Correlation of Viscosity of Aqueous Solutions of Alkanolamine Mixtures Based on the Eyring's Theory and Wong-Sandler Mixing Rule

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1 Iran. J. Che. Che. Eng. Vol. 3, No., 3 Correlaton of Vsosty of Aqueous Solutons of Alkanolane Mxtures Based on the Eyrng's Theory and Wong-Sandler Mxng Rule Ahad Kelayeh, Sara; hotb, Cyrus* + ; Taghkhan, Vahd Departent of Cheal & Petroleu Engneerng, Sharf Unversty of Tehnology, Tehran, I.R. IRAN Jall, Ar as Sene Departent, Researh Insttute of Petroleu Industry (RIPI), Tehran, I.R. IRAN ABSTRACT: A vsosty odel, based on Eyrng s absolute rate theory obned wth a ub PR equaton of state and Wong-Sandler xng rule, has been proposed n order to orrelate vsostes of aqueous solutons of alkanolane xtures at atospher pressure and dfferent teperatures. In the proposed ethod, the energy and sze paraeters n studed Equaton of State (EoS) have been obtaned usng the Wong Sandler (WS) xng rule obned wth the NL and Wlson bbs equatons. The NL and Wlson paraeters for aqueous solutons of alkanolane xtures have been orrelated usng easured vsosty data at atospher pressure and dfferent teperatures. The overall average devaton between the experental and alulated vsostes of studed aqueous solutons of alkanolane xtures usng Wlson odel s.9%. KEY WORDS: WS xng rule, Vsosty odels, Equaton of state, NL, Wlson. INTRODUCTION The vsosty, ostly that of lqud xtures, s very portant n engneerng alulatons nvolved n the proess desgn for petroleu and other heal ndustres. A reasonable desgn or analyss of a heal proess serously depends on the true llustraton of the therophysal propertes of the proess streas. Aong these propertes, lqud vsosty eerges as one of the key transport varables needed n proess desgn and developent. Several attepts have appeared n the lterature dealng wth the developent of dependable ethods for estatng lqud vsosty of bnary and ultoponent xtures. Despte all these efforts, a theoretal desrpton of the vsosty of lqud xtures nowadays reans defent due aybe to the poor understandng of the lqud state tself. Therefore, ost of the estaton ethods for lqud vsosty appearng n the lterature are essentally epral or se-epral n nature []. Exellent revews and evaluatons of the ost portant vsosty odels so far reported for non-eletrolyte pure lquds and lqud xtures are gven by Red et al. [], Mehrotra [3], Monnery et al. [4]. Other odels for lqud xture vsosty orgnally developed under the one-flud bass are extensons to ultoponent systes through * To who orrespondene should be addressed. + E-al: ghotb@sharf.edu -9986/3//9 9/$/.9 9

2 Iran. J. Che. Che. Eng. Ahad Kelayeh S. et al. Vol. 3, No., 3 the use of proper xng rules. As noted by Polng et al. [5], essentally all vsosty odels for lqud xtures refer to solutons of lquds under or slghtly hgher than ther noral bolng ponts, for exaple, they are lted to redued teperatures of the pure fluds below about.7. At these teperature ondtons, lqud vsostes are notably senstve to the struture of the onsttuent oleules. For an deal lqud xture, there s a nearly lnear anner between vsosty and oposton. For a xture ontanng alohols and/or water, however, ts orrespondng vsostyoposton funton often exhbts a axu or a nu and soetes both of the [6]. A oonly used and suggested lqud xture vsosty orrelaton s the runberg Nssan approah [5,6]. The alulaton of the low-teperature lqud vsosty for a ultoponent syste usng ths approah s as follows: () n n = j= j j ln η = x ln η + x x sne =, x s the lqud ole fraton and j s an nteraton paraeter whh s a funton of the oponents and j as well as the teperature (and, n soe ases, the oposton). Unfortunately, the runberg Nssan ethod does not over aqueous xtures. Aong other approahes, the orrespondng-states prnple and the Eyrng s absolute rate theory have been also extensvely used to represent the vsosty of lqud xtures. On the bass of the orrespondng-states fundaental rule, Teja & Re [7] proposed the followng lqud xture vsosty odel: ln ln R η ε = ηε + () R R ω ω ln ( ηε) ln ( ηε) R ω ω where the supersrpts (R) and (R) refer to two referene fluds, η s the vsosty, ω the aentr fator, and ε s defned here as V ε = (3) 3 ( T M) By usng two referene fluds and n obnaton wth a van Laar-type of xng rule, vsostes of non aqueous polar bnary lqud xtures an be orrelated over a spef teperature range. R R Unfortunately, for forefully related systes suh as aqueous solutons, where a axu exsts n the vsosty-oposton urve [8], the perforane of the above entoned odels and ts extenson to ternary systes s not very suessful [9]. Lee &We [] proposed a three-referene-flud orrespondng-states vsosty odel for both non-aqueous and aqueous solutons. The Lee-We approah norporates oxygen, otane and water as the referene fluds. Chevaler et al. [] and aston-bonhoe et al. [] adapted and norporated the UNIFAC atvty oeffent ethod nto the struture of the Eyrng s absolute rate theory to predt lqud xture vsostes as follows: g g ln η = x ln ηv ln V + + * EC * ER (4) * gec where whh s a obnatoral ter, s the sae as that n the UNIQUAC odel whereas the * ger resdual ter s oputed usng the UNIFAC ethod as odfed by the above entoned authors. The ethod, tered UNIFAC-VISCO, was suessfully appled n the predton of vsostes of xtures ontanng oleules that dffer onsderably n sze. Based on the Eyrng s absolute rate theory, Cao et al. [3] also developed a UNIFAC-based ethod for lqud xture vsostes. For the ethods based on the Eyrng's theory, the estaton of the atvaton bbs energy of flow plays an portant role. MAllster [4] alulated ths quantty by usng an epral ub oposton-dependent funton. The resultng odel s very suessful n orrelatng vsostes of lqud xtures. However, ts paraeters are strongly teperature- dependent and for ternary systes, addtonal ternary paraeters are neessary. Lee et al. [5]obned the Eyrng's theory wth Patel-Teja Equaton of State (PTEoS) to for an Eyrng- Patel-Teja vsosty odel. Ths odel orrelates the vsostes of bnary systes very well even at elevated pressures and s suessfully extended to ternary systes. However, the results for aqueous solutons are not very satsfatory possbly beause the Redlh-Kster(RK)-type xng rule was eployed[6] whh s not very sutable for ultoponent syste[7].

3 Iran. J. Che. Che. Eng. Correlaton of Vsosty of Aqueous Solutons of Alkanolane Mxtures... Vol. 3, No., 3 Aqueous solutons of alkanolanes are usually used n ndustral proesses for sour gas purfaton (e.g., natural, refnery, and synthess gas streas) prarly to elnate ad gases, suh as CO and H S. The alkanolanes that have been wdely utlzed n suh sweetenng proesses are onoethanolane (MEA), dethanolane (DEA), and N-ethyldethanolane (MDEA) n aqueous soluton of a sngle ane. In the past few years, aqueous solutons of xed alkanolanes (a prary or seondary alkanolane wth a tertary alkanolane) have reeved rsng attenton for the sultaneous reoval of CO n the presene of H S fro dfferent gas streas sne those solutons obne the advantages of eah sole ane wth the a to generate a onsderable proveent n absorpton apaty as well as seletve reatons and easer regeneraton of the ad gas-loaded xed anes solutons [8]. Ane oleules are often used as organ base opounds n several ndustral proesses. Partularly, for the optzed desgn of these proesses, relable experental data are needed. For these opounds, voluetr propertes suh as densty and ts derved propertes are portant therodyna propertes whh haraterze the heal nature. These quanttes provde portant nforaton on ther oleular nteratons. Ths s even ore obvous n the ase of assoatng substanes lke anes [9]. Based on the apabltes and ltatons of the lqud vsosty odels desrbed above, n ths paper, we propose an Eyrng-theory-based odel oupled wth a Peng Robnson ub equaton of state to properly orrelate lqud vsosty of aqueous solutons of threthanolane (TEA) + sulfolane (TMS) and dsopropanolane (DIPA) + sulfolane (TMS) over a wde range of teperature n low onentratons and at atospher pressure. In ths work the Wong-Sandler (WS) xng rules oupled wth PR EOS are used to alulate the exess bbs free energy and olar volues of aqueous solutons of alkanolane xtures needed wthn the Eyrng s fraework to orrelate the vsostes of studed solutons at dfferent teperatures. VISCOSITY MODEL Along wth the absolute rate theory of Eyrng, the dyna vsosty η an be estated by[]: * V V N h exp η = η = A O Where, * s the atvaton bbs energy of flow that s needed to get rd of oleules wthn the flud fro ther energetally ost favorable state to the atvated state and the quanttes V, N A and h o represent the olar volue, the Avogadro and the Plank onstant, respetvely. Eq.(5) an be used ether for pure fluds or for xtures. For a lqud soluton the atvaton bbs energy of flow an be separated nto a hypothetal deal soluton part and an exess part. * *d *E = + (6) Fro the deal atvaton bbs energy of flow the vsosty of an deal soluton s gven by d η V = NAhO exp *d By obnng Eqs. (6), (7), and (5) the followng vsosty equaton of lqud xtures s obtaned. *E V V exp d η = η (5) (7) (8) Where ( η V ) d an be estated by a sple obnaton of the vsostes of the pure fluds ( V ) d ( η V) = exp x ln ( η V ) η : (9) = There are several ways to alulate the exess atvaton bbs energy of flow ( *E ) n the lterature. One suh alulaton s to relate t to the exess bbs free energy ( E ). We & Rowley [] proposed a sple relaton *E E = k () where k s a proportonal fator. Rather than usng the above expresson, the value of an be dretly alulated fro an equaton of state, wth k = as follows: *E E o = = ϕ ϕ = x ln ln () Wthn ths fraework, the use of an equaton of state s useful sne t allows the sultaneous deternaton

4 Iran. J. Che. Che. Eng. Ahad Kelayeh S. et al. Vol. 3, No., 3 of the fugaty oeffent of n the xture φ (x, T, P), the olar volue of the lqud xture V (x, T, P), o the fugaty oeffent of the pure flud φ (T, P) and the olar volue of the pure lqud V (T, P). In the present work, the alulaton of these propertes was perfored va the use of the one-flud Peng Robnson [] Cub Equaton of State (C EoS) []. a(t) p = V b V V + b b V b Wth ( ) () a(t) = α (T) (3) P b = (4) P 3 k = ω.644ω +.667ω (5) ( ) α (T) = + k T (6) r The applaton of Eq. () to hghly non-deal xtures should be done by norporatng a sutable opostonal dependene of a and b paraeters nto the CEoS. The xng rules proposed by Wong & Sandler [3] that obne exess free-energy odels wth a CEoS were used for ths purpose D a = Q D b (7) Q = (8) D Wth D = x + b C EX a γ (9) Q = a x x b + b a k j j j, j j () Where C s a onstant that depends on the EoS (.635 for PR).The above xng rules satsfy the low-densty boundary ondton: quadrat oposton dependene of the seond vral oeffent (Eq. ()) and EX EX the hgh-densty ondton: A = at nfnte EOS γ pressure (Eq. (9)). The WS approah thus produes the desred equaton of state behavor at both low and hgh denstes wthout beng densty dependent and allows extrapolaton over wde ranges of teperature and pressure. We have set the bnary nteraton paraeters k j n Eq. () to zero n our work. Usng the PR EoS and WS xng rule, fugaty equaton beoes [4]: f T, P, x Nb bp ln = ( Z ) ln Z () x b N T,N a N a Nb b Na N b N T,N j T,N j Z + + bp ln Z + bp Where j j Nb N Q = N D N N T,N T,N Q ND ( D) N T,N j N Q Nb Nb = D + b N N N N j T,N T,N T,N j j j N Q a = x j j b T,N j j () (3) (4) N N ND a ln γ = + N b C T,N j (5) The NL and Wlson equatons were norporated nto Eq. (9) as the exess bbs free energy odel needed n the WS xng rules. For xtures, the NL EX γ odel s: E τj j jx = j = x = l lx = l g j ( j ) (6) = exp ατ (7)

5 Iran. J. Che. Che. Eng. Correlaton of Vsosty of Aqueous Solutons of Alkanolane Mxtures... Vol. 3, No., 3 Table : Dyna Vsosty for Pure DIPA, TEA, and TMS[5]. T/K DIPA TEA TMS Table : Dyna Vsosty of (TEA+TMS +H O) xture [6]. x TEA x TMS Teperature () Table 3: Dyna Vsosty of (DIPA+TMS +H O) xture[6]. x DIPA x TMS Teperature () τ = g g (8) j j jj gk = gj g jj = gk + akt (9) Whh α=. and Wlson EX γ odel s: ( x A ) ge = x ln j j j = (3) = A j υ = ( λ j λ jj ) j exp υ (3) λ k = λj λ jj = ak + akt (3) In whh the effet of the olar volue ter an be negleted. The fnal for of the vsosty odel s thus obtaned by obnng Eqs. (8) and (): ( η ) d C V al exp x ln ln V = η = ( ϕ ϕ ) (33) The alulaton of the kneat vsosty for deal soluton (V) d, Eq. (7), requres the value of the vsosty of the pure oponent nterest that are gven n Table [5]. η at the teperature of RESULTS AND DISCUSSION Eq. (33) was appled to the orrelaton of experental lqud vsostes of ternary xtures nludng aqueous solutons of alkanolane xtures [6]. Experental results of vsostes of two dfferent ternary aqueous solutons of alkanolanes at atospher pressure and at dfferent teperatures are gven n Tables and 3. Table shows experental vsosty values for trethanolane + sulfolane + water xture and Table 3 shows experental vsosty values for dsopropanolane + sulfolane + water xture. 3

6 Iran. J. Che. Che. Eng. Ahad Kelayeh S. et al. Vol. 3, No., 3 Table 4: Vsosty paraeters for TEA()+TMS() +H O(3) xture n PR-Eyrng-WS-NL odel. g k a K (kj/ol) a K (kj/ol.k) g = g -g g = g -g g 3 = g 3 -g E+. g 4 = g 3 -g g 5 = g 3 -g g 6 = g 3 -g Table 5: Vsosty Paraeters for DIPA()+TMS()+H O(3) xture n PR-Eyrng-WS-NL odel. g k a K (kj/ol) a K (kj/ol.k) g = g -g g = g -g 9.6. g 3 = g 3 -g E+3 -. g 4 = g 3 -g g 5 = g 3 -g g 6 = g 3 -g.8.4 Table 6: Vsosty Paraeters for TEA()+TMS()+H O(3) xture n PR-Eyrng-WS-Wlson odel. λ k a K (kj/ol) a K (kj/ol.k) λ = λ -λ λ = λ -λ λ 3 = λ 3 -λ λ 4 = λ 3 -λ λ 5 = λ 3 -λ λ 6 = λ 3 -λ The values for the paraeters of atvty oeffent odels n Eq. (33) were obtaned by nzng the devatons between the orrelated and the experental vsosty of the lqud xtures usng the followng objetve funton. OF = ( ηal ηexp ) Nexp = (34) N exp Where N exp s the nuber of experental data, the nuber of paraeters, and exp and al are experental and alulated vsostes of the ternary xture, respetvely. The orrelaton results obtaned at atospher pressure are suarzed n Tables 4-7 for two studed ternary aqueous alkanolane systes. The resultng perent of A.A.D.s between alulated and observed vsosty data s defned by: exp N al η η AAD = N exp (35) = η Tables 4 and 5 show the bnary NL paraeters at atospher pressure obtaned usng the PR WS- NL odel for Trethanolane + Sulfolane + water and 4

7 Iran. J. Che. Che. Eng. Correlaton of Vsosty of Aqueous Solutons of Alkanolane Mxtures... Vol. 3, No., 3 Table 7: Vsosty Paraeters for DIPA()+TMS()+H O(3) xture n PR-Eyrng-WS-Wlson odel. λ k a K (kj/ol) a K (kj/ol.k) λ = λ -λ λ = λ -λ λ 3 = λ 3 -λ λ 4 = λ 3 -λ λ 5 = λ 3 -λ λ 6 = λ 3 -λ Vsosty [Pa.s] 4 3 Vsosty [Pa.s] T(K) T(K) Fg. : Coparson of alulated vsostes of the syste TEA()+TMS() +H O by PR-Eyrng-WS-NL odel wth experental values Experental values: : x =; : x =.; x : x =.35. Fg. : Coparson of alulated vsostes of the syste DIPA()+TMS() +H O by PR-Eyrng-WS-NL odel wth experental values Experental values: : x =; : x =.35; : x =.36. Dsopropanolane+ Sulfolane+ water ternary systes. Fgs. and opare the orrelated values of vsostes systes obtaned usng PR-WS-NL odel wth the experental values at dfferent teperature for the Trethanolane + Sulfolane + water and Dsopropanolane+ Sulfolane+ water systes. Tables 6 and 7 show the bnary Wlson paraeters at atospher pressure obtaned usng the PR-WS-Wlson odel. Fgs. 3 and 4 opare the orrelated values of vsostes for two studed ternary aqueous alkanolane solutons wth the experental values at dfferent teperatures usng PR-WS-Wlson odel. As seen n Table 8, the PR-WS-Wlson odel orrelates better the experental results for the vsostes of two studed ternary aqueous alkanolane solutons at dfferent teperatures. CONCLUSIONS The PR CEoS has been norporated nto the absolute rate theory of Eyrng to alulate the vsosty of aqueous alkanolane solutons. A Wong Sandler E -xng rule based on the zero pressure referene state, usng the NL and Wlson exess bbs free energy odels, was also eployed. The experental vsostes of ternary (DIPA+ TMS+H O) and (TEA+TMS+H O) systes at dfferent teperatures were orrelated usng the above entoned odels. Both the PR WS NL and PR-WS-Wlson odels orrelate aurately the experental data, but the auray of the PR WS Wlson odel n orrelatng the vsosty of the studed solutons s better than that of the PR WS NL odel. 5

8 Iran. J. Che. Che. Eng. Ahad Kelayeh S. et al. Vol. 3, No., 3 Table 8: The AAD% between the alulated and easured vsosty usng WS-NL and WS-Wlson odels AAD% overall TEA+TMS+water DIPA+TMS+water NL Wlson Vsosty [Pa.s] 4 3 Vsosty [Pa.s] T(K) T(K) Fg. 3: Coparson of alulated vsostes of the syste TEA()+TMS() +H O by PR-Eyrng-WS-Wlson odel wth experental values Experental values: : x =; : x =.; : x =.35; : x =.35. Reeved : July, ; Aepted : Ot. 3, REFERENCES [] Maıas-Salnas R., Maıas-Salnas F., Elosa-Jénez., An Equaton-of-State-Based Vsosty Model for Non-Ideal Lqud Mxtures, Flud Phase Equlbra,, p. 39 (3). [] Red R.C, Prausntz J.M., Polng B.E., The Propertes of ases and Lquds, Fourth ed. Mraw-Hll, New York (987). [3] Mehrotra A.K, A eneralzed Vsosty Equaton for Pure Heavy Hydroarbons, Ind. Eng. Che. Res., 3, p. 4 (99). Mehrotra A.K, eneralzed One-Paraeter Vsosty Equaton for Lght and Medu Lqud Hydroarbons, Ind. Eng. Che. Res., 3, p. 367 (99). [4] Monnery W.D., Svrek W.Y., Mehrotra A.K., Vsosty: A Crtal Revew of Pratal Predtve and Correlatve Methods, Can. J. Che. Eng., 73, p. 3 (995). [5] Polng B.E., Prausntz J.M., O Connell J.P., The Propertes of ases and Lquds, Ffth ed., Mraw-Hll, New York (). Fg. 4: Coparson of alulated vsostes of the syste DIPA()+TMS() +H O by PR-Eyrng-WS-Wlson odel wth experental values Experental values: : x =; : x =.35; : x =.36. [6] Irvng J.B., Vsostes of Bnary Lqud Mxtures: The Effetveness of Mxture Equatons, Natl. Eng. Lab., Rept. 63, East Klbrde, lasgow, Sotland (977). [7] Teja A.S., Re P., eneralzed Correspondng States Method for the Vsostes of Lqud Mxtures, Ind. Eng. Che. Funda.,, p. 77 (98). [8] Lu H., Wang W., Chang C.H., Model wth Teperature-Independent Paraeters for the Vsostes of Lqud Mxtures, Ind. Eng. Che. Res., 3, p.67 (99). [9] Papaloannou D., Evangelou T., Panayotou C., Dyna Vsosty of Multoponent Lqud Mxtures, J. Che. Eng. Data., 36, p. 43 (99). [] Lee M.-J., We M.-C., Correspondng-States Model for Vsosty of Lquds and Lqud Mxtures, J. Che. Eng. Japn., 6, p.59 (993). [] Chevaler J.L., Petrno P., aston-bonhoe Y., Estaton Method for the Kneat Vsosty of a Lqud-Phase Mxture, Che. Eng. S., 43, p.33 (988). 6

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