Aspectos Climatológicos

The gas holdup and the superficial liquid velocity can be estimated for the riser section of an airlift using equations 3.5, 3.16, 3.19 and 3.30. The model applies to airlifts operating in bubbly flow, coalesced bubble flow and chum turbulent flow regimes. In order to obtain numerical solutions to these equations, values for certain parameters have to be obtained. For a given superficial gas velocity, the distribution parameter (Co), the loss coefficient (Kf) and the terminal bubble rise velocity (Ubt) must be known, together with the physical properties of the liquid and the gas. We shall now consider the distribution parameter, loss coefficient and the terminal bubble rise velocity in more detail.

3.1.2.1 The distribution parameter

In their general expression, for the average volumetric concentration, Zuber and Findlay (1965) invented the distribution parameter term (Co) to take into account the effect of non-uniform flow and concentration profiles in any two phase flow regime. They defined the distribution parameter as

C = < « ; )

_

(«> O')

To investigate the effects of non-uniform flow and concentration distribution on the value of the distribution coefficient, we consider an axially symmetric flow through a circular pipe and assume that the flow and concentration distributions are given by (Zuber and Findlay, 1965)

3.32

and

(« - « J

a . - a . = 1 - KRJ 3.33

where the subscripts c and w refer to the values evaluated at the centre line and at the wall of the circular pipe. The superscripts m and p are the exponents on velocity and void distribution, respectively. Inserting equations 3.32 and 3.33 into Eqn 3.31, we obtain the following expressions for the distribution parameter:

C = 1 +

1 - a .

( « >

3.34

when expressed in terms of the volumetric concentration (aw) at the wall or when

C = m + 2 1 + pa^ 3.35

_{^jn + p + 2^_ _ ( / M 4-

expressed in terms of the volumetric concentration (ac) at the centre line.

Zuber and Findlay (1965) gave three situations where the distribution parameter changes with the concentration:

1) if the concentration is uniform across the pipe, then

aw = ccc = <a> 3.36

from equations 3.34 and 3.35

C o = l 3.37

2) if the concentration at the centre line is smaller than that close to the wall, then

t t c < t t v

and

3 3 8

3.39

C o < l

3) if the concentration at the centre line is larger than that at the wall, then

Œc > aw 3.40

and

C o > l 3.41

In the hydrodynamic model, the distribution parameter ( C o ) characterises the shape

of the liquid velocity profile in the column. The value of the distribution parameter ( C o )

also depends on the flow and concentration profiles (Clark and Flemmer, 1985; Zuber and Findlay, 1965). The flow and distribution of bubbles across the column are affected by the type and design of the sparger (Ayazi Shamlou et al., 1994). Therefore, the distribution parameter is also expected to be influenced by sparger design since the liquid velocity profile in the column is dependent on the flow and distribution of bubbles across the column.

Zuber and Findlay (1965) stated that for fully established parabolic profiles (similar to laminar profiles), the distribution parameter attained a value of 1.5 and for flat profiles, it tended to reach a value of 1.0 (when the concentration at the centre line is larger than that at the wall). For most two phase flow situations, including bubble columns and airlift devices, the gas holdup at the centre exceeds that at the wall (for fully established profiles)

and this would suggest that Co > 1. However, Ayazi Shamlou et al. (1994) have used a Cq value of 0.7 for a concentric tube airlift with a ring sparger because this was found to give a better agreement between model predictions and experimental data. They explained that since their ring sparger ejected air close to the draft tube, it was not surprising that the liquid flow profile in the riser had a velocity higher nearer the wall than at the centre (close to the sparger). Furthermore, they stated that there was a gradual change in the velocity profile as the liquid moved up the riser and hence the value of Co represented the average of the liquid velocity profiles in the riser section of an airlift.

Theoretical calculations suggested a maximum value of 1.6 for Co (Zuber and Findlay, 1965). Govier and Aziz (1972) proposed a value of 1.15 for continuous bubble swarm and bubble sizes ranging from very small bubbles up to an equivalent bubble diameter of 2 cm. In chum turbulent flow, where bubble interaction and waking are strong, Co has been found to assume values between 1.1 and 1.3 (Nassos and Bankoff, 1967; Wallis, 1969). Hatch (1973) determined the Co value experimentally in a draft tube of<%<\ internal loop airlift reactor and found it to be 1.065. Clark and Jones (1987) employed a Co value of 1.2 in their calculation; they also implied that higher values of the distribution parameter (between 2.0 and 5.0) may be required to explain certain two phase flow situations (e.g. circulation due to the maldistribution of air caused by a single-pipe sparger). Kelkar and Shah (1985) experimentally determined the value of Co for various CMC solutions in a bubble column. They found the distribution parameter to vary from 2.36 to 2.76 as the concentration of the CMC solution changed.

The effect of varying the distribution parameter, in the hydrodynamic model, on riser gas holdup and liquid velocity for increasing superficial gas velocity (keeping all other parameters constant) are shown in Figures 3.1 and 3.2. The external loop airlift reactor with water as the liquid was chosen. The loss coefficient was taken to be 0.1, while 0.25 m/s was the value of the terminal bubble rise velocity. Co was varied from 0.7 to 1.7 in steps of 0.2. It can seen that higher values of Co gave lower holdup values (Fig 3.1) and higher liquid velocity values (Fig 3.2) than lower values of Co.

0.045 1 Co=0.7 Co=0.9 Co=1,1 0.035 - Co=1.3 Co=1.5 Co=1.7 I Q. D Ô 0.025 - SI (/) (D CD 0.015 - 0.005 -I 0.000 0.005 0.010 0.015 0.020 0.025 Superficial g a s velocity (m /s) 0.030

Figure 3.1: The effect of the distribution parameter (Co) on the riser gas holdup - model predictions. 0.200 Co=17 Co=0.7 O 0.150 - • n 0 .1 0 0 - Q. 0.050 0.000 0.005 0.010 0.015 0.020 0.025 0.030 Superficial g a s velocity (m /s)

Figure 3.2: The effect o f the distribution parameter (C o ) on the riser liquid circulation velocity - model predictions.

3.1.2.2 The loss coefficient

The Kf is the loss coefficient for the top and the bottom section of an airlift reactor. Naturally, it is expected to vary with different airlift reactor geometries and with the type of fluid employed in the airlift contactor. Ayazi Shamlou et al. (1994) employed a Kf value of

5.0 for an air/yeast {Saccharomyces cerevisiae) system in a pilot-plant internal loop airlift