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Choosing a Thermodynamic Model

Every number a simulator produces passes through the property package: enthalpies, K values, densities, the whole phase split. A wrong package gives a flowsheet that solves perfectly and means nothing. This page gives the reasoning behind the choice and the tools DWSIM has for checking it against evidence.

What you will learn

  • The two families: equations of state and activity coefficient models
  • Why interaction parameters matter, and what happens without them
  • How an azeotrope shows up, and why some models cannot see one
  • How to compare packages against measured data before trusting one

1. Two ways to describe a liquid

A vapour at moderate pressure is nearly ideal; the liquid is where the models differ.

Equations of state (Peng-Robinson, Soave-Redlich-Kwong, PC-SAFT, GERG) describe vapour and liquid with one equation P = f(T, V, composition) and a mixing rule. They are consistent across the critical point, handle high pressure and light gases well, and give densities and enthalpies from the same equation. Their weakness is the liquid of a polar or hydrogen-bonding mixture: with the plain mixing rule and no fitted binary interaction parameter k_ij, a cubic equation treats the liquid as nearly ideal.

Activity coefficient models (NRTL, UNIQUAC, Wilson, UNIFAC) describe the liquid's non-ideality through activity coefficients gamma_i, so that y_i P = x_i gamma_i P_sat,i at low pressure. Their parameters are fitted to data (NRTL, UNIQUAC, Wilson) or built from functional groups (UNIFAC, which needs no data and is correspondingly rougher). They are the right tool for polar liquids near atmospheric pressure, and they know nothing about the vapour beyond the ideal gas unless paired with an equation of state for that phase.

Raoult's law takes every gamma_i = 1: the ideal solution. Right only for molecules that look alike (benzene and toluene, neighbouring alkanes); a useful reference line against which the others are measured.

2. A decision path

  1. Light gases, hydrocarbons, high pressure, anything near a critical point: an equation of state. Peng-Robinson is the workhorse; SRK is close; for refrigerants and natural gas with accurate reference data, CoolProp or GERG-2008.
  2. Polar liquids at low to moderate pressure (alcohols, water, acids, ketones): an activity coefficient model. NRTL or UNIQUAC when interaction parameters exist in the database for the pairs that matter; UNIFAC when they do not.
  3. Water and steam alone: the steam tables (IAPWS-IF97).
  4. Electrolytes: an electrolyte package (eNRTL); an ordinary model will not see the ions.
  5. Polymers: PC-SAFT with the polymer parameters.
  6. Two liquid phases expected (water and hydrocarbons, extraction): the model must be able to predict liquid-liquid equilibrium; NRTL and UNIQUAC can, an equation of state with a k_ij often can, Raoult's law cannot.

Then check the pairs that decide the process. A distillation column lives on the relative volatility of its key pair; a flash on the K values of the compounds it splits. Those pairs need parameters, and those parameters need checking.

3. Interaction parameters

An interaction parameter corrects the model for one pair of compounds: k_ij in a cubic equation, A_ij and A_ji (and alpha_ij for NRTL) in an activity coefficient model. DWSIM ships databases of them and estimates some from structure when none is found. The property package editor shows which pairs have values and which are estimated or zero.

Without a parameter, an equation of state predicts near-ideal mixing; for ethanol and water that means no azeotrope and a column that separates what no column can. With a parameter regressed to the wrong temperature range, the error is smaller and harder to see. The Data Regression tool (Utilities menu) fits parameters to measured points, and the local phase-equilibrium database (NIST ThermoML, downloaded on first use) supplies the points.

4. Azeotropes

An azeotrope is a composition where the vapour and the liquid have the same composition: the relative volatility crosses 1 and distillation cannot pass it. On a T-x-y diagram it is the point where the bubble and dew curves touch at a minimum (ethanol and water) or a maximum (acetone and chloroform). Whether a model sees it depends entirely on how it describes the liquid: an activity coefficient model with fitted parameters usually does; a cubic equation without k_ij usually does not.

Try it

Open Tutorial 12 - Ethanol Plant (ethanol and water), then Utilities > Property Package Comparison. Pick ethanol and water, T-x-y at 1 atm, and tick every package in the simulation (add Raoult's law and Peng-Robinson to the simulation first, so there is something to compare). Press From the database... to load a measured dataset, or type a few literature points, and Compare. The report ranks the packages by their deviation from the data, says which of them see the azeotrope, and explains in a paragraph why they differ.

Then Utilities > McCabe-Thiele Diagram on the same pair: the equilibrium curve crossing the diagonal is the azeotrope, and the stages pile up against it.

5. What a cubic equation is

The Equation of State Explorer (Utilities menu) draws the P-V isotherms of van der Waals, Redlich-Kwong, SRK and Peng-Robinson for one compound: the loop below the critical temperature with its three volume roots, the Maxwell tie line at the saturation pressure the equation predicts, the compressibility factor against pressure, and the saturation pressure of the equation beside the compound's vapour pressure correlation. It shows in one picture why van der Waals is history and why Soave's alpha(T) was the step that made cubic equations useful.

6. When packages disagree

Run the same flowsheet with two packages (or use the Property Package Comparison on the key pair) and read the spread:

  • Small spread, both plausible: the choice does not matter here; take the cheaper one.
  • Large spread on a polar pair: the equation of state is likely wrong; check for missing parameters.
  • Large spread on a light-gas pair at high pressure: the activity coefficient model is likely wrong; it has no idea of the vapour.
  • Different phase counts: one model sees a second liquid or a solid the other misses; look at the data, and at whether the process is known to form that phase.

Exercises

  1. Compare Peng-Robinson and NRTL on benzene and toluene at 1 atm (Tutorial 10). Do they differ? Why is this pair forgiving?
  2. Compare the same two on ethanol and water. Which sees the azeotrope? What does the deviation table say about the one that does not?
  3. Open the Equation of State Explorer for propane at 0.9 Tc with each of the four equations. Rank them by the error of their saturation pressure against the database correlation.
  4. In the property package editor, find the interaction parameters for the key pair of Tutorial
  5. Are they from the database, estimated, or zero? Set them to zero, solve, and compare the distillate purity with Scenario Comparison.