Balances in Multi-Component Separation

The solution to a multi-component, multi-phase, multi-stage separation problem is found in the simultaneous or iterative solution of the material balances, the energy balance and the phase equilibrium equations (see Chapter 1). This implies that a sufficient number of design variables are specified so that the number of remaining unknown variables exactly equals the number of independent equations. When this is done, a separation process is said to be specified. 

The separation of a multi-component mixture into products with different compositions in a multistage process is governed by phase equilibrium relations and energy and material balances. It is not uncommon in simulation studies to require certain column product rates, compositions, or component recoveries to satisfy given specifications with no concern for conditions within the column. Such would be the case when downstream processing of the products is of primary interest. In these instances, one would be concerned only with overall component balances around the column but not necessarily with heat balances or equilibrium relations. Separation would thus be arbitrarily defined, and the problem would be to calculate product rates and compositions. The actual performance of the separation process is analyzed independently in all the following chapters. 

This approach was further explored by Hakemi (2000) who prepared blends that contain both a wholly aromatic and an aromatic-aliphatic LCP that are miscible with each other. The ultimate goal of this approach was to develop multi-component blends that have components of thermoplastics. The miscible LCP blends could be useful as reinforcing agents for the thermoplastic matrix polymer and, due to the fact that the LCP s contain some of the components of the thermoplastic polymer, there is expected to be improved adhesion between the LCP portion and the matrix portion of the mixture. This is another example of an attempt to balance the phase separation that is inherent in high temperature polymer blends due to molecular conformation differences by strengthening the enthalpic interaction between the two polymers. 

There are several characteristics common to the describing equations of all types of multicomponent, vapor-liquid separation processes, both single- and multi-stage, that make it possible to exploit the inside-out concept in similar ways to solve them efficiently and reliably. The equations have as common members component and total mass balance, enthalpy balance, constitutive and phase equilibrium equations. In addition, all such processes require K-value or fugacity coefficient and vapor and liquid enthalpy models. In all cases the describing equations have similar forms, and depend on the primitive variables (temperature, pressure, phase rate and composition) in essentially the same ways. Before presenting the inside-out concept, it will be useful to identify two classes of conventional methods and discuss their main characteristics. 

---