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  1. 1. 18: Tanks 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
  2. 2. 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 Table 1 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- example. 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 SEAL AXIS 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 fixed roofs.
  3. 3. SEAL AXIS TYPE AND CONDITION OF SEAL (REFER TO TABLE 1) Reference AxIt Evaporation loss, bbl/year ( x 1 for refined stocks, x 0.4 for crude oil) Figure 2. Welded deck, column-supported fixed roofs. SEAL AXIS 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 fixed roofs. • Liquid-mounted primary seal only and an average Solution seal fit • 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.
  4. 4. SEAL AXIS 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 fixed roofs. 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. tank. 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. Reference 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
  5. 5. 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.
  6. 6. 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: scales. 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. following equation: DIAMETER, Feet CAPACITY, Cubic Feet HEIGHT, Feef CAPACfTY, Barrels CAPACITY, Gallons CAPACITY, Barrels
  7. 7. 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: Shrinkage 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 = (5.88)(144)(16) 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
  8. 8. BBL PER HR BBL CFH 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 portable calculator 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
  9. 9. DD, S, LS or SS. Tank DWT DWT Top base Run 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 stipulations are: • 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.
  10. 10. DIKE PROGRAM 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. tions! 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) 00—Boilover calculation 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.
  11. 11. PRP -DIKEquot; Example 3. (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.
  12. 12. 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.