CHE 205 Programming Project 1 Due: Oct 1, 2015 Consider a vapor/liquid separation performed by flash vaporization in a drum: The feed stream has flow rate F and compositions (in mole fraction) zi for n components, giving compositions z1, z2, , zn. In the drum, this feed is separated into a liquid phase that leaves the system with flow rate L and compositions xi and a vapor phase that leaves the system with flow rate V and compositions yi . The thermodynamic principles governing this process are described by n vapor-liquid equilibrium ratios Ki , one for each component. Given these K-values, a feed flow rate, and feed compositions, it is possible to find the product flow rates and compositions by finding the root of the following equation in the interval [0,1]: zi (1?Ki ) 1+ ?(Ki ?1) = 0 i=1 n ? , where the independent variable ? is defined as ? = V/F. In other words, the system can be solved by finding a value of ? that makes the left-hand side of the equation above equal to zero. Once this v
alue of ? is found, L can be found as L = F V and the compositions in each phase can be found as: xi = zi 1+ ?(Ki ?1) and yi = xi Ki . Write a program that to find the output flow rates and compositions for such a separation system with an input flow rate (in mol/h), input compositions (in mole fraction) and K-values (dimensionless). Your program should be able to handle any number of components in the feed. Consider a 7-component system where the feed compositions are: z1 = 0.16, z2 = 0.09, z3 = 0.21, z4 = 0.13, z5 = 0.06, z6 = 0.15, and z7 = 0.20; the K-values are K1 = 3.52, K2 = 1.92, K3 = 1.22, K4 = 0.84, K5 = 0.43, and K6 = 0.08. The total feed rate is 1500 mol/h. Plot the output compositions and flow rates in both phases as functions of K7 as K7 varies from 0.05 to 4.00. Note: While there are several root-finding routines built into MATLAB as functions, avoid using them in this project. Instead, write your own root-finding routine based the one of the algorithms we studied in class.