SECTION 6

Storage

This section provides general guidelines that will aid in the

selection of the proper type of storage to be used in a particular

A′, B′,C′, D′ = coefficients used in Fig. 6-14

A = surface area, ft2

b = ellipse minor radius, ftBmax = vapor pressure of liquid at maximum surface

temperature, psiaBmin = vapor pressure of liquid at minimum surface

temperature, psiaD = cylinder diameter, ft

f(Zc) = cylinder partial volume factor, dimensionlessf(Ze) = head partial volume factor, dimensionless

H = correction factor for horizontal surfacesHn = depth of liquid in cylinder, ftHp = height of liquid, ftHT = height, ft

k = thermal conductivity, Btu/[(hr • sq ft • °F)/in.]K = equilibrium constant, y/x, dimensionlessKl = head coefficient, dimensionlessL = length, ft

MWi = molecular weight of component i, lb/lb moleng = number of moles of vaporni = number of moles of component iP = absolute pressure, psia

Pa = atmospheric pressure, psiaPc = critical pressure, psiaPR = reduced pressure, dimensionlessQ = heat flow, Btu/sq ft • hrR = gas constant, 10.73 psia • ft3/(R • lb mole)Rl = cylinder radius, ftRi = thermal resistance of insulation (X/k),

(hr • sq ft • °F)/BtuT = temperature, °R

Ta = ambient air temperature, °FTc = critical temperature, °R or °FTf = temperature drop through surface air film, °FTh = hot face temperature, °FTi = temperature drop through insulation, °F

Tm = mean temperature of insulation, °FTmax = maximum average temperature, °FTmin = minimum average temperature, °F

TR = reduced temperature, dimensionlessTs = outside surface temperature, °FV = volume, ft3

W = width, ft

FIG.

Nomenc

6-1

application. Fig. 6-2 will assist with the selection. Variouscodes, standards, and recommended practices should be used

xi = mole fraction of component i in the liquid phaseX = insulation thickness, in.yi = mole fraction of component i in the vapor phaseZ = compressibility factor

Greekα = radians∆ = absolute internal tank pressure at which vacuum

vent opens, psiaπ = 3.14159...φ = required storage pressure, psiaΣ = summation

DP = design pressure is the pressure at which the mostsevere condition of coincident pressure and tem-perature expected during normal operation isreached. For this condition, the maximum differ-ence in pressure between the inside and outside ofa vessel or between any two chambers of a combi-nation unit shall be considered. (ASME Code forUnfired Pressure Vessels, Section VIII)

MAWP = maximum allowable working pressure shall be de-fined as the maximum positive gauge pressure per-missible at the top of a tank when in operation,which is the basis for the pressure setting of thesafety-relieving devices on the tank. It is synony-mous with the nominal pressure rating for the tankas referred to in API Standards 620 and 650.

OP = operating pressure is the pressure at which a vesselnormally operates. It shall not exceed the maxi-mum allowable working pressure of the vessel. Asuitable margin should be allowed between thepressure normally existing in the gas or vaporspace and the pressure at which the relief valvesare set, so as to allow for the increases in pressurecaused by variations in the temperature or gravityof the liquid contents of the tank and other factorsaffecting the pressure in the gas or vapor space.(API Standard 620)

RVP = Reid Vapor Pressure is a vapor pressure for liquidproducts as determined by ASTM test procedure D-323. The Reid vapor pressure is defined as poundsper sq in. at 100°F. The RVP is always less than thetrue vapor pressure at 100°F.

TVP = true vapor pressure is the pressure at which the gasand liquid in a closed container are in equilibriumat a given temperature.

6-1

lature

AtmosphericPressure†‡

0 to *2.5psig†‡

2.5 to 15psig‡

Above 15psig§ Underground

Crude Oils X X X – XCondensate X X X X XOils X X – – XNatural Gasoline X X X – XButanes – X° X° X XPropane – X° X° X XRaw NGLs – X° X° X XEthane – X° X° X XPetrochemicals – X° X° X XNatural Gas – – – X XLNG – X° X° X –Treating Agents X X – – –Dehydration Fluids X X – – –Specialty Chemicals X X X – –Solid Materials X – – – –Water X – – – –

* Some materials may require a slight positive pressure to exclude air, oxygen, and/or water, and conserve valuable/toxicvapors. API specifications 12D and 12F may also apply.

† API Standard 650 governs‡ API Standard 620 governs§ ASME Unfired Pressure Vessel Code, Section VIII governs° Refrigerated only

Note: Vacuum conditions may exist and must be considered in tank design. Examples: low ambient temperatures orevacuating without relieving.

FIG. 6-2

Storage

to supplement the material provided. Manufacturers shouldbe consulted for specific design information pertaining to aparticular type of storage.

STORAGE CLASSIFICATION

Above GroundAtmospheric — Atmospheric pressure tanks are de-

signed and equipped for storage of contents at atmosphericpressure. This category usually employs tanks of vertical cy-lindrical configuration that range in size from small shopwelded to large field erected tanks. Bolted tanks, and occasion-ally rectangular welded tanks, are also used for atmosphericstorage service.

Low Pressure (0 to 2.5 psig) — Low pressure tanksare normally used in applications for storage of intermediatesand products that require an internal gas pressure from closeto atmospheric up to a gas pressure of 2.5 psig. The shape isgenerally cylindrical with flat or dished bottoms and sloped ordomed roofs. Low pressure storage tanks are usually of weldeddesign. However, bolted tanks are often used for operatingpressures near atmospheric. Many refrigerated storage tanksoperate at approximately 0.5 psig.

Medium Pressure (2.5 to 15 psig) — Medium pres-sure tanks are normally used for the storage of higher volatil-ity intermediates and products that cannot be stored in low

6-2

pressure tanks. The shape may be cylindrical with flat ordished bottoms and sloped or domed roofs. Medium pressuretanks are usually of welded design. Welded spheres may alsobe used, particularly for pressures at or near 15 psig.

High Pressure (Above 15 psig) — High pressuretanks are generally used for storage of refined products or frac-tionated components at pressure above 15 psig. Tanks are ofwelded design and may be of cylindrical or spherical configu-ration.

UndergroundGas processing industry liquids may be stored in under-

ground, conventionally mined or solution mined caverns. Noknown standard procedures are available for this type storage;however, there are many publications and books covering thesubject in detail.

WORKING PRESSURES

A design working pressure can be determined to preventbreathing, and thereby save standing storage losses. However,this should not be used in lieu of any environmental regulatoryrequirements regarding the design of storage tanks. The en-vironmental regulatory requirements for the specific locationshould be consulted prior to the design of storage facilities.Generally there are regulatory requirements specifying thetype of storage tank to be used, based on the storage tank

capacity and the vapor pressure of the product being stored.In addition there are usually specific design requirements, forexample in the type of seals to be used in a floating roof tank.

The working pressure required to prevent breathing lossesdepends upon the vapor pressure of the product, the tempera-ture variations of the liquid surface and the vapor space, andthe setting of the vacuum vent.

φ = Bmax + (∆ − Bmin) (Tmax + 460)( Tmin + 460 )

− Pa Eq 6-1

The above relation holds only when Bmin is less than ∆; thatis, when the minimum vapor pressure is so low that air isadmitted into the vapor space through the vacuum vent. WhenBmin is equal to or greater than ∆, the required storage pres-sure is,

φ = Bmax − Pa Eq 6-2

Under this condition air is kept out of the vapor space.

Fig. 6-3 is presented as a general guide to storage pressuresfor gasolines of various volatilities in uninsulated tanks.These data for plotting the curves were computed from Eqs 6-1and 6-2 using the following assumptions:

• Minimum liquid surface temperature is 10°F less thanthe maximum liquid surface temperature.

• Maximum vapor space temperature is 40°F greater thanthe maximum liquid surface temperature.

• Minimum vapor space temperature is 15°F less than themaximum liquid surface temperature.

• Stable ambient conditions (ambient temp. 100°F).

These temperature variations are far greater than would beexperienced from normal night to day changes. Therefore, thelower, nearly horizontal line, which shows a required storagepressure of 2.5 psig for the less volatile gasolines is conserva-tive and allows a wide operating margin.

Maximum liquid surface temperatures vary from 85 to115°F. Sufficient accuracy will generally result from the as-

FIG. 6-3

Storage Pressure vs. True Vapor Pressure

6-3

sumption that it is 10°F higher than the maximum tempera-ture of the body of the liquid in a tank at that location.Example 6-1 — To illustrate the use of Fig. 6-3, suppose a24 psia true vapor pressure (TVP) natural gasoline is to bestored where the liquid surface temperature may reach amaximum of 100°F. A vertical line extended upward from the24 psia mark at the bottom of the chart intersects the 100°Fline at 9.3 psig. The design pressure of the tank should be aminimum of 10.23 psig (9.3 psig + 10%).

Fig. 6-4 can be used as follows:

• As quick reference to determine true vapor pressures oftypical LPGs, natural gasolines, and motor fuel compo-nents at various temperatures.

• To estimate the operating pressure of a storage tank nec-essary to maintain the stored fluid in a liquid state atvarious temperatures.

• For converting from true vapor pressure to Reid VaporPressure (RVP).

• For simple evaluation of refrigerated storage versus am-bient temperature storage for LPGs.

Example 6-2 — Determine the TVP of a 12 psi RVP gasoline.In addition, estimate the design pressure of a tank needed tostore this same 12 RVP gasoline at a maximum temperatureof 120°F. Using Fig. 6-4, a vertical line is extended upwardsfrom the 100°F mark (100°F is used as the reference point fordetermining RVP) at the bottom of the chart to the intersectionof the 12 psi RVP line, read true vapor pressure of 13.2 psia.A vertical line is also extended from the 120°F mark to inter-sect the 12 RVP gasoline line. Now going horizontal, the truevapor pressure axis is crossed at approximately 18.1 psia. Thestorage tank should therefore be designed to operate at18.1 psia (3.4 psig) or above. The design pressure of the tankshould be a minimum of 10% above the operating gauge pres-sure or approximately 18.5 psia.

Example 6-3 — Evaluate the options of refrigerated storageversus ambient temperature storage for normal butane. FromFig. 6-4 the vertical line is extended up from the 100°F (as-sumed maximum) mark to intersect the normal butane line atapproximately 51.5 psia (36.8 psig). The working pressure ofthe tank should be 36.8 psig plus a 10% safety factor, or55.2 psia. This same product could be stored in an atmosphericpressure tank if the product is chilled to 32°F. This tempera-ture is determined by following the normal butane line downuntil it intersects the 14.7 psia horizontal vapor pressure line.Reading down to the bottom scale indicates the storage tem-perature at 32°F. The pressurized tank would require moreinvestment due to the higher working pressure of 55.2 psia(40.5 psig) and the thicker shell requirement. The refrigeratedtank would require less investment for the tank itself, but anadditional investment would be necessary for insulation andfor refrigeration equipment which requires additional operat-ing expenses. The economics of each type of storage systemcan be evaluated to determine which will be the most attrac-tive.

The graphical method of converting from RVP to TVP is anapproximation and is generally more accurate for lighter com-ponents. Crude oils with very low RVPs could vary signifi-cantly from this graphical approach. This is due to the factthat during the Reid test the highest vapor pressure materialstend to evaporate leaving a residue which has a lower vaporpressure than the original sample. Equation 6-3 was devel-oped by A. Kremser in 1930 to relate the two vapor pressuresat 100°F.

TVP = (1.07) (RVP) + 0.6 Eq 6-3

FIG. 6-4

True Vapor Pressures vs. Temperatures for Typical LPG, Motor, and Natural Gasolines

6-4

Courtesy of C-E Natco

FIG. 6-5

Typical Spherical Storage Tank

Courtesy of C-E Natco

FIG. 6-6

Typical Nod ed Sphe roidal S torage Tank

SUPPORT PAD (TYP.)

CONCRETE PIER OR STEEL SADDLES

Courtesy of C-E Natco

FIG. 6-7

Horizontal-Cylindrical Type Vessel

6-5

Using this formula for the 12 psi RVP gasoline examplewould calculate a 13.4 psia TVP versus the 13.2 determinedgraphically. The RVP is less than the true vapor pressure at100°F. Published data indicate the ratio of true vapor pressureto Reid vapor pressure may vary significantly, depending onthe exact composition of the stored liquids. Ratios from 1.03to 1.60 have been verified by test data.1,2 Before entering thefinal design phase of any storage project, test data should begathered on the fluid to be stored.

TYPES OF STORAGE

Above GroundFor operating pressures above 15 psig, design and fabrica-

tion are governed by the ASME Code, Section VIII.

Spheres — Spherical shaped storage tanks (Fig. 6-5) aregenerally used for storing products at pressures above 5 psig.

Spheroids — A spheroidal tank is essentially spherical inshape except that it is somewhat flattened. Hemispheroidaltanks have cylindrical shells with curved roofs and bottoms.Noded spheroidal tanks (Fig. 6-6) are generally used in thelarger sizes and have internal ties and supports to keep shellstresses low. These tanks are generally used for storing prod-ucts above 5 psig.

Horizontal Cylindrical Tanks — The working pres-sure of these tanks (Fig. 6-7) can be from 15 psig to 1000 psig,or greater. These tanks often have hemispherical heads.

Fixed Roof — Fixed roofs are permanently attached tothe tank shell. Welded tanks of 500 barrel capacity and largermay be provided with a frangible roof (designed for safety re-lease of the welded deck to shell joint in the event excess in-ternal pressure occurs), in which case the design pressureshall not exceed the equivalent pressure of the dead weight ofthe roof, including rafters, if external.

Floating Roof — Storage tanks may be furnished withfloating roofs (Fig. 6-8) whereby the tank roof floats upon thestored contents. This type of tank is primarily used for storagenear atmospheric pressure. Floating roofs are designed tomove vertically within the tank shell in order to provide aconstant minimum void between the surface of the storedproduct and the roof. Floating roofs are designed to provide aconstant seal between the periphery of the floating roof andthe tank shell. They can be fabricated in a type that is exposedto the weather or a type that is under a fixed roof. Internalfloating roof tanks with an external fixed roof are used in areasof heavy snowfalls since accumulations of snow or water onthe floating roof affect the operating buoyancy. These can beinstalled in existing tanks as well as new tanks.

Both floating roofs and internal floating roofs are utilized toreduce vapor losses and aid in conservation of stored fluids.

Bolted — Bolted tanks are designed and furnished as seg-mental elements which are assembled on location to providecomplete vertical, cylindrical, above ground, closed and opentop steel storage tanks. Standard API bolted tanks are avail-able in nominal capacities of 100 to 10,000 barrels, designedfor approximately atmospheric internal pressures. Boltedtanks offer the advantage of being easily transported to de-sired locations and erected by hand. To meet changing require-ments for capacity of storage, bolted tanks can be easilydismantled and re-erected at new locations.

Tank Shell

Shoe

Seat Fabric Roof

Pantagraph hangar

Liquid level

Counterweight

Detail 1 - Shoe sealExample Types of Seals for

Floating Roof Tanks

Tank Shell

Seal envelope

Resilienturethane

fabric

Curtain seat

Roof

Hangar bar

Seal support ring

Rim

BumperLiquid level

Detail 2 - Tube Seal

COVER ACCESSHATCH

GROUNDCABLE

GROUND CABLE ROOFATTACHMENT

ANTI ROTATION ROOFFITTING

ANTI-ROTATION

CABLE

ANTI-ROTATION

LUG, WELDEDTO FLOOR

PONTOONS

TANK SUPPORT COLUMN

VACUUM BREAKER ANDACTUATOR LEG

PONTOON

SHELLMANWAY

SEAL(See details 1&2)

(Also applicable to external floating roof tanks if dome roof is removed) Courtesy of CE Natco

FIG. 6-8

Typical Arrangement of Internal Floating Roof Tank

6-6

FIG. 6-9

Pipe Storage

Specialty — Pipe Storage (Fig. 6-9) — Pipe that is usedspecifically for storing and handling liquid petroleum compo-nents or liquid anhydrous ammonia must be designed and con-structed in accordance with any applicable codes.

Flat-Sided Tanks — Although cylindrical shaped tanks maybe structurally best for tank construction, rectangular tanksoccasionally are preferred. When space is limited, such as off-shore, requirements favor flat-sided tank construction be-cause several cells of flat-sided tanks can be easily fabricatedand arranged in less space than other types of tanks. Flat-sided or rectangular tanks are normally used for atmospherictype storage.1

Lined Ponds2 — Ponds are used for disposal, evaporation,or storage of liquids. Environmental considerations may pre-clude the use of lined ponds for the storage of more volatile ortoxic fluids. Linings are used to prevent storage liquid losses,seepage into the ground, and possible ground water contami-nation. Clay, wood, concrete, asphalt, and metal linings havebeen used for many years. More recently, a class of imperviouslining materials has been developed that utilize flexible syn-thetic membranes. Commonly used lining materials are poly-vinyl chloride, natural rubber, butyl rubber, and Hypalon®.Polyethylene, nylons, and neoprenes are used to a lesser ex-tent.

Some of the most important qualities of a suitable liner are:• High tensile strength and flexibility.• Good weatherability.• Immunity to bacterial and fungus attack.• Specific gravity greater than 1.0.• Resistance to ultraviolet-light attack.• Absence of all imperfections and physical defects.• Easily repaired.

Leak detection sometimes must be built into the pond sys-tem, especially where toxic wastes or pollutants are to bestored. Types of leak-detection systems that are commonly

6-

used are underbed (French) drainage system, ground resistiv-ity measurement, and monitor wells, and any combinationthereof.

Pit Storage — Pit storage is similar to pond storage but isonly used on an emergency basis. The use of this type of stor-age is limited by local, state, and federal regulations.

UndergroundUnderground storage is most advantageous when large vol-

umes are to be stored. Underground storage is especially ad-vantageous for high vapor pressure products.

Types of underground storage are: (1) caverns constructedin salt by solution mining or conventional mining, (2) cavernsconstructed in nonporous rock by conventional mining, and(3) caverns developed by conversion of depleted coal, lime-stone, or salt mines to storage.

Solution Mined Caverns — The cavern is constructedby drilling a well or wells into the salt and circulating lowsalinity water over the salt interval to dissolve the salt asbrine.

The cavern may be operated by brine displacement of prod-uct, pumpout methods, vapor displacement, or as in the caseof gas, by product expansion (see Figs. 6-10, 6-11, and 6-12).

Most solution mined caverns are operated using the brinedisplacement technique (Fig. 6-10). A suspended displace-ment string of casing is installed near the bottom of the cavernand product is injected into the annulus between the productcasing (casing cemented at cavern roof) and the displacementcasing, forcing brine up the displacement casing. The proce-dure is reversed for product recovery. In this type of operation,a brine storage reservoir is usually provided. Detail 1 of Fig. 6-10 provides the typical piping for the wellhead of an under-ground storage well.

Some solution mined caverns are operated “dry” by install-ing a pump at cavern depth either within the cavern or in awell connected to the cavern. Both submersible electric drivenpumps and line shaft pumps (deep well vertical turbinepumps) are used for this purpose (see Fig. 6-11).

Conventional Mined Caverns — Conventional minedcaverns can be constructed any place a nonporous rock is avail-able at adequate depth to withstand product pressures. Anengineer or geologist experienced in underground storageshould evaluate any specific site for the feasibility of con-structing underground storage. Most product caverns are con-structed in shale, limestone, dolomite, or granite. This typecavern is operated “dry” (product recovered by pumping).

Refrigerated StorageThe decision to use refrigerated storage in lieu of pressur-

ized storage is generally a function of the volume of the liquidto be stored, the fill rate, the physical and thermodynamicproperties of the liquid to be stored, and the capital investmentand operating expenses of each type of system.

The parameters involved in selecting the optimum refriger-ated storage facility are:

• Quantity and quality of product to be stored.• Fill rate, temperature, and pressure of incoming stream.• Shipping conditions for the product.• Composition of the product.• Cooling media (air, water, etc.) available.• Availability and cost of utilities.

7

FIG. 6-10

Brine Displacement Cavern Operation (Solut ion Miined Cavern)

6-8

FIG. 6-11

Pump-Out Cavern Operation (Fracture Connected Solu tion Mined Cavern in Bedd ed Salt)

GAS PIPELINE DEHYDRATOR

GASHEATER

GASWITHDRAWAL

FACILITIES

GASINJECTIONFACILITIES

Courtesy Fenix and Scisson

FIG. 6-12

Compression/Expansion Cavern Operation(Solu tion Mined Cavern)

6-

• Load bearing value of soil.

The proper choice of storage and the proper integration ofthe storage facility with the refrigeration facilities are impor-tant to overall economy in the initial investment and operatingcosts. Fig. 6-13 provides some general guidelines to use whenselecting a storage system for propane.

When using refrigerated storage, the liquid to be stored isnormally chilled to its bubble point temperature at atmos-pheric pressure. Refrigerated storage tanks normally operateat an internal pressure between 0.5 and 2.0 psig.

In some cases, pressurized-refrigerated storage is attrac-tive. In this type of refrigerated storage, the product to bestored is chilled to a temperature that allows it to be stored ata pressure somewhere between atmospheric pressure and itsvapor pressure at ambient temperature.

Refrigeration requirements normally include the followingbasic functions:

• Cooling the fill stream to storage temperature.• Reliquefying product vaporized by heat leak into the sys-

tem.• Liquefying vapors displaced by the incoming liquid.

Other factors which should be considered are:

• Pump energy requirements• Barometric pressure variations• Product compositions• Non-condensables• Solar radiation effects• Superheated products

9

FIG. 6-13

General Guidelines for the Economic Storage of Pure Propane

Refer to Section 14 of this Data Book for information on re-frigeration. Tables R.2.2, R.2.3, and R.2.4 of API 620, Appen-dix R, should be consulted for specific service temperaturesand impact requirements of materials used as primary andsecondary components in refrigerated storage tanks. Refrig-erated facilities require specialized insulation systems, whichare described later in this Section.

Foundations for the various types of low temperature stor-age vessels are designed much the same as foundations forordinary spheres and pressure cylinders. One caution must benoted. Most low temperature liquids are lighter than waterand the vessels are designed to store this lighter liquid. There-fore, it is a common practice to design foundations for the totalweight of contained product and to water test the vessel at 1.25times the product weight.

Flat bottom vessel foundations in low temperature servicepresent an additional problem. The container is a heat-sinkand, if no provision is made to supply heat, a large quantity ofsoil eventually will reach temperatures below the freezingpoint of water. Moisture in the sub-soil will freeze and some“heaving” could occur. A heat source consisting of electricalresistance heating cable or pipe coils with a warm circulatingliquid is generally installed below the outer tank bottom tomaintain the soil temperature above 32°F. Foundations for

6-1

low temperature vessels must also be designed to minimizedifferential settling.

Liquids at low temperatures can be stored in frozen earthcaverns at essentially atmospheric or very low pressures. Anexcavated hole (usually lined) is capped by an insulated metaldome and refrigerated to maintain impervious “walls of ice.”Vapors from the liquid are continuously recompressed andcondensed.

MATERIALS OF CONSTRUCTION

Vessel/Tank MaterialsMetallic — Shop welded, field welded, and bolted storage

tanks are customarily fabricated from mild quality carbonsteel. Most common for welded tanks are A-36 structural steeland A-283 grade “C” structural quality carbon steel. Sheetgauge steels for bolted tanks are of commercial quality havinga minimum tensile strength of 52,000 psi. A-612, A-515, andA-516 mild quality low carbon steels are used for fabricatingthe higher pressure storage products such as spheres and “bul-lets.” Various API and ASME Codes (listed in the References)to which the storage tank is fabricated, set forth the weldingprocedures, inspection procedures, testing requirements, andmaterial selection. Some storage applications or service con-

0

ditions (low temperature storage) require storage tanks to befabricated from metals such as low alloy stainless steel, alu-minum, or other specialty materials.

Non-Metallic — Older non-metallic tanks were custom-arily constructed from wood. Plastic materials have now re-placed wood. These materials have the advantage of beingnon-corroding, durable, low cost, and lightweight. Plastic ma-terials used in the construction are polyvinyl chloride, poly-ethylene, polypropylene, and fiberglass-reinforced polyesters.The fiberglass-reinforced polyester (FRP) tanks are availablein the larger sizes and are the most common. FRP tanks aresuitable for outdoor as well as indoor applications. FRP tankswith special reinforced shells are designed for undergroundstorage service. Above ground tanks are primarily vertical,with or without top heads.

Non-metallic tanks constructed of unreinforced plasticssuch as polyvinyl chloride or polyethylene materials are avail-able in sizes up to about 6 ft in diameter by 11 ft high(2400 gallons). Horizontal underground FRP tanks will holdup to 12,000 gallons. Above ground vertical FRP tanks canstore from 12,000 to 24,000 gallons, depending upon the shellconstruction.

The temperature limits of plastic tanks are 40°F to 150°F.Color must be added to the outer liner for protection againstultraviolet radiation. The inner liner must be selected for com-patibility with the chemical or product stored. Protection frommechanical abuse such as impact loads is a necessity. Goodplanning dictates that plastic storage should not be locatednext to flammable storage tanks. All closed plastic tanksshould be equipped with pressure relief devices.

Protective CoatingsInternal — Use of internal coatings is primarily to protect

the inside surface of the tank against corrosion while also pro-tecting the stored contents from contamination.

Consideration must always be given to such factors as thetype of product being stored, type of coating available, type ofsurface to be coated, surface preparation, compatibility of coat-ings, and number of coats required to obtain maximum pro-tection.

Many types of internal coatings are available. Due to theunlimited types and applications, only a few will be describedas follows:

Coal Tar — Among the oldest and most reliable coatings.Extremely low permeability; protects surface by the mechani-cal exclusion of moisture and air; extremely water resistant;good resistance to weak mineral acids, alkalis, salts, brine so-lutions, and other aggressive chemicals.

Epoxy Resin Coatings — Excellent adhesion, toughness,abrasion resistance, flexibility, durability, and good chemicaland moisture resistance. Typical applications include liningsfor sour crude tanks, floating roof tanks, solvent storage tanks,drilling mud tanks, sour water, treated water, and pipelines.

Rubber Lining — Used as internal lining for storage tankswhich are subjected to severe service such as elevated tem-peratures or for protection from extremely corrosive contents,such as concentrated chlorides and various acids such as chro-mic, sulfuric, hydrochloric, and phosphoric.

Galvanized — Galvanizing (zinc coating) is highly resis-tant to most types of corrosion. Bolted steel tanks are ideallysuited for galvanizing since all component parts are galva-

6-1

nized by the hot-dip process after fabrication but before erec-tion. Galvanized bolted tanks are recommended where the oilproduced contains sulfur compounds and/or is associated withhydrogen sulfide gas. Galvanizing is also effective against cor-rosion in seacoast areas where atmospheric salt conditions ac-celerate corrosion problems.

External — The basic requirements for external coatingsare appearance and weather protection.

Numerous types of external coatings are available, rangingfrom basic one-coat primers to primers with one or more top-coats. Environmental conditions usually dictate the extent ofcoating applied. Offshore and coastal installations requiremore extensive coatings as compared to inland locations.

InsulationTypes — The four basic types of thermal insulating mate-

rial are: fibrous, cellular, granular, and reflective. These ma-terials differ in many characteristics. Refer to Fig. 6-14 for adescription of these materials and typical conductivity valuesand principal properties of common industrial insulations.

Uses — Principal uses of insulation are for personnel pro-tection, process temperature control, prevention of condensa-tion, and conservation of energy.

Personnel Protection — Personnel protection is accom-plished by the application of insulation of proper thicknesswhere the surface temperature should be limited to approxi-mately 150°F or as specified by applicable codes or companystandards.

Process Temperature Control — Insulation thickness isspecified in this case to help control the temperature of theprocess fluid. Electrical, steam, hot process fluid, hot oil, gly-col-water tracing is used to add heat to the process line tobalance the heat loss. The insulation thickness must bematched to the energy input to achieve the desired result.Freeze protection is another use for insulation. This includesfluids which have higher viscosities or freeze points.

Condensation — Insulation thickness must be sufficientto keep the outside surface of the insulation above the dewpoint of the surrounding air. Moisture condensation on a coolsurface in contact with warmer humid air must be preventedbecause of the deterioration of the insulation. In addition tothe required thickness of insulation, a vapor tight membranemust be properly applied to the insulation. As a rule, insula-tion thickness for condensation control is much greater thanthe thickness required for conservation of energy.

Conservation of Energy — High fuel costs increase theneed for more insulation. A rule of thumb for estimating thethickness of insulation is to apply the thickness that producesa heat loss of 3 to 5 percent or less from the surface. Specificinsulating materials and thicknesses for any large applicationshould be determined with the assistance of the manufacturer.Fig. 6-15 contains 3 graphs which permit the rapid estimationof the thickness of thermal insulation required to give a de-sired heat flow or surface temperature when the hot face andambient temperature are known. The method is based on ele-mentary heat transfer theory and reliable experimental data.The following examples illustrate the use of these graphs.Example 6-4 — A rectangular duct is operating at 450°F. Theduct is finished with a silicone coated fabric. The ambient tem-perature is 80°F. It is desired to maintain a surface tempera-ture of 130°F. What thickness of cellular glass foam isrequired? What is the heat loss?

1

Insulation A′ B′ C′ D′ Temperaturerange, °F

Calcium silicate ASTM C533-80 Class 1 0.3504 5.196 x 10-4 100-700White fiberglass blankets with binder

density = 3.0 lb/ft3 0.2037 6.161 x 10-6 1.403 x 10-6 –5.0 x 10-10 50-800density = 6.0 lb/ft3 0.2125 –2.325 x 10-4 1.797 x 10-6 –7.97 x 10-10 50-900

Rigid fiberglass sheetASTM C-547-77 Class 1 0.2391 9.192 x 10-4 6.942 x 10-10 11-121ASTM C-547-77 Class 2 0.2782 1.226 x 10-3 37-204ASTM C-612-77 Class 1 0.2537 3.051 x 10-4 1.950 x 10-6 0-250ASTM C-612-77 Class 3 0.2631 2.301 x 10-4 1.614 x 10-6 0-275density = 4.0 lb/ft3 0.2113 3.857 x 10-4 1.20 x 10-6 0-300density = 6.0 lb/ft3 0.1997 2.557 x 10-4 9.048 x 10-7 0-300

Cellular glass foamASTM C-552-79 Class 1 0.3488 5.038 x 10-4 1.144 x 10-7 7.172 x 10-10 –300-500

Mineral woolBasaltic rock blanket, 9 lb/ft3 0.2109 3.382 x 10-4 5.495 x 10-7 0-800Basaltic rock blanket, 12 lb/ft3 0.2798 9.508 x 10-5 6.478 x 10-7 0-800Metallic slag block, 6 lb/ft3 0.1076 5.714 x 10-4 3.124 x 10-7 0-600Metallic slag block, 18 lb/ft3 0.3190 8.870 x 10-5 2.174 x 10-7 0-1200

Mineral-wool-based-cement 0.4245 6.293 x 10-4 –1.638 x 10-7 3.533 x 10-10 0-950Preformed expanded perlite

ASTM C-610-74 0.3843 3.0 x 10-4 2.2381 x 10-7 50-750Expanded perlite-based cement 0.6912 5.435 x 10-4 50-650Expanded polystyrene block

ASTM C-578-69 GR2 0.1711 2.760 x 10-4 1.796 x 10-6 –3.997 x 10-9 –58-110Polyurethane, 2.2 lb/ft3

aged 720 days at 77°F and 50% relative humidity 0.1662 –4.094 x 10-4 –5.273 x 10-6 2.534 x 10-8 –58-32(85% closed cell) 0.1516 –3.370 x 10-4 7.153 x 10-6 –2.858 x 10-8 32-122

new polyurethane 0.1271 –2.490 x 10-4 –7.962 x 10-7 4.717 x 10-8 –58-32(95% closed cell) 9.72 x 10-2 7.813 x 10-4 –7.152 x 10-6 2.858 x 10-8 32-122

Exfoliated vermiculite (insulating cement)Aislagreen* 0.480 6.0 x 10-4 0-1200ASTM C-196-77 0.8474 5.071 x 10-4 0-1200

*Trademark of Cia. Mexicana de Refractarios A.P. Green S.A. (Mexico City)

FIG. 6-14

Constants for Determining Thermal Conduc tivity and Unit Heat-Transfer Rate for Some Common Insulating Materials

k = A′ + B′ T + C′ T2 + D′ T3 where T = °F

Solution Steps using Fig. 6-15

Th = 450 ∆Ti = 450 – 130 = 320Ts = 130 ∆Tf = 130 – 80 = 50Ta = 80 Tm = (450 + 130)/2 = 290

In Fig. 6-15 at ∆Tf of 50, project vertically to curve A, thenhorizontally to the left to a heat loss (Q) of 98 Btu/(hr • sq ft).

Project horizontally to the right along the 98 Btu/hr • sq ftQ line to the point in Fig. 6-15b corresponding to a tempera-ture drop through the insulation (∆Ti) of 320, then verticallydownward to an insulation resistance (Ri) of 3.3.

From Fig. 6-14, ASTM C-552-79 Class 1 cellular glass foamhas a k at Tm = 290°F:

k = 0.3488 + (5.038) (10−4) (290) + (1.144) (10−7) (290)2

+ (7.172) (10−10) (290)3

k = 0.52

Multiply required insulation resistance Ri by k to obtain re-quired thickness (X).

X = (3.3) (0.52) = 1.7 inches

6-12

Example 6-5 — In Example 6-4, if the heat loss [98 Btu/(hr • sqft)] is specified instead of a surface temperature of 130°F, thefollowing procedure is used.

Project a line horizontally on Fig. 6-15a from a heat loss of98 Btu/(hr • sq ft) to curve A, then vertically downward to a∆Tf of 50. Surface temperature = 80 + 50 = 130°F. The rest ofthe solution remains the same.Example 6-6 — Assume the same conditions as Example 6-4except that the surface to be insulated is a 4" O.D. duct.

After determining the required thickness of 1.7 inches for aflat surface, go to Fig. 6-15c. Project horizontally from 1.7" fora flat surface to the line representing a 4" O.D. duct then ver-tically to an actual thickness of 1.35". The heat loss of98 Btu/hr • sq ft of outside insulation surface remains thesame.*

The heat loss per linear foot of outside duct surface (includ-ing insulation) is:

π OD 12

(Q) =

6.7 • π 12

98 = 171 Btu/hr / linear ft

*The insulation surface temperature on tubing and ducts inthe horizontal position is generally higher than in the verticalposition for the same heat flow. To correct for the horizontal

Q

AB

C

TfRi

∆Τ Ι

Insulation thickness-XOutside insulation surface:

Surface air film

∆Tl = Th-Ts

∆Tf = Ts-Ta

Ts

Ta

Th

Tm = (Th + Ts)/2

Courtesy John MansvilleCourtesy Johns Manville

FIG. 6-15

Heat Flow Through Insulation

How to Use Figs. 6-15 a & b6-15c

6-15b6-15a

6-13

position, multiply the ∆Tf for flat surfaces obtained fromFig. 6-15a by the following factors (H):

Q (Btu/hr • sq ft) 10-99 100-199 200-299 300 and up

H 1.35 1.2 1.10 15.0

Example 6-7 — A furnace is operating at 1100°F. The outsidesurface is stainless steel. The ambient temperature is 75°F. Itis desired to limit the heat loss to 150 Btu/hr • sq ft.

What thickness of mineral wool and cellular glass foam isrequired? What is the surface temperature?Solution Steps Th = 1100 Ta = 75

Q = 150 Btu/hr • sq ftFrom Fig. 6-15a at Q of 150 Btu/hr • sq ft, project horizon-

tally to curve B, then vertically to ∆Tf = 105. Ts is (105 + 75) =180. In this case a combination of mineral wool (metallic slagblock, 18 lb/ft3) on the hot face backed by cellular glass foam(ASTM C 552-79 Class 1) is to be used. From Fig. 6-14, thetemperature limit of cellular glass foam is 500°F. The innerface temperature between the two materials should be closeto, but not above, this limit.

∆Ti (mineral wool) (1100 – 500) = 600

Tm (mineral wool) (1100 + 500)/2 = 800

k (from Fig. 6-14) of mineral wool at 800°F (Tm) = 0.53

∆Ti(cellular glass foam) (500 – 180) = 320

Tm(cellular glass foam) (500 + 180)/2 = 340

k (from Fig. 6-14) of cellular glass foam at 340°F (Tm)=0.56Using Fig. 6-15b, project horizontally along the 150 Q line

to a ∆Ti (mineral wool) of 600°F, then vertically to an insulationresistance of 4.0. Thickness of mineral wool required (4.0 x .53)= 2.12 or 2.5 inches.

Similarly, project horizontally along the 150 Q line to a ∆Ti(cellular glass foam) of 320°F then vertically to an insulationresistance of 2.2. Thickness of cellular glass foam (2.2)(0.56) =1.23 or 1.5 inches.

In the case of multiple layer construction Fig. 6-15c shouldnot be used to convert to a circular cross section.

Refrigerated Tank Insulation Systems — Lowtemperature insulation is required for both spherical and flatbottomed cylindrical refrigerated tanks. Two types of insula-tion systems are commonly used for low temperature service— single wall and double wall.

In the single wall system, the vessel wall is designed to with-stand the design service conditions of the liquid to be stored.The outer surface of this wall is then covered with a suitableinsulating material such as rigid polyurethane foam. An alu-minum jacket is then installed to provide protection againstthe elements and physical damage. It is extremely importantthat the insulation be sealed with a good vapor barrier to mini-mize air leakage and thereby reduce the quantity of water thatmay migrate into the insulation. Such moisture migration canultimately damage the insulation.

The welded steel plate outer shell of a double wall systemprovides containment and vapor protection for the insulationmaterial, generally perlite. The outer wall also provides pro-tection against fires at temperatures up to 600°F. Double walltanks are considered in storing products at temperatures be-low –28°F. This system minimizes heat leak which generallymeans lower operating and maintenance costs. As an addedsafety feature, the outer wall is completely sealed and there-

6-1

fore permits the insulation space to be continually purged withan appropriate inert gas, which keeps the insulation isolatedfrom outside humid air. Figs. 6-14 and 6-16 provide a range oftypical thermal conductivities for various types of insulatingand tank shell materials.

APPURTENANCES

Storage tanks can be provided with any number of appurte-nances, depending on the appropriate design codes and therequirements of the user. A tank may be fitted with mixers,heaters, relief/vacuum breaking devices, platforms and lad-ders, gauging devices, manways, and a variety of other con-nections which include manways, sumps, inlet and outletnozzles, temperature gauges, pressure gauges, vents, andblowdowns.

SITE PREPARATION AND INSTALLATION

DikesDikes are often required to contain the volume of a certain

portion of the tanks enclosed depending on the tank contents.Dikes are used to protect surrounding property from tankspills or fires. In general, the net volume of the enclosed dikedarea should be the volume of the largest tank enclosed (singlefailure concept). The dike walls may be earth, steel, concrete,or solid masonry that are designed to be water tight with a fullhydrostatic head behind it. Local codes and specifications maygovern construction. If more than one tank is within the dikedarea, curbs or preferably drainage channels should be pro-vided to subdivide the area in order to protect the adjacenttanks from possible spills.

Many codes, standards, and specifications regulate the lo-cation, design, and installation of storage tanks depending ontheir end use. Selecting the proper specification and providingadequate fire protection for the installation may allow lowerinsurance rates over the life of the installation. A partial listof applicable codes, standards, and specifications can be foundat the end of this section.

GroundingMetallic storage tanks used to store flammable liquids

should be grounded to minimize the possibilities of an explo-sion or fire due to lightning or static electricity.

CATHODIC PROTECTION

Cathodic protection can be applied to control corrosion that iselectrochemical in nature where direct current is dischargedfrom the surface area of a metal (the anodic area) through anelectrolyte. Cathodic protection reduces corrosion of a metal sur-face by using a direct current from an external source to opposethe discharge of metal immersed in a conducting medium or elec-trolyte such as soil, water, etc.

PRODUCT RECOVERY

Vapor LossesVapors emitted from the vents and/or relief valves of a stor-

age tank are generated in two ways:• Vapors that are forced out of the tank during filling op-

erations.

4

FIG. 6-16

Summary of Specificat ions f or Low-Temperature and Cryogenic Steels (1) (2)

6-15

• Vapors that are generated by vaporization of the liquidstored in the tank.

A vapor recovery system should be sized to handle the totalvapor from these two sources.

Displacement Losses — Vapors that are forced out ofthe tank are generally called displacement losses. A storagetank is generally not pumped completely dry when emptied.The vapor above the remaining liquid in the tank will expandto fill the void space at the vapor pressure of the liquid storedin the tank at storage temperature. As the tank is filled, thevapors are compressed into a smaller void space until the setpressure on the vent/relief system is reached. There are alsosome filling losses that are associated with the expansion ofthe liquid into the tank. Fig. 6-17 provides a graphical ap-proach to estimating the filling losses as a percentage of theliquid being pumped into the tank.

Vaporization Losses — This type of loss is charac-terized as the vapors generated by heat gain through the shell,bottom, and roof. The total heat input is the algebraic sum ofthe radiant, conductive, and convective heat transfer. Thistype of loss is especially prevalent where light hydrocarbonliquids are stored in full pressure or refrigerated storage. Thisis less prevalent but still quite common in crude oil and fin-ished product storage tanks. These vapors may be recoveredby the use of a vapor recovery system.

To calculate vaporization in tanks, sum up the effects of ra-diant, conductive, and convective heat inputs to the tank. Ap-proximate vapor losses in lb/hr can then be calculated bydividing the total heat input by the latent heat of vaporizationof the product at the fluid temperature.

FIG. 6

Filling Lo sses from S

6-16

Liquid Equivalents of Tank Vapors — The follow-ing procedure may be followed to calculate the liquid equiva-lent of vapor volumes above stored LP-gas liquids:General Approach

Data Required:1. Liquid product composition in mole % or mole fraction.2. Temperature and pressure of the product from which the

liquid sample was obtained.3. Vapor-liquid equilibrium K values at an assumed 1,000

psia convergence pressure (see Section 25).Calculation Procedure:

1. With the liquid product composition, calculate the bubblepoint pressures of the product at assumed temperatures:i.e., 60°F, 80°F. From the bubble point calculations, a va-por pressure chart can be made for this specific productcomposition.

2. From the bubble point calculation in (1), the product va-por composition can be obtained: i.e.,

Σ(yi) = Σ(Kixi) = 1.0 Eq 6-4

3. Calculate the compressibility factor for the vapor byeither (a) or (b).

a. Compressibility factor charts, Section 23. Pseudo-critical and pseudoreduced temperatures and pres-sures must be calculated to obtain a compressibilityfactor.

b. Equations of state.4. Calculate the total number of moles of vapor for volume

V, by using the modified ideal-gas equation:

-17

torage Containers

FIG. 6-18

Liquid Equiv alent o f Tank Vapor

AMBIENTTEMPERATURE

STORAGETANK

COMPRESSOR CONDENSER

FIG. 6-19

Ambient Temperature Vapor Recov ery Cycle

PV = ngZRT, ng = PV/ZRT = total moles vaporEq 6-5

5. Calculate the gallons of liquid equivalent in the vaporphase by multiplying the total number of moles of vaporby the mole fraction of each component by the gal./molefactors for that component from Fig. 23-2.

Σ[ng(yi) (gal./mole)i] = 60°F gallons in vapor phaseEq 6-6

Example 6-8 — Determine three points of data used to plotFig. 6-18.

1. Calculate composition of vapor at the three data points.Liquid C3

CompositionBubble-point pressures

0°F, 42 psia 60°F, 114 psia 120°F, 255 psiax K y K y K y

C2 0.03 4.35 0.1305 3.15 0.0945 2.55 0.0765C3 0.95 0.909 0.8633 0.945 0.8975 0.962 0.9136iC4 0.02 0.309 0.0062 0.398 0.0080 0.493 0.0099

1.00 1.0000 1.0000 1.0000

2. Determine compressibility factor at the three points.VaporAverage MW, Σ (yiMWi) 42.353 42.884 43.163Pseudo Tc, °R 651 655 658Pseudo Pc, psia 628 624 622TR 0.707 0.794 0.881PR 0.067 0.183 0.410Z (Section 23) 0.913 0.855 0.730

3. Calculate moles of vapor per 1000 gal. of vapor.

ng = PV ZRT

and ni = (ngyi)

V = 1,000 7.48

= 133.7 cu ft

+ni, moles C2 0.1626 0.3019 0.5741C3 1.0757 2.8673 6.8556iC4 0.0077 0.0256 0.0743ng = Σni 1.2460 3.1948 7.5040

4. Calculate liquid equivalent gallons (60°F) per 1000 gal-lons vapor.

gal./mole

C2 10.126 1.646 3.057 5.813

C3 10.433 11.223 29.915 71.524

iC4 12.386 0.095 0.317 0.920

Liquid equivalent, gal. 12.964 33.289 78.257

Suggested Simplified ApproachBy using a typical product analysis, calculations can be

made as outlined above, and from these calculations (see ex-ample 6-8) vapor pressure and gallon equivalent charts can bedrawn as shown in Fig. 6-18. A convenient unit of vapor spacevolume should be used, such as 1,000 gal.

Vapor Recovery SystemsVapor recovery systems are generally used to prevent pollu-

tion of the environment and to recover valuable product. Twobasic types of vapor recovery systems may be encountered.One is designed to gather toxic wastes that would pollute theatmosphere but are not valuable enough to warrant full recov-ery. In this type system, the vapors are generally gathered andincinerated. If incineration will not meet government disposalstandards, the vapors are generally compressed and con-densed into a liquid and sent to a liquid disposal system.

6-17

The vapor recovery systems that are typically used with re-frigerated storage tanks are generally integrated with theproduct refrigeration systems. In these types of systems, thevapors are generally compressed, condensed, and put backinto the tank with the fill stream.

Vapor recovery systems on atmospheric pressure, ambienttemperature storage tanks do not normally require a refrig-eration system to condense the vapors. They are generallycompressed through one stage of compression, condensed ineither an air cooled or water cooled exchanger, and then putback into the tank. Fig. 6-19 provides the flow schematic ofthis system.

PARTIAL VOLUMES IN STORAGE TANKS

The volume or size of a storage tank is determined by theconfiguration of the tank that is used (horizontal or vertical

Diam. ftCircumference Area of Circle

Feet Meters sq ft sq m

1 3.14 0.9576 0.785 .072 6.28 1.9151 3.142 .293 9.42 2.8727 7.069 .654 12.57 3.8302 12.566 1.165 15.71 4.7878 19.635 1.82

6 18.85 5.7454 28.274 2.627 21.99 6.7029 38.485 3.578 25.13 7.6605 50.266 4.669 28.27 8.6180 63.617 5.9110 31.42 9.5756 78.540 7.29

11 34.56 10.5332 95.033 8.8212 37.70 11.4907 113.097 10.513 40.84 12.4483 132.732 12.314 43.98 13.4059 153.938 14.315 47.12 14.3634 176.715 16.4

16 50.27 15.3210 201.062 18.617 53.41 16.2785 226.980 21.018 56.55 17.2361 254.469 23.619 59.69 18.1937 283.529 26.320 62.83 19.1512 314.159 29.1

22 69.12 21.0663 380.133 35.324 75.40 22.9815 452.389 42.026 81.68 24.8966 530.929 49.328 87.97 26.8117 615.752 57.230 94.25 28.7268 706.858 65.6

32 100.53 30.6420 804.248 74.734 106.81 32.5571 907.920 84.336 113.10 34.4722 1,017.88 94.538 119.38 36.3873 1,134.11 105.340 125.66 38.3024 1,256.64 116.7

42 131.95 40.2176 1,385.44 128.744 138.23 42.1327 1,520.53 141.246 144.51 44.0478 1,661.90 154.348 150.80 45.9629 1,809.56 168.150 157.08 47.8781 1,963.50 182.4

55 172.79 52.6659 2,375.83 220.760 188.50 57.4537 2,827.43 262.665 204.20 62.2415 3,318.31 308.270 219.91 67.0293 3,848.45 357.575 235.62 71.8171 4,417.86 410.4

80 251.33 76.6049 5,026.55 466.985 267.04 81.3927 5,674.50 527.190 282.74 86.1805 6,361.73 591.095 298.45 90.9683 7,088.22 658.5100 314.16 95.7561 7,853.98 729.6

110 345.58 105.3317 9,503.32 882.8120 376.99 114.9073 11,309.73 1,050130 408.41 124.4829 13,273.23 1,233140 439.82 134.0585 15,393.80 1,430150 471.24 143.6342 17,671.46 1,641

160 502.65 153.2098 20,106.19 1,867170 534.07 162.7854 22,698.00 2,108180 565.49 172.3610 25,446.90 2,364190 596.90 181.9366 28,352.87 2,634200 628.32 191.5122 31,415.93 2,918

NOTES:

1.

2.

If diameters are assumed as meters, values in the columns "CircumferencFeet" and "Area of Circle Square Feet" will represent circumference inmeters and area of circle in square meters respectively.If diameters are assumed as meters, values in column "Area of CirclSquare Feet" will represent volume of cylinder in cubic meters per verticameter of height.

FIG.

Circumference, A rea, and Vol

6-1

cylinder, sphere, rectangle). Each configuration uses differentformulas for determining the total and partial volumes.Figs. 6-21 through 6-26 can be used to determine total andpartial volumes in most common storage tanks.

Volume of cylinder/foot of heightDiam., ft

eters U.S. gal. Imperial gal. U.S. bbls(42 gal.)

30 5.9 4.9 0.140 119 23.5 19.6 0.560 267 52.9 44.0 1.259 375 94.0 78.3 2.238 441 146.9 122.3 3.497 5

68 211.5 176.1 5.04 653 287.9 239.7 6.85 798 376.0 313.1 8.95 802 475.9 396.3 11.33 966 587.5 489.2 13.99 10

89 710.9 591.9 16.93 11071 846.0 704.5 20.14 12312 992.9 826.8 23.64 13013 1,151.5 958.9 27.42 14173 1,321.9 1,100.7 31.47 15

792 1,504.0 1,252.4 35.81 16871 1,697.9 1,413.8 40.43 17409 1,903.6 1,585.1 45.32 18407 2,120.9 1,766.1 50.50 19863 2,350.1 1,956.9 55.95 20

154 2,843.6 2,367.8 67.70 22283 3,384.1 2,817.9 80.57 24249 3,971.6 3,307.1 94.56 26052 4,606.1 3,835.4 109.67 28692 5,287.7 4,402.9 125.90 30

170 6,016.2 5,009.6 143.24 32485 6,791.7 5,655.3 161.71 34637 7,614.2 6,340.2 181.29 36626 8,483.8 7,064.3 201.99 38453 9,400.3 7,827.4 223.82 40

117 10,363.8 8,629.7 246.76 42618 11,374.4 9,471.2 270.82 44956 12,431.9 10,351.8 296.00 46132 13,536.4 11,271.5 322.30 48145 14,688.0 12,230.4 349.71 50

215 17,772.4 14,798.7 423.15 55769 21,150.7 17,611.7 503.59 60805 24,822.7 20,669.3 591.02 65324 28,788.4 23,971.5 685.44 70326 33,047.9 27,518.3 786.86 75

811 37,601.2 31,309.7 895.27 80779 42,448.2 35,345.8 1,010.67 85230 47,589.0 39,626.4 1,133.07 90163 53,023.5 44,151.6 1,262.47 95580 58,751.9 48,921.5 1,398.85 100

862 71,089.7 59,195.0 1,692.61 110.7075 84,602.7 70,446.9 2,014.35 120.1220 99,290.6 82,677.3 2,364.06 130.1297 115,153.6 95,886.1 2,741.75 140.7305 132,191.7 110,073.3 3,147.42 150

.9245 150,404.7 125,239.0 3,581.07 160

.7116 169,792.8 141,383.1 4,042.69 170

.0919 190,356.0 158,505.6 4,532.29 180

.0654 212,094.2 176,606.5 5,049.86 190

.6320 235,007.4 195,685.9 5,595.42 200

Formula to determine capacity per foot of vertical height of cylinder.

e

el

D = Diameter in Feet0.1398854 D2 = Barrels of 42 U.S. Gallons per vertical foot.5.875185 D2 = U.S. Gallons per vertical foot.4.892148 D2 = Imperial Gallons per vertical foot.0.022240 D2 = Cubic Meters per vertical foot.0.785398 D2 (D in meters) = Cubic meters per vertical meter.

6-20

u me of Circles and Cylinders

8

Total volume = volume in 2 heads + volume in cylinder α = 2 x Atan

H1

√2 x H1 x

D2

−H1 2

= 1/6 π K1 D3 + 1/4 π D2 L

K1 = 2 b/D Ze = H1/D Zc = H1/D where α is in radians

Partial volume = 1/6 π K1 D3 × [f(Ze)] + 1/4 π D2 L × [f(Zc)]

f(Zc) = Horizontal cylinder coefficient (see Fig. 6−22) or f(Zc) =

α − sin (α ) x cos (α )π

f(Ze) = Ellipsoidal coefficient (see Fig. 6−23) or f(Ze) = −

H1

D

2

x −3 +

2H1

D

For elliptical 2:1 heads, b = 1/4 D , K1 = 1⁄2

Total volume = volume in heads + volume in cylinder= 1/6 π K1 D

3 + 1/4 π D2 L

Partial volume = 1/6 π K1 D3 × [f(Ze)] + 1/4 π D2 H3

K1 = 2 b/D

Ze = (H1 + H2)/K1 D

f(Ze) = Ellipsoidal coefficient (see Fig. 6−23) or f(Ze) = −

H1

D

2

x −3 +

2H1

D

FIG. 6-21

Partial Volume in Ho rizontal and Vertical Storage Tanks with Ellip soid al or Hemispherical Heads

L

D

b

H1 b

D

b

H3

H2

bH1

LL

D

b

H1 b

H3

VERTICAL CYLINDRICAL TANKS

6-19

Zc 0 1 2 3 4 5 6 7 8 9

.00 .000000 .000053 .000151 .000279 .000429 .000600 .000788 .000992 .001212 .001445

.01 .001692 .001952 .002223 .002507 .002800 .003104 .003419 .003743 .004077 .004421

.02 .004773 .005134 .005503 .005881 .006267 .006660 .007061 .007470 .007886 .008310

.03 .008742 .009179 .009625 .010076 .010534 .010999 .011470 .011947 .012432 .012920

.04 .013417 .013919 .014427 .014940 .015459 .015985 .016515 .017052 .017593 .018141

.05 .018692 .019250 .019813 .020382 .020955 .021533 .022115 .022703 .023296 .023894

.06 .024496 .025103 .025715 .026331 .026952 .027578 .028208 .028842 .029481 .030124

.07 .030772 .031424 .032081 .032740 .033405 .034073 .034747 .035423 .036104 .036789

.08 .037478 .038171 .038867 .039569 .040273 .040981 .041694 .042410 .043129 .043852

.09 .044579 .045310 .046043 .046782 .047523 .048268 .049017 .049768 .050524 .051283

.10 .052044 .052810 .053579 .054351 .055126 .055905 .056688 .057474 .058262 .059054

.11 .059850 .060648 .061449 .062253 .063062 .063872 .064687 .065503 .066323 .067147

.12 .067972 .068802 .069633 .070469 .071307 .072147 .072991 .073836 .074686 .075539

.13 .076393 .077251 .078112 .078975 .079841 .080709 .081581 .082456 .083332 .084212

.14 .085094 .085979 .086866 .087756 .088650 .089545 .090443 .091343 .092246 .093153

.15 .094061 .094971 .095884 .096799 .097717 .098638 .099560 .100486 .101414 .102343

.16 .103275 .104211 .105147 .106087 .107029 .107973 .108920 .109869 .110820 .111773

.17 .112728 .113686 .114646 .115607 .116572 .117538 .118506 .119477 .120450 .121425

.18 .122403 .123382 .124364 .125347 .126333 .127321 .128310 .129302 .130296 .131292

.19 .132290 .133291 .134292 .135296 .136302 .137310 .138320 .139332 .140345 .141361

.20 .142378 .143398 .144419 .145443 .146468 .147494 .148524 .149554 .150587 .151622

.21 .152659 .153697 .154737 .155779 .156822 .157867 .158915 .159963 .161013 .162066

.22 .163120 .164176 .165233 .166292 .167353 .168416 .169480 .170546 .171613 .172682

.23 .173753 .174825 .175900 .176976 .178053 .179131 .180212 .181294 .182378 .183463

.24 .184550 .185639 .186729 .187820 .188912 .190007 .191102 .192200 .193299 .194400

.25 .195501 .196604 .197709 .198814 .199922 .201031 .202141 .203253 .204368 .205483

.26 .206600 .207718 .208837 .209957 .211079 .212202 .213326 .214453 .215580 .216708

.27 .217839 .218970 .220102 .221235 .222371 .223507 .224645 .225783 .226924 .228065

.28 .229209 .230352 .231498 .232644 .233791 .234941 .236091 .237242 .238395 .239548

.29 .240703 .241859 .243016 .244173 .245333 .246494 .247655 .248819 .249983 .251148

.30 .252315 .253483 .254652 .255822 .256992 .258165 .259338 .260512 .261687 .262863

.31 .264039 .265218 .266397 .267578 .268760 .269942 .271126 .272310 .273495 .274682

.32 .275869 .277058 .278247 .279437 .280627 .281820 .283013 .284207 .285401 .286598

.33 .287795 .288992 .290191 .291390 .292591 .293793 .294995 .296198 .297403 .298608

.34 .299814 .301021 .302228 .303438 .304646 .305857 .307068 .308280 .309492 .310705

.35 .311918 .313134 .314350 .315566 .316783 .318001 .319219 .320439 .321660 .322881

.36 .324104 .325326 .326550 .327774 .328999 .330225 .331451 .332678 .333905 .335134

.37 .336363 .337593 .338823 .340054 .341286 .342519 .343751 .344985 .346220 .347455

.38 .348690 .349926 .351164 .352402 .353640 .354879 .356119 .357359 .358599 .359840

.39 .361082 .362325 .363568 .364811 .366056 .367300 .368545 .369790 .371036 .372282

.40 .373530 .374778 .376026 .377275 .378524 .379774 .381024 .382274 .383526 .384778

.41 .386030 .387283 .388537 .389790 .391044 .392298 .393553 .394808 .396063 .397320

.42 .398577 .399834 .401092 .402350 .403608 .404866 .406125 .407384 .408645 .409904

.43 .411165 .412426 .413687 .414949 .416211 .417473 .418736 .419998 .421261 .422525

.44 .423788 .425052 .426316 .427582 .428846 .430112 .431378 .432645 .433911 .435178

.45 .436445 .437712 .438979 .440246 .441514 .442782 .444050 .445318 .446587 .447857

.46 .449125 .450394 .451663 .452932 .454201 .455472 .456741 .458012 .459283 .460554

.47 .461825 .463096 .464367 .465638 .466910 .468182 .469453 .470725 .471997 .473269

.48 .474541 .475814 .477086 .478358 .479631 .480903 .482176 .483449 .484722 .485995

.49 .487269 .488542 .489814 .491087 .492360 .493633 .494906 .496179 .497452 .498726

FIG. 6-22

Coefficients for Partial Volumes of Horizontal Cylinders, f(Zc)

6-20

Zc 0 1 2 3 4 5 6 7 8 9

.50 .500000 .501274 .502548 .503821 .505094 .506367 .507640 .508913 .510186 .511458

.51 .512731 .514005 .515278 .516551 .517824 .519097 .520369 .521642 .522914 .524186

.52 .525459 .526731 .528003 .529275 .530547 .531818 .533090 .534362 .535633 .536904

.53 .538175 .539446 .540717 .541988 .543259 .544528 .545799 .547068 .548337 .549606

.54 .550875 .552143 .553413 .554682 .555950 .557218 .558486 .559754 .561021 .562288

.55 .563555 .564822 .566089 .567355 .568622 .569888 .571154 .572418 .573684 .574948

.56 .576212 .577475 .578739 .580002 .581264 .582527 .583789 .585051 .586313 .587574

.57 .588835 .590096 .591355 .592616 .593875 .595134 .596392 .597650 .598908 .600166

.58 .601423 .602680 .603937 .605192 .606447 .607702 .608956 .610210 .611463 .612717

.59 .613970 .615222 .616474 .617726 .618976 .620226 .621476 .622725 .623974 .625222

.60 .626470 .627718 .628964 .630210 .631455 .632700 .633944 .635189 .636432 .637675

.61 .638918 .640160 .641401 .642641 .643881 .645121 .646360 .647598 .648836 .650074

.62 .651310 .652545 .653780 .655015 .656249 .657481 .658714 .659946 .661177 .662407

.63 .663637 .664866 .666095 .667322 .668549 .669775 .671001 .672226 .673450 .674674

.64 .675896 .677119 .678340 .679561 .680781 .681999 .683217 .684434 .685650 .686866

.65 .688082 .689295 .690508 .691720 .692932 .694143 .695354 .696562 .697772 .698979

.66 .700186 .701392 .702597 .703802 .705005 .706207 .707409 .708610 .709809 .711008

.67 .712205 .713402 .714599 .715793 .716987 .718180 .719373 .720563 .721753 .722942

.68 .724131 .725318 .726505 .727690 .728874 .730058 .731240 .732422 .733603 .734782

.69 .735961 .737137 .738313 .739488 .740662 .741835 .743008 .744178 .745348 .746517

.70 .747685 .748852 .750017 .751181 .752345 .753506 .754667 .755827 .756984 .758141

.71 .759297 .760452 .761605 .762758 .763909 .765059 .766209 .767356 .768502 .769648

.72 .770791 .771935 .773076 .774217 .775355 .776493 .777629 .778765 .779898 .781030

.73 .782161 .783292 .784420 .785547 .786674 .787798 .788921 .790043 .791163 .792282

.74 .793400 .794517 .795632 .796747 .797859 .798969 .800078 .801186 .802291 .803396

.75 .804499 .805600 .806701 .807800 .808898 .809993 .811088 .812180 .813271 .814361

.76 .815450 .816537 .817622 .818706 .819788 .820869 .821947 .823024 .824100 .825175

.77 .826247 .827318 .828387 .829454 .830520 .831584 .832647 .833708 .834767 .835824

.78 .836880 .837934 .838987 .840037 .841085 .842133 .843178 .844221 .845263 .846303

.79 .847341 .848378 .849413 .850446 .851476 .852506 .853532 .854557 .855581 .856602

.80 .857622 .858639 .859655 .860668 .861680 .862690 .863698 .864704 .865708 .866709

.81 .867710 .868708 .869704 .870698 .871690 .872679 .873667 .874653 .875636 .876618

.82 .877597 .878575 .879550 .880523 .881494 .882462 .883428 .884393 .885354 .886314

.83 .887272 .888227 .889180 .890131 .891080 .892027 .892971 .893913 .894853 .895789

.84 .896725 .897657 .898586 .899514 .900440 .901362 .902283 .903201 .904116 .905029

.85 .905939 .906847 .907754 .908657 .909557 .910455 .911350 .912244 .913134 .914021

.86 .914906 .915788 .916668 .917544 .918419 .919291 .920159 .921025 .921888 .922749

.87 .923607 .924461 .925314 .926164 .927009 .927853 .928693 .929531 .930367 .931198

.88 .932028 .932853 .933677 .934497 .935313 .936128 .936938 .937747 .938551 .939352

.89 .940150 .940946 .941738 .942526 .943312 .944095 .944874 .945649 .946421 .947190

.90 .947956 .948717 .949476 .950232 .950983 .951732 .952477 .953218 .953957 .954690

.91 .955421 .956148 .956871 .957590 .958306 .959019 .959727 .960431 .961133 .961829

.92 .962522 .963211 .963896 .964577 .965253 .965927 .966595 .967260 .967919 .968576

.93 .969228 .969876 .970519 .971158 .971792 .972422 .973048 .973669 .974285 .974897

.94 .975504 .976106 .976704 .977297 .977885 .978467 .979045 .979618 .980187 .980750

.95 .981308 .981859 .982407 .982948 .983485 .984015 .984541 .985060 .985573 .986081

.96 .986583 .987080 .987568 .988053 .988530 .989001 .989466 .989924 .990375 .990821

.97 .991258 .991690 .992114 .992530 .992939 .993340 .993733 .994119 .994497 .994866

.98 .995227 .995579 .995923 .996257 .996581 .996896 .997200 .997493 .997777 .998048

.99 .998308 .998555 .998788 .999008 .999212 .999400 .999571 .999721 .999849 .9999471.00 1.000000

FIG. 6-22 (Cont’d)

Coefficients for Partial Volumes of Horizontal Cylinders, f(Zc)

6-21

Coefficients for Partial Volumes of Ellipsoids or Spheres, f(Ze)Ze 0 1 2 3 4 5 6 7 8 9.00 .000000 .000003 .000012 .000027 .000048 .000075 .000108 .000146 .000191 .000242.01 .000298 .000360 .000429 .000503 .000583 .000668 .000760 .000857 .000960 .001069.02 .001184 .001304 .001431 .001563 .001700 .001844 .001993 .002148 .002308 .002474.03 .002646 .002823 .003006 .003195 .003389 .003589 .003795 .004006 .004222 .004444.04 .004672 .004905 .005144 .005388 .005638 .005893 .006153 .006419 .006691 .006968

.05 .007250 .007538 .007831 .008129 .008433 .008742 .009057 .009377 .009702 .010032

.06 .010368 .010709 .011055 .011407 .011764 .012126 .012493 .012865 .013243 .013626

.07 .014014 .014407 .014806 .015209 .015618 .016031 .016450 .016874 .017303 .017737

.08 .018176 .018620 .019069 .019523 .019983 .020447 .020916 .021390 .021869 .022353

.09 .022842 .023336 .023835 .024338 .024847 .025360 .025879 .026402 .026930 .027462

.10 .028000 .028542 .029090 .029642 .030198 .030760 .031326 .031897 .032473 .033053

.11 .033638 .034228 .034822 .035421 .036025 .036633 .037246 .037864 .038486 .039113

.12 .039744 .040380 .041020 .041665 .042315 .042969 .043627 .044290 .044958 .045630

.13 .046306 .046987 .047672 .048362 .049056 .049754 .050457 .051164 .051876 .052592

.14 .053312 .054037 .054765 .055499 .056236 .056978 .057724 .058474 .059228 .059987

.15 .060750 .061517 .062288 .063064 .063843 .064627 .065415 .066207 .067003 .067804

.16 .068608 .069416 .070229 .071046 .071866 .072691 .073519 .074352 .075189 .076029

.17 .076874 .077723 .078575 .079432 .080292 .081156 .082024 .082897 .083772 .084652

.18 .085536 .086424 .087315 .088210 .089109 .090012 .090918 .091829 .092743 .093660

.19 .094582 .095507 .096436 .097369 .098305 .099245 .100189 .101136 .102087 .103042

.20 .104000 .104962 .105927 .106896 .107869 .108845 .109824 .110808 .111794 .112784

.21 .113778 .114775 .115776 .116780 .117787 .118798 .119813 .120830 .121852 .122876

.22 .123904 .124935 .125970 .127008 .128049 .129094 .130142 .131193 .132247 .133305

.23 .134366 .135430 .136498 .137568 .138642 .139719 .140799 .141883 .142969 .144059

.24 .145152 .146248 .147347 .148449 .149554 .150663 .151774 .152889 .154006 .155127

.25 .156250 .157376 .158506 .159638 .160774 .161912 .163054 .164198 .165345 .166495

.26 .167648 .168804 .169963 .171124 .172289 .173456 .174626 .175799 .176974 .178153

.27 .179334 .180518 .181705 .182894 .184086 .185281 .186479 .187679 .188882 .190088

.28 .191296 .192507 .193720 .194937 .196155 .197377 .198601 .199827 .201056 .202288

.29 .203522 .204759 .205998 .207239 .208484 .209730 .210979 .212231 .213485 .214741

.30 .216000 .217261 .218526 .219792 .221060 .222331 .223604 .224879 .226157 .227437

.31 .228718 .230003 .231289 .232578 .233870 .235163 .236459 .237757 .239057 .240359

.32 .241664 .242971 .244280 .245590 .246904 .248219 .249536 .250855 .252177 .253500

.33 .254826 .256154 .257483 .258815 .260149 .261484 .262822 .264161 .265503 .266847

.34 .268192 .269539 .270889 .272240 .273593 .274948 .276305 .277663 .279024 .280386

.35 .281750 .283116 .284484 .285853 .287224 .288597 .289972 .291348 .292727 .294106

.36 .295488 .296871 .298256 .299643 .301031 .302421 .303812 .305205 .306600 .307996

.37 .309394 .310793 .312194 .313597 .315001 .316406 .317813 .319222 .320632 .322043

.38 .323456 .324870 .326286 .327703 .329122 .330542 .331963 .333386 .334810 .336235

.39 .337662 .339090 .340519 .341950 .343382 .344815 .346250 .347685 .349122 .350561Note: Coefficients apply for the volume of 2 ellipsoidal or hemispherical heads not the volume for 1 head.

FIG. 6-23

Table of Coefficients and Formulas for Determining Partial Volumes in Ellipsoids and Spheres

6-22

Coefficients for Partial Volumes of Ellipsoids or Spheres, f(Ze)Ze 0 1 2 3 4 5 6 7 8 9.40 .352000 .353441 .354882 .356325 .357769 .359215 .360661 .362109 .363557 .365007.41 .366458 .367910 .369363 .370817 .372272 .373728 .375185 .376644 .378103 .379563.42 .381024 .382486 .383949 .385413 .386878 .388344 .389810 .391278 .392746 .394216.43 .395686 .397157 .398629 .400102 .401575 .403049 .404524 .406000 .407477 .408954.44 .410432 .411911 .413390 .414870 .416351 .417833 .419315 .420798 .422281 .423765

.45 .425250 .426735 .428221 .429708 .431195 .432682 .434170 .435659 .437148 .438638

.46 .440128 .441619 .443110 .444601 .446093 .447586 .449079 .450572 .452066 .453560

.47 .455054 .456549 .458044 .459539 .461035 .462531 .464028 .465524 .467021 .468519

.48 .470016 .471514 .473012 .474510 .476008 .477507 .479005 .480504 .482003 .483593

.49 .485002 .486501 .488001 .489501 .491000 .492500 .494000 .495500 .497000 .498500

.50 .500000 .501500 .503000 .504500 .506000 .507500 .509000 .510499 .511999 .513499

.51 .514998 .516497 .517997 .519496 .520995 .522493 .523992 .525490 .526988 .528486

.52 .529984 .531481 .532979 .534476 .535972 .537469 .538965 .540461 .541956 .543451

.53 .544946 .546440 .547934 .549428 .550921 .552414 .553907 .555399 .556890 .558381

.54 .559872 .561362 .562852 .564341 .565830 .567318 .568805 .570292 .571779 .573265

.55 .574750 .576235 .577719 .579202 .580685 .582167 .583649 .585130 .586610 .588089

.56 .589568 .591046 .592523 .594000 .595476 .596951 .598425 .599898 .601371 .602843

.57 .604314 .605784 .607254 .608722 .610190 .611656 .613122 .614587 .616051 .617514

.58 .618976 .620437 .621897 .623356 .624815 .626272 .627728 .629183 .630637 .632090

.59 .633542 .634993 .636443 .637891 .639339 .640785 .642231 .643675 .645118 .646559

.60 .648000 .649439 .650878 .652315 .653750 .655185 .656618 .658050 .659481 .660910

.61 .662338 .663765 .665190 .666614 .668037 .669458 .670878 .672297 .673714 .675130

.62 .676544 .677957 .679368 .680778 .682187 .683594 .684999 .686403 .687806 .689207

.63 .690606 .692004 .693400 .694795 .696188 .697579 .698969 .700357 .701744 .703129

.64 .704512 .705894 .707273 .708652 .710028 .711403 .712776 .714147 .715516 .716884

.65 .718250 .719614 .720976 .722337 .723695 .725052 .726407 .727760 .729111 .730461

.66 .731808 .733153 .734497 .735839 .737178 .738516 .739851 .741185 .742517 .743846

.67 .745174 .746500 .747823 .749145 .750464 .751781 .753096 .754410 .755720 .757029

.68 .758336 .759641 .760943 .762243 .763541 .764837 .766130 .767422 .768711 .769997

.69 .771282 .772563 .773843 .775121 .776396 .777669 .778940 .780208 .781474 .782739

.70 .784000 .785259 .786515 .787769 .789021 .790270 .791516 .792761 .794002 .795241

.71 .796478 .797712 .798944 .800173 .801399 .802623 .803845 .805063 .806280 .807493

.72 .808704 .809912 .811118 .812321 .813521 .814719 .815914 .817106 .818295 .819482

.73 .820666 .821847 .823026 .824201 .825374 .826544 .827711 .828876 .830037 .831196

.74 .832352 .833505 .834655 .835802 .836946 .838088 .839226 .840362 .841494 .842624

.75 .843750 .844873 .845994 .847111 .848226 .849337 .850446 .851551 .852653 .853752

.76 .854848 .855941 .857031 .858117 .859201 .860281 .861358 .862432 .863502 .864570

.77 .865634 .866695 .867753 .868807 .869858 .870906 .871951 .872992 .874030 .875065

.78 .876096 .877124 .878148 .879170 .880187 .881202 .882213 .883220 .884224 .885225

.79 .886222 .887216 .888206 .889192 .890176 .891155 .892131 .893104 .894073 .895038

.80 .896000 .896958 .897913 .898864 .899811 .900755 .901695 .902631 .903564 .904493

.81 .905418 .906340 .907257 .908171 .909082 .909988 .910891 .911790 .912685 .913576

.82 .914464 .915348 .916228 .917103 .917976 .918844 .919708 .920568 .921425 .922277

.83 .923126 .923971 .924811 .925648 .926481 .927309 .928134 .928954 .929771 .930584

.84 .931392 .932196 .932997 .933793 .934585 .935373 .936157 .936936 .937712 .938483

.85 .939250 .940013 .940772 .941526 .942276 .943022 .943764 .944501 .945235 .945963

.86 .946688 .947408 .948124 .948836 .949543 .950246 .950944 .951638 .952328 .953013

.87 .953694 .954370 .955042 .955710 .956373 .957031 .957685 .958335 .958980 .959620

.88 .960256 .960887 .961514 .962136 .962754 .963367 .963975 .964579 .965178 .965772

.89 .966362 .966947 .967527 .968103 .968674 .969240 .969802 .970358 .970910 .971458

.90 .972000 .972538 .973070 .973598 .974121 .974640 .975153 .975662 .976165 .976664

.91 .977158 .977647 .978131 .978610 .979084 .979553 .980017 .980477 .980931 .981380

.92 .981824 .982263 .982697 .983126 .983550 .983969 .984382 .984791 .985194 .985593

.93 .985986 .986374 .986757 .987135 .987507 .987874 .988236 .988593 .988945 .989291

.94 .989632 .989968 .990298 .990623 .990943 .991258 .991567 .991871 .992169 .992462

.95 .992750 .993032 .993309 .993581 .993847 .994107 .994362 .994612 .994856 .995095

.96 .995328 .995556 .995778 .995994 .996205 .996411 .996611 .996805 .996994 .997177

.97 .997354 .997526 .997692 .997852 .998007 .998156 .998300 .998437 .998569 .998696

.98 .998816 .998931 .999040 .999143 .999240 .999332 .999417 .999497 .999571 .999640

.99 .999702 .999758 .999809 .999854 .999892 .999925 .999952 .999973 .999988 .9999971.00 1.000000

Note: Coefficients apply for the volume of 2 ellipsoidal or hemispherical heads not the volume for 1 head.

FIG. 6-23 (Cont’d)

Table of Coefficients and Formulas for Determining Partial Volumes in Ellipsoids and Spheres

6-23

Diameter inFt.

Surface ofSphere in

Sq. Ft.

Volume of Sphere Diameter inFt.

Surface ofSphere in

Sq. Ft.

Volume of Sphere

Cu. Ft. U.S. Gals. U.S. Bbls. Cu. Ft. U.S. Gals. U.S. Bbls.

1 3.14 0.52 3.92 .09 61 11,690 118,847 889,037 21,1682 12.57 4.19 31.33 .75 62 12,076 124,788 933,481 22,2263 28.27 14.14 105.75 2.52 63 12,469 130,924 979,382 23,3194 50.27 33.51 250.67 5.97 64 12,868 137,258 1,026,764 24,4475 78.54 65.45 489.60 11.66 65 13,273 143,793 1,075,649 25,611

6 113.10 113.10 846.03 20.14 66 13,685 150,533 1,126,062 26,8117 153.94 179.59 1,343.46 31.99 67 14,103 157,479 1,178,026 28,0488 201.06 268.08 2,005.40 47.75 68 14,527 164,636 1,231,565 29,3239 254.47 381.70 2,855.34 67.98 69 14,957 172,007 1,286,701 30,63610 314.16 523.60 3,916.79 93.26 70 15,394 179,594 1,343,460 31,987

11 380 697 5,213 124 71 15,837 187,402 1,401,863 33,37812 452 905 6,768 161 72 16,286 195,432 1,461,935 34,80813 531 1,150 8,605 205 73 16,742 203,689 1,523,699 36,27914 616 1,437 10,748 256 74 17,203 212,175 1,587,178 37,79015 707 1,767 13,219 315 75 17,671 220,893 1,652,397 39,343

16 804 2,145 16,043 382 76 18,146 229,847 1,719,378 40,93817 908 2,572 19,243 458 77 18,627 239,040 1,788,145 42,57518 1,018 3,054 22,843 544 78 19,113 248,475 1,858,721 44,25519 1,134 3,591 26,865 640 79 19,607 258,155 1,931,131 45,97920 1,257 4,189 31,334 746 80 20,106 268,083 2,005,398 47,748

21 1,385 4,849 36,273 864 81 20,612 278,262 2,081,544 49,56122 1,521 5,575 41,706 993 82 21,124 288,696 2,159,594 51,41923 1,662 6,371 47,656 1,135 83 21,642 299,387 2,239,571 53,32324 1,810 7,238 54,146 1,289 84 22,167 310,339 2,321,498 55,27425 1,963 8,181 61,200 1,457 85 22,698 321,555 2,405,400 57,271

26 2,124 9,203 68,842 1,639 86 23,235 333,038 2,491,299 59,31727 2,290 10,306 77,094 1,836 87 23,779 344,792 2,579,219 61,41028 2,463 11,494 85,981 2,047 88 24,328 356,818 2,669,184 63,55229 2,642 12,770 95,527 2,274 89 24,885 369,121 2,761,217 65,74330 2,827 14,137 105,753 2,518 90 25,447 381,704 2,855,341 67,984

31 3,019 15,599 116,685 2,778 91 26,016 394,569 2,951,581 70,27632 3,217 17,157 128,345 3,056 92 26,590 407,720 3,049,959 72,61833 3,421 18,817 140,758 3,351 93 27,172 421,161 3,150,499 75,01234 3,632 20,580 153,946 3,665 94 27,759 434,893 3,253,225 77,45835 3,848 22,449 167,932 3,998 95 28,353 448,921 3,358,160 79,956

36 4,072 24,429 182,742 4,351 96 28,953 463,247 3,465,327 82,50837 4,301 26,522 198,397 4,724 97 29,559 477,875 3,574,750 85,11338 4,536 28,731 214,922 5,117 98 30,172 492,807 3,686,453 87,77339 4,778 31,059 232,340 5,532 99 30,791 508,048 3,800,459 90,48740 5,027 33,510 250,675 5,968 100 31,416 523,599 3,916,792 93,257

41 5,281 36,087 269,949 6,427 101 32,047 539,465 4,035,475 96,08342 5,542 38,792 290,187 6,909 102 32,685 555,647 4,156,531 98,96543 5,809 41,630 311,412 7,415 103 33,329 572,151 4,279,984 101,90444 6,082 44,602 333,648 7,944 104 33,979 588,978 4,405,858 104,90145 6,362 47,713 356,918 8,498 105 34,636 606,131 4,534,176 107,957

46 6,648 50,965 381,245 9,077 106 35,299 623,615 4,664,962 111,07147 6,940 54,362 406,653 9,682 107 35,968 641,431 4,798,239 114,24448 7,238 57,906 433,166 10,313 108 36,644 659,584 4,934,030 117,47749 7,543 61,601 460,807 10,972 109 37,325 678,076 5,072,359 120,77150 7,854 65,450 489,599 11,657 110 38,013 696,910 5,213,250 124,125

51 8,171 69,456 519,566 12,371 111 38,708 716,090 5,356,726 127,54152 8,495 73,622 550,732 13,113 112 39,408 735,619 5,502,811 131,01953 8,825 77,952 583,120 13,884 113 40,115 755,499 5,651,527 134,56054 9,161 82,448 616,754 14,685 114 40,828 775,735 5,802,900 138,16455 9,503 87,114 651,656 15,516 115 41,548 796,329 5,956,951 141,832

56 9,852 91,952 687,851 16,377 116 42,273 817,284 6,113,705 145,56457 10,207 96,967 725,362 17,271 117 43,005 838,603 6,273,185 149,36258 10,568 102,160 764,213 18,196 118 43,744 860,290 6,435,415 153,22459 10,936 107,536 804,427 19,153 119 44,488 882,348 6,600,417 157,15360 11,310 113,097 846,027 20,144 120 45,239 904,779 6,768,217 161,148

Note: If diameters are assumed as meters, values in columns "Surface ofSphere in Square Feet" and "Volume of Sphere — Cubic Feet" will representSurface of Sphere in Square Meters and Volume of Sphere in Cubic Metersrespectively.Surface area of sphere = 3.141593 D2 Square Feet

Volume of Sphere =

0.523599 D3 Cubic Feet 0.093257 D3 Barrels of 42 U.S. Gallons

Number of barrels of 42 U.S. Gallons at any inch in a true sphere =(3d – 2h) h2 x 0.000 053 968 1 where d is diameter of sphere and h is depth ofliquid both in inches.

FIG. 6-24

Approximate Surface and Volume of Spheres

6-24

Diameterof Tank Depth of Liquid, ft.

ft (in.) 2 4 6 8 10 12 14 16 18 20 25 30 35 40 45 50

2 (24) 31.3 –

4 (48) 125.3 250.7 –

6 (72) 219.3 626.7 846 –

8 (96) 313.3 1003 1692 2005 –

10 (120) 407.3 1329 2538 3509 3917 –

12 (144) 501.3 1755 3384 5013 6267 6768 –

14 (168) 595.4 2131 4230 6518 8617 10152 10748 –

16 (192) 689.4 2507 5076 8022 10967 13536 15354 16043 –

18 (216) 783.4 2883 5822 9526 13317 16920 19960 22059 22843 –

20 (240) 877.4 3259 6768 11030 15667 20305 24566 38075 30457 31334 –

25 (300) 1112 4199 8883 14790 21542 28765 36081 43116 49492 54832 51200 –

30 (360) 1347 5139 10998 18550 27417 37225 47597 58156 68528 78336 97920 105753 –

35 (420) 1582 6079 13113 22310 33293 45685 59112 73197 87564 101836 134639 158630 167932 –

40 (480) 1817 7019 15228 26070 39168 54146 70627 88237 106599 125338 171359 211506 239903 250676 –

45 (540) 2052 7959 17344 29830 45053 52606 82143 103278 125635 148838 208079 264383 311874 344677 356918 –

50 (600) 2287 8899 19459 33530 50918 71066 93658 118318 144670 172338 244799 317259 383845 438679 475889 489599

FIG. 6-25

Partial Volumes of Spheres — U.S. Gallons

TankWidth,

ft

Tank Length, ft

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

1 3.74 7.48 11.22 14.96 18.70 22.44 26.18 29.92 33.66 37.40 41.14 44.882 7.48 14.96 22.44 29.92 37.40 44.88 52.36 59.84 67.32 74.81 82.29 89.773 11.22 22.44 33.66 44.88 56.10 67.32 78.55 89.77 100.99 112.21 123.43 134.654 14.96 29.92 44.88 59.84 74.81 89.77 104.73 119.69 134.65 149.61 164.57 179.535 18.70 37.40 56.10 74.81 93.51 112.21 130.91 149.61 168.31 187.01 205.71 224.426 22.44 44.88 67.32 89.77 112.21 134.65 157.09 179.53 201.97 224.42 246.86 269.307 26.18 52.36 78.55 104.73 130.91 157.09 183.27 209.45 235.64 261.82 288.00 314.188 29.92 59.84 89.77 119.69 149.61 179.53 209.45 239.38 269.30 299.22 329.14 359.06

TankWidth,

ft

Tank Length, ft

6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0

1 48.62 52.36 56.10 59.84 63.58 67.32 71.06 74.81 78.55 82.29 86.03 89.772 97.25 104.73 112.21 119.69 127.17 134.65 142.13 149.61 157.09 164.57 172.05 179.533 145.87 157.09 168.31 179.53 190.75 201.97 213.19 224.42 235.64 246.86 258.08 269.304 194.49 209.45 224.42 239.38 254.34 269.30 284.26 299.22 314.18 329.14 344.10 359.075 243.12 261.82 280.52 299.22 317.92 336.62 355.32 374.03 392.73 411.43 430.13 448.836 291.74 314.18 336.62 359.06 381.51 403.95 426.39 448.83 471.27 493.71 516.16 538.607 340.36 366.55 392.73 418.91 445.09 471.27 497.45 523.64 549.82 576.00 602.18 628.368 388.99 418.91 448.83 478.75 508.68 538.60 568.52 598.44 628.36 658.29 688.21 718.13

1 cu ft = 7.4805 U.S. gal.

Total Volume = W • L • HT = cu ft

Partial Volume = W • L • Hp = cu ft

* For imperial gallons, divide above capacities by 1.2

FIG. 6-26

Approximate Capacities (U.S. Gallons) of Rectangular Tanks for Each Foot of Liquid*

6-25

STANDARDS AND CODES

ANSI A12.1Safety Requirements for Floor and Wall Openings, Railings,and Toeboards.

ANSI A14.1Requirements for Fixed Industrial Stairs.

ANSI A14.3Safety Code for Fixed Ladders.

ANSI A11.197Measurement and Calibration of Upright Cylindrical Tanks,Method for (ASTM D 1220-65, API 2550).

ANSI Z11.198Measurement and Calibration of Horizontal Tanks, Methodfor (ASTM D 1410-65, API 2551).

ANSI A11.1988Measurement and Calibration of Spheres and Spheroids,Method for (ASTM D 1408-65, API 2552).

ANSI Z11.202Liquid Calibration of Tanks (ASTM D 1406-65 API 2555).

ANSI/ASME B31.4Liquid Petroleum Transportation Piping System.

API Recommended Practices for Leached Underground Storage pre-pared by API Committee 510.

API Specification 12 BSpecifications for Bolted Tanks for Storage of Production Liq-uids.

API Specification 12 DSpecifications for Field Welded Tanks for Storage of Produc-tion Liquids.

API Specification 12 FSpecifications for Shop Welded Tanks for Storage of Produc-tion Liquids.

API Standard 620Recommended Rules for Design and Construction of Large,Welded Low-Pressure Storage Tanks.

API Standard 650Welded Steel Tanks for Crude Storage.

API Standard 2000Venting Atmospheric and Low-Pressure Storage Tanks.

API RP 12 RIRecommended Practice for Setting, Connecting, Maintenanceand Operation of Lease Tanks.

API RP 50Recommended Gas Plant Good Operating Practices for Pro-tection of Environment.

6-26

API RP 200Fire Protection for Refineries.

ASME Code for Unfired Pressure Vessels, Section VIII, Division I &II.

AWWA D-100Welded Tanks

AWWA D-103Bolted Tanks

Federal Register, Part 1910, Occupational Safety & Health Standards,Subpart D, Walking-Working Surfaces.

GPA North American Storage Capacity for Light Hydrocarbons andU.S. LP-Gas Import Terminals.

IOCC Underground Storage of Liquid Petroleum Hydrocarbons in theUnited States. (Interstate Oil Compact Commission.)

National Association of Corrosion Engineers. Item No. 51101 - Electrochemical Techniques for Corrosion.Item No. 52044 - Coatings and Linings for Immersion Service.

NACE - TPC Publication No. 5Corrosion Control in Petroleum Production.

National Board of Fire Underwriters (NBFU)National Fire Protection Association (NFPA)

No. 11, 30-25, and 20-26

REFERENCES

1. Blodbett, Omer W., Design of Welded Structures, James F. LincolnArc Welding Foundation, Cleveland, Ohio.

2. Kuman, J. and Jed Lieka, J. A., Calculation & Shortcut Deskbook,McGraw-Hill Publications, New York, New York.

3. Graphic Methods for Thermal Insulation, Johns-Manville Ken-Caryl Ranch, Denver, Colorado 80217.

BIBLIOGRAPHY

1. Nelson, W. L., Petroleum Refinery Engineering, 4th Edition,McGraw-Hill Book Co. (1958).

2. Oil Insurance Association Recommendations & Guidelines forGasoline Plants - No. 301.

3. Perry, Robert H., Perry’s Chemical Engineer’s Handbook, 6thEdition, 1985.

4. Selby, Samuel M., Standard Mathematical Tables, 21st Edition,1973.

5. Underwriters Laboratories (UL)No. 142 Steel Above Ground TanksNo. 58 Steel Underground Tanks