DETERMINATION OF CO 2 MINIMUM MISCIBILITY PRESSURE USING SOLUBILITY PARAMETER

Transcription

1 DETERMINATION OF CO 2 MINIMUM MISCIBILITY PRESSURE USING SOLUBILITY PARAMETER Rocha, P. S. 1, Rbero, A. L. C. 2, Menezes, P. R. F. 2, Costa, P. U. O. 2, Rodrgues, E. A. 2, Costa, G. M. N. 2 *, glora.costa@unfacs.br, fax PETROBRAS Undade de Negócos da Baha Av. ACM, 1.113, Itagara CEP: Salvador BA, 2 Centro de Estudos em Petróleo e Gás Natural (CEPGN) Unversdade Salvador (UNIFACS). Av. Cardeal da Slva, 132, Federação CEP: Salvador BA ABSTRACT Gas necton process s one of the most effcent Enhanced Recovery Methods. A key parameter of a gas necton proect s the Mnmum Mscblty Pressure (MMP), the pressure whch the effcency of the local dsplacement comes close to 100%. Based on the concept of solublty parameter and havng as ndependent varables only saturaton pressure and ol temperature, a methodology was developed to calculate the MMP for pure CO 2 wth good results. INTRODUCTION The gas necton above the Mnmum Mscblty Pressure (MMP) s a large used resource to mprove the ol recovery from reservors. The MMP s the lowest pressure for the development of mscblty through multple contacts wth specfc ol at reservor temperature. The reservor whch the process s appled must be operated n or above the MMP developng mscblty for multple contacts [1]. Expermental determnaton of the MMP s slow and expensve; therefore, new methods have been developed based on equaton of state and emprcal correlatons Equaton of state s useful to calculate the reservor flud phase behavor, but t s necessary to adust ts parameters to ft lab experments. These expermental data are obtaned from PVT measurements: the constant composton expanson (CCE); dfferental lberaton (DL); swellng tests. Therefore ths systematc becomes costly due to the necessary experments for ts applcaton. The determnaton of the MMP through correlatons s based on sets of expermental data, and s lmted to the range of avalable data. The ndependent varables are the temperature and, some ntrnsc ol characterstcs lke composton, heavy fracton densty, etc. Emprcal correlatons researchers dsagree about nfluence of ol characterstcs n the MMP. The error s mportant, when comparng the MMP expermental wth the calculated ones. It s possble to conclude that the correlaton s restrcted to the range of expermental data used n ts generaton. Lange [2] has developed a procedure for calculatng the MMP based on the dfference between the ol and gas solublty parameter. Practcal experments conducted n the CEPGN (Petroleum and Natural Gas Study Center of Salvador Unversty - UNIFACS) have shown unsatsfactory results when applyng ths methodology. Ths work presents a new methodology to calculate the MMP for pure CO 2 based on the concept of solublty parameter. The ndependent varables are the saturaton pressure and the reservor temperature. The ndependent varables are very well known for any reservor; therefore, no addtonal expermental data s necessary.

2 MMP DETERMINATION USING THE LANGE PROCEDURE The solublty parameter, orgnates n regular soluton theory for mxtures of nonpolar lquds developed by Hldebrand and Scatchard [3]. The solublty parameter of a pure compound s defned as 0,5 ΔH ' RT + PV = (1) V where V s the molar volume, ΔH' s resdual enthalpy. Two substances wth same solublty parameters 1 and 2 must be soluble n each other n accordance wth the general rule: solublty s favored by chemcal and structural smlarty. As soon as the dfference between 1 and 2 ncreases, the dssoluton capacty decreases. Lange [2] presented a smplfed correlaton to estmate the ol solublty parameter ( o ) from the average molecular weght of the ol M and ts temperature T: o = 0,01. M + 6,54 0,01.( T 25) (2) Accordng to Lange [2], the correspondence between the MMP and the dfference between solublty parameters can be transformed nto a useful tool for MMP determnaton through the followng method: the gas solublty parameter (solvent) s determned n some pressures usng equaton (3) - developed for Gddngs et al. [4] that s an extenson of solublty parameter for supercrtcal fluds ( ) 0, 5 g = 0, 326 P c ρr ρ ( ) r lq (3) where g s gas solublty parameter n (cal/cm 3 ) 0,5 ; P C the crtcal pressure n psa; ρ r the reduced densty, defned as ρ/ρ c, where ρ s the densty and ρ c s the crtcal densty; ρ r(lq) the gas reduced densty at bolng pont, consdered constant and equal to 2,66. Lange [2] has used lterature data of ρ, ρ c and P c ; The ol solublty parameter s determned n the temperature of nterest through the equaton (2); 0,5 cal The MMP s the pressure n whch: o g 3,0 3 cm The dfference between the solublty parameters reflects the chemcal smlarty of the nected gas and the ol, whch can determne, n last nstance, the gas capacty (solvent) to promote a small nterfacal tenson wth the ol. Then smaller dfference between solublty parameters of the lqud and gaseous phases means more mscblty between fluds. Practcal experments conducted n the CEPGN (Petroleum and Natural Gas Study Center of Salvador Unversty - UNIFACS) have shown unsatsfactory results when applyng ths procedure.

3 A NEW METHODOLOGY TO CALCULATE THE MMP Usng ol temperature and bolng pont, and 28 ol samples (25 from publshed publcatons and 3 propretary samples) a correlaton was developed to calculate the ol solublty parameter: ocorrel = ( P ) a c T Sat d b (4) where: a = 4, ; = -0, b ; c = 0, ; d = 0, ; T reservor temperature ( K), dvded by 100; P Sat ol saturaton pressure (atm), dvded by 10. To evaluate the correlaton t was accomplshed a comparson between the values obtaned by the correlaton - equaton (4) - and the value from a more accurate solublty parameter, suppled by an equaton of state. The equaton Soave-Redlch-Kwong (SRK) Soave [5] was selected. The calculaton of the ol solublty parameter was realzed wth the equaton (1) wth the resdual enthalpy H' and the molar volume V obtaned by the equaton of state SRK, expressed as: R. T a( T ) P = V b V.( V + b) (5) For mxtures, the classc mxture rules have used: 1 ( a. a ).( K ) a = z. z 2 1 b = z b (6) where z s the component molar fracton. The pure components parameters a and b are descrbed n terms of crtcal temperature Tc, crtcal pressure Pc, acentrc factor w and K are the bnary nteracton parameters. The resdual enthalpy expresson for the SRK equaton s explct by: H ' b 1 da Δ = ln a. T + R. T Z. R T V b dt. (7) where V s the molar volume, Z s the compressblty factor and : da dt = 0.5 [ ] d ( K ). ( a. a ) z. z.1 dt (8) To calculate H' and V the crtcal temperature Tc, crtcal pressure Pc, acentrc factor w of each component and the nteracton parameter K must be known. For the defned components, pure components parameters are known, however for the TBP fractons and

4 TBP resdue s necessary characterzaton procedures. In ths n case Pedersen et al [6] characterzaton have used n smulator SPECS (Techncal Unversty of Denmark). The comparson between solublty parameter obtaned by Eq.(4) and by equaton of state SRK have gven very good results (average error of 6,82%): from 28 ols evaluated only for two ols the results was not so good, for 21 ols the error was less than 5%, for 3 ols the error was between 5 and 10%. The target of ths study was the MMP calculaton. Further evaluatons detected the need an addtonal correcton factor to be appled to ol solublty parameter to calculate MMP. The adusted functonal form for correcton factor (G) s gven by: G = d e [( P ) ( )] f Sat T where: d = 8, ; e = 0, ; f = -1,67852 ; T reservor temperature ( K), dvded by 100; P Sat ol saturaton pressure (atm), dvded by 10. Therefore the next step s CEPGN crteron determnaton to calculate the MMP. Ths crteron s explct by: 0, 5 ( ) = G ocorrel (10) Wth the ol temperature and ts saturaton pressure the correcton factor (G), and the ol solublty parameter ocorrel are obtaned. Wth the CEPGN crteron Eq (10), the value s obtaned. The MMP s the pressure n whch, n the gas temperature, the solublty parameter corresponds to. To calculate the gas solublty parameter the Eq. (3) s employed and an equaton of state or lterature data are used to calculate the gas densty ρ An effcent supercrtcal flud solublty parameter calculaton s assocated wth the qualty of the pressure-volume-temperature descrpton of the flud. Accordng to Shm [7], an effcent CO 2 equaton of state s Reynolds equaton [8], gven by: 2 P = ρ. M1+ ρ. M ρ. RT. + ρ [( ρ. M3+ ρ. M4.exp ) ( A20. ρ )] 5 6 ( A9. T + A10) + ρ.( A11. T + A12) + ρ. A13 where T s the temperature n C, P s the pressure n atm, ρ densty n g/ cm 3 and other parameters are temperature functon. RESULTS In order to valdate the CEPGN methodology several samples from Recôncavo Basn were used. The data were obtaned from expermental tests n CEPGN. For confdentalty reasons, the saturaton pressure and temperature data are not suppled. The results can be seen n Table 1. The tested ols were not used for correlaton development. + (9) (11)

5 The results n Table 1 show that the methodology s good enough for tested ols, wth dfferent range of saturaton pressure and reservor temperature. For a better vsualzaton, the MMP values are presented n Fgure 1, showng the correlaton qualty Table 1- Percentle error between expermental and predcted MMP wth CEPGN methodology Ol MMP exp (psa) ocorrel (cal/cm 3 ) 0,5 (cal/cm 3 ) 0,5 MMP calc (psa) Error % ,2990 3, ,11 7,01% ,0209 4, ,26 1,05% ,9250 5, ,00 1,21% ,8712 5, ,39 7,12% ,8121 6, ,09 7,90% ,0130 5, ,50 4,61% ,9709 5, ,72 7,80% ,9174 5, ,94 6,76% ,1753 4, ,82 13,71% ,7235 4, ,62 2,50% ,6502 5, ,05 0,67% ,7970 4, ,68 6,94% ,8750 5, ,70 7,42% ,7448 5, ,05 9,28% ,8662 4, ,18 13,25% Calculated MMP (psa Expermental MMP (psa) Fgure 1 Comparson between expermental MMP and calculated MMP wth CEPGN methodology CONCLUSION An alternatve methodology was created for MMP evaluaton. Usng ol temperature and ts saturaton pressure as ndependent varables, a methodology was developed for 28 samples (25 from publshed publcatons and 3 propretary samples). Expermental MMP

6 for new 15 propretary samples were used to valdate the methodology. The followng ponts have been consdered as relevant: It s possble to obtan ol solublty parameter usng an equaton of state. The necessary nformaton s: the molar composton, the molecular weght of the C 7 + fracton, temperature and the saturaton pressure. Two tools are necessary: the materal characterzaton and the computatonal program development, snce s not possble to calculate the ol solublty parameter n the commercal smulators; gas solublty parameter (CO 2 ) can be calculated wth good accuracy by usng the Reynolds equaton of state [8] to calculates the densty of CO 2 and the Gddngs equaton [4] to calculate gas solublty parameter; ol solublty parameter calculated, based on an emprcal correlaton presented by Lange [2], was not approprate; Lange procedure to calculate MMP, where MMP s the pressure n whch the dfference between ol and gas solublty parameter s around 3 (cal/cm 3 ) 0,5, was not approprate; a new emprcal correlaton was developed (CEPGN correlaton) to calculate ol solublty parameter, havng as ndependent varables ol saturaton pressure and temperature; a CEPGN methodology was developed to calculate MMP based on ol solublty parameter and a correcton factor (G). REFERENCES: [1] ABDASSAH, D.; KRISTANTO, D.; The Potental of Carbon Doxde Gas necton Applcaton n Improvng Ol Recovery; SPE 64730, [2] LANGE, E. A.; Correlaton and Predcton of Resdual Ol Saturaton for Gas- Inecton-Enhanced Ol-Recovery Processes; SPE 35425, SPE Reservor Evaluaton & Engneerng, 1998, p.127. [3] HILDEBRAND, J. H AND SCOTT, R. L.; The solublty of Non-eletrolytes; Renhold Publshng Corp., New York, [4] GIDDINGS, J. C.; MEYERS, M. N.; MCLAREN, S. E KELLER, R. A.; Hgh pressure gas chromatography of non volatle speces. Scence, Vol. 162, 1968, p.67. [5] SOAVE, G.; Equlbrum Constants from a Modfed Redlch-Kwong Equaton of State; Chem. Eng. Sc., Vol.27, 1972, p [6] PEDERSEN, K. S., THOMASSEN, P., FREDENSLUND, AA. On the dangers of tunng equaton of state parameters. Chem. Eng. Scence, Vol.43, n.2, 1988, p.269. [7] SHIM, JAE-JIM, Thermodynamcs and phase equlbra of polymer-solutesupercrtcal flud systems by supercrtcal flud chromatography, Dssertaton for Doctor of Phlosophy The Unversty of Texas at Austn, august,1990. [8] REYNOLDS, W. C.; Thermodynamc Propertes n SI: Graphs, Tables and Computatonal Equatons for Forty Substances; Stanford Unversty, 1979.