lnz ln z, C (4) Wth the new arables X x exp ( ), that the new ndependent arables X can formally be nterpreted as mole numbers, the Eq. 4 can be wrtten as follow [3] ()

3 nd atonal Iranan Conference on Gas Hydrate (ICGH) Semnan Unersty x X lnx ln x lnz ln z (5) TPD where; x (6) X X By usng X, the constrant (Eq. ) s conerted to a more smple constrant. X (7) Therefore, we can mnmze TPD functon wth only restrcton of X to obtan. * When the system s unstable, concentratons that mnmze ths functon ( x ), are good ntal guesses for components composton n the new phase. When the system s unstable, by usng these concentratons for components composton n the new phase, we can calculate and mnmze TPD functon for any phase. Then accordng to stablty crteron, the numbers and type of phases n equlbrum state are determned and subsequently the amount and composton of new phases can be calculated by flash calculatons. 3. Calculaton of fugacty of components n apor and lqud phases In ths wor, the fugacty of components n apor and lqud phases s calculated by usng Valderama-Patel & Tea equaton of state [4,5]. 4. Calculaton of fugacty of components n sold phase (SI, SII) The fugacty of components n sold phase (SI, SII) by usng Van der Waals and Platteeuw model [] and the hara potental parameters that are reported by Alonts et al. [5] s calulated. 5. Calculaton of fugacty of components n sold phase (SH) The fugacty of components n sold phase (SH) s calculated as followng method [6]: In structure H of gas hydrate accordng to numbers of cates wrtng would be possble; C C C C 3 In these equatons, C, are longmur coeffcents of cates. Wth defnton of and follow: 3 n n 3 that, n aboe equatons n empty cates for any mole of water. Subsequently; (8) (9) as () () s a fracton of cates that are empty and s the number of

4 Determnaton of Structure and Formaton Condtons of Gas Hydrate (), C F (3) 3, C G By solng these two nonlnear equatons by usng ewton-raphson method, and are calculated. Wth determnaton of and, fugacty of components n sold phase (SH) s calculated by Eq 4. (4) C f The fugacty of water n hydrate phase (SH) s calculated by Eq 5. (5) 3 3 ln ln ln ln ln f f M T w H w n aboe equaton, M T w f s the fugacty of water n empty lattce of hydrate. 6. Flash calculatons In flash calculatons, frst at dstnct pressure and temperature and wth prmary guess of mole fracton of components n lqud and apor phase and by usng Valderama- Patel & Tea equaton of state, the fugacty of components n lqud and apor phases s calculated. Subsequently, by usng the fugacty of components n apor phase and wth consderng equalty of fugacty of one component at equlbrum state n all phases, mole fracton of components n hydrate phase s calculated. Wth determnaton of mole fractons n hydrate phase, by usng Teta method [7], fugacty of components n hydrate phase s calculated. Wth determnaton of mole fractons, the dstrbuton coeffcent of component n phase and wth selecton of one phase as reference phase (wth ndex for reference phase) s calculated by usng the followng equaton. (6) P C x x,...,,..., Accordng to ths pont that n calculatons of gas hydrate formaton, the apor phase s always present, we can consder ths phase as reference phase. By wrtng mass balance equatons, we can obtan the below relatons; (7) P F x Z (8) C F Z x P,...,

5 nd atonal Iranan Conference on Gas Hydrate (ICGH) Semnan Unersty Z x m P F m,... C, (9) subsequently; C x x m,... P, m,... P, () C Z m P F m,... P, These two nonlnear equatons wth prmary guesses for and F and by usng ewton- Raphson method are soled. Wth determnaton of new amount of F and calculaton of x through usng relatons, equalty of fugactes by usng Eq. can be checed. C P f l n f 6 If equalty of fugactes s not establshed, new amounts of are calculated by the below equaton. t t f f t,.. C.,,.. P., that, ndex t represents computaton tmes. 7. Results and dscusson One of the mportant calculatons before equlbrum calculatons s determnaton of numbers and type of phases n equlbrum state. In other words, wthout nformaton about stable phases n equlbrum state, performng equlbrum calculatons are mpossble. In ths wor TPD method for stablty analyss and determnaton of equlbrum pressure of gas hydrate formaton for methane-water, propane-water and methane-methyl cyclo pentane-water systems are used. Calculatons at 74 and 75 temperatures and arous pressures are performed. Results of mnmzaton of TPD functon show that the apor phase n any temperature and pressure s always stable, but the lqud phase n certan temperature and specfc pressure s unstable and decomposed. As a result of decomposton of lqud phase two new phases are formed. When the system s unstable, concentratons that are mnmze * TPD functon ( x ), are good ntal guesses for components composton n the new phase. Subsequently, by usng these concentratons for components composton n the new phase, agan calculaton and mnmzaton of TPD functon for any phase s performed. Then accordng to stablty crteron, numbers and type of phases n equlbrum state are determned. Subsequently, multphase flash calculatons for determnaton of amount and () () (3)

6 Determnaton of Structure and Formaton Condtons of Gas Hydrate composton of phases n equlbrum state are performed. Algorthm Genetc s used for mnmzaton of TPD functon. 7.. methane-water system at 74 and composton (.5,.5) The results of TPD functon mnmzaton for methane-water system show that the apor phase s always stable, but lqud phase at certan temperature and specfc pressure s unstable and decomposed. The results of mnmzaton of TPD functon for lqud phase of methanewater system are dsplayed n Table. Accordng to ths Table, functon for lqud phase of methane-water system at 7 bar pressure s negate and after ths pressure, lqud phase s unstable and decomposed. Changes of functon ersus pressure are dsplayed n Fg. Table. The results of calculaton of functon for lqud phase of methane-water system at 74 T = 74 X * l X * l P = bar P = bar P = 7 bar P = 3 bar P = 4 bar Fg. Changes of functon ersus pressure for lqud phase of methane-water system at 74 * Concentratons that are mnmze TPD functon ( x ), are good ntal guesses for components composton n the new phase. In order to determne the numbers and type of stable phases as a result of decomposton of unstable lqud phase, n ths step TPD functon for any phase n certan temperature and determned pressure and by usng concentratons of frst step as components composton n new phase s mnmzed. The results of ths mnmzaton are dsplayed n Table. Table. The results of calculaton of functon for lqud phase of methane-water system by usng concentratons as a result of frst step mnmzaton as components composton n the new phase at 74

7 nd atonal Iranan Conference on Gas Hydrate (ICGH) Semnan Unersty T = 74 Z Z ew lqud apor Hydrate I Hydrate II P = 7 bar P = 3 bar P = 4 bar Based on the results that dsplayed n Table. and wth consderng stablty crteron (TPD ), as a result of decomposton of unstable lqud phase, two stable phases, a new lqud and hydrate wth structure I are formed. Subsequently, for determnaton of amount and composton of phases n equlbrum state, flash calculatons are performed. The results of these calculatons are shown n Table 3. and Fg. Table 3. Composton and phases fracton n equlbrum state for methane-water system at 74 Composton Phase fracton T = 74 P (bar) V Lw H(I) V Lw H(I) Fg. Changes of phase fracton ersus pressure for methane-water system at 74 These calculatons for methane-water system at 75 temperature were performed and the results are shown below:

8 Determnaton of Structure and Formaton Condtons of Gas Hydrate 7.. methane-water system at 75 and composton (.5,.5) Table 4. The results of calculaton of functon for lqud phase of methane-water system at 75 T = 75 X * l X * l P = bar P = bar P = 3 bar P = 4 bar Fg 3. Changes of functon ersus pressure for lqud phase of methane-water system at 75 Table 5. The results of calculaton of functon for lqud phase of methane-water system by usng concentratons as a result of frst step mnmzaton as components composton n the new phase at 75 T = 75 Z Z ew lqud Vapor Hydrate I Hydrate II P = 3 bar P = 4 bar Table 6. Composton and phases fracton n equlbrum state for methane-water system at 75 Composton Phase fracton T = 75 P (bar) V Lw H(I) V Lw H(I)

9 nd atonal Iranan Conference on Gas Hydrate (ICGH) Semnan Unersty Fg 4. Changes of phase fracton ersus pressure for methane-water system at 75 In ths wor equlbrum pressure of gas hydrate formaton wth expermental data and Herot Watt unersty hydrate model (HWHYD) [8] s compared and the results show a good accuracy. Aerage error based on expermental data s 3.5% and the results of comparson wth HWHYD model are dsplayed n Table 7. Table 7. Comparson of equlbrum pressure of gas hydrate formaton n methane-water system between TPD method and HWHYD model T () Peq TPD Peq HWHYD %Error propane-water system at 74 and composton (.5,.5) The results of mnmzaton of TPD functon for lqud phase of propane-water system are shown n Fg 5. Fg 5. Changes of functon ersus pressure for lqud phase of propane-water system at 74 As a result of decomposton of lqud phase of propane-water system, a new lqud and hydrate wth structure II are formed. These results are shown n Table 8. The results of flash calculatons for propane-water system are dsplayed n Table 9. and Fg 6. Table 8. The results of calculaton of functon for lqud phase of propane-water system by usng concentratons as a result of frst step mnmzaton as components composton n the new phase at 74

10 Determnaton of Structure and Formaton Condtons of Gas Hydrate T = 74 Z Z ew lqud Vapor Hydrate I Hydrate II P = bar P = 3 bar Table 9. Composton and phases fracton n equlbrum condtons for propane-water system at 74 Composton Phase fracton T = 74 P (bar) V Lw H(II) V Lw H(II) Propane Propane Propane Fg 6. Changes of phase fracton ersus pressure for propane-water system at 74 These calculatons for propane-water system at 75 temperature were performed and the results are shown as follow: 7.4. propane-water system at 75 and composton (.5,.5) Fg 7. Changes of functon ersus pressure for lqud phase of propane-water system at 75

11 nd atonal Iranan Conference on Gas Hydrate (ICGH) Semnan Unersty Table. The results of calculaton of functon for lqud phase of propane-water system by usng concentratons as a result of frst step mnmzaton as components composton n the new phase at 75 T = 75 Z Z ew lqud Vapor Hydrate I Hydrate II P =.5 bar P = 3.5 bar Table. Composton and phases fracton n equlbrum state for propane-water system at 75 Composton Phase fracton T = 75 P (bar) V Lw H(II) V Lw H(II) Propane Propane Propane Fg 8. Changes of phase fracton ersus pressure for propane-water system at 75 The results of comparson of equlbrum pressure of gas hydrate formaton between TPD method and HWHYD model for propane-water system are shown n Table. Table. Comparson of equlbrum pressure of gas hydrate formaton n propane-water system between TPD method and HWHYD model T () Peq TPD Peq HWHYD % Error

12 Determnaton of Structure and Formaton Condtons of Gas Hydrate 7.5. methane-methyl cyclo pentane-water system at 74 and composton (5,5,.9) The results of mnmzaton of TPD functon for lqud phase of methane-methyl cyclo pentane-water system are shown n Fg 9. Fg 9. Changes of functon ersus pressure for lqud phase of methane-methyl cyclo pentane-water system at 74 As a result of decomposton of lqud phase of methane-methyl cyclo pentane-water system, a new lqud and hydrate wth structure H are formed. These results are shown n Table 3. The results of flash calculatons for methane-methyl cyclo pentane-water system are dsplayed n Table 4. and Fg. Table 3. The results of calculaton of functon for lqud phase of methane-methyl cyclo pentanewater system by usng concentratons as a result of frst step mnmzaton as components composton n the new phase at 74 T = 74 Z Z Z3 ew lqud Vapor Hydrate I Hydrate II Hydrate H P = bar P = bar Table 4. Composton and phases fracton n equlbrum state for methane-methyl cyclo pentane-water system at 74 Composton Phase fracton T = 74 P (bar) V Lw H(H) V Lw H(H) MCP MCP MCP

13 nd atonal Iranan Conference on Gas Hydrate (ICGH) Semnan Unersty Fg. Changes of phase fracton ersus pressure for mehane-methyl cyclo pentane-water system at 74 These calculatons for methane-methyl cyclo pentane-water system at 75 temperature were performed and the results are shown as follow: 7.6. methane-methyl cyclo pentane-water system at 75 and composton (5,5,.9) Fg. Changes of functon ersus pressure for lqud phase of methane-methyl cyclo pentane-water system at 75 Table 5. The results of calculaton of functon for lqud phase of methane-methyl cyclo pentanewater system by usng concentratons as a result of frst step mnmzaton as components composton n the new phase at 75 T = 75 Z Z Z3 ew lqud Vapor Hydrate I Hydrate II Hydrate H P = bar P = 3 bar Table 6. Composton and phases fracton n equlbrum state for methane-methyl cyclo pentane-water system at 75 Composton Phase fracton T = 75 P (bar) V Lw H(H) V Lw H(H) MCP

14 Determnaton of Structure and Formaton Condtons of Gas Hydrate MCP MCP Fg. Changes of phase fracton ersus pressure for mehane-methyl cyclo pentane-water system at 75 The results of comparson of equlbrum pressure of gas hydrate formaton between TPD method and HWHYD model for methane-methyl cyclo pentane-water system are shown n Table 7. Table 7. Comparson of equlbrum pressure of gas hydrate formaton n methane-methyl cyclo pentane water system between TPD method and HWHYD model T () Peq TPD Peq HWHYD %Error conclusons In ths wor, TPD method for determnaton of condtons of gas hydrate formaton s used. The results show that the apor phase s always stable, but the lqud phase n certan temperature and specfc pressure s unstable and decomposed. As a result of decomposton of unstable lqud phase two new phase, a new lqud and hydrate are formed. Subsequently, n order to determne the numbers and type of phases as a result of decomposton of lqud phase, wth new concentratons as a result of frst step mnmzaton, TPD method s used agan for any phase. Calculatons for methane-water system wth structure I, propane-water system wth structure II and methane-methyl cyclo pentane-water system wth structure H are performed. Subsequently, for determnaton of amount and composton of phases n equlbrum state, multphase flash calculatons are performed. Acnowledgments Fundng for ths research was proded by the gas company of Semnan pronce.

15 nd atonal Iranan Conference on Gas Hydrate (ICGH) Semnan Unersty Lst of symbols C Longmur coeffcent f fugacty of components n sold phase (SH) H f w fugacty of water n hydrate phase MT f w fugacty of water n empty lattce of hydrate f fugacty of component n phase chemcal potental dfference dmensonless chemcal potental dfference dstrbuton coeffcent of component n phase C number of component P number of phase number of empty cates for any mole water n fracton of empty caty P pressure TPD tangent plane dstance, obecte functon TPD mnmum of TPD functon T temperature X mole number of component x mole fracton of component x concentraton that are mnmze TPD functon Z components composton of mxture φ fugacty coeffcent of component chemcal potental of component References [] E.G. Hammerschmdt, "Formaton of Gas Hydrate n atural Gas Transmsson lnes", Ind. Eng. Chem., 6 (8), pp , (934). [] J.H. Van der Waals and J.C. Platteeuw, "Clathrate Solutons", Ad. Chem. Phys., pp. - 57,(959). [3] M.L. Mchelsen, "The Isothermal Flash Problem", Part I. Stablty, Flud Phase Equlbra, 9,, (98). [4] J.O. Valderrama, "A Generalzed Patel-Tea Equaton of State for Polar and onpolar Fluds and ther Mxtures", J. Chem. Eng. Jpn., 3(87), (99). [5] D. Alonts, A. Danesh and A.C. Todd, "Predcton of VL & VLL Equlbra of Mxtures Contanng Petroleum Reseror Fluds & Methanol wth a Cubc EOS", Flud Phase Equlbra, ol. 94, pp. 8-6, (994). [6] H. Behat Rad, F. Varamnan, "Modelng of Stablty Condtons n Phase Equlbra of Gas Hydrate", MSc Thess, Department of Chemcal Engneerng, Gas and Petroleum, Semnan Unersty, Iran, (8). [7] M.L. Mchelsen, "Calculaton of Hydrate Fugactes", Chem. Eng. Sc., 46, (99), pp [8] Herot-Watt Unersty Hydrate Model: See also: D. Alonts, "Thermodynamcs of Gas Hydrate Equlbra", Ph.D. Thess, Department of Petroleum Engneerng, Herot-Watt Unersty, Ednburgh, U, (99).