For the design of flash evaporators the thermodynamic vapour-liquid equilibrium needs to be described. For this, the Ratchford-Rice equation is commonly used: n zi(1 K;) K; + P(1 K;) = = 0 (1) i In this equation n is the total number of components in the mixture, zi is the molar fraction of the th component in the mixture, and K; is the distribution coefficent of the th species and can be calculated using: pysat 2 Ki (1) P in which P is the pressure at which the system is operated and P,sat is the vapour pressure of component i (in bar), which can be calculated through the Antoine equation (where T is in Kelvin): B = In Psat A T+C (1) B (between 0 and 1) is the fraction of the mixture that is condensed at any given combination of temperature and pressure in which there is a vapor-liquid equilibrium. For a plant where mixtures of benzene, toluene and heptane are produced, we are trying to find the values of at a temperature of 80 C and a pressure of 0.6 bar. The values for A, B and C for Antoine's equation are in the table below, together with the design mole fractions of the process. Zi Ai Bi Ci 0.3 9.3935 3096.52 -53.67 Component Toluene (t) Heptane (h) Benzene (b) 0.4 9.2535 2911.32 -56.51 0.3 9.2806 2788.51 -52.36 D A E Part 1 - The bisection method (50 points) For the composition given above, calculate how many iterations of the bisection method you require to find , if you use values of 0 and 1 as your initial boundaries and you want to achieve a tolerance of es : 10-6. (5 points) In the cells below, write a Python code for the bisection method and use this code to find the value of for the composition given in the table above. (15 points) Due to variations in the production process, the composition of the mixture can change with time. For the following compositions, calculate the value of B. Use initial guesses that are reasonable and find your answers with 3 = 10-6. Fill the table in the answer cell below. (15 points) o Can you find reasonable solutions for all compositions? Can you use the same initial guesses for your boundaries for all compositions? What is the effect of using other initial guesses for the boundaries? (15 points) The number of iterations required to find is FILL YOUR ANSWER HERE The value of with the composition given above is YOUR ANSWER HERE Fill the following table (n is the number of required iterations): Zh Zt Z B1,i | Biun 0.05 0.65 0.30 ... ... 0.10 0.60 0.30 ... 0.15 0.55 0.30 wee ... 0.20 0.50 0.30 wee 0.25 0.45 0.30 .. ... 0.30 0.40 0.30 ... ... ... *** *** *** *** *** *** *** *** *** 0.35 0.35 0.30 ... 0.40 0.30 0.30 ... 0.45 0.25 0.30 ... ... ... 0.50 0.20 0.30 0.55 0.15 0.30 ... ... ... ... 0.60 0.10 0.30
