Abstract
Transfer function of liquid composition of arbitrary tray of binary distillation column is derived here for reflux flow change and vapor flow change. Material balance equations are derived on several assump tions and then Laplace-transformed. The signal flow diagram drawn from the equations is reduced into asimpler form. The transmittances in the diagram are expressed in the form of continued fractions, which are reduced into a compact form by averaging the elements in the continued fractions and using the complex hyperbolic functions. The transfer function for arbitrary tray is expressed in the form of containing the hyperbolic functions. This method of obtaining the transfer function is free from physically unreasonable boundary conditions which are inevitable in the case of solving material balance equations as finite difference equations. The time for calculating frequency response from the transfer function is independent of the number of trays. This feature is quite advantageous in the case of large number of trays. Frequency responses calculated from the transfer function in the case of methanol-water distillation column of sixtrays are compared with the strict solutions of material balance equations. The calculated values well approximate the strict values in the important frequency range of phase lag of π/2-π radians.
