Dynamics and control of a bubble-cap absorption column

Dynamic modelling of countercurrent mass transfer processes

“…Hsu43 later extended the approach to the multiple stage case. Boland and van der Kaa41 also indicated an important effect in modelling a centrifugal contactor which exhibited an inverse response in fluid flowrate, analogous to Eqn (21). 4…”

“…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.…”

“…have been obtained by several authors.5>21,22 For the case where N is large the complexity of the analysis is reduced by treating n as a continuous variable. This allows the conversion of the model into a single partial differential equation in time and stage number n, provided the holdups are the same ~+~)―+(.L-~G)―-=(L+~G')―― ...has some analytical advantages although the responses generated are not in as close agreement with those of the plug flow model as might be expected.s However, the alternative and more powerful technique of digital simulation now enables numerical solution of the simultaneous differential equations of the model even when N is large.…”