Charts give vapor loss from internalfloating-roof tanks 558Estimating the contents of horizontal cylindrical tanks 560How to gauge a horizontal cylindrical tank 561Use nomograph to find tank capacity 561Correct the volume of light fuels from actual temperature to

a base of 600F 563Volume of liquid in vertical cylindrical tanks 563Chart gives tank's vapor formation rate 563Hand-held calculator program simplifies dike computations 564

18: Tanks

Nomographs, based on the guidelines presented inAmerican Petroleum Institute (API) Publication No. 2519,have been constructed to estimate the average evaporationloss from internal floating-roof tanks.1 Loss determined fromthe charts can be used to evaluate the economics of sealconversion and to reconcile refinery, petrochemical plant,and storage terminal losses.

The losses represent average standing losses only. They donot cover losses associated with the movement of productinto or out of the tank.

The average standing evaporation loss from an internalfloating-roof tank depends on:

• Vapor pressure of the product• Type and condition of roof seal• Tank diameter• Type of fixed roof support

The nomographs (Figures 1-4) can estimate evaporationloss for product true vapor pressures (TVP) ranging from 1.5to 14 psia, the most commonly used seals for average and tightfit conditions, tank diameters ranging from 50-250 ft, weldedand bolted designs, and both self-supporting and column-supported fixed roof designs. The charts are purposelylimited to tank diameters 250 ft and less, because internalfloating-roof tanks are generally below this diameter.

Typical values of the deck fitting loss factors presentedas a function of tank diameters in the API Publication 2519

have been used in the preparation of these nomographs. Inaddition, for the calculations of the evaporation loss for thebolted deck design, a typical deck seam loss factor value of0.2 has been assumed.

Table 1 gives the proper axis to use for various seal designsand fits.

Table 1Selection of seal axis

Seal axis

Seal type Average fit Tight fit

Vapor-mounted primary seal only H GLiquid-mounted primary seal only F EVapor-mounted primary seal plus

secondary seal D CLiquid-mounted primary seal plus

secondary seal B A

Use of these nomographs is illustrated by the followingexample.

Example. Determine the evaporation loss for an internalfloating roof tank given the following:

• Tank diameter 200 ft

Figure 1. Loss from welded deck, self-supportingfixed roofs.

Charts give vapor loss from internal floating-roof tanks

S. Sivaraman, Exxon Research & Engineering Co., Florham Park, NJ .

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SEAL AXIS

TYPE AND CONDITION OF SEAL (REFER TO TABLE 1|

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Reference AxIt

SEAL AXIS

TYPE AND CONDITION OF SEAL (REFER TO TABLE 1)

Figure 2. Welded deck, column-supportedfixed roofs.

Figure 3. Bolted deck, self-supportingfixed roofs.

SEAL AXIS

TVPE ANO CONDITION OF SEAL (REFER TO TABLE 1)

• Liquid-mounted primary seal only and an averageseal fit

• Product true vapor pressure of 10 psia• Welded deck with self-supporting fixed roof

Solution

1. Use Figure 1 for the welded deck and self-supportingfixed roof.

2. From Table 1 select the seal axis. The seal axis for theexample problem is F.

3. Locate the point of intersection F l between the seal axisF and the tank diameter contour for the 200-ft diametertank.

4. From the point F l traverse horizontally to intersect thereference axis R at Rl.

5. Locate the true vapor pressure point Pl correspondingto lOpsia on the pressure axis P.

6. Connect the point Rl on the reference axis R and thepoint Pl on the pressure axis P and extend in to inter-sect the evaporation loss axis L at Ll.

Estimating the contents of horizontal cylindrical tanks

Horizontal cylindrical tanks are frequently used for waterand fuel storage, and in many cases it is important to be ableto gauge these vessels to determine the volume of liquidcontained in them. However, it is normally much moredifficult to establish a volume-per-inch scale for a horizontaltank than for one in a vertical position. The accompanyingnomograph simplifies this problem.

To use the nomograph, it is necessary to gauge the tankand determine the ratio of the depth of liquid in the tankto the tank diameter. After this is found, draw a straight linefrom the point on the "ratio" scale through the known pointon the "diameter of tank" scale and read the intercept onthe "gallons per ft of length" scale. From this point, draw a

Read the evaporation loss in bbl/year at Ll. The averageevaporation loss is 188 bbl/year for this example. The sameexample is shown in Figures 2, 3, and 4 for other deckdesigns and roof supports.

Source

Oil & Gas Journal, March 9, 1987.

Reference

1. "Evaporation Loss from Internal Floating-Roof Tanks,"American Petroleum Institute Publication No. 2519.

second line through the known point on the "length of tank"scale and read the intercept on the "gallons (or barrels) intotal length" scale.

Example. Find the volume of liquid contained in ahorizontal cylindrical tank 7 ft in diameter and 20 ft longwhen the depth of the liquid is 4 ft, 10.8 in.

The ratio of depth of liquid to tank diameter is:

58.8/84 = 0.70

Connect 0.70 on the ratio scale with 7 ft on the diameterscale and continue the straight line to obtain the intercept215 on the gallons per ft of length scale. Draw a second line

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SEAL AXIS

TYPE ANO CONDITION OF SEAL (REFER TO TABLE 1)

Figure 4. Bolted deck, column-supportedfixed roofs.

How to gauge a horizontal cylindrical tank

Express the depth in % of the diameter; then the resultwill be given in % of total capacity of the tank.

Rule 1. For depth up to 30; multiply the square root ofthe depth by the depth, and then by 0.155.

Example. Liquid depth is 16% of tank diameter

16 x 16 x 0.155 = 4 x 16 x 0.155 = 9.9%

The correct answer is 10.3%; error is about .4%.

Use nomograph to find tank capacity

This simple nomograph can be used to find the capacity ofyour vertical cylindrical tanks. Here's how it works:

Rule 2. For depth between 30 and 50; subtract 10 fromthe depth, multiply by 1.25.

Example. Liquid depth is 44% of tank diameter

(44 - 10) x 1.25 = 34 x 1.25 = 42.5%

The correct answer is 42.4%.The maximum error for depths less than 5% may be as great

as 10%; gauging in this range is always difficult, and a verysmall slope can introduce a much larger error than this. Whenthe depth is greater than 50%, apply the same rule to get thevolume of the empty space above the fluid, and subtract.

Draw a straight line from the "height" scale through the"diameter" scale and to the first "capacity, barrels" scale.

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Read directly the capacity of the tank in barrels. (Note: The"height" scale may be used to indicate the overall height ofthe tank or the depth of liquid in the tank.)

Draw a second straight line connecting the two "capacity,barrels" scales at the same reading on each scale. Read thecapacity of the tank in gallons and cubic ft on the properscales.

The nomograph was constructed as follows:

1. The "height" scale is based on two log cycles per 10 in.with a range of 1-60 ft.

2. The "capacity, barrels" scale is based on four log cyclesper 10 in. with a range of 20-150,000 barrels.

3. The "diameter" scale is based on three log cycles per10 in. with a range of 4-150 ft.

4. The distance between the height and diameter scales isexactly two-thirds the distance between the height and"capacity, barrels" scale.

5. Determine points to locate the diameter scale from thefollowing equation:

Capacity, barrels = 0.1399 (diameter)2 (height),

units in ft

6. The "capacity, gallons" scale is based on four log cyclesper 10 in. The initial point on the scale is determined asfollows:

20 barrels x 42 gallons per barrel — 840 gallons

The range of the scale is 900 to 6 million gal.

7. The "capacity, cubic feet" scale is based on four log cyclesper 10 in. The initial point on the scale is determined asfollows:

20 barrels x 5.6146 cu. ft per barrel

= 112.292 cu. ft

The range of the scale is 120 to 800,000 cu. ft.

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Correct the volume of light fuels from actual temperature to a base of 600F

To approximate quickly the volume of gasoline or otherlight liquid fuel at 600F from a known volume at any tem-perature in the atmospheric range, use the formula:

V a - V 6 0 = 0.0006(T-6O)V60

where: Va = Volume at actual temperatureV60 = Volume corrected to 600FTa = Actual temperature of fuel

Example. A tank contains 5,500 gallons of gasoline at46°F. Correct the volume to a base of 600F.

(5,500-V60) = 0.0006(46-6O)V60

(5,500-V60) = 0.0006(-14)V60

5,500 = V60-0.0084V60

5,500 = 0.9916V60

Volume at 600F = 5,546.6 gallons

Volume of liquid in vertical cylindrical tanks

Measure the depth of the liquid and either the diameter orcircumference of the tank, then the volume in:

Gallons = 0.0034 d2h or 0.00034 c2hBarrels = 0.000081 d2h or 0.00082 c2hGallons =5.88 D2H or 0.595C2HBarrels = 0.140 D2H or 0.0142 C2H

where: d = Diameter, inchesc = Circumference, inchesh = Depth, inches

D = Diameter, feetC = Circumference, feetH = Depth, feet

If the circumference is measured on the outside, then threetimes the thickness of the tank wall should be subtractedbefore using the formula. Naturally, these rules cannot

Chart gives tank's vapor formation rate

When sizing the vapor piping for a manifolded expansion-roof tank system, the rate of vapor formation must be known.While the rate of vapor formation can be computed bylonghand methods, the calculation is tedious and takes muchvaluable time.

Shrinkage

To approximate the shrinkage or expansion, obtain thedifference between the actual volume measured and thecorrected volume. In this case:

Shrinkage = 5,546.6 - 5,500 = 46.6 gallons

supplant the results of accurate tank strapping, which takemany other factors into account.

Example. How many gallons will a tank 12 ft in diameterand 16 ft high hold when full?

Gallons =5.88 D2H

= (5.88)(144)(16)

= 13,548 gallons

Example. How many barrels will a tank 8 ft in diameterand 16 ft high hold when full?

Barrels = 0.140 D2H

= (0.140)(64)(16)

= 143 barrels

Example. Determine the rate of formation of vapor in a140,000 barrel capacity tank when it is filled at the rate of8,000 barrels per hour.

Solution. Enter the chart on the left at a capacity of140,000 barrels and draw a straight line through the fillingrate of 8,000 barrels per hour on the right. At the intersection

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with the central scale read the vapor formation rate as 55,000cu. ft per hour. The vapor piping for this tank would have tobe designed for this formation rate if the maximum fillingrate anticipated were 8,000 barrels per hour. But if a greatfilling rate were expected, the vapor formed would have tobe computed for the higher rate. The chart could, of course,also be used for this computation.

This chart is based on the following equation:

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 aportable calculator

Frank E. Hangs, Sovereign Engineering Co., Houston

Earthen dikes are widely used all over the world to containflammable volumes of above-ground storage. They performtwo vital functions: to prevent loss of fluid into the

environment and to reduce the likelihood of fire spreadingfrom one tank to another.

Sizing dikes by conventional methods is a time-consuming,trial-and-error process. A complete assessment of theproblem involves: applicable codes and regulations; land

DD, S, LS or SS.

DHX run DWB

DWT

Run

Grade

Dike volume

Lower base

DH

DWTTop base

Tank

Figure 1. Cross section of a typical dike.

area available; topography of the area; soil characteristics;and the stipulated volume contained by dike and otherdimensions of the dike section.

The following program for the HP-41CV hand-heldcalculator enables one to enter required data at a promptand to calculate the height of the dike to retain therequired volume of fluid, cross section of dike, width ofthe base, and the cubic yards of earth required, quickly.When a printer is available, a record of the input andoutput (results) is made. Without a printer, the input andoutput items (all identified) can be displayed one at a timeand advanced at will.

Many "what if" questions can be answered readily, anddifferent configurations compared as desirable. This isexplained in detail in text and examples.

The Flammable and Combustible Liquids Code, aspromulgated by the National Fire Protection Association,NFPA No. 30, is used as a basis for this program. Importantstipulations are:

• Volume contained in dike area shall not be less than thefull tank. (We have taken one tank per dike.)

• For crude petroleum with boilover characteristics,stored in fixed roof tanks, the contained volume aboveshall be calculated by deducting the volume of the tankbelow the height of the dike.

• Earthen dikes 3 ft or more in height shall have a flatsection at the top not less than 2 ft wide.

• The slope of the earth wall shall be consistent with thenatural angle of repose of the material of construction.

• The walls of the diked area shall be restricted to anaverage height of 6 ft above interior grade.

Dikes are constructed in circular, square, or rectangularconfigurations. For the purposes of this program, thevolumes contained in the dikes are calculated as inventedfrustums of a cone or pyramid. The dike volume(converted to barrels) is compared to the total volume

EXfiKPLE 1 EXfiHPLE 2

Figure 2. Examples of the dike computation program for theHP-41CV hand-held calculator.

DIKE PROGRAM

Legend and storageregisters

REG.TV = Tank vol. (bbl) 00

TOT BBL = Total bbl TV+ boilover (if

needed) 01TD = Tank dia (ft) 02TH = Tank height (ft) 03

Run = For angle of reposeof dike earth ex-pressed as bevelRise/Run = 1/Run,1/1.5 is widely used 04

DWT = Dike width top—ftMin. 2 ft for dikes 3ft and higher—NFPA No. 30. 05

DH INCR = Dike height incre-ment Suggest 0.10ft for prelim, run;Use 0.05 ft (0.60-in.)to finalize 06

TRIAL DH = Trial dike height (ft)Try 3 ft for tanks10,000 bbl andlarger 07

DD = Dike dia (ft) 10EARTH YD3 = Dike vol. (cu yd) 20

SQ = Square side (ft) 21LS = Long side (rectan-

gle) ft 22SS = Short side (rectan-

gle) ft 23BO BBL = Boilover barrels 24

Registers 8, 9, 13 and 17 not used.Registers 11, 12, 14 and 15 scratch.

FLAGS00—Boilover calculation01—Single calculation02—Circular dike03—Square dike04—Rectangular dike21—Printer enables following: Allows data

and results to be displayed one by onewithout printer. (Must be set each timecalculator is turned on.)

Note: Flags 01 and 21 must be manually set.Flag 01—Clear manually—other flagsset and cleared in program. See Exam-ple 3 for "short cut" exceptions.

PRINCIPAL LABELS01—Calculates X-SECT and DWB; directs

program to proper EARTH VOLUME rou-tine, i.e., SQ ? etc.

03, 11 and 13 Bypass incrementation in aloop for a single calculation06, 07 and 08 Calculates EARTH VOLUMEfor A, B, and C, respectively.09 Summarizes data and results for display orprintout.A, B and C Subroutines for circular, square

and rectangular dikes, respectively, calcu-lating dike volumes for DH increments toconverge dike volume and total volume.

a. Subroutine for calculating boilover vol-ume,

b. Sets flag 00 for boilover calculations.DV = Dike vol. (bbl) 16

X-SECT = Cross sect, dike (sq ft) 18DWB = Dike width base (ft) 19

FORMULA: For right truncated cone or pyra-mid:

V = - ( A + VABTB)

H = Height; A = Area of larger base,B = Area of smaller base.

(See Fig. 1.)

Dia or side of top base = (DD, S, LS orSS) - DWTDia or side of lower base = (DD, S, LS orSS) - DWT -2(DH x Run.)

USER INSTRUCTIONS1) Put dike program in calculator.2) XEQ size 25 and set User Mode.3) XEQ "Dike."4) Key in data according to prompts and R/S.

Notice Run = 1.5? and DWT = 2? If thesevalues are acceptable, key in and R/S. DHINCR = ? Can be 0.10 ft for preliminaryruns, otherwise, use 0.05 ft (0.60-in.).Trial DH = ? Try 3 ft. If this is too much,machine will stop, STO smaller value inR07 and try again ("A," "B " or "C"). Like-wise, if it is known that DH is much greaterthan 3—try larger value: This saves itera-tions!

A? Key in "A" for circular dikes (Be sureUser Mode!)

B? Key in "B " for square dikes. (Be sureUser Mode!)

C? Key in "C" for rectangular dikes. (Be sureUser Mode!)

Boilover? Y? N?This routine is available when needed.

Usually answer is no. Press " N " and R/S.Whichever key A, B, or C is pressed, a dia orside(s) will be called for; key in appropriatedata and calculator will converge DV with to-tal barrels for solution of DH (See Fig. 2).Example 1: Illustrates a 54,200-bbl tank in acircular dike. Notice how data are entered ac-cording to prompts. A printer is a great con-venience but is not indispensible. Withoutprinter, SF 21 each time calculator is turnedon, now data and results will be displayed oneat time and advanced by pressing R/S key.Notice formating of data and results—zerosare shown for inactive dimensions or boilovervolume.Example 2: Demonstrates an approach,where most input data do not change: Calcu-late DH for above tank for boilover crude.(This avoids going through entering routineXEQ Dike.) SF 00 and a new trial DH try 4,STO 07. (Result of Example 1 is DH = 3.75 ft.It is evident dike will be higher to contain

larger volume.) Press "A," re-enter DD (330).Results: DH = 4.25 ft. larger X-SECT, MOREEARTH, a boilover volume is shown and in-cluded in total volume.Example 3: Same tank, no boilover, what isDD for 4.5 ft. dike? CF 00 (Notice it appears inannunciator when set). SF 01 (This is not alooping routine!) RCL 00 STO 01, 0.00 STD24. STO 4.5 in 07. Press "A"; put some valuefor DD less than 330 (as above). Try 300 keyin and R/S. One calculation will be made.Compare total volume and dike volume.Press "A" and key new DD. Repeat until sat-isfactory convergence is achieved.The following table shows convergence forExample 3:

Total vol 54,200 bbl DH = 4.5 ft.

Trial DD ft DV bbl300 53,406.62305 55,255.73302 54,142.48302.5 54,727.24302.3 54,253.30

It is evident that with a few iterations, one canhome-in on a precise solution.

SUMMARYFor a new tank size, one should XEQ "Dike"and enter data according to prompts.Subroutines "B" and "C" are similar to "A."One can build up a dike height for given cen-ter line distances (square or rectangle) withand without boilover.Consider same tank as Example 1. (Let3 = Trial DH STO 07.)

Square 300 ft (No B.O)Square 300 ft B.O.

DH = 3.60DV = 54,894.66

DH = 4.05DV = 61,473.78

Total volume = 61,055.09Rectangle LS 450: SS 200 (3.00 STO 07)LS 450: SS 200 B.O.H—3.60 DV = 54,655.16 DH = 4.10

DV = 61,900.04Total volume = 61,139.72

One can "free-wheel" with "B" and "C" asfor "A" for a fixed dike height. SF 01 and trydifferent dike centerline distances. CompareDV and TOT. VaI. and continue to desired con-vergence.Warning: Be sure Flag 00 is clear whenboilover routine is not required. When clear-ing Flag 00 STD 0.00 in 24 to prevent extrane-ous volume from being involved in program.BO VOL should be 0.00 when there is noboilover. Flat 01 must be clear for increment-ing routines. Always STO new trial DH in 07each run.Note: XEQ 09 for printout or display of inputand results in storage registers.

Example 3.

(volume of tank or volume of tank plus boilover,if applicable). The calculations begin with given dikecenterline, dike width at top, repose angle of soil, and trialDH. As long as the dike volume is less than the total

volume the program loops, increment DH for the nextcalculation. When the two volumes converge, calculationsstop and input data and results are displayed or printed.The DH value, when the volumes converge, is the solution.

PRP -DIKE"

In some cases, it will be required to ascertain dike diam-eter or sides for a fixed dike height (DH). This isaccomplished by storing DH Value in 07, setting Flag Ol(for single calculation). Press "A," "B," or "C" key intrial centerline distances. The results of any calculation giveone an opportunity to compare total barrels with dikevolume. Then alter centerline distances to fit trend andcontinue. See Example 3.

This program is based on the site being essentially level.

Source

Pipe Line Industry, August 1986.