EXAMPLE 2: Visualization and Animation of Enthalp Method in Binar Distillation A graphical method that includes energ balances as well as material balances and phase equilibrium relations is the Ponchon-Savarit method, which utilizes the enthalp-composition diagram. The enthalp and material balances in the rectifing and stripping sections give,2 Ln D h n H + = = V h h n+ n+ D n n (2.) Lm H m B m h = = V h h m m B m (2.2) where h = H L + ( H h D D ) and h = ( hf F h D)/B are erence points in the rectifing and stripping sections, respectivel. In Eqs, (2.) and (2.2), h n and H n represent the liquid and vapor molar enthalpies in stage n. The visualization of the Ponchon-Savarit method consists of i) identifing erence points, and ii) displaing operating lines and equilibrium tie lines. We again use the commands plot and movie in Matlab to visualize and animate the diagrams. 3 i) Difference Points and Feed Point At a given reflu ratio L/D in the rectifing section and feed rate F, the erence points in the rectifing and stripping sections h and h are calculated from their definitions given above. The enthalp of the feed h F is then determined from the feed composition and condition, z F and q. From the tie lines that passes (z F,h F ) in the enthalp-composition diagram together with the lever rule, the compositions of the equilibrium vapor and liquid in the feed ( F,h F_ ) and ( F,h F_ ) are calculated.
B ii) Operating Lines, Tie Lines and Equilibrium Stages From Eq. (2.) for an two passing streams in the rectifing section, the operating line comes from a sequence of lines radiating out from the erence point ( D,h ), passing ( n+, H n+ ) and ( n, h n ) in the enthalp composition diagram. Likewise, from Eq. (2.2) for an two passing streams in the stripping section, the operating line comes from a sequence of lines radiating out from the erence point ( B, B diagram. h ), passing ( m, H m ) and ( m-, h m- ) in the enthalp composition Meanwhile, equilibrium tie lines in the enthalp diagram can be obtained from the equilibrium relations ( n, n ). The interpolation function interp in Matlab is used to find the intersection points between the operating (or tie) line and enthalp curve. 3 B alternating between the equilibrium tie lines and operating lines, from the distillate composition D to the bottoms composition B, the number of equilibrium stages allowing for variation in flow rates through enthalp-composition diagram is obtained. The transfer in the operating line from the rectifing section to stripping section was made when the liquid composition, passes that of the feed, F in the enthalp-composition diagram. The snap shots of the Ponchon-Savarit method for distillation of acetone and water mitures are shown in Fig. 2.2. REFERENCES. Seader, J.D. and Henle, E.J., Separation Process Principles (John Wile & Sons, 998) 2. King, C.J., Separation Processes, (McGraw Hill, 98) 3. Pratap, R., Getting Started with MATLAB, A Quick Introduction for Scientists and Engineers (Oford Universit Press, 22). 2
Obtain equilibrium and enthalp data Step : Displa vs. and enthalp Thermodnamic Input Actual equilibrium & enthalp data Design Input Reflu ratio & feed condition Distillate, bottoms compositions Step 2: Determine and displa erence and feed points On enthalp diagram Displa operating lines that passes erence point and liquid (vapor) composition Displa equilibrium tie line to determine the corresponding vapor (liquid) composition. Step 3: Determine the number of equilibrium stages Figure 2.. Flow chart of Eample 2: Ponchon-Savarit method for binar distillation 3
2 vs. diagram.9 5.8.7 Enthalp, H or h 5.6.5.4.3.2. 5 Composition, or 2 vs. diagram.9 5.8.7 Enthalp, H or h 5.6.5.4.3.2. 5 Composition, or 4
2 vs. diagram.9 5.8.7 Enthalp, H or h 5.6.5.4.3.2. 5 Composition, or 2 vs. diagram.9 5.8.7 Enthalp, H or h 5.6.5.4.3.2. 5 Composition, or Figure 2.2. Snap shots of graphical output of Eample 2: Pochon Savarit method for binar distillation of acetone and water: a) enthalp diagram from enthalp data, b) erence points and feed line for z A =.5, D =.9, B =.26, q =.5, R =.288, c) operating (solid) and equilibrium (dashed) lines in the rectifing section, and d) operating and equilibrium tie lines in the rectifing section. Corresponding vs. diagram is shown in the right for comparison. 5