UNIVERSIDADE FEDERAL DE SANTA CATARINA CENTRO TECNOLÓGICO
PROGRAMA DE PÓS-GRADUAÇÃO EM ENGENHARIA MECÂNICA
Fernando Freitas Czubinski
PHASE-EQUILIBRIUM AND DYNAMIC VISCOSITY OF GAS MIXTURES AT HIGH PRESSURES AND LIQUID MIXTURES OF HEAVY OILS AND LIQUEFIED
GASES
Florianópolis
Fernando Freitas Czubinski
EQUILÍBRIO DE FASES E VISCOSIDADE DINÂMICA DE MISTURAS GASOSAS EM ALTA PRESSÃO E MISTURAS LÍQUIDAS DE ÓLEOS PESADOS E GASES
LIQUEFEITOS
Tese submetida ao Programa de Pós-Graduação em Engenharia Mecânica para a obtenção do título de Doutor em Engenharia Mecânica.
Orientador: Prof. Jader Riso Barbosa Jr., Ph.D. Coorientador: Moisés A. Marcelino Neto, Dr. Eng.
Florianópolis
Ficha de identificação da obra elaborada pelo autor,
através do Programa de Geração Automática da Biblioteca Universitária da UFSC.
Czubinski, Fernando Freitas
Phase-equilibrium and dynamic viscosity of gas mixtures at high pressures and liquid mixtures of heavy oils and liquefied gases / Fernando Freitas Czubinski ; orientador, Jader Riso Barbosa Jr., coorientador, Moisés Alves
Marcelino Neto, 2019. 142 p.
Tese (doutorado) - Universidade Federal de Santa
Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2019.
Inclui referências.
1. Engenharia Mecânica. 2. Equilíbrio de fases. 3. Viscosidade. 4. Termodinâmicas misturas. 5. Propriedades termofísicas. I. Barbosa Jr., Jader Riso. II. Neto, Moisés Alves Marcelino. III. Universidade Federal de Santa
Catarina. Programa de Pós-Graduação em Engenharia Mecânica. IV. Título.
Fernando Freitas Czubinski
PHASE-EQUILIBRIUM AND DYNAMIC VISCOSITY OF GAS MIXTURES AT HIGH PRESSURES AND LIQUID MIXTURES OF HEAVY OILS AND LIQUEFIED
GASES
O presente trabalho em nível de Doutorado foi avaliado e aprovado por banca examinadora composta pelos seguintes membros:
Prof. Marcos Lúcio Corazza, Dr. Eng.
Universidade Federal do Paraná / Dep. Engenharia Química
Prof. Marcelo Lanza, Dr. Eng.
Universidade Federal de Santa Catarina / Dep. Engenharia Química
Prof. Alexandre Kupka da Silva, Ph.D.
Universidade Federal de Santa Catarina / Dep. Engenharia Mecânica
Certificamos que esta é a versão original e final do trabalho de conclusão que foi julgado adequado para obtenção do título de “Doutor em Engenharia Mecânica”.
Prof. Jonny Carlos da Silva, Dr. Eng. Coordenador do Programa
Prof. Jader Riso Barbosa Jr., Ph.D. Orientador
Florianópolis, 13 de Setembro de 2019.
Jader Riso Barbosa
Junior:01002620740
Digitally signed by Jader Riso Barbosa Junior:01002620740 Date: 2019.11.03 16:16:41 -03'00'
Assinado de forma digital por Jonny
Carlos da Silva:51451506449
Amargo doce que eu sorvo num beijo em lábios de prata. Tens o perfume da mata, molhada pelo sereno. E a cuia, seio moreno, que passa de mão em mão. Traduz, no meu chimarrão, em sua simplicidade, a velha hospitalidade da gente do meu rincão . (Glaucus Saraiva)
AGRADECIMENTOS
First of all, I would like to thank Prof. Jader Riso Barbosa Jr. for accepting me as a student in his laboratory and for the opportunity of professional and existential growth. I am also thankful to Prof. Moises Marcelino Neto for sharing his knowledge which was important at the beginning of my Ph.D.
I also would like to thank Prof. Eric May from UWA for welcoming me in his research group and for enriching my professional formation. I also thank Drs. Thomas Hughes and Saif Al Ghafri for their friendship and experience.
Besides, I would like to thank the committee members: Prof. Marcos Corazza, Prof. Marcelo Lanza and Prof. Alexandre Kupka da Silva for their comments and contributions to this thesis.
During my time at PosMEC, I was very lucky to have made “new” good friends: Paulo Trevizoli, Gustavo Gondran, Michele Lazzari, Luigi Passos, Alvaro Nacif and Carlos Noriega.
I’m also grateful to my family [Jose, Maria, Mauricio, Cristina and Cristina (Kike)] by their dedication towards me.
RESUMO
O conhecimento acerca do equilíbrio de fases e da viscosidade de misturas de gases a altas pressões e de misturas de gases liquefeitos em óleos pesados é de grande importância em apli-cações nas áreas de motores e combustíveis, refrigeração (lubrificação de compres-sores) e na exploração de petróleo. De modo a preencher uma lacuna existente na literatura com relação à disponibilidade de dados experimentais, esta tese se dedica ao estudo dos seguintes sistemas: (i) mistura binária metano-propano xCH4 + (1-x)C3H8, x = 0,8881 (fração molar), 203 < T < 424
K e 2 < p < 31 MPa; (ii) mistura ternária metano-propano-dióxido de carbono xCH4 + yC3H8
+ (1-x-y)CO2, x = 0,6511, y = 0,0808 (frações molares), 203 < T < 420 K e 3 < p < 31 MPa;
(iii) mistura binária de dióxido de carbono (CO2) e n-dodecano (C12H26) para frações molares
de CO2 entre 0,2 e 0,8, 283 < T < 353 K e 1,2 < p < 14 MPa; (iv) mistura binária de propano
(R-290) e óleo POE ISO 22 para frações molares de R-290 entre 0,2 e 0,8, 283 < T < 353 K e 0,17 < p < 2,3 MPa; (v) mistura binária de isobutano (R-600a) e óleo LAB ISO 2 para frações molares de R-600a entre 0,15 e 0,9, 293 < T < 353 K e 0,18 < p < 1,3 MPa.
Para os sistemas (i) e (ii), a viscosidade dinâmica das misturas gasosas a alta pressão foi avaliada experimentalmente no Laboratory of Fluid Science and Resources do School of Mechanical and Chemical Engineering, da University of Western Australia, por meio da técnica do fio vibrante (vibrating wire viscometer), operando em regime permanente com o fio preso nas duas extremi-dades. Para os sistemas (iii), (iv) e (v), dados experimentais de equilíbrio de fases (pressão de ponto de bolha) e de viscosidade dinâmica da fase líquida foram obtidos simultaneamente por meio do método estático sintético em uma célula de equilíbrio de volume variável conectada em série com um viscosímetro de alta pressão baseado no método do pistão oscilante. Estes expe-rimentos foram conduzidos no Polo – Laboratórios de Pesquisa em Refrigeração e Termofísica, no Departamento de Engenharia Mecânica da Universidade Federal de Santa Catarina.
Para a avaliação do equilíbrio de fases nos sistemas (iii), (iv) e (v), as equações de estado (EoS) de Peng-Robinson, PC-SAFT (Perturbed Chain Statistical Associating Fluid Theory) e PCP-SAFT (Perturbed Chain Polar Statistical Associating Fluid Theory) foram utilizadas para correlacionar as medições de pressão de ponto de bolha. Para a viscosidade de misturas líqui-das, foi utilizado o model de Quiñones-Cisneros (baseado na teoria de cisalhamento, f -theory). A viscosidade das misturas gasosas dos sistemas (i) e (ii) foram correlacionadas dois modelos baseados na teoria dos estados correspondentes, ECS (Extended Corresponding State) e Su-perTRAPP (modificação do modelo TRAPP – Transport Proper-ties Predictions), um modelo preditivo baseado em resultados de simulação molecular para moléculas de Lennard-Jones, LJ, e um modelo semi-teórico, VW, que é um extensão para misturas base-ado no modelo de esferas duras de Enskog para gases densos.
Os resultados experimentais de equilíbrio de fase para a mistura de R600a/LAB ISO 2 foi cor-relacionado com as EoS com um average absolute deviation (AAD) de 7,3 %. Para as misturas de CO2/n-C12H26 e R290/POE ISO 22, os AADs foram de 2,2 e 6,56 %, para o equilíbrio de
fases, e 8,51 e 24,77 % para a viscosidade, respectivamente. As misturas de gas também foram correlacionadas como os modelos teóricos de viscosidade com AADs de 0,63 % para a mistura binaria e 2,53 % para a mistura ternária.
RESUMO EXPANDIDO
Introdução
Dióxido de carbono, assim com outros compostos diferente dos hidrocarbonetos, inerentemente estão presentes nas reservas de petróleo e gás. Entretanto, a importância do CO2 é maior que
a dos outros compostos devido a sua importância em processos como a recuperação avançada de petróleo e armazenamento/sequestro em reservas exauridas. Por essa razão, o conhecimento das propriedades termodinâmicas e de transporte de misturas envolvendo CO2 e
hidrocarbone-tos são importantes para o setor de Óleo & Gás. Dados experimentais dessas propriedades são importantes pois auxiliam na validação de modelos teóricos utilizados na simulação de reserva-tórios e projeto de equipamentos, bem como em problemas mais específicos como precipitação de óleos pesados e formação de hidratos.
Sistemas de refrigeração doméstica operam com compressores herméticos lubrificados a óleo e utilizam fluido refrigerante para promover o efeito de resfriamento. Durante o processo de ope-ração do sistema, esses dois fluidos interagem resultando na formação de uma mistura. Dessa forma, uma certa quantidade de fluido refrigerante fica solubilizada no óleo do compressor, alterando as características de lubrificação das partes móveis, bem como um pouco de óleo es-coa junto com o fluido refrigerante pelos trocadores de calor degradando a eficiência global de transferência de calor do sistema de refrigeração.
Devido às constantes substituições de fluidos refrigerantes nas últimas décadas, se fez necessá-rio também substituir os óleos minerais por sintéticos, pois os primeiros já não mais apresen-tavam compatibilidade com os novos fluidos refrigerantes. Atualmente, devido a suas caracte-rísticas termodinâmicas e ambientais favoráveis, hidrocarbonetos como o propano, isobutano e propileno surgem como opções. Esse cenário justifica a importância do conhecimento prévio de compatibilidade termodinâmica dos novos fluidos de refrigeração com os óleos lubrificantes.
Objetivos
O objetivo geral da presente tese de doutorado é a investigação, teórica e experimental, do equi-líbrio de fases e viscosidade de misturas aplicadas nos setores de Óleo & Gás e Refrigeração. Para cumprir esse objetivo, as seguintes atividades específicas foram estipuladas: (i) desenvolver um procedimento experimental para avaliação do equilíbrio de fases e medição de viscosidade de misturas líquidas utilizando a mesma amostra de mistura; (ii) determinar pressão de transi-ção de fase e viscosidade das seguintes misturas, considerando temperaturas entre 10 e 80∘C e
frações molares do componente leve entre 0,2 e 0,8; (ii-a) R-290 (propano) e POE ISO 22 (óleo Poliolester); (ii-b) R-600a (isobutano) e LAB ISO 2 (óleo linear Alkil Benzeno); (ii-c) CO2 e
n-C12H26 (n-dodecano); (iii) Implementar equações de estado do tipo cúbica e também do tipo SAFT para avaliação teórica do equilíbrio de fases e o modelo baseado na teoria-f para as vis-cosidade de líquidos; (iv) Propor um procedimento experimental para medição de visvis-cosidade de misturas de gás em elevadas pressões para as seguintes misturas, considerando temperatu-ras entre -70 e 150 ∘C e pressões até 32 MPa; (iv-a) xCH
4 + (1-x)C3H8, sendo x = 0.8881;
(iv-b) xCH4 + yC3H8 + (1-x-y)CO2, sendo x = 0.6511 e y = 0.0808; (vi) avaliar a capacidade
de descrever o comportamento experimental de viscosidade de 4 modelos teóricos, sendo dois baseados no princípio dos estados correspondentes, um proveniente de resultados de simulação molecular e o último uma extensão da teoria de esferas duras de Enskog.
Metodologia
A avaliação do equilíbrio de fases e viscosidade das misturas líquidas foi realizada através do método sintético utilizando uma célula PVT de volume variável, e de um viscosímetro base-ado no método de pistão-oscilante conectbase-ado em série com a célula PVT. Ambos os aparatos foram calibrados e validados, reproduzindo valores disponíveis na literatura com desvios rela-tivos máximos de 3 % para pontos de bolha e 1,5 % para viscosidade de líquidos. Ainda com relação as misturas líquidas, as equações de estado (EoS) de Peng e Robinson (PR), PC-SAFT e PCP-SAFT foram empregadas para correlacionar os dados experimentais de equilíbrio do fa-ses, através do método-K. Os dados experimentais de viscosidade foram correlacionados com o modelo de Quiñones-Cisneros, apresentado como teoria-f (friction theory), onde as pressões obtidas pelas equações de estado já citadas servem como dado de entrada.
Com relação à medição de viscosidade de misturas de gás em altas pressões, foi empregado o método do fio vibrante (vibrating wire viscometer) operando em regime permanente com o fio preso em ambas extremidades. A bancada experimental foi calibrada e a performance foi avaliada através da comparação de medições com dados da literatura, resultando em desvios relativos menor que 2 %. Para as misturas de gás, 4 modelos teóricos foram utilizados para cor-relacionar os dados experimentais. Os dois primeiros modelos teóricos, ECS e ST, são baseados na teoria dos estados correspondentes e se encontram disponíveis em softwares comercias como REFPROP 9.1 e MULTIFLASH 4.4, respectivamente. O terceiro modelo, LJ, é uma correlação desenvolvida, a partir de dados provenientes de simulação molecular utilizando o potencial in-termolecular de Lennard-Jones, também baseada no principio dos estados correspondentes. Por fim, um quarto modelo teórico, VW, foi utilizado sendo esse uma extensão da teoria de Enskog para esferas duras.
Resultados e discussão
Os resultados experimentais de equilíbrio de fases para mistura de R-600a e LAB ISO 2 mos-tram aumento linear da pressão de bolha até a fração molar de R-600a igual a 0,72, e uma eleva-ção mais acentuada para frações mais elevadas. Embora todas as transições de fases observadas tenham sido do tipo líquido-vapor, esse comportamento indica surgimento de imiscibilidade. A EoS de PR utilizando a regra de mistura de van der Waals correlacionou os dados experi-mentais com um AAD (average absolute deviation) de 11,4 % e de 7,3 % quando utilizando a regra de mistura de Wong-Sandler (WS). Ainda para essa mistura, a EoS PC-SAFT foi aplicada produzindo AAD = 10,9 %. A mistura formada por CO2 e n–C12H26também produziu
transi-ções de fase do tipo líquido-vapor. Para essa mistura, as EoSs de PR, PC-SAFT e PCP-SAFT foram aplicadas com AADs iguais a 3,86 %, 8,34 % e 2,2 %, respectivamente. Com relação aos resultados de viscosidade, os dados experimentais foram comparados com misturas simila-res na literatura para verificar a consistência das medidas e correlacionadas com o modelo de viscosidade, teoria-f, utilizando as pressões fornecidas pelas EoS de PR e PC-SAFT. O modelo correlacionou os dados experimentais com uma AAD de 10,85 %, quando usando a EoS de PR, e 8,51 % com a PC-SAFT. Por fim, a mistura de R-290 e POE ISO 22 também apresentou tran-sições de fase somente do tipo líquido-vapor. A correlação dos dados experimentais com a EoS de PR teve AAD = 8,39 % e a EoS PC-SAFT de 6,56 %. As medições de viscosidade dessa mis-tura tiveram sua consistência checada comparando com medidas experimentais do óleo puro. Essa avaliação é baseada através de observações empíricas fundamentadas no modelo Eyring. Por fim, o modelo teórico de viscosidade, teoria-f, resultou em AAD igual a 24,77 %.
Com relação à medição de viscosidade de misturas de gás, a mistura binária de CH4 e C3H8
foi comparada com dados experimentais de outros autores mostrando uma boa concordância. Ainda, o comportamento visual da curva de viscosidade residual dos dados experimentais em
função da densidade mostrou ser independente de temperatura. Para essa condição, um polinô-mio de quarta ordem foi ajustado com um AAD de 0,78 %. Com relação a investigação de capacidade descrever o comportamento dos 4 modelos teóricos utilizados, o modelo ECS resul-tou em um AAD de 1,93 %, o modelo ST um AAD de 4,65 %, o modelo LJ um AAD de 0,86 % e o modelo VW um AAD de 0,63 %. Já a viscosidade da mistura ternária de CH4/C3H8/CO2
foi verificado a consistência dos resultados experimentais somente utilizando a curva de vis-cosidade residual em função da densidade. Nesse caso, esse gráfico também se mostrou ser independente de temperatura, com um AAD de 0,86 % utilizado o modelo free-volume. Para essa mistura, somente 3 modelos teóricos foram testados, resultando em AADs iguais a 2,53 % para o modelo ECS, 6,44 % para o modelo ST e 3,89 % para o modelo LJ.
Considerações Finais
A presente tese de doutorado apresentou dados experimentais de equilíbrio de fases e viscosi-dade de cinco misturas relevantes para o segmento industrial de Óleo & Gás e Refrigeração. Dessas cinco misturas, três foram avaliadas na condição de líquido e duas na condição de gás visando preencher lacunas de dados experimentais encontrados na literatura.
Para as misturas líquidas, foi desenvolvido uma metodologia experimental para avaliação em série de equilíbrio de fases e viscosidade utilizando mesma amostra de mistura. O aparato ex-perimental foi calibrado e validado, apresentando desvios relativos máximos de 3 % para equi-líbrio de fases e 1,5 % para viscosidade.
Para os resultados experimentais de equilíbrio de fase, as três misturas apresentaram transições de fase do tipo líquido-vapor para as faixas de pressão, temperatura e composição analisada. Para essas misturas, os modelos teóricos utilizados foram capazes de correlacionar os dados experimentais, sendo a EoS de PR/WS apresentado a melhor descrição para a mistura de R-600a/LAB ISO 2, PCP-SAFT para a mistura de CO2/n-C12H26 e PC-SAFT para R-290/POE
ISO 22. Com relação as medições de viscosidade para as misturas líquidas, os dados experi-mentais da mistura de CO2/n-C12H26 apresentaram consistência quando comparados com
da-dos de misturas semelhantes disponíveis da literatura. Para essa mistura, o modelo teórico de viscosidade, teoria-f, acoplado com a EoS PC-SAFT, foi o que apresentou melhor concordância com os dados experimentais. Por fim, os dados experimentais de viscosidade da mistura de R-290/POE ISO 22 teve sua consistência checada comparando com dados experimentais de óleo puro. No entanto, para essa mistura, o modelo teórico de viscosidade, teoria-f acoplada com PC-SAFT, apresentou desvios consideráveis para baixas temperaturas.
Com relação aos dados experimentais de viscosidade para mistura de CH4 e C3H8, os
resulta-dos foram compraresulta-dos com daresulta-dos da literatura mostrando consistência nas medidas. Para essa mistura, o modelo de VW apresentou a melhor concordância entre os outros três modelos tes-tados. Já a mistura ternária, CH4/C3H8/CO2, teve sua consistência avaliada através do gráfico
da viscosidade residual em função da densidade. Para essa mistura, o modelo ECS foi o que melhor reproduziu os dados experimentais.
ABSTRACT
The knowledge about phase-equilibrium and dynamic viscosity of gas mixtures under high pressure and mixtures of heavy oils and liquified gases is of great importance in the areas of engines and fuels, refrigeration (compressor lubrication) and oil & gas. In or-der to fulfill some of the experimental data gaps encountered in the literature, the present thesis is focused on the following systems: (i) methane-propane binary mixture xCH4 + (1-x)C3H8, x = 0.8881 (molar fraction), 203 < T < 424 K and 2 < p < 31 MPa; (ii) methane-propane-carbon dioxide ternary mixture xCH4+ yC3H8+ (1-x-y)CO2, x = 0.6511, y = 0.0808 (molar fractions), 203 < T < 420 K
and 3 < p < 31 MPa; (iii) binary mixture of car-bon dioxide (CO2) and n-dodecane (n-C12H26)
for CO2mole fraction between 0.2 and 0.8, 283 < T < 353 K and 1.2 < p < 14 MPa; (iv) binary
mixture of propane (R-290) and POE ISO 22 lubricating oil for R-290 mole fractions between 0.2 and 0.8, 283 < T < 353 K and 0.17 < p < 2.3 MPa; (v) binary mixture of isobutane (R-600a) and LAB ISO 2 lubricating oil for R-600a mole fractions between 0.15 and 0.9, 293 < T < 353 K and 0.18 < p < 1.3 MPa.
For systems (i) e (ii), the dynamic viscosity of the gas mixtures at high pressures was experi-mentally evaluated in the Fluid Science and Resources Laboratory at the School of Mechanical and Chemical Engineering of the University of Western Australia, by means of a steady-state vibrating wire viscometer with the wire clamped at both ends. For systems (iii), (iv) e (v), the phase-equilibrium (bubble point pressure) and liquid dynamic viscosity data were gathered by means of an oscillating-piston viscometer connected in series with a synthetic variable–volume view PVT cell. These experiments were conducted at Polo – Research Laboratories for Emerg-ing Technologies in CoolEmerg-ing and Thermophysics at the Mechanical EngineerEmerg-ing Department of the Federal University of Santa Catarina.
For the theoretical evaluation of the phase-equilibrium in systems (iii), (iv) e (v), the Peng-Robinson cubic equations of state, EoS, the PC-SAFT (Perturbed Chain Statistical Associating Fluid Theo-ry) and the PCP-SAFT (Perturbed Chain Polar Statistical Associating Fluid Theory) were used to correlate the experimental bubble point pressure. For the liquid mixture viscosities, the theoretical model of Quiñones-Cisneros (based on the classical mechanics and van der Waals fluid theory, f-theory) was used.
The viscosity of the gas mixtures in systems (i) and (ii) were correlated with with four theoreti-cal models where two of them are based on the corresponding states theory, the ECS (Extended Corresponding States) and SuperTRAPP (modified TRAPP – Transport Properties Predictions), the LJ model which is based on molecular dynamics simulations of Lennard Jones fluids and a semi-theoretical model, VW, which is an extension to mixture of the Enskog hard-sphere theory of dense gas.
The phase-equilibrium experimental results for the R-600a/LAB ISO 2 system were correlated with an absolute average deviation, AAD, of 7.3%. For CO2/n-C12H26 and R290/POE ISO 22
mixtures, the AADs were 2.2 e 6.56%, for phase-equilibrium, and 8.51 and 24.77% for liquid viscosities, respectively. For the gas mixture viscosities, the AADs were 0.63% for the binary mixture and 2.53% for the ternary system.
LIST OF FIGURES
Figure 1 – Experimental facility for simultaneous phase equilibrium and viscosity
mea-surement. . . 53
Figure 2 – (a) Phase equilibrium cell in the isothermal bath; (b) Exploded view of the components of the PVT cell. . . 54
Figure 3 – LabVIEW interface (pressure and temperature measurements) and micro-scope image of the front chamber for saturated CO2. . . 55
Figure 4 – Viscometer valves, fluid orientations and schematic diagram of inner parts. . 56
Figure 5 – (a) Phase equilibrium cell positioned in a vice for charging; (b) Small reser-voir and tube connection. . . 57
Figure 6 – Schematic drawing of the isobaric transfer from the PVT cell to the viscometer. 59 Figure 7 – Comparison of saturation pressure measurements against reference values from REFPROP 9.1 and bubble point pressure against data from Lee et al. (2000). . . 63
Figure 8 – Dead volume evaluation effect on bubble point pressure. . . 64
Figure 9 – Comparison of liquid viscosity measurements against reference data. . . 65
Figure 10 – Schematic diagram of the VWV assembly. . . 66
Figure 11 – Picture from the wire holder and the pressure vessel. . . 67
Figure 12 – Schematic diagram of the VWV electric circuit. . . 68
Figure 13 – Illustration of a typical resonance curve measured by the lock-in amplifier. . 69
Figure 14 – Obtained vacuum damping and wire radius used in the present work. . . 72
Figure 15 – Comparison of the experimental pure fluid measurement with reference data for helium, methane and nitrogen. . . 73
Figure 16 – Illustration of PC-SAFT molecular interaction interpretation adapted from Al-Ghafri et al. (2014). . . 80
Figure 17 – Molecular models for the 2CLJ and TS-LJ. . . 82
Figure 18 – Experimental and theoretical bubble point pressure as a function of the mole fraction according to the PR EoS/vdW EoS for R-600a/LAB ISO 2. . . 96
Figure 19 – Experimental and theoretical bubble point pressure as a function of the mole fraction according to the PC-SAFT EoS for R-600a/LAB ISO 2. . . 96
Figure 20 – Experimental and theoretical bubble point pressure as a function of the mole fraction according to the PR EoS/WS model for R-600a/LAB ISO 2. . . 97 Figure 21 – Experimental and theoretical bubble point pressure as a function of the mole
fraction according to the PR/vdW EoS for CO2/n-C12H26. . . 99
Figure 22 – Experimental and theoretical bubble point pressure as a function of the mole fraction according to the PC-SAFT EoS for CO2/n-C12H26. . . 100
Figure 23 – Experimental and theoretical bubble point pressure as a function of the mole fraction according to the PCP-SAFT EoS for CO2/n-C12H26. . . 100
Figure 24 – Experimental and theoretical bubble point pressure as a function of the mole fraction according to the PR/vdW EoS for R-290/POE ISO 22. . . 102 Figure 25 – Experimental and theoretical bubble point pressure as a function of the mole
fraction according to the PC-SAFT EoS for R-290/POE ISO 22. . . 102 Figure 26 – Experimental data on the viscosity of CO2 / n-C12H26mixtures as a function
of the inverse of the absolute temperature. The black triangles are experi-mental data from Barrufet et al. (1996) for CO2 / n-C10H22mixtures. . . 105
Figure 27 – Prediction of the experimental dynamic viscosity for CO2 / n-C12H26
ac-cording to the f -theory/PR. Upper graph: ab-solute values; bottom graph: relative deviation. . . 105 Figure 28 – Prediction of the experimental dynamic viscosity for CO2/ n-C12H26
accord-ing to the f -theory/PC-SAFT. Upper graph: absolute values; bottom graph: relative deviation. . . 106 Figure 29 – Relative deviations of f -theory/PC-SAFT with respect to experimental data.
Circles: CO2/n-C10H22 (BARRUFET et al., 1996), squares: CO2/n-C12H26
[present work] and triangles: CO2/n-C16H34(MOHAMMED et al., 2016). . 106
Figure 30 – Comparison between the POE ISO 22 viscosity data generated in the present work and the manufacturer data. . . 110 Figure 31 – R-290 / POE ISO 22 mixture viscosity data as a function of the inverse of
the absolute temperature. . . 110 Figure 32 – Analysis of the experimental dynamic viscosity for R-290/POE ISO 22
ac-cording to the f -theory. Upper graph: absolute values; bottom graph: relative deviation. . . 111 Figure 33 – Pressure and temperature conditions of the viscosity measurements for the
Figure 34 – Upper graph: residual viscosity as a function of density for each temperature. Lower graph: relative deviation between the correlation and the experimen-tal data for {xCH4+ (1 - x)C3H8} with x = 0.8881. . . 116
Figure 35 – Analysis of the present binary mixture gas viscosity data, together with other data from the literature by four theoretical models (a-ECS, b-LJ, c-ST, d-VW), xCH4+ (1 - x)C3H8. . . 117
Figure 36 – Relative deviation of the present binary measurement with respect to the the-oretical models, (a-ECS, b-LJ, c-ST, d-VW), for each temperature, {xCH4 +
(1 - x)C3H8} with x = 0.8881. . . 118
Figure 37 – Pressure and temperature conditions of the viscosity measurements for the ternary mixture {0.6511CH4 + 0.0808C3H8 + 0.2681CO2}. . . 119
Figure 38 – Upper graph: residual viscosity as a function of density for each temperature. Lower graph: relative deviation between the correlation and the experimen-tal data for {0.6511CH4 + 0.0808C3H8+ 0.2681CO2}. . . 123
Figure 39 – Relative deviation of the theoretical models (a-ST, b-LJ, c-ECS) from exper-imental, {0.6511CH4+ 0.0808C3H8 + 0.2681CO2}. . . 124
Figure 40 – Influence of the presence of CO2on the viscosity of a methane/propane
mix-ture. Solid lines represent the ternary mixture, dotted lines are for the binary correlation. . . 125
LIST OF TABLES
Table 1 – Literature phase behavior data for CO2and n-alkane mixtures. . . 44
Table 2 – Literature viscosity data for CO2and n-alkane mixtures. . . 46
Table 3 – Literature data for hydrocarbon refrigerant and synthetic lubricating oil. . . . 48 Table 4 – Literature viscosity data for natural gas mixtures. . . 51 Table 5 – Relative uncertainties contributions for the VWV. . . 72 Table 6 – Experimental data AAD, RMSD and bias from reference. . . 74 Table 7 – Input parameters for cubic EoS and viscosity models. . . 93 Table 8 – Input parameters for PC-SAFT EoS, PCP-SAFT EoS and f -theory viscosity
model. . . 94 Table 9 – Experimental data and expanded uncertainties for R-600a/LAB ISO 2. . . 95 Table 10 – Experimental data and expanded uncertainties for CO2/n-C12H26. . . 98
Table 11 – Experimental data and bubble point pressure expanded uncertainty for R-290 / POE ISO 22. . . 101 Table 12 – Summary of AADs for each EoS used to the phase equilibrium of the three
binary mixtures. . . 103 Table 13 – Experimental data and viscosity expanded uncertainty for CO2/n-C12H26. . . 104
Table 14 – Coefficients used in the f -theory/PR for the pure components and the AAD for the pure fluids and for the mixture. . . 107 Table 15 – Coefficients used in the f -theory/PC-SAFT for the pure components and the
AAD for the pure fluids and for the mixture. . . 108 Table 16 – Experimental data and viscosity expanded uncertainty for R-290 / POE ISO 22.109 Table 17 – Viscosity of pure POE ISO 22 as a function of pressure and temperature. . . 109 Table 18 – Adjusted coefficients used in the f -theory/PC-SAFT for the pure components
and mixture followed by the AAD for each fitting/verification. . . 112 Table 19 – Viscosity �, type A uncertainty Ua(�) and combined uncertainty Uc(�) as a
function of pressure, p, and temperature, T, for xCH4 + (1 - x)C3H8, with x =
0.8881. Density, �, was calculated using the GERG-2008 EoS. . . 113 Table 20 – Summary of the AAD of the theoretical models with respect to the
Table 21 – Viscosity �, type A uncertainty Ua(�) and combined uncertainty Uc(�) as a function of pressure, p, and temperature, T, for {0.6511CH4 + 0.0808C3H8 +
0.2681CO2}, with x = 0.8881. Density, �, was calculated using the
GERG-2008 EoS. . . 120 Table 22 – Summary of the AAD of the theoretical models with respect to the
LIST OF SYMBOLS
Roman
� Helmholtz energy J·mol−1
� energy parameter J·m3
·mol−2
� magnetic field strength
-� molecular volume m3
·mol−1
� temperature dependent segmanet diameter
� frequency Hz
�0 vacuum resonance frequency Hz
�� resonance frequency Hz
� Gibbs energy J·mol−1
� radial distribution function
-� mean segment number
-� mass g
� segment number
-� -� molecular mass g·−1
� number of number mol
� � Avogadro number 6.022·1023mol−1
� pressure MPa and Bar
� quadrupole moment D
�(�) type-A standard uncertainty of x variable
�(�) expanded uncertainty of x variable
-�(�) standard uncertainty of x variable
-� volume ml
� specific volume cm3
·mol−1
�1 stationary wire impedance V
�2 complex induced impedance V
�2 root mean square tension V
� mass fraction -� mean value of x -� molar fraction -Greek � co-volume cm3 ·mol−1
∆0 self-wire vacuum damping
-∆� residual dynamic viscosity cP
� energy parameter J
� dynamic viscosity cP
� scale parameter
-� Boltzmann Constant 1.38·10ˆ−23 J·K−1
� binary interaction parameter
-� coverage factor
-� friction coefficient cP·bar−1
� reduced friction coefficient
-� shape factor
-� density kg·m−3
�* switch-over density
kg·m−3
�� molar density mol·cm−3
� sphere diameter
� shape factor
-Abreviation
2CLJ Two-center Lennard-Jones AB Alkyl beneze
BIP Binary Interaction Parameter BP Bubble Point
CFC Chlorofluorocarbon CLS Chung, Lee and Starling CS Corresponding State DAQ Data Acquisition System ECS Extended Corresponding State EoS Equation of State
f-theory Friction Theory
GERG Groupe Européen de Recherches Gazièries HCFC Hydrochlorofluorocarbon
HC Hydrocarbon HFC Hydrofluorocarbon ID Inner Diameter
ISO International Standards Organization LAB linear alkyl benzene
LBC Lohrenz, Bray and Clark LGE Lee, Gonzalez and Eakin LJ Lennar-Jones
LLE Liquid-Liquid-Equilibrium LLVE Liquid-Liquid-Vapor-Equilibrium LNG Liquefied Natural Gas
LVE Liquid-Vapor-Equilibrium MO Mineral Oil
NRTL Non-Random Two Liquid OD Outer Diameter
PAG polyalkylene glycol PAO poly alpha olefin
PC-SAFT Perturbed-Chain Statistical Associating Fluid Theory
PCP-SAFT Perturbed-Chain Polar Statistical Associating Fluid Theory PFTC Pedersen, Fredenslund, Thomassen and Christensen
POE polyol ester
PR Peng and Robinson
PRT Platinum Resistance Thermometer PSRK Predictive Soave-Redlich-Kwong PVE polyvinylether
R-1234a 1,1,1,2-tetrafluoroetano R-1234yf 2,3,3,3-tetrafluoropropeno R-227ea heptafluoropropane R-22 clorodifluorometano R-290 propane R-600a isobutane R-744 carbon dioxide
RMSD Root Mean Square Deviation RTD Resistance Temperature Detector SAFT Statistical Associating Fluid Theory
SPRT Standard Platinum Resistance Thermometer SRK Soave-Redlich-Kwong
ST SuperTRAPP
TPT1 Thermodynamic Perturbation Theory of First Order TRAPP Transport Properties Prediction
vdW van der Waals VG viscosity grade
VWV Vibrating Wire Viscometer VW Vesovic and Wakeham WS Wong and Sandler Subscript
0 dilute gas condition ����, � Compressor inlet
����, � Compressor outlet ����, � Condenser inlet ����, � Condenser outlet ���� dispersion ������ dispersion ℎ���− �ℎ��� dispersion ℎ���− ��ℎ��� dispersion �� Jet cooler
��, � Jet cooler inlet ��, � Jet cooler outlet ���� prediction
�� quadrupolar-quadrupolar ��� reference
��� residual Superscript
0 dilute gas condition 1 component 1 2 component 2 � attraction �� attraction �� analytical balance �� bubble pressure � combined
� critical ��� calculate � friction � component i � component j ��� maximum ��� minimum ��� mixture �� nonplanar � reduced � repulsion ��� reference �� repulsion �� pressure transducer ����� viscometer �� wire radius
CONTENTS
1 INTRODUCTION . . . 35 1.1 HISTORICAL BACKGROUND . . . 35 1.2 IMPORTANCE AND APPLICATIONS OF FLUID PHASE EQUILIBRIA IN
VA-POR COMPRESSION REFRIGERATION . . . 36 1.3 IMPORTANCE AND APPLICATIONS OF FLUID PHASE EQUILIBRIA IN OIL
AND GAS APPLICATIONS . . . 37 1.4 OBJECTIVES . . . 37 1.5 THESIS OUTLINE . . . 39
2 LITERATURE REVIEW . . . 41 2.1 LIQUID MIXTURES . . . 41 2.1.1 CO2 + n-alkane mixtures . . . 41
2.1.2 Hydrocarbon refrigerants + lubricant mixtures . . . 46 2.2 GAS MIXTURES . . . 48
3 EXPERIMENTAL WORK . . . 53 3.1 PHASE EQUILIBRIUM AND LIQUID VISCOSITY – POLO/UFSC . . . 53 3.1.1 Experimental Procedure . . . 57 3.1.2 Uncertainty Analysis . . . 60 3.1.3 Validation . . . 63 3.2 VIBRATING WIRE VISCOMETER – FSR/UWA . . . 65 3.2.1 Calibration and Uncertainty Analysis . . . 70 3.2.2 Validation . . . 73
4 THEORETICAL MODELS . . . 75 4.1 EQUATIONS OF STATE . . . 75 4.1.1 Peng-Robinson EoS . . . 76 4.1.2 PC-SAFT EoS . . . 78 4.1.3 Phase Equilibrium Calculation . . . 83 4.2 VISCOSITY . . . 84 4.2.1 Friction Theory . . . 84 4.2.2 Corresponding States Theory . . . 88 4.2.3 LJ Fluid Model . . . 89 4.2.4 Vesovic-Wakeham (VW) Viscosity Method . . . 90
5 RESULTS AND DISCUSSIONS . . . 93 5.1 PHASE EQUILIBRIUM . . . 93 5.1.1 R-600a / LAB ISO 2 . . . 94 5.1.2 CO2 / n-alkane mixtures . . . 97
5.1.3 R290 / POE ISO 22 . . . 100 5.2 LIQUID MIXTURE VISCOSITY . . . 103 5.2.1 CO2 / n-alkane mixtures . . . 103
5.2.2 R-290 / POE ISO 22 . . . 108 5.3 GAS MIXTURE VISCOSITY . . . 112 5.3.1 xCH4+ (1 - x)C3H8; x=0.8881 . . . 113 5.3.2 0.6511CH4 + 0.0808C3H8 + 0.2681CO2 . . . 119
6 CONCLUSIONS . . . 127
35
1 INTRODUCTION
1.1 HISTORICAL BACKGROUND
Thermodynamics is the branch of the physical sciences that deals with energy transfor-mations and provides a mathematical framework to guide practical solutions. Although energy conservation concepts have been presented by Leibnitz in 1693 in the context of the motion of heavenly bodies (i.e., kinetic and potential energy conservation), the energy conservation in a more general way (the first law of thermodynamics) emerged almost two centuries later, pushed by the invention of the steam engine (KONDEPUDI; PRIGOGINE, 2014).
The correspondence between heat and work was first announced by Count Rumford in 1798. Then, following Carnot, the works of Mayer, Kelvin, Joule, Helmholtz and Clausius, around 1850, developed the concept of energy conservation, where heat and work began to be treated as two different kinds of energy interaction. Philosophically, however, maybe the first relation between these two forms of energy were already present in the Greek mythology (700 BC). According to them, the human race started when Prometheus defies the Olympian gods by stealing the forbidden divine fire (heat) and breathed it over a clay shaped human giving life (motion) (MEIS; RANGEL, 2004; SCHMITZ, 2007).
Although studies of thermodynamics began with heat and steam power investigations, J. Willard Gibbs, in the second half of 1800s, broadened thermodynamic applications developing procedures to deal with phase-equilibrium behavior of multicomponent chemical systems, es-tablishing the concept of chemical potential (PRAUSNITZ et al., 1998). As expressed by Callen (1985), the basic thermodynamic problem can be described as the determination of the equilib-rium state that eventually results after the removal of internal constraints in a closed, composite system. In other words, phase-equilibrium thermodynamics seek to determine properties such as temperature, pressure, and phase compositions that ultimately prevail when two or more phases reach a state where all tendencies for further change have disappeared (PRAUSNITZ et al., 1998). In practical engineering applications, equilibrium thermodynamics calculations play a central role in the design of several processes such as fluid extraction, adsorption and distillation. The present thesis is focused on the use of the thermodynamic framework in the Refrigeration and Oil & Gas industrial segments.
36 Chapter 1. Introduction
1.2 IMPORTANCE AND APPLICATIONS OF FLUID PHASE EQUILIBRIA IN VAPOR COMPRESSION REFRIGERATION
Hermetic reciprocating compressors are commonly used in domestic refrigeration. In these systems, there is significant inter-action between the lubricating oil and the refrigerant inside the compressor crankcase. As a result of the temperatu and pressudependent re-frigerant absorption in the lubricating oil, the viscosity of the latter is reduced, which must be considered in the design of bearings and lubrication systems (MARSH; KANDIL, 2002). Also, small amounts of oil are carried by the refrigerant through the refrigeration circuit. If miscibil-ity gaps are present at some conditions, especially at low temperatures, the oil may accumulate in the evaporator and not return to the compressor sump. As a consequence, the overall heat transfer performance is reduced, while the compressor becomes oil depleted, which is a serious reliability concern.
In the past, due the miscibility compatibility, mineral oils were used as lubricants in refrigeration system together with chlorinated refrigerants. During the last decades, however, because of the necessity to replace chlorofluorocarbons, CFCs, and hydrochlorofluorocarbons, HCFCs, by hydrofluorocarbons, HFCs, synthetic lubricating oil research became an issue due to the limited miscibility (LLE) of mineral oils and the new generation of refrigerants. Also, in this context, hydrocarbons fluids, HCs, such as R-290 (propane) and R-600a (isobutane), also appeared as alternatives known (together with CO2, or R-744) as “natural refrigerants”
(CAVALLINI et al., 2014).
Following the refrigerant substitutions, the five main types of synthetic oils used to sat-isfy the miscibility requirements are: Polyalkylene glycol (PAG), Polyol ester (POE), Alkyl benzenes (AB), Poly-alfa olefin (PAO) and Polyvinylether (PVE). For domestic refrigeration systems, POE and AB are the main ones. PAG is mostly used for in automotive air-conditioning systems, PAO in aerospace and military applications, due to their superior performance and stability and PVE which shows superior performance than POE, but it is still an expensive op-tion (RUDNICK; SHUBKIN, 1999; RUDNICK, 2005). These oils are also classified by their kinematic viscosity (cSt) at 40∘C according to International Standards Organization Viscosity
1.3. Importance and Applications of Fluid Phase Equilibria in Oil and Gas Applications 37
1.3 IMPORTANCE AND APPLICATIONS OF FLUID PHASE EQUILIBRIA IN OIL AND GAS APPLICATIONS
Carbon dioxide, like other inorganic/non-hydrocarbon elements are inherent compounds in oil and gas reserves. Some reservoirs in the Brazilian Pre-Salt cluster, located in ultra-deep waters (depth > 1500 m), have shown a high carbon dioxide content (ARAÚJO et al., 2017). From the reservoir up to the three-phase vessel separator, the oil and gas mixture flows through the wells and risers being subjected to temperature and pressure gradients. As exposed by Bel-trão et al. (2009), the reservoir can exhibit temperatures between 80 and 150∘C, with pressures
up to 100 MPa. In contrast, fluid flow in risers are exposed to temperatures around 4∘C on the
seabed.
Besides problems such as heavy hydrocarbon precipitation and hydrate formation, as pointed by Beltrão et al. (2009), the knowledge of thermodynamic and thermophysical prop-erties at different pressure, temperature and compositions, are useful as input information for the reservoir simulation or equipment design. Since the oil is often a complex multicompo-nent mixture (containing paraffins, naphthenes and aromatics), depending the characteristic of the reservoir, these theoretical evaluations can be approximated assuming binary interactions involving CO2 and the average properties of the crude oil by a representative compound.
The resulting gas from the three-phase vessel separator must be conditioned to comply with transport specifications (pipelines or liquefied natural gas, LNG). Both processes require CO2 and other inorganics, as well as some residual “heavier” hydrocarbons, to be removed.
In the same way, for a first theoretical evaluation, a binary interaction may be assumed. As presented in Araújo et al. (2017), the binary mixture formed by CO2and CH4represents one of
the main constitutes elements to be splited in this resulting gas stream.
1.4 OBJECTIVES
As exposed above, the selection of the lubricating oil for a specific refrigeration system, apart from economic and lubricity issues, greatly depends on the refrigerant used in a specific application. In domestic systems (R-600a), the search for new lubricants is driven by the need to reduce the compressor mechanical power consumption, as this is directly linked to the oil viscosity. This explains the progressive reduction in the viscosity of lubricants used in domestic refrigeration compressors observed over the past two decades or so (i.e., from ISO 10 to ISO 5 viscosity grades). In commercial refrigeration and air conditioning applications (R-290), the
38 Chapter 1. Introduction
search for new lubricants is largely motivated by the need to reduce the mass of refrigerant in the system (the refrigerant charge) to comply with safety regulations on the maximum amount of flammable fluids in cooling equipment.
As far as the applications in the Oil & Gas industry are concerned, the use of theoretical methods with a strong theoretical basis is becoming more common in equipment design and process simulations. Such models, however, need to be checked against experimental data to verify their accuracy and limitations. Although the majority of mixtures encountered in real applications have multiple components, most models are usually developed through regression using binary interaction parameters.
The aim of the present thesis is to investigate both experimentally and theoretically – using mathematical models based on cubic and molecular equations of state – the vapor-liquid equilibrium and the liquid-phase viscosity of mixtures which are relevant to the two industrial segments discussed above.
In order to fulfill this general objective, the following specific tasks have been pursued (specific objectives):
1. Devise an experimental procedure through which bubble point pressure measurements in a synthetic variable volume PVT cell could be combined with measurements of liquid-phase viscosity in a high-pressure oscillating piston viscometer using the same fluid mix-ture sample;
2. Experimentally determine, using the proposed procedure, the phase equilibrium and vis-cosity of the following systems:
a) binary mixture of propane, R-290, and POE ISO 22 lubricating oil for R-290 mole fractions between 0.2 and 0.8, temperatures be-tween 283 and 353 K, and pressures between 0.17 and 2.3 MPa;
b) binary mixture of isobutane, R-600a, and LAB ISO 2 lubricating oil for R-600a mole fractions between 0.15 and 0.9, temperatures between 293 and 353 K, and pressures be-tween 0.18 and 1.3 MPa;
c) binary mixture of carbon dioxide, CO2 (R-744), and n-dodecane (n-C12H26) for
CO2mole fractions between 0.2 and 0.8, temperatures between 283 and 353 K, and
1.5. Thesis Outline 39
3. Implement cubic (PENG; ROBINSON, 1976) and SAFT-type (GROSS; SADOWSKI, 2001; GROSS, 2005) equations of state (EoS) to correlate the phase equilibrium (bubble-point pressure) of the above mixtures, and models based on the friction theory (f -theory) (CISNEROS et al., 2000; CISNEROS et al., 2006; QUIÑONES-CISNEROS; DEITERS, 2006), which rely on these EoS to correlate the liquid viscosity behavior as a function of pressure and concentration;
4. Propose an experimental procedure to measure the viscosity of the following high-pressure gas mixtures using a steady-state vibrating-wire viscometer:
a) binary mixture of methane and propane {xCH4 + (1 − x)C3H8}, x = 0.8881 (mole
fraction), temperatures between 203 and 424 K, and pressures between 2 and 31 MPa;
b) ternary mixture of methane-propane-carbon dioxide {xCH4 + yC3H8 + (1 − x −
y)CO2}, x = 0.6511, y = 0.0808 (mole fraction), temperatures between 203 and 420
K, and pressures between 2 and 31 MPa;
5. Evaluate four mathematical models based on the theories of corresponding state theory, implemented in REFPROP 9.1 (LEMMON et al., 2013) and Multiflash 4.4 (MULTI-FLASH, 2012; MULTI(MULTI-FLASH, 2014), a LJ model based on molecular simulations of Lennard-Jones fluids (GALLIERO et al., 2009) and a semi-theoretical model based on an extended hard-sphere scheme from Enskog theory, VW, (VESOVIC; WAKEHAM, 1989) to correlate the high-pressure gas viscosity behavior of the above systems.
Specific objectives (1)-(3) have been completed at the Polo – Research Laboratories for Emerging Technologies in Cooling and Thermophysics at the Federal University of Santa Catarina. Specific objectives (4) and (5) were executed at the University of Western Australia at the Fluid Science & Resources Laboratory, during a “Sandwich” Program sponsored by the Brazilian National Research Council, CNPq.
1.5 THESIS OUTLINE
The present thesis fulfills literature experimental data gaps of vapor-liquid equilibrium and viscosity of mixtures applied to the Oil & Gas and Refrigeration industries. The main works available in the literature are shown in the next chapter (Chapter 2), identifying the gaps
40 Chapter 1. Introduction
where the current measurements fit. Chapter 3 exposes the experimental facilities as well as the methodology, uncertainties and validations. Chapter 4 describes the equations of state and viscosity theoretical models used to correlate the experimental data. The results and their dis-cussion are illustrated in Chapter 5 followed by the thesis conclusion in Chapter 6 and recom-mendations for future works in Chapter 7 .
41
2 LITERATURE REVIEW
The archival literature on phase equilibrium and viscosity behavior of mixtures of liquids and liquefied gases and on the viscosity of natural gas mixtures at high pressures is abundant. Considering that the mixtures evaluated in the present thesis are concerned with applications in different industrial segments — oil & gas and refrigeration — a complete bibliographic review would result in an extensive text. Therefore, this review is focused on works dealing with mixtures that are similar to the ones evaluated in this thesis, i.e. liquid mixtures of CO2
and n-alkanes (phase equilibrium and viscosity); hydrocarbon refrigerants (e.g., R-600a, R-290) and synthetic lubricant mixtures (phase equilibrium and viscosity) and gas mixtures involving CO2 and CH4 (high-pressure viscosity).
2.1 LIQUID MIXTURES
2.1.1 CO2 + n-alkane mixtures
Reamer and Sage (1963) evaluated the phase behavior of CO2 and n-C10H22 mixtures
using a variable inner volume synthetic apparatus driven by mercury. The phase transitions (bubble point, BP) were determined from discontinuities in the isothermal volume-pressure relationship. The temperature varied from 5 to 240∘C, the CO
2 mole fraction ranged from 0.05
to 0.9 and, for most temperatures, the resulting BP pressures were between 0.1 and 15 MPa. Orr et al. (1981), studied the low-temperature phase behavior of CO2and crude oil
sam-ples from the Eastern New Mexico region. The mixtures were evaluated by visual inspection using a mercury driven variable volume synthetic apparatus. The CO2 mole fraction varied
between 0.3 and 0.9. For temperatures above 50 ∘C, just VLE (vapor-liquid equilibrium) was
observed while for 32∘C LLE (liquid-liquid equilibrium) and VLLE (vapor-liquid-liquid
equi-librium) were observed for CO2 mole fractions greater than 0.8.
Hottovy et al. (1981), and Fall and Luks (1985), studied the VLLE for four binary mix-tures: CO2 + n-dodecane, CO2 + n-tridecane, CO2 + n-tetradecane and CO2 + n-pentadecane.
These authors, also considering other works available in the literature, reported that mixtures involving CO2 and n-alkanes up to 6 carbons exhibit type-I phase equilibrium (accord-ing to
the van Konynenburg and Scott classification). Mixtures of CO2 with n-alkanes between 7 and
42 Chapter 2. Literature Review
n-alkanes with a carbon number greater than 14. According the authors, there was no consensus about the interactions with n-dodecane (type II, III or IV) and the interaction with n-tridecane corresponded to type IV. More recently, using the PC-SAFT EoS, García et al. (2004) classified [CO2 + n-C12H26] as a case of type-IV phase equilibrium.
Charoensombut-Amon et al. (1986) evaluated the phase equilibrium for the binary mix-ture formed by CO2 and n-C16H34 by measuring the liquid and vapor compositions. The CO2
liquid mole fraction and the pressures varied between 0.07 and 0.96 and 0.5 and 25 MPa for temperatures equal to 35, 40, 50, 60 and 70∘C. All isotherms exhibited VLE except for 35∘C,
where LLE was identified for x > 0.76.
Henni et al. (1996) used an analytic apparatus to evaluate the phase equilibrium of a CO2 + n-C12H26 mixture. Three temperatures were measured resulting in pressures between 1
and 8.5 MPa. For 40 ∘C, the CO
2 mole fraction varied between 0.0097 and 0.712, for 80 ∘C
between 0.01 and 0.5, and for 120∘C between 0.03 and 0.424. For these conditions, no
immis-cibility behavior was reported. The authors used the PR EoS to correlate the experimental data, and obtained an AAD (average absolute deviation) of 6.82 % when using a binary interaction parameter in the energy term.
Gardeler et al. (2002) , using an analytic apparatus, evaluated the phase equilibrium of a series of binary mixtures by measuring the composition of each phase. The binary mixture of CO2 and n-C12H26, with CO2 mole liquid fractions varying from 0.1 to 0.8, was measured
for a temperature of 318 K resulting in pressures between 1 and 9 MPa. The Predictive Soave-Redlich-Kwong, PSRK, group contribution EoS was used to correlate the experimental data but no quantitative evaluation was reported.
Fenghour et al. (2001) measured densities and bubble point pressure phase transition using an isochoric apparatus. The binary mixture formed by [xCO2 + (1 − x)n-C7H16] with
mole fraction x equal to 0.2918, 0.3888 and 0.4270 was evaluated for temperatures between 362 and 459 K. From the compressed liquid state (pressure around 50 MPa) the bubble point pressure was identified by discontinuities in the isotherm pressure relieve curve for a constant rate. Also, three ternary mixtures [xC4H10+ (1 − x)C7H16 + (1 − x-y)C16H34] with x = 0.0904
and y = 0.7358, x = 0.1564 and y = 0.6825 and x = 0.1856 and y = 0.6588 were evaluated. The bubble point pressures were correlated using the PR EoS. Using a binary interaction parameter in the energy term, the relative deviations were less than 1.5 %.
Kariznovi et al. (2011), Nourozieh et al. (2012), Kariznovi et al. (2012), Kariznovi et al. (2013b) and Kariznovi et al. (2013a), authors from the same research group, reported a
2.1. Liquid Mixtures 43
series of measurements involving light fluids (methane, ethane and carbon dioxide) with heavy n-alkanes. The experimental facility was employed to measure solubility and saturated liquid-phase density and viscosity.
In Kariznovi et al. (2011), binary mixtures of ethane and n-tetradecane were evaluated at 323, 373 and 423 K, for pressures between 1 and 8 MPa and ethane mole fractions between 0.1 and 0.87. The same authors, investigated the phase behavior of binary and ternary mixtures as follows: [C1H4+n-C14H30] for temperatures between 295 and 448 K in Nourozieh et al. (2012);
[C1H4+n-C10H22+n-C14H30] for 295 K in Kariznovi et al. (2012); [CO2+n-C10H22+ n-C14H30]
for 323 K in Kariznovi et al. (2013b) and [CO2+n-C10H22+ n-C18H38] for 378 K in Kariznovi
et al. (2013a). In these mixtures, the molar fraction of the light component varied, on average, between 0.1 and 0.5, in three binary mixtures with molar fractions, initially, formed by 0.25, 0.5 and 0.75. In all these works, the authors used the SRK and PR EoS to correlate the experimental data.
Li and Yang (2010) studied the LLVE boundaries for mixtures involving CO2 and a
Canadian crude oil with and without alkane solvents. The mole fractions of the three mixtures were (0.944CO2 + 0.056crude oil), (0.672CO2 + 0.236C3H8 + 0.092crude oil) and (0.832CO2
+ 0.118C4H10 + 0.05crude oil), evaluated at three temperatures: 288, 298 and 304 K. Starting
from a high-pressure condition (LLE), the pressure was relieved until LLVE and LVE were de-termined by visual inspection. Among other observations, the authors showed that the presence of solvents expands the pressure range of LLVE.
Al-Ghafri et al. (2014) used a synthetic variable volume apparatus to study the influ-ence of CO2 on the phase behavior of three multicomponent hydrocarbon mixtures. The first
mixture, classified as dead oil, was formed by 17 components including n-alkanes, branched-alkanes, cycle-alkanes and aromatics. In the second and third mixtures, a gas blend (0.813CH4
+ 0.126C2H6 + 0.061C3H8, per mole) was added to the dead oil, generating gas-oil-ratios of 58
and 160, respectively. The temperature ranged from 298 to 423 K, the CO2 liquid mole
frac-tion was varied between 0.1 and 0.98, and the pressures were as high as 36 MPa. The authors observed LLE at 298 K for CO2 mole fractions above 0.6. The data were correlated using the
PPR78 (JAUBERT; MUTELET, 2004) and PR2SRK (JAUBERT; PRIVAT, 2010) EoS. These two EoS use group-contribution scheme to predict the binary interaction parameter between pair components.
Table 1 shows a summary of the works reviewed so far, highlighting mixture composi-tions and their temperature and pressure condicomposi-tions. From the table, it can be seen that the phase
44 Chapter 2. Literature Review
equilibrium of CO2 and n-C12H26has been evaluated in (HENNI et al., 1996; GARDELER et
al., 2002) for a certain range of conditions.
Table 1 – Literature phase behavior data for CO2 and n-alkane mixtures.
Reference Fluids x1 T[K] p[MPa] parameter
Reamer and
Sage (1963) x1CO2/x2C10H22 0.05 - 0.9 278 - 513 0.1 - 15 BP
Orr et al. (1981) x1CO2/x2crude oil 0.3 - 0.9 305 and 323 - LLVE
Hottovy et al. (1981) Fall and Luks (1985)
x1CO2/x2C12H26 x1CO2/x2C13H28 x1CO2/x2C14H30 x1CO2/x2C15H32 -254 - 267 255 - 278 269 - 11 270 - 309 2 - 2.8 2 - 3.9 3 - 8.2 3 - 8 LLVE Charoenombut-Amon et al. (1986) x1CO2/x2C16H34 0.07 - 0.96 308 - 343 0.5 - 25 LLVE
Henni et al. (1996) x1CO2/x2C12H26 0.01 - 0.71 313 - 393 1 - 8.5 LVE
Gardeler et al. (2002) x1CO2/x2C12H26 0.1 - 0.8 318 0.9 - 9.1 LVE
Fenghour et al. (2001) x1CO2/x2C7H16 0.29 - 0.42 362 - 459 liq��� -50 BP Nourozieh et al. (2012) x1C1H4/x2C14H30 0.1 - 0.34 295 - 447 2 - 9.5 BP Kariznovi et al. (2012) x1C1H4/x2C10H22/ x3C14H30 0.05 - 0.32 295 1 - 8 BP Kariznovi et al. (2013b) x1CO2/x2C10H22/ x3C14H30 0.09 - 0.51 323 1 - 6 BP Kariznovi et al. (2013a) x1CO2/x2C10H22/ x3C18H38 0.07 - 0.35 372 0.75 - 6 BP Li and Yang (2010) x1CO2/x2crude oil 0.6 - 0.94 288 - 304 3.7 - 6.7 LLVE
Al-Ghafri et al. (2014) x1CO2/ x2syn. mixture 0.1 - 0.98 298 - 423 liq��� -36 BP and LLVE
Liquid viscosity data for liquefied CO2 in oils or heavy hydrocarbons are less abundant
in the open literature. The following review is also focused on CO2 and n-alkane mixtures.
Cullick and Mathis (1984) used a capillary viscometer to measure the liquid viscosity of a CO2 + n-decane mixture. The temperature ranged from 310 to 403 K, the pressures were
be-tween 7 and 35 MPa and the CO2 mole fraction was equal to 0.15, 0.301, 0.505, 0.649 and
0.85. The authors used the TRAPP (Transport Properties Prediction) model to correlate the experimental viscosity data. The average absolute deviation, AAD, was 46.5% without a binary interaction parameter, BIP, in the mixing rule and 9.4 % with a BIP in the mixing rule.
Barrufet et al. (1996) used a rolling-ball viscometer to measure the liquid viscosity of several mixtures involving CO2 and n-alkanes. In total, twelve mixtures containing n-pentane,
n-hexane, n-heptane, n-octane and n-decane with CO2 were studied. For the CO2 + n-C10H22
2.1. Liquid Mixtures 45
were between 310 and 403 K, with pressures between 7 and 12 MPa. The authors used the Orbey and Sandler viscosity correlation (ORBEY; SANDLER, 1993) for which the AAD was 2.1, 3.2 and 5.9 %, respectively for each composition.
Ciotta et al. (2009) reported measurements using a vibrating wire viscometer for the [xCO2 + (1 − x)C30H62] mixture where x is equal to (0.423, 0.604 and 0.788). The evaluations
covered temperatures from 303.15 to 448.15 K and pressures ranging from approximately the minimum miscibility pressure up to 170 MPa. The authors used the hard sphere model of Assael et al. (1992), with linear mixing rules for the roughness factor and molar core volume obtaining relative deviations of up to 60 %.
Kariznovi et al. (2012), Kariznovi et al. (2013b) and Kariznovi et al. (2013a) used an oscillating piston viscometer to measure the viscosity of three ternary liquid mixtures containing liquefied gases. In Kariznovi et al. (2012), the methane mole fraction varied from 0.06 to 0.33 in three (initially) binary mixtures formed by [xC10H22+(1 − x)C14H30] with x equal to 0.25, 0.5
and 0.75. The measurements were conducted at a temperature of 295 K with pressures between 1 and 8 MPa. In Kariznovi et al. (2013b), the carbon dioxide mole fraction varied from 0.08 to 0.5 in the same [xC10H22+(1 − x)C14H30] binary mixture studied Kariznovi et al. (2012). The
measurements were conducted at a temperature of 323 K at pressures between 1 and 6 MPa. Finally, in Kariznovi et al. (2013a), the carbon dioxide mole fraction varied from 0.06 to 0.36 in three (initially) binary mixtures formed by [xC10H22+(1 − x)C18H38] with x equal to 0.25, 0.5
and 0.75. The measurements were conducted at a temperature of 372 K at pressures between 1 and 6 MPa.
Recently, Mohammed et al. (2016) used a vibrating wire viscometer to measure the liquid viscosity of [CO2 + C16H34] and [CH4 + C16H34] mixtures. In the first mixture, the
temperature ranged from 298 to 473 K, the pressure varied between 10 and 120 MPa and the CO2 mole fraction was equal to 0.069, 0.5877 and 0.727. In the CH4 mixture, the temperature
was set between 298 and 473 K, the pressures ranged from 10 to 80 MPa and the CH4 mole
fraction was equal to 0.1013, 0.2021, 0.2976 and 0.3979. The authors used the extended Enskog hard-sphere theory (CIOTTA et al., 2014) to correlate the experimental data using different mixing rules. The AADs were all above 10 % for the mixture with CO2for each composition.
Table 2 summarizes the above mentioned works highlighting mixture compositions, temperature and pressure conditions. As can be seen, the available works dealing with the vis-cosity of mixtures of CO2 and n-alkanes are less abundant than those dedicated to studying the
46 Chapter 2. Literature Review
found.
Table 2 – Literature viscosity data for CO2 and n-alkane mixtures.
Reference Fluids x1 T[K] p[MPa] method
Cullick and
Mathis (1984) x1CO2/x2C10H22 0.15 - 0.64 310 - 403 7 - 35 capillary
Barrufet
et al. (1996) x1CO2/x2crude oil 0.15 - 0.505 310 - 403 7 - 12 rolling ball
Ciotta et al. (2009) x1CO2/x2C30H62 0.42 - 0.78 303 - 448 liq��� -170 VWV Kariznovi et al. (2012) x1C1H4/x2C10H22/ x3C14H30 0.06 - 0.33 295 1 - 8 oscillating piston Kariznovi et al. (2013b) x1CO2/x2C10H22/ x3C14H30 0.08-0.5 323 1 - 6 oscillating piston Kariznovi et al. (2013a) x1CO2/x2C10H22/ x3C18H38 0.06-0.36 372 1 - 6 oscillatingpiston Mohammed et al. (2016) x1CO2/x2C16H34 0.06 - 0.72 298 - 473 10 - 80 VWV
2.1.2 Hydrocarbon refrigerants + lubricant mixtures
Literature works containing HFCs (R-134a) and CO2 lubricant oil interaction is
abun-dant. As pointed out in the introductory sections of the present chapter, the focus of the present analysis is on the behavior of binary (or pseudo-binary) mixtures of light hydrocarbon refriger-ants, i.e., propane (R-290) and iso-butane (R-600a) and lubricating oils.
Spauschus et al. (1994) reported solubility and viscosity data for mixtures using two naphthenic mineral oils, MO ISO 46 and 114, and three synthetic oils, AB ISO 100, PAG ISO 100 and POE ISO 120, with R-290 and R-600a. The temperature varied between 30 and 90
∘C for a 0.8 mass fraction of the light component. Both refrigerants presented an immiscibility
region with PAG, but were fully miscible with the other oils.
Zhelezny et al. (2007) reported solubility, density and capillary constant data for binary mixtures formed by R-600a and a commercial mineral oil, MO, Azmol. The temperature varied between 30 and 90∘C, with pressures up to 1.7 MPa.
In a series of measurement (Marcelino Neto (2011), Marcelino Neto and Barbosa Jr. (2008), Marcelino Neto and Barbosa Jr. (2010) and Marcelino Neto and Barbosa Jr. (2009)), the authors reported experimental data of hydrocarbon refrigerants and lubricant mixtures used in domestic refrigeration systems. An experimental facility was developed to measure solubility, density and viscosity of such mixtures. Marcelino Neto and Barbosa Jr. (2008), a mixture of
2.1. Liquid Mixtures 47
R-600a and POE ISO 7 lubricating oil was experimentally tested for R-600a mole fractions between 0.1 and 0.8, temperatures between 10 and 60 ∘C, resulting in pressures as high as 8
bar. The PR EoS was used to correlate the experimental data with an AAD of 6.98 %. At the same experimental conditions, the mixture viscosity was correlated using the Eyring-theory correlations of Grunberg and Nissan (1949) and Katti and Chaudry (1964). Binary interaction parameters to ac-count for non-ideal effects were used in both models, resulting in AADs of 14.51 and 15.15 %, respectively.
In Marcelino Neto and Barbosa Jr. (2010), the R-600a + LAB ISO 5 lubricant was tested for R-600a mole fractions between 0.1 and 0.9, temperatures be-tween 20 and 80∘C and
pressures up to 13 bar. The data were correlated with the PR EoS with an AAD of 8.01 %. The mixture viscosity was evaluated using the classical Eyring approach in which the relation due to Macıas-Salinas et al. (2003) for the excess Gibbs energy was included to account for non-ideal effects. An AAD of 6.09 % was obtained.
In Marcelino Neto and Barbosa Jr. (2009), two binary mixtures formed by CO2and AB
ISO 32 and POE ISO 68 lubricating oils were evaluated. The CO2 solubility (mass fraction) in
the AB ISO 32 mixture varied from 0.03 to 0.31, while in the POE ISO 68 mixture it ranged from 0.03 to 0.53. The temperatures of both mixtures varied between 10 and 60 ∘C resulting
pressures up 111 and 120 bar. The authors used the PC-SAFT EoS to correlate the experimental data. Using a temperature dependent binary interaction parameter, the AADs were 5.32 and 5.87 %, respectively, for the AB and POE oils.
Using another experimental facility, Marcelino Neto et al. (2014) evaluated the phase equilibrium of two mixtures, namely R-134a + POE ISO 10 and R-1234yf + POE ISO 10. Using a variable volume synthetic method, the phase transition was characterized by pressure measurement and visual inspection. The mass fraction of the light component (refrigerant) var-ied between 0.15 and 0.9, the temperatures ranged from 10 to 80 ∘C resulting in pressures as
high as 27 bar. The authors used the PR EoS to correlate the measurements with an AAD of 3.53 % (R-1234yf) and 3.22 % (R-134a).
Yang et al. (2015) evaluated the experimental critical solubility temperature, T��, for
mixtures involving R-600a/R-227ea (heptafluoropropane) with naphthenic mineral oil ISO 32. The overall composition was known by previously measuring each component load, and the immiscibility limit was checked by visual inspection in a transparent quartz test tube. The tem-perature ranged from 223 to 303 K and the oil mass fraction was varied from 5 to 20%.
ro-48 Chapter 2. Literature Review
tary compressor using a compressor performance test platform. An oscillating piston viscome-ter was positioned in the oil sump. Viscosity and temperature were measured during the system operation, while the solubility was estimated using Seeton and Hrnjak correlation (SEETON; HRNJAK, 2006). Resulting from the different operation conditions, the temperatures varied between 48 and 70∘C resulting in viscosities between 2.25 and 5.4 cP and mass solubilities
between 13 and 26 %.
Table 3 summarizes the above mentioned works, highlighting their mixture composi-tions, temperature and pressure conditions. As can be seen, not many works reported phase equilibrium and viscosity data for mixtures involving the hydrocarbon refrigerants R-600a and R-290.
Table 3 – Literature data for hydrocarbon refrigerant and synthetic lubricating oil.
Reference Refrigerant Oil x1 T[K] parameter
Spauschus et al. (1994) x1R-290/ x1R-600a MO ISO 46 MO ISO 114 AB ISO 100 PAG ISO 100 POE ISO 120 0.8 303 - 363 x,� Zhelezny
et al. (2007) x1R-600a MO Azmol - 303 - 363 x,�
Marcelino and
Barbosa (2008) x1R-600a POE ISO 7 0.1 - 0.8 283 - 333 x,�,�
Marcelino and
Barbosa (2010) x1R-600a LAB ISO 5 0.1 - 0.9 283 - 353 x,�,�
Marcelino and Barbosa (2009) x1CO2 AB ISO 32 POE ISO 68 0.03 - 0.31 0.03 - 0.53 283 - 333 x,�,� Yang et al. (2015) x1R-600a/
x1R-227a
MO ISO 32 0.05 - 0.2 223 - 303 T��
Wu et al. (2018) x1R-290 MO 0.13 - 0.26 321 - 351 x,�
2.2 GAS MIXTURES
As commented in the introductory section of this chapter, the gas viscosity measurement was carried out in the context of CO2 and natural gas interactions. It is common practice to
synthetically represent natural gases as a binary mixture of methane and propane. In order to review the previous literature on the binary and ternary mixtures assessed in the present thesis, the following paragraphs focus on gas mixtures involving methane, propane and carbon dioxide. Considering the binary mixture formed by methane and propane, Bicher Jr and Katz (1943) used a rolling ball viscometer to measure the viscosity of this mixture at temperatures
2.2. Gas Mixtures 49
between 298 and 498 K, pressures in the range of 0.1 to 34.4 MPa, and methane mole fractions of 0.2, 0.5 and 0.75. Giddings et al. (1966) used a capillary viscometer to measure the viscosity of gas mixtures of methane and propane at temperatures ranging from 311 to 41 K, pressures in the range of 0.1 to 55.1 MPa and methane mole fractions equal to 0.2207, 0.3878, 0.6139 and 0.791. Huang et al. (1967) used a falling cylinder viscometer to study the same mixture at temperatures between 153 and 311 K, pressures in the range of 3.4 to 34 MPa, and methane mole fractions of 0.2, 0.4, 0.6 and 0.8.
Locke et al. (2014) reported the development of a vibrating wire viscometer, VWV, which operates at steady state clamped at both ends. In their work, besides the description of the apparatus, the viscosity of methane and propane mixture was also reported. The measure-ments were carried out at 280 and 298 K, pressures in the range of 0.61 to 6.97 MPa, with a methane mole fraction of 0.9452. Later, Stanwix et al. (2014), using the same experimental apparatus, extended the pressure and temperature ranges of Locke et al. (2014) work. The re-ported methane mole fraction was 0.949 for temperatures between 200 and 423 K and pressures between 10 and 31 MPa. Also in their work, a detailed analysis was performed using the ex-tended corresponding states (ECS) method available in REFPROP 9.1 (LEMMON et al., 2013) and the data from (BICHER JR; KATZ, 1943; GIDDINGS et al., 1966; HUANG et al., 1967). Among other conclusions, the experimental results from Stanwix et al. (2014) and Giddings et al. (1966), for x = 0.791, showed the same relative deviation with respect to the ECS predictions, mostly within ± 2 %. Moreover, both sets of results showed a systematic deviation of about 5 % in the predictions of the ECS model around � ≈ 160 kg·m−3, which is, coincidentally, near
the critical density of pure methane. The authors also commented that the relative deviation be-tween the model and the Giddings et al. (1966) data increased systematically with the propane concentration in the mixture.
Viscosity measurements considering the presence of CO2 were first carried out by
De-witt and Thodos (1966) and Kestin and Yata (1968) both in the 1960’s. DeDe-witt and Thodos (1966) used a capillary viscometer to measure the viscosity at temperatures ranging from 323 to 473 K, pressures in the range of 3.4 to 68 MPa and methane mole fractions equal to 0.243, 0.464 and 0.755, which corresponded to densities in the range of 1 to 729 kg·m−3. Kestin and
Yata (1968) used an oscillating-disk viscometer to measure the viscosity of mixtures of methane and carbon dioxide at temperatures of 293 and 303 K, pressures in the range of 0.1 to 2.5 MPa and methane mole fractions equal to 0.1435, 0.3376, 0.5194 and 0.6743.
