Al-Khwarizmi Engineering!!! Journal Al-Khwarizmi Engineering Journal, Vol. 6, No. 1, PP 1-13 (2010) Estimation of Extract Yield and Mass Transfer Coefficient in Solvent Extraction of Lubricating Oil HHuussssaaiinn KK.. HHuussssaaiinn Department of Chemical Engineering/ College of Engineering/University of Baghdad (Received 12 April 2009: accepted 13 July 2009) Abstract An investigation was conducted to suggest relations for estimating yield and properties of the improved light lubricating oil fraction produced from furfural extraction process by using specified regression. Mass transfer in mixer-settler has been studied. Mass transfer coefficient of continuous phase, mass transfer coefficient of dispersed phase and the overall mass transfer coefficient extraction of light lubes oil distillate fraction by furfural are calculated in addition to all physical properties of individual components and the extraction mixtures. The effect of extraction variables were studied such as extraction temperature which ranges from 70 to 110°C and solvent to oil ratio which ranges from 1:1 to 4:1 (wt/wt) were studied. The results of this investigation show that the extract yield E decreased with decreasing solvent to oil ratio in extract layer and increased with increasing temperature. The fraction of total solvent in the raffinate phase decreased with increasing oil to solvent ratio in raffinate layer and increased with increasing temperature. Solvent to oil ratio in extract layer decreased with increasing temperature and increased with increasing solvent to charge oil ratio at constant temperature. Oil to solvent ratio in raffinate decreased with increasing temperature and increased with increasing solvent to charge oil ratio at constant temperature. Estimated functions are the best modeling function for prediction extraction data at various operating conditions. Mass transfer coefficient of continuous phase kc and mass transfer coefficient of dispersed phase kd are increased with increasing temperature and solvent charge to oil ratio at constant temperature. The over all mass transfer coefficient Kod is increased with increasing temperature and solvent to charge oil ratio; while Kod a is increased with temperature and decreased with solvent to charge oil ratio. Keywords: Mass transfer coefficient, solvent extraction, modeling, lube oil, furfural 1. Introduction Base oils made from crude petroleum are made up of a great variety of molecules, which contain aromatic rings, naphthenic rings, paraffin and isoparaffin chains. The hydrocarbons found in mineral oils are mainly of three general types: straight and branched–chain paraffinic compounds, polycyclic and fused–ring saturated hydrocarbons based on cyclopentane and cyclohexan prototype ring structures, collectively known as naphthenes, and aromatics, both mono and polynuclear, which are unsaturated ring structures. Selective solvent extraction offers a useful method for separating liquid mixtures[1]. Because of the large number of organic compounds contained in such mixtures, theoretical knowledge of the extraction equilibria which would be of assistance in the solution of practical problems has been meager. There are many theoretical approaches to the solvent extraction of lubricating oil based on the classical laws of physical chemistry. The errors of extrapolation or interpolation in most of these theories can be traced to the use of distribution coefficients and the assumption that the extract and raffinate fractions are pure compounds. Kalichevsky[2] suggested a relation for estimating extract yield for constant number of stages as: log E = (m+nT) log S + (p+qT) …(1) Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 2 Since both solvent and oil act as solvents for each other, the modified form of Eqn.1 for calculating the solvent fraction in the raffinate as[3]: log SR = (a1+bT) log R + (c+fT) …(2) Analysis of constant temperature extraction shows that the extraction yield may be expressed as: log E = C log SE + Cl …(3) And the fraction of the total solvent loss to raffinate is: log SR = K log R + Kl …(4) Assuming a temperature effect similar to that found by Kalichevsky, Equations 3 and 4 become: log E = (ml + nl T) log SE + (pl +ql T) …(5) log SR = (al +bl T) log R + (cl +fl T) …(6) Mass Transfer studies in mixer-settler have been mostly confined to estimations of stage efficiency[4, 5]. Few investigations report data on mass transfer coefficients kc and kd. The procedure suggested for the estimation of extraction rates in mixer-settlers[6,7] involves the use of the continuous phase coefficient based on solid dissolution studies[6,8,9,10]. As for the application of the solid dissolution model to liquid-liquid systems, Jordan[10] has analyzed the results of Barker and Treybal for liquid-liquid systems by Rushton et al.[11]. The calculated continuous phase of coefficient data of Rushton et al. showed variation with impeller speed; they could be favourably compared for dispersed phase viscosity of 1 cp with the following equation[6]: kcdT/ Dc =0.052 (dR 2 N ρc / µc) 0.833 (µc /ρc Dc) 0.5 …(7) The equation was proposed on the bases of data obtained in vessels with dT = 0.5-2.5 ft, dR/ dT = 0.25-0.67 and x = 0.005-0.232. However, for high dispersed phase viscosities, viz. 10,50 and 100 cp, the data of Rushton et al.[12] showed wide deviation from the above correlation indicating a pronounced effect due to dispersed phase viscosity as well as impeller speed. The above correlation also fails to correlate data for baffled and unbaffled vessels[13]. On the basis of solid dissolution data, Calderbank[8, 9] suggests the following equation for kc: kc (µc / ρc Dc) 2/3 = 0.13 ((P/v) µc / ρc 2 )1/4 …(8) The starting point of agitation design is properly a mass transfer coefficient known empirically or from correlations in terms of parameters impeller size and rotation, power input and gas flow rate. Few correlations are in the open literature, but some have come from two of the industries that employ aerated stirred tanks on a large scale[14, 15]. The aim of this research is to obtain a representation of lubricating oil extraction system using specified regression that leads to prediction of extract yield and fraction of total solvent in raffinate phase in addition to determining individual mass transfer coefficient of continuous and dispersed phase and over all mass transfer coefficients based on dispersed phase. This is a theoretical research that depends on data base of Sadiq[16]. 2. Results and Discussion Figure1 shows the effect of solvent to oil ratio in extract phase SE on the extract yield E in different temperatures. The extract yield decreased with decreasing solvent to oil ratio in extract layer because the extraction efficiency of aromatics and poly aromatics decreased with decreasing solvent to charge oil S. Figure 1 also shows the increasing of extract yield with increasing temperature but in limitation, solvent extraction of oil is usually carried out at temperatures as close as possible to the miscibility temperature of oil-solvent system in order to reduce the necessary solvent to oil ratio and to operate at the lowest possible viscosity of the oil phase in addition to increasing solubility of undesired compounds in furfural which lead to high extract yield. The extraction temperature 212oF is the most close to the miscibility temperature of extraction system in which two phases will be kept immiscible and which allow extraction to be carried out with high extract yield. As temperature increased up to 230oF, the extract yield slightly increased which confirms that further increasing in temperature above 212oF caused the dropping of extraction efficiency because the miscibility temperature of system exceeded. Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 3 0 0.2 0.4 0.6 0.8 1 1.2 2 3 4 5 6 7 8 9 10 solvent to Oil Ratio in Extract layer (SE) E x tr a c t Y ie ld ( E ) T=158 F T=176 F T=194 F T=212 F T=230 F Solvent to Oil Ratio in Extract Layer (SE) E xt ra ct Y ie ld ( E ) Fig.1. Effect of SE on E in Extraction of Light Lube Oil by Furfural. Figure 2 shows the effect of oil to solvent ratio in raffinate layer R on the fraction of total solvent loss to raffinate layer SR in different temperatures. The fraction of total solvent in the raffinate phase decreased with increasing oil to solvent ratio in raffinate layer because the increasing solvent power (solvent to charge oil ratio) at constant temperature gives high extraction efficiency and as solvent power increased, the solvent in raffinate decreased proportionally with the decreasing of raffinate yield of oil which keeps the increase of R. The reverses of extract phase in which solvent increased, in the solvent power also increased. There is no significant effect of increasing temperature on the fraction of total solvent in the raffinate phase. Figure 3 shows the effect of temperature on the solvent to oil ratio in extract layer at a given solvent to charge oil ratio. The solvent to oil ratio in extract layer SE decreased with increasing temperature because the temperature of the extraction has a very great effect on the solubility characteristics of solvent and increasing extraction temperature increases the solubility of undesired compounds in furfural which lead to high extract yield which necessarily decreases solvent in the extract phase at constant solvent to charge oil ratio. The reverses in raffinate phase in which solvent increased with increasing temperature. While Solvent to oil ratio in extract layer increased with increasing solvent to charge oil ratio at constant temperature because the power of solvent dominates. Figure 4 shows the effect of temperature on the fraction of total solvent in raffinate layer. SR increased with increasing temperature because as temperature rose close to the miscibility temperature of oil-solvent system which increases the solubility of the undesired compounds in furfural. Decreasing raffinate yield of oil necessarily increases solvent in the raffinate phase at constant solvent to charge oil ratio. Fraction of total solvent in raffinate layer decreased with increasing solvent to charge oil ratio at constant temperature and the reason is that the dropping of temperature effect and the power of solvent dominates. While Oil to solvent ratio in raffinate decreased with increasing temperature because of the reducing solvent for extraction which is increased in raffinate phase rather than extract phase which seems to increase with increasing solvent to charge oil ratio at constant temperature as shown in Figure 5. Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 4 0 0.05 0.1 0.15 0.2 0.25 0.3 0 5 10 15 20 Oil to Solvent Ratio in Raffinate Layer (R) T=158 F T=176 F T=194 F T=212 F T=230 F F ra ct io n of T ot al So lv en t L os s to R af fi n at e L ay er ( S R ) Fig.2. Effect of R on SR in Extraction of Light Lube Oil by Furfural. Fig.3. Effect of Temperature on the Solvent to Oil Ratio in Extract Layer. 0 1 2 3 4 5 6 7 8 9 10 150 170 190 210 230 250 Temperature(F) S o lv en t to O il R at io i n E xt ra ct L ay er (S E ) Ratio 1:1 Ratio 2:1 Ratio 3:1 Ratio 4:1 So lv en t to O il R at io in E xt ra ct L ay er ( S E ) Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 5 0 0.05 0.1 0.15 0.2 0.25 0.3 150 160 170 180 190 200 210 220 230 240 Temperature(F) F ra ct io n o f t o ta l s o lv en t l o ss to R af fin at e la ye r( S R ) Ratio 1:1 Ratio 2:1 Ratio 3:1 Ratio 4:1 F ra ct io n o f T ot al S ol ve nt L os s to R af fi na te L ay er ( S R ) 0 2 4 6 8 10 12 14 16 18 150 170 190 210 230 250 Temperature(F) O il t o S o lv en t R at io i n R af fi n at e( R ") Ratio 1:1 Ratio 2:1 Ratio 3:1 Ratio 4:1 O il to S ol ve nt R at io in R af fi na te L ay er (R ) Fig.4. Effect of Temperature on the Fraction of Total Solvent in Raffinate Layer. Fig.5. Effect of Temperature on the Oil to Solvent Ratio in Raffinate. Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 6 Specified regression is applied using the experimental results of extraction lube oil with furfural and that depends on Eqns.3-6 as estimated functions and Quasi-Newton estimation method[17]. This model is applied at optimum extraction temperature 212 oF and solvent charge to oil ratio 1-4. Figures 6 and 7 show the relations of predicted vs. observed extract yield values. There is a good similarity in 1:1and 2:1 solvent charge to oil ratio; while there is some difference in 3:1 and 4:1. Figures 8 and 9 show predicted versus observed fraction of total solvent loss to raffinate layer values. There is an excellent similarity in all range of solvent charge to oil ratio. All statistical values of applied empirical equations are tabulated in Table1. The statistical values and figures refer to the high representation of these selective equations to the extraction system where the predicted and observed values are so close. Equations 3-6 are good modeling function for prediction extraction data at various operating conditions. Table 1, Statistical Values of Estimated Functions. log E = 0.75 log SE - 2.1 log E = (0.2+ 0.005l T) log SE + (0.14 - 0.02 T) log SR = - 0.82 log R - 0.48 log SR = (0.19 - 0.01T) log R + (0.14 - 0.006l T) σ (variance) 90.926% 90.926% 99.929% 99.929% R (correlation factor) 0.954 0.953 0.999 0.999 Final loss 0.026 0.026 0.0002 0.0002 E=a*SE+b 100C Predicted Values O bs er ve d V al ue s 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.24 0.30 0.36 0.42 0.48 0.54 Fig.6. Predicted vs. Observed Extract Yield Values of Extraction Lube Oil with Furfural. log E = C log SE + Cl Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 7 E=(m+n*100)*SE+(p+q*100) Predicted Values O bs er ve d V al ue s -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 Fig.7. Predicted vs. Observed Extract Yield Values of Extraction Lube Oil with Furfural. SR=k*R+s 100 Predicted Values O bs er ve d V al ue s -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 Fig.8. Predicted vs. Observed Fraction of Total Solvent Loss to Raffinate Layer Values of Extraction Lube Oil with Furfural. log E = (ml + nl T) log SE + (pl +ql T) log SR = K log R + Kl Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 8 SR=(g+d*100)*R+(h+y*100) Predicted Values O bs er ve d V al ue s -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 Fig.9. Predicted vs. Observed Fraction of Total Solvent Loss to Raffinate Layer Values of Extraction Lube Oil with Furfural. 3. Mass Transfer Coefficient in Mixer-settler Mass transfer coefficient of continuous phase is calculated from Eqn.7 as follows: kcdT/Dc = 0.052(dR 2N ρc / µc) 0.833 (µc / ρc Dc) 0.5 …(7) Physical properties such as density and viscosity of mixture are calculated from Eqns.9&10: ρm = x ρd + (1-x) ρc …(9) µm = (µc / 1-x)(1+ (6x µd / µc+ µd)) …(10) Diffusivity coefficients of solute in the continuous and dispersed phase are calculated from Eqn.11[18, 19] D = 9.96*10-16 T / µ (V) 1/3 …(11) Mass transfer coefficient of dispersed phase is calculated from Eqn.12[20]: kd = 17.9 Dd/dvs …(12) The volume surface diameter of drops dvs is calculated from Eqn.13: dvs= 6x/a …(13) Where a is calculated from Eqn.14[21]: a=25.9(Nwe) 0.5(NRe) 0.1(x) 0.84/dR …(14) Figures 10 and 11 show the effect of temperature on the mass transfer coefficient of continuous phase kc and dispersed phase kd respectively. Mass transfer coefficients of continuous and dispersed phase are increased with increasing temperature and solvent to charge oil ratio. The reason of this temperature effect is that mass transfer coefficient is directly proportional directly and a function of diffusivity which is proportional with temperature increase which necessarily leads to the increase of mass transfer coefficients. The inverse proportion of mass transfer coefficient with viscosity and density decreased with increasing temperature. On the other hand the increase of mass transfer coefficient of dispersed phase with increasing solvent to charge oil ratio at constant temperature caused by the effect of dispersed phase holds up on the interfacial area of drops and then on mean drop size that necessarily has an effect on mass transfer coefficient of dispersed phase. It is noted that the interfacial area of drops decreased with increasing solvent to charge oil ratio (or decreasing dispersed phase hold up) and this caused the mean drop size the decrease, and mass transfer coefficient of dispersed phase to increase in addition to the effect of dispersed phase hold up on density of mixture and in other word on Weber number. Also Mass transfer coefficient of continuous phase increased with increasing solvent to charge oil ratio because the effect of log SR = (al +bl T) log R + (cl +fl T) Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 9 hold up of dispersed phase on viscosity of mixture decreased with decreasing hold up at constant temperature that lead to the increasing of mass transfer coefficient of continuous phase. The overall mass transfer coefficient extraction of light lubes oil distillate fraction by furfural is calculated from Eqn.15: 1/Kod = m/kc+1/kd …(15) Figure 12 shows the effect of temperature on the overall mass transfer coefficient Kod which increases with increasing temperature and solvent to charge oil ratio; while in Figure 13 (Kod*a) increases with temperature and decreases with solvent charge to oil ratio. 0 0.1 0.2 0.3 0.4 0.5 0.6 150 170 190 210 230 250 Temperature(F) Kc (ft /h ) Ratio 2:1 Ratio 3:1 Ratio 4:1 Fig.10. Effect of Temperature on Mass Transfer Coefficient of Continuous Phase Extraction of Light Lube Oil by Furfural. 0 0.02 0.04 0.06 0.08 0.1 0.12 150 170 190 210 230 250 Temperature(F) K d (f t/ h ) Ratio 2:1 Ratio 3:1 Ratio 4:1 Fig.11. Effect of Temperature on Mass Transfer Coefficient of Dispersed Phase Extraction of Light Lube Oil by Furfural. k c (f t/ h ) k d (f t/ h) Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 10 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 150 170 190 210 230 250 Temperature(F) K o d (ft /h ) Ratio 2:1 Ratio 3:1 Ratio 4:1 Fig.12. Effect of Temperature on the Over All Mass Transfer Coefficient Extraction of Light Lube Oil by Furfural. 0 20 40 60 80 100 120 140 150 170 190 210 230 250 Temperature(F) (K o d )a (h -1 ) Ratio 2:1 Ratio 3:1 Ratio 4:1 Fig.13. Effect of Temperature on the Over All Mass Transfer Coefficient Extraction of Light Lube Oil by Furfural. K od a (h -1 ) K od (f t/ h) Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 11 4. Conclusions 1. Mathematical analysis of solvent extraction equilibria shows that the extraction yield and fraction of total solvent loss to raffinate at constant temperature extraction may be expressed by equation 3 & 4; while assuming temperature effect similar to that found by Kalichevsky, the extraction yield and fraction of total solvent loss to raffinate may be expressed by equation 5 & 6. Equations 3-6 are good predicting function for extraction data at various operating conditions. 2. Operating conditions have a significance effect on the mass transfer coefficient of continuous and dispersed phase which increased with increasing temperature and solvent to charge oil ratio. 3. The overall mass transfer coefficients Kod and Kod*a are related directly with temperature. They increases with increasing temperature but they differ in their response to solvent to charge oil ratio where Kod is increased and Kod*a is decreased. Nomenclature a Interfacial area of drop ft2/ft3 D Diffusivity, m2/s Dc Diffusivity of solute in the continuous phase, ft2/h Dd Diffusivity of solute in the dispersed phase, ft2/h dR Diameter of rotor, ft dT Vessel diameter, ft dvs Volume surface diameter of drops, ft E Extract yield kc Individual mass transfer coefficient of continuous phase, ft/h kd Individual mass transfer coefficient of dispersed phase, ft/h Kod a Over all mass transfer coefficient based on dispersed phase, h-1 M Equilibrium distribution coefficient N Speed of rotor, rph P Power consumption.ft Ibf / min R Ratio of Oil to solvent in raffinate phase S Solvent to charge oil ratio SE Ratio of solvent to oil in extract phase SR Fraction of total solvent in raffinate phase T Temperature, K V Solute molar volume, m3/g mol v Volume of mixing vessel,ft3 x Holdup of the dispersed phase a1, b, al ,bl, C, Cl, cl, c, f, K, Kl, m, n, ml, nl ,p, pl ,q, ql, Constants Greek Symbols ρc Density of continuous phase, Ib/ft3 ρm Density of mixed phase, Ib/ft3 ρd Density of dispersed phase, Ib/ft3 µ Viscosity of mixed phase, Pa.s µc Viscosity of continuous phase, Ib/ft h µm Viscosity of mixed phase, Ib/ft h 5. References [1] Denis, J., Briant, J., and Hipeaux, J.C., “Lubricant Properties Analysis and Testing”, Editions Technip, Paris, 1997. [2] Kalichevsky,V.A.,Ind.Eng.Chem.,38,1009(19 46) [3] Kalichevsky,V.A.,Natl.Petroleum News,38,R- 613(1946) [4] Takahashi, K., Nii, S., Merrories of the School of Engineering, Nagoya University, Science Research, 51(1), 1999. [5] Wichterlova, J., Rod, V., Chemical Engineering Science, 54, 4041(1999). [6] Mostaedi,M.,Safdari,S. and Moosavian,M.,Braz.J.Chem.Eng.,25(3),2008 [7] Treybal,R.E.,Chem.Eng.Prog.,60(5),77(1964) ;62(9),67(1966) [8] Hossein,A.,Mohammad,A. and Reza,S.R,Iran.J.Chem.Eng.,25(4)2006. [9] Calderbank,P.H. and M.B.Moo- Young,Chem.Eng.,16,39(1961) [10] Jordan,D.G.,Chem.Process Development, Part 2,New York(1968) Hussain K. Hussain! Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) 12 [11] Rushton,J.H.s.Nagata and T.B.Rooney,A.I.Cb.E.Jl,10,298(1964) [12] Rushton,J.H.,E.W.Costich and H.J.Everett,Chem.Eng,Prog.,52,515(1956) [13] Treybal,R.E.,Ind.Eng.Chem.,53,597(1961) [14] Stanley,M.W.,"Chemical Process Equipment Selection and Design",1990 [15] Treybal,R.E.,"Mass Transfer operations",Mc Graw-Hill,New York,1980 [16] Sadiq, R. J,M.Sc.Thesis, Baghdad University (2006). [17] Stanley,C.L. and Mary,C.,"Mathematics for Engineers and Applied Scientists",1985 [18] Warren,L.M.,Julian,C.S,Peter,H.,"Unit Operations of Chemical Engineering", Mc Graw-Hill,2001 [19] Christie,J.G,"Transport Processes and Unit Operation",1983 [20] Treybal, R. E., Chem.Eng. Proog., 62(9), 67(1966). [21] Kafarov, V. V. and M. Babanov, Zb. Prikl. Kbim., 32, 789(1959). )2010( 13-1، صفحة 1، العدد 6مجلة الخوارزمي الھندسیة المجلد حسین قاسم حسین 13 عملیة االستخالصتخمین ناتج االستخالص و معامل انتقال المادة في بالمذیب لزیت التزییت حسین قاسم حسین جامعة بغداد/ كلیة الھندسة / الھندسة الكیمیاویةقسم الخالصة ة ن عملی ن م ف المحس ت الخفی ت التزیی الفرفورال تناول ھذا البحث ایجاد عالقات لحساب الناتج والخواص لمقطع زی تخالص ب ودیالت االس تخدام م باس تت .ریاضیة ور المش ي الط ادة ف ال الم ل انتق تمر ومعام ور المس ي الط ادة ف ال الم ل انتق ل تم دراسة انتقال المادة في نظام الخلط والفصل تم حساب معام ومعام ط انتقال المادة الكلي لعملیة االستخالص لمقطع زیت التزیت الخفیف ده وخالئ ى ح ل عل ات ك بواسطة الفرفورال باالضافة الى كل الخواص الفیزیاویة للمركب ر °١١٠الى ٧٠تم دراسة المتغیرات المؤثرة على عملیة االستخالص والتي ھي درجة حرارة االستخالص وتتراوح من . نظام االستخالص ر األخ م، والمتغی . ١:٤ الى ١:١ھو نسبة المذیب الى الزیت وتتراوح من رارة ة الح ادة درج زداد بزی بة . اظھرت نتائج ھذا البحث بان ناتج االستخالص یقل بنقصان نسبة المذیب الى زیت التزییت في طبقة المستخلص وی إن نس رارة ة الح ادة درح ي .المذیب الكلي في طور الرافیینت یقل بزیادة نسبة زیت التزییت الى المذیب في طبقة الرافیینت ویزداد بزی ت ف ى الزی ذیب إل بة الم إن نس ي . یقل بزیادة درجة الحرارة ویزداد بزیادة نسبة المذیب الى زیت التزییت اللقیم بثبوت درجة الحرارةطور االستخالص ذیب ف ى الم ت ال ت التزیی إن نسبة زی .وت درجة الحرارة الرافینیت یقل بزیادة درجة الحرارة ویزداد بزیادة نسبة المذیب الى زیت التزییت اللقیم بثب .ان الدوال الریاضیة التي تم اقتراحھا ھي تعتبر من افضل المودیالت الریاضیة لتمثیل نظام االستخالص ھذا بمختلف الظروف التشغیلیة لى زیت التزییت اللقیم بثبوت یزداد معامل انتقال المادة في الطور المستمر ومعامل انتقال المادة في الطور المشتت بزیادة درجة الحرارة ونسبة المذیب ا بزیادة درجة الحرارة ویقل a Kodیزداد معامل انتقال المادة الكلي بزیادة درجة الحرارة ونسبة المذیب الى زیت التزییت اللقیم بینما یزداد. درجة الحرارة .بزیادة نسبة المذیب الى زیت التزییت اللقیم 0 0.2 0.4 0.6 0.8 1 1.2 2345678910 solvent to Oil Ratio in Extract layer (SE) Extract Yield (E) T=158 F T=176 F T=194 F T=212 F T=230 F 0 0.05 0.1 0.15 0.2 0.25 0.3 05101520 Oil to Solvent Ratio in Raffinate Layer (R) T=158 F T=176 F T=194 F T=212 F T=230 F 0 1 2 3 4 5 6 7 8 9 10 150170190210230250 Temperature(F) Solvent to Oil Ratio in Extract Layer(SE) Ratio 1:1 Ratio 2:1 Ratio 3:1 Ratio 4:1 Linear (Ratio 1:1) Linear (Ratio 2:1) Linear (Ratio 3:1) Linear (Ratio 4:1) 0 0.05 0.1 0.15 0.2 0.25 0.3 150160170180190200210220230240 Temperature(F) Fraction of total solvent loss to Raffinate layer(SR) Ratio 1:1 Ratio 2:1 Ratio 3:1 Ratio 4:1 Series5 Series6 Series7 Linear (Ratio 4:1) Linear (Ratio 3:1) Linear (Ratio 2:1) Linear (Ratio 1:1) 0 2 4 6 8 10 12 14 16 18 150170190210230250 Temperature(F) Oil to Solvent Ratio in Raffinate(R") Ratio 1:1 Ratio 2:1 Ratio 3:1 Ratio 4:1 Linear (Ratio 1:1) Linear (Ratio 2:1) Linear (Ratio 4:1) Linear (Ratio 3:1) E=a*SE+b 100C Predicted Values Observed Values 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.24 0.30 0.36 0.42 0.48 0.54 E=(m+n*100)*SE+(p+q*100) Predicted Values Observed Values -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 SR=k*R+s 100 Predicted Values Observed Values -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 SR=(g+d*100)*R+(h+y*100) Predicted Values Observed Values -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 0 0.1 0.2 0.3 0.4 0.5 0.6 150170190210230250 Temperature(F) Kc(ft/h) Ratio 2:1 Ratio 3:1 Ratio 4:1 0 0.02 0.04 0.06 0.08 0.1 0.12 150170190210230250 Temperature(F) Kd(ft/h) Ratio 2:1 Ratio 3:1 Ratio 4:1 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 150170190210230250 Temperature(F) Kod(ft/h) Ratio 2:1 Ratio 3:1 Ratio 4:1 0 20 40 60 80 100 120 140 150170190210230250 Temperature(F) ( Kod ) a ( h - 1 ) Ratio 2:1 Ratio 3:1 Ratio 4:1 Introduction Hussain K. Hussain Al-Khwarizmi Engineering Journal, Vol.6, No.1, PP 1-13 (2010) Al-Khwarizmi Engineering Journal Al-Khwarizmi Engineering Journal, Vol. 6, No. 1, PP 1-13 (2010) Estimation of Extract Yield and Mass Transfer Coefficient in Solvent Extraction of Lubricating Oil Hussain K. Hussain Department of Chemical Engineering/ College of Engineering/University of Baghdad (Received 12 April 2009: accepted 13 July 2009) Abstract An investigation was conducted to suggest relations for estimating yield and properties of the improved light lubricating oil fraction produced from furfural extraction process by using specified regression. Mass transfer in mixer-settler has been studied. Mass transfer coefficient of continuous phase, mass transfer coefficient of dispersed phase and the overall mass transfer coefficient extraction of light lubes oil distillate fraction by furfural are calculated in addition to all physical properties of individual components and the extraction mixtures. The effect of extraction variables were studied such as extraction temperature which ranges from 70 to 110°C and solvent to oil ratio which ranges from 1:1 to 4:1 (wt/wt) were studied. The results of this investigation show that the extract yield E decreased with decreasing solvent to oil ratio in extract layer and increased with increasing temperature. The fraction of total solvent in the raffinate phase decreased with increasing oil to solvent ratio in raffinate layer and increased with increasing temperature. Solvent to oil ratio in extract layer decreased with increasing temperature and increased with increasing solvent to charge oil ratio at constant temperature. Oil to solvent ratio in raffinate decreased with increasing temperature and increased with increasing solvent to charge oil ratio at constant temperature. Estimated functions are the best modeling function for prediction extraction data at various operating conditions. Mass transfer coefficient of continuous phase kc and mass transfer coefficient of dispersed phase kd are increased with increasing temperature and solvent charge to oil ratio at constant temperature. The over all mass transfer coefficient Kod is increased with increasing temperature and solvent to charge oil ratio; while Kod a is increased with temperature and decreased with solvent to charge oil ratio. Keywords: Mass transfer coefficient, solvent extraction, modeling, lube oil, furfural 1. Introduction Base oils made from crude petroleum are made up of a great variety of molecules, which contain aromatic rings, naphthenic rings, paraffin and isoparaffin chains. The hydrocarbons found in mineral oils are mainly of three general types: straight and branched–chain paraffinic compounds, polycyclic and fused–ring saturated hydrocarbons based on cyclopentane and cyclohexan prototype ring structures, collectively known as naphthenes, and aromatics, both mono and polynuclear, which are unsaturated ring structures. Selective solvent extraction offers a useful method for separating liquid mixtures[1]. Because of the large number of organic compounds contained in such mixtures, theoretical knowledge of the extraction equilibria which would be of assistance in the solution of practical problems has been meager. There are many theoretical approaches to the solvent extraction of lubricating oil based on the classical laws of physical chemistry. The errors of extrapolation or interpolation in most of these theories can be traced to the use of distribution coefficients and the assumption that the extract and raffinate fractions are pure compounds. Kalichevsky[2] suggested a relation for estimating extract yield for constant number of stages as: log E = (m+nT) log S + (p+qT) …(1) Since both solvent and oil act as solvents for each other, the modified form of Eqn.1 for calculating the solvent fraction in the raffinate as[3]: log SR = (a1+bT) log R + (c+fT) …(2) Analysis of constant temperature extraction shows that the extraction yield may be expressed as: log E = C log SE + Cl …(3) And the fraction of the total solvent loss to raffinate is: log SR = K log R + Kl …(4) Assuming a temperature effect similar to that found by Kalichevsky, Equations 3 and 4 become: log E = (ml + nl T) log SE + (pl +ql T) …(5) log SR = (al +bl T) log R + (cl +fl T) …(6) Mass Transfer studies in mixer-settler have been mostly confined to estimations of stage efficiency[4, 5]. Few investigations report data on mass transfer coefficients kc and kd. The procedure suggested for the estimation of extraction rates in mixer-settlers[6,7] involves the use of the continuous phase coefficient based on solid dissolution studies[6,8,9,10]. As for the application of the solid dissolution model to liquid-liquid systems, Jordan[10] has analyzed the results of Barker and Treybal for liquid-liquid systems by Rushton et al.[11]. The calculated continuous phase of coefficient data of Rushton et al. showed variation with impeller speed; they could be favourably compared for dispersed phase viscosity of 1 cp with the following equation[6]: kcdT/ Dc =0.052 (dR2 N ρc / µc) 0.833 (µc /ρc Dc) 0.5 …(7) The equation was proposed on the bases of data obtained in vessels with dT = 0.5-2.5 ft, dR/ dT = 0.25-0.67 and x = 0.005-0.232. However, for high dispersed phase viscosities, viz. 10,50 and 100 cp, the data of Rushton et al.[12] showed wide deviation from the above correlation indicating a pronounced effect due to dispersed phase viscosity as well as impeller speed. The above correlation also fails to correlate data for baffled and unbaffled vessels[13]. On the basis of solid dissolution data, Calderbank[8, 9] suggests the following equation for kc: kc (µc / ρc Dc)2/3 = 0.13 ((P/v) µc / ρc2 )1/4 …(8) The starting point of agitation design is properly a mass transfer coefficient known empirically or from correlations in terms of parameters impeller size and rotation, power input and gas flow rate. Few correlations are in the open literature, but some have come from two of the industries that employ aerated stirred tanks on a large scale[14, 15]. The aim of this research is to obtain a representation of lubricating oil extraction system using specified regression that leads to prediction of extract yield and fraction of total solvent in raffinate phase in addition to determining individual mass transfer coefficient of continuous and dispersed phase and over all mass transfer coefficients based on dispersed phase. This is a theoretical research that depends on data base of Sadiq[16]. 2. Results and Discussion Figure1 shows the effect of solvent to oil ratio in extract phase SE on the extract yield E in different temperatures. The extract yield decreased with decreasing solvent to oil ratio in extract layer because the extraction efficiency of aromatics and poly aromatics decreased with decreasing solvent to charge oil S. Figure 1 also shows the increasing of extract yield with increasing temperature but in limitation, solvent extraction of oil is usually carried out at temperatures as close as possible to the miscibility temperature of oil-solvent system in order to reduce the necessary solvent to oil ratio and to operate at the lowest possible viscosity of the oil phase in addition to increasing solubility of undesired compounds in furfural which lead to high extract yield. The extraction temperature 212oF is the most close to the miscibility temperature of extraction system in which two phases will be kept immiscible and which allow extraction to be carried out with high extract yield. As temperature increased up to 230oF, the extract yield slightly increased which confirms that further increasing in temperature above 212oF caused the dropping of extraction efficiency because the miscibility temperature of system exceeded. Fig.1. Effect of SE on E in Extraction of Light Lube Oil by Furfural. Figure 2 shows the effect of oil to solvent ratio in raffinate layer R on the fraction of total solvent loss to raffinate layer SR in different temperatures. The fraction of total solvent in the raffinate phase decreased with increasing oil to solvent ratio in raffinate layer because the increasing solvent power (solvent to charge oil ratio) at constant temperature gives high extraction efficiency and as solvent power increased, the solvent in raffinate decreased proportionally with the decreasing of raffinate yield of oil which keeps the increase of R. The reverses of extract phase in which solvent increased, in the solvent power also increased. There is no significant effect of increasing temperature on the fraction of total solvent in the raffinate phase. Figure 3 shows the effect of temperature on the solvent to oil ratio in extract layer at a given solvent to charge oil ratio. The solvent to oil ratio in extract layer SE decreased with increasing temperature because the temperature of the extraction has a very great effect on the solubility characteristics of solvent and increasing extraction temperature increases the solubility of undesired compounds in furfural which lead to high extract yield which necessarily decreases solvent in the extract phase at constant solvent to charge oil ratio. The reverses in raffinate phase in which solvent increased with increasing temperature. While Solvent to oil ratio in extract layer increased with increasing solvent to charge oil ratio at constant temperature because the power of solvent dominates. Figure 4 shows the effect of temperature on the fraction of total solvent in raffinate layer. SR increased with increasing temperature because as temperature rose close to the miscibility temperature of oil-solvent system which increases the solubility of the undesired compounds in furfural. Decreasing raffinate yield of oil necessarily increases solvent in the raffinate phase at constant solvent to charge oil ratio. Fraction of total solvent in raffinate layer decreased with increasing solvent to charge oil ratio at constant temperature and the reason is that the dropping of temperature effect and the power of solvent dominates. While Oil to solvent ratio in raffinate decreased with increasing temperature because of the reducing solvent for extraction which is increased in raffinate phase rather than extract phase which seems to increase with increasing solvent to charge oil ratio at constant temperature as shown in Figure 5. Fig.2. Effect of R on SR in Extraction of Light Lube Oil by Furfural. Fig.3. Effect of Temperature on the Solvent to Oil Ratio in Extract Layer. Fig.4. Effect of Temperature on the Fraction of Total Solvent in Raffinate Layer. Fig.5. Effect of Temperature on the Oil to Solvent Ratio in Raffinate. Specified regression is applied using the experimental results of extraction lube oil with furfural and that depends on Eqns.3-6 as estimated functions and Quasi-Newton estimation method[17]. This model is applied at optimum extraction temperature 212 oF and solvent charge to oil ratio 1-4. Figures 6 and 7 show the relations of predicted vs. observed extract yield values. There is a good similarity in 1:1and 2:1 solvent charge to oil ratio; while there is some difference in 3:1 and 4:1. Figures 8 and 9 show predicted versus observed fraction of total solvent loss to raffinate layer values. There is an excellent similarity in all range of solvent charge to oil ratio. All statistical values of applied empirical equations are tabulated in Table1. The statistical values and figures refer to the high representation of these selective equations to the extraction system where the predicted and observed values are so close. Equations 3-6 are good modeling function for prediction extraction data at various operating conditions. Table 1, Statistical Values of Estimated Functions. log E = 0.75 log SE - 2.1 log E = (0.2+ 0.005l T) log SE + (0.14 - 0.02 T) log SR = - 0.82 log R - 0.48 log SR = (0.19 - 0.01T) log R + (0.14 - 0.006l T) σ (variance) 90.926% 90.926% 99.929% 99.929% R (correlation factor) 0.954 0.953 0.999 0.999 Final loss 0.026 0.026 0.0002 0.0002 Fig.6. Predicted vs. Observed Extract Yield Values of Extraction Lube Oil with Furfural. Fig.7. Predicted vs. Observed Extract Yield Values of Extraction Lube Oil with Furfural. Fig.8. Predicted vs. Observed Fraction of Total Solvent Loss to Raffinate Layer Values of Extraction Lube Oil with Furfural. Fig.9. Predicted vs. Observed Fraction of Total Solvent Loss to Raffinate Layer Values of Extraction Lube Oil with Furfural. 3. Mass Transfer Coefficient in Mixer-settler Mass transfer coefficient of continuous phase is calculated from Eqn.7 as follows: kcdT/Dc = 0.052(dR2N ρc / µc) 0.833 (µc / ρc Dc) 0.5 …(7) Physical properties such as density and viscosity of mixture are calculated from Eqns.9&10: ρm = x ρd + (1-x) ρc …(9) µm = (µc / 1-x)(1+ (6x µd / µc+ µd)) …(10) Diffusivity coefficients of solute in the continuous and dispersed phase are calculated from Eqn.11[18, 19] D = 9.96*10-16 T / µ (V) 1/3 …(11) Mass transfer coefficient of dispersed phase is calculated from Eqn.12[20]: kd = 17.9 Dd/dvs …(12) The volume surface diameter of drops dvs is calculated from Eqn.13: dvs= 6x/a …(13) Where a is calculated from Eqn.14[21]: a=25.9(Nwe) 0.5(NRe) 0.1(x) 0.84/dR …(14) Figures 10 and 11 show the effect of temperature on the mass transfer coefficient of continuous phase kc and dispersed phase kd respectively. Mass transfer coefficients of continuous and dispersed phase are increased with increasing temperature and solvent to charge oil ratio. The reason of this temperature effect is that mass transfer coefficient is directly proportional directly and a function of diffusivity which is proportional with temperature increase which necessarily leads to the increase of mass transfer coefficients. The inverse proportion of mass transfer coefficient with viscosity and density decreased with increasing temperature. On the other hand the increase of mass transfer coefficient of dispersed phase with increasing solvent to charge oil ratio at constant temperature caused by the effect of dispersed phase holds up on the interfacial area of drops and then on mean drop size that necessarily has an effect on mass transfer coefficient of dispersed phase. It is noted that the interfacial area of drops decreased with increasing solvent to charge oil ratio (or decreasing dispersed phase hold up) and this caused the mean drop size the decrease, and mass transfer coefficient of dispersed phase to increase in addition to the effect of dispersed phase hold up on density of mixture and in other word on Weber number. Also Mass transfer coefficient of continuous phase increased with increasing solvent to charge oil ratio because the effect of hold up of dispersed phase on viscosity of mixture decreased with decreasing hold up at constant temperature that lead to the increasing of mass transfer coefficient of continuous phase. The overall mass transfer coefficient extraction of light lubes oil distillate fraction by furfural is calculated from Eqn.15: 1/Kod = m/kc+1/kd …(15) Figure 12 shows the effect of temperature on the overall mass transfer coefficient Kod which increases with increasing temperature and solvent to charge oil ratio; while in Figure 13 (Kod*a) increases with temperature and decreases with solvent charge to oil ratio. Fig.10. Effect of Temperature on Mass Transfer Coefficient of Continuous Phase Extraction of Light Lube Oil by Furfural. Fig.11. Effect of Temperature on Mass Transfer Coefficient of Dispersed Phase Extraction of Light Lube Oil by Furfural. Fig.12. Effect of Temperature on the Over All Mass Transfer Coefficient Extraction of Light Lube Oil by Furfural. Fig.13. Effect of Temperature on the Over All Mass Transfer Coefficient Extraction of Light Lube Oil by Furfural. 4. Conclusions 1. Mathematical analysis of solvent extraction equilibria shows that the extraction yield and fraction of total solvent loss to raffinate at constant temperature extraction may be expressed by equation 3 & 4; while assuming temperature effect similar to that found by Kalichevsky, the extraction yield and fraction of total solvent loss to raffinate may be expressed by equation 5 & 6. Equations 3-6 are good predicting function for extraction data at various operating conditions. 2. Operating conditions have a significance effect on the mass transfer coefficient of continuous and dispersed phase which increased with increasing temperature and solvent to charge oil ratio. 3. The overall mass transfer coefficients Kod and Kod*a are related directly with temperature. They increases with increasing temperature but they differ in their response to solvent to charge oil ratio where Kod is increased and Kod*a is decreased. Nomenclature a Interfacial area of drop ft2/ft3 D Diffusivity, m2/s Dc Diffusivity of solute in the continuous phase, ft2/h Dd Diffusivity of solute in the dispersed phase, ft2/h dR Diameter of rotor, ft dT Vessel diameter, ft dvs Volume surface diameter of drops, ft E Extract yield kc Individual mass transfer coefficient of continuous phase, ft/h kd Individual mass transfer coefficient of dispersed phase, ft/h Kod a Over all mass transfer coefficient based on dispersed phase, h-1 M Equilibrium distribution coefficient N Speed of rotor, rph P Power consumption.ft Ibf / min R Ratio of Oil to solvent in raffinate phase S Solvent to charge oil ratio SE Ratio of solvent to oil in extract phase SR Fraction of total solvent in raffinate phase T Temperature, K V Solute molar volume, m3/g mol v Volume of mixing vessel,ft3 x Holdup of the dispersed phase a1, b, al ,bl, C, Cl, cl, c, f, K, Kl, m, n, ml, nl ,p, pl ,q, ql, Constants Greek Symbols ρc Density of continuous phase, Ib/ft3 ρm Density of mixed phase, Ib/ft3 ρd Density of dispersed phase, Ib/ft3 µ Viscosity of mixed phase, Pa.s µc Viscosity of continuous phase, Ib/ft h µm Viscosity of mixed phase, Ib/ft h 5. 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Kbim., 32, 789(1959). تخمين ناتج الاستخلاص و معامل انتقال المادة في عملية الاستخلاص بالمذيب لزيت التزييت حسين قاسم حسين قسم الهندسة الكيمياوية / كلية الهندسة / جامعة بغداد الخلاصة تناول هذا البحث ايجاد علاقات لحساب الناتج والخواص لمقطع زيت التزييت الخفيف المحسن من عملية الاستخلاص بالفرفورال باستخدام موديلات رياضية.تم دراسة انتقال المادة في نظام الخلط والفصل تم حساب معامل انتقال المادة في الطور المستمر ومعامل انتقال المادة في الطور المشتت ومعامل انتقال المادة الكلي لعملية الاستخلاص لمقطع زيت التزيت الخفيف بواسطة الفرفورال بالاضافة الى كل الخواص الفيزياوية للمركبات كل على حده وخلائط نظام الاستخلاص . تم دراسة المتغيرات المؤثرة على عملية الاستخلاص والتي هي درجة حرارة الاستخلاص وتتراوح من 70 الى 110°م، والمتغير الأخر هو نسبة المذيب الى الزيت وتتراوح من 1:1 الى 1:4 . اظهرت نتائج هذا البحث بان ناتج الاستخلاص يقل بنقصان نسبة المذيب الى زيت التزييت في طبقة المستخلص ويزداد بزيادة درجة الحرارة . إن نسبة المذيب الكلي في طور الرافيينت يقل بزيادة نسبة زيت التزييت الى المذيب في طبقة الرافيينت ويزداد بزيادة درحة الحرارة .إن نسبة المذيب إلى الزيت في طور الاستخلاص يقل بزيادة درجة الحرارة ويزداد بزيادة نسبة المذيب الى زيت التزييت اللقيم بثبوت درجة الحرارة. إن نسبة زيت التزييت الى المذيب في الرافينيت يقل بزيادة درجة الحرارة ويزداد بزيادة نسبة المذيب الى زيت التزييت اللقيم بثبوت درجة الحرارة . ان الدوال الرياضية التي تم اقتراحها هي تعتبر من افضل الموديلات الرياضية لتمثيل نظام الاستخلاص هذا بمختلف الظروف التشغيلية. يزداد معامل انتقال المادة في الطور المستمر ومعامل انتقال المادة في الطور المشتت بزيادة درجة الحرارة ونسبة المذيب الى زيت التزييت اللقيم بثبوت درجة الحرارة. يزداد معامل انتقال المادة الكلي بزيادة درجة الحرارة ونسبة المذيب الى زيت التزييت اللقيم بينما يزدادa Kod بزيادة درجة الحرارة ويقل بزيادة نسبة المذيب الى زيت التزييت اللقيم. Fraction of Total Solvent Loss to Raffinate Layer (SR) Solvent to Oil Ratio in Extract Layer (SE) Fraction of Total Solvent Loss to Raffinate Layer (SR) Solvent to Oil Ratio in Extract Layer (SE) Oil to Solvent Ratio in Raffinate Layer (R) k c (ft/h) kd (ft/h) Kod (ft/h) Kod a (h-1) log E = C log SE + Cl log E = (ml + nl T) log SE + (pl +ql T) log SR = K log R + Kl log SR = (al +bl T) log R + (cl +fl T) Extract Yield (E) � EMBED PBrush ��� PAGE 6 _1260690138 _1260690492 _1260691110 _1260688596 _1173207870