PREDICTION OF GAS HYDRATE PHASE BEHAVIOR IN THE PRESENCE OF ALCOLHOLS AND GLYCOLS WITH PRSV EQUATION OF STATE AND THE VDW-P MODEL

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1 Proceedngs of the 7th Internatonal Conference on Gas Hydrates (ICGH 2011), Ednburgh, Scotland, Unted Kngdom, July 1721, PREDICTION OF GAS HYDRATE PHASE BEHAVIOR IN THE PRESENCE OF ALCOLHOLS AND GLYCOLS ITH PRSV EQUATION OF STATE AND THE VDP MODEL LJen Chen, ChHung Ln, YenTng Yeh, MnKang Hseh, ShangTa Ln and YanPng Chen Department of Chemcal Engneerng Natonal Tawan Unversty Tape TAIAN ABSTRACT In ths study, a smple hydrate thermodynamc model s developed to calculate the phase equlbrum of pure gas hydrates (CH, C 2 H 6, C 3 H 8, CO 2 ) and to predct the phase behavor of gas hydrate systems n the presence of nhbtors e.g. methanol, ethanol, and ethylene glycol. The equalty of fugacty approach s used to model the vaporlqudhydrate phase equlbrum. The van der aals and Platteuw model s appled to descrbe the hydrate phase, and PengRobnsonSt ryjekvera equaton of state s chosen to evaluate the fugactes of vapor and lqud phases. The model parameters are ftted to expermental data for pure gas hydrate, and ths model s able to precsely descrbe vaporlqudhydrate equlbrum pressure system for sngle guest hydrates and predct the phase equlbrum for the hydrate systems wth nhbtors. Keywords: gas hydrates, nhbtors NOMENCLATURE Roman Characters a = attractve parameter n PRSV EoS b = volume parameter n PRSV EoS A = Langmur constant parameter B = Langmur constant parameter C = Langmur constant f = fugacty k j = bnary nteracton parameter k = Boltzmann constant N data = number of data r = radal dstance P = pressure R = gas constant R(cell) = cell radus T = temperature V= molar volume ( r) = cell potental x = molar composton Superscrpts and Subscrpts H=hydrate phase L=lqud phase l = guest gas m =cage type V = vapor phase w = water Greek characters = empty hydrate phase = fugacty coeffcent = occuped fracton INTRODUCTION Ga s hydrates are celke crystallne solds that comprse water and usually smaller gas guest e.g. CH, C 2 H 6, whch usually form under hgh pressure and low temperature envronment. The water molecules consttute cagelke crystal lattce Correspondng author: Phone: +886 (0) Fax +886 (0) Emal:ljchen@ntu.edu.tw

2 due to hydrogen bondng, and the lattce s stablzed by encapsulatng of gas molecules. There are three manly structure for gas hydrates: structure I (si), structure II (sii) and structure H (sh).gas hydrates had been wdely nvestgated snce 1930s due to the hydrate formaton trggerng the blockng problem nsde equpments and ppelnes n ol and natural gas ndustry [2]. Recently, there has been a great nterest n ts energy potental and the capablty of gas storage and gas transportaton. To understand the phase behavor and stablty of gas hydrates n the large range of temperature and pressure, and the phase equlbrum of hydrate systems wth nhbtors, an accurate thermodynamc model s necessary. Many thermodynamc models for phase equlbrum n the hydrate system had been revewed and dscussed [1, 3]. Van der aals and Platteuw derved the basc statstc thermodynamc model wth LeonardJones potental functon to calculate pure gas hydrate dssocaton pressure n 199, and most of models for the hydrate phase are based on vdp model []. In 1972, Parrsh and Prausntz used the vdp model wth Khara potental to extend the vdp model n calculatng phase equlbra for sngle and mxed gas hydrates [6]. In the vdp model, the equlbrum crtera s that the chemcal potental of water n dfferent phases must be equal, and there are many reference energy parameters should be regressed to evaluate the fugacty n the hydrate phase. To avod ths problem, the fugactybased approach for modelng hydratelqudvapor (HL w V) phase equlbrum wa s developed. Chen and Guo used fugacty approach n the vdp model, and evaluated the fugactes n the flud phases by PatelTeja (PT) Equaton of st ate [78]. Klauda and Sandler also proposed the fugacty approach model. They used the PengRobnsonSt ryjek Vera equaton of state (PRSV EoS) n the vapor phase, and modeled the lqud phase by Henry s law correlaton and modfed UNIFAC, then used modfed vdp model and Khara potental n the hydrate phase [9]. In Klauda s model, the Khara potental parameters were based on Tse et al. [10] and there are three parameters ftted by pure gas hydrate expermental data for reference fugacty n the empty hydrate phase. Zhang followed Sandler s fugacty approach, and only used two adjustable parameters n ther model to calculate the equlbrum pressure for the sngle gas hydrate systems below 300 K, and usng the unfed PRSV EoS to model both lqud and hydrocarbon phases [11]. In 2011, Bandyopadhyay and Klauda used predctve SoaveRedchKwong (PSRK) EoS to descrbe the fugacty of nonhydrate phases that n equlbrum wth gas hydrates, but the fugacty of water n the lqud phase was modfed nstead of obtanng from PSRK EoS drectly [12]. To understand the nhbtng effect of alcohols or glycols on hydrate formaton, t s mportant to predct the phase equlbrum condton n hydrate systems wth nhbtors. And many work studed on the nhbton of gas hydrate by methanol [1316]. In 2003, Ma used PatelTeja (PT) EoS wth Kurhara mxng rule and the hydrate model proposed by Chen and Guo [8] n predcton of hydrate formaton condtons of systems contanng nhbtors [17]. In 2006, L used statstcal assocatng flud theory (SAFT) equaton of state coupled wth vdp model for predcton of hydrate systems wth methanol and glycols [18]. In ths study, we use PRSVEoS coupled wth van der aals oneflud (vdw) mxng rule and modfed HuronVdaw (MHV1) mxng rule to model both lqud and vapor phases nstead of usng dfferent models n these two phases. The bnary nteracton parameters between gas, water, and nhbtors are determned by regresson of vaporlqud equlbrum data. The fugacty of water n the hydrate phase wa s descrbed by the vdp model, however, the Langmur adsorpton constants are expressed as a functon of temperature nstead that calculated by potental functon. There are two to four parameters n evaluatng the Langmur constants, and the parameters are regressed by pure gas hydrate equlbrum data. Ths model use the basc EoS and mxng rule wth modfed vdp model and gve good accuracy n HL w V phase equlbrum for pure gas hydrate.moreover, ths smple model can gve good predcton of hydrate systems wth methanol, ethanol and ethylene glycol va the parameters obtaned from calculaton of equlbrum pressure for pure gas hydrates. THERMODYNAMIC MODEL Component fugacty n flud phases In order to gve correct descrpton of the hydrate phase, the phase behavor of nonhydrate phases at equlbrum s mportant. Prevous work for hydratelqudvapor (HL w V) phase modelng

3 [9, 13, 1] used cubc equaton to model the vapor phase and chosen lqud model to descrbe the lqud phase. To smplfy the thermodynamc model n ths work, a sngle equaton of state (EoS) s used to descrbe both vapor and lqud phases. The PengRobnsonSt ryjekvera equaton of state (PRSV EoS) modfed from PengRobnson equaton of state (PR EoS) s used n ths study [1920]. P RT a v b v 2bv b 2 2 (1) where T and P s the temperature and the pressure, R s gas constant, and a and b are attractve parameter and volume parameter n PRSV EoS. There s an added adjustable characterstc parameter, 1,of each compound n PRSV EoS n order to modfy orgnal PR EoS, and the 1 of components n ths paper are from Stryjek and Vera [1920]. Each system ncluded n ths work contans at least two compounds, so the PRSV EoS must be combned wth the mxng rule for mxtures. In ths work, we use the Van der aal oneflud (vdw) mxng rule and the modfed HuronVda w (MHV1) mxng rule [21] wth UNIQUAC model to acqure the parameters n PRSV EoS for mxtures. The parameters a and b n PRSV Eo S evaluated by vdw mxng rule are gven by The MHV1 mxng rule retans equaton (9), and the parameter am s replaced wth equaton (11) a 1 EX bm a b x [ ln ] m m b g RT x m b q b () where q s 0.3 correlated by Mchelsen [21], EX EX and g s excess Gbbs energy ( g ) evaluated by UNIQUAC lqud model. There are two adjustable parameters uj and uj n UNIQUAC model and obtaned from regresson of VLE data, and they are also defned as a functon of temperature. ater fugacty n hydrate phases The model for the hydrate phase s based on the vdp model [], and used fugacty approach to calculate the water fugacty n the hydrate phase. The fugacty of water n the hydrate phase s as follows H f T, P f T exp C ( T) f (,, ) l T P y ln(1 )) 1 C ( T) f ( T, P, y) vm m l l l am bm x xa (2) j j j xb (3) a a a 1k a () j j j j where a, b are pure parameters and parameters of mxture n PRSV EoS. a m, b m are aj and a j are cross terms, assumng they are equal. The kj s the bnary nteracton parameter. In ths work kj s obtaned from regressng expermental vaporlqud equlbrum (VLE) data, and t s expressed as a functon of temperature. where fl (6) s the fugacty of the vapor phase, and f s the fugacty of the hypothetcal empty hydrate lattce and gven by sat, sat, f T, P P T exp w P V (, ) sat, T PdP P (7) RT where the saturated vapor pressure of empty sat, hydrate P correlated by Sloan for the si and the sii hydrate s as follows sat, ln P 17.0 for si (8) T

4 sat, ln P for sii (9) T sat, w ( T) s the fugacty coeffcent of water n the sat, empty hydrate lattce, and ( T) s assumed to w be unty because the vapor pressure of water n the sold phase s low. V ( T, P), s the molar volume of the empty lattce, depends on temperature T and pressure P, and t s gven by Klauda and Sandler [9]. Instead of assumng that V does not change wth P n Poyntng correcton, here we used the basc defnton for the correcton term. s the number of cages In equaton (1), m of type m per water molecule n the hydrate lattce. C ( T) s the Langmur adsorpton constant for guest gas l n type m cage. In the vdp model, C s expressed as approach s used n ths work to model hydratelqudvapor (HL w V) phase equlbrum. At equlbrum, the fugacty of water n vapor (V), lqud water (L), and hydrate phase (H) s equal at temperature T and pressure P, V L H f ( T, Py, ) f ( T, Px, ) f ( T, P) (12) w w w where y and x s the molar composton n the vapor and lqud phase. The fugacty of water n the vapor and lqud phase s descrbed by equaton of state ncorporated wth mxng rule, and the fugacty of water n the hydrate phase s evaluated by the modfed vdp model. RESULTS AND DISCUSSION The comparson between the results from ths model and expermental data s defned by average absolute devaton (AAD). The average absolute devaton n pressure (AADP) and the average absolute devaton n temperature (AADT) are defned as follows: R( cell) r ( ) 2 C ( T) exp( ) rdr 0 (10) kt kt AADP 1 p p (%)= 100 N N exp model data exp data 1 p (13) where r ( ) s the sphercally symmetrc cell potental, and the Khara potental functon was commonly used n vdp model. However, the ntegraton of potental functon s complcated for engneerng applcaton, thus, some correlaton relaton of C ( T) are proposed [6, 8, 22]. In order to smplfy the calculaton of C ( T) n ths model, the emprcal relaton of C ( T) correlated by Parrsh and Prausntz [6] s used here to descrbe the temperaturedependence of the Langmur constant. C A B exp( ) (11) T T where A and B are the fttng parameters and obtaned by data regresson of expermental phase equlbrum pressure of pure gas hydrates, e.g. methane hydrate, and there are only two to four adjustable parameters n ths model. Phase equlbrum crtera The classcal thermodynamc fugacty 1 T T AADT (%)= 100 N where N data N exp mod el data exp data 1 T (1) s the number of data ponts. Sngle gas hydrate results To calculate the sngle gas hydrate equlbrum, the Langmur constant parameters n equaton (20) need to be regressed from expermental phase equlbrum data. Table 1 shows the Langmur constant Parameters for four guest hydrates. It s well understood that the CH and CO 2 molecule s small enough to be trapped ether n the large cage or n the small cage of the si. Thus, there are two Langmur constant parameters A m and B m for each (small or large) cage. The C 2 H 6 +H 2 O hydrate system has a very lttle occupaton for small cage and the C 3 H 8 molecule s too large to be trapped n the small cage, thus, C 2 H 6 and C 3 H 8 molecule have only two parameters. There are two mxng rules (vdw and MHV1) n ths model, and we found that the Langmur constants regressed by dfferent mxng rules coupled wth PRSV EoS and hydrate model

5 Guest Large cage Small cage St ructure No. of A 10 6 B A 10 6 B type parameter (K/KPa) (K) (K/KPa) (K) CH si C 2 H 6 si C 3 H 8 sii CO 2 si Table 1 Langmur constant parameters for pure gas hydrate Guest Equlbra % AADP from experment data Data Temp. range Zhang Ths work Ths work pts. (K) sloan Klauda (QL1) (vdw) (MHV1) CH H(sI) L w V ( 300K) C 2 H 6 H(sI) L w V C 3 H 8 H(sII)L w V CO 2 H(sI) L w V Table 2 Comparson pure gas hydrate equlbrum predcton results (Expermental data are from Sloan) are close, therefore we chose the parameters regressed through vdw mxng rule for the followng calculaton and predcton. Ths can reduce the parameters n our model, and t means that the behavors of the vapor an lqud phase descrbed by dfferent mxng rules are consstent. The results for calculatng HL w V phase equlbrum for sngle gas hydrate by ths model are compared to Sloan s model, and two fugacty approach models (Zhang et al. [11] and Bandyopadhyay and Klauda [12]) n Table 2. The number of fttng parameters n our model s two or four, and there are two and three fttng parameters n, respectvely, Zhang s and Bandyopadhyay and Klauda s work. And we assume that the Langmur constant s only temperaturedependent and use an exponental form nstead of potental functon to descrbe Langmur constants. It has been found that our smple model can gve consstent results wth expermental data. Fgure 1 shows that the model can well descrbe the varaton of pressure as a functon of temperature for the HL w V phase equlbra of the CH, C 2 H 6, C 3 H 8 and CO 2 + H 2 O hydrate system, and the results obtaned from dfferent mxng rules (vdw and MHV1) are overlapped. For C 2 H 6 and C 3 H 8, the average absolute devatons n pressure (AADPs) obtaned by ths model ( PRSV + vdw + vdp and PRSV + MHV1 + vdp) are smallest among three compared papers for whole temperature range. However, the accuracy of CH n ths work s slghtly worse than the other three papers, and ths model cannot perform well n the CH +H 2 O hydrate system above 300 K. The AADPs of CH +H 2 O system are 2.89 % (vdw) and 2.93 % (MHV1) below 300 K, whch are close to Zhang s work, but the AADPs become.1 (vd) and.28 (MHV) for whole temperature range up to K. Fgure 1 shows that the calculated results of pressure versus temperature have a good agreement wth that of the expermental data of H L w V phase equlbra below 300 K for the methane hydrate system. Sngle gas hydrate systems wth nhbtors Ths model can be extended to predct the hydrate system wth nhbtors wthout any addtonal adjustable parameters. Table 3 shows the predcton results for the CH and CO 2 hydrate equlbrum temperature wth methanol (CH 3 OH), ethanol (C 2 H OH) and ethylene glycol (EG) by our model, and there are total 18 nhbtor contanng systems and 90 expermental data ponts ncluded n ths work. In addton, the comparson wth Ma et al.[17] n predcton for some systems s also lsted n Table 3. In Ma s work, they used PT EoS wth Kurhara mxng rule and combned wth ChenGuo hydrate model [8] to gve predctons for the hydrate systems wth nhbtors. There are three bnary fttng parameters n the lson

6 Guest Inhbtor Conc. of Inhbtor (wt %) Data pts. Prange (KPa) Trange (K) Ths work (vdw) AADT (%) Ths work (MHV1) Ma References CH CH 3 OH C 2 H OH [23] [23] EG CO 2 CH 3 OH C 2 H OH [23] [23] EG [2] [2] Table 3 Pure gas hydrate equlbrum temperature predcton n the presence of nhbtors

7 Fgure 1 Phase equlbrum of CH + H 2 O, C 2 H 6 + H 2 O, C 3 H 8 + H 2 O and CO 2 + H 2 O hydrate system. Symbols are expermental data and the sold lne s the results proposed by ths model (PRSV + mxng rule + vdp). Fgure 3 HLwV phase dagram for CH hydrate n equlbrum wth aqueous CH 3 OH soluton at the gven wt %. Symbols are expermental data. The sold lne s the predcton results from PRSV + vdw + vdp. The dashed lne s the predcton results from PRSV+ MHV1+ vdp. equaton to evaluate Gbbs free energy n the Kurhara mxng rule, n addton, ChenGuo hydrate model also has three fttng parameters for reference empty hydrate. In our work, we use the PRSV EoS that contans two parameters, and there are one and two bnary fttng parameters respectvely n vdw and MHV1 mxng rule, and two or four Langmur constant parameters n the hydrate model. Therefore, our method s smpler than that of Ma s and capable for gvng relable results. For the CH + water + CH 3 OH system, our Fgure 2 HLwV phase dagram for CO 2 hydrate n equlbrum wth aqueous EG soluton at the gven wt %. Symbols are expermental data. The sold lne s the predcton results from PRSV+ vdw + vdp. The dashed lne s the predcton results from PRSV + MHV1 + vdp. all predcton are better than Ma s. And PRSV + MHV1 mxng rule + vdp performs much better than vdw mxng rule at 0 wt% methanol, the absolute average devaton n temperature (AADT) s 0.8 (MHV1)and much lower than 2.83 (vdw). Fgure 2 shows the comparson between the predcton and expermental data for methane hydrate formaton condton n methanol aqueous soluton. For the C 2 H 6 + water + CH 3 OH and C 2 H 6 + water + CH 3 OH systems, our model gve larger devaton wth expermental data at hgher concentraton of methanol, and vdw mxng rule gve more consstent results than MHV1 mxng rule at the concentraton above 3 wt%. In these two systems, our results are worse than Ma s. For CO 2 systems wth methanol, the results of dfferent mxng rules by our model are close to Ma s work. The predcton results for CH and CO 2 hydrate n the presence of C 2 H OH and EG by proposed model have good accuracy. Except that the AADT of CH hydrate + 0 wt% EG system s above 1%, the AADTs of other systmes are smaller than 0. %. Fgure 3 shows that the hydrate formaton condton of CO 2 n an aqueous EG soluton. CONCLUSION In ths study, a smple model s proposed to accurately calculate HL w V Phase equlbrum for pure gas hydrates and predct the gas hydrate systems contanng nhbtors. The model s composed of the PRSV EoS, the vdw mxng rule or the

8 MHV1 mxng rule and the vdp model. Instead of usng complcated energy functon to descrbe the Langmur constants n the vdp model, there are only two or four fttng parameters n systems to determne the temperaturedependent Langmur constants, and these model parameters are used drectly n gvn g predcton n hydrate systems wth nhbtors. Ths smple model can well descrbe the phase behavor of HL w V Phase equlbrum for gas hydrate systems as well as for gas hydrate systems wth nhbtors. REFERENCES Sloan ED, Koh CA. Clathrate hydrates of natural gases. New York: CRC Press, [2] Hammerschmdt EG. Formaton of gas hydrates n natural gas transmsson lnes. Industral and Engneerng Chemstry 193;26:818. [3] Holder GD, Zetts SP, Pradhan N. Phasebehavor n systems contanng clathrate hydrates a revew. Rev Chem Eng 1988;(1):170. [] Englezos P. Clathrate hydrates. Industral & Engneerng Chemstry Research 1993;32(7): [] van der aals JH, Platteeuw JC. Clathrate solutons. Advances n Chemcal Physcs 199;2:1 7. [6] Parrsh R, Prausntz J. Dssocaton pressures of gas hydrates formed by gasmxtures. Industral & Engneerng Chemstry Process Desgn and Development 1972;11(1):26&. [7] Chen GJ, Guo TM. Thermodynamc modelng of hydrate formaton based on new concepts. Flud Phase Equlbra 1996;122(12):36. [8] Chen GJ, Guo TM. A new approach to gas hydrate modellng. Chem Eng J 1998;71(2):1 11. [9] Klauda JB, Sandler SI. A fugacty model for gas hydrate phase equlbra. Industral & Engneerng Chemstry Research 2000;39(9): [10] Tse JS. Thermalexpanson of the clathrate hydrates of ethyleneoxde and tetrahydrofuran. Journal De Physque 1987;8(C1):39. [11] Zhang YF, Debenedett PG, Prud'homme RK, Pethca BA. Accurate predcton of clathrate hydrate phase equlbra below 300 K from a smple model. Journal of Petroleum Scence and Engneerng 2006;1(12):3. [12] Bandyopadhyay AA, Klauda JB. Gas Hydrate Structure and Pressure Predctons Based on an Updated FugactyBased Model wth the PSRK Equaton of State. Industral & Engneerng Chemstry Research 2011;0(1):1817. [13] Du YH, Guo TM. Predcton of hydrate formaton for systems contanng methanol. Chemcal Engneerng Scence 1990;(): [1] Robnson DB, Ng HJ. Hydrate formaton and nhbton n gas or gas condensate streams. J Can Pet Technol 1986;2():2630. Anderson FE, Prausntz JM. Inhbton of gas hydrates by methanol. Ache Journal 1986;32(8): [16] Munck J, Skjoldjorgensen S, Rasmussen P. Computatons of the formaton of gas hydrates. Chemcal Engneerng Scence 1988;3(10): [17] Ma QL, Chen GJ, Guo TM. Modellng the gas hydrate formaton of nhbtor contanng systems. Flud Phase Equlbra 2003;20(2): [18] L XS, u HJ, Englezos P. Predcton of gas hydrate formaton condtons n the presence of methanol, glycerol, ethylene glycol, and trethylene glycol wth the statstcal assocatng flud theory equaton of state. Industral & Engneerng Chemstry Research 2006;(6): [19] St ryjek R, Vera JH. PRSV An mproved PengRobnson equaton of state for pure compounds and mxtures. Canadan Journal of Chemcal Engneerng 1986;6(2): [20] St ryjek R, Vera JH. PRSV An mproved PengRobnson equaton of state wth new mxng rules for strongly nondeal mxtures. Canadan Journal of Chemcal Engneerng 1986;6(2): [21] Mchelsen ML. A modfed HuronVdal mxng rule for cubc equatons of state. Flud Phase Equlbra 1990;60(12): [22] Yang SO, Yang IM, Km YS, Lee CS. Measurement and predcton of phase equlbra for water plus CO2 n hydrate formng condtons. Flud Phase Equlbra 2000;17(12):789. [23] Mohammad AH, Aftal, Rchon D. Expermental data and predctons of dssocaton condtons for ethane and propane smple hydrates n the presence of dstlled water and methane, ethane, propane, and carbon doxde smple hydrates n the presence of ethanol aqueous solutons. Journal of Chemcal and Engneerng Data 2008;3(1):7376. [2] Maekawa T. Equlbrum Condtons for Carbon Doxde Hydrates n the Presence of Aqueous Solutons of Alcohols, Glycols, and Glycerol. Journal of Chemcal and Engneerng Data 2010;(3):

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