A generalized model for the dynamic behavior of a distillation column

A very general form of the basic column equations is presented which allows a wide choice in the form of the specifications of variables required to define the column operation. Variable plate holdups, variable plate efficiencies, heat losses from the column, and finite time liquid flow dynamics are some of the specifications considered. The values of the implicit column variables during the unsteady state period are found by a method which is independent of the numerical procedure chosen to solve the differential equations. Computer runs with the Kutta‐Merson method used to solve the differential equations were made for a column approaching steady state at total reflux. The effect of different variable specifications on this computer column are discussed.

mentioning

confidence: 99%

Unsteady state behavior of multicomponent distillation columns: Part I: Simulation

Howard

1970

Determination of transient plate efficiencies from operational data

Groves¹,

Tetlow²,

Holland³

1967

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

The calculation of unsteady state multicomponent distillation using partial differential equations

Osborne

1971

t ( h ) = average age of the molecules having a life expectation, t pmax = maximum specific growth rate, t T = p m a x t = mean holding time in the overall system, dimensionless LITERATURE CITEDA method i s presented for calculating unsteady state multicomponent distillation using partial differential equations. The equations are solved by treating them as continuous i n theoretical stage direction and stepped i n time. Although some restrictions were placed on the problems actually salved, the method i t s e l f i s not restricted by number of trays, number of components, number, type or combination of upsets, or by the thermodynamics of the system, and the method readily lends i t s e l f t o hybrid computer solution.