Charts give vapor loss from internal
floating-roof tanks 558
Estimating the contents of horizontal cylindrical tanks 560
How to gauge a horizontal cylindrical tank 561
Use nomograph to find tank capacity 561
Correct the volume of light fuels from actual temperature to
a base of 600F 563
Volume of liquid in vertical cylindrical tanks 563
Chart gives tank's vapor formation rate 563
Hand-held calculator program simplifies dike computations 564
Charts give vapor loss from internal floating-roof tanks
S. Sivaraman, Exxon Research & Engineering Co., Florham Park, N J .
Nomographs, based on the guidelines presented in have been used in the preparation of these nomographs. In
American Petroleum Institute (API) Publication No. 2519, addition, for the calculations of the evaporation loss for the
have been constructed to estimate the average evaporation bolted deck design, a typical deck seam loss factor value of
loss from internal floating-roof tanks.1 Loss determined from 0.2 has been assumed.
the charts can be used to evaluate the economics of seal Table 1 gives the proper axis to use for various seal designs
conversion and to reconcile refinery, petrochemical plant, and fits.
and storage terminal losses.
The losses represent average standing losses only. They do
not cover losses associated with the movement of product
Selection of seal axis
into or out of the tank.
The average standing evaporation loss from an internal Seal axis
floating-roof tank depends on: Seal type Average fit Tight fit
• Vapor pressure of the product Vapor-mounted primary seal only H G
• Type and condition of roof seal Liquid-mounted primary seal only F E
• Tank diameter Vapor-mounted primary seal plus
• Type of fixed roof support secondary seal D C
Liquid-mounted primary seal plus
The nomographs (Figures 1-4) can estimate evaporation secondary seal B A
loss for product true vapor pressures (TVP) ranging from 1.5
to 14 psia, the most commonly used seals for average and tight
fit conditions, tank diameters ranging from 50-250 ft, welded
Use of these nomographs is illustrated by the following
and bolted designs, and both self-supporting and column-
supported fixed roof designs. The charts are purposely
limited to tank diameters 250 ft and less, because internal
Example. Determine the evaporation loss for an internal
floating-roof tanks are generally below this diameter.
floating roof tank given the following:
Typical values of the deck fitting loss factors presented
as a function of tank diameters in the API Publication 2519 • Tank diameter 200 ft
TYPE AND CONDITION OF SEAL (REFER TO TABLE 1|
Evaporation loss, bbl/year (x 1 for refined stocks, x 0.4 for crude oil)
Figure 1. Loss from welded deck, self-supporting
TYPE AND CONDITION OF SEAL (REFER TO TABLE 1)
Evaporation loss, bbl/year ( x 1 for refined stocks, x 0.4 for crude oil)
Figure 2. Welded deck, column-supported
TVPE ANO CONDITION OF SEAL (REFER TO TABLE 1)
Evaporation loss, bbl/year (x 1 for refined stocks, x 0.4 for crude oil)
Figure 3. Bolted deck, self-supporting
• Liquid-mounted primary seal only and an average Solution
• Product true vapor pressure of 10 psia 1. Use Figure 1 for the welded deck and self-supporting
• Welded deck with self-supporting fixed roof fixed roof.
TYPE ANO CONDITION OF SEAL (REFER TO TABLE 1)
Evaporation loss, bbl/year (x 1 for refined stocks, x 0.4 for crude oil)
Figure 4. Bolted deck, column-supported
2. From Table 1 select the seal axis. The seal axis for the Read the evaporation loss in bbl/year at Ll. The average
example problem is F. evaporation loss is 188 bbl/year for this example. The same
3. Locate the point of intersection F l between the seal axis example is shown in Figures 2, 3, and 4 for other deck
F and the tank diameter contour for the 200-ft diameter designs and roof supports.
4. From the point F l traverse horizontally to intersect the Source
reference axis R at Rl.
Oil & Gas Journal, March 9, 1987.
5. Locate the true vapor pressure point Pl corresponding
to lOpsia on the pressure axis P.
6. Connect the point Rl on the reference axis R and the
point Pl on the pressure axis P and extend in to inter- 1. quot;Evaporation Loss from Internal Floating-Roof Tanks,quot;
sect the evaporation loss axis L at Ll. American Petroleum Institute Publication No. 2519.
Estimating the contents of horizontal cylindrical tanks
Horizontal cylindrical tanks are frequently used for water second line through the known point on the quot;length of tankquot;
and fuel storage, and in many cases it is important to be able scale and read the intercept on the quot;gallons (or barrels) in
to gauge these vessels to determine the volume of liquid total lengthquot; scale.
contained in them. However, it is normally much more
difficult to establish a volume-per-inch scale for a horizontal Example. Find the volume of liquid contained in a
tank than for one in a vertical position. The accompanying horizontal cylindrical tank 7 ft in diameter and 20 ft long
nomograph simplifies this problem. when the depth of the liquid is 4 ft, 10.8 in.
To use the nomograph, it is necessary to gauge the tank The ratio of depth of liquid to tank diameter is:
and determine the ratio of the depth of liquid in the tank
58.8/84 = 0.70
to the tank diameter. After this is found, draw a straight line
from the point on the quot;ratioquot; scale through the known point Connect 0.70 on the ratio scale with 7 ft on the diameter
on the quot;diameter of tankquot; scale and read the intercept on scale and continue the straight line to obtain the intercept
the quot;gallons per ft of lengthquot; scale. From this point, draw a 215 on the gallons per ft of length scale. Draw a second line
Ratio- Depth Of Liquid To Diameter
Barrels Per Foot Of Length
Gallons Per Foot Of Length
Barrels In Total Length
Gallons In Total Length
How to gauge a horizontal cylindrical tank
Express the depth in % of the diameter; then the result Rule 2. For depth between 30 and 50; subtract 10 from
will be given in % of total capacity of the tank. the depth, multiply by 1.25.
Example. Liquid depth is 44% of tank diameter
Rule 1. For depth up to 30; multiply the square root of
the depth by the depth, and then by 0.155. (44 - 10) x 1.25 = 34 x 1.25 = 42.5%
The correct answer is 42.4%.
Example. Liquid depth is 16% of tank diameter The maximum error for depths less than 5% may be as great
as 10%; gauging in this range is always difficult, and a very
16 x 16 x 0.155 = 4 x 16 x 0.155 = 9.9% small slope can introduce a much larger error than this. When
the depth is greater than 50%, apply the same rule to get the
The correct answer is 10.3%; error is about .4%. volume of the empty space above the fluid, and subtract.
Use nomograph to find tank capacity
This simple nomograph can be used to find the capacity of Draw a straight line from the quot;heightquot; scale through the
your vertical cylindrical tanks. Here's how it works: quot;diameterquot; scale and to the first quot;capacity, barrelsquot; scale.
Read directly the capacity of the tank in barrels. (Note: The Capacity, barrels = 0.1399 (diameter)2 (height),
quot;heightquot; scale may be used to indicate the overall height of units in ft
the tank or the depth of liquid in the tank.)
Draw a second straight line connecting the two quot;capacity, 6. The quot;capacity, gallonsquot; scale is based on four log cycles
barrelsquot; scales at the same reading on each scale. Read the per 10 in. The initial point on the scale is determined as
capacity of the tank in gallons and cubic ft on the proper follows:
The nomograph was constructed as follows: 20 barrels x 42 gallons per barrel — 840 gallons
1. The quot;heightquot; scale is based on two log cycles per 10 in. The range of the scale is 900 to 6 million gal.
with a range of 1-60 ft.
2. The quot;capacity, barrelsquot; scale is based on four log cycles 7. The quot;capacity, cubic feetquot; scale is based on four log cycles
per 10 in. with a range of 20-150,000 barrels. per 10 in. The initial point on the scale is determined as
3. The quot;diameterquot; scale is based on three log cycles per follows:
10 in. with a range of 4-150 ft.
4. The distance between the height and diameter scales is 20 barrels x 5.6146 cu. ft per barrel
exactly two-thirds the distance between the height and
= 112.292 cu. ft
quot;capacity, barrelsquot; scale.
5. Determine points to locate the diameter scale from the
The range of the scale is 120 to 800,000 cu. ft.
CAPACITY, Cubic Feet
Correct the volume of light fuels from actual temperature to a base of 600F
To approximate quickly the volume of gasoline or other
light liquid fuel at 60 0 F from a known volume at any tem-
perature in the atmospheric range, use the formula:
V a - V 6 0 = 0.0006(T-6O)V 60
where: Va = Volume at actual temperature
V60 = Volume corrected to 60 0 F
Ta = Actual temperature of fuel
Example. A tank contains 5,500 gallons of gasoline at
46°F. Correct the volume to a base of 60 0 F.
(5,500-V 60 ) = 0.0006(46-6O)V60 To approximate the shrinkage or expansion, obtain the
(5,500-V 60 ) = 0.0006(-14)V60 difference between the actual volume measured and the
5,500 = V 60 -0.0084V 60 corrected volume. In this case:
5,500 = 0.9916V60
Volume at 60 0 F = 5,546.6 gallons Shrinkage = 5,546.6 - 5,500 = 46.6 gallons
Volume of liquid in vertical cylindrical tanks
Measure the depth of the liquid and either the diameter or supplant the results of accurate tank strapping, which take
circumference of the tank, then the volume in: many other factors into account.
Gallons = 0.0034 d2h or 0.00034 c2h Example. How many gallons will a tank 12 ft in diameter
Barrels = 0.000081 d2h or 0.00082 c2h and 16 ft high hold when full?
Gallons =5.88 D 2 H or 0.595C 2 H
Barrels = 0.140 D 2 H or 0.0142 C 2 H Gallons =5.88 D 2 H
where: d = Diameter, inches = 13,548 gallons
c= Circumference, inches
h= Depth, inches Example. How many barrels will a tank 8 ft in diameter
D= Diameter, feet and 16 ft high hold when full?
C= Circumference, feet
H= Depth, feet Barrels = 0.140 D 2 H
If the circumference is measured on the outside, then three = (0.140)(64)(16)
times the thickness of the tank wall should be subtracted = 143 barrels
before using the formula. Naturally, these rules cannot
Chart gives tank's vapor formation rate
When sizing the vapor piping for a manifolded expansion- Example. Determine the rate of formation of vapor in a
roof tank system, the rate of vapor formation must be known. 140,000 barrel capacity tank when it is filled at the rate of
While the rate of vapor formation can be computed by 8,000 barrels per hour.
longhand methods, the calculation is tedious and takes much
valuable time. Solution. Enter the chart on the left at a capacity of
140,000 barrels and draw a straight line through the filling
rate of 8,000 barrels per hour on the right. At the intersection
BBL PER HR
T A N K C A P A C I T Y , 1000's
VAPOR FORMED, l O O O ' s
FILLING R A T E , lOOO's
with the central scale read the vapor formation rate as 55,000 This chart is based on the following equation:
cu. ft per hour. The vapor piping for this tank would have to
be designed for this formation rate if the maximum filling
rate anticipated were 8,000 barrels per hour. But if a great
filling rate were expected, the vapor formed would have to
be computed for the higher rate. The chart could, of course,
also be used for this computation. where V = vapor formed, cubic feet per hour
Hand-held calculator program simplifies dike computations
Calculating height of earthen dikes around above-ground storage can be done easily with a program for a
Frank E. Hangs, Sovereign Engineering Co., Houston environment and to reduce the likelihood of fire spreading
from one tank to another.
Earthen dikes are widely used all over the world to contain Sizing dikes by conventional methods is a time-consuming,
flammable volumes of above-ground storage. They perform trial-and-error process. A complete assessment of the
two vital functions: to prevent loss of fluid into the problem involves: applicable codes and regulations; land
DD, S, LS or SS.
Dike volume DH
Grade Lower base
DHX run DWB
Figure 1. Cross section of a typical dike.
area available; topography of the area; soil characteristics; EXfiKPLE 1 EXfiHPLE 2
and the stipulated volume contained by dike and other
dimensions of the dike section.
The following program for the HP-41CV hand-held
calculator enables one to enter required data at a prompt
and to calculate the height of the dike to retain the
required volume of fluid, cross section of dike, width of
the base, and the cubic yards of earth required, quickly.
When a printer is available, a record of the input and
output (results) is made. Without a printer, the input and
output items (all identified) can be displayed one at a time
and advanced at will.
Many quot;what ifquot; questions can be answered readily, and
different configurations compared as desirable. This is
explained in detail in text and examples.
The Flammable and Combustible Liquids Code, as
promulgated by the National Fire Protection Association,
NFPA No. 30, is used as a basis for this program. Important
• Volume contained in dike area shall not be less than the
full tank. (We have taken one tank per dike.)
• For crude petroleum with boilover characteristics,
stored in fixed roof tanks, the contained volume above
shall be calculated by deducting the volume of the tank
below the height of the dike.
• Earthen dikes 3 ft or more in height shall have a flat
section at the top not less than 2 ft wide.
• The slope of the earth wall shall be consistent with the
natural angle of repose of the material of construction.
• The walls of the diked area shall be restricted to an
average height of 6 ft above interior grade.
Dikes are constructed in circular, square, or rectangular
configurations. For the purposes of this program, the
volumes contained in the dikes are calculated as invented
frustums of a cone or pyramid. The dike volume Figure 2. Examples of the dike computation program for the
(converted to barrels) is compared to the total volume HP-41CV hand-held calculator.
Legend and storage a. Subroutine for calculating boilover vol- larger volume.) Press quot;A,quot; re-enter DD (330).
registers ume, Results: DH = 4.25 ft. larger X-SECT, MORE
REG. b. Sets flag 00 for boilover calculations. EARTH, a boilover volume is shown and in-
TV = Tank vol. (bbl) 00 DV = Dike vol. (bbl) 16 cluded in total volume.
TOT BBL = Total bbl TV X-SECT = Cross sect, dike (sq ft) 18 Example 3: Same tank, no boilover, what is
+ boilover (if DWB = Dike width base (ft) 19 DD for 4.5 ft. dike? CF 00 (Notice it appears in
needed) 01 FORMULA: For right truncated cone or pyra- annunciator when set). SF 01 (This is not a
TD = Tank dia (ft) 02 mid: looping routine!) RCL 00 STO 01, 0.00 STD
TH = Tank height (ft) 03 24. STO 4.5 in 07. Press quot;Aquot;; put some value
Run = For angle of repose V =-(A+ VABTB) for DD less than 330 (as above). Try 300 key
of dike earth ex- in and R/S. One calculation will be made.
pressed as bevel Compare total volume and dike volume.
H = Height; A = Area of larger base,
Rise/Run = 1/Run, Press quot;Aquot; and key new DD. Repeat until sat-
B = Area of smaller base.
1/1.5 is widely used 04 isfactory convergence is achieved.
DWT = Dike width top—ft (See Fig. 1.) The following table shows convergence for
Min. 2 ft for dikes 3 Example 3:
ft and higher— Dia or side of top base = (DD, S, LS or
NFPA No. 30. 05 SS) - DWT Total vol 54,200 bbl DH = 4.5 ft.
DH INCR = Dike height incre- Dia or side of lower base = (DD, S, LS or
ment Suggest 0.10 SS) - DWT -2(DH x Run.) Trial DD ft DV bbl
ft for prelim, run; 300 53,406.62
Use 0.05 ft (0.60-in.) USER INSTRUCTIONS 305 55,255.73
to finalize 06 1) Put dike program in calculator. 302 54,142.48
TRIAL DH = Trial dike height (ft) 2) XEQ size 25 and set User Mode. 302.5 54,727.24
Try 3 ft for tanks 3) XEQ quot;Dike.quot; 302.3 54,253.30
10,000 bbl and 4) Key in data according to prompts and R/S.
larger 07 It is evident that with a few iterations, one can
Notice Run = 1.5? and DWT = 2? If these home-in on a precise solution.
DD = Dike dia (ft) 10 values are acceptable, key in and R/S. DH
EARTH YD3 = Dike vol. (cu yd) 20 INCR = ? Can be 0.10 ft for preliminary
SQ = Square side (ft) 21 SUMMARY
runs, otherwise, use 0.05 ft (0.60-in.).
LS = Long side (rectan- Trial DH = ? Try 3 ft. If this is too much, For a new tank size, one should XEQ quot;Dikequot;
gle) ft 22 machine will stop, STO smaller value in and enter data according to prompts.
SS = Short side (rectan- R07 and try again (quot;A,quot; quot; B quot; or quot;Cquot;). Like- Subroutines quot; B quot; and quot; C quot; are similar to quot;A.quot;
gle) ft 23 One can build up a dike height for given cen-
wise, if it is known that DH is much greater
BO BBL = Boilover barrels 24 ter line distances (square or rectangle) with
than 3—try larger value: This saves itera-
Registers 8, 9, 13 and 17 not used. and without boilover.
Registers 11, 12, 14 and 15 scratch. Consider same tank as Example 1. (Let
A? Key in quot;Aquot; for circular dikes (Be sure
FLAGS User Mode!) 3 = Trial DH STO 07.)
B? Key in quot; B quot; for square dikes. (Be sure Square 300 ft (No B.O)
01—Single calculation User Mode!) Square 300 ft B.O.
02—Circular dike C? Key in quot; C quot; for rectangular dikes. (Be sure DH = 3.60
03—Square dike User Mode!) DV = 54,894.66
04—Rectangular dike Boilover? Y? N? DH = 4.05
21—Printer enables following: Allows data This routine is available when needed. DV = 61,473.78
and results to be displayed one by one Usually answer is no. Press quot; N quot; and R/S. Total volume = 61,055.09
without printer. (Must be set each time Whichever key A, B, or C is pressed, a dia or Rectangle LS 450: SS 200 (3.00 STO 07)
calculator is turned on.) side(s) will be called for; key in appropriate LS 450: SS 200 B.O.
Note: Flags 01 and 21 must be manually set. data and calculator will converge DV with to- H—3.60 DV = 54,655.16 DH = 4.10
Flag 01—Clear manually—other flags tal barrels for solution of DH (See Fig. 2). DV = 61,900.04
set and cleared in program. See Exam- Example 1: Illustrates a 54,200-bbl tank in a Total volume = 61,139.72
ple 3 for quot;short cutquot; exceptions. circular dike. Notice how data are entered ac- One can quot;free-wheelquot; with quot; B quot; and quot; C quot; as
cording to prompts. A printer is a great con- for quot;Aquot; for a fixed dike height. SF 01 and try
PRINCIPAL LABELS venience but is not indispensible. Without
different dike centerline distances. Compare
01—Calculates X-SECT and DWB; directs printer, SF 21 each time calculator is turned
DV and TOT. VaI. and continue to desired con-
program to proper EARTH VOLUME rou- on, now data and results will be displayed one
tine, i.e., SQ ? etc. vergence.
at time and advanced by pressing R/S key.
03, 11 and 13 Bypass incrementation in a Notice formating of data and results—zeros Warning: Be sure Flag 00 is clear when
loop for a single calculation are shown for inactive dimensions or boilover boilover routine is not required. When clear-
06, 07 and 08 Calculates EARTH VOLUME volume. ing Flag 00 STD 0.00 in 24 to prevent extrane-
for A, B, and C, respectively. Example 2: Demonstrates an approach, ous volume from being involved in program.
09 Summarizes data and results for display or where most input data do not change: Calcu- BO VOL should be 0.00 when there is no
printout. late DH for above tank for boilover crude. boilover. Flat 01 must be clear for increment-
A, B and C Subroutines for circular, square (This avoids going through entering routine ing routines. Always STO new trial DH in 07
and rectangular dikes, respectively, calcu- XEQ Dike.) SF 00 and a new trial DH try 4, each run.
lating dike volumes for DH increments to STO 07. (Result of Example 1 is DH = 3.75 ft. Note: XEQ 09 for printout or display of input
converge dike volume and total volume. It is evident dike will be higher to contain and results in storage registers.
(volume of tank or volume of tank plus boilover, volume the program loops, increment DH for the next
if applicable). The calculations begin with given dike calculation. When the two volumes converge, calculations
centerline, dike width at top, repose angle of soil, and trial stop and input data and results are displayed or printed.
DH. As long as the dike volume is less than the total The DH value, when the volumes converge, is the solution.
In some cases, it will be required to ascertain dike diam- This program is based on the site being essentially level.
eter or sides for a fixed dike height (DH). This is
accomplished by storing DH Value in 07, setting Flag Ol
(for single calculation). Press quot;A,quot; quot;B,quot; or quot;Cquot; key in Source
trial centerline distances. The results of any calculation give
one an opportunity to compare total barrels with dike Pipe Line Industry, August 1986.
volume. Then alter centerline distances to fit trend and
continue. See Example 3.