Determination of transient plate efficiencies from operational data

Abstract

that the efficiencies were known and that it was required to find the transient solution of the problem under consideration.It appeared that a suitable method for the determination of the transient plate efficiencies could be developed by replacing the steady state equations in the methods developed by Davis et al. and Taylor et al. by corresponding equations for the unsteady state models proposed by Waggoner et al. This approach, a logical extension of previous work, was successful, and the resulting methods are described in the first two sections that follow.A third procedure was developed for the determination of the transient plate efficiencies for the case where the compositions and plate temperatures are known functions of time. The equations needed in the application of this method are presented in a subsequent section.Also, a method was developed for separating the mixing effects of the liquid on each plate and in its downcomer which was not involved in mass transfer from the plate efficiencies of the liquid on each plate that was involved in mass transfer. This method was developed by replacing the steady state equations in the methods of Taylor et al. and Davis et al. by the unsteady state equations for the model described by Tetlow et al. (8). An example of this method is presented in which the plate efficiencies and mixing effects are determined simultaneously,In the method described in the next section, it is supposed that the product distributions (bi/di) and the tem- specifications such as the distillate rate, reflux rate, column pressure, type of condenser, number of plates, location of the feed plate, the complete definition of the feed, and the holdups are known. Information over and above this, such as any combination of product distributions (bi/di) and temperatures ( T j ) , is hereafter referred to as additional specifications. A D D I T I O N A L SPECIFICATIONS: ALL PRODUCT F U N C T I O N S OF T I M EOn the basis of these known values of the operating variables, the procedure that follows determines a set of plate efficiencies required to obtain agreement between results calculated by Waggoner's model (10) and the results of field tests.In the method developed, the transient operation period is subdivided into time increments. At the beginning of and the K values of component i (evaluated at the temperature and ressure at which the liquid leaves plate for Kjt, it is also evaluated on the basis of the temperature, pressure, and composition of the liquid leaving plate i.Since the sum of the yjls at the end of the time period (t, + A t ) under consideration has the value of unity, it follows that j ) by Kji. When t R e activity yj~ji is included as a multiplier 0 f j = 2 Eli Kji xji -1

Distillation

“…They dealt with the experimental transient response of small columns (39, 48, 98), the theoretical frequency response of multicomponent distillation columns (151), theoretical dynamic response of packed columns (61), and the mathematical analysis of the startup of a plate-type gas absorber (33). Generalized models for the dynamic behavior of a distillation column were developed by Tetlow et al ( 136) and Osborne et al ( 106); and methods for obtaining transient plate efficiencies from transient operating data were developed by Groves et al (55). The importance of considering holdup in dynamic analyses was stressed by Howard (69).…”