I. Objective:
To Calculate Volume and dimensions for non-pressurized Pulp stock and Water storage tanks for various designs such as Cylindrical, Square/Rectangular and Inverted milk-bottle types.
II. Cylindrical Tanks:
Cylindrical tanks are common design and stable one among other designs for both indoor and outdoor
Inlet Flow : in m3/min
Retention time : in min
H/D ratio : ratio (factor)
Location : Indoor, Outdoor
Formula-1: (Calculation of Tank
Volume from required Retention time for storage)
Retention time:
Tank
volume is decided based on required retention time which indicates how long
(minutes or hour) the tank should retain the fluid inlet flow before
overflowing. The more the retention time needed, higher the volume of tank
required. Hence, each application in the process requires different retention
time based on the particular unit operation, purpose and location.
Where
V
– Tank Volume (m3)
Q – Inlet Flow (m3/min)
Tr – Retention time (min)
Example:
Q
= 1.2 m3/min
Let
required retention time Tr = 45 min
V
= 1.2 x 45
V
= 54 m3
Formula-2: (Calculation of Tank Diameter – Cylindrical Tank)
H/D ratio:
It
is the ratio between the tank diameter and its height; and is important factor
to be considered for cylindrical tank design. In general, the recommended ratio
is between 1 to 1.5 for stability of the tank and to optimize the cost.
Where
D
– Diameter of the Tank required (m)
V – Tank Volume (m3) calculated from Formula-1
R – H/D ratio
Example:
V
= 54 m3
Let
H/D ratio ‘R’ = 1.2
D
= [(54 ÷ (2 x ∏ x 1.2))1/3]
x 2
D = 3.86 m
Calculation of Tank Heights:
Various Tank Heights:
Effective height (He) – is the actual working volume height that is demanded by the process requirement and basically, we need to have this height to have enough retention at the tank. It is the height between the pump suction and Overflow nozzle of the tank.
Controllable height (Hc)
- is the actual height set between Level transmitter and Overflow nozzle of the
tank; the DCS measures, reads and controls volume based on this height. In general,
the Level transmitter is kept above the pump suction nozzle to avoid dry-run
and cavitation of the pump.
Total height (Ht)
- is the actual height set between tank
bottom most point and to the tank roof bottom. By calculating the tank
effective height, the total height is calculated keeping enough breathing room
between overflow nozzle top and tank roof bottom (min 1.0 D of overflow pipe);
drain pipe below the pump suction nozzle; ASME codes should be referred.
Formula-3: (Calculation of Effective Tank Height – Cylindrical Tank)
He = D x
R
Where
He
– Effective Height of the Tank (m)
D – Diameter of the Tank (m) calculated from Formula-2
R – H/D ratio used in Formula-2
Example:
D
= 3.86 m
R = 1.2
He = 3.86 x 1.2
He = 4.63 m
Formula-4: (Calculation of Total Tank Height – Cylindrical Tank)
Ht = He +
(Height between overflow nozzle and tank roof bottom) + (Height between
pump suction nozzle to tank bottom)
Where
Ht
– Total Height of the Tank (m)
He – Effective Height of the Tank (m)
Factors to be considered for Cylindrical Tank design:
The
following factors to be considered when designing the cylindrical tank
1.
H/D - ratio considerations
a. Higher the ratio means higher the tank
height compared to diameter; this will help to save the footprint area occupied
by the tank. However, other factors to be considered carefully when considering
higher H/D ratio more than 1:1
b. When we increase the H/D ratio, the
tank surface area increases and it eventually increases the steel cost
c. When tank height increases the ability
of tank for self-supporting decreases; where additional tank wall support rings and stiffeners are required
d. When the tank height increases the
load on soil per square meter increases which increases the civil reinforcement
structure cost
e. Agitator design and power requirement
increases w.r.t increase in tank height
f. Hence, H/D ratio is to be optimized considering
above factors
g. Typically, larger storage tanks are
designed at 1.5 ratio or above where adequate reinforcement is to be done
h. Wind load and Seismic design loads are
other important factors to be considered
2.
Indoor
design considerations
a. When cylindrical tanks are designed
for indoor, the available floor-to-floor height will be the deciding factor for
H/D ratio
b. The primary goal when tanks are
designed for indoor would be utilizing less foot print area as the indoor
layout requires room for locating more process equipment / components
c. When the volume required permits
design of an indoor tank at H/D ratios between 1 to 1.5, it can be designed so.
However, when the available floor height limits the tank height meeting 1 to
1.5 ratio, the design can be at lower ratios. In such cases, adequate
reinforcement around the tank is to be given; and the design and location of
agitators and other nozzles to be carefully selected and in some cases there
may more than 1 agitator required to avoid localized agitation.
d. Indoor tank designs need maintenance
room between the tank roof top and next floor level to approach the top man-hole
or to maintain the top entry vertical agitators
e. In some cases, the RCC tanks are
designed enclosing the entire floor-to-floor height and manhole will be kept at
next floor operating level.
3.
Outdoor
design considerations
a. Outdoor tanks are generally larger
storage tanks of higher volume to have enough retention of stock and waters to
manage the fluctuations of operations
b. In tropical countries the larger
volume storage tanks are normally kept outside as the ambient temperature
doesn’t affect the stock or water. In countries where the temperature nears the
freezing point, complete insulation is provided to the metallic tanks.
c. Outdoor tanks can be designed at
higher H/D ratio if the volume and footprint required are major factors and in
such cases the tank wall to be designed with adequate support rings
d. The tank wall thickness will be more
at bottom level and reduces gradually when raising to top level
e. Mill ground level normally at lower
than plant indoor first floor level; the elevation between these two level is
to be considered when designing the pump heads
f. Flood level and Safety bund wall are
generally to be considered for outdoor tanks
g. Larger tanks require larger concrete
foundations; tanks of nearest volumes requirement shall be sized with same
dimensions to ease the civil construction and tank fabrication with lesser
effort and cost (for example if two filtrate water tank requires volume of 700
and 800 m3, both tanks can be designed to 800 m3)
4.
General
factors
a. Nozzles and its orientation are to be
considered to determine the tank diameter to have enough surface area to equip
required nozzles such as Pump suction, Level Transmitter, Agitator, Drain,
Manhole etc.
b. Overflow nozzles should be properly
piped to process drains
c. Area around the tank for maintenance
of the equipment connected with nozzles is another major factor to be
considered in the designing the tank
d. Tank bottom slope and its inclination
is essential to drain the tank completely during maintenance
e. Maintenance ladders are required to
inspect the tank from the top man-hole
f. Vent pipe size should be properly
sized to have adequate breathing of atmospheric storage tanks; ASME/API codes
should be followed to size the vents.
g. Tank wall thickness should be
calculated properly based on the material of construction, pressure at each level
and diameter of the tank and other factors.
III. Non-Cylindrical Tanks:
Formula-5: (Calculation
of Tank Length – Square or Rectangular Tank)
L = (V÷ (H x W))
Where
L
– Length of the Tank required (m)
V – Tank Volume (m3) calculated from Formula-1
H – Height of the Tank (m)
W – Width of the Tank (m)
Example:
V
= 54 m3
Let
Height be 4 m and Width be 3 m
L
= (54 ÷ (4 x 3))
L
= 4.5 m
Factors to be considered for Square
/ Rectangular (non-cylindrical) Tank design:
1.
Square
/ Rectangular tanks (non-cylindrical) for stock or water storage are mostly indoor
2.
Broke
pulper pit and Vacuum seal-pit tanks are most common non-cylindrical metallic tanks
in paper machine building. Stock and water tanks of stock preparation are
designed either by RCC (mostly preferred for non-cylindrical) or metallic.
3.
The
cost of the non-cylindrical design is higher than cylindrical for both metallic
and RCC material of construction
4.
The
location of the tank and space available are the factors to go with such
non-cylindrical designs
5.
These
types of tank design will help to utilize the available space and avoid
dead-pockets which normally occurs in cylindrical designs
6.
Non-cylindrical
designs agitation effect is major factor to be considered to orient the fluid
for agitation. A square design will be more effective for agitation than
rectangular shape where the chances of localized agitation and consistency variation
occurs. In some cases, more than one agitator is required
7.
Wall
thickness and Wall strengthening supports are to be considered, if the tank is
designed with metal
8.
All
design factors which are considered for cylindrical design is applicable for
non-cylindrical
IV. Inverted Milk-bottle Tanks:
Inverted milk bottle tanks are generally outdoor large storage tanks.
1.
It
consists of 3 parts namely the upper part with cylindrical shape, middle part
with truncated cone shape and bottom part with smaller cylindrical shape
2.
Larger
storage tanks need larger diameter which limits the agitation effect and affects
homogenous consistency of stock and hence ‘Inverted milk bottle’ design is chosen
to have optimized diameter at bottom part and increase the storage volume at
middle and upper parts by increasing the diameter.
3.
High
consistency stocks are preferred to store with this design of the tank
4.
This
design also saves bottom footprint of the tank which can be utilized to locate
the tank connected equipment around it.
5.
The
construction of this design takes more effort and cost than the cylindrical design
Formula-6: (Calculation
of Tank Volume – Upper part)
Upper
part is “Cylindrical” design
Vu = (∏ x Du2 x Hu ÷ 4)
Where
Vu – Tank Volume of upper part (m3)
Du – Diameter of the upper part tank (m)
Hu – Height of the upper part tank (m)
Example:
Let Du
= 8 m
Let Hu
= 15.5 m
Vu
= (∏ x 82
x 15.5 ÷ 4)
Vu = 779 m3
Formula-7: (Calculation
of Tank Volume – Middle part)
Middle
part is inverted “Truncated cone” design
Let Ru
be the radius of upper part = Du ÷ 2
Let Rb
be the radius of bottom part = Db ÷ 2
Vm = (∏ x
Hm ÷ 3) x (Ru2 + Ru
x Rb + Rb2)
Where
Vm – Tank Volume of middle part (m3))
Hm – Height of the middle part tank (m)
Ru - Radius of
upper part
Rb - Radius of bottom
part
Example:
Du
= 8 m
Ru
= 8 ÷ 2 = 4 m
Let Db
= 4 m
Rb
= 4 ÷ 2 = 2 m
Let Hm
= 5 m
Vm
= (∏ x 5 ÷ 3) x (42 + (4 x 2) + 22)
Vm
= 147 m3
Formula-8: (Calculation
of Tank Volume – Bottom part)
Bottom
part is “Cylindrical” design
Vb
= (∏ x
Db2 x Hb ÷ 4)
Where
Vb – Tank Volume of bottom part (m3)
Db – Diameter of the bottom part tank (m)
Hb – Height of the bottom part tank (m)
Example:
Db
= 4 m
Let Hb
= 6 m
Vb
= (∏ x 42
x 6 ÷ 4)
Vb = 75 m3
Formula-9: (Calculation
of Tank Volume – Total tank)
V = Vu + Vm + Vb
V – Total Volume of the tank (m3)
Vu – Tank Volume of Upper part (m3)
Vm – Tank Volume of Middle part (m3)
Vb – Tank Volume of Bottom part (m3)
Example:
V = 779 + 147 + 75
V = 1001 m3
