Aromatics Extraction with Sulfolane from Reformate Gasoline —Measurement of Liquid-Liquid Equilibrium and Extraction Rate—
180 Journal of the Japan Petroleum Institute, 52, (4), 180-189 (2009)
[Regular Paper] Aromatics Extraction with Sulfolane from Reformate Gasoline —Measurement of Liquid-liquid Equilibrium and Extraction Rate—
Hiroaki Habaki†1)＊, Ryuichi Egashira†1), and Junjiro Kawasaki†2)
†1) Dept. of Chemical Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, JAPAN †2) Dept. of Chemical Engineering, Thammasat University, Bangkok, 12120, THAILAND
(Received June 4, 2008)
Aromatics extraction was investigated using aqueous solution of sulfolane as the solvent phase and model gaso- line, consisting of a benzene, toluene, xylene and hexane mixture, and reformate gasoline as the feed phase. Firstly, the liquid-liquid equilibrium was measured to examine the distribution coefficient and the separation selectivity of aromatics relative to hexane. The distribution coefficients and selectivities of benzene were the highest, followed by those of toluene and xylene. Increased water content of the solvent phase reduced the dis- tribution coefficients and increased the selectivities. The measured equilibria were compared with the results estimated by the UNIFAC method. Countercurrent extraction was conducted, using a packed column with glass Rashig rings as the contactor. The solvent and feed phases were contacted as the continuous and dispersed phases, respectively, and the flow rates of both phases and the water content in the solvent phase were selected as experi- mental parameters to examine the yield, separation selectivity and volumetric overall mass transfer coefficient. The selectivities for benzene were the highest, followed by toluene and xylene. In the case of extraction from the reformate gasoline with 9 wt％ water content in the solvent phase, the selectivity for benzene was approximately equal to 20, showing higher selectivities for aromatic components. The volumetric overall mass transfer co- efficients were mainly affected by the flow rate of the continuous phase and the mass transfer resistance in the continuous phase was the controlling factor in the overall mass transfer resistance.
Keywords Aromatic extraction, Reformate gasoline, Sulfolane, Packed column extractor, Extraction rate
1. Introduction urements must be fully investigated and the rate param- eters should be also obtained for the development of the Aromatics such as benzene, toluene and xylene are extraction process. essential in many areas of the chemical industry, and Sulfolane was invented as a solvent for aromatics demands are still growing with the expansion of poten- recovery, and the sulfolane process was developed by tial markets for engineering plastics and chemicals. the Shell Oil Company1), and remains a proprietary The conventional processes for aromatic separation/ process. The details of extraction process have not recovery involve liquid-liquid extraction, and so many been fully reported and only process performances have types of solvents have been studied, such as sulfolane1), been published. Some research has been reported on N-methylpyrrolidone2),3), N-formylmorpoline4),5), the extraction rates of aromatics, mostly on measure- dimethyl sulfoxide6) and many other organic solvents. ments of separation with model oil phases. Some Sulfolane is one of the most common solvents and the results have described reformate naphtha fractions uti- Sulfolane process, developed by the Shell Oil lized as the feed oil phases10),11), but the fundamental Company1), is one of the most famous commercial proc- data of the actual system are still inadequate. esses for the recovery of aromatics. Various research This study analyzed the multi-component extraction findings on liquid-liquid equilibrium measurements behaviors of reformate gasoline used as the feed oil have been published7)～9). The separation performance phase and sulfolane as the solvent phase. Reformate of sulfolane extraction was compared with the liquid gasoline, a gasoline fraction rich in aromatic compo- membrane separation technique, but did not involve the nents such as benzene, toluene and xylene, is a multi- extraction rates9). However, the extraction rate meas- component system which can be expected to make the analysis of the extraction behaviors more difficult and ＊ To whom correspondence should be addressed. complicated. To overview the extraction behaviors in ＊ E-mail: [email protected] the multi-component system, the fundamental parame-
J. Jpn. Petrol. Inst., Vol. 52, No. 4, 2009 181 ters of the equilibrium and extraction rate were empiri- column maintained at 353 K for the initial 10 min, and cally examined. Firstly, the liquid-liquid equilibrium then increased at 5 K/min up to 423 K. A Karl Fischer was experimentally measured to obtain the trends of aquameter (KYOTO ELECTRONICS MKC-501) was hydrocarbon distributions between the sulfolane aque- used with dehydrated methanol of HYDRANAL meth- ous and oil phases. The UNIFAC method was em- anol and titration solution of HYDRANAL composite ployed to outline the liquid-liquid equilibrium trend and 5, purchased from Sigma-Aldrich Co., to measure the the extraction behaviors were analyzed. The packed water concentration of each solution. column was employed as one of the most common con- 2. 2. Continuous Extraction tactors for the extraction operations, and the extraction The material systems and experimental conditions rates of the hydrocarbons were measured. The extrac- for the continuous extraction experiments are summa- tion rate was analyzed based on the mass transfer rized in Table 3 and the experimental apparatus is phenomena in the multicomponent system and the shown in Fig. 1. The model and reformate gasolines liquid-liquid equilibrium data. were used as the feed oil, with compositions selected as for the equilibrium measurement. A packed glass col- 2. Experimental umn, 2.7×10-2 m (i.d.)×0.5 m (high), was used as the main contacting column. Glass Rashig ring packings 2. 1. Extraction Equilibrium were used to height 0.1 m in the column. The solvent Extraction equilibrium was measured between the and feed solutions were introduced from the top and aqueous sulfolane solutions and gasolines, and the bottom of the column, respectively. A distributor was experimental conditions and the compositions of the used for feed phase introduction to disperse the feed model and reformate gasolines are listed in Tables 1 solution in the column. After reaching the steady state, and 2, respectively. All chemicals were special grade the solvent and feed solutions, and extract and raffinate and purchased from Wako Pure Chemical Ind., Ltd. phases, were sampled and analyzed by the same methods The aqueous solution of sulfolane was used as the sol- used for the extraction equilibrium measurements. vent phase. The water composition was varied to en- hance the selective dissolution of the aromatics relative to the paraffins. The model gasoline was prepared based on the reformate gasoline. The compositions of benzene, toluene and xylene were adjusted to be equiv- alent to those in the reformate gasoline, and the other representative component was hexane. The specified Table 2 Compositions of Selected Components in Feed Phases amounts of the aqueous and oil phases were put in con- (mass fraction) ical flasks with screw tops, and continuously shaken in Component Model gasoline Reformate gasoline the isothermal bath for 24 h, and assumed to have reached the equilibrium condition, as shown in Table 1. Benzene 0.077 0.0647 Toluene 0.20 0.238 The two phases were then separated in a separating fun- Xylene 0.26 (meta) 0.264 nel. The obtained solutions were analyzed by gas n-Hexane 0.46 0.0364 chromatography (HITACHI GC-663-50) with a BX-1 others 0 0.398
Table 1 Experimental Conditions of Liquid-liquid Equilibrium Measurement
Feed phase model gasoline and reformate gasoline Solvent phase aqueous solution of sulfolane Temperature [K] 303 Initial concentration of sulfolane in solvent phase [—] 0.88-0.98 (mass fraction) Mass ratio of aqueous phase and oil phase(＝S/F) [—] 0.42-6.3 Operation time [h] 24
Table 3 Experimental Conditions of Countercurrent Extraction with Packed Column
Feed phase model gasoline and reformate gasoline Solvent phase aqueous solution of sulfolane Initial concentration of sulfolane in solvent phase [—] 0.91, 0.98 (mass fraction) Height of column [m] 0.1 Inner diameter of column [m] 0.027 -1 -2 Flow rate of feed phase (Rb, dispersed phase) [kg・h ・m ] 1700-6800 -1 -2 Flow rate of solvent phase (Et, continuous phase) [kg・h ・m ] 600-1700 Temperature [K] 303
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y 0.91, M: model gasoline, Ref: reformate gasoline. Fig. 1 Schematic Diagram of Experimental Apparatus for W,0＝ Continuous Extraction Fig. 3 Effects of Concentration of Each Component in Oil Phase, xi, on Distribution Coefficient, m i
reduced the mi values for all hydrocarbon components. The mi values of the hydrocarbons were smaller than unity, and those of the aromatics were approximately ten times greater than the values of hexane. The mi values of each aromatic compound remained constant in this measurement range, and showed only slight dif- ferences between the model and reformate gasolines. Although the hexane mass fractions were so different in the model and reformate gasolines, the mi values were approximately identical. The mi values of sulfolane and water were approximately similar, and much larger than those of hydrocarbons. Only small amounts of water can dissolve into the hydrocarbon phase, so the xi ranges of water and sulfolane were very different. Figure 4 shows the effects of water content on the sep- aration selectivities of aromatic component relative to hexane, βi,Hx, defined as follows, yW,0＝0.98, M: model gasoline, Ref: reformate gasoline. yi xi βi,Hx = (2) Fig. 2 Effects of Concentration of Each Component in Oil Phase, yHx xHx xi, on Distribution Coefficient, m i The βi,Hx values increased with yW,0 and were largest for benzene, approximately 30 for model gasoline and 20 3. Results and Discussion for reformate gasoline. This trend indicates that extraction with sulfolane solvent can be expected to 3. 1. Extraction Equilibrium achieve higher separation performance. Generally, Figures 2 and 3 show the equilibrium measurement water content has a large effect on the polarity of the results and the distribution coefficient, mi, defined by solvent, affecting extraction rates, yields, selectivities the following Eq. (1), and other parameters of extraction, and the effects can be investigated by countercurrent extraction experi- mi = yi xi (1) ments. where xi and yi are the mass fractions of component i in The estimation of equilibrium is the most important the oil and aqueous phases, respectively. The meas- parameter for process design. The UNIFAC method is ured mass fractions were within 0.01 errors in the mass one of the well-known procedures for estimation of balance of each component. Increase in water content activity coefficients, as summarized in the Appendix,
J. Jpn. Petrol. Inst., Vol. 52, No. 4, 2009 183 and various results have been reported for the binary or values, and the other compositions were averaged out in ternary systems of sulfolane and hydrocarbons. In the proportion to the measured values. general sulfolane extraction process, the solvent should Figure 5(a) compares the estimation and the experi- contain a small amount of water to enhance the separa- mental results. The estimation fully predicted the be- tion selectivities of aromatics. UNIFAC parameters haviors of aromatics, but the mis of hexane were higher have been reported, including those of sulfolane, water, than the experimental results. This study aimed to ex- aromatics and paraffins7). Liquid-liquid equilibrium amine the hydrocarbon extraction rates so the parame- estimation by the UNIFAC method was conducted with ters relevant to hydrocarbons were corrected (see these parameters to check the application potential for Appendix). The functional groups are represented by this measurement. the interaction parameters, group volume parameters The conditions of the model gasoline and model re- and group surface area parameters. The group volume formate gasoline used in the estimation are summarized and surface area parameters are characteristic for each in Table 4. The model gasoline was the same as that functional group and the interaction parameters were used for the equilibrium measurement. The compo- selected to achieve better estimation. Among the nents and compositions in the model reformate gasoline hydrocarbons, the mi values of hexane were estimated were predetermined according to the following proce- higher than the experimental values, and the interaction dure. The components were selected from those of the parameters expressing hexane behavior were chosen to reformate gasoline, with concentrations higher than correct the underlined parameters in Table A1. 1％. The compositions of benzene, toluene, xylene Figure 5(b) compares the experimental and corrected ＊ and hexane were selected according to the measured estimation results when a 4,1 was corrected to 492.4. The parameter correction left the mi values of aromatics and hexane unchanged and closer to the experimental values, respectively, and the parameters were used in the analysis of extraction in the packed column. The estimation of water and sulfolane behaviors will not be discussed here because no interaction parameter correc- tion would be satisfactory. However, the values of the corrected parameters have no physical meaning, as de- scribed in Appendix, so that the parameters would be valid in the measurement range, and only the extraction performances of hydrocarbons are discussed below. 3. 2. Extraction in the Packed Column Figures 6 show the effects of the solvent and feed flow rates, Et and Rb, on the yield, Yi, defined as the fol- lowing Eq. (3),
Et ⋅ yi,t Yi = (3) Rb ⋅ xi,b
where E , R , xi and yi represent the flow rate of ex- Fig. 4 Effects of Initial Sulfolane Concentration on the Selectivity t b ,b ,t of Each Aromatic Component Relative to Hexane (S/F＝1.6, tract at the top of the column, the flow rate of raffinate keys are same as in Fig. 2) phases at the bottom, the mass fraction of component i
Table 4 Compositions of Model Gasolines for Equilibrium Estimation (mass fraction)
Component Model gasoline Model reformate gasoline Benzene 0.077 0.0646 Toluene 0.20 0.2209 Xylene 0.26 (meta) 0.2590 Ethylbenzene 0 0.0545 1,2,3-Trimethylbenzene 0 0.1028 n-Butane 0 0.0278 n-Pentane 0 0.0396 2-Methylbutane 0 0.0562 n-Hexane 0.46 0.0247 2-Methylpentane 0 0.0432 3-Methylpentane 0 0.0331 n-Heptane 0 0.0686
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Fig. 6 Yields of Each Component
relative to hexane, βi,Hx, was defined as follows,
yi,b xi,b βi,Hx = (4) yHx,b xHx,b (a) estimation with parameters by Magnussen et al.7), (b) estimation with corrected parameters. where xi,b, xHx,b, yi,b and yHx,b are the concentrations of component i in the raffinate phase at the bottom of col- Fig. 5 Comparison Distribution Coefficients between Experimental umn and hexane in the raffinate phase at the bottom, and Estimation Results (keys are same as in Fig. 2) and the concentrations of component i in the extract phases at the bottom of column and hexane in the ex- tract phase at the bottom, respectively. Figure 7 in the extract at the bottom and the mass fraction of shows the effects of the flow rate ratio, Et/Rb, on the component i in the raffinate phases at the bottom of the separation selectivity, βi,Hx. In all cases, the selectivity column, respectively. In all cases Yi increased with Et/ for benzene was the largest, followed by toluene and Rb, increasing the holdup of dispersed phase resulting xylene. As a general trend, the effects of Et/Rb were in larger mass transfer rate. The yield of benzene was relatively small, showing almost constant βi,Hx. The the largest, followed by toluene, xylene and hexane, in changes in Et and Rb caused the holdup changes, which the same order as the mi values. The extractions at had only small effects on βi,Hx. The values of βi,Hx de- ySul,t＝0.98 gave higher yields for hydrocarbons than creased with increased sulfolane concentration, ySul,t. those at ySul,t＝0.91. Water content in the solvent might The higher water content in the solvent phase increases increase the polarity of the solvent, so an increase in the polarity of the solvent and should affect the paraffin water content, higher yW,t, gave smaller yields of hydro- contents more than the aromatic contents; i.e. the solu- carbons. Model and reformate gasolines showed little bility of hexane in the solvent phase became much lower difference in the yields of aromatics and the value of Yi than those of other aromatics. The values of βi,Hx for for each aromatics component were approximately the the model gasoline were larger than for the reformate same. The separation selectivity for each component i gasoline because of the larger hexane concentration in
J. Jpn. Petrol. Inst., Vol. 52, No. 4, 2009 185 the feed solutions. 1 m 1 The volumetric overall mass transfer coefficient in = + (6) Kc,i kd,i kc,i the continuous phase, Kc,・i a, was defined as follows The distribution coefficient was estimated by the d(E ⋅ yi ) * UNIFAC method with the parameters corrected above. =Kc,i ⋅ a ⋅(y i - y i ) (5) dz Figures 8 and 9 show the effects of experimental con- ＊ where y i is the hypothetical concentration of compo- ditions on Kc,・i a. The Kc,・i a values of aromatics were nent i in the extract phase in equilibrium with the con- larger than those of hexane or other paraffins. As a centration of component i in the raffinate phase. Kc,i general trend of Kc,・i a, the values of aromatics were ap- can be expressed as, proximately ten fold larger than those of paraffins, and lower water content in the solvent increased the Kc,・i a values. The Kc,・i a values increased with both Et and Rb mainly due to increased holdup in the dispersed phase and the effects of Et on Kc,・i a were larger than those of Rb for all cases. The distribution coefficients had few effects on the Kc,・i a values of the aromatic components and the first term in the right side of the Eq. (6) had little influence. The effects of the continuous phase flow rates were larger than those of the dispersed phase flow rates. These observations might suggest that the mass transfer of this system should be controlled by the continuous phase. The mass transfer rates for hexane were simi- lar to the mass transfer rates for aromatics, which might show that the hexane mass transfer should be controlled in the same way as the aromatics components. However, whether the Kc,・i a values of hexane were much smaller than those of aromatics remained unclear. Sulfolane was chosen as the solvent in this study for the selective extraction of aromatics components. Of course, the aromatics were extracted from the reformate gasoline to the sulfolane solvent phase and the sulfo- lane was transferred into the raffinate phase. The sol- ubility into the oil phase was relatively large resulting Fig. 7 Selectivity of Each Aromatic Component Relative to Hexane in larger mass transfer rates, as expected from the (keys are same as in Fig. 6) results of the liquid-liquid equilibrium measurements,
Feed oil phase: model gasoline.
Fig. 8 Effects of Rb and Et on Kc,・i a (keys are same as in Fig. 6)
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Feed oil phase: reformate gasoline.
Fig. 9 Effects of Rb and Et on Kc,・i a (keys are same as in Fig. 6) and the transfer rate was the largest in this system. aromatics and hexane. The water content in the sol- The mass transfer rates of aromatics and hexane were vent affected the yields, selectivities and extraction approximately 30％ and 5％ relative to the sulfolane rates. The yields and selectivities of benzene were the transfer rate. Therefore, the hydrocarbon components highest, followed by toluene and xylene, and the water should transfer into the solvent phase against the sulfo- content in the solvent phase reduced the yields of aro- lane flows despite the large mass transfer rate. matics but increased the selectivities. The volumetric Moreover, the system contained multiple components overall mass transfer coefficients of each component which made the mass transfer more complicated. were measured to examine the effects of both phase Many mechanisms have been considered but we do not flow rates and the water content in the solvent phase. yet have corroborative evidence. We would like to The coefficients of aromatics were almost 10 times continue studies to clarify the mass transfer mechanism. higher than that of hexane because the multi-component system made the mass transfer more complicated, and 4. Conclusions the differences in the mass transfer rates must have affected the outcomes. However, we could not clarify Liquid-liquid equilibrium was measured in systems the mechanism and further research is necessary. The of model or reformate gasoline, sulfolane and water effects of the continuous phase flow rates on the co- mixtures. The distribution coefficients of aromatics efficients were greater than those of the dispersed phase were much higher than those of hexane, with the high- flow rates. The mass transfer resistance in the contin- est for benzene, followed by toluene and xylene. The uous phase was larger than that in the dispersed phase, separation selectivities for aromatics were high enough and was the controlling factor in the overall mass trans- to expect good separation performances. The distribu- fer resistance. These findings should be valuable for tions of aromatics, benzene, toluene and xylene, were the design of the aromatic recovery process. The sul- maintained constant, independent of the ratios of oil folane process has already been validated and has and aqueous phases and model or reformate gasolines. entered industrial use. However, the present findings The liquid-liquid equilibrium was estimated by the should allow better design and operation of the process UNIFAC model with the parameters previously meas- to enhance productivity, although more systematic equi- ured7), which could predict the behaviors of the aromat- librium data and kinetic parameters are required. ics. The behaviors of hexane were estimated as higher than the experimental results and one of the parameters Acknowledgment was adjusted to predict the extraction equilibrium data Reformate gasoline was provided by Idemitsu Kosan of hydrocarbons. However the behaviors of water and Co., Ltd. sulfolane could not be fully estimated and the estima- tion was limited in usefulness for the analysis of the Appendix extraction rates of hydrocarbons. The UNIFAC model is expressed as the following The packed column with Rashig ring packings was equations11),12). For component i, the activity co- used as a contactor to measure the extraction rates of efficient, γ i, is given as,
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Fig. A1 Effects of Interaction Parameters on Distribution Coefficients
C C R parameters for group k. The residual contribution, γ i , lnγ i = lnγ + lnγ (A-1) i i is expressed as C The combinatorial contribution, γ i , is expressed as, R (i) (i) lnγ = ν ⋅ lnΓ k - lnΓ (A-7) C z i ∑ k ( k ( k )) lnγ i = ln(φix i ) + 2 + ln(θi φi ) + (A-2) The activity coefficient, Γ k, is given by l x x l i- (φ i i)∑ jj ( j⋅ j ) here NG NG ’ * ’ θm ⋅ψ k, m lnΓ k = Qk 1 - ln θm ⋅ψ m, k - ∑ ∑ NG li = z ⋅(ri - qi ) / 2 - (ri - 1) (A-3) m=1 m=1 ’’ ∑ θm ⋅ψ m, k The segment fraction, θi, and surface area fraction, fi, m=1 are expressed as (A-8) q x q x , r x r x where θi = i ⋅ i ∑ j ( j ⋅ j ) φi = i ⋅ i ∑ j ( j ⋅ j ) an , m (A-4) ψ n, m = exp - (A-9) T (i) * (i) * ri =ν ⋅Rk , qi =ν ⋅Qk ∑ k ( k ) ∑ k ( k ) The group fraction for group m, Xm, is expressed as (A-5), (A-6) ＊ ＊ R k and Q k are the group volume and surface area
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＊ Table A1 UNIFAC Group Interaction Parameters (a m, n) by Magunussen et al. Nomenclatures
＊ m,n a m,n a : specific interfacial area [m-1] 1,2 －114.8 a＊ : group interaction parameter [K] 1,3 －115.7 E : mass of extract phase in equilibrium measurement [kg] 1,4 130.0 Et : superficial velocity of extract phase in extraction 1,5 561.4 measurement [kg・h-1・m2] 2,1 156.5 F : mass of feed [—] 2,3 167.0 Ki,j : overall mass transfer coefficient of componenti in phase j 2,4 859.4 [kg・h-1・m2] 2,5 21.97 ki,j : local mass transfer coefficient of componenti in phase j 3,1 104.4 [kg・h-1・m2] 3,2 －146.8 l : defined in Eq. (A-3) [—] 3,4 5695.0 mi : distribution coefficient of componenti [—] 3,5 238.0 Qk : group area parameter of group k [—] 4,1 342.4 R : mass of raffinate phase in equilibrium measurement [kg] 4,2 372.8 Rb : superficial velocity of raffinate phase in extraction 4,3 203.7 measurement [kg・h-1・m2] 4,5 18.41 Rk : group volume parameter of group k [—] 5,1 67.84 S : mass of solvent [kg] 5,2 59.16 xi : mass fraction of component i in raffinate phase [—] 5,3 26.59 xi,j : mass fraction of component i in raffinate phase at 5,4 1.110 position j [—] Yi : yield of component i [—] 1: CH2, 2: ACH, 3: ACCH2, 4: H2O, 5: Sulfolane. yi : mass fraction of component i in extract phase [—] yi,j : mass fraction of component i in extract phase at position j [—] NC y＊ : mass fraction of component i in extract phase ν m, i ⋅ xi i ∑ equilibrium to [—] i=1 xi Xm (A-10) = NC NG Z : height of column [m] ∑∑νn, i ⋅ xi
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要 旨
スルホランによるリフォーメートガソリンからの芳香族抽出 ̶液液平衡と抽出速度の測定̶
広顕†1)，江頭 竜一†1)，川崎 順二郎†2)
†1) 東京工業大学大学院理工学研究科国際開発工学専攻，152-8552 東京都目黒区大岡山2-12-1 †2) Dept. of Chemical Engineering, Thammasat University, Bangkok, 12120, THAILAND
スルホラン水溶液を用いたリフォーメートガソリンからの芳 族成分の選択率は向上した。UNIFAC 法による液液平衡の推算 香族抽出，特にベンゼン，トルエン，キシレンの抽出を行った。 値との比較も行った。向流連続抽出実験では分散相をガソリン モデルガソリン（ベンゼン，トルエン，キシレンおよびヘキサ 原料相，連続相をスルホラン溶媒相とし，芳香族およびヘキサ ンの混合物）およびリフォーメートガソリンを原料相として， ンの抽出を測定した。収率および選択率はベンゼンが最も大き スルホラン水溶液を溶媒相として用いて液液平衡を測定，次い く，次いでトルエン，キシレンの順となった。リフォーメート でガラス製ラシヒリングを充填物とした充填塔を用いて同様の ガソリンの抽出ではベンゼンの選択率は約 20 程度（溶媒中の 系において向流連続抽出実験を行った。平衡測定において，分 水分が 9 wt％ の場合）となり，芳香族に関して高い選択性を 配係数および選択率はベンゼン，トルエン，キシレンの順となっ 示した。総括物質移動容量係数は連続相流量の影響が大きく， た。水分濃度の増加とともに分配係数は小さくなったが，芳香 これにより物質移動が連続相支配であることを確認した。
J. Jpn. Petrol. Inst., Vol. 52, No. 4, 2009