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Chapter 5 Generalised computational methods in thermodynamics

DOI: 10.1016/s1570-7946(03)80029-9
  • Design
  • Mathematics
  • Physics


Summary This chapter reviews the fundamental concepts in thermodynamics that a user should master to obtain reliable results in simulation. The thermodynamic network (equations 5.39 to 5.42, and 5.68 to 5.74) links the fundamental thermodynamic properties of a fluid, as enthalpy, entropy, Gibbs free energy and fugacity, with the primary measurable state parameters, as temperature, pressure, volumes, concentrations. The key consequence of the thermodynamic network is that a comprehensive computation of properties is possible with a convenient PVT model and only a limited number of fundamental physical properties, as critical co-ordinates and ideal gas heat capacity. Two types of PVT representation are used in simulation: equation of state and corresponding states principle. The equations of state are today the most applied. Particularly advantageous are the cubic equations of state, since they offer a consistent computation of both thermodynamic properties and phase equilibria. However, there is no single equation of state that could predict accurately the properties of all components, from hydrogen and methane up to polar species and polymers. That is why there are many models, each being accurate for a particular application. Fugacity is a key concept in phase equilibria. The phase equilibrium condition consists of the equality of fugacities of a component among coexistent phases. The computation of fugacities implies two routes: equation of states, for both pure components and mixtures, and liquid activity coefficients for non-ideal liquid mixtures. The methods based on equations of state are more general. Cubic EOS, as Soave-Redlich-Kwong and Peng-Robinson are today standard options in flowsheeting, but are suitable only for processes involving hydrocarbons. On the contrary, modified cubic EOS with several adjustable parameters can be used also for polar components. The improvement in accuracy is determined by the form of the alpha function that corrects the attraction term, namely by the number of parameters and their depdndency on temperature. In addition, the capability of a particular EOS in calculations involving mixtures depends greatly on the ‘mixing rules’ applied to average the parameters by composition. Simple geometrical mixing rules can be used for hydrocarbon, but not for the treatment of non-ideal mixtures (see Chapter 6.) Generalised methods for calculating thermodynamic properties of fluids are based on the concept of ‘departure functions’. A departure function designates the difference between the property of a real fluid and its counterpart as ideal fluid, at given pressure and temperature. On this basis a complete set of thermodynamic properties can be determined, as enthalpy, entropy, Gibbs free energy and fugacity. The integration of the closed-form equations for different functions makes necessary the availability of an accurate PVT relationship. Therefore, the generalised computer methods are competitive in accuracy with specialised tables and charts if the parameters of models have been carefully calibrated by regression. Many thermodynamic options and routes of methods are possible when performing a simulation. Model compatibility with the physical situation, as well as the availability of parameters, should guide the user's choice.

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