A binary distillation column has three tray temperature measurements (17th, 24th, 30th trays) that can be used as possible controlled variables. Controlling temperature is equivalent to controlling composition. Step testing gives the following steady-state input-output relationships (u1 = steam pressure in reboiler; u2 = reflux ratio): Th = 1.5ul + 0.5uz (1) Tz4 = 2.0u1 + 1.7uz (2) T3o = 3.4ul + 2.9uz (3)All variables are deviation variables. Select the 2 X 2 control system that has the most desirable interactions, as determined by the RGA (note that there are three possible 2 X 2 control configurations). Explain why the combination of Tz4 and T3o is the least desirable controlled variable set, based on analyzing Eqs. (2) and (3) and the resulting determinant
Uses of the Equations of Motion • Very few exact solutions of the full equations: – Unidirectional laminar flows are one class of exact solutions. – Simple shapes: spheres, ellipsoids, tori, etc., have solutions. – Most problems not amenable to exact analytical solutions. – Linear vs. nonlinear mathematics. • Dimensional analysis: – Insights even without solving the equations. – Scaling for length, velocity, pressure, etc. • Computational (numerical) solution: – Modern digital computers and the rise of CFD. – Commercial CFD software. Special team projects during the week of the AICHE Annual Meeting (Nov. 9-13) CHE377 – Fall 2016 Dimensionless Equations (BSL Ch. 3)
