Prediction of Solid Paraffin Precipitation Using Solid Phase Equation of State

Transcription

1 Predton of old Paraffn Preptaton Usng old Phase Equaton of tate Proeedngs of European Congress of Chemal Engneerng (ECCE-6) Copenhagen, 16- eptember 7 Predton of old Paraffn Preptaton Usng old Phase Equaton of tate Mohsen Vafae eft, a Hamd Mehdzadeh, a Al Mousav, b a Department of Chemal Engneerng, Tarbat Modares Unversty, Tehran, Iran b Iran's Researh Insttute of Petroleum Industry, Pazhooheshgah, Blvd.Kharabad Junton, Old Qom Road, Tehran, Iran Abstrat In the tradtonal methods for wax preptaton predton, the fugaty of sold s alulated usng a hypothetal thermodynam yle. In ths study, a new method based on TT sold equaton of state s proposed to alulate the fugates of sold phases. The mult-sold approah s used for desrpton of sold phases. Obtaned parameters for ths equaton of state s useful for future works. Keywords: wax preptaton, sold equaton of state, mult-sold 1. Introduton Wax deposton from gas and ol produton faltes and ppelnes s undesrable. The flow-lnes and proess equpments may be plugged by wax deposton. Dfferent physal and hemal methods have been proposed to remove deposted solds, whh nreases operatng osts. A relable model for wax preptaton alulatons s hghly valued for desgn and operaton of flowlnes. ne 199s, so many efforts have been done to predt ondtons under whh the waxes an preptate and the amount of preptated wax n funtons of pressure, temperature and omposton. At frst, the alulatons were based on the sold-lqud equlbrum assumpton. Later on, the gas phase was nluded n the alulatons [1, ]. There are two learly defned assumptons for the determnaton of the thermodynam equlbrum wax lqud n establshed mult-omponent hydroarbons systems: sold soluton, and the formaton of multple sold phases. In the former ase, dfferent methods were proposed based on the atvty oeffent model assumng the non-dealty of lqud and sold phases [3, 4]. old phase transton and vapor phase were then onsdered n other works [5-7]. The non-dealty was defned usng Wlson or UNIQUAC equatons. Lra-Galeana et al. [8] developed the mult-sold approah n In ths model, t s assumed that the sold wax onssts of several pure sold phases, n whh the number and nature of them wll be obtaned from phase stablty analyss. Coutnho showed that the sold phase s a mult-sold soluton n nature and supported by expermental data [9].

2 M. Vafae eft et al. In ths work, the wax-preptaton model based on sold phase equaton of state wll be presented. The mult-sold approah s used beause of ts wde aeptablty and lmtaton of usng sold phase equaton of state. The parameters of the equaton of state are obtaned n the ase that vapor, lqud and sold phases are nluded n the system.. old Phase Equaton of tate The equatons of state that an be appled to a system ontanng sold, lqud and vapor phases smultaneously are sare[1,11]. In ths projet, TT 1 equaton of state s used [11]. The general form of the equaton s as below RT a P = (1) v b ( v + ub)( v + wb) In ths equaton, u and w are 3 and -.5 respetvely. Also, a =.4757R T / P b =.7474RT / P Z =.9696 a = α a (5) Alpha funton for lqud and vapor phases ould be used n onventonal polynomal form or n exponental form. In ths equaton, a new alpha funton s ntrodued for the sold phase, whh wll be dsussed later. In order to alulate fugaty of eah omponent n pure sold state, the followng equaton s used [1]. ΔH v (6) d ln f = dt + dp RT RT Where, f: fugaty Δ H : enthalpy hange n result of hange n system temperature v: partal molar volume By ntegratng the above equaton from the trple pont pressure to the system pressure for lqud and sold phases and dvdng the two equatons, the followng f relaton wll be obtaned. In ths equaton, ΔH and Δ v are supposed to be ndependent of pressure and temperature. f f ΔH T ΔvP ln = 1 L (7) f RT Tr RT () (3) (4) 1 Twu-m-Tassone

3 Predton of old Paraffn Preptaton Usng old Phase Equaton of tate uppose that the pressure system s equal to zero, we wll have f f ΔH T ln = 1 L f RT Tr (8) Ths equaton s smlar to the equaton that was proposed by Prausntz et al. [13] for the alulaton of sold phase fugaty. If the fugaty s alulated at zero pressure, * * f * * 1 a v + w ln = 1 ln b ln( v 1) ln * * (9) P ( w u) b v + u Where, 1/ * * * * 1 a a a v = u w u + w 4 uw + * * * (1) b b b * Pa a = (11) RT * Pb b = (1) RT And, u and w are the parameters of the equaton of state. By equalzng the two equatons, we wll get * * L f + Δ = H * * 1 a v w f T 1 ln b ln( v 1) ln ln 1 * * + t ( w u) b v u P RT (13) T The only unknown varable n the above equaton s. Therefore, the equaton s solved to obtan a * for dfferent temperatures. The parameters of predefned sold alpha funton are alulated by orrelatng the data to the followng equaton.5 n α ( T ) = 1+ l (1 T ) + m (1 T ) (.7 T ) (14) In whh α = a / a a a = * s r α an be alulated usng R T P r r In order to alulate the optmum parameters, the followng goal funton was used to mnmze the dfferene between the presented data and the alulated data from eq (1.5 ) (1 ) n (.7 ) (17) f x = + l T + m T T α ( ) ( ) s r, r, r, The smplex-nelder-mead algorthm was utlzed to obtan the optmum parameters, whh mnmzes the goal funton. Due to the nonlnearty of the funton, the results a * (15) (16)

4 M. Vafae eft et al. wll drastally depend on the ntal guess for the optmal parameters. To avod ths problem, the optmzaton problem s run for dfferent startng ponts. 3. Wax Preptatng Model The followng expressons are used to desrbe the system n whh vapor, lqud and pure solds are n equlbrum state. Mass balane for preptatng omponents: v V L L f F y n + x n + n z n = (18) Where = 1,..., N, j = 1,..., N P N P : Number of preptated solds N C : Number of omponents Mass balane for non-preptatng omponents: v V L L f F y n + x n z n = Equalty of fugates n the lqud and gas phases for eah omponent: V L f f = Equalty of fugates n the lqud and sold phases for preptatng omponents: f f = L ummaton of mole fratons n lqud and gas phases are equal to unty N x 1= = 1 N = 1 y 1= (19) () (1) () (3) All the equatons above onsttute a system of equatons, whh should be solved n order to defne the equlbrum system ompletely. An error funton s ntrodued to hek the onvergene of the system of equatons. NC + N P + (4) f ( δ ) = δ = 1 Where δ 's are the rght hand expressons n equatons Results and Dsussons The omposton of ol samples and some synthet mxtures, whh were used n ths projet are shown n tables 1-4. ne the referenes are dfferent, the omponents onsdered for eah sample are not the same.

5 Predton of old Paraffn Preptaton Usng old Phase Equaton of tate Table 1. Mole fratons for two synthet mxtures [7] Component Mxture C Mxture B n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c 3.17 Table. Mole fratons for a synthet mxture [14] Component Bm 13 Component Bm 13 C C C C C C C Table 3. Mole fratons of heavy ol fratons [5] Ol 5 Peusoomponent Mole perent MW P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-CP A-CP N-CP A-CP

6 M. Vafae eft et al. Table 4. Mole fratons of heavy ol fratons [5] Ol 6 Pseudoomponent Mole perent MW P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP N-CP A-CP The parameters of the equaton of state (l s, m s, n s ) are alulated as dsussed n the prevous seton. The optmal values for the mentoned parameters for the ol samples are n tables 5-9. The ntal guess for the system of equlbrum equatons s gven from the results of a two-phase flash alulaton. Then, the dogleg method [15] s appled to hek the onvergene rtera,.e. the rght-hand sde expresson n equaton 19 should be less than 1e-7. If the rteron s not met, the program wll shft to smplex algorthm that uses the results of the prevous step as the ntal ponts. There s a normalzng step, whh flters the nomng physally unaeptable data. The physal propertes data are derved from databooks or are estmated from proposed methods n the lterature. Table 5. Parameters of EO for mxture B Component l m n n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c

7 Predton of old Paraffn Preptaton Usng old Phase Equaton of tate Table 5. Parameters of EO for mxture B (ontd.) n-c n-c Table 6. Parameters of EO for mxture C Component l m n n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c n-c Table 7. Parameters of EO for bm13 Component l m n C C C C C C C 36 Table 8. Parameters of EO for Ol 5 Pseudoomponent l m n P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-C A-C P-C N-CP A-CP N-CP A-CP

8 M. Vafae eft et al. Table 9. Parameters of EO for Ol 6 Pseudoomponent l m P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP P-CP N-CP A-CP N-CP A-CP n α s ndependent of pressure and t an be used for the sold volume predton [11]. The error funton for lghter omponents, lke C 1, are greater than heavy fratons. The reason s that the alulatons are done n a temperature far from the meltng pont. Preptated Wax Wt% Ths Work 6 Expt Temperature, K Fgure 1. Expermental and alulated amount of preptated wax for Ol 5

9 Predton of old Paraffn Preptaton Usng old Phase Equaton of tate Preptated Wax Wt% Ths Work Expt Temperature (K) Fgure. Expermental and alulated amount of preptated wax for Ol Preptated Wax Wt% Ths Work Expt Temperature (K) Fgure 3. Expermental and alulated amount of preptated wax for bm13 6 Preptated Wax Wt% Ths Work Expt Temperature (K) Fgure 4. Expermental and alulated amount of preptated wax for mxture B

10 M. Vafae eft et al. 6 mxture C Preptated Wax Wt% Ths Work Expt Temperature (K) Fgure 5. Expermental and alulated amount of preptated wax for mxture C 5. Conluson Complex behavor of sold phase n ol mxture and wde range of ts applaton n sold preptaton and deposton petroleum fluds (wax, asphaltene, ) need to be modeled va applable and effent methods. Here applaton of a sold EO for desrpton of sold phase was tested for wax preptaton n petroleum mxtures. In ths work, TT sold equaton of state s used for desrbng wax preptaton phenomena n some synthet and real ol mxtures. Ths sold equaton of state s based on an alpha funton. Usng thermodynam yle for pure sold fugaty from pure lqud fugaty, the TT parameters were tuned before ts applaton for wax preptaton predton. The multsold phase approah s used for determnaton of the nature and number of sold phases. As t an be seen n the prevous setons, the obtaned results n ths work are n good agreements wth the expermental data. Referenes [1] Won K. V., Flud Phase Equlbra, 53, 377 (1989). [] Won K. V., Flud Phase Equlbra, 3, 65 (1986). [3] Dardon J.-L., Pauly J., Coutnho J. A. P., and Montel F., Energy and Fuels, 15, (1). [4] Coutnho J. A. P. and Dardon J.-L., Energy and Fuels, 15, 1454 (1). [5] Vafae-eft M., Mousav-Dehghan. A., and Mohammad-Zadeh Bahar M., Flud Phase Equlbra, 173, 65 (). [6] Nhta D. V., Gousl L., and Froozabad A., PE (1). [7] Feyz F. and Dalrsefat R., Fuel (7), do:1.116/j.fuel , Artle n Press. [8] Lra-Galeana C., Froozabad A., and Prausntz J. M., AIChE, 4, 39 (1996).

11 Predton of old Paraffn Preptaton Usng old Phase Equaton of tate [9] Coutnho J. A. P., Edmonds B., Moorwood T., zzepansk R., and Zhang X., PE 7834 (). [1] Yokozek A., Internatonal Journal of Thermophyss, 4, 589 (3). [11] Twu C. H., Tassone V., and m W. D., AIChEJ, 49, 957 (3). [1] Ness H. C. V. and Abbott M. H., Classal Thermodynams of Non-Eletrolyte olutons wth Applaton tp Phase Equlbra. New York: M-Graw Hll (198). [13] Prausntz J., Lhtenthaler M., R. N., and de Azevedo E. G., Moleular Thermodynams of Flud-Phase Equlbra. Upper addle Rver, New Jersey: Prnte Hall (1999). [14] Esobar-Remolna J. C. M., Flud Phase Equlbra, 4, 197 (6). [15] Powell, M. J. D., Numeral Methods for Nonlnear Algebra Equatons, P. Rabnowtz (197)