RESUMEN
In order to obtain the thermodynamic properties of compressed liquids, it is usual to consider them as incompressible systems, since liquids and solids are well represented by this thermodynamic model. Within this model, there are two usual hypotheses that can be derived in two different submodels: the strictly incompressible (SI) model, which supposes a constant specific volume v=v0, and a more general model, called temperature-dependent incompressible (TDI) model, which relates a specific volume to temperature, v=vT. But, usually, this difference ends here in the thermal equation of state, and only the SI model was developed for caloric and entropic equations. The aim of this work is to provide a complete formulation for the TDI model and show where it can be advantageously used rather than the SI model. The study concludes that the proposed model outperforms the traditional model in the study of subcritical liquid. One conceivable utilization of this model is its integration into certain thermodynamic calculation software packages (e.g., EES), which integrate the more elementary SI model into its code for certain incompressible substances.
RESUMEN
The optimum pressure ratio for the stages of a multistage compression process is calculated with a well known formula that assigns an equal ratio for all stages, based on the hypotheses that all isentropic efficiencies are also equal. Although the derivation of this formula for two stages is relatively easy to find, it is more difficult to find for any number of stages, and the examples that are found in the literature employ complex mathematical methods. The case when the stages have different isentropic efficiencies is only treated numerically. Here, a step by step derivation of the general formula and of the formula for different stage efficiencies are carried out using Lagrange multipliers. A main objective has been to maintain the engineering considerations explicitly, so that the hypotheses and reasoning are clear throughout, and will enable the readers to generalise or adapt the methodology to specific problems. As the actual design of multistage compression processes frequently meet engineering restrictions, a practical example has been developed where the previous formulae have been applied to the design of a multistage compression plant with reciprocating compressors. Special attention has been put into engineering considerations.
