You are to simulate a flash evaporator that converts a liquid feed stream (SF) containing V species at a high pressure to liquid and vapor product streams (SL. SV) in equilibrium at temperature T(˚C) and pressure P(mm Hg). The Compositions of the liquid and vapor product streams are related by Raoult’s law (Equation 6.4-1), and the Component vapor pressures are expressed b the Antoine equation, Table B.4.

(a) Write the system mass and energy balances and equilibrium relations in terms of the following variables:

NF, NL, NV The molar flow rates (mob’s) of feed, liquid product, and vapor product.

XF (I) The mole fractions of the ith component in the feed,

XL (I) liquid product, and vapor product, where I runs from

XV (I) 1 to (N — 1)

TF, T, P Feed temperature, vaporizer temperature and pressure, respectively

PV (I) Vapor pressures of the N species at temperature T, where I runs from 1 to N.

A (I) Antoine equation constants for the N species involved in the process

B (I) (transmitted to the subroutine via a COF4’ION or GLOBAL

C (I)statement).

CP (I) Liquid-phase heat capacities [kJ/(mol∙°C)J of the N species

(Transmitted via COMMON or GLOBAL) Assume independent of temperature.

HV (I) Heats of vaporization (kJ/mol) of the N species (transmitted via COMMON or GLOBAL).

Assume independent of temperature.

Q The required heat input (kW) to the vaporizer.

Show that the system has (N + 3) degrees of freedom, counting as the system variables three stream flow rates, 3(N – 1) mole fractions, N vapor pressures, TF, T, P, and Q. Then work out a trial-and-error procedure for determining the product stream flow rates and mole fractions and Q from specified values of TF, T, P. and the feed stream molar flow rate and component mole fractions.

(b) Write a module subroutine FLASHN to implement the procedure outlined in part (a) for a feed stream containing up to seven components. The arguments of the subroutine should be N, SF, SV, SL, P, and Q, where SF, SV, and SL are eight-membered arrays. The first N elements of each array are the component molar flow rates and the (N + 1) st element is the stream temperature. The input variables are SL (N + 1) and SV (N + 1) (both of which equal the vaporizer temperature), P, and the attributes of SF (N molar flow rates and the feed temperature), and the outlet variables are Q and the remaining attributes of SV and SL. 

(c) Test your code for a feed stream containing 34.8 mole% n-pentane, 30.0 mole% n-hexane, and the balance n-heptanes flowing at a rate of 1.00 molls which is to be flashed from 363 K and a high pressure to 338 K and 611 mm Hg. The heat capacities of liquid pentane hexane and heptanes [in kJ/ (mol ∙K)] may be taken to be 0.188. 0.216, and 0.213, respectively, and the heats of vaporization may be taken to have their values at the normal boiling points of these substances. Write and run a calling program that defines the attributes of SF and other input parameters (including the heat capacities and heats of vaporization), calls the module subroutine, and prints out the attributes of the product streams and the required heat input.

(d) Use a process simulator to perform the same calculations.

(e) Use an equation-solving program to perform the same calculations.