原油中石蜡沉积的热力学研究
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摘要
含有蜡(长链烷烃化合物的混合物)的原油体系,当温度降低到一定值时,原先溶于原油中的蜡逐渐饱和析出。当温度进一步降低,析出的蜡晶增多,它们之间聚结成大的晶体进而连接成三维空间网络结构,造成输送管道的阻塞,影响原油的输送和生产。因此,预测给定条件下原油体系的析蜡点和析蜡量,对油气生产过程中有效防止石蜡沉积有非常重要的意义。
本论文进行的原油体系石蜡沉积研究,分为石蜡沉积的实验研究和热力学模型研究两个方面,主要有如下内容:
1.建立了差示扫描量热法(DSC)测石蜡沉积条件的实验方法,该方法可以同时测定析蜡点和析蜡量,而且分析速度快,试样用量少,实验重复性好,具有工业推广和应用价值。
2.用DSC法测定了模拟原油体系在不同冷却速率下的沉积变化规律,确定了最佳冷却速率,测定了模拟油体系的析蜡点及其在不同的温度下的石蜡沉积量。通过以上实验研究获得了一套完善的石蜡沉积实验数据。
3.用气相色谱法测定了模拟油体系中石蜡的组成,作为模型研究的输入数据。
4.本文从正规溶液理论角度,结合固-液相平衡热力学,建立了石蜡沉积的正规溶液理论热力学模型。
本文建立了一个改进的用于计算石蜡沉积的热力学固-液相平衡模型。该模型认为原油温度低于析蜡点温度时,正构烷烃以旋转相、三斜晶、单斜晶和正交晶四种形式存在,随着温度的进一步降低,它们都以正交晶的形式稳定存在,其间不同碳原子数的正构烷烃经历了不同晶形到正交晶的转换,因此模型考虑了固-固转换。拟组分的热力学参数采用经验关系式来计算,其中对于正构烷烃的固-固转换焓、固固转换温度、熔解焓以及溶解温度,基于文献资料建立了新的关系式。
运用上述模型与文献中Leelavanichkul模型对文献中的三个原油体系以及本文实验体系进行了模拟计算并与实验结果进行了比较,发现不管是复杂的原油体系还是简单的模拟原油,对于不同温度下的石蜡沉积量本文新建立的模型其模拟结果要远远优于Leelavanichkul模型。对于石蜡沉积点,本文模型的模拟结果要稍大于实验值。
For the crude oils which contain wax (mixture of long chain alkanes), when the temperature of crude oil drops, the solubility of the heavy hydrocarbons would be sufficiently reduce and they will precipitate in the form of wax. With the more decrease of temperature, the amount of wax precipitated increase and they assemble into large crystal and finally the three-dimensional network structure is constructed. The plug of pipeline caused by wax precipitation has important influence on the production and transportation of crude oils. A model that can predict the conditions under which solids will precipitate and the amount of solids formed under different conditions can be used as a fundamental tool to prevent the solid precipitation.The research work on the wax precipitation principally involves:1. The DSC method for determination of wax precipitation condition has been established. The wax appearance temperature and the amount of wax precipitated under different temperature can be obtained at the same time by DSC method. The method is quickly and reliable and can be done in industry.2. Detail experiments have been conducted to study the best wax precipitation condition under different cooling rate. The wax appearance temperature and the amount of wax precipitated under different temperatures are obtained using DSC method.3. The composition of wax is obtained by gas chromatography, the characterization data are used for the model input data.4. Regular solution thermodynamic theories: a modified thermodynamic solid-liquid equilibrium model which is used to calculate wax precipitation in crude oils has been established in resent work. The researches indicate that when temperature of crude oil lower WAT, the solid paraffin exist in forms of hexagonal 、 orthorhombic、 triclinic and monoclinic phases, with the decrease of temperature, all of the solid alkane become steady orthorhombic phase, so the solid-solid transition is considered in the model. The properties of the pseudo-components are determined by using empirical correlations. New correlations for solid-solid transition enthalpy、 solid-solid transition temperature、 fusion enthalpy and fusion temperature are also established in this work based on the data from literatures.The calculation results for three crude oil systems from literature and the model crude oil system studied in this research by the modified thermodynamic model present in this work and the regular solution model proposed by Leelavanichkul are compared with the
experimental ones, it can be seen that not only for complicated crude oil systems but also for simple model system, the modified thermodynamic model is much better than the regular solution model proposed by Leelavanichkul for calculating the amount of wax precipitation under different temperatures. For the wax precipitation temperature, the calculation results by the model present in this work are little higher than the experiment ones.
本论文进行的原油体系石蜡沉积研究,分为石蜡沉积的实验研究和热力学模型研究两个方面,主要有如下内容:
1.建立了差示扫描量热法(DSC)测石蜡沉积条件的实验方法,该方法可以同时测定析蜡点和析蜡量,而且分析速度快,试样用量少,实验重复性好,具有工业推广和应用价值。
2.用DSC法测定了模拟原油体系在不同冷却速率下的沉积变化规律,确定了最佳冷却速率,测定了模拟油体系的析蜡点及其在不同的温度下的石蜡沉积量。通过以上实验研究获得了一套完善的石蜡沉积实验数据。
3.用气相色谱法测定了模拟油体系中石蜡的组成,作为模型研究的输入数据。
4.本文从正规溶液理论角度,结合固-液相平衡热力学,建立了石蜡沉积的正规溶液理论热力学模型。
本文建立了一个改进的用于计算石蜡沉积的热力学固-液相平衡模型。该模型认为原油温度低于析蜡点温度时,正构烷烃以旋转相、三斜晶、单斜晶和正交晶四种形式存在,随着温度的进一步降低,它们都以正交晶的形式稳定存在,其间不同碳原子数的正构烷烃经历了不同晶形到正交晶的转换,因此模型考虑了固-固转换。拟组分的热力学参数采用经验关系式来计算,其中对于正构烷烃的固-固转换焓、固固转换温度、熔解焓以及溶解温度,基于文献资料建立了新的关系式。
运用上述模型与文献中Leelavanichkul模型对文献中的三个原油体系以及本文实验体系进行了模拟计算并与实验结果进行了比较,发现不管是复杂的原油体系还是简单的模拟原油,对于不同温度下的石蜡沉积量本文新建立的模型其模拟结果要远远优于Leelavanichkul模型。对于石蜡沉积点,本文模型的模拟结果要稍大于实验值。
For the crude oils which contain wax (mixture of long chain alkanes), when the temperature of crude oil drops, the solubility of the heavy hydrocarbons would be sufficiently reduce and they will precipitate in the form of wax. With the more decrease of temperature, the amount of wax precipitated increase and they assemble into large crystal and finally the three-dimensional network structure is constructed. The plug of pipeline caused by wax precipitation has important influence on the production and transportation of crude oils. A model that can predict the conditions under which solids will precipitate and the amount of solids formed under different conditions can be used as a fundamental tool to prevent the solid precipitation.The research work on the wax precipitation principally involves:1. The DSC method for determination of wax precipitation condition has been established. The wax appearance temperature and the amount of wax precipitated under different temperature can be obtained at the same time by DSC method. The method is quickly and reliable and can be done in industry.2. Detail experiments have been conducted to study the best wax precipitation condition under different cooling rate. The wax appearance temperature and the amount of wax precipitated under different temperatures are obtained using DSC method.3. The composition of wax is obtained by gas chromatography, the characterization data are used for the model input data.4. Regular solution thermodynamic theories: a modified thermodynamic solid-liquid equilibrium model which is used to calculate wax precipitation in crude oils has been established in resent work. The researches indicate that when temperature of crude oil lower WAT, the solid paraffin exist in forms of hexagonal 、 orthorhombic、 triclinic and monoclinic phases, with the decrease of temperature, all of the solid alkane become steady orthorhombic phase, so the solid-solid transition is considered in the model. The properties of the pseudo-components are determined by using empirical correlations. New correlations for solid-solid transition enthalpy、 solid-solid transition temperature、 fusion enthalpy and fusion temperature are also established in this work based on the data from literatures.The calculation results for three crude oil systems from literature and the model crude oil system studied in this research by the modified thermodynamic model present in this work and the regular solution model proposed by Leelavanichkul are compared with the
experimental ones, it can be seen that not only for complicated crude oil systems but also for simple model system, the modified thermodynamic model is much better than the regular solution model proposed by Leelavanichkul for calculating the amount of wax precipitation under different temperatures. For the wax precipitation temperature, the calculation results by the model present in this work are little higher than the experiment ones.
引文
[1] Ferns S W, Cowles H C Jr and Hendersen L W. Composition of paraffin wax. Ind & Eng Chem, 1929, No 21, 1090-1092.
[2] Speight J M. The chemistry and technology of petroleum. 3th, Marcel Dekker: New York, 1999.
[3] McCain W D Jr. The properties of petroleum fluids. Second Edition Pennwell Publishing Co, Tulsa (1989), 9912-18.
[4] Nathan C C. Solubility studies on high molecular weight paraffin hydrocarbons obtained from petroleum rod waxes. Trans, IME (955)204, 151-55.
[5] Newbery M E, Addison G E and Barker K W. Paraffin control in the northern michigan niagaran reef tread. Paper SPE 12320 presented at the 1983 SPE Eastern Regiongal Meeting, Chamption, PA, Nov, 9-11.
[6] Woo G T, Garbis S J and Gray T C. Long-term control of paraffin deposition exhibition. Housten, Sept, 16-19.
[7] 林明,王贤清.石油蜡的开发和利用.石油与天然气化工,Vol24,No.4,1995.
[8] Broadhurst M G. An analysis of the solid phase behavior of the normal paraffins. Res Natl Bur Stand (US), 66A, 241-249 (1962).
[9] Bucaram S M. An improved paraffin in producing inhibitor. JPT (Feb, 1967) 150-156.
[10] McCall J M and Johnson R L. Paraffin treatment in the well service industry. Presented at the 31st annual southwestern petroleum short course, lubbock TX, April 25-26, 1984.
[11] Newberry M E, Addison G E and Barker K M. Paraffin control in the northern michigan niagaran reef trend. Paper SPE 12320 presented at the 1983 SPE eastern regional meeting, champion, PA, Nov, 9-11.
[12] Won K W. Thermodynamic for solid-liquid-vapor equilibria: wax phase formation from heavy hydrocarbon mixtures. Paper presented at the 4th International Conference on Fluid Properties and Phase Equilibria for Chemical Process Design, Helsinger, Denmark, May 11-16, 1986.
[13] Carnahan N F. Paraffin deposition in petroleum production. JPT (Oct. 1989) 1024-1025.
[14] 刘志泉,李剑新.中国原油性质及综合评价.北京,石油出版社,1996.
[15] Dollhohf H. Thermal behavior and non-isothermal crystallization kinetics of normal-alkanes and their waxy mixtures under quiescent conditions. A Dissertation of Ph. D Calary, Alberta, 1994.
[16] Zhou X, Thomas F B and Moore R G. Modeling of solid precipitation from reservoir fluid. Journal of Canadian Petroleum Technology, 1996, 35(10): 37-45.
[17] 梅海燕,孔祥言等.预测石蜡沉积的热力学模型.石油勘探与开发,2002,Vol.27,No.1,(84-87).
[18] Weingarten J S, Euchner J A. Methods for predicting wax precipitation and deposition. SPE Production Engineering, 1988, 121-126.
[19] 马殿坤.原油中蜡的沉积及影像因素.油田化学,1988,No.1,64-70.
[20] 岳福山.关于原油中蜡的沉积过程.油田化学,1987,Vol4,No,4.
[21] Kabir C S, Hasan A R. An approach to mitigating well bore solids deposition. SPE 71558.
[22] Alex R F, Fuhr B J, Rawluk M et al. Characterization of waxy crudes and waxes symposium on modern analytical techniques for the analysis of petroleum. American Chemical Society, New York City Meeting, 8, 25-31, 1991.
[23] Claudy P, Jean M, Chague B et al. Crude oils and their distillates: characterization by differential scanning calorimetry. Fuel, Vol 67, Jan, 1988.
[24] 李鸿英,黄启玉,张帆等.用差示扫描量热法确定原油的含蜡量.石油大学学报,Vol.27,No.1,Feb,2003.
[25] Won K W. Thermodynamic for solid-liquid equilibria: wax formation from heavy hydrocarbon mixtures. Paper presented at the AIChE National Spring Meeting, Houston, Texas, March 1985.
[26] Pedersen K S, Skovborg P. Wax Precipitation from North Sea Crude Oils 4. Thermodynamic Modeling. Energy & Fuels, 1991, 5, 924-935.
[27] Erickson D D, Niesen V G, Brown T S. Thermodynamic measurement and precipitation of paraffin precipitation in crude oil. SPE 26604, 1993, 933-948.
[28] Thomas J B, Bennian D B, Bennion D W. Experimental and theoretical studies of solids Precipitation from reservoir fluid. Jan, 1992.
[29] Chungn T H. Thermodynamic model for organic solid precipitation. NIPER-623, Sept, 1992.
[30] Deo M D, Miharia A, Zumar R. Solids Precipitation in Reservoirs Due to Nonisothermal Injections. SPE 28967, 1995, 225-235.
[31] Hansen J H, Fredenslund A, Pedersen K Set al. A thermodynamic model for predicting wax formation in crude oils. AIChE J, 1988, 34(12): 1937-1942.
[32] Coutinho J A P, Andersen S L, Stenby E H. Evaluation of activity coefficient models in prediction of alkane solid-liquid equilibria. Fluid Phase Equilibria 1995, 103, 23-39.
[33] Pauly J, Dauphin C and Daridon J L. Liquid-solid equilibria in a decane plus multi-paraffins system. Fluid Phase Equilibria, 1998.
[34] Coutinho J A P, Andersen S L, Stenby, E H. Solid-liquid lquilibrium of non-alkanes using the chain delta lattice parameter model. Fluid Phase Equilibria 1996, 117, 138-145.
[35] Coutinho J A P, Stenby E H. Predictive local composition models for solid/liquid equilibrium in n-alkane systems: Wilson Equation for Multicomponent Systems. Ind Eng Chem Res, 1996, 35, 918-925.
[36] Coutinho J A P, Ruffier-Meray V. Experimentalmeasurements and thermodynamic modeling of paraffinic wax formation in undercooled solutions. Ind Eng Chem Res, 1997, 36, 4977-4983.
[37] Singh P, Youyen A and Fogler H S. Existence of a critical carbon number in aging of a wax-oil gel. AIChE J, 2001, 47(9).
[38] Lira-Galeana C, Firoozabadi A, Prausnitz J M. Thermodynamics of wax precipitation in petroleum mixtures. AIChE Journal 1996, 42, 239-248.
[39] Pan H, Firoozabadi A, Fotland P. Pressure and composition effect of wax precipitation: experimental data and model results. SPE 26740,1996, 579-592.
[40] Leontaritis K J. PARA-based (paraffin-aromatic-resin-asphaltene) reservoir oil characterizations. SPE 37252, 1997, 421-440.
[41] Zuo J Y, Zhang D D. A thermodynamic model for wax precipitation. Paper presented at the 2nd International Conf. on. Pet. and Gas Phase Behavior and Fouling, Denmark, August 27-31, 2000.
[42] Riazi M R, Al-Sahhaf T A. Physical properties of heavy petroleum fractions and crude oils. Fluid Phase Equilibria, 117, 217-224 (1996).
[43] Leelavanichkul P, Deo M D, Hanson F V. Crude oil characterization and regular solution approach to thermodynamic modeling of solid precipitation at low pressure. Petroleum Science and Technology, v22, n 7-8, July, 973-990 (2004).
[44] 潘竟军,张焱,韩晓强.差示扫描量热法测定原油含蜡量的研究.石油天然气学报,Dec2005,Vol.27 NO.6.
[45] 李凤艳,赵天波,冀德坤.气相色谱法则定石蜡正异构烃及碳数分布积分方式的选择.分析化学,1995,23(10):1208-1210.
[46] 王素琴,王萌,辛玉芬等.原油及渣油族组成定量分析—高效液相色谱法.油气田地面工程,1996,15(6):17-19.
[47] Hsu C S, Mclean M A, Qian K Net al. On-line liquid chromatography/mass spectrometry for heavy hydrocarbon characterization. Energy& Fuels, 1991. 5: 395-398.
[48] Ji H Y, Bahman Ti, All D et al. Wax phase equilibria: developing a thermodynamic model using a systematic approach. Fluid Phase Equilibria, v216, n2, Feb 29, 201-217 (2004).
[49] 马庆兰,郭天民.用局部组成活度系数模型计算原油中石蜡沉积量.石油大学学报(自然科学版,2003,v27,n5,October,99-102.
[50] Jean-Pierre C. Temperatures and enthalpies of (solid+solid) and (solid+liquid) transitions of n-alkanes. J Chem Thermodynamics, 34, 1255-1277 (2002).
[2] Speight J M. The chemistry and technology of petroleum. 3th, Marcel Dekker: New York, 1999.
[3] McCain W D Jr. The properties of petroleum fluids. Second Edition Pennwell Publishing Co, Tulsa (1989), 9912-18.
[4] Nathan C C. Solubility studies on high molecular weight paraffin hydrocarbons obtained from petroleum rod waxes. Trans, IME (955)204, 151-55.
[5] Newbery M E, Addison G E and Barker K W. Paraffin control in the northern michigan niagaran reef tread. Paper SPE 12320 presented at the 1983 SPE Eastern Regiongal Meeting, Chamption, PA, Nov, 9-11.
[6] Woo G T, Garbis S J and Gray T C. Long-term control of paraffin deposition exhibition. Housten, Sept, 16-19.
[7] 林明,王贤清.石油蜡的开发和利用.石油与天然气化工,Vol24,No.4,1995.
[8] Broadhurst M G. An analysis of the solid phase behavior of the normal paraffins. Res Natl Bur Stand (US), 66A, 241-249 (1962).
[9] Bucaram S M. An improved paraffin in producing inhibitor. JPT (Feb, 1967) 150-156.
[10] McCall J M and Johnson R L. Paraffin treatment in the well service industry. Presented at the 31st annual southwestern petroleum short course, lubbock TX, April 25-26, 1984.
[11] Newberry M E, Addison G E and Barker K M. Paraffin control in the northern michigan niagaran reef trend. Paper SPE 12320 presented at the 1983 SPE eastern regional meeting, champion, PA, Nov, 9-11.
[12] Won K W. Thermodynamic for solid-liquid-vapor equilibria: wax phase formation from heavy hydrocarbon mixtures. Paper presented at the 4th International Conference on Fluid Properties and Phase Equilibria for Chemical Process Design, Helsinger, Denmark, May 11-16, 1986.
[13] Carnahan N F. Paraffin deposition in petroleum production. JPT (Oct. 1989) 1024-1025.
[14] 刘志泉,李剑新.中国原油性质及综合评价.北京,石油出版社,1996.
[15] Dollhohf H. Thermal behavior and non-isothermal crystallization kinetics of normal-alkanes and their waxy mixtures under quiescent conditions. A Dissertation of Ph. D Calary, Alberta, 1994.
[16] Zhou X, Thomas F B and Moore R G. Modeling of solid precipitation from reservoir fluid. Journal of Canadian Petroleum Technology, 1996, 35(10): 37-45.
[17] 梅海燕,孔祥言等.预测石蜡沉积的热力学模型.石油勘探与开发,2002,Vol.27,No.1,(84-87).
[18] Weingarten J S, Euchner J A. Methods for predicting wax precipitation and deposition. SPE Production Engineering, 1988, 121-126.
[19] 马殿坤.原油中蜡的沉积及影像因素.油田化学,1988,No.1,64-70.
[20] 岳福山.关于原油中蜡的沉积过程.油田化学,1987,Vol4,No,4.
[21] Kabir C S, Hasan A R. An approach to mitigating well bore solids deposition. SPE 71558.
[22] Alex R F, Fuhr B J, Rawluk M et al. Characterization of waxy crudes and waxes symposium on modern analytical techniques for the analysis of petroleum. American Chemical Society, New York City Meeting, 8, 25-31, 1991.
[23] Claudy P, Jean M, Chague B et al. Crude oils and their distillates: characterization by differential scanning calorimetry. Fuel, Vol 67, Jan, 1988.
[24] 李鸿英,黄启玉,张帆等.用差示扫描量热法确定原油的含蜡量.石油大学学报,Vol.27,No.1,Feb,2003.
[25] Won K W. Thermodynamic for solid-liquid equilibria: wax formation from heavy hydrocarbon mixtures. Paper presented at the AIChE National Spring Meeting, Houston, Texas, March 1985.
[26] Pedersen K S, Skovborg P. Wax Precipitation from North Sea Crude Oils 4. Thermodynamic Modeling. Energy & Fuels, 1991, 5, 924-935.
[27] Erickson D D, Niesen V G, Brown T S. Thermodynamic measurement and precipitation of paraffin precipitation in crude oil. SPE 26604, 1993, 933-948.
[28] Thomas J B, Bennian D B, Bennion D W. Experimental and theoretical studies of solids Precipitation from reservoir fluid. Jan, 1992.
[29] Chungn T H. Thermodynamic model for organic solid precipitation. NIPER-623, Sept, 1992.
[30] Deo M D, Miharia A, Zumar R. Solids Precipitation in Reservoirs Due to Nonisothermal Injections. SPE 28967, 1995, 225-235.
[31] Hansen J H, Fredenslund A, Pedersen K Set al. A thermodynamic model for predicting wax formation in crude oils. AIChE J, 1988, 34(12): 1937-1942.
[32] Coutinho J A P, Andersen S L, Stenby E H. Evaluation of activity coefficient models in prediction of alkane solid-liquid equilibria. Fluid Phase Equilibria 1995, 103, 23-39.
[33] Pauly J, Dauphin C and Daridon J L. Liquid-solid equilibria in a decane plus multi-paraffins system. Fluid Phase Equilibria, 1998.
[34] Coutinho J A P, Andersen S L, Stenby, E H. Solid-liquid lquilibrium of non-alkanes using the chain delta lattice parameter model. Fluid Phase Equilibria 1996, 117, 138-145.
[35] Coutinho J A P, Stenby E H. Predictive local composition models for solid/liquid equilibrium in n-alkane systems: Wilson Equation for Multicomponent Systems. Ind Eng Chem Res, 1996, 35, 918-925.
[36] Coutinho J A P, Ruffier-Meray V. Experimentalmeasurements and thermodynamic modeling of paraffinic wax formation in undercooled solutions. Ind Eng Chem Res, 1997, 36, 4977-4983.
[37] Singh P, Youyen A and Fogler H S. Existence of a critical carbon number in aging of a wax-oil gel. AIChE J, 2001, 47(9).
[38] Lira-Galeana C, Firoozabadi A, Prausnitz J M. Thermodynamics of wax precipitation in petroleum mixtures. AIChE Journal 1996, 42, 239-248.
[39] Pan H, Firoozabadi A, Fotland P. Pressure and composition effect of wax precipitation: experimental data and model results. SPE 26740,1996, 579-592.
[40] Leontaritis K J. PARA-based (paraffin-aromatic-resin-asphaltene) reservoir oil characterizations. SPE 37252, 1997, 421-440.
[41] Zuo J Y, Zhang D D. A thermodynamic model for wax precipitation. Paper presented at the 2nd International Conf. on. Pet. and Gas Phase Behavior and Fouling, Denmark, August 27-31, 2000.
[42] Riazi M R, Al-Sahhaf T A. Physical properties of heavy petroleum fractions and crude oils. Fluid Phase Equilibria, 117, 217-224 (1996).
[43] Leelavanichkul P, Deo M D, Hanson F V. Crude oil characterization and regular solution approach to thermodynamic modeling of solid precipitation at low pressure. Petroleum Science and Technology, v22, n 7-8, July, 973-990 (2004).
[44] 潘竟军,张焱,韩晓强.差示扫描量热法测定原油含蜡量的研究.石油天然气学报,Dec2005,Vol.27 NO.6.
[45] 李凤艳,赵天波,冀德坤.气相色谱法则定石蜡正异构烃及碳数分布积分方式的选择.分析化学,1995,23(10):1208-1210.
[46] 王素琴,王萌,辛玉芬等.原油及渣油族组成定量分析—高效液相色谱法.油气田地面工程,1996,15(6):17-19.
[47] Hsu C S, Mclean M A, Qian K Net al. On-line liquid chromatography/mass spectrometry for heavy hydrocarbon characterization. Energy& Fuels, 1991. 5: 395-398.
[48] Ji H Y, Bahman Ti, All D et al. Wax phase equilibria: developing a thermodynamic model using a systematic approach. Fluid Phase Equilibria, v216, n2, Feb 29, 201-217 (2004).
[49] 马庆兰,郭天民.用局部组成活度系数模型计算原油中石蜡沉积量.石油大学学报(自然科学版,2003,v27,n5,October,99-102.
[50] Jean-Pierre C. Temperatures and enthalpies of (solid+solid) and (solid+liquid) transitions of n-alkanes. J Chem Thermodynamics, 34, 1255-1277 (2002).