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Abstract
The complexity of industrial processes is increasing rapidly in the last decades, allowing the production of important materials in more efficient ways. Some examples are the use of nearcritical and supercritical fluids to substitute traditional separation methods, and the exploitation of unconventional reservoirs. In such cases, the feasible implementation of the processes requires a broad and accurate knowledge of the thermophysical properties of the systems.The experimental measurement of the thermodynamic properties is extremely important in the understanding of the behavior of fluids, yet, this activity is timeconsuming and expensive. An alternative is to use theoretical thermodynamic models to represent the systems, which can also be applied in process simulators for the design of the equipment and optimal control of the operations.
In this work, one of the limitations of the classical thermodynamic models was investigated, that is the incorrect description of the behavior of fluids close to the critical point. In this region, the properties of the system are modified due to the strong fluctuation srelated to the longrange correlations between the molecules. Classical equations of state (EoS), like SoaveRedlichKwong (SRK) and CubicPlusAssociation (CPA), are based on a meanfield theory, in which an average interaction potential is assumed for the particles, therefore they do not account for these longrange fluctuations. The improvement of such models is fundamental for the correct simulation of processes in the nearcritical regions, and for the modeling of operations encompassing a wide range of conditions, which is relevant to the oil & gas industry and other sectors.
The incorporation of the longrange fluctuations into the classical EoS, i.e. SRK and CPA, was achieved using a recursive procedure developed by White and coworkers, following the renormalization group (RG) treatment proposed by Wilson. It is a simple method that consists of a set of recursive relations where the fluctuations with respect to the density are considered in several iterations. The procedure yields amodel that possesses a nonanalytical/asymptotic behavior close to the critical point,but reduces to the traditional equation far from the critical region. The extended models are called the crossover SRK and crossover CPA EoS, and they are capable of accurately representing the phase behavior of fluids far away and close to the critical point. However, while the first one is only used to describe the properties of systems with nonassociating species, the latter can be used to model the phase behavior of highly nonideal systems composed of molecules that form hydrogen bonds, due to an additional term that explicitly accounts for the association between molecules.The nonmeanfield equations were compared with different classical thermodynamic models in the representation of the experimental saturated and critical properties of pure fluids. In addition to the SRK and CPA EoS, the PatelTeja (PT) EoS was also used for the comparisons. The results of the computations indicated that only the crossover equations were able to describe both the saturated and critical properties with high accuracy for nonassociating and associating species. Moreover, a new method for rescaling the pure component parameters of CPA was tested, but it showed some of the intrinsic limitations of meanfield equations, that is, different parameters might enhance the models’ performance for certain regions. Nonetheless, large deviations regarding some properties, either critical or subcritical, will be observed,as long as an average potential is used for describing the interactions betweenthe particles.
Afterward, the calculations were extended to binary and ternary mixtures. Several groups of systems containing nalkanes, nalkanols, and carbon dioxide were studied. This is an important test to evaluate the capacity of the models to represent the different phase type behaviors that are observed in some homolog series, e.g. methane/nalkane. Additionally, the comparison with experimental data showed the importance of the renormalization group corrections for the precise description of the volumetric properties of mixtures of nonassociating components in nearcritical regions. Furthermore, the calculations indicated that the performance of the models deteriorated due to asymmetry, i.e. the difference in size between the components.
In the case of systems with hydrogen bonding components, the incorporation of density fluctuations in the classical models proved to be even more crucial. This is due to the fact that the overestimation of the critical properties with CPA is higher for associating components, which affects the representation of the phase behavior of mixtures, and cannot be completely corrected with the used of binary interaction parameters. On the other hand, the classical cubic models cannot represent the correct behavior of such systems, because they do not account for the formation of hydrogen bonds in the fluid.
Further evaluation of the crossover models to describe other systems, e.g. different associating species like glycols and very asymmetric mixtures, are needed to expand the applicability of the nonmeanfield equations in the oil & gas sector. However, the current work has already shown that the utilization of the recursive procedure basedon RG theory corrects the behavior of the classical models near the critical point, thus becoming a relevant and useful tool for engineering applications, which include the design of equipment and control of the operation of complex processes.
In this work, one of the limitations of the classical thermodynamic models was investigated, that is the incorrect description of the behavior of fluids close to the critical point. In this region, the properties of the system are modified due to the strong fluctuation srelated to the longrange correlations between the molecules. Classical equations of state (EoS), like SoaveRedlichKwong (SRK) and CubicPlusAssociation (CPA), are based on a meanfield theory, in which an average interaction potential is assumed for the particles, therefore they do not account for these longrange fluctuations. The improvement of such models is fundamental for the correct simulation of processes in the nearcritical regions, and for the modeling of operations encompassing a wide range of conditions, which is relevant to the oil & gas industry and other sectors.
The incorporation of the longrange fluctuations into the classical EoS, i.e. SRK and CPA, was achieved using a recursive procedure developed by White and coworkers, following the renormalization group (RG) treatment proposed by Wilson. It is a simple method that consists of a set of recursive relations where the fluctuations with respect to the density are considered in several iterations. The procedure yields amodel that possesses a nonanalytical/asymptotic behavior close to the critical point,but reduces to the traditional equation far from the critical region. The extended models are called the crossover SRK and crossover CPA EoS, and they are capable of accurately representing the phase behavior of fluids far away and close to the critical point. However, while the first one is only used to describe the properties of systems with nonassociating species, the latter can be used to model the phase behavior of highly nonideal systems composed of molecules that form hydrogen bonds, due to an additional term that explicitly accounts for the association between molecules.The nonmeanfield equations were compared with different classical thermodynamic models in the representation of the experimental saturated and critical properties of pure fluids. In addition to the SRK and CPA EoS, the PatelTeja (PT) EoS was also used for the comparisons. The results of the computations indicated that only the crossover equations were able to describe both the saturated and critical properties with high accuracy for nonassociating and associating species. Moreover, a new method for rescaling the pure component parameters of CPA was tested, but it showed some of the intrinsic limitations of meanfield equations, that is, different parameters might enhance the models’ performance for certain regions. Nonetheless, large deviations regarding some properties, either critical or subcritical, will be observed,as long as an average potential is used for describing the interactions betweenthe particles.
Afterward, the calculations were extended to binary and ternary mixtures. Several groups of systems containing nalkanes, nalkanols, and carbon dioxide were studied. This is an important test to evaluate the capacity of the models to represent the different phase type behaviors that are observed in some homolog series, e.g. methane/nalkane. Additionally, the comparison with experimental data showed the importance of the renormalization group corrections for the precise description of the volumetric properties of mixtures of nonassociating components in nearcritical regions. Furthermore, the calculations indicated that the performance of the models deteriorated due to asymmetry, i.e. the difference in size between the components.
In the case of systems with hydrogen bonding components, the incorporation of density fluctuations in the classical models proved to be even more crucial. This is due to the fact that the overestimation of the critical properties with CPA is higher for associating components, which affects the representation of the phase behavior of mixtures, and cannot be completely corrected with the used of binary interaction parameters. On the other hand, the classical cubic models cannot represent the correct behavior of such systems, because they do not account for the formation of hydrogen bonds in the fluid.
Further evaluation of the crossover models to describe other systems, e.g. different associating species like glycols and very asymmetric mixtures, are needed to expand the applicability of the nonmeanfield equations in the oil & gas sector. However, the current work has already shown that the utilization of the recursive procedure basedon RG theory corrects the behavior of the classical models near the critical point, thus becoming a relevant and useful tool for engineering applications, which include the design of equipment and control of the operation of complex processes.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  191 
Publication status  Published  2018 
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 1 Finished

Application of an association equation of state to enchanced oil recovery processes
Vinhal, A. P. C. M., Kontogeorgis, G., Yan, W., Solms, N. V., Gross, J. & Llovell, F.
01/05/2015 → 10/12/2018
Project: PhD