Chemical Engineering June 2012 - 38

Cover Story
Feature Report
Draining Vessels
Determine how long it will take for units
with flat, cone- or dish-shaped bottoms
Edward H. Steve
Chemical Engineer
T
hroughout the chemical process
industries (CPI), the need to
drain a tank or process vessel
arises. In batch-type plants, it is
a regular occurrence and is one factor
that affects the total cycle time per
batch and ultimately the entire production
capacity of the plant itself.
Some operations rely on draining a
freely flowing Newtonian liquid from
a process vessel to another vessel or to
elsewhere without the assistance of a
pump. This article develops the equations
that a process engineer can use
to easily estimate the time required
for draining a vertical, cylindrical process
vessel with a flat bottom, a cone
bottom or an ASME F&D (dish) bottom.
Unlike other articles on the subject
[1], this one includes the effect of
the connected drain line.
Using the equations and the examples
in this article, the reader can
construct an Excel spreadsheet for
repeating the calculations to estimate
the approximate drain times for a series
of cylindrical, cone-bottom and
dish-bottom tanks.
Tanks with other head styles and
horizontal and non-cylindrically
shaped tanks are not considered here.
Meanwhile, this article does not deal
with special fluids such as slurries or
non-Newtonian liquids.
FLAT BOTTOM
Equation and its basis
Figure 1 shows the height of liquid
(h) above the outlet nozzle of a vertical
cylindrical flat-bottom tank during
draining. The liquid is flowing into
the outlet nozzle (point 1) located at x
distance above the bottom of the tank
and through a pipeline to some terminus
(point 2). Equations in this article
are based on the assumption that the
hL
∆Z
FIGURE 1. In a vertical
cylindrical, lat-bottom
tank, liquid is lowing
into the outlet nozzle
(point 1) located at x distance above
the bottom of the tank and through a
pipeline to some terminus (point 2)
Z2
Pt
2
size of the pipeline is the same size as
the outlet nozzle and does not change
between points 1 and 2. The pressures
above the liquid in the tank and at the
terminus are both Pt.
Before draining begins, the liquid
fills the tank to some initial height (hi)
above the outlet nozzle. If the inside
surface of the outlet nozzle is aligned
with the inside surface of the tank bottom
as shown in Figure 2, distance x
is zero and hi incorporates the entire
contents of the tank. As draining progresses,
h decreases.
The Bernoulli Equation applies to
the flow in the pipeline between points
1 and 2:
(1)
This article assumes isothermal flow,
so the liquid density remains unchanged;
because the pipeline size does
not change, the velocities at points 1
and 2 are the same. Thus, Equation (1)
can be rearranged as follows:
hL = ∆Z + [(144 /ρ ) (P1 - P2)]
(2)
The ∆Z term is the change in elevation
of the discharge pipeline and is a
fixed value.
Because P1 = Pt + (hρ/144) and P2 =
Pt, Equation (2) becomes:
hL = ∆Z + h
(3)
Equation (3) indicates that the friction
caused by flow in the pipeline between
points 1 and 2 consumes the entire
34 CHEMICAL ENGINEERING WWW.CHE.COM JUNE 2012
Tank bottom
X
Tank side wall
h
Z1
1
D
Pt
FIGURE 2. If the inside surface
of the outlet nozzle is
aligned with the inside surface of the
tank bottom as shown here, distance x is
0 and hi incorporates the entire contents
of the tank
Drain nozzle
static pressure represented by ∆Z +
h. Note that hL also decreases during
draining because differentiating
Equation (3) gives the following:
dhL = dh
(4)
A basic material balance applies to developing
the equation needed to predict
the drain time for the tank:
In - Out = Accumulation
Because no liquid is being added to
the tank, In = 0.
Out is the rate of liquid discharge
from the outlet pipeline and is given
by [3]:
Q = 19.65 d2 (hL/K)0.5
(5)
Because hL decreases during draining,
Q decreases as well. Therefore, the
Reynolds Number (NRe) in the pipeline
also changes during draining.
The K in Equation (5) is the total resistance
to flow and is the sum of four
individual resistances:
K = KEntrance + KValves&Fittings
+ KPipe + KExit
(6)
The values for two of the resistances
in Equation (6) are found in the litera
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