孟現(xiàn)陽(yáng)，于野，吳江濤

（西安交通大學(xué)能源與動(dòng)力工程學(xué)院，熱流科學(xué)與工程教育部重點(diǎn)實(shí)驗(yàn)室，陜西 西安 710049）

正丙醇黏度方程研究

孟現(xiàn)陽(yáng)，于野，吳江濤

（西安交通大學(xué)能源與動(dòng)力工程學(xué)院，熱流科學(xué)與工程教育部重點(diǎn)實(shí)驗(yàn)室，陜西 西安 710049）

正丙醇被廣泛應(yīng)用于化工、醫(yī)藥和農(nóng)業(yè)等領(lǐng)域，可靠的熱物性數(shù)據(jù)是理論研究和工程應(yīng)用的基礎(chǔ)。黏度作為流體重要的熱物理性質(zhì)之一，在生產(chǎn)流程的設(shè)計(jì)與優(yōu)化和產(chǎn)品質(zhì)量監(jiān)測(cè)等方面具有重要意義。通過(guò)實(shí)驗(yàn)測(cè)量得到的黏度數(shù)據(jù)一般離散分布于不同的熱力學(xué)狀態(tài)，在工程中難以直接應(yīng)用，因此，建立可靠的黏度方程以實(shí)現(xiàn)任意狀態(tài)黏度的計(jì)算非常必要。經(jīng)文獻(xiàn)調(diào)研發(fā)現(xiàn)，目前缺少寬范圍、高精度的正丙醇黏度方程，基于國(guó)內(nèi)外已發(fā)表的實(shí)驗(yàn)數(shù)據(jù)開(kāi)發(fā)了正丙醇高精度黏度方程。該方程不僅能夠很好地復(fù)現(xiàn)實(shí)驗(yàn)數(shù)據(jù)，而且具有合理的外推性，其溫度適用范圍為150～400 K，壓力適用范圍為0.1～120 MPa，方程在計(jì)算范圍內(nèi)估計(jì)不確定度為1%～5%。

正丙醇；黏度；模型；熱力學(xué)

引 言

正丙醇被廣泛應(yīng)用于化工、醫(yī)藥和農(nóng)業(yè)等領(lǐng)域。在化工生產(chǎn)中，可以作為原料參與乙酸丙酯的生產(chǎn)；在醫(yī)藥生產(chǎn)中，可以用其制取黏合止血?jiǎng)⒓t霉素等；在農(nóng)業(yè)中，其衍生物可以用于制取菌達(dá)滅和滅草蜢等，此外其衍生出的醇醚類物質(zhì)可以作為添加劑加入飼料中。正丙醇在不同領(lǐng)域的應(yīng)用離不開(kāi)準(zhǔn)確的熱物性數(shù)據(jù)，黏度作為其中一種重要的熱物性參數(shù)，對(duì)于生產(chǎn)流程的設(shè)計(jì)與優(yōu)化和產(chǎn)品質(zhì)量監(jiān)測(cè)等具有重要意義，因此對(duì)黏度進(jìn)行研究有利于正丙醇在工程中的實(shí)際應(yīng)用。雖然每年都有大量的黏度實(shí)驗(yàn)數(shù)據(jù)發(fā)表，但是這些數(shù)據(jù)一般離散分布于不同的溫度和壓力下，在工業(yè)應(yīng)用中難以直接應(yīng)用，因此有必要建立可靠的黏度方程以實(shí)現(xiàn)數(shù)據(jù)的連續(xù)計(jì)算。本文基于文獻(xiàn)中公開(kāi)發(fā)表的黏度實(shí)驗(yàn)數(shù)據(jù)，采用多參數(shù)黏度模型，開(kāi)發(fā)了高精度、寬范圍的正丙醇黏度方程。

1 黏度實(shí)驗(yàn)數(shù)據(jù)

通過(guò)系統(tǒng)全面的文獻(xiàn)調(diào)研，對(duì)正丙醇黏度實(shí)驗(yàn)數(shù)據(jù)進(jìn)行了廣泛搜集，共得到132篇正丙醇黏度實(shí)驗(yàn)數(shù)據(jù)文獻(xiàn)，共包含538個(gè)實(shí)驗(yàn)數(shù)據(jù)，其中7篇文獻(xiàn)包含高壓狀態(tài)下的實(shí)驗(yàn)數(shù)據(jù)，3篇文獻(xiàn)包含 0.1 MPa下氣相實(shí)驗(yàn)數(shù)據(jù)，其余數(shù)據(jù)均為常壓液相實(shí)驗(yàn)數(shù)據(jù)。然而并非所有數(shù)據(jù)都可以用于方程開(kāi)發(fā)，不同作者、不同年代、不同的實(shí)驗(yàn)方法得到的實(shí)驗(yàn)數(shù)據(jù)相互之間存在較大差異，因此需要對(duì)實(shí)驗(yàn)數(shù)據(jù)進(jìn)行有效評(píng)價(jià)，篩選出可靠的黏度實(shí)驗(yàn)數(shù)據(jù)用于方程的開(kāi)發(fā)。本文將搜集到的黏度實(shí)驗(yàn)數(shù)據(jù)分為了兩類：第一類是基本數(shù)據(jù)，這類數(shù)據(jù)用于方程的開(kāi)發(fā)；第二類數(shù)據(jù)主要用于方程的檢驗(yàn)。數(shù)據(jù)的篩選遵循以下原則[1]：（1）文獻(xiàn)中黏度實(shí)驗(yàn)測(cè)量方法具備完善的工作方程，并且其中的相關(guān)參數(shù)能夠通過(guò)標(biāo)定或者實(shí)驗(yàn)測(cè)量得到；（2）文獻(xiàn)中應(yīng)包含實(shí)驗(yàn)所用樣品的純度信息；（3）文獻(xiàn)中應(yīng)給出實(shí)驗(yàn)數(shù)據(jù)的不確定度分析。此外，還需考慮實(shí)驗(yàn)數(shù)據(jù)的溫度、壓力范圍，應(yīng)盡可能拓展方程的適用范圍。

按照以上數(shù)據(jù)篩選原則，對(duì)132篇文獻(xiàn)中正丙醇的黏度實(shí)驗(yàn)數(shù)據(jù)進(jìn)行了詳細(xì)分析和評(píng)價(jià)。在常壓實(shí)驗(yàn)數(shù)據(jù)篩選中，選取了溫度覆蓋范圍較廣、精度較高的6 篇文獻(xiàn)實(shí)驗(yàn)數(shù)據(jù)作為基本數(shù)據(jù)[2-7]。其中，Komarenko等[2]的實(shí)驗(yàn)溫度范圍為153～298 K，其最低溫度接近三相點(diǎn)溫度。Kumagai等[3]、Tu等[4]、Saleh等[5]、Yang等[6]和 Pang等[7]采用了毛細(xì)管黏度計(jì)，測(cè)量溫度范圍為273～363 K，測(cè)量不確定度大部分小于 1%。高壓黏度實(shí)驗(yàn)數(shù)據(jù)[8-13]，Weber[8]的實(shí)驗(yàn)方法為滾球黏度計(jì)，實(shí)驗(yàn)壓力范圍為 0.1～49.1 MPa，溫度范圍為 273～373 K，不確定度為1.5%。Tanaka等[9]的實(shí)驗(yàn)方法為落體黏度計(jì)，實(shí)驗(yàn)壓力范圍為0.1～117.8 MPa，溫度范圍為283～323 K，不確定度為2%。Papaioannou等[10]、Assael等[11]的實(shí)驗(yàn)方法為落體黏度計(jì)，實(shí)驗(yàn)壓力范圍分別為0.1～71.75 MPa和0.1～51.8 MPa，溫度為298 K，不確定度小于2.5%。Papaioannou等[12]的實(shí)驗(yàn)方法為振動(dòng)弦黏度計(jì)，實(shí)驗(yàn)壓力范圍為0.1～27.86 MPa，溫度范圍為 295～328 K，不確定度為 0.5%。Baylaucq等[13]的實(shí)驗(yàn)方法為落體黏度計(jì)，實(shí)驗(yàn)壓力范圍為0.1～100 MPa，溫度范圍為293～353 K，不確定度為 2%。通過(guò)對(duì)高壓黏度數(shù)據(jù)的對(duì)比，并結(jié)合方程的適用范圍，本文選用以上6篇文獻(xiàn)高壓實(shí)驗(yàn)數(shù)據(jù)作為基本數(shù)據(jù)。最終用于正丙醇黏度方程開(kāi)發(fā)的實(shí)驗(yàn)數(shù)據(jù)包括12篇文獻(xiàn)，共計(jì)178個(gè)數(shù)據(jù)點(diǎn)，表1給出了基本實(shí)驗(yàn)數(shù)據(jù)相關(guān)信息。

表1 正丙醇黏度基本實(shí)驗(yàn)數(shù)據(jù)Table 1 Primary data used in developing viscosity correlation of n-propanol

表2 密度方程式(1)～式(4)的系數(shù)Table 2 Coefficients for Eq. (1) to Eq.(4)

2 黏度方程形式

根據(jù)現(xiàn)有黏度理論研究和已有黏度方程開(kāi)發(fā)經(jīng)驗(yàn)[19-24]，純質(zhì)黏度的計(jì)算以溫度和密度為自變量，并由四項(xiàng)互相獨(dú)立的項(xiàng)組成。

式中，η0(T)為零密度項(xiàng)；η1(T)ρ為初始密度依賴項(xiàng)，通常認(rèn)為在0.2 MPa內(nèi)黏度和密度之間是線性關(guān)系[23]；Δηc(ρ,T)為臨界增強(qiáng)黏度項(xiàng)，作用是修正黏度在臨界點(diǎn)附近區(qū)域的奇異現(xiàn)象，已有文獻(xiàn)研究表明[19-24]，對(duì)于黏度僅在臨界點(diǎn)溫度1%～2%范圍內(nèi)，Δηc/η可能超過(guò)0.01。此外，鑒于所搜集的黏度實(shí)驗(yàn)數(shù)據(jù)中沒(méi)有近臨界區(qū)的實(shí)驗(yàn)數(shù)據(jù)，無(wú)法開(kāi)發(fā)準(zhǔn)確的臨界增強(qiáng)型表達(dá)式，參考已有文獻(xiàn)研究，本文采用了同樣的辦法，將該項(xiàng)設(shè)為零。Δη(ρ,T)為剩余黏度項(xiàng)，該項(xiàng)幾乎沒(méi)有理論指導(dǎo)，其形式主要是參考已有黏度模型并結(jié)合實(shí)驗(yàn)數(shù)據(jù)得到。

2.1 零密度項(xiàng)和初始密度依賴項(xiàng)

該項(xiàng)的主要理論基礎(chǔ)為分子運(yùn)動(dòng)理論，為了更準(zhǔn)確地復(fù)現(xiàn)實(shí)驗(yàn)數(shù)據(jù)，本文采用了Chung等[25]提出的修正模型，該模型引入了參數(shù)Fc用于修正分子結(jié)構(gòu)、分子極性和締合性質(zhì)對(duì)正丙醇黏度的影響。零密度下的黏度計(jì)算方程如式(6)～式(10)所示。

式(6)～式(10)中需要確定的關(guān)鍵參數(shù)為勢(shì)能尺度特征參數(shù)σ和勢(shì)能能量特征參數(shù)ε/kB，確定方法分為兩種，一種為關(guān)聯(lián)臨界參數(shù)[25]，另一種為關(guān)聯(lián)實(shí)驗(yàn)數(shù)據(jù)進(jìn)行求解，本文采用了后者。因沒(méi)有搜集到正丙醇在極低密度下的黏度實(shí)驗(yàn)數(shù)據(jù)，故無(wú)法通過(guò)推導(dǎo)得到零密度下氣體的黏度值，本文將η0(T)+η1(T)ρ作為低密度黏度項(xiàng)與Titani[26]的實(shí)驗(yàn)數(shù)據(jù)相關(guān)聯(lián)，并結(jié)合Golubev等[27]的密度實(shí)驗(yàn)數(shù)據(jù)，回歸得到σ和ε/kB。式(6)～式(10)中的相關(guān)參數(shù)、系數(shù)和指數(shù)見(jiàn)表3。

文獻(xiàn)研究表明，無(wú)論是極性還是非極性物質(zhì)，在一定溫度范圍內(nèi)，低壓下氣體的黏度會(huì)沿等溫線隨密度的增加而降低，這種現(xiàn)象可以通過(guò)第二黏度維里系數(shù)進(jìn)行量化說(shuō)明，其主要理論依據(jù)為Rainwater and Friend 理論[28-30]，并可由式(1)關(guān)聯(lián)得到。

為了方便與實(shí)驗(yàn)數(shù)據(jù)進(jìn)行對(duì)比，引入量綱1第二黏度virial系數(shù)B*η(T)，該系數(shù)與溫度的關(guān)系式由文獻(xiàn)[31]給出，其溫度適用范圍為 0.3

式中，NA為Avogadro常數(shù)，式(13)中的相關(guān)系數(shù)見(jiàn)表3。

2.2 剩余黏度項(xiàng)

剩余黏度項(xiàng)形式的選擇，需要考慮黏度在高密度區(qū)域的數(shù)量級(jí)變化特性以及方程的外推性等因素，結(jié)合正丙醇的黏度特性并參考已有黏度方程研究[19-24]，最終確定剩余黏度項(xiàng)的形式如下

表3 式(6)～式(13)中的系數(shù)Table 3 Coefficients for Eq. (6) to Eq.(13)

表4 剩余黏度項(xiàng)系數(shù)和指數(shù)Table 4 Coefficients and parameters for Eq. (14)

其中，Δη(ρ,T)的單位為 μPa?s，ρr=ρ/ρc，Tr=T/Tc。由于基本實(shí)驗(yàn)數(shù)據(jù)的不確定度不盡相同，因此需要對(duì)不同的實(shí)驗(yàn)數(shù)據(jù)進(jìn)行權(quán)重設(shè)置，初始權(quán)重采用不確定度平方分之一進(jìn)行設(shè)置，即w=1/(ηu)2。對(duì)于不確定度不明確的黏度實(shí)驗(yàn)數(shù)據(jù)，參考其實(shí)驗(yàn)方法、發(fā)表年代和樣品純度信息等進(jìn)行初始權(quán)重設(shè)置。通過(guò)合理的權(quán)重設(shè)置，最終得到的擬合結(jié)果如表4所示。

表5給出了黏度文獻(xiàn)實(shí)驗(yàn)數(shù)據(jù)與開(kāi)發(fā)的方程計(jì)算值偏差情況，方程很好地復(fù)現(xiàn)了實(shí)驗(yàn)數(shù)據(jù)，其基本實(shí)驗(yàn)數(shù)據(jù)與方程計(jì)算值的平均偏差（Bias）為0.14%，平均絕對(duì)偏差（AAD）為 0.74%（Bias和AAD計(jì)算方法與密度一樣），最大偏差為-5.02%。

3 實(shí)驗(yàn)數(shù)據(jù)分析

下述實(shí)驗(yàn)數(shù)據(jù)分析來(lái)自于文獻(xiàn)[2-13,33-50]。圖1給出了0.1 MPa下溫度范圍為153～363 K的液相黏度實(shí)驗(yàn)數(shù)據(jù)與方程的計(jì)算值之間的偏差，圖2給出在壓力范圍為 0.1～117.8 MPa，溫度范圍為273～373 K下的實(shí)驗(yàn)數(shù)據(jù)與方程計(jì)算值間的偏差隨密度變化的分布，從圖中可以看出偏差基本在±2.5%以內(nèi)，且均勻分布在正負(fù)兩側(cè)，沒(méi)有明顯的趨勢(shì)走向。

表5 正丙醇黏度方程相關(guān)統(tǒng)計(jì)指標(biāo)Table 5 Evaluation of n-propanol viscosity correlation for primary data

在常壓狀態(tài)下，Komarenko等[2]的實(shí)驗(yàn)數(shù)據(jù)的溫度范圍為153～298 K，黏度在低溫區(qū)域隨著密度的增加會(huì)呈現(xiàn)出數(shù)量級(jí)的變化，方程很好地復(fù)現(xiàn)了這種特性，實(shí)驗(yàn)數(shù)據(jù)與計(jì)算值的Bias為0.17%，AAD為0.31%；Yang等[6]的實(shí)驗(yàn)數(shù)據(jù)與方程的計(jì)算值的AAD為1.18%，與其不確定度相當(dāng)；Pang等[7]的實(shí)驗(yàn)數(shù)據(jù)與方程的計(jì)算值的 AAD為 0.20%，在其不確定度0.4%以內(nèi)。在高壓黏度實(shí)驗(yàn)數(shù)據(jù)中，Tanaka等[9]的實(shí)驗(yàn)數(shù)據(jù)與方程的計(jì)算值的AAD為0.89%，在其不確定度 2%內(nèi)；Baylaucq等[13]的實(shí)驗(yàn)數(shù)據(jù)與方程的計(jì)算值的AAD為1.69%，在其不確定度2%內(nèi)。根據(jù)實(shí)驗(yàn)數(shù)據(jù)范圍，最終方程可適用于溫度范圍為150～400 K，壓力范圍為0.1～120 MPa的狀態(tài)區(qū)域內(nèi)。150～373 K、0.1 MPa范圍內(nèi)方程的不確定度為1%，273～373 K、壓力120 MPa以內(nèi)方程的不確定度估計(jì)為 2%，其他區(qū)域根據(jù)范圍不同估計(jì)不確定度為2%～5%。

圖1 正丙醇常壓下液相黏度實(shí)驗(yàn)數(shù)據(jù)與計(jì)算值偏差Fig.1 Percentage deviations of primary data at 0.1 MPa for n-propanol

圖2 正丙醇高壓下液相黏度實(shí)驗(yàn)數(shù)據(jù)與計(jì)算值偏差Fig.2 Percentage deviations of primary data at high pressure for n-propanol

圖3為方程在不同等溫線下黏度與密度的曲線，由圖可以發(fā)現(xiàn)黏度的變化曲線平滑，為混合物黏度的預(yù)測(cè)奠定了基礎(chǔ)。表6給出了不同溫度和密度下方程的計(jì)算值，以便實(shí)際應(yīng)用中方程的檢驗(yàn)。

在第二類數(shù)據(jù)中，張建侯等[33]測(cè)量了298.15 K下壓力范圍為0.1～29.5 MPa的正丙醇黏度，其實(shí)驗(yàn)數(shù)據(jù)與計(jì)算值的Bias為1.50%，AAD為1.54%，雖然偏差不算太大，但該溫度下偏差隨壓力變化存在系統(tǒng)偏差。在剩余的第二類數(shù)據(jù)中，部分?jǐn)?shù)據(jù)與其他數(shù)據(jù)有著明顯的偏差，例如 Mokhtarani等[34]采用滾球式黏度計(jì)測(cè)量了常壓下溫度范圍為 283～333 K的正丙醇黏度，其實(shí)驗(yàn)數(shù)據(jù)與計(jì)算值的偏差從 7.6%增大到 17.6%；Kermanpour等[35]采用了毛細(xì)管黏度計(jì)測(cè)量了溫度范圍為293～333 K的正丙醇黏度，其實(shí)驗(yàn)數(shù)據(jù)與計(jì)算值的最大偏差為-52%，結(jié)果明顯存在錯(cuò)誤。為了驗(yàn)證方程的合理性，對(duì)于第二類數(shù)據(jù)首先排除了與其他實(shí)驗(yàn)數(shù)據(jù)有明顯偏差的文獻(xiàn)實(shí)驗(yàn)數(shù)據(jù)，并選擇包含5個(gè)以上實(shí)驗(yàn)數(shù)據(jù)的文獻(xiàn)[36-53]與方程計(jì)算值進(jìn)行了對(duì)比，結(jié)果如圖4所示，第二類數(shù)據(jù)偏差基本在±5%以內(nèi)，整體AAD為1.99%，Bias為-0.28%，證明所擬合的正丙醇黏度方程能夠很好地復(fù)現(xiàn)實(shí)驗(yàn)數(shù)據(jù)。

圖3 正丙醇黏度沿不同等溫線隨密度的變化曲線Fig.3 Viscosity of n-propanol as a function of density along isotherms

表6 正丙醇黏度方程計(jì)算驗(yàn)證值Table 6 Sample points for computer verification of correlating equations

4 結(jié) 論

圖4 第二類數(shù)據(jù)0.1 MPa下液相黏度實(shí)驗(yàn)值與計(jì)算值偏差Fig.4 Percentage deviations of the secondary data

本文對(duì)正丙醇公開(kāi)發(fā)表的黏度文獻(xiàn)實(shí)驗(yàn)數(shù)據(jù)進(jìn)行全面搜集和整理，對(duì)文獻(xiàn)中的黏度實(shí)驗(yàn)數(shù)據(jù)進(jìn)行了評(píng)價(jià)和篩選，利用篩選出的基本數(shù)據(jù)開(kāi)發(fā)了寬范圍高精度正丙醇黏度方程，基本實(shí)驗(yàn)數(shù)據(jù)與方程計(jì)算值的平均絕對(duì)偏差為 0.74%。方程的溫度適用范圍為 150～400 K，壓力適用范圍為 0.1～120 MPa，在適用范圍內(nèi)估計(jì)不確定度為 1%～5%。本文所開(kāi)發(fā)的正丙醇黏度方程不僅很好地復(fù)現(xiàn)了實(shí)驗(yàn)數(shù)據(jù)，而且具有合理的外推特性。

符 號(hào) 說(shuō) 明

Bη——第二黏度 virial系數(shù)，m3?kg-1

M——物質(zhì)的摩爾質(zhì)量，g?mol-1

NA——Avogadro常數(shù)

p——壓力，MPa

T——熱力學(xué)溫度，K

T*——對(duì)比溫度

Tc——臨界溫度，K

Tr——臨界對(duì)比溫度

vc——臨界比體積，cm3?mol-1

η——?jiǎng)恿︷ざ龋蘌a·s

ηc——臨界黏度增強(qiáng)項(xiàng)，μPa·s

η0——稀薄氣體黏度，μPa·s

η1——密度線性相關(guān)項(xiàng)，μPa·s·m3·kg-1

Δη——剩余黏度，μPa·s

κ——經(jīng)驗(yàn)性締合參數(shù)

μ——偶極矩，D

μr——對(duì)比偶極矩

ρ——密度，kg?m-3

ρc——臨界密度，kg?m-3

ρr——臨界對(duì)比密度

Ω*——分子碰撞積分

ω——偏心因子

下角標(biāo)

exp ——實(shí)驗(yàn)值

cal ——計(jì)算值

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date:2017-03-30.

MENG Xianyang, associate professor,xymeng@ mail.xjtu.edu.cn

supported by the National Natural Science Foundation of China (51676159) and the Natural Science Basic Research Plan in Shaanxi Province of China (2015JM5214).

Correlation of viscosity ofn-propanol

MENG Xianyang, YU Ye, WU Jiangtao
(Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education,School of Energy and Power Engineering,Xi’an Jiaotong University,Xi’an710049,Shaanxi,China)

n-Propanol is widely used in different industries such as pharmaceutical manufacturing and agriculture.The thermophysical properties are the fundamentals for those processes. Viscosity is an important property which influences the design of process equipment, product quality monitoring and so on. However, the experimental data of viscosity are often obtained with discrete points. Correlating equations with these experimental data are prerequisite to use. To author’s best knowledge, there is no such a viscosity correlation forn-propanol available in wide temperature and pressure ranges. The aim of this work is to develop the viscosity correlation ofn-propanol with high accuracy, which can be used over the whole thermodynamic surface. Based on the selected reliable experimental data, the correlation for the viscosity ofn-propanol was presented. The extrapolation behavior of the correlation is reasonable, and the temperature is valid from 150 to 400 K at pressures up to 120 MPa. The estimated uncertainties of this correlation are from 1% to 5%.

n-propanol; viscosity; model; thermodynamics

TK 121

A

0438—1157（2017）11—4035—08

10.11949/j.issn.0438-1157.20170328

2017-03-30收到初稿，2017-07-17收到修改稿。

聯(lián)系人及第一作者：孟現(xiàn)陽(yáng)（1978—），男，副教授。

國(guó)家自然科學(xué)基金項(xiàng)目（51676159）；陜西省自然科學(xué)基礎(chǔ)研究計(jì)劃項(xiàng)目（2015JM5214）。