PRUEBAS DE CAPACITACIONES AL PERSONAL DE PIL S.A

The filter bed condition at the end of a filtration run and prior to backwashing can be determined fi-om a suitable filtration model Essentially the requirement is to provide the total volume or mass of deposit accumulated during the filter run and hence the amount of deposit to be removed during the backwash. It is also important to determine the axial concentration distribution of the filtrate throughout the depth of the bed at the end of the filtration period.

The total volume or mass of deposit accumulated during the filtration run can be derived fi-om a specific deposit distribution profile obtained at the end of the filter run. Such a deposit profile can be obtained fi-om a number o f suitable filtration models. One such model was developed by Ives (1975) based on the following set o f partial differential equations relating the suspension concentration, C, and specific deposit,

cry, to bed depth, Z, and time, t

â^C

â C

ô C

= A— + a , — (52)

ô^a

d a

d a

= yi—r~ + cr,

d t dL

d t

dL

The equations do not take into account the effects of difiusion gradients. Assuming a linear form for the filter coefficient as follows

1- — (54)

where Ào and So are the initial filter coefficient and clean bed porosity respectively, equations (1) and (2) can be solved to give C and eras fimctions of L and t as follows

a exp exp ( /1 .4 + exp (55) - 1 (7 exp X . P v C o t - 1 exp (a o T) + exp (56) - 1

The above equations are a simplified version of the filtration equations. For a complete discussion refer to Ives (1960 and 1963).

Equation (56) therefore allows the distribution of specific deposit with filter depth and time to be determined. Figure 3-2 shows specific deposit profiles calculated using equation (56) for one of the experimental filter columns described in chapter 4.

Specific D eposit Profile (C o= 200 ppm) 0,06 ^ 0 ,0 4 ^ 0,02 0 0,0 5 0,3 0,35 0,4 0,45 0 0.1 0,1 5 0.2 0.25 filter d ep th (m etres) 2 h o u r s filtra tio n 4 h o u rs filtra tio n 6 h o u rs filtra tio n

Figure 3-2. Specific deposit profiles against bed depth using equation (5). Influent concentration (Co) is 200 ppm (vol./vol.), A o is 5.69 m'* and (5 is 4.

One disadvantage of such a model is in its assumption that the influent suspension contains particles of a mono-size range. This is not the case in practise, for example, the kaolin clay suspension used as a clogging suspension for the experimental work herein was found to have a Gaussian size range distribution (refer to chapter 4 for details).

But what effect does the influent particle size range have on the specific deposit profiles, particularly if an average particle size range is assumed? This question can be partially answered from the work carried out by Huang and Garcia-Maura (1986) who developed a filtration model that takes into consideration the influent suspension characteristics. The model allows a specific deposit profile to be calculated for each of the individual particle sizes present in the influent suspension. It also takes into account the proportion of each particle size present in the suspension. The final deposit profile is determined by summing the individual profiles. This offers the opportunity to observe the deposit profiles obtained for individual influent particles, as well as the combined additive effect.

Figure 3-3 shows the individual specific deposit profiles produced using the model and data taken fi-om a Coulter counter analysis of the kaolin clogging suspension used during the experimental programme. From this analysis the 500 mg/1 kaolin

suspension was found to consist of particle diameters in the range 2 to 9 pm with the following percentage volumes 9.04, 24.89, 33.53, 17, 8.63, 3.2, 1.7 and 0.97 % respectively. Details of the Huang and Garcia-Maura model set-up using Mathcad, version 6.0, are given in appendix I.

Using the same model, figure 3-4 highlights the difference between assuming an average particle diameter and summing the contributions made by individual particle diameters. Although the difference is not significant throughout the depth o f the filter it is greatest within the top few layers and this may be a possible source of error in assuming an average influent suspension diameter.

In order to determine the total volume of deposit in the filter bed prior to the start of backwashing, consider an arbitrary single layer, of depth Æ , the volume of deposit for this layer is given by

AF„ = Acr„ALA (57)

where AV„ and Aa„ are the total volume of deposit and total specific deposit for layer

n.

Integration of expression (57) with respect to filter depth, between the bed depth limits gives the total volume of deposit within the filter bed at the start of the backwash

V j . = A ^ a { l ) d l (58)

An ideal backwash, therefore, would be one in which expression (58) reduces to zero in the shortest possible time. We can now quantify the requirements of the backwash, using a filtration model, in terms of the volume of deposit to be removed for any preceding filtration run.

S p ecific D eposit V s d ep th (pd= 2 m icrons) S p ecific D ep o sit V s d epth (pd= 3 m icrons)

2 2 .5 d ep th (cm )

22 .5 d ep th (cm )

S p ecific D ep o sit V s d ep th (pd= 4 m icrons) S p ecific D eposit V s d ep th (pd= 5 m icrons)

22.5 d ep th (cm ) 2 2.5

d ep th (cm )

S p ecific [deposit V s d ep th (pd= 6 m icrons) S p ecific D eposit V s d ep th (pd= 7 m icrons)

2 2.5 d ep th (cm )

2 2.5 d ep th (cm )

S p ecific D eposit V s d ep th (p d = 8 m icrons) S p ecific D eposit V s d ep th (p d = 9 m icrons)

22 .5 d ep th (cm )

2 2 5

d ep th (cm )

Figure 3-3. Specific deposit profiles versus bed depth for various influent suspension particle diameters (pd), using method by Huang and G arcia-M aura (1986).

100 o o o 'x

I

F igure 3-4. Specific deposit versus bed depth for average influent particle diameter and the sum o f individual particle diameters.