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

Fatoorehchi, Hooman; Abolghasemi, Hossein; Rach, Randolph

doi:10.1016/j.fluid.2015.03.024

Cited by 36 publications

(15 citation statements)

References 40 publications

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“…The next section briefly covers a simple P T -flash algorithm, which will serve to illustrate the basic theory behind solving vapor-liquid equilibrium problems. Examples of some more specific and complex algorithms are given in [8,21,[24][25][26][27][28].…”

Section: Flash Calculationsmentioning

confidence: 99%

Solving vapor-liquid flash problems using artificial neural networks

Poort

Ramdin

Kranendonk³

et al. 2019

Fluid Phase Equilibria

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Vapor-liquid phase equilibrium (flash) calculations largely contribute to the total computation time of many process simulation models. As a result, process simulations, especially dynamic cases, are limited in the amount of detail that can be included due to time restrictions. In addition, under certain conditions flash calculations can fail to provide acceptable results. In this work, artificial neural networks were investigated as a potentially faster and more robust alternative to conventional flash calculation methods. Classification neural networks were used to determine the phase stability of a given mixture of fluids, while regression networks were used to make predictions of thermodynamic property values. In addition to conventional flash types such as the constant pressure, constant temperature (P T ), and constant pressure, constant entropy (P S) flash, neural networks are used to develop two concept flash types: a constant entropy, constant volume (SV ), and a constant enthalpy, constant volume (HV ) flash. All neural networks were trained on, and compared to, data generated using the P T -flash algorithm from the Thermodynamics for Engineering Applications (TEA) property calculator. Data was generated for mixtures of water and methanol over a wide range of pressures and temperatures. The artificial neural networks showed speed improvements over TEA of up to 35 times for phase classification and 15 times for property predictions. Overall phase classification accuracy scores of around 97% were achieved. Average property value prediction errors range between 0.5% and 7% when compared to the spread in magnitude of the test data, and R 2 scores were in the general order of 0.95 and higher, although classification and property prediction in the two-phase region showed markedly higher errors than properties in the pure liquid or vapor regions. Moreover, thermodynamic consistency and the stability of a system consisting of multiple neural network flash types both still require considerable improvement. Finally, this work shows that artificial neural networks can be used to create unconventional flash types such a the SV -and HV -flash.i

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Section: Flash Calculationsmentioning

confidence: 99%

Solving vapor-liquid flash problems using artificial neural networks

Poort

Ramdin

Kranendonk³

et al. 2019

Fluid Phase Equilibria

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“…We continue with the case where the power p varies in the interval (1,10], which is of course the case of the stronger Newtonian gravity. The Newton-Raphson basins of attraction for six values of the power p are presented in Fig.…”

Section: Stronger Newtonian Gravity (P > 1)mentioning

confidence: 99%

“…The Newton-Raphson method, and of course the corresponding multivariate version of it, may be a very simple computational tool for numerically solving system of equations however it is not the most robust algorithm. Being more precisely, its main inefficiency lies to the fact that the convergence of the algorithm is greatly affected by the particular initial guess (e.g., [9,10,12,17]).…”

Section: Introductionmentioning

confidence: 99%

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Investigating the Newton–Raphson basins of attraction in the restricted three-body problem with modified Newtonian gravity

Zotos¹

2016

J. Appl. Math. Comput.

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The planar circular restricted three-body problem with modified Newtonian gravity is used in order to determine the Newton-Raphson basins of attraction associated with the equilibrium points. The evolution of the position of the five Lagrange points is monitored when the value of the power p of the gravitational potential of the second primary varies in predefined intervals. The regions on the configuration (x, y) plane occupied by the basins of attraction are revealed using the multivariate version of the Newton-Raphson iterative scheme. The correlations between the basins of convergence of the equilibrium points and the corresponding number of iterations needed for obtaining the desired accuracy are also illustrated. We conduct a thorough and systematic numerical investigation by demonstrating how the dynamical quantity p influences the shape as well as the geometry of the basins of attractions. Our results strongly suggest that the power p is indeed a very influential parameter in both cases of weaker or stronger Newtonian gravity.Keywords Three-body problem · Non-linear algebraic equations · Basins of attraction · Fractal basin boundaries

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“…Recently, the Adomian's decomposition method (ADM) for solving differential and integral equations, linear or nonlinear, has been the subject of extensive analytical and numerical studies because the ADM provides the solution in a rapid convergent series with elegantly computable components [18][19][20][21][22][23]. The Jacobi pseudo spectral approximation method [24], the fully spectral collocation approximation method [25,26], the Jacobi tau approximation method [27], and the homotopy perturbation Sumudu transform method [28,29] are powerful and effective tools for solving nonlinear PDEs.…”

Section: Introductionmentioning

confidence: 99%

The homogeneous balance of undetermined coefficients method and its application

Yang

2016

Open Mathematics

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Abstract:The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers. The proposed method can also be used to derive more general bilinear equation of nonlinear PDEs. The Eckhaus equation, the KdV equation and the generalized Boussinesq equation are chosen to illustrate the validity of our method. The proposed method is also a standard and computable method, which can be generalized to deal with some types of nonlinear PDEs.

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

Cited by 36 publications

References 40 publications

Solving vapor-liquid flash problems using artificial neural networks

Solving vapor-liquid flash problems using artificial neural networks

Investigating the Newton–Raphson basins of attraction in the restricted three-body problem with modified Newtonian gravity

The homogeneous balance of undetermined coefficients method and its application

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