Elsevier

Fluid Phase Equilibria

Volume 530, 15 February 2021, 112896
Fluid Phase Equilibria

One-parameter friction theory viscosity model for the cubic-plus-chain equation of state

https://doi.org/10.1016/j.fluid.2020.112896Get rights and content

Abstract

A general one-parameter friction theory model based on the recently developed cubic-plus-chain equation of state (Sisco and Abutaqiya et al., Industrial & Engineering Chemistry Research, 2019, 58, 7341) is proposed to describe the viscosity behavior of n-alkanes. The model is considered a one-parameter model because it only requires one characteristic critical viscosity per compound to predict viscosity. This general model showed accurate viscosity modeling results for 15 n-alkanes ranging from methane to n-octadecane over a wide range of temperatures and pressures up to 1000 bar (1.51% AAPD). By using simple mixing rules, the model is further applied to predict the viscosity of 13 binary to quaternary mixtures of n-alkanes with accuracies close to experimental uncertainty (3.77% AAPD), making it a promising viscosity prediction methodology for industrial applications. A quantitative and qualitative comparison of the different friction theory viscosity models is also included. Additionally, an empirical correlation for estimating the characteristic critical viscosity is provided to extend the model to n-alkanes whose characteristic critical viscosity is not reported. The proposed viscosity model strikes a reasonable balance between the accuracy of viscosity predictions, simplicity of use and faster computational times.

Introduction

Many engineering disciplines and design decisions require a strong understanding of fluid properties such as viscosity. It has a wide range of applications ranging from the design of crude oil transportation equipment to planning remediation measures for costly oil spill accidents [1]. Uncertainties in viscosity data can also lead to errors in oil production rates, thus impacting reservoir profitability [2]. During hydrocarbon production, fluids undergo changes in temperature, pressure, composition, and even phase separations and therefore, accurate viscosity information over a wide range of conditions is crucial. Consequently, predictive viscosity models are gaining popularity due to their reliability and applicability over wide ranges of temperature, pressure, and composition. Some of the well-known models include the empirical models such as the Lohrenz-Bray-Clark (LBC) correlation [3] and the semi-theoretical models given by friction theory [4], expanded fluid (EF) theory [5] and the corresponding states methods [6], [7], [8]. Several review articles on the performance of these models along with their comparison can be found in the literature [9], [10], [11] and many of these viscosity models have been extensively applied by the petroleum industry to model the viscosity of crude oils [3,8,[12], [13], [14], [15], [16], [17], [18]].

Friction theory (FT) [4] has recently gained popularity as a viscosity model that links viscosity to the attractive and repulsive pressure terms from an equation of state (EoS). The general concept has been demonstrated to predict viscosity with satisfactory accuracy [19] in conjunction with various cubic EoS including the commonly applied Peng-Robinson (PR) EoS [20]. Unlike many viscosity models, friction theory does not require density as an input parameter, which is an advantage since cubic EoS are often limited in their ability to accurately predict condensed phase volumes [21]. However, despite the simplicity and accurate predictions offered by cubic EoS-based models, friction theory models combined with more advanced EoS have also been developed [22]. Along with an accurate representation of viscosity, these models can provide an improved representation of phase behavior and thermophysical properties. Some of the popular molecular-based EoS include the Statistical Association Fluid Theory (SAFT) [23] and a modified version called the Perturbed-Chain Statistical Association Fluid Theory (PC-SAFT) [24]. Following these lines, the combination of PC-SAFT EoS with friction theory (PC-SAFT FT) was developed by Quiñones-Cisneros et al. [22].

Recently, Sisco and Abutaqiya et al. [25,26] proposed cubic-plus-chain (CPC), a new equation of state framework for non-polar chain molecules. It hybridizes the standard cubic EoS with the chain term from SAFT [23].The cubic equation of state serves as the physical description of the monomer and the chain term from SAFT EoS bonds these monomers to form chains of homogenous beads. On one hand, CPC has an improved physical description of molecules enabling it to better represent chain-like molecules than the cubic EoS while on the other hand, CPC is less complicated and approximately 4× computationally faster than PC-SAFT. Owing to its hybrid nature, the CPC framework presents a balance between accuracy and computational time.

With this line of thought, a general one-parameter friction theory model based on CPC EoS (CPC FT) is developed in this study. By combining CPC EoS with friction theory, an accurate representation of viscosity and good predictions for phase behavior can be achieved with the added benefit of fast computational time stemming from a relatively simplified framework. The general CPC FT viscosity model, like previous general FT models, is derived based on the viscosity behavior of 15 pure normal alkanes (n-alkanes) ranging from methane to n-octadecane. The applicability of this viscosity model is then extended to other pure n-alkanes using an additional empirical correlation and also to n-alkane mixtures using simple mixing rules.

Section snippets

Friction theory for viscosity modeling

The friction theory is a well-recognized model that predicts the viscosity of dilute gases and dense fluids with satisfactory accuracy [4,19,22,27]. The uniqueness of this model stems from treating viscosity, the resistance of the fluid to gradual deformation by shear stress, as a mechanical property rather than a transport property. Viscosity η is expressed as given by Eq. (1):η=η0+ηf where η0, the dilute gas contribution, is the viscosity given by kinematics of colliding molecules at

General model for pure n-alkanes

Using a database of smoothed viscosity data for 15 n-alkanes from methane up to n-octadecane [18] and the concepts of general friction theory models based on cubic and PC-SAFT EoS [19,22], a CPC EoS-based one-parameter general viscosity model (CPC FT) valid over a wide range of temperatures and pressures up to 1000 bar has been derived. The reduced form of the friction contribution to viscosity (η^f) is been defined by Eq. (9):η^f=ηfηc where ηc is the characteristic critical viscosity, a

Results for CPC FT and discussion

Fig. 1 represents a schematic of the data treatment for the development of the CPC FT viscosity model. There are six steps in the illustration that are used to develop and optimize the CPC FT model using viscosity data of pure n-alkanes. Steps 1 to 4 are explained in detail as part of Section 4.1 whereas steps 5 to 6 are implemented and explained in Section 4.2. Once the CPC FT model is fully developed following the results outlined in Section 4.1 and 4.2, it is used to predict the viscosity of

Conclusion

A general one-parameter friction theory model based on the cubic-plus-chain equation of state is developed in this study. The CPC FT model is derived based on the viscosity behavior of 15 pure n-alkanes ranging from methane to n-octadecane over a wide range of temperatures and pressures up to 1000 bar. Two different approaches were implemented where the optimization procedure is carried out using an empirical correlation for critical viscosity (Method 1) and alternatively, using individual

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

CRediT authorship contribution statement

Yash Khemka: Conceptualization, Methodology, Software, Investigation, Visualization, Writing - original draft, Writing - review & editing. Caleb J. Sisco: Software, Resources, Investigation, Writing - review & editing. Mohammed I.L. Abutaqiya: Software, Resources. Walter G. Chapman: Conceptualization, Supervision, Writing - review & editing. Francisco M. Vargas: Conceptualization, Supervision, Visualization, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors are grateful to Dr. Sergio E. Quiñones-Cisneros for fruitful discussions regarding the friction theory viscosity model.

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