Advancing Rational Thermodynamics: A Comprehensive Approach to Thermodynamic Modeling
This document explores the evolution of thermodynamic modeling within chemical engineering, emphasizing the principles of Rational Thermodynamics. It addresses the complexities of existing models, highlights the challenges of programming and implementation, and proposes simplifications through algebraic operators. The need for improved notation and a structured approach to variable contributions is discussed, along with practical examples. The text advocates for a modernized perspective on thermodynamic frameworks, ensuring ease of use, clarity, and adaptability in computational applications.
Advancing Rational Thermodynamics: A Comprehensive Approach to Thermodynamic Modeling
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Presentation Transcript
Rational Thermodynamics • Physical chemistry is the ancestor of chemical engineering thermodynamics: => Lots of definitions inherited from laboratory work. => Theory is adequate for hand calculations, but not for general computer programming.
Rational Thermodynamics • Let the following VLE condition serve as an example: • Equation of state: • Activity coefficient model: • Unsymmetric reference:
Rational Thermodynamics • There is now a bewildering number of symbols and indices:
Rational Thermodynamics • Complex notation! Model errors are likely at two levels: 1) Inconsistencies made during the implementation (semantic bugs). 2) Inconsistencies in the user interface (syntactic bugs).
Rational Thermodynamics • In both cases errors will be hard to capture. Typically, the presence of an expert (programmer) will be required. • Conclusion: Thermodynamic modelling is an old subject ready for a thorough face-lift.
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 following the same rules:
Rational Thermodynamics • Proposition: Only three algebraic operators are needed for a general thermodynamic framework! 1) The chain operator for doing things like: 2) The patch operator for defining sub-graphs:
Rational Thermodynamics • Operator precedence: patch (*) > chain (+) • The equation of state VLE model can now be written: • Where the standard state is defined as:
Rational Thermodynamics • The operators are type safe:
Rational Thermodynamics • Note that a list operator has been introduced to make the expression more legible. • Similar, albeit more complex, expressions can be written for Gibbs energy models.
+ * * * Rational Thermodynamics • An equivalent calculation graph is:
Rational Thermodynamics n = [‘Nitrogen’,’Oxygen’,’Argon’] G = Surface.new(n) * Gibbs.new(n) * ( Poynting.new(n) * MuTP.new(n,:idealgas,’ig’) * MuT_cp.new(n,:poly3,’ig’) * MuT_hg.new(n,:hogo,’ig’) + Residual.new(n) * ModTPN.new(n,:srk,’gas’) + Activity.new(n) * ModTN_ideal.new(n,:molmix,’ig’))
Rational Thermodynamics • The thermodynamic object G is explicit in (T,p,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’) * G
Rational Thermodynamics • Use of operators => thermodynamic frameworks can be broken down into small, manageable, expressions. • Model description is not tied to any particular implementation => easy to export, exchange and update model info. • Export formats are Matlab, LaTeX, XML
H P T H Rational Thermodynamics • Example: Propane-butane splitter with multiple coordinate specifications.
Rational Thermodynamics • Thermodynamic surface transformations => canonical (and aesthetically pleasing) equation system.
