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’,’O2’,’ARGON’] A =Surface.new(n) * ( Helmholtz.new(n) * ( StandardState.new(n) * ( MuT_cp.new(n,:poly3,’ig’,:reid77) * ( MuT_hs.new(n,:h0,’ig’,:reid87) + MuT_hs.new(n,:s0,’ig’,:dippr96) ) ) + EquationOfState.new(n) * ( ModTVN_ideal.new(n,:idealgas,’ig’)) + EquationOfState.new(n) * ( ModTVN.new(n,:srk,’fl’,:reid77).tell(:m_gd,[‘fl’,’a’,’mfac’],:reid87) ) ) )

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, LaTeX, XML, etc.

Flowsheet calculations Example: Propane-butane splitter with multiple coordinate specifications. TPHH

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 multi- component 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 ArBeidsBokEn. Matlab exercises for SIK2005, SIK2010, SIK2015, SIK2025, SIK3035. Sublattice NRTL: