An Efficient Numerical Scheme to Solve a Quintic Equation of State for Supercritical Fluids

Fatoorehchi, Hooman; Rach, Randolph; Tavakoli, Omid; Abolghasemi, Hossein

doi:10.1080/00986445.2013.843529

Cited by 22 publications

(4 citation statements)

References 25 publications

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“…This feature also allows a fast and robust evaluation of the density root at the given pressure because there is no need for checking the additional Maxwell loop. Although an algorithm is available for solving a quintic EOS, the numerical solving for the density root is adopted for the present model.…”

Section: Results and Discussionmentioning

confidence: 99%

Development of an Accurate Quintic Equation of State: The Necessity of the Irreducible Quadratic Polynomial in the Attractive Term

Lee

Jeon

Lee

et al. 2015

Ind. Eng. Chem. Res.

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In conventional van der Waals type equation of state (EOS) modeling, the denominator of the attractive contribution is regarded as being a necessarily factorable quadratic polynomial for the closed-form expression of the corresponding Helmholtz free energy. This study evaluates the effect of the opposite case, irreducible quadratic polynomial, on the description of the volumetric behavior of real fluid through a comparison with the critical isotherm data, coexistence curve and PVT isotherm data. In a generalized cubic EOS, an irreducible quadratic polynomial was found to yield an improved description of the flattened region around the critical density while a nonclosed form of Helmholtz free energy is resulted. For an improved volumetric description using irreducible quadratic polynomial and a derivation of the closed-form of Helmholtz free energy, we developed a quintic EOS containing seven parameters, two of which are determined by correlating the critical isotherm data and others by regressing the sub and supercritical properties.In the description of the critical isotherms of nine pure compounds, a comparison with BenedictWebb-Robinson-Soave(BWRS) EOS showed that the present model exhibits slightly larger deviations than BWRS EOS, however, a good agreement was obtained with the reference model of REFPROP 8.0 in the description of the saturated vapor pressure, saturated density and PVT isotherm data over a wide range of temperature.

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Section: Results and Discussionmentioning

confidence: 99%

Development of an Accurate Quintic Equation of State: The Necessity of the Irreducible Quadratic Polynomial in the Attractive Term

Lee

Jeon

Lee

et al. 2015

Ind. Eng. Chem. Res.

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show abstract

“…For more details on the theory and application of the ADM, the reader is advised to consult references [19][20][21][22][23][24][25][26][27][28][29][30][31][32], and particularly [33][34][35][36][37][38][39] for applications in chemical engineering.…”

Section: Analysis Of the Adomian Decomposition Methodsmentioning

confidence: 99%

A new parametric algorithm for isothermal flash calculations by the Adomian decomposition of Michaelis–Menten type nonlinearities

Fatoorehchi

Abolghasemi

Rach

2015

Fluid Phase Equilibria

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“…This modification is referred to as the multi‐stage Adomian decomposition method and has been proven to be very computationally efficient . Further discussion on the Adomian decomposition methodology and its modifications is beyond the scope of this paper; however the interested reader is recommended to consult the relevant literature …”

Section: Control Strategiesmentioning

confidence: 99%

Feedback control strategies for a cerium‐catalyzed Belousov–Zhabotinsky chemical reaction system

et al. 2015

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A number of control schemes including nonlinear feedback, dislocated feedback, and speed feedback have been proposed and assessed for a bromate-malonic acid-cerium Belousov-Zhabotinsky batch reaction process. The tuning parameters of the Oregonator model were firstly adjusted based on a UV-vis spectrophotometric analysis in the experimental part of the research. The adjusted Oregonator model successfully reproduced the innate induction time and periodicity of the BZ-batch system. Subsequently, the controllers were implemented and numerical simulations were carried out by employing the multi-stage Adomian decomposition method. The nominal analysis method was used to study the linear stability of each design. All the controlled systems were found to be linearly stable for certain continuous regions of controller gain. The performance of the proposed control laws was assessed and the dislocated feedback control strategy was shown to be able to drive the system states toward desired setpoints quickly. Furthermore, the validity of the dislocated feedback control design was doubly ensured by the sliding mode control theory. It was found that those feedback schemes which manipulate cerium ion concentration can be practically realized by means of electrochemical oxidation or oxygen aeration. Our results were confirmed by the Simulink software package and the block diagram representations are included in the paper.

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An Efficient Numerical Scheme to Solve a Quintic Equation of State for Supercritical Fluids

Cited by 22 publications

References 25 publications

Development of an Accurate Quintic Equation of State: The Necessity of the Irreducible Quadratic Polynomial in the Attractive Term

Development of an Accurate Quintic Equation of State: The Necessity of the Irreducible Quadratic Polynomial in the Attractive Term

A new parametric algorithm for isothermal flash calculations by the Adomian decomposition of Michaelis–Menten type nonlinearities

Feedback control strategies for a cerium‐catalyzed Belousov–Zhabotinsky chemical reaction system

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