ENCH 445: Lecture 5 --  Single Stage Processes

The "bubble T" calculation method described in Lecture 4 can be extended to solve the problem of single stage flash calculation where the product pressure and enthalpy are specified.  To accomplish this, the enthalpy and material balance relations are included as equations to be solved.  More specifically, if the feed composition and product enthalpy and pressure are specified, then we have the following 12 unknowns (assuming five components are present):

    5 liquid phase mole fractions

    5 vapor phase mole fractions

    The fraction of the feed that ends up in the vapor, i.e., V/F.

    Temperature

These are solved for using the following 12 equations

    5 equilibrium equations, one for each component

    Sum of mole fraction in vapor is unity (one equation)

    5 material balances, one equation for each component

    1 Enthalpy balance

Note that the fact that the sum of the liquid phase mole fractions is unity is not an independent equation if all 5 component material balances are used.

The above 12 equations and 12 unknows can be solved using MS Excel or MATLAB by making some simple extensions to the software developed for Problem Set 2.

Material balances can also be solved graphically using various versions of the "lever rule," which can stated as follows:  On a diagram where one (or more) of the axes correspond to a conserved quantity, if you locate the feed and product streams corresponding to a single stage process on the diagram, then the product streams will be located on a straight line that includes the feed stream, and distance between the feed and one product stream is proportional to the amount of the other product stream.

Versions of the lever rule can be applied graphically to accomplish the following:

    1.  Simultaneous solution of material balance and equilibrium relations on a T-(x,y) phase diagram for the case of a two component system where the feed composition and product temperature and pressure are specified.

    2.  Simultaneous solution of material balance, enthalpy balance, and equilibrium relations on a  H-(x,y) phase diagram for the case of a two component system where the feed composition and product enthalpy and pressure are specifed.     

    3.  Simultaneous solution of two independent material balance relations and equilibrium relations on a x_a, x_b, x_c triangular phase diagram for the case of a three component system liquid system where the feed composition and the temperaure and pressure are specified