Distributed‐Parameter dynamics by correlation analysis

Abstract

1. Brown, D. E.;and K. Pitt, paper presented at CHEMECA, 2. Calderbank, P. H., Trans. Inst. Chem. Engrs., 36, 443 3. Chen, H. T., and S . Middleman, AlChE J., 13, 989 (1967). 4. Collins, S. B., Ph.D. thesis, Oregon St., Univ., Corvallis (1967). 5. Doulah, M. S., and J. D. Thornton, paper presented atThe experimental dynamic response of a distributed-parameter, simultaneous heat and mass transfer system was investigated using correlation analysis. The system was a wetted-wall column operating as a nonadiabatic humidifier with both liquid and gas phases in turbulent flow.The experimental frequency response results were compared t o the values predicted by an existing mathematical model. The investigation also included a study of the effect of employing forcing functions having nonideal power spectra. Analog-simulated, first-order systems were tested to verify the computational procedure and to support the conclusions for the humidification system. System dynamic identifications, acceptable for most engineering purposes, were obtained from forcing signals having power spectra which differed significantly from ideality. For the reduction technique employed, o time-domain record of approximately 2,500 pairs of inputoutput data points was found to suffice for a satisfactory analysis. The correlation technique yielded reliable results over approximately the same range of frequencies as reported for previous pulse test studies based on a comparable forcing procedure. However, the results showed an upper frequency limit below that previously achieved by direct frequency forcing of the same system. A simple thermodynamic expression determining the infinite dilution ternary activity coefficients from the dew point isobar is presented. A flow method measuring the dew point temperature for ternary and binary isobaric systems is proposed. An analysis determining the infinite dilution ternary activity coefficients for ethanol-isopropyl alcohol-water system a t 1 atm. is illustrated.Knowledge of the infinite dilution ternary activity coefficients in the liquid phase is important for the design of distillation equipment, especially for the proper choice of solvent in distillation operation.There have been several studies for experimentally determining the activity coefficients at infinite dilution. For binary systems the useful procedure, which is based on readily obtained data such as total pressure-concentration curve ( Pz), bubble point-concentration curve (2'x) and dew point-concentration curve ( Ty, or Py), has been proposed by Carlson and Colburn (5), Redlich and Kister ( 1 3 ) , Gautreaux and Coates ( 7 ) , and Ellis and Jonah (6), and recently examined by Slocum and Dodge (15), and Kojima et al. (9, 11). K. Kojima is

Dynamic modelling of countercurrent mass transfer processes

“…is embodied by a pair of nonlinear differential equations for each column stage (ie, composition and liquid flowrate equations). These equations can be integrated directly using a numerical technique, although for the purposes of control studies many authors prefer to use local linearisation, which permits the use of analog computers 17,18,28,30 The performance of the equations has been checked experimentally.4, i6-is, 30, 3i 1 Where plate design is such that liquid overflow does not conform to (12) Although gas flow dynamics may be considered fast, gas flowrate may still have a significant effect on liquid flowrate and holdup.4 In terms of modelling this involves a modification to Eqn (13) which on linearisation might produce a relationship of the form Ln = ~t Mm '~ ~2 G ... (21 ) The mechanism involved is not well-understood, but an increase in vapour flowrate during distillation can reduce liquid overflow from some columns which may result in an inverse response in composition. This phenomenon has been modelled and simulated by both Luyben29 and Stainthorp63 in the course of studying the control of such systems.…”

“…In stagewise absorption and distillation columns a change in liquid flowrate to the column head must be transmitted from plate to plate which necessitates a corresponding change in liquid holdup. If the plates have weir overflow then the Francis equation is applicable Ln « hwn .. (12). and the liquid crest height over the weir hwn is related to plate holdup Ln =,fw(Mm)~ ... (13) Therefore, for a single stage with variable flows the compon-~+~)=~~+~_t-(~+GJ... (15).…”