Thermodynamic RE Rational Thermodynamics Identify the canonical variables

Thermodynamic R&E

Rational Thermodynamics • Identify the canonical variables of the model. In practice either or • These are homogeneous functions which can be added to yield a total contribution:

Rational Thermodynamics • The standard state contribution can be split into new (sub)contributions:

Rational Thermodynamics • Proposition: Only 3 algebraic operators are needed for a thermodynamic setup! 1) The chain operator for doing things like: 2) The patch operator for defining sub-graphs:

Rational Thermodynamics • Operator precedence: patch (*) > chain (+) • An equation of state VLE model can now be written: • Where the standard state is defined as:

Rational Thermodynamics • An equivalent calculation graph is: + * * *

Rational Thermodynamics • The object is stored in an “onion-structure”:

Rational Thermodynamics n = [‘Nitrogen’, ’O 2’, ’ARGON’] A= Surface. new(n) * ( Helmholtz. new(n) * ( Standard. State. new(n) * ( Mu. T_cp. new(n, : poly 3, ’ig’, : reid 77) * ( Mu. T_hs. new(n, : h 0, ’ig’, : reid 87) + Mu. T_hs. new(n, : s 0, ’ig’, : dippr 96) ))+ Equation. Of. State. new(n) * ( Mod. TVN_ideal. new(n, : idealgas, ’ig’) Equation. Of. State. new(n) * ( )+ Mod. TVN. new(n, : srk, ’fl’, : reid 77). tell(: m_gd, [‘fl’, ’a’, ’mfac’], : reid 87) )

Rational Thermodynamics • Helmholtz is explicit in (T, V, N). For practical use the output needs to be transformed into (H, P, N), (S, P, N), (T, V, N), etc: • Legendre: extensive <=> intensive variable. • Massieu: function <=> extensive variable. • A new object is required to take care of the transformations.

Rational Thermodynamics More Ruby code => air=f(H, V/T, N) air = Surface. new(n, : legendre, ’p’) * Surface. new(n, : massieu, ’s’) * Surface. new(n, : legendre, ’-t’) * A

Rational Thermodynamics • Use of operators => thermodynamic frameworks can be described by small, manageable, expressions. • The algebra is not tied to any particular implementation => easy to export, exchange and update model info. • Export formats are Matlab, La. Te. X, XML, etc.

Flowsheet calculations • Example: Propane-butane splitter with multiple coordinate specifications. H P T H

Flowsheet calculations • Proposition: Networks of thermodynamic nodes can be described in terms of U(S, V, N) and f(H, V/T, N). • The functions A(T, V, N), H(S, p, N), S(H, p, N) are obtained by Legendre and Massieu transformations. • Constraints in the extensive coordinates = Euler integration.

Flowsheet calculations • Flash block: • Transformation block: • Mixer block:

Flowsheet calculations • Thermodynamic surface transformations => canonical (and aesthetically pleasing) equation system.

Truths and myths I • Thermodynamics will play an increasingly important role in e. g. model predictive control and fluid dynamics. • Monolithic thermodynamic software has no future (ASPEN, FACT, etc. ) • The future lies in distributed & modular software communicating through open protocols (e. g. XML).

Truths and myths II • There will be increased focus on complex systems like acetic acid + HC, urea, formaldehyde, electrolytes, etc. • Statistical mechanics models will replace old work-horses like SRK, PR, etc. • The newer models will be incredibly complex compared to the old ones.

Truths and myths III • Physicists master field theory (e. g. Maxwell’s equations). • Mechanical engineers master turbulence theory (e. g. combustion). • Chemical engineers master multicomponent phase theory (e. g. VLLE) => if we don’t succeed in this respect we will be extinct in <10 years.

Challenges for the classroom • • • Physical chemistry. Statistical mechanics. Multi-component phase theory. Numerical mathematics. Programming. Measurements.

Challenges for the future • Phase modeling (reliable & flexible model, predictable cost, fast delivery). • Distributed & modular programming (no waste of time writing & maintaining proprietary program interfaces). • Thermodynamics made easy (high level modeling based on physical insight without numerical fuss).

Things I have not mentioned • TABBE = den Termodynamiske Ar. Beids. Bok. En. • Matlab exercises for SIK 2005, SIK 2010, SIK 2015, SIK 2025, SIK 3035. • Sublattice NRTL: