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choose

my
model!

Practical guide to process modeling

START

Importance of a good choice

Definitions to know

Credits

This project was realized by:

IFP-School team:

- Ulysse Lefevre

- Rafael Rodrigues Silva Ferreira

We are three IFP -School students, part of the program Energy and Processes, and working with the help and supervision of Dr. Jean-Charles de Hemptinne, ourThermodynamics professor, Laetitia Salessy, director of the Process program, and Clément Cahagne, educational engineer of the center.

IFP Energies nouvelles team:

- Nicolas Ferrando

- Jean-Charles de Hemptinne

We are research engineers in the Thermodynamic and Molecular Simulation Department.

This work was granted by the Elether Chair.

Definitions to know

What is a thermodynamic model?

What is a parameter?

What is a property?

What do you mean by data?

A thermodynamic model is an equation which aims to calculate thermodynamic properties using some parameters. They can be used to predict various properties such as enthalpy or phase equilibrium.

Categories of models include:

Equations of state: relationship between pressure, temperature, volume and number of moles. Such models are well adapted for all phases

Example: Peng-Robinson, Soave-Redlich-Kwong, …

Activity coefficient models: based on the excess Gibbs energy. Such models are often pressure-independent, and thus are well adapted only for liquid phases.

Example: NRTL, UNIQUAC, …

Empirical models or system-specific models.

Example: MBWR

The choice of model may depend on parameters such as process species and compositions, pressure and temperature ranges, data availability, and others. These models can help in understanding the behavior of the system. For industrial applications, thermodynamic models can help predict liquid-vapor equilibrium, as well as understand flame temperature, furnace temperature profiles and other parameters. Thermodynamic models can also be used to evaluate equibrium constant of chemical reactions.

A model parameter is a variable that is internal to the model and whose value can be estimated from data. The parameters and their significance depend on the model used. Many of them have no true physical meaning. Yet, a number of physical properties of the pure components are used as model parameters.

Data refers to the experimental data obtained in a database or in the laboratory. It refers to all the information that can be used on the model or that can help to validate it or not.

The more data you have, the more you can predict with accuracy the process, by optimizing a correlative model using these data.

Thermodynamic properties are the characteristics (identifiable and observable) of a system by which it can be specified.

For example: mass, volume, temperature, pressure etc.

Thermodynamic properties are values that can either be directly measured (physical properties), or may be fitted on pure component properties (as liquid molar volume and saturated vapour pressure for example).

Why should I choose the right thermodynamic model?

SAFETY

COST OPTIMIZATION

INNOVATION

Illustration: Methane hydrate

Methane hydrate is a solid phase, resulting from the crystallization of a mixture of water and methane under certain conditions of temperature (typically low) and pressure (typically high). These conditions of pressure and temperature can be reached invarious situations, such as in pipelines resting on the ocean floor, or on the top of cryogenic columns for light gas separation.

Therefore, the evaluation of formation hydrate formation is of primary importance since there is a risk of pipe plugging. The choice of an inappropriate model can thus have significant consequences on pipe and equipment design. The choice of a correct thermodynamic model can prevent accidents in this context.

Accidents caused by a bad choice of a thermodynamic model:

"An example of a wrong decision made because of a combination of insufficient or wrong phase equilibrium data with improper interpretation of column parameters, was the explosion at a butadiene distillation facility in Texas City in 1969 (Jarvis, 1971; Freeman and McCready, 1971; King, 1990). In order to repair the stripper compressor, the distillation unit was placed on total reflux. However, the column was slowly losing material because of a leaking valve in the overhead line. Vinylacetylene is the most dangerous impurity to be separated in the process, since it becomes explosive above a certain concentration. Based on the fact that it has the highest boiling temperature among all components in the distillation column, its concentration was monitored at the column base and was shown to be below the hazardous level, while aftermath modeling showed non-ideal mixture behavior with the highest concentration expected higher up, between 10th and 15th trays. That is exactly where the explosion happened.

One panelist provided another example, although references were not provided (Peters). This incident related to the release of gas from a high pressure (80 MPa) gas condensate reservoir. Such a release follows the Joule–Thomson effect. The process simulator calculated a temperature drop, while in practice a temperature increase was observed. The main reason for such dramatic disagreement was that parameters of an equation of state (EOS) were fitted to a wrong data set. Also, when comparing working fluids for thermodynamic cycles,the net power outputs the key relevant quantity. When one takes into consideration its 0.95 confidence interval, for each fluid, additional quantitative information becomes vital for the fluid selection. The ranking of working fluids can be significantly different based on whether the mean value of the net power output is used as a criterion, or, alternatively, whether uncertainties (e.g., the lower bound of the 0.95 confidence interval) are incorporated (Frutiger et al., 2016).

A final example mentioned by the panel concerns the use of temperature-independent binary interaction parameters for vapour–liquid equilibrium (VLE) computations in the design of a pressure swing absorption tower. This may lead to significant errors in the estimation of the number of theoretical stages of the column. The panel concluded that all these examples clearly demonstrate the effect of uncertainty on the quality of the design and the ability to anticipate unsafe plant operation."

Source: Data quality and assessment, validation methods and error propagation through the simulation software: Report from the Round-Table Discussion at the 10th World Congress of Chemical Engineering in Barcelona (October 1–5, 2017). (2018). Chemical Engineering Research and Design, 137, A1–A8. https://doi.org/10.1016/j.cherd.2018.08.010 p.A2

The use of a thermodynamic model not appropriate for a type of mixture can lead to results far from reality. If we take the example of a distillation, a bad thermodynamic model will lead to an erroneous determination of the number of plates necessary to achieve the separation. As a consequence, one can obtain a distillate with a lower quality (number of plates too low) or higher than what is required (number of plates too high). In addition, thermodynamic models allow to properly size the units and also to have optimal CAPEX / OPEX

The choice of an appropriate thermodynamic model can be useful at the earliest stages of a new project to know what is possible to do and what is not.

In the earliest stage of a project, all thermodynamic data may be not available to correctly parameterize the model: it is thus necessary to select the most robust predicive model.

Q U I Z

Just a few questions to define your perfect model!

Play

show

Play

1° step:
Process type

2° step:
Fluid type

Individual examples of use

Which data ?

Which model?

Knowing the process type will help to know the key properties (experimental data) to be used for the thermodynamic model parameterization / validation

Knowing the fluid type will help to choose the right thermodynamic model, according to the nature of components, the composition, the temperature and the pressure.

These are two examples developed by IFP-School students to show how to compare two or more models using the information of this quiz.

1- Which process?

Separation

Reaction

Flow Assurance

Energy system

Separation:

Liquid-vapour: distillation, absorption, stripping, etc.

Liquid-liquid: decanter, extraction, etc.

Liquid-solid: crystallization, hydrates, etc …

Reaction:

Thermodynamic requirements to model a chemical reactor.

Fluid Flow:

Thermodynamic considerations to prevent risks due to phase change in fluid flow (flow assurance)

Energy system:

Units requiring energy considerations: compressor, pump, heat exchangers, etc.

You can have more than one type of process in your system (separation including reactions, energy system with a fluid flow, etc.). In that case, you need to consider all the properties needed.

Select the type of separation process

Liquid-liquid extraction

Crystallization

Solvent absorption

Distillation

Stripping

Supercritical extraction

LIQUID-VAPOR

Equilibrium between a vapor phase and a liquid phase

LIQUID-LIQUID

Equiibrium between two liquid phases

LIQUID-SOLID

Equilibrium between a liquid phase and a solid phase

Flash drum

Liquid-liquid decantation

Select the type of distillation process?

Close boiling

Severe specifications

Extractive Distillation

There are different types of distillation processes. To help you find the key properties, please specify the type of distillation.

Severe Specifications

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part 2

Key data to collect for model parameterization / validation:

A severe specification consists in not exceeding very low concentration of some impurities in the distillate

Inifinite dilution activity coefficient of impurities in the main component in the distillate

Inifinite dilution activity coefficient of a solute i in a solvent S is directly related to the Henry constant of the solvent and the saturation pressure of the solute:

This coefficient can be measured in laboratory in specifc devices such as Exponential Dilutor.

Close boiling

Azeotrope data (temperature, pressure, composition)
Only azeotropes in the cut point region are of interest!

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Compounds with close boiling point are expected to form an azeotropic mixture

An azeotrope is a mixture whose composition can not be altered or changed by simple distillation. The composition of the liquid phase is the same of the vapour phase. It corresponds to a junction between the dew curve and the bubble curve.

An azeotrope can be "positive": it corresponds to a maximum in the bubble curve in an isothermal diagram:

or "negative": it corresponds to a minimum in the bubble curve in an isothermal diagram:

Key data to collect for model parameterization / validation:

Close boiling pure compounds vapour pressures

Extractive distillation

Distribution coefficients (Ki) of key compounds in the solvent

Distribution coefficients, usually named "Ki" are defined by the ratio of the molar fraction of a given component in the vapour phase by its molar fraction in the liquid phase:

Molar fraction measurements (often named "TPxy" data in usual databanks) are often carried out in PVT-cells using either on-line chromatography analysis (analytic method) or mass balance considerations (static method).

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Key data to collect for model parameterization / validation:

Flash drum

Distribution coefficients (Ki) of key compounds

Distribution coefficients, usually named "Ki" are defined by the ratio of the molar fraction of a given component in the vapour phase by its molar fraction in the liquid phase:

Molar fraction measurements (often named "TPxy" data in usual databanks) are often carried out in PVT-cells using either on-line chromatography analysis (analytic method) or mass balance considerations (static method).

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part 2

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Key data to collect for model parameterization / validation:

Azeotrope data for close boiling components

An azeotrope is a mixture whose composition can not be altered or changed by simple distillation. The composition of the liquid phase is the same of the vapour phase. It corresponds to a junction between the dew curve and the bubble curve.

An azeotrope can be "positive": it corresponds to a maximum in the bubble curve in an isothermal diagram:

or "negative": it corresponds to a minimum in the bubble curve in an isothermal diagram:

Solvent absorption

Henry constant of solutes in the liquid solvent

Henry constant of a solute i in a solvent S is defined by the ratio of the liquid fugacity of the solute by its liquid molar fraction, when this fraction tends to zero (infinite dilution). In this condition, the total pressure tends to the vapor pressure of the pure solvent:

At the thermodynamic equilibrium, the liquid fugacity of the solute i is equal in both liquid and vapor phases: liquid fugacity can be replaced by vapor fugacity. At low pressure (typically less than 5 bar), vapor fugacity can be approximated by partial pressure. If the solubility is low enough to ensure the infinite dilution assumption, the Henry constant can be expressed in a more convenient way:

Henry constant can be measured in laboratory by specific devices such as Exponential Dilutor, based on on-line chromatography analysis.

Older measurement techniques were based on volumetric considerations, and results were provided in term of equivalent properties such as Kuenen coefficient, Bunsen coefficient and Ostwald coefficient. Conversion rules into Henry constant can be found in general textbooks [1].

[1] de Hemptinne et al., Select thermodynamic model for process simulation, ed. Technip, Paris, France, 2012.

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Key data to collect for model parameterization / validation:

Low solubility of the solutes:

Low and high solubilities of the solutes:

Solubility (mole fraction) of the solutes in the liquid solvent

The molar fraction of the solute in the solvent can be directly measured in laboratory using specific devices such as PVT-cells. The molar fraction can be measured either by a chromatography analysis of a sample (analytic method), or by mass balance consideration (static method). These data are often called "TPx data" in usual databanks.

Supercritical extration

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part 2

part 2

Key data to collect for model parameterization / validation:

Distribution coefficients (Ki) of key compounds in the solvent

Distribution coefficients, usually named "Ki" are defined by the ratio of the molar fraction of a given component in the vapour phase by its molar fraction in the liquid phase:

Molar fraction measurements (often named "TPxy" data in usual databanks) are often carried out in PVT-cells using either on-line chromatography analysis (analytic method) or mass balance considerations (static method).

Stripping

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part 2

part 2

Key data to collect for model parameterization / validation:

Distribution coefficients (Ki) of key compounds in the solvent

Distribution coefficients, usually named "Ki" are defined by the ratio of the molar fraction of a given component in the vapour phase by its molar fraction in the liquid phase:

Molar fraction measurements (often named "TPxy" data in usual databanks) are often carried out in PVT-cells using either on-line chromatography analysis (analytic method) or mass balance considerations (static method).

Henry constant of the stripping gas in the solvent

Henry constant of a solute i in a solvent S is defined by the ratio of the liquid fugacity of the solute by its liquid molar fraction, when this fraction tends to zero (infinite dilution). In this condition, the total pressure tends to the vapor pressure of the pure solvent:

At the thermodynamic equilibrium, the liquid fugacity of the solute i is equal in both liquid and vapor phases: liquid fugacity can be replaced by vapor fugacity. At low pressure (typically less than 5 bar), vapor fugacity can be approximated by partial pressure. If the solubility is low enough to ensure the infinite dilution assumption, the Henry constant can be expressed in a more convenient way:

Henry constant can be measured in laboratory by specific devices such as Exponential Dilutor, based on on-line chromatography analysis.

Older measurement techniques were based on volumetric considerations, and results were provided in term of equivalent properties such as Kuenen coefficient, Bunsen coefficient and Ostwald coefficient. Conversion rules into Henry constant can be found in general textbooks [1].

[1] de Hemptinne et al., Select thermodynamic model for process simulation, ed. Technip, Paris, France, 2012.

Liquid-liquid decantation

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part 2

part 2

Key data to collect for model parameterization / validation:

Low solubility of the solutes:

Low and high solubilities of the solutes:

Liquid-liquid equilibrium data (tie-lines)

The liquid-liquid equilibrium data, often named " Txx' " in usual databanks, consist in measuring the composition of both liquid phases for a given temperature T and pressure P. Liquid-liquid equilibrium can be assumed pressure-independant as a first approximation. Data are often measured at atmospheric pressure if the boiling point of the components are higher than room temperature.

In a liquid-liquid extraction process, two components are separated using an extraction solvent. Equilibrium data are thus related to ternary systems, and must be plot on ternary diagram:

According to the Gibbs phase rule, the variance of ternary systems in a liquid-liquid operation is equal to 3: it is necessary to fix 3 independant intensive variables to entirely define the system: temperature, pressure and composition. Consequently, the compositions of the liquid phases in equilibrium depend on the initial composition of the mixture. That is why it is important for modeling consideration to have both phase compositions. The line joining the two composition points at the equilibrium is named "Tie-Line".

Note that the two border curves delimiting the monophasic / diphasic area converge in a point named critical point.

Inifinite dilution activity coefficient of low-concenration components

Inifinite dilution activity coefficient of a solute i in a solvent S is directly related to the Henry constant of the solvent and the saturation pressure of the solute:

This coefficient can be measured in laboratory in specifc devices such as Exponential Dilutor.

Liquid-liquid extraction

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part 2

Key data to collect for model parameterization / validation:

Partitioning coefficients of the key components to be extracted

Partitioning coefficients refer to the ratio of molar fraction of a given component between the two liquid phases:

If low solubility of the solutes:

Inifinite dilution activity coefficient of solutes in the solvent / co-solvent

Inifinite dilution activity coefficient of a solute i in a solvent S is directly related to the Henry constant of the solvent and the saturation pressure of the solute:

This coefficient can be measured in laboratory in specifc devices such as Exponential Dilutor.

(often, ternary data between solute + solvent 1 + co-solvent)

Crystallization

Pure component : melting temperature and melting enthalpy

Mixtures : Solid + Fluid equilibrium data
Beware to eutectic points !

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Key data to collect for model parameterization / validation:

An eutectic point is a homogeneous mixture of compounds that melts or solidifies at a single temperature lower than the melting point of any of the components of the system. On a temperature-composition diagram, it corresponds to the minimal temperature that a liquid mixture can reach.

Crystallisation is often kinetically-driven, so a purely thermodynamic analysis may not be enough to describe the phenomena: supersaturation information may be needed.

Specify the type of reactor modelling

Thermodynamic control

Kinetic control

Wagner, N., & Pross, A. (2011). The nature of stability in replicating systems. Entropy, 13(2), 518–527. https://doi.org/10.3390/e13020518

Kinetic control: The rate of products' formation determine the product ratio.

-> The kinetic product is the one that is formed the fastest in a chemical reaction).

Thermodynamic control: The thermodynamic stability of products determine the products ratio.

--> The thermodynamic product is the most stable product formed in a chemical reaction).

Kinetic control

Solubilities of reactants and products in the reacting phase must be known. Focus on the rate limiting species.

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part 2

Key data to collect for model parameterization / validation:

Single phase systems

No thermodynamic issues

Multiphase systems

Thermodynamic control

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part 2

part 2

Key data to collect for model parameterization / validation:

All systems:

Equilibrium constant of the reaction(s)

Enthalpies of the reaction(s)

Multiphase systems:

Solubilities of reactants and products in the reacting phase must be known.

In which phase is the fluid flow?

Gas flow

Liquid flow

Two phase flow

Which is the most likely risk of appearance?

Solid appearance

Vapor appearance

Consider the eventual presence of bubbles or crystals in your fluid to avoid major problems. For this, you need to know some key data to correctly understand the process and validate the model.

We suggest considering both of the risks.

Liquid flow
Vapor appearance risk

Bubble temperature (or pressure) of the liquid mixture

Bubble temperature (or pressure) is the temperature (or pressure) for which the first bubble of gas appears for a given liquid mixture.

It is usually measured in laboratory using an ebulliometric method or specific PVT-cells.

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part 2

part 2

Key data to collect for model parameterization / validation:

Focus on data involving the lighest component of the mixture

Liquid flow
Solid appearance risk

Which kind of solid is expected to form ?

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HYDRATES

WAXES

ASPHALTENES

SCALES

Hydrate

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Key data to collect for model parameterization / validation:

Hydrate appearance temperature (or pressure)
with or without hydrate inhibitor

The hydrate appearance temperature (or pressure) at a given pressure (or temperature) corresponds to the conditions at which hydrate starts to form. In presence of hydrate inhibitor (like methanol, MEG, TEG, salt, ...), this temperature can be lowered.

Illustration: temperature appearance of methane hydrate without inhibitor and with 5% methanol. Calculations from Carbone software.

When water and some light components coexist (light hydrocarbons,CO2, H2S, N2), so-called water hydrates can be formed [64]. This is a specific crystalline water structure physically resembling ice, in which small non-polar molecules (typically gases) are trapped inside “cages” of hydrogen bonded water molecules. Without the support of the trapped molecules, the lattice structure of hydrate (or clathrate) would collapse into

conventional ice crystal structure or liquid water. Most low molar mass gases (including O2, H2, N2, CO2, CH4, H2S, Ar, Kr, and Xe) as well as some higher hydrocarbons and freons will form hydrates at suitable temperatures and pressures. These crystalline structures are non stoichiometric, as the number of gas molecules per water molecule may vary within limits, depending on pressure and temperature. Three structures have so far been identified: structureI, structure II and structure H, in which the size and distribution of large and small cages are different. Hydrate formation will occur at moderate temperature (up to around 300 K) and high pressure (several MPa). Consequently, the risk of solid deposit is of industrial interest in gas production and transportation, due to possible plugging of pipes.

[1] de Hemptinne et al., Select thermodynamic model for process simulation, ed. Technip, Paris, France, 2012.

Wax

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Key data to collect for model parameterization / validation:

Wax appearance temperature (WAT)

The wax appearance temperature (WAT) at a given pressure corresponds to the temperature at which wax starts to crystallise.

In laboratory, this temperature is often obtained from calorimetric measurements, since the heat capacity of the mixture significantly changes when solid starts to form.

Illustration: exemple of WAT computation for a paraffinic fluid. From Carbone software.

Wax amount formed at a given temperature and pressure

The wax amount corresponds to the mass of wax formed for a given temperature and pressure. It is often expressed in term of fraction of the liquid fluid mass.

Illustration: Wax amount formed in a paraffinic fluid. Calculations from Carbone software.

When fluids contain heavy paraffinic compounds, this components may precipitate as a solid or solid like material called wax if the fluid is cooled down. Some example of applications where solid wax may appear: fluid reservoir modeling, residue conversion process, Fisher-Tropsh process, etc.

Wax precipitation may cause operational problems when unprocessed well streams are transported in cold pipelines. Wax may deposit as a solid layer inside the pipeline. With continued transport, this layer will build up and eventually plug the pipeline if not mechanically removed. Not all formed wax will deposit at the wall. Some will precipitate as solid particles in the bulk phase of the oil and will be transported in suspended form. The suspended wax particles will lead to an increase in the apparent viscosity of the oil and thereby affect the flow properties [1]

[1] Pedersen and Christensen., Phase behavior of petroleum reservoir fluids, ed. CRC Taylor & Francis, Boca Raton, Florida, 2007.

Asphaltene

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part 2

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Key data to collect for model parameterization / validation:

Onset pressures: upper (UOP) and/or lower (LOP)

The asphaltene onset pressure corresponds to the pressure at which asphaltenes start (or end) to precipitate for a given temperature.

For an asphaltenic fluid, two onset pressures exists: when pressure increases, the first pressure at which asphaltenes start to precipitate is called Lower Asphaltene Onset Pressure (LAOP) (see PL on the picture below). The asphaltene precipitation reaches a maximum at the saturation pressure of the fluid (Psat). Finally, asphaltenes stop to precipitate at the Upper Asphaltene Onset Pressure (UAOP) (see PU on the picture).

Various techniques can be used in laboratory to measure onset pressures, such as viscosity measurements, filtration techniques, transfer-based approaches, refractive index, light scaterring ... [1].

[1] Shadman et al., Petroleum, 2017, 3(3), 287

Fraction of asphaltene precipitated

The fraction of asphaltene precipitated corresponds to the quantity of asphaltene deposit with respect to the quantity of the liquid phase for a given temperature and pressure.

Petroleum fluids often include a very heavy residue that contains large, complex molecules of relatively unknown molecular structure. They are generally referred to as resins and asphaltenes and are identified by various standards. Resins for example are soluble in n-heptane (ASTM D3279, NFT 60115 – IP 143); asphaltenes are not, but are soluble in toluene. Other standards define solubility using propane or n-pentane as solvent.

Asphaltenes are in fact heavy hydrocarbons of molar mass in the range 400-1500 g mol–1 containing heteroatoms such as oxygen, nitrogen and sulphur. They have a H/C ratio of about 1.2.

The presence of asphaltene in a petroleum fluid may result in phase separation and deposition of a heavy, very viscous material, which in some cases is identified as a solid, in other cases as a liquid. Deposition occurs either as a result of mixing, for example in refinery operations, or upon pressure change in reservoir draining and extraction [1].

[1] de Hemptinne et al., Select thermodynamic model for process simulation, ed. Technip, Paris, France, 2012.

Scales

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part 2

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Key data to collect for model parameterization / validation:

Brine analysis

The brine analysis consists in quantifying the concentration of the ionic species in the aqueous phase. These concentrations are required for mass balance considerations when computing salt precipitation. The experimental pH can also be an input for modeling, by adding an additional constraint on H+ concentration.

Equilibrium constants of the salt formation reactions

Consider the reaction of salt formation from its constituting cation and anion :

Cation + Anion <--> Salt

The equilibrium constant of such a reaction is a mandatory input for modeling salt precipitation (or, in an equivalent way, the Gibbs formation energy of the reactants and products).

An aqueous phase to be processed may contain ionic species coming from salt or rock dissolution. Under certain condition of temperature, pressure and ion concentration, salt could precipitate and form a solid deposit. This deposition is often reffered as "Scaling", and is a major issue in pipes where salted water flows.

Which is the most likely risk of appearance?

Solid appearance

Liquid appearance

Consider the eventual presence of dew or crystals in your fluid to avoid major problems. For this, you need to know some key data to correctly understand the process and validate the model.

We suggest considering both of the risks.

Gas flow
Liquid appearance risk

Dew temperature (or pressure) of the vapor mixture

Dew temperature (or pressure) is the temperature (or pressure) for which the first droplet of liquid appears for a given vapor mixture.

TRY AGAIN

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part 2

part 2

Key data to collect for model parameterization / validation:

Focus on data involving the heaviest component of the mixture

Gas flow
Solid appearance risk

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DEPOSITION

Deposition is the direct transformation of a vapor phase to a solid phase. It is the reverse process of sublimation.

Which kind of solid is expected to form ?

HYDRATES

In rare cases, hydrates can be formed in absence of any aqueous phase. Under certain conditions of temperature and pressure, a small amount of water in a gas flow may be enough to start hydrate formation.

This phenomenon is often observed in cryogenic distillation columns, such as deethanizer or depropanizer. The gas to be processed must be carefully dried to avoid hydrate formation.

Two phase flow

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part 2

part 2

Distribution coefficients (Ki) of key compounds

Distribution coefficients, usually named "Ki" are defined by the ratio of the molar fraction of a given component in the vapour phase by its molar fraction in the liquid phase:

Molar fraction measurements (often named "TPxy" data in usual databanks) are often carried out in PVT-cells using either on-line chromatography analysis (analytic method) or mass balance considerations (static method).

Key data to collect for model parameterization / validation:

Look also the specific properties for the liquid flow and vapor flow !

Energy system

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part 2

part 2

Key data to collect for model parameterization / validation:

Compressor, pump, heat exchangers,...

Look also the specific risks for the liquid flow and vapor flow !

Phase density

Many thermodynamic properties of a fluid flowing in an energetic device depend on phase density (viscosity, enthalpy, etc ...).

It is thus of primary importance to model accurately this property before designing a compressor, pump, valve, heat exchanger, etc.

Phase enthalpy

To calculate the duty required for your energetic device (or to evaluate the outlet temperature or pressure), the phase enthalpy must be correctly modeled. For compressor, entropy must also be calculated (an ideal compressor is an isentropic device; a real compressor involves a correction factor to isentropicity).

Both enthalpy and entropy can be determined from heat capacity of the fluid. It is thus necessary to measure this property.

2- Model Selection

Select the type of fluid to model

PURE COMPONENT

Fluid containing only one type of compound (e.g. pure CO2, pure water, ...)

MIXTURE

Fluid containing different types of molecules.

This is the very large majority of fluids to be processed.

This selection guide is based on two textbooks recommendations:

[1] de Hemptinne et al., Select thermodynamic model for process simulation, ed. Technip, Paris, France, 2012.

[2] Jaubert et al., Modèles thermodynamiques pour le génie des procédés, ISTE ed., Great Britain, 2021

More details can be found in these textbooks.

The choice of a thermodynamic model is often not unique, and the model accuracy also strongly depends on the temperature/pressure/composition ranges and the quality of the data used for parameterization.

Use this module as a guide, and not as an ultimate truth!

Validation by thermodynamic experts is highly recommended!

Pure component

What is the state of the pure component fluid ?

Liquid (or unknown)

Vapor - Low pressure
( < 10 bara)

Vapor - High pressure
( > 10 bara)

Finally!

Here are the models proposed for your process.

IDEAL GAS

At low pressure (typically less than 10 bar), a vapor phase behaves like an ideal gas. In such a gas, molecules do not interact each other.

The equation of state associated to an ideal gas is:

PV = nRT

where P is the pressure (Pa), V the volume (m3), n the number of mol, T the temperature (K) and R the ideal gas constant (8.314 J/mol/K).

Pure component
Liquid state

Do I need only properties of the saturated liquid ?

Yes!

No!

Finally!

Here are the models proposed for your process.

Specific correlations for

pure liquid saturated properties

Many correlations exist to calculate liquid properties along the saturation curve, as a function of temperature. They are usually reported in pure component databank like DIPPR [1] or TRC-NIST [2]. Most of process simulation software give access to these correlations.

Correlations are available for:

- vapor pressure

- saturated liquid density

- saturated liquid heat capacity

- heat of vaporization

- saturated liquid viscosity

- ...

[1] https://www.aiche.org/dippr/events-products/801-database

[2] https://trc.nist.gov/

Pure component

Is there a specific equation of state for your component ?

Yes!

No! (or I don't know!)

Finally!

Here are the models proposed for your process.

Specific Equation of State

Specific equations of state have been developed for various common pure components.

WARN: this list is not exhaustive! Make also your own literature review!

Water: Steam tables (W. Wagner and A. Pruss, "The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use," J. Phys. Chem. Ref. Data, 31, 387-535 (2002). http://www.iapws.org/newform.html.

Natural Gas: GERG-2008 , The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures: an Expension of GERG-2004, J. Chem. Eng. Data 2012, 57, 11, 3032–3091 https://pubs.acs.org/doi/10.1021/je300655b)

Pure component REFPROP base (NIST) (https://www.nist.gov/srd/refprop): MBWR equation of state. List of pure compounds available:

 Name Chemical Formula 1,3-Butadiene C4H6 Butene C4H8 1-Butyne C4H6 1-Pentene C5H10 2,2-Dimethylbutane C6H14 2,3-Dimethylbutane C6H14 3-Methylpentane C6H14 Acetone C3H6O Acetylene C2H2 Ammonia NH3 Argon Ar Benzene C6H6 Butane C4H10 Undecane C11H24 Dodecane C12H26 Hexadecane C16H34 Methylcyclohexane C7H14 Docosane C22H46 cis-Butene C4H8 Propylcyclohexane C9H18 Perfluorobutane C4F10 Perfluoropentane C5F12 Perfluorohexane C6F14 R13I1 CF3I Chlorine Cl2 Chlorobenzene C6H5Cl Carbon monoxide CO Carbon dioxide CO2 Carbonyl sulfide COS Cyclobutene C4H6 Cyclohexane C6H12 Cyclopentane C5H10 Cyclopropane C3H6 Deuterium D2 Heavy water D2O D4 C8H24O4Si4 D5 C10H30O5Si5 D6 C12H36Si6O6 Diethanolamine C4H11NO2 Decane C10H22 Diethyl ether C4H10O Dimethyl carbonate C3H6O3 Dimethyl ether C2H6O Ethylbenzene C8H10 Ethylene glycol C2H6O2 Ethane C2H6 Ethanol C2H6O Ethylene C2H4 Ethylene oxide C2H4O Fluorine F2 Hydrogen sulfide H2S Hydrogen chloride HCl Helium He Heptane C7H16 Hexane C6H14 Hydrogen (normal) H2 Isobutene C4H8 Isohexane C6H14 Isooctane C8H18 Isopentane C5H12 Isobutane C4H10 Krypton Kr MD2M C10H30Si4O3 MD3M C12H36Si5O4 MD4M C14H42O5Si6 MDM C8H24O2Si3 Monoethanolamine C2H7NO Methane CH4 Methanol CH4O Methyl linoleate C19H34O2 Methyl linolenate C19H32O2 MM C6H18OSi2 Methyl oleate C19H36O2 Methyl palmitate C17H34O2 Methyl stearate C19H38O2 m-Xylene C8H10 Nitrous oxide N2O Neon Ne Neopentane C5H12 Nitrogen trifluoride F3N Nitrogen N2 Nonane C9H20 Novec 649, 1230 C6F12O Octane C8H18 Orthohydrogen H2 Oxygen O2 o-Xylene C8H10 Parahydrogen H2 Pentane C5H12 Propadiene C3H4 Propane C3H8 Propylene C3H6 Propylene oxide C3H6O Propyne C3H4 p-Xylene C8H10 R11 CCl3F R1123 C2HF3 R113 C2Cl3F3 R114 C2Cl2F4 R115 C2ClF5 R116 C2F6 R12 CCl2F2 R1216 C3F6 R1224yd(Z) C3HClF4 R123 C2HCl2F3 R1233zd(E) C3H2ClF3 R1234yf C3F4H2 R1234ze(E) C3F4H2 R1234ze(Z) C3F4H2 R124 C2HClF4 R1243zf C3H3F3 R125 C2HF5 R13 CClF3 R1336mzz(Z) C4H2F6 R134a C2H2F4 R14 CF4 R141b C2H3Cl2F R142b C2H3ClF2 R143a C2H3F3 Dichloroethane C2H4Cl2 R152a C2H4F2 R161 C2H5F R21 CHCl2F R218 C3F8 R22 CHClF2 R227ea C3HF7 R23 CHF3 R236ea C3H2F6 R236fa C3H2F6 R245ca C3H3F5 R245fa C3H3F5 R32 CH2F2 R365mfc C4H5F5 R40 CH3Cl R41 CH3F RC318 C4F8 RE143a C2H3F3O RE245cb2 C3H3F5O RE245fa2 C3H3F5O RE347mcc (HFE-7000) C4H3F7O Sulfur hexafluoride SF6 Sulfur dioxide O2S trans-Butene C4H8 Toluene C7H8 Vinyl chloride C2H3Cl Water H2O Xenon Xe

Phase equilibrium property

Phase property

Select the property type to analyze

Phase equilibrium property: You have a process where phase split may or will occur: you need to calculate the partitionning coefficients of the components.

Phase property: Your process requires accurate modeling of single phase properties, such as volume, enthalpy, heat capacities, entropy, etc. If your system has two phases, you can model this single phase properties in each phase.

Which type of mixture ?

Mixture with
polar compounds

Mixture of
non polar compounds

Mixture with H2
(large quantity)

Polar components

Polar compounds are compounds that have slight partial electrostatic charges (slightly positive and slightly negative) within the compound. The slight charges are due to electronegativity differences (electronegativity is defined as the attraction an element has for electrons- the greater the electronegativity, the more electrons are pulled toward an element.).

The presence of heteroatoms (N, O, S, ...) often lead to a polar behavior of the compound.

Compounds forming hydrogen bonds (H -- O interaction), such as alcohols, water, esters, ... are also polar molecules.

Non-polar components

An usual familiy of non_polar compounds are hydrocarbons (exept polyaromatics, in which the multiple aromatic rings may generate polar interactions).

Symetric light gases which can not form hydrogen bonds, such as N2, O2, CO2, ..., can also be assumed as non-polar (strictly speaking, their polar moment is zero due to symetriy, their quadrupolar moment not).

Which other components ?

H2

+

Hydrocarbons < C16

Other molecules

Finally!

Here are the models proposed for your process.

GRAYSON - STREED

Cubic EOS (PR, SRK)

with T-dependent kij

The Grayson-Streed model [1] is a predictive approach to compute partitionning coefficients of components in mixture of H2 and hydrocarbons up to C16 (the mixture can also include CO2 and H2S).

The fugacity in vapor phase is calculated with the Redlich-Kwong equation of state.

The non-ideality in the liquid phase is caculated with the regular solution theory.

Reference liquid fugacity of pure components are given by an empirical correlation, whose parameters are specific to each components.

As a predictive approach, it does not require exeprimental data. The internal correlations of this model have been parameterized for hydrocarbons up to C16. For heaviest hydroacarbons, the accuracy of the model decreases significantly.

[1] Grayson, H. G. and Streed, C. W. “Vapor-Liquid Equilibria for High Temperature, High Pressure Hydrogen-Hydrocarbon Systems” 6th World Congress for Petroleum; Frankfurt, 1963.

A cubic equation of state such as Peng-Robinson (PR) or Soave-Redlich-Kwong (SRK) with classical mixing rule can be used.

Nevertheless, due to the large asymetry of the system, a special care must be paid to adjust appropriate binary interaction parameters (kij) on experimental data covering the operating condition range. The presence of hydrogen often requires to use temperature-dependent kij [1]

[1] Ferrando et al.,Hydrogen/hydrocarbon phase equilibrium modelling with a cubic equation of state and a Monte Carlo method, Fluid Phase Equilibria 254 (2007) 211–223

Finally!

Here are the models proposed for your process.

Cubic EOS (PR, SRK)

with T-dependent kij

A cubic equation of state such as Peng-Robinson (PR) or Soave-Redlich-Kwong (SRK) with classical mixing rule can be used.

Nevertheless, due to the large asymetry of the system, a special care must be paid to adjust appropriate binary interaction parameters (kij) on experimental data covering the operating condition range. The presence of hydrogen often requires to use temperature-dependent kij [1]

[1] Ferrando et al.,Hydrogen/hydrocarbon phase equilibrium modelling with a cubic equation of state and a Monte Carlo method, Fluid Phase Equilibria 254 (2007) 211–223

Close boiling point process ?

Yes!

No

Finally!

Here are the models proposed for your process.

Cubic EOS (PR, SRK)

- Beware to alpha function !

Reminder of data needs

A cubic equation of state such as Peng-Robinson (PR) or Soave-Redlich-Kwong (SRK) is adapted to your process.

Nevertheless, some points require a very special care!

1/ Alpha function

You need to separate compounds with close boiling points: it means you need to have a very accurate modeling of the pure component vapor pressure. This can be achieved by tuning a specific alpha function. Indeed, the original alpha function of PR and SRK is predictive and depends on the acentric factor of the component. Other empirical alpha functions are often available in process simulator, for which parameters (usually 3) can be tuned to perfectly match experimental vapor pressures.

Among the most common alpha functions:

Close boiling points may lead to the formation of azeotropes. It is of primary importance to check that your model is able to reproduce them, after having adjusted the alpha function. If not, you must adjust a binary interaction coefficient kij to reproduce azeotropes in your system.

Do you have key experimental data for your process?

No, I have no data

Yes, it is available

Almost there...

Finally!

Here are the models proposed for your process.

Cubic EOS (PR, SRK)

A cubic equation of state such as Peng-Robinson (PR) or Soave-Redlich-Kwong (SRK) is adapted to your process.

If you are far from the mixture critical point, and if the molecule sizes are quite similar, the binary interaction parameters kij can be taken equal to zero as a first approximation.

In other cases (molecule sizes significantly different, or vicinity of the critical point), it becomes necessary to adjust the kij of the key binaries on your experimental data.

Finally!

Here are the models proposed for your process.

Consider this!

PPR78

The PPR78 model [1] is based on the Peng-Robinson equation of state for which the binary interaction parameters kij are determined from the chemical structure of the components. Hence, no experimental data are required: it is a predictive model.

[1] Xu, X.; Jaubert, J.N.; Privat, R. ; Arpentinier, P. Ind. Eng. Chem. Res. 2017, 56, 28, 8143–8157

Don't forget that a predictive model is less accurate than a correlative model parameterized on suitable experimental data. Such family of models must be used in the first steps of a process development, to evaluate various designs before starting experimental campains.

Large size asymetry ?

Yes!

No!
(or I don't know)

The size asymmetry refers to a large difference in molecular length or shape between components.

For exemple:

- mixture of polymers + monomers

- mixture with heavy paraffins and light paraffins

- mixture with light alcohols and fatty oils or fatty acid esters

A large size asymmetry leads to entropic deviations from ideality (size effects), in opposition to the enthalpic deviations which refer to strong energetic interactions between components.

What is the operating pressure?

High pressure
P > 10 bara

Low pressure
P < 10 bara

Do you have key experimental data for your process?

No, I have no data

Yes, it is available

Almost there...

Finally!

Here are the models proposed for your process.

UNIQUAC

SAFT

Activity coefficient models

Equations of state

The SAFT equations of state [1] (SAFT-0, VR-SAFT, PC-SAFT, …) are a recent family of models based on the perturbation theory of statistical thermodynamics. SAFT is built by a sum of various energy contributions, each of these contributions describing a specific interaction in the system.

This approach offers to this equation a wide range of use, including low and high pressures, liquid and vapor phases, for non-polar and polar compounds, associative compounds but also electrolytes. More specifically, the framework of this equation of state, based on the formation of chain of segments, suits very well for long-chain molecules such as polymers.

Each contribution of the equation of state may contain parameters which can be adjusted on experimental data. For non-associative molecules (molecules not forming hydrogen-bonds), the usual pure component parameters to adjust are the dispersive energy, the diameter and the number of segments. For associative molecules, the association energy and volume can also be tuned. Empirical binary interaction parameters can also be introduced in both dispersive and associative terms of the equation of state.

[1] Chapman, W. G., Gubbins, K. E., Jackson, G. and Radosz, M. “New Reference Equation of State for Associating Liquids” Industrial & Engineering Chemistry Research 1990, 29, 1709-1721.

The UNIQUAC model [1] is an activity coefficient model consisting of a sum of a combinatorial term (entropic effects) and a residual term (energetic interactions between molecules).

It is an empirical model: the residual term requires at least 2 binary interaction parameters (simulators often propose a version with 4 parameters to introduce a temperature-dependance in the parameters). If these parameters are set to zero, only the contribution part is taken into account. It is thus necessary to parameterize this model on relevant experimental data.

As any other activity coefficient model, UNIQUAC can be used only to model a liquid phase. If your process also involves a vapor phase, a model for this vapor phase is also required to calculate phase equilibrium. At low pressure (typically less than 10 bar), it can be the ideal gas model. It can also be an equation of state if pressure is higher.

The UNIQUAC model does not depend on pressure. It means that it is preferable to avoid its use for pressure above 10 bar. Nevertheless, for moderate pressures (typically less than 20 bar), a pressure-effect can be introduced in the liquid fugacity calculation with a Poynting correction.

[1] Abrams, D. S. and Prausnitz, J. M. “Statistical Thermodynamics of Mixtures: a New Expression for the Excess Gibbs Free Energy of Partly or Completely Miscible Systems” AIChE Journal 1975, 21, 116-128.

Finally!

Here are the models proposed for your process.

Activity coefficient models

Equations of state

UNIFAC

GC-SAFT

Consider this!

FLORY

UNIFAC [1] is an activity coefficient model directly inspired by the UNIQUAC equation, but it is designed as a group contribution model, and as such, it is a predictive model. Each molecule is split into its composing chemical group.

As UNIQUAC, UNIFAC can be used only to model a liquid phase. If your process also involves a vapor phase, a model for this vapor phase is also required to calculate phase equilibrium. At low pressure (typically less than 10 bar), it can be the ideal gas model. It can also be an equation of state if pressure is higher.

The UNIFAC model does not depend on pressure. It means that it is preferable to avoid its use for pressure above 10 bar. Nevertheless, for moderate pressures (typically less than 20 bar), a pressure-effect can be introduced in the liquid fugacity calculation with a Poynting correction.

WARNING: before using UNIFAC, be sure that the group databank selected contains parameters for the chemical groups involved in your molecules, as well as the binary parameters between the different groups. Process simulators usually offer several databanks: a public one (published parameters), and private databanks (UNIFAC-Dortmund, UNIFAC-Lyngby, …).

[1] Fredenslund, A., Jones, R. L. and Prausnitz, J. M. “Group Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures” AIChE Journal 1975, 21, 6, 1089-1099.

Don't forget that a predictive model is less accurate than a correlative model parameterized on suitable experimental data. Such family of models must be used in the first steps of a process development, to evaluate various designs before starting experimental campains.

Although quantitatively not accurate enough, the Flory model [1] offers a simple way of understanding the effect of differences in molecular volume. It is predictive, requiring only pure component molecular properties (the volume) as input and is used for monomer+ polymer mixtures.

The Flory model can be used only to model a liquid phase. If your process also involves a vapor phase, a model for this vapor phase is also required to calculate phase equilibrium. At low pressure (typically less than 10 bar), it can be the ideal gas model. It can also be an equation of state if pressure is higher.

The Flory model does not depend on pressure. It means that it is preferable to avoid its use for pressure above 10 bar. Nevertheless, for moderate pressures (typically less than 20 bar), a pressure-effect can be introduced in the liquid fugacity calculation with a Poynting correction.

[1] Flory, P. J. “Thermodynamics of Polymer-Solutions” Abstracts of Papers of the American Chemical Society 1976, 12-12.

The GC-SAFT equations of state [1] is directly inspired from the SAFT equation of state, but it is designed as a group contribution model, and as such, it is a predictive model. Each molecule is split into its composing chemical group. Each of the terms of the GC-SAFT equation contains parameters which can be determined only from this chemical structure.

Similarly to the SAFT equation of state, this model has a wide range of use, including low and high pressures, liquid and vapor phases, for non-polar and polar compounds, associative compounds but also electrolytes. More specifically, the framework of this equation of state, based on the formation of chains, suits very well for long-chain molecules such as polymers.

WARNING: before using GC-SAFT, be sure that the group databank used contains parameters for the chemical groups involved in your molecules.

[1] Tamouza, S., Passarello, J. P., Tobaly, P. and de Hemptinne, J. C. “Group Contribution Method with SAFT EOS Applied to Vapor Liquid Equilibria of Various Hydrocarbon Series” Fluid Phase Equilibria 2004, 222-223, 67-76.

Do you have key experimental data for your process?

No, I have no data

Yes, it is available

Almost there...

Finally!

Here are the models proposed for your process.

SAFT

Equations of state

The SAFT equations of state [1] (SAFT-0, VR-SAFT, PC-SAFT, …) are a recent family of models based on the perturbation theory of statistical thermodynamics. SAFT is built by a sum of various energy contributions, each of these contributions describing a specific interaction in the system.

This approach offers to this equation a wide range of use, including low and high pressures, liquid and vapor phases, for non-polar and polar compounds, associative compounds but also electrolytes. More specifically, the framework of this equation of state, based on the formation of chain of segments, suits very well for long-chain molecules such as polymers.

Each contribution of the equation of state may contain parameters which can be adjusted on experimental data. For non-associative molecules (molecules not forming hydrogen-bonds), the usual pure component parameters to adjust are the dispersive energy, the diameter and the number of segments. For associative molecules, the association energy and volume can also be tuned. Empirical binary interaction parameters can also be introduced in both dispersive and associative terms of the equation of state.

[1] Chapman, W. G., Gubbins, K. E., Jackson, G. and Radosz, M. “New Reference Equation of State for Associating Liquids” Industrial & Engineering Chemistry Research 1990, 29, 1709-1721.

Finally!

Here are the models proposed for your process.

Equations of state

GC-SAFT

Consider this!

Don't forget that a predictive model is less accurate than a correlative model parameterized on suitable experimental data. Such family of models must be used in the first steps of a process development, to evaluate various designs before starting experimental campains.

The GC-SAFT equations of state [1] is directly inspired from the SAFT equation of state, but it is designed as a group contribution model, and as such, it is a predictive model. Each molecule is split into its composing chemical group. Each of the terms of the GC-SAFT equation contains parameters which can be determined only from this chemical structure.

Similarly to the SAFT equation of state, this model has a wide range of use, including low and high pressures, liquid and vapor phases, for non-polar and polar compounds, associative compounds but also electrolytes. More specifically, the framework of this equation of state, based on the formation of chains, suits very well for long-chain molecules such as polymers.

WARNING: before using GC-SAFT, be sure that the group databank used contains parameters for the chemical groups involved in your molecules.

[1] Tamouza, S., Passarello, J. P., Tobaly, P. and de Hemptinne, J. C. “Group Contribution Method with SAFT EOS Applied to Vapor Liquid Equilibria of Various Hydrocarbon Series” Fluid Phase Equilibria 2004, 222-223, 67-76.

Does your process contain electrolyte species?

Yes!

Just in case...

No!

Do you have key experimental data for your process?

No, I have no data

Yes, it is available

Almost there...

Finally!

Here are the models proposed for your process.

Activity coefficient model

LIFAC

Consider this!

Don't forget that a predictive model is less accurate than a correlative model parameterized on suitable experimental data. Such family of models must be used in the first steps of a process development, to evaluate various designs before starting experimental campains.

LIFAC [1] is a group-contribution version of the LIQUAC model [2]. LIQUAC is an extension of the UNIQUAC model to electrolytic systems by the addition of a long-range coumobic interaction term (Pitzer-Debye-Hückel) and a middle-range interaction term.

In the LIFAC model, the binary parameters are between ion and group instead of molecule (group-contribution concept).

LIFAC is an activity coefficient model, and thus does not depend on pressure. Such kind of model must be used for low pressure processes only.

Important: it is necessary to check if the group parameters (unary and binary) concerning molecules involved in your system are present in the LIFAC database (see [1])

[1] Yan, W. et al., Fluid Phase Equilib., 1999, 162, 97-113

[2] Kiepe, J.K. et al., Ind. Eng. Chem. Res, 2006, 45, 2361-2373

Finally!

Here are the models proposed for your process.

Activity coefficient models
(low pressure)

Equations of state
(low and high pressure)

e-NRTL

(pure and mixed solvents)

e-CPA

e-PC-SAFT

Soreide & Whitson

Pitzer

(water)

Global salinity

Ion-dependant

LIQUAC

(pure and mixed solvents)

The Soreide & Whitson equation of state [1] is a modification of Peng-Robinson equation of state where the "salt water" is considered as a signle component. To take into account the global salinity, the alpha function of water is modified by introducing a dependence on the salt concentration. This EoS also considers different binary interaction parameters in the aqueous and non-aqueous phases.

[1] Soreide, I. et al., Fluid Phase Equilib., 1992, 77, 217-240

The e-SAFT equation of state is a modification of the original SAFT model to take into account perturbations related to ion-ion and ion-solvent interactions.

Various versions of this model exist (e.g. [1],[2],[3]), depending on the nature of the repulsive term (PC-SAFT, VR-SAFT, ...), on how are considered the long-range electrolytic interactions (Debye-Hückel, MSA, ...), and how ions are supposed to interact for short range interactions (dispersion or association).

[1] Ahmed, S. et al., Fluid Phase Equilib., 2018, 459, 138-157

[2] Held, C. et al., Chem. Eng. Sci., 2012, 68, 328-339

[3] Schrekenberg, J.M. et al., Mol. Phys., 2014, 112(17), 2339-2364

The e-CPA equation of state [1] is a modification of the original CPA model by the addition of specific contributions to take into account ion-ion and ion-solvent interactions.

[1] Maribo-Mogensen, B., et al., AIChE J., 2015, 61, 2933-2950

e-NRTL [1] is an extension of the activity coefficent model NRTL (short-range interaction, SR), by addition of a long-range (LR) coulombic tem (Pitzer-Debye-Hückel). The expression of the activity coefficient becomes:

Ion-ion and ion-solvent binary interaction parameters are required.

[1] Chen, C.C. et al., AIChE J., 1986, 32(3), 444-454

The LIQUAC model [1] is an extension of the activity coefficient model UNIQUAC (short-range interactions, SR), by the addition of two additional terms: a long-range (LR) coulombic interaction term, and a middle range (MR) ion-ion and ion-solvent interaction term:

Ion-ion and ion-solvant binary interaction parameters are required for both middle-range and short range terms.

[1] Kiepe, J.K. et al., Ind. Eng. Chem. Res, 2006, 45, 2361-2373

The Pitzer model [1], based on a theoritical development, remains one of the most well-known and most accurate models up to very high salt concentration. This model is widely used in upstream or geoscience industry, more specifically to calculate phase equilibrium involving brines.

This model involve binary and ternary interaction parameters.

[1] Pitzer, K.S., J. Chem. Phys., 1973, 77(2), 298-277

and temperature

P < 10 bara

AND

T < min(Tc,i)

P > 10 bara

OR

T > min(Tc,i)

Temperature less or greater than the minimal critical temperature of the components in the system.

Do you have key experimental data for your process?

No, I have no data

Yes, it is available

Almost there...

Finally!

Here are the models proposed for your process.

Activity coefficient models

UNIFAC

Consider this!

UNIFAC [1] is an activity coefficient model directly inspired by the UNIQUAC equation, but it is designed as a group contribution model, and as such, it is a predictive model. Each molecule is split into its composing chemical group.

As UNIQUAC, UNIFAC can be used only to model a liquid phase. If your process also involves a vapor phase, a model for this vapor phase is also required to calculate phase equilibrium. At low pressure (typically less than 10 bar), it can be the ideal gas model. It can also be an equation of state if pressure is higher.

The UNIFAC model does not depend on pressure. It means that it is preferable to avoid its use for pressure above 10 bar. Nevertheless, for moderate pressures (typically less than 20 bar), a pressure-effect can be introduced in the liquid fugacity calculation with a Poynting correction.

WARNING: before using UNIFAC, be sure that the group databank selected contains parameters for the chemical groups involved in your molecules, as well as the binary parameters between the different groups. Process simulators usually offer several databanks: a public one (published parameters), and private databanks (UNIFAC-Dortmund, UNIFAC-Lyngby, …).

[1] Fredenslund, A., Jones, R. L. and Prausnitz, J. M. “Group Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures” AIChE Journal 1975, 21, 6, 1089-1099.

Don't forget that a predictive model is less accurate than a correlative model parameterized on suitable experimental data. Such family of models must be used in the first steps of a process development, to evaluate various designs before starting experimental campains.

Finally!

Here are the models proposed for your process.

UNIQUAC

NRTL

Activity coefficient models

The NRTL model [1] is an activity coefficient model bases on the local composition theory. It takes into account enthalpic interactions between molecules.

It is an empirical model, and requires at least 2 binary interaction parameters (simulators often propose a version with 4 parameters to introduce a temperature-dependance in the parameters, and even 6 parameters if the alpha parameter is assumed variable). Nul parameters mean an ideal behaviour of the mixture. It is thus necessary to parameterize this model on relevant experimental data.

As any other activity coefficient model, NRTLcan be used only to model a liquid phase. If your process also involves a vapor phase, a model for this vapor phase is also required to calculate phase equilibrium. At low pressure (typically less than 10 bar), it can be the ideal gas model. It can also be an equation of state if pressure is higher.

The NRTL model does not depend on pressure. It means that it is preferable to avoid its use for pressure above 10 bar. Nevertheless, for moderate pressures (typically less than 20 bar), a pressure-effect can be introduced in the liquid fugacity calculation with a Poynting correction.

[1] Renon, H., Praunitz, J.M. “Local Composition in Thermodynamic Excess Functions for Liquid Mixtures” AICHE.J. 1968, 14, 135-144.

The UNIQUAC model [1] is an activity coefficient model consisting of a sum of a combinatorial term (entropic effects) and a residual term (energetic interactions between molecules).

It is an empirical model: the residual term requires at least 2 binary interaction parameters (simulators often propose a version with 4 parameters to introduce a temperature-dependance in the parameters). If these parameters are set to zero, only the contribution part is taken into account. It is thus necessary to parameterize this model on relevant experimental data.

As any other activity coefficient model, UNIQUAC can be used only to model a liquid phase. If your process also involves a vapor phase, a model for this vapor phase is also required to calculate phase equilibrium. At low pressure (typically less than 10 bar), it can be the ideal gas model. It can also be an equation of state if pressure is higher.

The UNIQUAC model does not depend on pressure. It means that it is preferable to avoid its use for pressure above 10 bar. Nevertheless, for moderate pressures (typically less than 20 bar), a pressure-effect can be introduced in the liquid fugacity calculation with a Poynting correction.

[1] Abrams, D. S. and Prausnitz, J. M. “Statistical Thermodynamics of Mixtures: a New Expression for the Excess Gibbs Free Energy of Partly or Completely Miscible Systems” AIChE Journal 1975, 21, 116-128.

Do you have key experimental data for your process?

No, I have no data

Yes, it is available

Almost there...

Does your process contain Hydrogen-bonded molecules ?

Yes!
(or I don't know!)

No!

Hydrogen-bonded molecules are molecules able to form a hydrogen-bond between a hydrogen atom covalently bonded to an electronegative heteroatom (O, N, S, ...) with another electronegative heteroatom (in the same molecule, or with another one).

Example of such molecules: water, alcohols, carboxylic acids, aldehydes, primary and secondary amines, etc.

Finally!

Here are the models proposed for your process.

Consider this!

PPR78

Equations of state

The PPR78 model [1] is based on the Peng-Robinson equation of state for which the binary interaction parameters kij are determined from the chemical structure of the components. Hence, no experimental data are required: it is a predictive model.

[1] Xu, X.; Jaubert, J.N.; Privat, R. ; Arpentinier, P. Ind. Eng. Chem. Res. 2017, 56, 28, 8143–8157

Don't forget that a predictive model is less accurate than a correlative model parameterized on suitable experimental data. Such family of models must be used in the first steps of a process development, to evaluate various designs before starting experimental campains.

Finally!

Here are the models proposed for your process.

Equations of state

PSRK

GC-SAFT

Consider this!

Don't forget that a predictive model is less accurate than a correlative model parameterized on suitable experimental data. Such family of models must be used in the first steps of a process development, to evaluate various designs before starting experimental campains.

The GC-SAFT equations of state [1] is directly inspired from the SAFT equation of state, but it is designed as a group contribution model, and as such, it is a predictive model. Each molecule is split into its composing chemical group. Each of the terms of the GC-SAFT equation contains parameters which can be determined only from this chemical structure.

Similarly to the SAFT equation of state, this model has a wide range of use, including low and high pressures, liquid and vapor phases, for non-polar and polar compounds, associative compounds but also electrolytes. More specifically, the framework of this equation of state, based on the formation of chains, suits very well for long-chain molecules such as polymers.

WARNING: before using GC-SAFT, be sure that the group databank used contains parameters for the chemical groups involved in your molecules.

[1] Tamouza, S., Passarello, J. P., Tobaly, P. and de Hemptinne, J. C. “Group Contribution Method with SAFT EOS Applied to Vapor Liquid Equilibria of Various Hydrocarbon Series” Fluid Phase Equilibria 2004, 222-223, 67-76.

PSRK [1] is a predictive version of the equation of state SRK. It uses the MHV2 (excess-G) mixing rules, with the UNIFAC model to calculate excess Gibbs energy. As UNIFAC is based on the group-contribution concept, PSRK is a predictive model, and only requires the knowledge of the chemical structure of the molecules.

WARNING: before using PSRK, be sure that the group databank used contains parameters for the chemical groups involved in your molecules.

[1] Holderbaum, T. and Gmehling, J. “PSRK: A Group Contribution Equation of State Based on UNIFAC” Fluid Phase Equilibria 1991, 70, 2-3, 251-265.

Finally!

Here are the models proposed for your process.

Equations of state

Cubic EOS + GE mixing rules

(ex: PRH, SRK-MHV2)

SAFT

CPA

Cubic EOS + asymetric kij mixing rules

(ex: SRK -Twu)

Because the excess Gibbs energy models (GE) often provide good results for strongly non-ideal mixtures at low pressure, Huron and Vidal [1] suggested to calculate the "a" parameter of the cubic equation of state using this type of model, and assuming a linear mixing rule for the "b" parameter. The GE model is thus integrated in the "a" parameter mixing rule, creating thus a new family of model named "CEOS-GE" (Cubic Equation of State with Gibbs Energy model).

Several approaches have been proposed on this principle, depending on the pressure chosen for solving the equation of state. The following table gives an overview of the most-known GE-based mixing rules (from [2]).

Usually, the GE model used is UNIQUAC or NRTL. The name of the resulting model must contain the name of the cubic equation of state, of the mixing-rule and of the GE model (for exemple, PR+HV+NRTL, also named "PRH" model)

For a predictive approach,it is also possible to use the UNIFAC model, yielding for exemple to the "PSRK" model (SRK+MHV1+UNIFAC)

[1] Vidal, J. “Mixing Rules and Excess Properties in Cubic Equations of State” Chemical Engineering Science 1978, 33, 6, 787-791.

[2] de Hemptinne et al., Select thermodynamic model for process simulation, ed. Technip, Paris, France, 2012.

The SAFT equations of state [1] (SAFT-0, VR-SAFT, PC-SAFT, …) are a recent family of models based on the perturbation theory of statistical thermodynamics. SAFT is built by a sum of various energy contributions, each of these contributions describing a specific interaction in the system.

This approach offers to this equation a wide range of use, including low and high pressures, liquid and vapor phases, for non-polar and polar compounds, associative compounds but also electrolytes. More specifically, the framework of this equation of state, based on the formation of chain of segments, suits very well for long-chain molecules such as polymers.

Each contribution of the equation of state may contain parameters which can be adjusted on experimental data. For non-associative molecules (molecules not forming hydrogen-bonds), the usual pure component parameters to adjust are the dispersive energy, the diameter and the number of segments. For associative molecules, the association energy and volume can also be tuned. Empirical binary interaction parameters can also be introduced in both dispersive and associative terms of the equation of state.

[1] Chapman, W. G., Gubbins, K. E., Jackson, G. and Radosz, M. “New Reference Equation of State for Associating Liquids” Industrial & Engineering Chemistry Research 1990, 29, 1709-1721.

The CPA (Cubic Plus Association) [1] is a recent equation of state in which van der Waals interaction are modeled with a classical cubic equation of state (PR or SRK), at which a specific term accounting for hydrogen-bond interactions is added. As for the SAFT equation of state, this last term comes from the Wertheim theory.

When dealing with non-associating molecules, the CPA equation of state is rigourosly equivalent to the cubic equation of state used for van der Waals forces (PR or SRK). This model applies well for polar and associating mixture, andhas been recently extended to electrolytic mixtures.

[1] Kontogeorgis et al., Intl. J. Thermophysics, 43, 54, 2022

For highly non-ideal mixtures, an alternative to the use of GE mixing rules is the use of mixing rules involving asymetric kij (for a i-j pair, kij is different of kji).

Various asymetric mixing rules have been proposed, such as Panagiotopoulos & Reid (1986) [1] and Modified Panagiotopoulos & Reid (also known as SRKM or PRM models). The most used mixing rules is probably the rule proposed by Twu et al [2]

When used with the SRK equation of state, the resulting model is often named SRK-Twu, SRKS, or SRK-ML, according to the commercial simulators.

[1] Panagiotopoulos et al., ACS Symp.Ser.300, American Chemical Society, Washington DC, 71-82, 1986

[2] Twu et al., Fluid Phase Equilib., 69, 33-50, 1991

What is the type of interaction in the system ?

Non polar interactions

Polar interactions

Polar components

Polar compounds are compounds that have slight charges (slightly positive and slightly negative) within the compound. The slight charges are due to electronegativity differences (Electronegativity is defined as the attraction an element has for electrons- the greater the electronegativity, the more electrons are pulled toward an element.) Examples of polar compounds would be: water (H2O), hydrogen fluoride (HF), hydrogen chloride (HCl), and ammonia (NH3).

Non-polar components (Hydrocarbons)

A hydrocarbon is an organic compound made of nothing more than carbons and hydrogens. Refinery gases can also be included in this category (CO2, H2S)

Finally!

Here are the models proposed for your process.

LEE-KESLER

The Lee–Kesler model [1] is an equation of state based on the corresponding state principle. It allows to compute phase properties of non-polar pure-components and mixtures with a good accuracy: liquid and vapor densities, liquid and vapor enthalpies, liquid and vapor heat capacities, etc.

[1] Lee, B.I. and Kesler, M.G. “A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States” AIChE Journal 1975, 21, 3, 510.

Do you have key experimental data for your process?

No, I have no data

Yes, it is available

Almost there...

Finally!

Here are the models proposed for your process.

SAFT

The SAFT equations of state (SAFT-0, VR-SAFT, PC-SAFT, …) are a recent family of models based on the perturbation theory of statistical thermodynamics. SAFT is built by a sum of various energy contributions, each of these contributions describing a specific interaction in the system.

All SAFT versions suit well to predict both liquid and vapor densities.

For other properties, and more specifically derivatives properties (such as Cp, Cv, speed of sound, etc ...), the SAFT-gamma-Mie model is particularly appropriate [1].

[1] Dufal et al., AIChE J., 61, 2891, 2015

Finally!

Here are the models proposed for your process.

Equations of state

VTPR

GC-SAFT

Consider this!

Don't forget that a predictive model is less accurate than a correlative model parameterized on suitable experimental data. Such family of models must be used in the first steps of a process development, to evaluate various designs before starting experimental campains.

The GC-SAFT equations of state is directly inspired from the SAFT equation of state, but it is designed as a group contribution model, and as such, it is a predictive model. Each molecule is split into its composing chemical group. Each of the terms of the GC-SAFT equation contains parameters which can be determined only from this chemical structure.

All SAFT versions suit well to predict both liquid and vapor densities.

For other properties, and more specifically derivatives properties (such as Cp, Cv, speed of sound, etc ...), the GC-SAFT-gamma-Mie model is particularly appropriate [1].

WARNING: before using GC-SAFT, be sure that the group databank used contains parameters for the chemical groups involved in your molecules.

[1] Haslam et al., J.Chem.Eng.Data, 65, 5862, 2020

VTPR (for Volume-Translated Peng-Robinson) equation of state is a predicitve version of the PR equation of state, coupled with a GE mixing rule using the UNIFAC activity coefficient model.

The use of a volume translation allows to obtain accurate predictions of both liquid and vapor densities, as well as density-dependant properties.

WARNING: before using VTPR, be sure that the group databank used contains parameters for the chemical groups involved in your molecules.

[1] Schmid, B, Gmehling, J. “Revised Parameters and Typical Results of the VTPR Group Contribution Equation of State” Fluid Phase Equilibria 2012, 317, 110-126.

3- Process examples

Ethanol to Ethylene
Dehydration Unit

CO2 capture unit

Ethanol to Ethylene
Dehydration unit

Which model?

Reactor

Flash
drum

Compressor

Water
washing

Dryer

Ethane / Ethylene
Splitter

Basic Principle:

1/ REACTOR

Fresh ethanol is heated up to 350 °C and feeds an adiabatic dehydration reactor.

Main reaction: Ethanol = Ethylene + Water

Secondary reactions : 2 Ethanol = DiethylEther + Water ; Ethanol + Ethylene = Ethane + Acetaldehyde

The main reaction is assumed to be under thermodynamic control

2/ FLASH DRUM

A flash drum at room temperature and pressure operates a separation between a ethylene-rich vapor phase and an aqueous phase sent to a water stripper and a recycle loop.

3/ COMPRESSOR

The ethylene-rich phase is compressed up to 35 bar.

4/ WATER WASHING

This flow is washed with water to eliminate residual oxygenated components like acetaldehyde. The bottom of the colomn is sent to the water stripper and a recycle loop. The top of the column is sent to a dryer.

5/ DRYER

The dryer is used to eleminate water before cooling up to -20 °C. This step is done by an adsorber. At low temperature, gas hydrate may be formed. It is thus necessary to know the maximal water content in the gas to avoid hydrate formation.

6/ ETHANE-ETHYLENE SPLITTER

This column aims to separate ethane and ethylene, two components with very close boiling points.

Monophasic adiabatic reactor, thermodynamic control (main reaction)

Reactor

Ethanol to Ethylene
Dehydration unit

Key data to collect for model parameterization / validation:

Equilibrium constant
to determine extend of reaction

Enthalpies of reaction
to determine outlet temperature

Ethanol to Ethylene
Dehydration unit

Key data to collect for model parameterization / validation:

Flash drum

Distribution coefficients (Ki) :
water, ethylene, non-converted ethanol, ethane, diethylether, acétaldehyde

To separate water from the ethylene-rich vapour phase

Ethanol to Ethylene
Dehydration unit

Key data to collect for model parameterization / validation:

Compressor

Phase density

Phase enthalpy

Ethanol to Ethylene
Dehydration unit

Key data to collect for model parameterization / validation:

Henry constant of light solutes (ethylene, ethane, ether) in liquid water

Solubilities (mole fraction) of the soluble solutes (ethanol, acetaldehyde) in liquid water

Water washing

Ethanol to Ethylene
Dehydration unit

Key data to collect for model parameterization / validation:

Dryer and cooler

Cool down a wet gas pressurized gas
Risk of hydrate formation!

To correctly size the dryer, the data needed are:
Hydrate appearance temperature as a function of water content

Ethanol to Ethylene
Dehydration unit

Key data to collect for model parameterization / validation:

Ethane - Ethylene splitter

Close boiling
distillation

Pure compounds vapour pressures

Azeotrope data (Possibly)

Cubic EOS + GE mixing rules

(ex: PRH, SRK-MHV2)

P > 10 bara

OR

T > min(Tc,i)

Cubic EOS + asymetric kij mixing rules

(ex: SRK -Twu)

Ethanol to Ethylene
Dehydration unit

Model Selection

Phase equilibrium property

Mixture with
polar compounds

No large size asymetry

No electrolytes

Data available

Because the excess Gibbs energy models (GE) often provide good results for strongly non-ideal mixtures at low pressure, Huron and Vidal [1] suggested to calculate the "a" parameter of the cubic equation of state using this type of model, and assuming a linear mixing rule for the "b" parameter. The GE model is thus integrated in the "a" parameter mixing rule, creating thus a new family of model named "CEOS-GE" (Cubic Equation of State with Gibbs Energy model).

Several approaches have been proposed on this principle, depending on the pressure chosen for solving the equation of state. The following table gives an overview of the most-known GE-based mixing rules (from [2]).

Usually, the GE model used is UNIQUAC or NRTL. The name of the resulting model must contain the name of the cubic equation of state, of the mixing-rule and of the GE model (for exemple, PR+HV+NRTL, also named "PRH" model)

For a predictive approach,it is also possible to use the UNIFAC model, yielding for exemple to the "PSRK" model (SRK+MHV1+UNIFAC)

[1] Vidal, J. “Mixing Rules and Excess Properties in Cubic Equations of State” Chemical Engineering Science 1978, 33, 6, 787-791.

[2] de Hemptinne et al., Select thermodynamic model for process simulation, ed. Technip, Paris, France, 2012.

For highly non-ideal mixtures, an alternative to the use of GE mixing rules is the use of mixing rules involving asymetric kij (for a i-j pair, kij is different of kji).

Various asymetric mixing rules have been proposed, such as Panagiotopoulos & Reid (1986) [1] and Modified Panagiotopoulos & Reid (also known as SRKM or PRM models). The most used mixing rules is probably the rule proposed by Twu et al [2]

When used with the SRK equation of state, the resulting model is often named SRK-Twu, SRKS, or SRK-ML, according to the commercial simulators.

[1] Panagiotopoulos et al., ACS Symp.Ser.300, American Chemical Society, Washington DC, 71-82, 1986

[2] Twu et al., Fluid Phase Equilib., 69, 33-50, 1991

CO2 Capture process

Which model?

Reactive
Absorber

Reactive
Stripper

Heat exchangers

Basic Principle:

1/ REACTIVE ABSORPTION

The rich-CO2 flue gas flows into a reactive absorption column: the gas is contacted with a solvent, typically an aquous amine solution. There is both a physical and a chemical absorption in such solvents, following these main chemical reactions:

CO2 + Amine + H2O = AmineH+ + HCO3-

CO2 + Amine + H2O = AmineCOO- + H+

This column operates at temperatures ranginf typically from 40 to 70 °C, and pressures lower that 5 bar.

2/ REACTIVE STRIPPER

The CO2-rich solvent at the bottom of the absorption column is first heated up to typically 120/130 °C and circulated through a reactive stripping, whose the purpose is to regenerate the solvents. The reverse reactions occur to release the dissolved CO2. The regenerated solvent at the bottom of this column is then cooled down and reused in the absorption column.

CO2 Capture process

Key data to collect for model parameterization / validation:

Equilibrium constants
to determine extend of reactions

Enthalpies of reaction
to determine duties

Reactive absorber

* Gas absorption/desorption
* Chemical reactions under thermodynamic control

Henry constant of light solutes (CO2, H2S, COS, ...) in liquid amine solvent

Reactive stripper

CO2 Capture process

Key data to collect for model parameterization / validation:

Phase density

Phase enthalpy

e-NRTL

CO2 Capture process

LIQUAC

Model Selection

Phase equilibrium property

Mixture with
polar compounds

No large size asymetry

with electrolytes

Data available

Activity coefficient models
(low pressure)
with mixed solvent
(aqueous amine)

e-NRTL [1] is an extension of the activity coefficent model NRTL (short-range interaction, SR), by addition of a long-range (LR) coulombic tem (Pitzer-Debye-Hückel). The expression of the activity coefficient becomes:

Ion-ion and ion-solvent binary interaction parameters are required.

[1] Chen, C.C. et al., AIChE J., 1986, 32(3), 444-454

The LIQUAC model [1] is an extension of the activity coefficient model UNIQUAC (short-range interactions, SR), by the addition of two additional terms: a long-range (LR) coulombic interaction term, and a middle range (MR) ion-ion and ion-solvent interaction term:

Ion-ion and ion-solvant binary interaction parameters are required for both middle-range and short range terms.

[1] Kiepe, J.K. et al., Ind. Eng. Chem. Res, 2006, 45, 2361-2373

THANK YOU FOR CHOOSING THE IFP-SCHOOL MODEL SELECTOR

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Credits

EXEMPLES

This project has been realized by:

Ulysse Lefevre