Filtration Systems: Theory and Technology

Theory and Technical Background

Uni-Minn Development Corporation was asked to design a filtration system

capable of filtering 500 gallons per hour of a slurry solution containing four percent

Celite-500 (17.3 μm particle diameter) by mass. The scaled up filtration system is to be

of rotary drum type, and capable of continuous operation. Two days of bench-scale

testing were performed in the Uni-Minn Development Corporation’s Unit Operations

Laboratory to determine the necessary parameters for scale up.

Basic Filtration Theory

Filtration is a mechanical separation process that separates the two phases of a

suspension from each other.[7] Filtration plays a critical role throughout industry, and is

particularly important in water treatment, paper making, and mineral processing.[8]

Filtration is used to recover solids, to clarify liquids, or to recover both phases.

The filtration apparatus in the Uni-Minn Development Cooperation’s Unit

Operations Laboratory is a vertical pressure leaf filter. Specific details of the apparatus

are contained in the apparatus subsection, but a basic schematic is shown in Figure 1.1

below. A vacuum is utilized to force flow of a slurry solution through a filter medium of

cross-sectional area A. Out the top of the filter, flows a volume, V, of filtrate. A filter

cake, of length L, forms on the bottom of the filter medium. The figure is drawn at time t

in the filtration cycle.

Figure 1.1 – Vertical Pressure Leaf Apparatus Setup.

The filter cake that forms on the bottom of the filter medium can be modeled as a

packed bed of particles. As such, the Carmen-Kozeny relation for laminar flow in a

packed bed of particles holds.[4] That is,

pc  k1 v 1    S0

2

2

(1)[4]



3

L

w...

... middle of paper ...

...terial.[3]

Error Analysis

The uncertainty associated with the measurements made in the lab can be

determined by making multiple measurements. For a measurement repeated n times,

the average is defined as

n

X

i

(22)

X

i1

n

where the Xi’s are the experimental measurements. The standard deviation, s, can be

calculated using the formula

n

 (X

 X)2

(23)

i

s

i1

n 1

Using the standard deviation, the 95 percent confidence level, Δ, is calculated using the

equation

t s



(24)

n

where t is the appropriate value from Student’s t table.

Error can also be propagated throughout calculations. When two values with

errors e1 and e2 are added, the resulting error, e, is

e  e1  e2

(25)

When two values, x1 and x2, with errors e1 and e2 are multiplied, the resulting error, e, is

2

2

 e1   e2 

e  x1 x2

   

 x1   x2 

(26)