Evaluation of Various References and Perturbation Terms of the Thermodynamic Perturbation Theory of the First Order

Evaluation of Various References and Perturbation Terms of the Thermodynamic Perturbation Theory of the First Order. Masters thesis, King Fahd University of Petroleum and Minerals.


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Arabic Abstract

تعتبر نظرية الاضطراب واحدة من أهم النظريات المستخدمة في علم الديناميكا الحرارية حيث اشتق منها عدة معادلات للحالة تعرف بمجموعها بنظريات الترابط الإحصائي للموائع. بالرغم من دقة هذه النظريات في حساب خصائص الموائع إلا أن هذه النظريات ولشدة تعقيد عباراتها الرياضية قد تؤدي إلى نتائج وهمية. هذا البحث يسلط الضوء على مجموعة من نظريات الترابط الإحصائي المبنية على نموذجي "لينارد جونز" و "ماي" للطاقة الكامنة للجزيئات. توصل البحث إلى أن جميع هذه النظريات تقوم بإعطاء نتائج وهمية للحجم المولي للموائع كما تم طرح بعض الحلول لتفادي هذه المشكلة عند استخدام هذه النظريات في برامج المحاكاة.

English Abstract

Thermodynamic perturbation theories have been widely accepted as a platform of theory-based equations of state. In this work, the mathematical structure of Wertheim's first order thermodynamic perturbation theory (TPT1) is investigated for its role in the existence of the non-physical pressure-volume-temperature (PVT) behavior. The study is focused on references constructed based on Lennard-Jones and Mie potentials. Two versions of TPT1 are utilized for this purpose; namely the soft-SAFT and SAFT-VR Mie. In addition, a new version denoted by SAFT-LJ3 is constructed based on the Lennard-Jones model of (Mecke et al., 1996). The study is carried out by evaluating the volume root loci of the three models. The variation of volume root loci with temperature and pressure is illustrated using bifurcation diagrams. The bifurcation diagrams are generated by the arc-length continuation method with the aid of Wagon’s method. The mathematical structures of these models are evaluated for spherical and non-spherical molecules. The SAFT-VR Mie equation of state is examined for the existence of multiple phase separation regions. The study reveals that all the three models exhibit non-physical branches demonstrated in volume-temperature bifurcation diagrams at fixed pressure. Unlike the SAFT-VR Mie, the soft-SAFT and SAFT-LJ3 models exhibit non-physical volume-temperature branches within the region of practical applications. The number of the non-physical branches is higher for non-spherical particles due to the addition of the chain part representing the size of particles. This problem is attributed to the empirical nature of the pair-correlation function at contact that is utilized in the chain term. Irrespective of the accuracy, the generated PVT behavior of the SAFT-LJ3 is more realistic that that of the soft-SAFT. For spherical molecules, the SAFT-VR Mie exhibits higher non-physical branches compared to the SAFT-LJ3 and soft-SAFT although they are far from the practical region. The investigation of the SAFT-VR Mie reveals that the model is not free from exhibiting additional phase separation regions as it was expected. It was found that the SAFT-VR Mie accommodates an artificial phase separation region termed as liquid-solid demixing region due to the non-existence of its critical point. The study reveals that it is possible to discard all non-physical regions in the SAFT-VR Mie due to the fact that these regions are located above a packing fraction value of 0.494. In addition, the non-physical branches in the SAFT-LJ3 and soft-SAFT cannot be eliminated without a modification in the mathematical structure.

Item Type: Thesis (Masters)
Subjects: Chemical Engineering
Department: College of Chemicals and Materials > Chemical Engineering
Committee Advisor: Al-Saifi, N.M.
Committee Members: Al-Mutairi, E.M. and Binous, H.
Depositing User: MOHAMMED AL KHATER (g200853980)
Date Deposited: 24 May 2016 10:10
Last Modified: 01 Nov 2019 16:34
URI: https://eprints.kfupm.edu.sa/id/eprint/139967