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Stacked
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Rapid
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Sand
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Filtration
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Theory
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The
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basic
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premise
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of
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the
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stacked
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filtration
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system
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is
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that
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the
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flow
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of
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filtration
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is
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equal
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to
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the
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flow
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of
...
backwash
...
so
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that
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we
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can
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use
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normal
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plant
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flow
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to
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backwash
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the
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filter.
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A
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conservative
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estimate
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of
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backwash
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velocity
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requires
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that
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it
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be
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10
...
times
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the
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normal
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filtration
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velocity.
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We
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achieve
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this
...
requirement
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by
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stacking
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layers
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of
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filtration
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on
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top
...
of
...
each
...
other.
...
Each
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layer,
...
or
...
plane,
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consists
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of
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a
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set
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of
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inlet
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tubes
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that
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introduce
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water
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to
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a
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layer
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of
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20
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cm
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of
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sand.
...
The
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water
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once
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filtered
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is
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then
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collected
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by
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a
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set
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of
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outlet
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tubes.
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Each
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layer
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is
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essentially
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its
...
own
...
filtration
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system.
...
When
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you
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stack
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the
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layer
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of
...
filtration
...
on
...
top
...
of
...
each
...
other,
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area
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for
...
backwash
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stays
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the
...
same
...
and
...
you
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can
...
technically
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backwash
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all
...
of
...
them
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with
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the
...
same
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backwash
...
water.
...
Figure
...
1
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Basic
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Concept
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of
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Stacked
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Filtration
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Operation
...
and
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the
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mathematical
...
derivations
...
demonstrate
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this
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relationship.
| Wiki Markup |
|---|
{latex}${{Q_{Plant} } \over 2} = V_{BW} A_{BW} ${latex} |
| Wiki Markup |
|---|
{latex}${{Q_{Plant} } \over {N_{Filter} }} = V_{Filter} A_{Filter} ${latex}
|
| Wiki Markup |
|---|
{latex}${\rm{V}}_{{\rm{BW }}} = 10{\rm{V}}_{{\rm{Filtration}}} ${latex}
|
Where
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BW=Back
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Wash
...
Q=Flow
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rate
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of
...
filtration,
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backwash,
...
or
...
entire
...
plant
...
depending
...
on
...
the
...
subscript.
...
V=Velocity
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of
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either
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filtration
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or
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backwash
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depending
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on
...
the
...
subscript.
...
A=Area
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of
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either
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filtration
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or
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backwash
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depending
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on
...
the
...
subscript.
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N=Number
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of
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any
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system,
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pipe,
...
and
...
etc
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which
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in
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this
...
case
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is
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the
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number
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of
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filtration
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unit
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that
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receives
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the
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plant
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flow
...
rate.
...
For
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our
...
design,
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we
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chose
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a
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conservative
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available
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backwash
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flow
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rate
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of
...
only
...
half
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of
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the
...
plant
...
design
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flow
...
rate.
...
We
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want
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the
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backwash
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flow
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rate
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to
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equal
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the
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filtration
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flow
...
rate.
...
So
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we
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arrange
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the
...
first
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two
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equations
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for
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the
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plant
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flow
...
rate
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and
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set
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them
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equal
...
to
...
each
...
other.
| Wiki Markup |
|---|
{latex}$V_{Filter} A_{Filter} N_{Filter} = Q_{Plant} = 2V_{BW} A_{BW} ${latex} |
When
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we
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substitute
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the
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10
...
to
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1
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relationship
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between
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backwash
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and
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filtration
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velocity
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into
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the
...
above
...
equation,
...
we
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derive
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the
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following
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relationship
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with
...
regards
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to
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area.
| Wiki Markup |
|---|
{latex}$V_{Filter} A_{Filter} N_{Filter} = 2{\rm{x10}}V_{Filter} A_{BW} ${latex} |
| Wiki Markup |
|---|
{latex}$A_{Filter} = {{20} \over {N_{Filter} }}V_{Filter} A_{BW} ${latex} |
With
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the
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velocity
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of
...
filtration
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cancelling
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each
...
other,
...
we
...
learn
...
that
...
in
...
order
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to
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use
...
the
...
same
...
flow
...
rate
...
to
...
backwash
...
and
...
filter
...
we
...
need
...
the
...
area
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of
...
the
...
filtration
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to
...
be
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10x
...
the
...
time
...
area
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of
...
backwash.
...
Consequently,
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if
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we
...
were
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to
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have
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two
...
filters,
...
then
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we
...
would
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need
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10
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filters
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stacked
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on
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top
...
of
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each
...
other.
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If
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we
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were
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to
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have
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four
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filters,
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like
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our
...
design,
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then
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we
...
would
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have
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5
...
layers
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for
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each
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filtration
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system.
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There
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is
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a
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tradeoff
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between
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the
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height
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of
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the
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individual
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filtration
...
unit
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and
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the
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number
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of
...
filtration
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units
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employed.
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When
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you
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decrease
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from
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four
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to
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two
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filters,
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the
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height
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of
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the
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individual
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filter
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essentially
...
doubles.
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This
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relationship
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exists
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because,
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in
...
order
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to
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have
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a
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geometry
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that
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allows
...
same
...
flow
...
rate
...
to
...
filter
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as
...
well
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as
...
backwash,
...
the
...
total
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ratio
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of
...
filtration
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area
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versus
...
backwash
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area
...
must
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be
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kept
...
constant.
...
Essentially,
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the
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number
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of
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filtration
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planes
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to
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backwash
...
planes
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is
...
set.
...
For
...
our
...
example,
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the
...
ratio
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is
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10
...
to
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1
...
because
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our
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backwash
...
velocity
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is
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ten
...
times
...
greater
...
than
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the
...
filtration
...
velocity.
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Consequently,
...
when
...
we
...
select
...
a
...
two
...
filter
...
system,
...
we
...
reduce
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the
...
number
...
of
...
backwash
...
planes
...
to
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two,
...
which
...
means
...
that
...
there
...
must
...
be
...
a
...
total
...
of
...
twenty
...
filtration
...
planes
...
which
...
now
...
must
...
be
...
split
...
between
...
two
...
filter
...
units.
...
The
...
height
...
of
...
the
...
individual
...
filter
...
increases
...
as
...
a
...
result.
Figure 1: Basic Concept of Stacked Filtration Operation
As shown in Figure 1, there are gate valves to introduce or restrict water to the individual filtration unit. For example, if plant flow decreases to a point where one filter unit can handle the flow rate, we can shut down flow to three of the filter units so that we can perform maintenance on them.
Refer to figure 1 for the following. During backwash operations, we will first use valves to close off the water leading to the distribution tank. As shown in figure 1, we would only need to close off the valves on the outlet manifold. Then we would introduce back wash water from the sedimentation tank through the inlet tubes. As the first layer expands, we would close off the water to the top layer of influent tubes. Once the top layer expands we will close off the top inlet manifold. Now all of the backwash water will be pouring through the bottom inlet manifold. These tubes will be designed to handle that flow and, since they are purposely located at the bottom, they would be able to fluidize the entire sand bed.
IV. Assumptions
In order for our design to work, we made the following assumptions. First we assumed that 20 cm of sand will effectively filter 5-10 NTU effluent water from the sedimentation tank to lower than 1 NTU without clogging at a reasonable rate. Second, we assumed that the unfiltered water from the sedimentation tank would be able to backwash the filter so that it can continuously filter water to 1 NTU or lower standard. Third, we assumed that, as long as the distance between the filtration tubes in a layer, is small compared to the depth of a layer of sand, the flow of water coming out of the tubes will converge and form a plane of filtration. For our purposes, we assumed that a ratio of 1 to 10, comparing the distance between the tubes and the sand layer, would be small enough. One of the future challenges for the filtration team would be test this assumption. Consequently, a layer of inlet tubes sandwiched between two layers of sand would effectively have two plane areas of filtration (Figure 2). All of the assumptions will be tested as described in more detail in the Future Challenge section.
Figure 2: Plane Area Concept
IV. Methods
Our design process consisted of 3 major steps. First we designed the individual filter bed itself based on the relationship equations mentioned in the theory section. Second, we sized the pipe in our system so that the head loss experienced by the pipes is never greater than 10% of the head loss experienced by the sand. If the head loss in the sand is not greater than the head loss in the pipes, there will be preferential flow and not all of the pipes in the manifold will have equal flow. Third step was to design the minimum distance between the entrance pipes from the sedimentation tank to the height of the gutter to ensure proper back wash.
Results and Discussion
Our complete filtration system for Agalteca consists of a four rapid sand filtration system (Figure 5). When arranged side by side with concrete wall with a thickness of 20 cm, the total width will be 2.90 m and the total height will be 1.65 m. Each filtration unit will be 1.65 m in height and the sand portion will be square with a side of 0.47 m. Each filter will have 5 layers with each layer, consisting of a set of inlet pipes, 20 cm sand layer, and a set of outlet pipes. Please see Figure 2 Top View Comparison of Agalteca versus Stacked Filtration and Figure 3 Side View Comparison of Agalteca versus Stacked Filtration. Each layer will hold 18 perforated pipes except for the bottom inlet layer which will hold only 12 because they are bigger tubes. Such arrangement will leave 0.5 in between each upper tubes and 0.75 in between the bottom filtration tubes. This is a very conservative design because it maximizes the number of filtration tubes which we believe would do a better job of acting as a plane of filtration than less tubes. The future challenge for the filtration team is to test this assumption and find out how much space we can have between tubes and still achieve a plane like effect.
Figure 3 Top View Comparison of Agalteca versus Stacked Filtration
Figure 4 Side View Comparison of Agalteca versus Stacked Filtration
All of the inlet and outlet tubes are 0.5 inch while the bottom is 0.75 inch in diameter. All of the manifold that connects to these filtration tubes will be 3 inch in diameter. All pipes and tubes used are schedule 40. This filter is designed for sands with typical characteristics of D60 of 0.55mm, porosity of 0.4, and specific gravity of 2.65. It will filter at rate of 1.4 mm/s and backwash at 14 mm/s with the expected 30% bed expansion. The filtration system should be located so that there is at least 1.1 m distance from the entrance pipe of the sedimentation tank to the gutter and the effluent pipe of the filtration unit should be slightly higher than the sand bed where it discharges into an elevation control box on its way to the distribution tank. This will keep the filter wet even when there is no flow.
Figure 5: Vertically Stacked Filtration Design
Our design should work as long as the following assumptions hold. First, we need to effectively backwash the sand filter with unfiltered water from the sedimentation tank so that it can continue to filter water to 1 NTU or lower. If there is decreasing filtration efficiency, as evident by high effluent NTU, then this design cannot work. Also we need to know whether or not 20 cm of sand is enough to lower the effluent NTU to 1 or lower. Also we need to find the clogging time of 20 cm of sand. If the 20 cm of sand clogs too frequently then that would be a weakness of this design. Lastly we are depending on the layer of inlet tubes to function as a plane of filtration instead of tubes of filtration if the distance between them is significantly smaller than the distance to the outlet tubes. Modeling the layer of tubes as a single layer that has a top and bottom plane area of filtration has enabled us to greatly reduce the size of our system.