A consistent and precise alpha function for cubic equations of state

Mahmoodi, Peyman; Sedigh, Maryam

doi:10.1016/j.fluid.2016.12.015

Cited by 17 publications

(10 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To comply with said criteria, Le Guennec et al parametrized the Twu a function according to all these constrains and Mahmoodi et al , modified five a functions that change forms at the critical point to fix any abnormal behaviors.…”

Section: Temperature Dependency Of the Attractive Term Of Cubic Eos (...mentioning

confidence: 99%

Prediction of Vapor–Liquid Equilibrium and Thermodynamic Properties of Natural Gas and Gas Condensates

Novak

Louli

Voutsas

2019

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

In this work, the performance of the UMR-PRU model, which combines the Peng−Robinson (PR) equation of state (EoS) with the original UNIFAC through the Universal Mixing Rules (UMR), is further improved and updated through the use of a Mathias−Copeman (MC) function for the attractive term parameter of the PR EoS. The new model, called UMR-MCPRU, utilizes a newly parametrized MC function for the a term, which satisfies consistency constraints that ensure its safe extrapolation to the supercritical region. Moreover, a correlation of the MC parameters of hydrocarbons with acentric factor is proposed. The MCPR EoS is then combined with the UMR mixing rules, resulting to the UMR-MCPRU model. All binary interaction parameters relevant to natural gas mixtures are determined by fitting binary vapor−liquid equilibrium data. UMR-MCPRU is used to predict vapor−liquid equilibrium, critical points, liquid dropouts, densities (ρ) and derivative thermodynamic properties, namely isobaric (c P ) and isochoric (c V ) heat capacity, Joule−Thomson coefficients (μ JT ) and speed of sound (w), of natural gas and gas condensate mixtures. The Peneloux volume translation is also examined, wherever relevant. The results reveal that UMR-MCPRU, coupled with the Peneloux translation, is able to accurately describe both phase equilibria and other important thermodynamic properties of natural gas and gas condensate mixtures.

show abstract

Section: Temperature Dependency Of the Attractive Term Of Cubic Eos (...mentioning

confidence: 99%

Prediction of Vapor–Liquid Equilibrium and Thermodynamic Properties of Natural Gas and Gas Condensates

Novak

Louli

Voutsas

2019

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

show abstract

“…In 2016, Le Guennec et al. , concluded and presented the list of constraints for an alpha function: The set of conditions reported in eq were the “consistency test for an alpha function”. In reality, the polynomial alpha functions cannot satisfy the requirements of the consistency test because of these inherent defects. ,− Although the Soave’s 1972 alpha function has the defects mentioned above, it is still widely used in the simulation and design of chemical and petroleum processes because the turning temperature is often higher than the maximum temperature in real applications. ,, For example, the turning temperatures of RK Soave’s alpha function for n -alkanes (C 1 –C 20 ), cycloalkanes (C 5 –C 8 ), and aromatics (from benzene to naphthalene) were around 1800, 1300, and 2100 K, respectively, and for the polar compounds (methanol, ethanol, acetone, and water), the extrema were about 1500–2600 K. , …”

Section: General Overview Of the Alpha Functionmentioning

confidence: 99%

“…That is, most functions do not monotonically decrease and tend to small positive values with increasing temperature. Although the piecewise alpha functions with three parameters have extended the scope of these functions to predict the thermodynamic properties of polar compounds accurately, this kind of alpha function has severe defects; for example, the second-order derivative at the dividing point is discontinuous, which results in significant deviation or incorrect values in the prediction of heat capability. , Overall, only a few polynomial functions in the literature pass the consistency test. ,− …”

Section: Development Trends In Polynomial Alpha Functionsmentioning

confidence: 99%

“…However, it is challenging to generalize the parameters for polar compounds, which is inconvenient in the simulation and design of technical process. At present, some generalized or component-specific exponential functions with the corresponding EoS are well adapted for the polar and associating compounds, which are better than the ones of EoS involving piecewise alpha functions. ,,, …”

Section: Conclusion and Prospectmentioning

confidence: 99%

“…At present, some generalized or component-specific exponential functions with the corresponding EoS are well adapted for the polar and associating compounds, which are better than the ones of EoS involving piecewise alpha functions. 24,33,34,116 In reality, the various alpha functions all originate from the Soave 1972 function, and they are modified by adding coefficients, exponent or variables to extend the applicable scope or improve the prediction of properties, such as the vapor pressure. In addition, the dedicated alpha functions have been improved by introducing characteristics such as the pseudonormal boiling temperature and pseudo-molecular-weight for the prediction of the thermodynamic properties of complex fluids, such as reservoir fluids, petroleum fractions, and natural gases.…”

Section: Conclusion and Prospectmentioning

confidence: 99%

See 2 more Smart Citations

Research into the Polynomial Alpha Function for the Cubic Equation of State

Zhao

Sun

et al. 2018

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

Alpha functions usually aim at predicting the thermodynamic properties of specific compounds in a limited range of reduced temperatures. The differences between polynomial alpha functions are mainly the functional forms and the parameter correlations. In this work, the functional forms, the parameter correlations, and the scope of 64 polynomial alpha functions are reviewed. The inherent relationships between the polynomial alpha functions as well as developing trends are also discussed. These functions were modified by changing the coefficients, exponents, or variable terms. The parameter formulas were re-correlated with the acentric factors or the other natural parameters. In recent years, research into polynomial alpha functions has mainly focused on reservoir fluids, and the alpha functions have been modified by adding characteristic constants of pseudocomponents to the equations or the parameter correlations. The Soave-type function has significant research value and will influence the development of polynomial alpha functions in the coming years.

show abstract

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Engle

Sahinidis

2021

AIChE Journal

View full text Add to dashboard Cite

Symbolic regression methods simultaneously determine the model functional form and the regression parameter values by generating expression trees. Symbolic regression can capture the complexity of real‐world phenomena but the use of deterministic optimization for symbolic regression has been limited due to the complexity of the search space of existing formulations. We present a novel deterministic mixed‐integer nonlinear programming formulation for symbolic regression that incorporates derivative constraints through auxiliary expression trees. By applying the chain rule to mathematical operations, binary expression trees are capable of representing the calculation of first and second derivatives. We apply this formulation to illustrative examples using derivative information to show increased model discrimination capability. In addition, we perform a case study of a thermodynamic equation of state to gain insight on valid functional forms with thermodynamics‐based constraints on the first and second derivatives.

show abstract

A consistent and precise alpha function for cubic equations of state

Cited by 17 publications

References 38 publications

Prediction of Vapor–Liquid Equilibrium and Thermodynamic Properties of Natural Gas and Gas Condensates

Prediction of Vapor–Liquid Equilibrium and Thermodynamic Properties of Natural Gas and Gas Condensates

Research into the Polynomial Alpha Function for the Cubic Equation of State

Deterministic symbolic regression with derivative information: General methodology and application to equations of state

Contact Info

Product

Resources

About