modelTrayColumn

Information

This model discribes a tray column.

Base classes for the following classes are instantiated her:

• liquid holdup
• pressure loss
• film model (BaseFilmTray)
• geometry
• heat transfer to wall

Volume flow rate of the liquid leaving the tray

Liquid leaves the tray if the height of the two-phase regime on the tray, h, gets higher than the height of the weir, h_w. The volume flow rate of the liquid, Vdot_l, is then proportional to the height over weir, h_ow = h-h_w and is calculated using the following formula:

Vdot_l = l_w · eps_liq_2ph · ((h / eps_liq_2ph - h_w) · g1/3 / 1.45)3/2

where l_w is the weir length and eps_liq_2ph the liquid fraction in the two-phase regime on the tray. This equation was obtained from Stichlmair [1]. However this equation would yield a negative volume flow rate, if h < h_w. Since this is not possible, Vdot_l is set to zero if h < h_w (which may be the case for the start-up of the column). It is supposed that there is only liquid leaving the tray, if the height of the two-phase regime is high enough; " raining " through the holes in the tray (which occurs if the vapour load is too small) is not considered.

Operating range

A very important point for tray columns is the operating range. There exists a minimum and a maximum vapour load as well as a minimum and maximum liquid load. In order to discribe the minimum vapour flow not the vapour flow Vdot_v itself is used but the vapour load F (which is defined as F = wV · ρV wV is the superficial velocity) or the vapour load Fh, where the velocity is the velocity in the holes. In theory the F-values are different for all elements of the column, however the F-values are calculated only once for each section using the inlet conditions for vapour and liquid. This is acceptable since during normal operation the F-values don't vary a lot over one section and for conditions like for example start-up operation the equations to calulate maximum and minimum load are not valid anyway. Also the F-values shall only give an idea of the operation range and in any case it is suggested to stay well in the operating range.

    Minimum vapour load

    A minimum vapour load exists for sieve trays, since if the vapour load is too small, liquid is going to rain through the plates. To avoid this Ruff [2] found out that the vapour load must be at least

    Fh,min,Ruff ≥ (0.37 · dh · (ρL - ρV)5/4 / ρV1/4)0.5

    where dh is the diameter of the holes in the tray and ρL and ρV are the densities of the liquid and the vapour respectively. However if the holes in the trays are rather small (around 2 mm - 3 mm) raining is not the major problem, but the fact that vapour is only passing a part of the tray. This can be avoided the following holdes:

    Fh,min,Mersmann ≥ (2 · &sigma / dh)0.5

    This formula was found by Mersmann [3]. So the minimum vapour load was defined to be Fh,min = min(Fh,min,Ruff ,Fh,min,Mersmann). The model allows for vapour loads which are smaller than the minimum vapour load (so no assert is used in the code), however one has to bear in mind that raining and maldistribution of the gas are not modelled and the results for Fh < Fh,min are not very reliable.

    Maximum vapour load

    If the vapour load is too high, entrainment occurs, i.e. vapour blows the liquid out of the column. An equation from Stichlmair [1] was taken in order to calulate the maximum vapour load:

    Fmax = 2.5 · (φ2 · σ · (ρL - ρV) · g)1/4 · (100 Vdot_l/Vdot_v)0.06 / (1 - 10 Vdot_l/Vdot_v)0.5

    Again the compliance with this rule is not ensured via an assert, but the user is advised to check that F < Fmax. If this is not the case the equation used to calculate Vdot_l is not longer valid.

    Minimum and maximum liquid load

    Theoretically the liquid load can get very small, however this will not be very efficient, so it is recommanded to have a minimum height over weir of 5 mm. The liquid flows through the column due to the earth gravity. Therefore the capacity is limited. However up to now no correlations are implemented.

Literature

[1] Stichlmair: Dimensionierung des Gas/Flüssigkeits-Kontaktapparates Bodenkolonne, Chem.-Ing.-Tech. 50 (1978), Nr. 4, p. 281-284

[2] Ruff et al., Chem.-Ing.Tech. 48 (1976) Nr. 9, p. 759-764

[3] Mersmann, Chem.-Ing.Tech. 35 (1963) Nr. 2, p. 103-107

Parameters

Connectors

Components

Contents

Name	Description
BalanceEquations
InitOption
Reaction
Geometry
PressureLoss
HeatTransferWall
Holdup

Revisions

created by	Karin Dietl & Andreas Joos
creation date	01.01.2009
revised by	nobody so far
last revision	this is an alpha version...
based on