Liquid-Solid Mass Transfer

(2.6)

Just as in the case of gas-liquid mass transfer, the liquid-sold mass transfer step may play an important role in the performance of a TPFBR for chemical or biological reactions. The structure of the biofi l m tends to slow the transport of substrate through the biofilm and therefore, the substrate concentration surrounding the microorganisms within the biofilm i s less than that in bulk l i quid. Thus the mass transport properties of the biofilm are of critical i mportance in assessing the overall performance of a FBBR.

Substrate conversion in a FBBR can be described by the following steps, as shown in Fig. 2.4, (La Motta, 1 976):

1 ) Transport of substrate from the bulk l iquid to the l iquid-biofilm i nterface (external mass transfer);

2) Transport of substrate with the biofilm (internal mass transfer), and

2.

Three-Phase Reactor -

20

Step

2)

and 3 ) take place simultaneously and thus neither can be said to control while step

1)

occurs i n series with steps

2)

and 3). For intrinsic reaction rates with positive dependence on substrate concentration (i.e., Monod kinetic), the gradients established by step

1)

and

2)

decrease the observed reaction rate by decreasing intrabiofilm substrate concentration (Shieh & Keenan, 1 986).

In order to describe mass transport from the bulk l iquid to the surface of the SUppOlt particle and reaction at that position, the

Nersnt d[ffils'ion layer and a stagnant film

theolJ! have widely been used and lead to the following equation for the flux }��.

of substrate from the bulk l i quid to the i nterface, as shown in Fig.

2.4:

}�

=

k1s(C; -C;)

(2.7)

where

C�

and

C;

are the substrate concentrations at the interface and i n the liquid, respectively, and

k/s

is the liquid-solid mass transfer coefficient.

Chapter 2. Three-Phase Fluidised-Bed B iofilm Reactor - Background 2 1

An analytical solution for

kls

is possible for the ideal case of a single sphere at rest in an infinite stagnant fluid.

k1s

is then given by:

k

_{I -}-

2l\,

S

d,p

(2. 8)

where

Dm

i s the molecular diffu sivity in l iquid.

For the general case of mass transfer between a moving fluid and a spherical particle, the Sherwood number, Sh, Schmidt number, Sc, Stanton number, St, and Froude number, Fr, relate the physical properties of the system to the mass-transfer coefficient and are more often used (Brodkey & Hershey, 1 98 8) . These correlations are most often expressed in terms of dimensionless numbers, often in the form of a power senes. Sh =

kl.,dsp

Dm

Sc = �

PLDm

5'

k1,5

L · - (lI, (le (2.9) (2. 1 0) (2. 1 1 ) (2. 1 2)

In general, steady-state theories for the liquid-solid mass transfer are largely classified into two categories; those based on the terminal velocity-slip velocity approach and the others based on Kolmogoroffs theory. In the terminal velocity-slip velocity approach, the steady slip velocity between soli d and liquid is used in the correlation for the Sherwood number. Based on this theory, the experimental data for the liquid-solid mass transfer coefficient

(kls)

are often correlated by a dimensionless equation of the form,

Chapter 2. Three-Phase Fluidised-Bed Biofilm Reactor - Background 22

Sh

== 2 . 0 + a Sel ! 3 ReI 1 2 (2. 1 3 ) The value of the constant a reported i n the literature lie between 0.03 and 1 .0 (Shah,

1 979). A review of the data of Rowe & Claxton ( 1 966) on the Reynolds number range 20 through 2000 indicates that a =0.76 for liquids.

Beek ( l 97 1 ) developed a more general correlation of liquid-solid mass transfer coefficient within a fluidised-bed based on the data of several researchers. The correlation of Beek is

S', Se2/3 == (O. S I ± O.05) Re -0 5 (2. 1 4)

Kolmogoroffs theory i s based on the length scale of the micro-scale eddi es, which is defined as

(V.3J)�

17 = -

_E

(2. 1 5)

and the velocity scale is defined as

I '

VI =

(vE)74

(2. 1 6)

where E is the local energy dissipation rate per unit mass. From the stochastic behavior of the fluid flow around the suspended particle and Kolmogorotrs theory of i sotropic turbulence the following relationship for the Reynolds number can be derived (Shah et ai., 1 982)

Hi > 17 >

d,p

(

� _<I

)

1/2 •

}'.,dsp

Re == e --

v3

•

(

E

d

sp <I

)

1/3 Re=e -­

v3

(2. 1 7)

Chapter 2. Three-Phase Fluidised-Bed Biofi l m Reactor - Background 23

where

c'

represents a dimensionless constant and Hi is a characteristic l ength, for instance, the suspension height. By using Kolmogoroff s theory, the energy dissipation rate in TPFBR can be calculated from the pressure drop experienced by the gas flow rate. The energy input P ' i s approximated by

(2. 1 8)

where

t.p

is the pressure drop in the bed. Therefore the specific energy dissipation rate, E, can be calculated as,

(2. 1 9)

Information i n the l iterature pertaining to liquid-solid mass transfer in related systems, such as two-phase FBBR i s fairly comprehensive. L ittle i s known, however, about l iquid-solid mass transfer in a TPFBBR. Arters & Fan ( 1 984) developed the l iquid-solid particle mass transfer coefficient in a TPFBR. They employed cylindrical particles of benzoic acid which were fluidised with water and air. Their results showed that liquid-solid mass transfer in a TPFBR is higher than that in a two-phase fluidised bed at a given l iquid velocity. Furthermore, the Sherwood number

(Sh)

for k1s increase with increasing gas velocity. Liquid-solid mass transfer i n a TPFBR appears to be relatively independent of the liquid velocity, as has been noted for a two-phase fluidised bed reactor. The correlation of Alters & Fan for kls is given as

. .

( - J0.3

5'h =:: =:: 0.228(1 + 0.0826 Rel: 623 )Ga1l 323ScOA PSI' PL

D

g

P

m L

and the Gall ileo number ( Ga ) is defined as

d3 Ga =

PZ

(2.20)

Chapter

2.

Three-Phase Fluidised-Bed Biofilm Reactor - Background

24

where

1\,

is molecular diffusivity in liquid and p"P is density of particle.

Recently, Nore et al.

( 1992)

studied hydrodynami cs, gas-solid and l iquid-solid mass transfer with in a TPFBBR with the low density ranging from

1300

to

1700kg/m3 .

In their studi es, i ncreasing the gas velocity increased

kls '

especially at low gas velocities for low particle densities and the liquid velocity had almost no effect on liquid-solid mass transfer coefficient. Nore et al. correlation for estimation of

kls

with good prediction of the

250

values measured are

k

=

1 10 (

In document Mechanistic, neural network, and intelligent hybrid models for a three phase fluidised bed biofilm reactor : a thesis presented in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Environmental Engineering at Institute of (Page 37-42)