58-2

Preface

PETROLEUM ENGINEERING HANDBOOK

The SPE Board in June 1982 endorsed revisions to “SPE Tentative Metric Standard” (Dec. 1977 JPT. Pages 1575 161 1) and adopted it for implementation as this

“SPE Metric Standard.” The following standard is the final product of 12 years’

work by the Symbols and Metrication Committee. Members of the Metrication Subcommittee included John M. Campbell, chairman. John M. Campbell & Co.: Robert A. Campbell. Magnum Engineenng Inc.; Robert E. Carlile. Texas Tech U.; J. Donald Clark, petroleum consultant; Hank Groeneveld, Mobil Oil Canada: Terry Pollard. retired. et--c@io member: and Howard B. Bradley. professional/technical training consultant.

With very few exceptions. the units shown are those

proposed and/or adopted by other groups involved in the metrication exercise, including those agencies charged with the responsibility (nationally and internationally) for establishing metric standards. These few exceptions, still to be decided, are summarized in the introduction to Part 2 of this report.

These standards include most of the units used com- monly by SPE members. The subcommittee is aware that some will find the list incomplete for their area of specialty. Additions will continue lo be made but too long a list can become cumbersome. The subcommittee believes that these standards provide a basis for metric practice beyond the units listed. So long as one maintains these standards a new unit can be “coined” that should prove acceptable.

Part 1: SI-The International System of Units* Introduction Worldwide scientific, engineering, industrial. and cotn- mercial groups are converting to SI metric units. Many in the U.S. arc now active in such conversion. based on work accomplished by national ’ and international’ authorities. Various U.S. associations. professional societies. and agencies are involved in this process. in- cluding. but not limited to. the American Sot. for Testing and Materials (ASTM)? American Petroleum Inst. (API).‘.’ American Nat]. Standards Inst. (AN- SI), ‘.’ American Sot. of Mechanical Engineers

(ASME).’ and American Natl. Metric Council

(ANMC).X The Canadian Petroleutn Assn. (CPA) and other Canadian groups have been especially active in conversion work. ” SPE intends to hccp its worldwide memberahlp informed on the conversion to and use of SI metric unit,.

The term “SI” is an abbreviation for Le Systgme In- ternational d’Unit& or The International System of Units.

SI is not identical with any of the former cgs, mks, or mksA systems of metric units but is closely related to them and is an extension of and improvement over them. SI measurement symbols are identical in all languages. As in any other language, rules of spelling, punctuation, and pronunciation are essential to avoid errors in numerical work and to make the system easier to use and understand on a worldwide basis. These rules, together with decimal usage, units coherence, and a series of standard prefixes for multiples and submultiples of most SI units, provide a rational system with minimum dif- ficulty of transition from English units or older systems of metric units. Refs. 1 through 4 of this paper are recommended to the reader wishing official information, development history, or more detail on SI: material from these and other references cited has been used freely in this report.

Appendix A provides definitions for some of the terms used.

‘Prepared by T A Pollard for the subcommittee Based on paper SPE 6212 presented by T A Pollard at Ihe ,976 SPE Annual Techn~ca, Conference and EXhlb, ho”. New Orleans. act 3-6

SI Units and Unit Symbols3 The short-form designations of units (such as ti for feet. kg for kilograms, m for meters, mol for moles, etc.) have heretofore been called unit “abbreviations” in SPE terminology to avoid confusion with the tetm “sym bols” applied to letter symbols used in mathematical equations. However, international and national standard practice is to call these unit designations “unit sym- bols”; the latter usage will be followed in this report.

SI Units

SI is based on seven well-defined “base units” that quantify seven hn.sc~ ymntitic~ that hi c,orz~wztiorz are regarded as dimensionally independent. It is a matter ot choice how many and which quantities arc considered

base quantities.’ SI has chosen the seven babe quantities and base units listed in Table I. I * as the basis of the ln- tcrnational System. In addition, there arc two “sup- plcmentary quantities” (Table I .2).

Tables 1. I and 1.2 show current practices for designating the dimensions of base and supplementary physical quantities, plus letter symbols for use in mathematical equations.

SI “&rived units” arc a third claxs. formed by con- boning. as needed, base units. supplementary units. and other derived units according to fhe algebraic relations linking the corresponding quantities. The symbols for derived units that do not have their own individual sytn- bols arc obtained by using the mathematical signs for multiplication and division. together with appropriate exponent> (e.g.. SI velocity. meter per second. m/s or I11 s I SI anoular velocity. radian per second. radis or rad.\-‘). e

Table I.3 contains a number of SI derived unit>. in- cluding all the I9 approved units assigned special names and individual unit hymbolh.

Appendix B provides a more dctallcd cxplanatmn oi the S! system of unils. their dct’initions. Xld

ahhr-aviations.

‘Table and flgure numbers of Ihe or,glnal SPE publ,cat,on are used fhroughout ,h,s chapter

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-3

SI Unit Prefixes*

The Sl unit prefixes. multiplication factors, and SI prefix symbols are shown in Table 1.4. Some of the prefixes may seem strange at first, but there are enough familiar ones in the list to make it relatively easy for technical personnel to adjust to their use; kilo, mega, deci, centi, milli, and micro are known to most engineers and scientists.

One particular warning is required about the prefixes: in the SI system, k and M (kilo and mega) stand for 1000 and 1 000 000, respectively, whereas M and MM or m and mm have been used previously in the oil industry for designating thousands and millions of gas volumes. Note carefully. however, that there is no parallelism because SI prefixes are raised to the power of the unit employed, while the customary M and MM prefixes were not. Ex- amples: km’ means cubic kilometers, not thousands of cubic meters; cm* means square centimeters, nor one- hundredth of a square meter. The designation for 1000 cubic meters is IO’ m3 and for I million cubic meters is 10’ m’--not km3 and Mm’, respectively.

Appendix C gives examples of the vital importance of following the precise use of upper-case and lower-case letters for prefixes and for unit symbols.

Application of the Metric System General SI is the form of the metric system preferred for all ap- plications. It is important that this modernized version be thoroughly understood and properly applied. This sec- tion, together with Appendix material, provides guidance and recommendations concerning style and usage of the SI form of the metric system.

Base Quantity or “Dimension”

length mass time” electric current* * thermodynamic temperature amount of substance luminous intensity

Style and Usage

Take care to use unit symbols properly: the agreements in international and national standards provide uniform rules (summarized in Appendix C). It is essential that these rules be followed closely to provide maximum ease of communication and to avoid costly errors. Handling of unit names varies somewhat among different countries because of language differences, but using the rules in Appendix C should minimize most difficulties of communication.

Usage for Selected Quantities Mass, Force, and Weight. The principal departure of SI from the gravimetric system of metric engineering units is the use of explicitly distinct units for mass and force. In SI. kilogram is restricted to the unit of mass. The nebtlton is the only SI unit of force, defined as I (kg. m)/s’, to be used wherever force is designated, in- cluding derived units that contain force-e.g., pressure or stress (N/m* =Pa), energy (N.m=J), and power [(N.m)/s=W].

There is confusion over the use of the term weight as a quantity to mean either force or mass. In science and technology, the term weight ofa body usually means the force that, if applied to the body, would give it an ac- celeration equal to the local acceleration of free fall (g, when referring to the earth’s surface). This acceleration varies in time and space; weight, if used to mean force, varies also. The term force of gravity (mass times ac- celeration of gravity) is more accurate than weight for this meaning.

In commercial and everyday use, on the other hand, the term weight nearly always means mass. Thus, when

TABLE 1.1 - SI BASE WANTiTlES AND UNITS

SI Unit - meter kilogram second ampere kelvin mole + candela

SI Unit Symbol (“Abbreviation”),

Use Roman (Upright) Type

k”

i K

mol cd

SPE Letter Symbol

for Mathematical Equations, Use Italic

(Sloping) Type

L m t

r n

‘The seven base unrls. two supplementary units and other terms are deiined I” Appendixes A and 6. Part 1. “SPE heretofore has arbrlrar~ly used charge q. the product of sfectrlc current and time, as a basic dunenslon. In untt symbols this would be A.s. m SPE mathematical symbols. IV tWh%nthe moleis used.the eler~ntaryentitw rWSt be Spenhed;they r~ybeatOrt~s. rm%WeS. iOnS. el8c1rOnS. other partlCla% OrSpW&l groupsof suchpartides. In petroleum work.

the terms kilogram m&.““pound mole.” etc., often are shortened erroneously to “mole.”

TABLE 1.2 - SI SUPPLEMENTARY UNITS’

Supplementary Quantity or “Dimension” SI Unit

SI Unit Symbol (“Abbreviation”),

Use Roman (Upright) Type

plane angle” radian rad solid angle’ ’ steradran sr

‘The seven base umts, two supplementary units. and other terms are defmed I” Appendaxes A and 8. Part 1 “IS0 speafn?s these two angles as dlmensnnless wth respect to the seven base quanhties

SPE Letter Symbol

for Mathematical Eauations. Use Italic’

(Sloping) Type

h

58-4

Quantity

absorbed dose acceleration activity (of radionuclides) angular acceleration angular velocity area Celsius temperature density dose equivalent electric capacitance electric charge electrical conductance electric field strength electric inductance electric potential electric resistance electromotive force energy entropy force frequency illuminance luminance luminous flux magnetic field strength magnetic flux magnetic flux density potential difference power pressure quantity of electricity quantity of heat radiant flux radiant intensity specific heat stress thermal conductivity velocity viscosity, dynamic viscosity, kinematic voltage volume* wave number work

PETROLEUM ENGINEERING HANDBOOK

TABLE 1.3 - SOME COMMON SI DERIVED UNITS

SI Unit Symbol (“Abbreviation”), Formula,

Unit Use Roman Type Use Roman Type

gray meter per second squared becquerel radian per second squared radian per second square meter degree Celsius kilogram per cubic meter sieverl farad coulomb siemens volt per meter henry volt ohm volt joule joule per kelvin newton hertz Iux candela per square meter lumen ampere per meter weber tesla volt watt Pascal coulomb joule watt watt per steradian joule per kilogram kelvin Pascal watt per meter kelvin meter per second Pascal second square meter per second volt cubic meter 1 per meter joule

GY

Bq

“C .., sv

E S

Ii V n V J

N HZ lx

Im

Wb T V W Pa C J W .

Pa

.

,.. V . . .

J

J/kg ml.9 1 Is rad/s2 rad/s m2 K kg/m3 J/kg A.sN ( = GN) As AN V/m V&A ( = Wb/A) W/A VIA W/A N.m J/K kgm/$ l/s lm/m2 cd/m2 cdsr A/m vs Wb/m2 W/A J/s N/m2 As N*m J/s Wlsr J(kgW Nlm2 W/(m.K) m/s Pas ml/s WIA m3 l/m N.m

‘In 1964, the General Conference on Welghls and Measures adopted liter as a special name for the cubic decimeter but discouraged the use of later for volume measurement 01 extreme precision (see Appendix 8).

SI Multiplication Factor Prefix

1 000 OOLl 000 000 000 000 = 10’8 exa** 1 ooo 000 000 000 000 = 10’5 peta”

1 000 000 000 000 = 10’2 tera 1 000 000 000 = 1 OQ giga

1000000 = 106 mega lOOO= 103 kilo

100 = 102 hectot 10 = 10 deka$

0.1 = 10-l deci$ 0.01 = 10m2 centi*

0.001 = 10m3 milli 0.000001 = 1Om6 micro

0.000 000 001 = 10eg nano 0.000 000 000 001 = lo-l2 pica

0.000 000 000 000 001 = lo-l5 femto

TABLE 1.4 - SI UNIT PREFIXES

SI Prefix Symbol,

Use Roman Meaning In Other

Type Pronunciation (U.S.)” Meaning (U.S.) Countries - ex’ a (a as in a bout) one quintillion timest trillion E

P T G M k h da

as in p eta1 as in terra ce jig’ a (a as in a bout) as in mega phone as in kilo watt heck’ toe deck’ a (a as in a bout) as in deci mal as in senri ment as in mili tary as in micro phone nan’ oh (an as in an t) peek’ oh fern’ toe (tern as in

fern inine) as in anafo my

one quadrillion timest one trillion timest one billion times7 one million limes one thousand times one hundred times ten times one tenth of one hundredth of one thousandth of one millionth of one billionth oft one trillionth oft one quadrillionth oft

thousand billion billion milliard

milliardth billionth thousand billionth

0.000 000 000 000 000 001 = 1Om’8 atto a one quintillionth oft trillionth ‘The l~rsl syllable of every prehx IS accented lo assure that the prellx will retain Its Ideniiiy Therefore. the prelerred pronunxlion of kllomeler places the accent on the first syllable, not the second.

“Approved by the 15th General Conlerencs of WaghIs and Measures (CGPM). May-June ,975. tThese terms should be avoided in technaal wrong because the denomlnatnns above 1 millon are dlflerent in most other countries. as lndlcated I” the last column. tWhtle hecto, deka.dect, and cents are St prehxes. their use generally should be avolded except for the SI UN mult~pleslorarea. volume, moment, and nontechmcal use of centmwer, as for body and clothing meas”reme”t.

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-5

one speaks of a person’s weight, the quantity referred to is mass. Because of the dual use, the term weight should be avoided in technical practice except under cir- cumstances in which its meaning is completely clear. When the term is used, it is important to know whether mass or force is intended and to use SI units properly as described above by using kilograms for mass and newtons for force.

Gravity is involved in determining mass with a balance or scale. When a standard mass is used to balance the measured mass, the effect of gravity on the two masses is canceled except for the indirect effect of air or fluid buoyancy. On a spring scale, mass is measured indirect- ly since the instrument responds to the force of gravity. Such scales may be calibrated in mass units if the varia- tion in acceleration of gravity and buoyancy corrections are not significant in their use.

The use of the same name for units of force and mass causes confusion. When non-9 units are being con- verted to SI units, distinction should be made between ,forcr and mass-e.g., use Ibf to denote force in gravimetnc engineering units, and use Ibm for mass.

Use of the metric ton, also called mnne (1.0 Mg), is common.

Linear Dimensions. Ref. 3 provides discussions of length units applied to linear dimensions and tolerances of materials and equipment, primarily of interest to engineers in that field.

Temperature. The SI temperature unit is the kelvin (not “degree Kelvin”); it is the preferred unit to express ther- modynamic temperature. Degrees Celsius (“C) is an SI derived unit used to express temperature and temperature intervals. The Celsius scale (formerly called centigrade) is related directly to the kelvin scale as follows: the temperature interval 1 “C= 1 K, exactly. Celsius temperature (Tot) is related to thermodynamic temperature (Tx) as follows: Tot =TK --To exactly, where To =273.1.5 K by definition. Note that the SI unit symbol for the kelvin is K without the degree mark, whereas the older temperature units are known as degrees Fahrenheit, degrees Rankine, and degrees Celsius, with degree marks shown on the unit symbol (“F, “R, “C).

Time. The SI unit for time is the second, and this is preferred, but use of the minute, hour, day, and year is permissible.

Angles. The SI unit for plane angle is the radian. The use of the arc degree and its decimal submultiples is per- missible when the radian is not a convenient unit. Use of the minute and second is discouraged except possibly for cartography. Solid angles should be expressed in steradians.

Volume. The SI unit of volume is the cubic meter. This unit, or one of its regularly formed multiples, is pre- ferred for all applications. The special name liter has been approved for the cubic decimeter (see Appendix B), but use of the liter is restricted to the measurement of liq- uids and gases.

Energy. The SI unit of energy, the joule, together with its multiples, is preferred for all applications. The kilowatt-hour is used widely as a measure of electric energy, but this unit should not be introduced into any new areas; eventually it should be replaced by the megajoule.

Torque and Bending Moment. The vector product of force and moment arm is expressed in newton meters

(N m) by SPE as a convention when expressing torque energies.

Pressure and Stress. The SI unit for pressure and stress is the Pascal (newton per square meter); with proper SI prefixes it is applicable to all such measurements. Use of the old metric gravitational units-kilogram-force per square centimeter, kilogram-force per square millimeter, torr, etc.-is to be discontinued. Use of the bar is discouraged by the standards organizations.

It has been recommended internationally that pressure units themselves should not be modified to indicate whether the pressure is “absolute” (above zero) or “gauge” (above atmospheric pressure). If the context leaves any doubt as to which is meant, the word “pressure” must be qualified appropriately: “...at a gauge pressure of 13 kPa,” or “. . .at an absolute pressure of 13 kPa,” etc.

Units and Names To Be Avoided or Abandoned Tables 1.1 through 1.3 include all SI units identified by formal names, with their individual unit symbols. Vir- tually all other named metric units formerly in use (as well as nonmetric units) are to be avoided or abandoned. There is a long list of such units (e.g., dyne. stokes. “esu,” gauss, gilbert, abampere, statvolt, angstrom. fermi, micron, mho, candle, calorie, atmosphere, mm Hg, and metric horsepower). The reasons for abandon- ing the non-9 units are discussed in Appendix B. Two of the principal reasons are the relative simplicity and the coherence of the SI units.

Rules for Conversion and Rounding3 Conversion Table 1.7, Appendix D, contains general conversion fac- tors that give exact values or seven-digit accuracy for im- plementing these rules except where the nature of the dimension makes this impractical.

The conversion of quantities should be handled with careful regard to the implied correspondence between the accuracy of the data and the given number of digits. In all conversions, the number of significant digits retained should be such that accuracy is neither sacrificed nor exaggerated.

Proper conversion procedure is to multiply the specified quantity by the conversion factor exactly as given in Table 1.7 and then round to the appropriate number of significant digits. For example, to convert 11.4 ft to meters: 11.4x0.3048=3.474 72, which rounds to 3.47 m.

Accuracy and Rounding Do not round either the conversion factor or the quantity before performing the multiplication; this reduces ac-

56-6 PETROLEUM ENGINEERING HANDBOOK

curacy. Proper conversion procedure includes rounding the converfed quantity to the proper number of signifi- cant digits commensurate with its intended precision. The practical aspects of measuring must be considered when using SI equivalents. If a scale divided into six- teenths of an inch was suitable for making the original measurements, a metric scale having divisions of 1 mm is obviously suitable for measuring in SI units, and the equivalents should not be reported closer than the nearest 1 mm. Similarly, a gauge or caliper graduated in divi- sions of 0.02 mm is comparable to one graduated in divi- sions of 0.001 in. Analogous situations exist for mass, force, and other measurements. A technique to deter- mine the proper number of significant digits in rounding converted values is described here for general use.

General Conversion. This approach depends on first establishing the intended precision or accuracy of the quantity as a necessary guide to the number of digits to retain. The precision should relate to the number of digits in the original. but in many cases that is not a reliable indicator. A figure of 1. I875 may be a very ac- curate decimalization of a noncritical I xh that should have been expressed as I. 19. On the other hand. the value 2 may mean “about 2” or it may mean a very ac- curate value of 2, which should then have been written as 2.0000. It is theretbre necessary to determine the intend- ed precision of a quantity before converting. 771;s cstitnale of ititertdnl precisiorl .~/7011/rl twlw he stnullet

thctt1 l/l? flrc’ut-flc~\’ c~f’tr7f~L4.slr~emrft txrr 1r.s14a11\ .s17014Id hc

.vt~ul/cr fhur7 one-tend7 the tcrlrrtrt7c~e ~f’otw exists. After the precision of the dimension is estimated. the con- verted dimension should be rounded to a minimum number of significant digits (see section on Significant Digits) such that a unit of the last place is equal to or smaller than the converted precision.

1. A stirring rod 6 in. long: In this case, precision is estimated to be about % in. (+ i/4 in.). Converted. ‘/z in. is 12.7 mm. The convened 6-in. dimension of 152.4 mm should be rounded to the nearest IO mm, or I50 mm.

2. SO,OO@psi tensile strength: In this case, precision is estimated to be about t_200 psi (i I .4 MPa) based on an accuracy of _+0.25% for the tension tester and other fac- tors. Therefore, the converted dimension, 344.7379 MPa. should be rounded to the nearest whole unit, 345 MPa.

3. Test pressure 2OOk 15 psi: Since one-tenth of the tolerance is + 1.5 psi (10.34 kPa). the converted dimen- hion should be rounded to the nearest 10 kPa. Thus. 1378.9514-t 103.421 35 kPa becomes 138Oi 100 kPa.

Special Cases. Converted values should be rounded to the minimum number of significant digits that will main- tain the required accuracy. In certain cases, deviation from this practice to use convenient or whole numbers may be feasible. In that case, the word “approximate” must be used following the conversion-e.g., I% in. =47.625 mm exact, 47.6 mm normal rounding, 47.5 mm (approximate) rounded to preferred or convenient half-millimeter. 48 mm (approximate) rounded to whole number.

A quantity stated as a limit, such as “not more than”

or “maximum,” must be handled so that the stated limit is not violated. For example, a specimen “at least 4 in. wide” requires a width of at least 101.6 mm, or (round- ed) at least 102 mm.

Significant Digits. Any digit that is necessuy to drjne the specific vulue or quantity is said to he significant. For example, a distance measured to the nearest I m may have been recorded as 157 m; this number has three significant digits. If the measurement had been made to the nearest 0.1 m, the distance may have been 157.4 m-four significant digits. In each case, the value of the right-hand digit was determined by measuring the value of an additional digit and then rounding to the desired degree of accuracy. In other words, 157.4 was rounded to 1.57; in the second case, the measurement may have been 157.36, rounded to 157.4.

Importance of Zeros. Zeros may be used either to in- dicate a specific value, as does any other digit, or to in- dicate the magnitude of a number. The 1970 U.S. population figure rounded to thousands was 203 185 000. The six left-hand digits of this number are significant; each measures a value. The three right-hand digits are zeros that merely indicate the magnitude of the number rounded to the nearest thousand. To illustrate further, each of the following estimates and measurements is of different magnitude, but each is specified to have only one significant digit:

1 000 100

10 0.01 0.001 0.000 1.

It is also important to note that, for the first three numbers, the identification of significant digits is possi- ble only through knowledge of the circumstances. For example, the number 1000 may have been rounded from about 965, or it may have been rounded from 999.7, in which case all three zeros are significant.

Data of Varying Precision. Occasionally, data required for an investigation must be drawn from a variety of sources where they have been recorded with varying degrees of ref-mement. Specific rules must be observed when such data are to be added, subtracted, multiplied, or divided.

The rule for addition and subtraction is that the answer shall contain no significant digits farther to the right than occurs in the least precise number. Consider the addition of three numbers drawn from three sources, the first of which reported data in millions, the second in thousands, and the third in units:

163 000 000 217 885 000

96 432 768

477 317 768

This total indicates a precision that is not valid. The numbers should jirst be rounded to one significant digit

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-7

farther to the right than that of the least precise number, and the sum taken as follows.

163 Ooo 000 217 900 000

96 400 000

477 300 ooo

Then, the total is rounded to 477 000 000 as called for by the rule. Note that if the second of the figures to be added had been 217 985 000, the rounding before addi- tion would have produced 218 000 000, in which case the zero following 218 would have been a significant digit.

The rule for multiplication and division is that the product or quotient shall contain no more significant digits than arc contained in the number with the fewest signijcant digits used in the multiplication or division. The difference between this rule and the rule for addition and subtraction should be noted; for addition and sub- traction, the rule merely requires rounding digits to the right of the last significant digit in the least precise number. The following illustration highlights this difference.

Multiplication: 113.2~1.43=161.876 rounded to 162.

Division: 113.2+1.43=79.16 rounded to 79.2

Addition: 113.2+1.43=114.63 rounded to 114.6

Subtraction: 113.2-1.43=111.77 rounded to 111.8.

The above product and quotient are limited to three significant digits because 1.43 contains only three significant digits. In contrast. the rounded answers in the addition and subtraction examples contain four signifi- cant digits.

Numbers used in the illustration are all estimates or measurements. Numben that ure cxwt counts (and con- aversion ,firctors that arc exuct) at-c treated as though thq cmsist of’otl injrzitr rumher oj’.sip$cant digit.,. Stated more simply. when a unmt is used in computation with a measurement. the number of significant digits in the answer is the same as the number of significant digit?, in rhe measurement. If a count of 40 is multiplied by a measurement of 10.2. the product is 408. However, if 40 wcrc an estimate accurate only to the nearest IO and, hence. contained one significant digit. the product would be 300.

Rounding Values lo When a figure is to be rounded to fewer digits than the total number available, the procedure should be as follows.

When the First Digit The Last Digit Discarded is Retained is

less than 5 unchanged more than 5 increased by 1 5 followed only unchanged if even,

by zeros* increased by I if odd

‘Unless a number of rounded values are lo appear I” a gfven problem, mosl roundlngs conform lo the ,,is, two procedures - 1.e rounding upward when the llrst dlgll dw carded IS 5 or hlg”er

Examples: 4.463 25 if rounded to three places would be 4.463. 8.376 52 if rounded to three places would be 8.377. 4.365 00 if rounded to two places would be 4.36. 4.355 00 if rounded to two places would be 4.36.

Conversion of Linear Dimensions of Interchangeable Parts Detailed discussions of this subject are provided by ASTM,” API,” and ASME’ publications and arc recommended to the interested reader.

Other Units Temperature. General guidance for converting tolerances from degrees Fahrenheit to kelvins or degrees Celsius is given in Table 1.5. Normally, temperatures expressed in a whole number of degrees Fahrenheit should be converted to the nearest 0.5 K (or 0.5”C). As with other quantities, the number of significant digits to retain will depend on implied accuracy of the original dimension: e.g.,*

100*5”F (tolerance); implied accuracy. estimated total 2°F (nearest I “C) 37.7778&2.7778”C rounds to 38+3”C.

1.000~50”F (tolerance): implied accuracy. estimated total 20°F (nearest 10°C) 537.7778k27.7778”C rounds to 54Ok3O”C.

Pressure or Stress. Pressure or stress values may be converted by the same prmciple used for other quan- tities. Values with an uncertainty of more than 2% may bc converted without rounding by the approximate factor:

1 psi=7 kPa.

For conversion factors see Table I .7.

Special Length Unit-the Vara. Table 1.8* Appendix E, provides conversion factors and explanatory notes on the problems ofconverting the several kinds of vara units

to mctcrs.

Special Terms and Quantities Involving Mass and Amount of Substance The Intl. Union of Pure and Applied Chemistry. the lntl. Union of Pure and Applied Physics. and the Intl.

‘See Appendlx A and pnor paragraph on “General Conversion.”

TABLE 1.5 -CONVERSION OF TEMPERATURE TOLERANCE REQUIREMENTS

Tolerance Tolerance (“F) (K or “C) 21 X0.5 z-2 *I -c5 +3

210 + 5.5 A15 -8.5 220 k-11 k-25 t 14

58-8 PETROLEUM ENGINEERING HANDBOOK

Organization for Standardization provide clarifying usages for some of the terms involving the base quan- tities “mass” and “amount of substance.” Two of these require modifying the terminology appearing previously in SPE’s Symbols Standards.

Table 1.6 shows the old and the revised usages.

Mental Guides for Using Metric Units Table 1.9. Appendix F, is offered as a “memory jog-

ger’ ’ or guide to help locate the “metric ballpark” relative to customary units. Table 1.9 is not a conversion table. For accurate conversions, refer to Table 1.7, or to Tables 2.2 and 2.3 for petroleum-industry units, and round off the converted values to practical precision as described earlier.

References* I.

7.

3

4

5

6.

“The lntematmnal System of Units (Sl).” NBS Special Publica- tion 330. U.S. Dept. of Commerce, Natl. Bureau of Standards, Superintendent of Documents. U.S. Government Printing Office, Washmgton. D.C. (1981). (Order by SD Catalog No. c13.10:330/3.) “S1 Units and Recommendations for the Use of Thctr Multtplca and of Certain Other Units,” wcond edition, 1981.02-15. Intl. Standard IS0 1000. lntl. Oganlzation for Standardlzatton. American Natl. Standards Inst. (ANSI). New York (1981). “Standard for Metrtc Practtce,” E 380-82. Amencan Sot. ftir Testing and Materials. Philadelphia. (Slmdar matcrlal published in 1EEE Std. 268-1982.)

“A Bibliography of Metric Standard,.” ANSI. New York (June 1975). (Alw &ee ANSI‘\ annual catalog of national and intrma- Imnal standard\.)

.&w~c Edirorid G&P. thlrd edition. American Natl. Metric Councd (ANMC). Washington. D.C. (July 1981).

‘For information on any 01 these references. Cantact the Book Order Dept at SPE headquarters

4

10.

II.

12.

13.

14.

IS.

16.

“General Principles Concerning Quantities. Unirs and Symbols,” Gm~rcrl fnrroducrion rcj /SO 31. second edition. Intl. Standard IS0 3110. Intl. Organization for Standardization. ANSI. New York City (1981). “American National Standard Practice for Inch-Millimeter Con- version for Industrial Use,” ANSI 848.1-1933 (Rl947). IS0 R370- 1964, Intl. Organization for Standardization. ANSI, New York. (A later edition has been issued: “Toleranced Dimen- sions--Conversion From Inches to Millimeters and Vice Versa.” IS0 370-1975.) “Factors for High-Precision Conversion.” NBS LC1071 (July 1976). “Information Processing-Representation5 of SI and Other Units for Uae in Systems With Limited Character Sets.” lntl. Standard IS0 2955-1974. Intl. Organization for Stdndardization. ANSI. New York Ctty. (Ref. 5 reproduces the 1973 editton of this stan- dard in its entirety.) “Supplementary Metnc Practxe Guide for the Canadian Petroleum Industry.” fourth edition. P.F. Moore (ed.). Canadian Petroleum Assn. (Oct. 1979). “Letter Symbols for Units of Measurement,” ANSI/IEEE Std. 260-1978. Available from American Natl. Standards Inst.. New York City. Mechtly. E.A.: “The International System trt Units-Physical Constants and Conversion Factors,” NASA SP-7012. Scientific and Technical Information Office, NASA, Washmgton. D C. 1973 edition available from U.S. Government Printing Office, Washington. D.C. McElwee, P.G.: The Terns Vlrrcj. Available from Commissioner. General Land Office, State of Texas. Auatm (April 30. 1940).

APPENDIX A3 Terminology To ensure consistently reliable conversion and rounding practices, a clear understanding of the related nontechnical terms is prerequisite. Accordingly, certain terms used in this standard are defined as follows.

Accuracy (as distinguished from precision). The degree of conformity of a measured or calculated value to some recognized standard or specified value. This concept involves the systematic error of an operation, which is seldom negligible.

Approximate. A value that is nearly but not exactly cor- rect or accurate.

Coherence. A characteristic of a coherent system of units, as described in Appendix B, such that the product or quotient of any two unit quantities is the unit of the

TABLE 1.6 - SPECIAL TERMS AND QUANTITIES INVOLVING MASS AND AMOUNT OF SUBSTANCE

Old Usage Standardized Usage

Dimensions (IS0 Symbols, SI Unit

Term See Table 1 .l) Term Symbol

atomic weight M mass of atom kg (SPE Symbols Standard)

atomic weight . relative atomic mass .

(elsewhere) equivalent - mole mol mass of molecule M molecular mass kg molar - molar (means, “divided by l/m01

amount of substance”) molar@ - concentration mo1/m3 molecular weight M molar mass kg/mol

(SPE Symbols Standard) molecular weight l relative molecular mass l

(elsewhere) normal - obsolete mDimensonless

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-9

resulting quantity. The SI base units, supplementary units, and derived units form a coherent set.

Deviation. Variation from a specified dimension or design requirement, usually defining upper and lower limits (see also Tolerance).

Digit. One of the 10 Arabic numerals (0 to 9).

Dimension(s). Two meanings: (1) A group of fun- damental (physical) quantities, arbitrarily selected, in terms of which all other quantities can be measured or identified. 9 Dimensions identify the physical nature of, or the basic components making up. a physical quantity. They are the bases for the formation of useful dimen- sionless groups and dimensionless numbers and for the powerful tool of dimensional analysis. The dimensions for the arbitrarily selected base units of the SI are length, mass, time, electric current. thermodynamic tempera- ture, amount of substance. and luminous intensity. SI has two supplementary quantities considered dimension- less-plane angle and solid angle. (2) A geometric ele- ment in a design, such as length and angle. or the magnitude of such a quantity.

Figure (numerical). An arithmetic value expressed by one or more digits or a fraction.

Nominal Value. A value assigned for the purpose of convenient designation; a value existing in name only.

Precision (as distinguished from accuracy). The degree of mutual agreement between individual measurements (repeatability and reproducibility).

Quantity. A concept used for qualitative and quan- titative descriptions of a physical phenomenon. 9

Significant Digit. Any digit that is necessary to define a value or quantity (see text discussion).

Tolerance. The total range of variation (usually bilateral) permitted for a size, position, or other required quantity; the upper and lower limits between which a dimension must be held.

U.S. Customary Units. Units based on the foot and the pound, commonly used in the U.S. and defined by the Natl. Bureau of Standards. ” Some of these units have the same name as similar units in the U.K. (British, English, or U.K. units) but are not necessarily equal to them.

APPENDIX B3 SI Units Advantages of SI Units SI is a rationalized selection of units from the metric system that individually are not new. They include a unit of force (the newton), which was introduced in place of the kilogram-force to indicate by its name that it is a unit of force and not of mass. SI is a coherent system with

seven base units for which names, symbols, and precise definitions have been established. Many derived units arc defined in terms of the base units, with symbols

assigned to each; in some cases, special names and unit symbols are given-e.g., the newton (N).

One Unit per Quantity. The great advantage of SI is that there is one, and only one, unit for each physical quantity-the meter for length (L), kilogram (instead of gram) for mass (m). second for time (r). etc. From these elemental units, units for all other mechanical quantities are derived. These derived units are defined by simple equations among the quantities, such as tB=dLldt (velocity), u=dv/dt (acceleration), F=ma (force), W=FL (work or energy), and P= Wit (power). Some of these units have only generic names. such as meter per second for velocity; others have special names and sym- bols, such as newton (N) for force, joule (J) for work or energy. and watt (W) for power. The SI units.fi,r jbrce, energy, and power are the same regardless of \r>hether the process is mechanical, electrid, chemiccd, or nuclear. A force of 1 N applied for a distance of 1 m can produce 1 J of heat, which is identical with what 1 W of electric power can produce in 1 second.

Unique Unit Symbols. Corresponding to the SI advan- tages of a unique unit for each physical quantity are the advantages resulting from the use of a unique and well- defined set of symbols. Such symbols eliminate the con- fusion that can arise from current practices in different disciplines, such as the use of “b” for both the hur (a unit of pressure) and barn (a unit of area).

Decimal Relation. Another advantage of SI is its reten- tion of the decimal relation between multiples and sub- multiples of the base units for each physical quantity. Prefixes are established for designating multiple and sub- multi le

P units from “exa” (10”) down to “atto”

(I 0 s) for convenience in writing and speaking.

Coherence. Another major advantage of SI is its coherence. This system of units has been chosen in such a way that the equations between numerical values, in- cluding the numerical factors, have the same form as the corresponding equations between the quantities: this constitutes a “coherent” system. Equations between units of a coherent unit system contain as numerical fac- tors only the number 1. In a coherent system, the product or quotient of any two unit quantities is the unit of the resulting quantity. For example, in any coherent system, unit area results when unit length is multiplied by unit length (1 m x 1 m= 1 m*), unit force when unit mass* is multiplied by unit acceleration (1 kgx 1 m/s* = 1 N), unit work when unit force is multiplied by unit length (1 N x 1 m= 1 J), and unit power when unit work is divided by unit time (I J+ 1 second= 1 W). Thus, in a coherent system in which the meter is the unit of length, the square meter is the unit of area, but the are** and hectare are not coherent. Much worse disparities occur in systems of “customary units” (both nonmetric and older metric) that require many numerical adjustment factors in equations.

Base Units. Whatever the system of units, whether it be coherent or noncoherent, particular samples of some

58-10

physical quantities must be selected arbitrarily as units of those quantities. The remaining units are defined by ap- propriate cxperimcnts related to the theoretical intcrrcla- tions of all the quantities. For convenience of analysis. units pertaining to c~r-fuin hrrsc> ylrrrfztitics ~Irf’ by (~~171*0- tior7 rc~~crrrld us dir77~~r7siot7all~~ ir7tlqxwder7t; tl7c.w ur7it.s

(I~C crr//c~! basr unirs (Table I I ). and all others (derived units) can be cxprcsscd algebraically in temls of the base units. In SI. the unit of mass. the kilogram, is defined as the mass of a prototype kilogram preserved by the Intl. Bureau of Weights and Measures (BIPM) in Paris. All other base units are defined in terms of reproducible phenomena-e.g., the wave lengths and frequencies of specified atomic transitions.

Non-S1 Metric Units Various other units are associated with SI but are not a part thereof. They are related to units of the system by powers of 10 and are used in specialized branches of physics. An example is the bar, a unit of pressure. ap- proximately equivalent to 1 atm and exactly equal to 100 kPa. The bar is used extensively by meteorologists. Another such unit is the gal. equal exactly to an accelera- tion of 0.01 m/s?. It is used in geodetic work. These. however. are not coherent units-i.e., equations involv- ing both thcsc units and SI units cannot be written without a factor of proportionality even though that fat- tor may be a simple power of 10.

Originally (1795). the liter was intended to be identical to the cubic decimeter. The Third General Conference on Weights and Measures (CGPM) in 1901 defined the liter as the volume occupied by the mass of 1 kilogram of pure water at its maximum density under normal at- mospheric pressure. Careful determinations subsequent- ly established the liter so defined as equivalent to 1.000 028 dm’. In 1964. the CGPM withdrew this definition of the liter and declared that “liter” was a special name for the cubic decimeter. Thus. its use is pemlitted in Sl but is discouraged because it creates two units for the same quantity and its use in precision measurements might conflict with measurements record- ed under the old definition.

SI Base Unit Definitions Authorized translations of the original French definitions of the seven base and two supplementary units of SI follow’ (parenthetical items added).

“Mrfer cm)-The meter is the length equal to I 650 763.73 wavelengths in vacuum of the radiation cor- responding to the transition between the levels 2p I~) and 5d5 of the krypton-86 atom.” (Adopted by I lth CGPM 1960.)

“Kilogmn7 (kg)-The kilogram is the unit of mass (and is the coherent SI unit); it is equal to the mass of the international prototype of the kilogram.” (Adopted by First and Third CGPM 1889 and 1901.)

“Sc~nrzci (s)-The second is the duration of 9 192 63 I 770 periods of the radiation corresponding to the transi- tion between the two hyperfine levels of the ground state of the cesium- 133 atom.*” (Adopted by 13th CGPM 1967.)

“Atnper~~ (A)-The ampere is that constant current which. if maintained in tw’o straight parallel conductors of infinite length. of ncgliglble circular cross-section.

PETROLEUM ENGINEERING HANDBOOK

and placed one mctcr apart in vacuum. would product hctwecn these conductors a force equal to 2 x IO -’ newton per meter of length.” (Adopted by Ninth CGPM lY48.)

“Kchi77 (K)-The kelvin. unit of thermodynamic temperature. is the fraction 11273. IS of the ther- modynamic temperature of the triple point of water.” ’ (Adopted by 13th CGPM 1967.)

“MCI/C (mol)-The mole is the amount of substance of a system which contains as many clcmcntary entities as thcrc are atoms in 0.012 kilograms of carbon-12.” (Adopted by 14th CGPM 1971.)

“Note-When the mole is used. the elementary en- tities must be specified and may be atoms. molecules. ions, electrons. other particles. or specified groups of such particles. ”

“Crrn&/u (cd)-The candela is the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency 540 (E + 12) hertz (Hz) and that has a radiant intensity In that direction ol l/683 watt per steradian.”

“Rudiurz (rad)-The radian is the plane angle between two radii of a circle which cut off on the circumfcrencc an arc equal in length to the radius.”

“Sr~~&iu~? (sr)-The stcradian i\ the solid angle which. having its vertex at the center of a sphere. cuts oft an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.”

Definitions of SI Derived Units Having Special Names3 Physical Quantity

Absorbed dose

Unit and Definition

The gray (Gy) is the absorbed dose when the energy per unit mass imparted to matter by ionizing radiation is I J/kg. The hrcyuerrl (Bq) is the activi- ty of a radionuclide decaying at the rate of one spontaneous nuclear transition per second, The degree Ce1siu.s (“C) is equal to the kelvin and is used in place of the kelvin for expressing Celsius temperature (symbol Tot) defined by Tot =T, -To, where TK is the thermodynamic temperature and To =273. IS K by definition. The sievcrt is the dose equivalent when the absorbed dose of ionizing radiation multiplied by the dimensionless factors Q (quality factor) and N (product of any other multiply- ing factors) stipulated by the Intl. Commission on Radiolog- ical Protection is I J/kg. The&r& (F) is the capacitance of a capacitor between the plates of which there appears a dif- ference of potential of I V when it is charged by a quantity of electricity equal to I C.

Activity

Celsius temperature

Dose equivalent

Electric capacitance

WE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-l 1

Electric conductance

Electric inductance

Electric potential difference, elec- tromotive force

Electric resistance

Energy

Force

Frequency

Illuminance

Luminous flux

Magnetic flux

Magnetic flux density magnetic induction

The siemens (S) is the electric conductance of a conductor in which a current of 1 A is pro- duced by an electric potential difference of 1 V. The hpn~l (H) is the inductance of a closed circuit in which an electromotive force of 1 V is produced when the electric cur- rent in the circuit varies uniform- ly at a rate of 1 A/s. The volr (V) is the difference of electric potential between two points of a conductor carrying a constant current of 1 A when the power dissipated between these points is equal to 1 W. The ohm (Q) is the electric resistance between two points of a conductor when a constant dif- ference of potential of I V, ap- plied between these two points, produces in this conductor a cur- rent of I A, this conductor not being the source of any elec- tromotive force. The joule (J) is the work done when the point of application of a force of 1 N is displaced a distance of 1 m in the direction of the force.

The nr~r~~ (N) is that force that, when applied to a body having a mass of 1 kg. gives it an acceleration of I m/s’. The hertz (Hz) is the frequency of a periodic phenomenon of which the period is 1 second. The Iu.r (Ix) is the illuminance produced by a luminous flux of I Im uniformly distributed over a surface of I m2 The lumen (Im) is the luminous flux emitted in a solid angle of 1 sr by a point source having a uniform intensity of 1 cd. The ember, is the magnetic flux that, liriking a circuit of one turn, produces in it an elec- tromotive force of 1 V as it is reduced to zero at a uniform rate in I s.

The teslu (T) is the magnetic flux density of 1 Wb/m2. In an alternative approach to defining the magnetic field quantities the tesla may also be defined as the magnetic flux density that pro- duces on a l-m length of wire carrying a current of 1 A,

oriented normal to the flux den- sity, a force of 1 N, magnetic flux density being defined as an axial vector quantity such that

Power

Pressure or stress

Electric charge, quantity of electricity

No other SI derived names at this time.

APPENDIX C3’**

the force exerted on an element of current is equal to the vector product of this element and the magnetic flux density. The wutt (W) is the power that represents a rate of energy transfer of I J/s. The pascul (Pa) is the pressure or stress of I Nim2. Electric charge is the time in- tegral of electric current; its unit, the coulomb (C), is equal to 1 A.s.

units have been assigned special

Style Guide for Metric Usage Rules for Writing Metric Quantities Capitals. I/nits-Unit names, including prefixes, are not capitalized except at the beginning of a sentence or in titles. Note that for “degree Celsius” the word “degree” is lower case; the modifier “Celsius” is always capitalized. The “degree centrigrade” is now obsolete.

Symbols-The short forms for metric units are called unit symbols. They are lower case except that the first letter is upper case when the unit is named for a person. (An exception to this rule in the U.S. is the symbol L for liter.) Examples: Unit Name Unit Symbol

meter** m

mm newton 6 Pascal Pa

Printed unit symbols should have Roman (upright) let- ters, because italic (sloping or slanted) letters are re- served for quantity symbols, such as m for mass and L for length.

Prejx Symbols-All prefix names, their symbols, and pronunciation are listed in Table I .4. Notice that the top five are upper case and all the rest lower case.

The importance of following the precise use of upper- case and lower-case letters is shown by the following ex- amples of prefixes and units.

G for giga; g for gram. K for kelvin; k for kilo. M for mega; m for milli. N for newton; n for nano. T for tera: t for tonne (metric ton).

information Processing-Limited Character Sets- Prefixes and unit symbols retain their prescribed forms regardless of the surrounding typography, except for systems with limited character sets. IS0 has provided a standard” for such systems; this standard is

recommended.

Plurals and Fractions. Names of SI units form their plurals in the usual manner, except for lux, hertz, and siemens.

‘The spellings “metre” and “l~tre” are preferred by IS0 but “meter” and “liter” are ottlclal u s QcNernmenl spelhngs.

58-12 PETROLEUM ENGINEERING HANDBOOK

Values less than one take the singular form of the unit name; for example, 0.5 kilogram or % kilogram. While decimal notation (0.5, 0.35, 6.87) is generally preferred, the most simple fractions are acceptable, such as those where the denominator is 2, 3, 4, or 5.

Symbols of units are the same in singular and plural-e.g., I m and 100 m.

Periods. A period is nof used after a symbol, except at the end of a sentence. Examples: “A current of 1.5 mA is found.. ” “The field measured 350x 125 m.”

The Decimal Marker. IS0 specifies the comma as the decimal marker9 ; in English-language documents a dot on the line is acceptable. In numbers less than one, a zero should be written before the decimal sign (to pre- vent the possibility that a faint decimal sign will be overlooked). Example: The oral expression “point seven five” is written 0.75 or 0,75.

Grouping of Numbers. Separate digits into groups of three, counting from the decimal marker. A comma should not be used between the groups of three9 ; in- stead, a space is left to avoid confusion, since the comma is the IS0 standard for the decimal marker.

In a four-digit number, the space is not required unless the four-digit number is in a column with numbers of five digits or more:

For 4,720,525 write 4 720 525 For 0.52875 write 0.528 75 For 6,875 write 6875 or 6 875 For 0.6875 write 0.6875 or

0.687 5

Spacing. In symbols or names for units having prefixes, no space is left between letters making up the symbol or the name. Examples are kA, kiloampere; and mg, milligram.

When a symbol follows a number to which it refers, a space must be left between the number and the symbol, except when the symbol (such as “) appears in the superscript position. Examples: 455 kHz, 22 mg, 20 mm, lo6 N, 30 K, 20°C.

When a quantity is used as an adjective, a hyphen should be used between the number and the symbol (ex- cept “C). Examples: It is a 35-mm film; the film width is 35 mm. I bought a 6-kg turkey; the turkey weighs 6 kg.

Leave a space on each side of signs for multiplication, division, addition, and subtraction, except within a com- pound symbol. Examples: 4 cm x 3 m (not 4 cm X 3 m); kg/m3; N.m.

Powers. For unit M~ZP.P, use the modifier .rquared or cubed after the unit name (except for area and volume)-e.g.. meter per second squared. For area or volume, place a modifier before the unit name. including derived units:-e.g.. cubic meter and watt per square meter.

For unit symbols. write the symbol for the unit fol- lowed by the power superscript-e.g., 14 m’ and 26 cm3.

Compound Units. For a unit name (not a symbol) de- rived as a quotient (e.g., for kilometers per hour), it is preferable not to use a slash (/) as a substitute for “per” except where space is limited and a symbol might not be understood. Avoid other mixtures of words and symbols. Examples: Use meter per second, not m/s. Use only one “per” in any combination of units-e.g., meter per sec- ond squared, not meter per second per second.

For a unit symbol derived as a quotient do not, for ex- ample, write k.p.h. or kph for km/h because the first two are understood only in the English language, whereas km/h is used in all languages. The symbol km/h also can be written with a negative exponent-e.g., km. h -’ .

Never use more than one slash (/) in any combination of symbols unless parentheses are used to avoid ambigui- ty; examples are m/s*, not m/s/s; W/(m.K), not W/m/K.

For a unit name derived as a product, a space or a hyphen is recommended but never a “product dot” (a period raised to a centered position)-e.g., write newton meter or newton-meter, not newton.meter. In the case of the watt hour, the space may be omitted-watthour.

For a unit symbol derived as a product, use a product dot-e.g., N.m. For computer printouts, automatic typewriter work, etc., a dot on the line may be used. Do not use the product dot as a multiplier symbol for calculations-e.g., use 6.2~5, not 6.2.5.

Do not mix nonmetric units with metric units, except those for time, plane angle, or rotation-e.g., use kg/m3, not kglft3 or kg/gal.

A quantity that constitutes a ratio of two like quantities should be expressed as a fraction (either common or decimal) or as a percentage-e.g., the slope is l/l00 or 0.01 or l%, not 10 mm/m or 10 m/km.

SI Prefix Usage. General--S1 prefixes should be used to indicate orders of magnitude, thus eliminating non- significant digits and leading zeros in decimal fractions and providing a convenient alternative to the powers- of-10 notation preferred in computation. For example, 12 300 m (in computations) becomes 12.3 km (in non- computation situations); 0.0123 hA (12.3 x 10m9 A for computations) becomes 12.3 nA (in noncomputation situations).

Selection-When expressing a quantity by a numerical value and a unit, prefixes should be chosen so that the numerical value lies between 0.1 and 1000. Generally, prefixes representing steps of 1000 are recommended (avoiding hecto, deka, deci, and centi). However, some situations may justify deviation from the above:

1. In expressing units raised to powers (such as area, volume and moment) the prefixes hecto, deka, deci, and

centi may be required-e.g., cubic centimeter for volume and cm4 for moment.

2. In tables of values of the same quantity, or in a discussion of such values within a given context, it generally is preferable to use the same unit multiple throughout.

3. For certain quantities in particular applications, one certain multiple is used customarily; an example is the millimeter in mechanical engineering drawings, even when the values lie far outside the range of 0.1 to 1000 mm.

Powers of Units-An exponent attached to a symbol

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-13

containing a prefix indicates that the multiple or sub- mulripie of the unit (the unit with its prefix) is raised to the power expressed by the exponent. For example,

1 cm3 =(10p2m)3 = 10 -6,3

1 ns-’ =(10P9s) -1 =109s-’

1 mm*/s =(10-“m)2/s = 10-5m2/s

Double Pre$xes-Double or multiple prefixes should not be used. For example,

use GW (gigawatt), not LMW; use pm (picometer), not ppm; use Gg (gigagram), not Mkg; use 13.58 m, not 13 m 580 mm.

Prefix Mixtures-Do not use a mixture of prefixes unless the difference in size is extreme. For example, use 40 mm wide and 1500 mm long, not 40 mm wide and 1.5 m long; however, 1500 m of 2-mm-diameter wire is acceptable.

Compound Units--It is preferable that prefixes not be used in the denominators of complex units, except for kilogram (kg) which is a base unit. However, there are cases where the use of such prefixes is necessary to ob- tain a numerical value of convenient size. Examples of some of these rare exceptions are shown in the tables contained in these standards.

Prefixes may be applied to the numerator of a com- pound unit; thus, megagram per cubic meter (Mg/m3), but not kilogram per cubic decimeter (kg/dm3) nor gram per cubic centimeter (g/cm3). Values required outside the range of the prefixes should be expressed by powers of 10 applied to the base unit.

Unit of Mass-Among the base units of SI, the kilogram is the only one whose name, for historical reasons, contains a prefix; it is also the coherent SI unit for mass (See Appendices A and B for discussions of coherence.) However, names of decimal multiples and submultiples of the unit of mass are formed by attaching prefixes to the word “gram.”

Prefises Alone-Do not use a prefix without a unit-e.g., use kilogram, not kilo.

Calculations-Errors in calculations can be minimized if, instead of using prefixes, the base and the coherent derived SI units are used, expressing numerical values in powers-of-10 notation-e.g., 1 MJ= lo6 J.

Spelling of Vowel Pairs. There are three cases where the final vowel in a prefix is omitted: megohm, kilohm, and hectare. In all other cases, both vowels are retained and both are pronounced. No space or hyphen should be used.

Complicated Expressions. To avoid ambiguity in com- plicated expressions, symbols are preferred over words.

Attachment. Attachment of letters to a unit symbol for giving information about the nature of the quantity is in- correct: MWe for “megawatts electrical (power), ” kPag for “kilopascais gauge (pressure),” Paa for “pascals ab- solute (pressure),” and Vat for “volts ac” are not ac- ceptable. If the context is in doubt on any units used, supplementary descriptive phrases should be added to making the meanings clear.

Equations. When customary units appear in equations, the SI equivalents should be omitted. Instead of inserting the latter in parentheses, as in the case of text or small tables, the equations should be restated using SI unit symbols, or a sentence, paragraph, or note should be added stating the factor to be used to convert the calculated result in customary units to the preferred SI units.

Pronunciation of Metric Terms

The pronunciation of most of the unit names is well known and uniformly described in U.S. dictionaries, but four have been pronounced in various ways. The follow- ing pronunciations are recommended:

candela - Accent on the second syllable and pronounce it like de/l.

joule Pascal

- Pronounce it to rhyme with pool. - The preferred pronunciation rhymes

with rascal. An acceptable second choice puts the accent on the second syllable.

siemens - Pronounce it like sea,nerl ‘.r.

For pronunciation of unit prefixes, see Table 1.4.

Typewriting Recommendations Superscripts. The question arises of how numerical superscripts should be typed on a machine with a con- ventional keyboard. With an ordinary keyboard. numerals and the minus sign can be raised to the superscript position by rolling the platen half a space before typing the numeral, using care to avoid in- terference with the text in the line above.

Special Characters. For technical work, it is useful to have Greek letters available on the typewriter. If all SI symbols for units are to be typed properly, a key with the upright Greek lower-case p (pronounced “mew.” not *‘moo”) is necessary, since this is the symbol for micro. meaning one millionth. The symbol can be approximated on a conventional machine by using a lower-case u and adding the tail by hand (p). A third choice is to spell out the unit name in full.

For units of electricity, the Greek upper-case omega (Q) for ohm also will be useful; when it is not available, the word “ohm” can be spelled out.

It is fortunate that, except for the more extensive use of the Greek p for micro and Q for ohm, the change to SI units causes no additional difficulty in manuscript preparation.

The Letter for Liter. On most U.S. typewriters, there is little difference between the lower-case “cl” (“I”) and the numerical “one” (“1”). The European symbol for liter is a simple upright bar; the Canadians I3 used a script P but now have adopted the upright capital L; AN- SI now recommends the upright capital L.

Typewriter Modification. Where frequently used, the thllowing symbols could be included on typewriters: superscripts ’ and ’ for squared and cubed; Greek p for micro; ’ for degree; . for a product dot (not a period) for symbols derived as a product; and Greek Q for ohm.

58-l 4 PETROLEUM ENGINEERING HANDBOOK

A special type-ball that contains all the superscripts, FL, Q, and other characters used in technical reports is vailable for some typewriters. Some machines have replaceable character keys.

Longhand. To assure legibility of the symbols m, n. and p. it is recommended that these three symbols be written to resemble printing. For example. write nm, not ,I~,,. The symbol p should have a long distinct tail and should have the upright form (not sloping or italic).

Shorthand. Stenographers will find that the SI symbols generally are quicker to write than the shorthand forms for the unit names.

APPENDIX D General Conversion Factors” General Table 1.7 is intended to serve two purposes:

1. To express the definitions of general units of mcasurc ah exact numerical multiples of coherent “m&c” units. Relationships that are exact in terms of the fundamental SI unit arc followed by an asterisk. Relationships that are not followed by an astcrlsk either arc the result of physical measurements or arc only appmximatc.

2. To provide tnultiplying factors for converting cx- prcssions of measurements given by numbers and 2encral or miscellaneous units to corresponding new numbers and metric units.

Notation Conversion factors are presented for ready adaptation to computer readout and electronic data transmission. The factors are written as a number equal to or greater than one and less than IO, with six or fewer decimal places (i.e.. seven or fewer total digits). Each number is fol- lowed by the letter E (for exponent), a plus or minus symbol, and two digits that indicate the power of 10 by which the number must be multiplied to obtain the cor- rect value. For example,

3.523 907 (E-02) is 3.523 907~ IO-’ or

0.035 239 07. Similarly,

3.386 389 (E+03) is 3.386 389~ IO3 or

3 386.389.

An asterisk (*) after the numbers shown indicates that the conversion factor is exact and that all subsequent digits (for rounding purposes) are zero. All other conver- sion factors have been rounded to the figures given in ac- cordance with procedures outlined in the preceding text.

‘Based on ASTM Pub E380-82 @?I 3), values Of CO”“elSlO” IaCtOrs tabulated herewth are identical with those in E380-82, generally slm~far material IS found m Ref 4 Conversion values in earlier edltlons of E 380 (for example E 380.74) are based on Ref 15 wh,ch has available some faclors w,,h more than seven d,g,,s

Where fewer than six decimal places are shown, more precision is not warranted.

The following is a further example of the use of Table 1.7.

To Convert From To Multiply By

pound-force per square foot

pound-force per square inch

inch

Pa 4.788 026 E+OI

Pa 6.894 757 E+03 m 2.540* E-02

These conversions mean that

I Ibf/ft’ becomes 47.880 26 Pa, I Ibf/in.’ becomes 6894.757 Pa or

6.894 757 kPa, and I inch becomes 0.0254 m (exactly).

The unit symbol for pound-force sometimes is written Ibf and sometimes lb, or lb/: the form Ibf is recommended.

Organization The conversion factors generally arc liatcd alphabetically by units having specific names and compound units derived from these specific units. A number of units starting with the pound symbol (lb) arc located In the “p” section of the list.

Conversion factors classified by physical quantities arc listed in Refs. 3 and 4.

The conversion factors for other compound units can be generated easily from numbers given in the alphabetical list by substitution of converted units. Two examples follow.

I. Find the conversion factor for productivity in&x, (B/D)/psi to (mj/d)/Pa. Convert 1 B/D to I.589 873 (E-01) m”/d and I psi to 6.894 7.57 (E+03) Pa. Then. substitute

[ 1.589 873 (E-01)]/]6.894 757 (E-03)] =2.305 916 (E-OS) (m3/d)/Pa.

2. Find the conversion factor for tonf.mile/ft to MJim. Convert I tonf to 8.896 444 (E+03) N: 1 mile to 1.609 344” (E+03) m; and I ii to 3.048* (E-01) m. Then. substitute

18.896 444 (E+03)] [I.609 344 (E+03)] +[3.048 (E-O])]

=4.697 322 (E+07) (N.m)/m or J/m =4.697 322 (E+Ol) MJim.

When conversion factors for complex compound units are being calculated from Table I .7. numerical uncer- tainties may be present in the seventh (or lesser last “significant”) digit of the answer because of roundings already taken for the last digit of tabulated values. Mechtly ” provides conversion factors of more than \cvcn digits for certain quantities.

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-15

To Convert From

abampere abcoulomb abfarad abhenry abmho

abohm abvolt acrefoot (U.S. survey)“’ acre (U.S survey)“’ ampere hour

are angstrom astronomical unit atmosphere (standard) atmosphere (technical = 1 kgf/cm2)

bar barn barrel (for petroleum, 42 gal) board foot

Elntish thermal unit (International Table)“’ Bntish thermal unit (mean) Bntish thermal unit (thermochemical) Bntish thermal unit (39°F) Bntish thermal umt (59°F) Bntlsh thermal unit (60°F)

Btu (International Table)-fV(hr-ft2-“F) (thermal conductlvrty)

Btu (thermochemical)-ft/(hr-ft*-OF) (thermal conductlvtty)

Btu (International Table)-m.i(hr-R*-“F) (thermal conductlvrty)

Btu (thermochemical)-in.‘(hr-RZ-“F) (thermal conductivity)

Btu (International Table)-in.i(s-Hz-“F) (thermal conductivity)

Btu (thermochemical)-in./(s-f12-“F) (thermal conductlvily)

B1u (International Table)/hr Btu (thermochemical)/hr Btu (thermochemical):mm Btu (thermochemical)%

Btu (International Table)ift? Btu (thermochemlcai)ifV Btu (thermochemical)i(ft*-hr) Btu (thermochemical)i(H2-min) Btu (thermochemical)i(ft*-s)

Btu (thermochemical)/(irxZ-s) Btu (International Table)I(hr-V-OF)

(thermal conductance) Btu (thermochemical)i(hr-V-OF)

(thermal conductance) Btu (International Table)i(s-R*-“F) Btu (thermochemical)@tt*-OF)

Btu (International Table)ilbm Btu (thermochemical):lbm Btu (International Table)i(lbm-“F)

(heat capacity) Btu (thermochemical)i(lbm-“F)

(heat capaaty)

TABLE 1.7-ALPHABETICAL LIST OF UNITS (symbols of SI units given in parentheses)

To ampere (A) coulomb (C) farad (F) henry (H) siemens (S)

ohm (0) volt (V) meter3 (m3) mete? (m’) coulomb (C)

meter* (m2) meter (m) meter (m) Pascal (Pa) Pascal (Pa)

Pascal (Pa) meter* (m*) meter3 (m”) meter3 (m”)

joule (J) loule (J) joule (J) joule (J) joule (J) joule (J)

watt per meter kelvin [W/(mK)]

watt per meter kelvin [W/(mK)]

watt per meter kelvin [W/(m.K)]

watt per meter kelvin [Wl(m.K)]

watt per meter kelvin [W/(m.K)]

watt per meter kelvin [Wl(m.K)]

watt(W) watt (W) watt(W) watt (W)

joule per meter2 (Jim*) joule per meter2 (Jim*) watt per mete? (W/ml) watt per meter2 (W/m’) watt per mete? (W/m*)

watt per mete? (W/m’)

watt per meter* kelvin [W/(m’.K)]

watt per meter* kelvin [W/(m*.K)] watt per meter* kelvin [W/(m*.K)] watt per meter2 kelvin [W/(m’.K)]

joule per kilogram (J/kg) joule per kilogram (J/kg)

joule per kilogram kelvin [J/(kg.K)]

joule per ktlogram kelvin [J/(kgeK)]

Multiply By 1 .O’ E+Ol 1 .O’ E+Ol 1 .O’ E+O9 1.0 E-09 1 .O’ E+09

1.0’ E-09 1.0’ E-08 1.233489 E+03 4.046 873 E + 03 3.6’ E+03

1 .O’ E+02 1 .O’ E-10 1.495979 E+ll 1.013250’ E+05 9.806 650’ E + 04

1 .O’ E+05 1 .O’ E-28 1.589873 E-01 2.359 737 E - 03

1.055 056 E + 03 1.05587 E+03 1.054 350 E + 03 1.05967 E+03 1.05480 E+03 1.05468 E+03

1.730 735 E f 00

1.729 577 E + 00

1.442 279 E ~ 01

1.441 314 E-01

5.192 204 E +02

5.188 732 E+02

2.930711 E-01 2.928 751 E - 01 1.757250 E+Ol 1.054350 E+03

1.135653 E+04 1.134893 E+04 3.152481 E-00 1.891 489 E + 02 1.134893 E+04

1.634 246 E + 06

5.678 263 E + 00

5.674 466 E + 00 2.044 175 E + 04 2.042 808 E + 04

2.326’ E+03 2.324 444 E + 03

4.186 8’ E+03

4.184 000 E +03

“Fence 1893 the U S bass 01 length measurement has been dewed IrOm metric standards In 1959 a small rellnement was made I” the defimlmn of the yard to resolve d,screpanc,es both I” this country and abroad. which changed ,ts length from 3600 3937 m lo 0 9144 m exactly This resulted I” the new value being shorter by two parts I” a rrvlnn At the same time it was deaded that any data r leet derived from and publIshed as a result of geodetic surveys withm the U S would wna~n with the old standard (1 f, = ,200 3937 m) unt,l further dec,s,on Th,s loot IS named the U S suvey loot As a result, all U S land measurements I” U S. c”stoma~ ““1,s WIII relate tothe meter by the old standard All the mnvers~on factors I” these tables for umts relerenced to thus loatnote are based on the U.S survey foot. ratherthaiihe inlernatu,nal loot Con&on Iactors for me land measure glen below may be delemned from the loltowlng relatlonships

1 league = 3 miles (exactly) 1 rod = 16”~ fl (exactly]

1 chain = 66 fl (exactly) 1 SectIon 1 sq mile

1 townsh,p = 36 sq m,les

@This value was adopted m 1956. Some of the older lnlernatlonal Tables use Ihe value 1 055 D4 E + 03 The exact con~ers!on factor IS 1 055 055 852 62‘ E + 03

58-16 PETROLEUM ENGINEERING HANDBOOK

TABLE 1.7-ALPHABETICAL LIST OF UNITS (continued) (symbols of SI units given in parentheses)

To Convert From bushel (U.S.) caliber (inchj calorie (International Table) calorie (mean) calorie (thermochemical)

calorie (15°C) calorie (20°C) calorie (kilogram, International Table) calorie (kilogram, mean) calorie (kilogram, thermochemical)

cal (thermochemical)/cm* cal (International Table)/g cal (thermochemical)ig cal (International Table)/(gX) cal (thermochemical)/(gX)

cal (thermochemical)imin cal (thermochemical)is cal (thermochemical)/(cmz.min) cal (thermochemical)/(cm**s) cal (thermochemical)~(cm+‘C) capture unit (cu. = 10m3 cm-‘)

carat (metric) centimeter of mercury (0°C) centimeter of water (4°C) centipoise centistokes

circular mil cl0 cup curie cycle per second

day (mean solar) day (sidereal) degree (angle)

degree Celsius degree centigrade (see degree Celsius) degree Fahrenheit degree Fahrenheit degree Rankine

“Fshr-ft2/Btu (International Table) (thermal resistance)

“F.hr-ftVBtu (thermochemical) (thermal resistance)

denier dyne dynecm dyne/cm2 electronvolt

EMU of capacitance EMU of current EMU of electric potential EMU of inductance EMU of resistance

ESU of capacitance ESU of current ESU of electnc potential ESU of inductance ESU of resistance

erg erg/cm% erg/s faraday (based on carbon-l 2) faraday (chemical) faraday (physical) fathom fermi (femtometer) fluid ounce (U.S.)

foot foot (U.S. survey)“1

To mete? (ml) meter (m) joule (J) joule (J) joule (J)

joule (J) joule (J) joule (J) joule (J) joule (J)

joule per meter* (J/m’) joule per kilogram (J/kg) joule per kilogram (J/kg) joule per kilogram kelvin [Jl(kgK)] joule per kilogram kelvin [J/(kg.K)]

watt (W) watt (W) watt per meter’ (W/m*) watt per mete? (W/m2) watt per meter kelvin [W/(m.K)] per meter (m-l)

kilogram (kg) Pascal (Pa) Pascal (Pa) Pascal second (Pas) mete? per second (m*/s)

mete? (m2) kelvin mete? per watt [(Km*)/W] meteP (m3) becquerel (Bq) hertz (Hz)

second (s) second (s) radian (rad)

kelvin (K)

degree Celsius kelvin (K) kelvin (K)

kelvin mete? per watt [(Km*)/W]

kelvin meter’ per watt [(K.m*)IW] kilogram per meter (kg/m) newton (N) newton meter (N.m) Pascal (Pa) joule (J)

farad (F) ampere (A) volt (V) henry U-V ohm (0)

farad (F) ampere (A) volt (V) henry 0-U ohm (0)

joule (J) watt per meter* (W/m>) watt (W) coulomb (C) coulomb (C) coulomb (C) meter (m) meter (m) meter’ (m3)

meter (m) meter (m)

Multiply By” 3.523 907 E - 02 2.54 E-02 4.1868’ E+OO 4.19002 E+OO 4.184’ E+OO

4.185 80 E+OO 4.181 90 E+OO 4.186 8’ E+03 4.190 02 E+03 4.184’ E+03

4.184’ E+04 4.186’ E+03 4.184’ E+03 4.186 8 E+03 4.184’ E+03

6.973 333 E - 02 4.184’ E+OO 6.973 333 E + 02 4.184’ E+O4 4.184’ E+02 1 .O’ E-01

2.0’ E-04 1.33322 Et03 9.806 38 E + 01 1 .O’ E-03 1 .O’ E-06

5.067 075 E - 10 2.003 712 E-01 2.365 882 E - 04 3.7’ Et10 1 .O’ E+OO

8.640 000 E + 04 8.616 409 E+04 1745329 E-02

T, = T,c + 273.15

r, = (T, - 32)11.8 T, = (T, + 459.67)/1.8 r, = J41.8

1.781 102 E-01

1.762 250 E - 01 1.111 111 E-07 1 .O’ E-05 1 .O’ E-07 1 .O’ E-01 1.602 19 E-19

1 .O’ E+O9 1 .O’ E+Ol 1 .O’ E-08 1 .O’ E-09 1 .O’ E-09

1.112650 E-12 3.335 6 E- 10 2.997 9 E+02 8.987554 E+ll 8.987 554 E + 11

1 .o E-07 1 .O’ E-03 1 .O’ E-07 9.648 70 E + 04 9.649 57 E + 04 9.652 19 E+04 1.828 8 E+OO 1 .o E-15 2.957 353 E - 05

3.048’ E-01 3.048 006 E -01

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD

TABLE 1.7-ALPHABETICAL LIST OF UNITS (continued) (symbols of SI units given in parentheses)

To Convert From foot of water (39.2”F) sq ft ft*/hr (thermal diffusivity) ftV3

cu ft (volume; section modulus) ftYmin W/S

ff (moment of section)@)

fUhr ft/min ftk ft/SZ

footcandle footlambert

ft-lbf ft-lbf/hr ft-lbfimin ft-lbf/s ft-poundal free fall, standard (g)

cm/s? qallon (Canadian liquid) gallon (U.K. liquid) gallon (U.S. dry) gallon (US liquid) gal (U.S. liquid)iday gal (US. liquid)/min gal (U.S. liquid)/hphr

(SFC, specific fuel consumption)

gamma (magnetic field strength) gamma (magnetic flux density) gauss gilbert gill (U.K.) gill (U.S.)

grad grad grain (117000 Ibm avoirdupois) grain (Ibm avoirdupoisi7000)lgaI

(U.S. liquid)

gram glcm3 gram-force/cm2 hectare horsepower (550 ft-lbfis)

horsepower (boiler) horsepower (electric) horsepower (metric) horsepower (water) horsepower (U.K.)

hour (mean solar) hour (sidereal) hundredweight (long) hundredweight (short)

inch inch of mercury (32°F) inch of mercury (60°F) inch of water (39.2”F) inch of water (60°F)

sq in. cu in. (volume; section modulus)i41 in.3/min in4 (moment of section)13’

in/s in .I$ kayser kelvin

To Pascal (Pa) meter2 (m’) mete? per second (m*is) meter? per second (m’is)

mete? (m3) mete? per second (m’1.s) mete? per second (mVs) mete? (ml)

meter per second (m/s) meter per second (m/s) meter per second (m/s) meter per second2 (misz) Iux (lx) candela per meter2 (cdim2)

joule (J) watf (W) watt (wj watt (W) joule (J) meter per second’ (m/s’)

meter per second2 (m/s’) mete? (m3) mete? (m3) mete? (m3) mete? (mJ) mete? per second (mVs) mete? per second (m%)

mete? per joule (mYJ)

ampere per meter (Aim) tesla (T) tesla (T) ampere (A) mete? (m3) mete? (ma)

degree (angular) radian (rad) kilogram (kg)

kilogram per mete? (kg/m3)

kilogram (kg) kilogram per mete? (kg/m3) Pascal (Pa) meter* (m2) watt (W)

watt (W) watt (W) watt (W) watt (W) watt (W)

second (s) second (s) kilogram (kg) kilogram (kg)

meter (m) Pascal (Pa) Pascal (Pa) Pascal (Pa) Pascal (Pa)

meter* (m*) meteP (m”) mete? per second (m%) meteP (ma)

meter per second (m/s) meter per second* (m/s2) 1 per meter (1 /m) degree Celsius

58-17

Multiply By” 2.988 98 E +03 9.290 304’ E - 02 2.580 640’ E - 05 9.290 304’ E - 02

2.831 685 E - 02 4.719 474 E -04 2.831 685 E -02 8.630 975 E -03

8.466 667 E - 05 5.080’ E-03 3.048’ E-01 3.048’ E-01 1.076391 E+Ol 3.426 259 E + 00

1.355818 E+OO 3.766 161 E -04 2.259 697 E - 02 1.355818 E+OO 4.214 011 E -02 9.806 650’ E + 00

1 .O’ E-02 4.546 090 E - 03 4.546 092 E - 03 4.404 884 E - 03 3.785412 E-03 4.381 264 E - 08 6.309 020 E - 05

1.410089 E-09

7.957 747 E - 04 1 .O’ E-09 1 .o E-04 7.957 747 E - 01 1.420 654 E - 04 1.182941 E-04

9.0’ E-01 1.570796 E-02 6.479 891 l E - 05

1.711 806 E-02

1 .O’ E-03 1 .O’ Et03 9.806 650’ E + 01 1 .O’ E+04 7.456 999 E + 02

9.809 50 E + 03 7.460’ E+02 7.354 99 E+02 7.460 43 E + 02 7.457 0 E+O2

3.600 000 E + 03 3.590 170 E + 03 5.080 235 E + 01 4.535 924 E + 01

2.54’ E-02 3.386 38 E + 03 3.376 85 E + 03 2.490 82 E + 02 2.488 4 E+02

6.451 6’ E-04 1.638 706 E ~ 05 2.731 177 E-07 4.162 314 E-07

2.54’ E-02 2.54’ E-02 1 .O’ E+02 T., = T, - 273.15

I31 Thus sometimes IS tailed the rrwment of merha of a plane sechon about a spafled ~XIS 14’ The exact c~nwrslon factor IS 1.636 706 4’E-05

58-18 PETROLEUM ENGINEERING HANDBOOK

TABLE 1.7-ALPHABETICAL LIST OF UNITS (continued) (symbols of SI units given in parentheses)

To Convert From To

kilocalorie (International Table) joule (J) kilocalorie (mean) joule (J) kilocalorie (thermochemical) joule (J) kilocalorie (thermochemical)imin watt (W) kilocalorie (thermochemical)/s watt (W)

kilogram-force (kgf) newton (N) kgf.m newton meter (N.m) kgfs*im (mass) kilogram (kg) kgf/cm2 Pascal (Pa) kgf/m* Pascal (Pa) kgf/mm? Pascal (Pa)

km/h meter per second (m/s) kilopond newton (N) kilowatthour (kW-hr) joule (J) kip (1000 Ibf) newton (N) kip/in.* (ksi) Pascal (Pa) knot (international) meter per second (m/s)

lambert candela per meteP (cd/m*) lambert candela per mete? (cd/m*) langley joule per mete? (J/mz) league meter (m) light year meter (m) IiteV’ meter-l (ml)

maxwell weber (Wb) mho siemens (S) microinch meter (m) microsecond/foot (@ft) microsecond/meter (&m) micron meter (m) mil meter (m)

mile (international) meter (m) mile (statute) meter (m) mile (U.S. survey)“) meter (m) mile (international nautical) meter (m) mile (U.K. nautical) meter (m) mile (U.S. nautical) meter (m)

sq mile (international) sq mile (U.S. survey)“’ mileihr (international) mileihr (international) mileimin (international) mile/s (international)

millibar millimeter of mercury (0°C) minute (angle) minute (mean solar) mcnute (sidereal) month (mean calendar)

oersted ohm centimeter ohm circular-mil per ft

ounce (avoirdupois) ounce {troy or apothecary) ounce (U.K. fluid) ounce (U.S. fluidj ounce-force ozf.in.

oz (avoirdupois)igal (U.K. liquid) oz (avoirdupois)/qal (U.S. liquid) oz (avoirdupois)&? oz (avoirdupois)/fF oz (avoirdupois)/yd2 parsec peck (U.S.)

pennyweight perm (‘C)@)

mete? (m2) mete? (m2) meter per second (m/s) kilometer per hour (kmih) meter per second (m/s) meter per second (m/s)

Pascal (Pa) Pascal (Pa) radian (rad) second (s) second (s) second (s)

ampere per meter (A/m) ohm meter (0.m) ohm millimeter* per meter

[(0.mm2)m]

kilogram (kg) kilogram (kg) meter3 (m”) mete? (m3) newton (N) newton meter (N.m)

kilogram per meterj (kg/m>) kilogram per metep (kgimJ) kilogram per meterj (kg/mJ) kilogram per meter2 (kg/m2) kilogram per meter’ (kg/m’) meter (m) mete? (m3)

kilogram (kg) kilogram per Pascal second meter*

[kg!(Pas.m2)]

Multiply By” 4.186 8’ E+03 4.190 02 E+03 4.184’ E+03 6.973 333 E + 01 4.184’ E+03

9.806 65’ E + 00 9.806 65’ E + 00 9.806 65’ E + 00 9.806 65’ E + 04 9.806 65’ E + 00 9.806 65’ E + 06

2.777 778 E - 01 9.806 65’ E + 00 3.6 E+06 4.448 222 E + 03 6.894 757 E + 06 5.144444 E-01

1 in’ E+04 3.183099 E+03 4.184 E+04 (see Footnote 1) 9.46055 E+15 1.0 E-03

1 .o E-08 1 .o E+OO 2.54’ E-08 3.280 840 E + 00 1 .O’ E-06 2.54’ E-05

1.609 344’ E + 03 1.609 3 E+03 1.609 347 E + 03 1.852 E+03 1.853 184’ E+03 1.852’ E+03

2.589 988 E + 06 2.589 998 E + 06 4.470 4’ E-01 1.609 344’ E + 00 2.682 24’ E +Ol 1.609 344’ E+03

1 .O’ E+02 1.33322 E+02 2.908 882 E - 04 6.0’ E+Ol 5.983617 E+Ol 2.628 000 E + 06

7.957 747 E + 01 1 .O’ E-02

1.662 426 E ~ 03

2.834 952 E ~ G2 3.110348 E-02 2.841 307 E-05 2.957 353 E - 05 2.780 139 E-01 7.061 552 E - 03

6.236 021 E + 00 7.489 152 E+OO 1.729994 E+03 3.051 517 E-01 3.390 575 E - 02 3.085 678 E + 16 8.809 768 E ~ 03

1.555 174 E-03

5.721 35 E-11

‘%, 1964 the General Conference on Weights and Measures adopted the name liter as a special name for the c,,blc decr,,eter Before ,h,s dec,s,on ,be ,,ter d,f,e,ed slightly (prewous value, 1 WO 028 dm3 and m expression of preclslon volume measurement this lact must be kept I” mind

t61Not the same as resewmr “per”, ”

THE Sf METRIC SYSTEM OF UNITS & SPE METRIC STANDARD

TABLE 1.7-ALPHABETICAL LIST OF UNITS (continued) (symbols of SI units given in parentheses)

To Convert From perm (23”C)16’

perm.in. (OC)c71

perm.in. (23°C)“’

phol oica (orinter’s) pint (U.S. dryj oint (U.S. liauid) point (printers)’ poise (absolute viscosity)

pound (lbm avoirdupois)@’ pound (troy or apothecary) Ibm-ftz (moment of Inertia) Ibm-in.? (moment of inertia)

Ibmift-hr lbmift -s IbmW I bm/ft3 Ibm/gal (U.K. liquid) lbmigal (U.S. liquid)

lbmihr Ibm/(hp hr)

(SFC, specific fuel consumption) Ibmlin.3 lbmimin lbmis Ibm/yd3

poundal poundalift’ poundal-s/R2

pound-force (lbf)‘91 IbfWO’ Ibf-ft:in.“‘J lbf-in.“‘l Ibf-rn.:ln.l”’ Ibf-sift’ lbfift IbfW Ibfiin. Ibf/itxz (psi) lbfllbm (thrust/weight [mass] ratio)

quart (U.S. dry) quart (U.S. liauid) rad (radiation’dose absorbed) rhe rod roentgen

second (angle) second (sidereal) section shake

kilogram per Pascal second mete? [kg/( Pasm2)]

krlogram per Pascal second meter [kg/(Pasm)]

kilogram per Pascal second meter [kmi(Pasm)]

lumen per mete? (lm/m2) meter (m) metep (m3) mete? (m3) meter (m) Pascal second (Pas)

kilogram (kg) kilogram (kg) kilogram meter’ (kg-m’) kilogram mete? (kg-m*)

Pascal second (Pas.) Pascal second (Pas) kilogram per mete? (kg/m2) kilogram per mete? (kg/m3) kilogram per mete? (kg/m3) kilogram per meter3 (kg/m3)

kilogram per second (kg/s)

slug slug/(ft-s) slug/fV

statampere statcoulomb statfarad stathenry statmho

statohm statvolt stere

krlogram per Joule (kg/J) krlogram per mete? (kg/ma) ktlogram per second (kg/s) kilogram per second (kg/s) kilogram per meter] (kgim3)

newton (N) Pascal (Pa) Pascal second (Pas)

newton (N) newton meter (N.m) newton meter per meter [(N-m)/m)] newton meter (N.m) newton meter per meter [(N-m)/mj Pascal second (Pas) newton per meter (N/m) Pascal (Pa) newton per meter (N/m) Pascal (Pa) newton per kilogram (N/kg)

mete? (m3) meter3 (m3) gray (GY) 1 per Pascal second [ 1 /(Pas)] meter (m) coulomb per kilogram (C/kg)

radian (rad) second (s) meter2 (m*) second (s)

kilogram (kg) Pascal second (Pas) kilogram per metel3 (kg/m3)

ampere (A) coulomb (C) farad (F) henry (H) sremens (S)

ohm (It) volt (V) mete? (m”)

58-19

Multiply By”

5.74525 E-11

1.45322 E-12

1.459 29 E- 12

1 .O’ E+04 4.217518 E-03 5.506 105 E-04 4.731 765 E - 04 3.514 598’ E - 04 1 .o E-01

4.535 924 E - 01 3.732417 E-01 4.214 011 E-02 2.926 397 E - 04

4.133 789 E -04 1.488 164 E+OO 4.882 428 E + 00 1.601 846 E +Ol 9.977 633 E + 01 1.198264 E+02

1.259979 E-04

1.689 659 E - 07 2.767 990 E + 04 7.559 873 E - 03 4.535 924 E - 01 5.932 764 E - 01

1.382 550 E - 01 1.488 164 E+OO 1.488 164 E+OO

4.448 222 E + 00 1.355818 E+OO 5.337 866 E +Ot 1.129848 E-01 4.448 222 E t 00 4.788 026 E + 01 1.459 390 E t 01 4.788 026 E + 01 1.751 268 Et 02 6.894 757 E + 03 9.806 650 E t 00

1.101 221 E-03 9.463 529 E - 04 1.0’ E-02 1 .O’ E+Ol (see Footnote 1) 2.58 E-04

4.848 137 E -06 9.972 696 E -01 (see Footnote 1) 1.000 000’ E - 08

1.459 390 E t 01 4.788 026 E t 01 5.153 788 E+02

3.335 640 E 110 3.335 640 E - 10 1.112650 E-12 8.987 554 E + 11 1.112650 E-12

8.987 554 Et 11 2.997 925 E + 02 1 .O’ E+OO

“‘Not the same dlmenslons as “m#!darcy-foot” ‘BJThe exacf conversion factor IS 4 535 923 7’E 01. lg’The exact conversion factor IS 4 448 221 615 260 5’E + 00

“@‘Torque unit. see text dwzusslon of “Torque and Bending Moment” ““Torque dlwded by length see fexf d!scuss!on 01 Torque and Bendmg Moment

58-20 PETROLEUM ENGINEERING HANDBOOK

ton (assay) ton (tong, 2,240 Ibm) ton (metric)

To Convert From

ton (nuclear equivalent of TNT) ton (refrigeration)

stilb

ton (register)

ton (short, 2000 Ibm)

stokes (kinematic viscosity)

ton (long)/ydJ ton (shott)/hr

tablespoon

ton-force (2000 Ibf) tonne

teaspoon

torr (mm Hg, 0°C) township

tex

unit pole watthour (W-hr)

therm

w.s W/cm2 W/in.?

yard yd2 Yd3 ydJ/min

year (calendar) year (sidereal) year (tropical) “2JOet~ned (not measured) value

TABLE 1.7-ALPHABETICAL LIST OF UNITS (continued)

kilogram (kg)

(symbols of SI units given in parentheses)

kilogram (kg) kilogram (kg) joule (J)

To

watt (W)

candela per meter* (cd/m*)

metep (m3)

kllogram (kg) kilogram per mete? (kg/m3)

meter* per second (m*/s)

kilogram per second (kg/s) newton (N)

metef (m3)

kilogram (kg)

Pascal (Pa)

mete? (m3)

mete? (mz) weber (Wb)

kilogram per meter (kg/m)

joule (J) joule (J)

joule (J)

watt per meter? (W/m’) watt per meter2 (W/m2)

meter (m) mete? (m2) mete? (m3) mete? per second (m%)

second (s) second (s) second (s)

Multiply By”

1 .O’ E+04 1 .O’ E-04

1.470 676 E - 05 4.928 922 E - 06 1 .O’ E-06 1.055 056 E + 08

2.916 667 E-02 1.016047 E+03 1 .o E+03 4.184 E+09”” 3.516 800 E +03 2.831 685 E + 00

9.071 847 E + 02 1.328 939 E + 03 2.519958 E-01 8.896 444 E + 03 1 .O’ E+03

1.33322 E+02 (see Footnote 1) 1.256 637 E - 67 3.60’ E+03 1 .O’ E+OO 1 .O’ Et04 1.550003 E+03

9.144’ E-01 8.361 274 E - 01 7.645 549 E - 01 1.274 258 E - 02

3.153600 Et07 3.155 815 Ei07 3.155693 E+07

APPENDIX E TABLE 1.8 - CONVERSION FACTORS FOR THE VARA’

Value of Conversion Factor, Location Vara in Inches Varas to Meters Source

Argentina, Paraguay 34.12 8.666 E-01 Ref. 16 Cadiz, Chile, Peru 33.37 8.476 E-01 Ref. 16 California,

except San Francisco 33.3720 8.478 49 E-01 Ref. 16 San Francisco 33.0 8.38 E-01 Ref. 16

Central America 33.87 8.603 E-01 Ref. 16 Colombia 31.5 8.00 E-01 Ref. 16 Honduras 33.0 8.38 E-01 Ref. 16 Mexico 8.380 E-01 Refs. 16 and 17 Portugal, Brazil 43.0 1.09 Et00 Ref. 16 Spain, Cuba, Venezuela, Philippine Islands 33.38” 8.479 E-01 Ref. 17 Texas

Jan. 26, 1801, to Jan. 27, 1838 32.8748 8.350 20 E-01 Ref. 16 Jan. 27, 1838 to June 17, 1919, for

surveys of state land made for Land Office 33-113 8.466 667 E-01 Ref. 16 Jan. 27, 1838 lo June 17, 1919, on private surveys

(unless changed to 33-113 in. by custom arising

to dignity of law and overcoming former law) 32.8748 8.350 20 E-01 Ref. 16 June 17, 1919, to present 33-113 8.466 667 E-01 Ref. 16

*It IS evident from Ref 16 that accurate defined lengths 01 the vala varied slgnlflcantly, according to hlslotlcal date and localay used For work rqulrlng accura& Co”“ers~~“s. the user should check Closely lnlo Lhe dale and localIon of the wrveys mvolved, with due regard lo what local ,x,cl,ce may have been at that t,me and place

“This value quoted horn Webster’s New lnternakmal D~chona~

THE St METRIC SYSTEM OF UNITS & SPE METRIC STANDARD

TABLE l.Q-“MEMORY JOGGER”-METRIC UNITS

APPENDIX F

barrel British thermal unit British thermal unit per pound-mass

calorie centipoise centistokes darcy degree Fahrenheit (temperature difference) dyne per centimeter foot

cubic foot (cu ft) cubic foot per pound-mass (fWbm) square foot (sq ft) foot per minute

foot-pound-force foot-pound-force per minute foot-pound-force per second horsepower horsepower, boiler inch kilowatthour mile ounce (avoirdupois) ounce (fluid) pound-force pound-force per square inch (pressure, psi) pound-mass pound-mass per cubic foot

section

ton, long (2240 pounds-mass) ton, metric (tonne) ton, short ‘Exact aqulvalents

“BallPark” Metnc Values; (Do Not Use As

Conversion Factors)

-i 4000 square meters

0.4 hectare 0.16 cubic meter

1000 joules 1 2300 joules per kilogram

2.3 kilojoules per kilogram 4 joules 1’ millipascal-second 1’ square millimeter per second 1 square micrometer 0.5 kelvin 1’ millinewton per meter

-i 30 centimeters 0.3 meter 0.03 cubic meter 0.06 cubic meter per kilogram 0.1 square meter

{ g’” ~i%%&n$%cond 1.4 joules 0.02 watt 1.4 watts

750 watts (% kilowatt) 10 kilowatts 2.5 centimeters 3.6’ megajoules 1.6 kilometers

28 grams 30 cubic centimeters 4.5 newtons 7 kilopascals 0.5 kilogram

16 kilograms per cubic meter 260 hectares

2.6 million square meters 2.6 square kilometers

1000 kilograms 1000’ kilograms 900 kilograms

58-21

Part 2: Discussion of Metric Unit Standards*

Introduction The standards and conventions shown in Part I are part of the SPE tentative standards. Table 2. I presents nomenclature for Tables 2.2 and 2.3. Table 2.2 is a modified form of a table in API 2564 reflecting SPE recommendations. Table 2.3 shows a few units com- monly used in the petroleum industry that are not shown in Table 1.7 and 2.2. The columns in these tables are based on the following.

Quantity and SI Unit. The quantity and the base or derived SI unit that describes that quantity.

Customary Unit. The unit most commonly used in ex- pressing the quantity in English units.

SPE Preferred. The base or derived SI unit plus the ap- proved prefix, if any, that probably will be used most

‘Prepared by John M Campbell for the subcommftfee

commonly to achieve convenient unit size. Any ap- proved prefix may be used in combination with an ap- proved SI unit without violation of these standards ex- cept where otherwise noted.

Other Allowable. A small, selected list of non-3 units that are approved temporuril~~ for the convenience of the English-metric transition. Use of the allowable units may be discouraged but is not prohibited. Any tradi- tional. non-9 unit not shown is prohibited under these standards.

Conversion Factor. For certain commonly used units, a conversion factor is shown. The primary purpose in these tables is to show how the preferrelf metric unit compares in size with the traditional unit. An effort has been made to keep the unit sizes comparable to minimize transition difficulties.

58-22 PETROLEUM ENGINEERING HANDBOOK

A detailed summary of general conversion factors is included as Table 1.7 in Part 1 of this report.

The notation for conversion factors in Tables 2.2 and 2.3 is explained in the introduction to Table 1.7.

Fig. 2. I shows graphically how SI units are related in a very coherent manner. Although it may not be readily apparent, this internal coherence is a primary reason for adoption of the metric system of units.

The SPE Metrication Subcommittee is endeavoring to provide SPE members with all information needed on the International System of Units and to provide tentative standards (compatible with SI coherence, decimal, and other principles) for the application of the SI system to SPE fields of interest. The tentative SPE standards are intended to reflect reasonable input from many sources, and we solicit your positive input with the assurance that all ideas will receive careful consideration.

Review of Selected Units Certain of the quantities and units shown in Tables 2.2 and 2.3 may require clarification of usage (see also the notes preceding Tables 2.2 and 2.3).

Time

Although second(s) is the base time unit, any unit of time may be used - minute (min), hour(h), day (d), and year

Unit Symbol

A

4 bar C cd “C

d F GY 9 H h Hz ha J K kg kn

L Im IX

m min

N naut. mile R Pa rad S s

sr T

v W Wb

Name

(a). Note that (a) is used as the abbreviation for year (an- num) instead of (yr). The use of the minute as a &me unit is discouraged because of abbreviation problems. It should be used only when another time unit is absolutciy inappropriate.

Date and Time Designation

The Subcommittee proposes to recommend a standard date and time designation to the American Nat]. Stan- dards Inst., as shown below. This form already has been introduced in Canada.

76 - 10 - 03 - 16 : 24 : I4 year month day hour minute second

(76-IO-03-16:24: 14)

The sequence is orderly and easy to remember: only needed portions of the sequence would be used - most documents would use the first three. No recommenda- tion has been made for distinguishing the century, such as 1976 vs. 1876 vs. 2076.

Area The hectare (ha) is allowable but its use should be con- fined to large areas that describe the area1 extent of a por-

TABLE 2.1 -NOMENCLATURE FOR TABLES 2.2 AND 2.3

Quantitv Tvpe of Unit

ampere annum (year) becquerel bar coulomb candela degree Celsius degree day farad gray gram henry hour hertz hectare joule kelvin kilogram knot

liter lumen Iux meter minute minute newton U.S. nautical mile ohm Pascal radian siemens second second steradian tesla tonne volt watt weber

electric current time activity (of radionuclides) pressure quantity of electricity luminous intensity temperature plane angle time electric capacitance absorbed dose mass inductance time frequency area work, energy temperature mass velocity

volume luminous flux illuminance length time plane angle force length electric resistance pressure plane angle electrical conductance time plane angle solid angle magnetic flux density mass electric potential power magnetic flux

base SI unit allowable (not official SI) unit derived SI unit = l/s allowable (not official SI) unit, = lo5 Pa derived SI unit, = 1 As base SI unit derived SI unit = 1.0 K allowable (not official SI) unit allowable (not official SI) unit, = 24 hours derived SI unit, = 1 A.sN derived SI unit, = J/kg allowable (not official SI) unit, = 10~3 kg derived SI unit, = 1 Vs/A allowable (not official SI) unit, = 3.6 x 10’s derived SI unit, = 1 cycle/s allowable (not official SI) unit, = lo4 m2 derived SI unit, = 1 N.m base SI unit base SI unit allowable (not official Sl) unit, = 5.144 444 x 10-j m/s

= 1.852 km/h allowable (not official Sl) unit, = 1 dm3 derived SI unit, = 1 cd.sr derived SI unit, = 1 Im/mZ base SI unit allowable (not official SI) unit Allowable cartography (not official SI) unit derived SI unit, = 1 kg,m/s2 allowable (not official SI) unit, = 1.652 x lo3 m derived SI unit, = 1 V/A derived SI unit, = 1 N/m* supplementary SI unit derived SI unit, = 1 AN base SI unit allowable cartography (not official 9) unit supplementary SI unit derived SI unit, = 1 Wb/mZ allowable (not official SI) unit, = lo3 kg = 1 Mg derived SI unit, = 1 W/A derived SI unit, = 1 J/s derived SI unit, = 1 V..s

THE Sf METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-23

tion of the earth’s crust (normally replacing the acre or section). Volume The liter is an allowable unit for small volumes only. It should be used for volumes not exceeding 100 L. Above this volume (or volume rate), cubic meters should be used. The only two prefixes allowed with the liter are “milli” and “micro:’

In the U.S., the “ -er” ending for meter and liter is of- ficial. The official symbol for the liter is “L.” In other countries the symbol may be written as “Y” and spelled out with the “ -re” ending (metre, litre). Since SPE is in- ternational. it is expected that members will use local conventions.

Notice that “API barrel” or simply “barrel” disap- pears as an allowable volume term.

BASE UNITS DERIVED UNITS WITH SPECIAL NAMES

MASS

HEAT FLOW RATE

CONOUCTINCE

ELECTRIC CURRENT

INDUCTANCE

SUPPLEMENTARY UNITS OENSITV

LUMINOUS FLUX lLLUMlNANCE

SOLID ANGLE SOLID LINES INDICATE MULTIPLICATION.

BROKEN LINES. OIVISION

Fig. Xl-Graphic relationships of SI units with names

58-24 PETROLEUM ENGINEERING HANDBOOK

Force Unit Standards Under Discussion Any force term will use the newton (N). Derived units involving force also require the newton. The expression

There are some quantities for which the unit standards

of force using a mass term (like the kilogram) is ab- have not been clarified to the satisfaction of all parties

solutely forbidden under these standards. and some controversy remains. These primary quantities are summarized below.

Mass

The kilogram is the base unit, but the gram, alone or with any approved prefix, is an acceptable SI unit.

For large mass quantities the metric ton (t) may be used. Some call this “tonne:’ However, this spelling sometimes has been used historically to denote a regular short ton (2,000 lbm). A metric ton is also a megagram (Mg). The terms metric ton or Mg are preferred in text references.

Energy and Work The joule (J) is the fundamental energy unit; kilojoules (kJ) or megajoules (MJ) will be used most commonly. The calorie (large or small) is no longer an acceptable unit under these standards. The kilowatthour is accep- table for a transition period but eventually should be replaced by the megajoule.

Power The term horsepower disappears as an allowable unit. The kilowatt (kW) or megawatt (MW) will be the multiples of the fundamental watt unit used most commonly.

Pressure The fundamental pressure unit is the Pascal (Pa) but the kilopascal (kPa) is the most convenient unit. The bar (100 kPa) is an allowable unit. The pressure term kg/cm2 is not allowable under these standards.

Viscosity The terms poise, centipoise, stokes, and centistokes are no longer used under these standards. They are replaced by the metric units shown in Table 2.2.

Temperature Although it is permissible to use “C in text references, it is recommended that “K” be used in graphical and tabular summaries of data.

Density The fundamental SI unit for density is kg/m3. Use of this unit is encouraged. However, a unit like kg/L is permissible.

The traditional term “specific gravity” will not be used. It will be replaced by the term “relative density.” API gravity disappears as a measure of relative density.

Relative Atomic Mass and Molecular Mass The traditional terms “atomic weight” and “molecular weight” are replaced in the SI system of units by “relative atomic mass” and “relative molecular mass,” respectively. See Table 1.6.

Permeability The SPE-preferred permeability unit is the square micrometer (pm*). One darcy (the traditional unit) equals 0.986 923 pm*.

The fundamental SI unit of permeability (in square meters) is defined as follows: “a permeability of one meter squared will permit a flow of I m’is of fluid of I Pa. s viscosity through an area of I m’ under a pressure gradient of 1 Pa/m.”

The traditional terms of “darcy” and “millidarcy” have been approved as preferred units of permeability. Note 11 of Table 2.2 shows the relationships between traditional and SI units and points out that the units of the darcy and the square micrometer can be considered equivalent when high accuracy is not needed or implied.

Standard Temperature Some reference temperature is necessary to show certain properties of materials, such as density. volume. viscosi- ty. and energy level. Historically, the petroleum industry almost universally has used 60°F [15.56”C] as this reference temperature, and metric systems have used O”C, 2O”C, and 25°C most commonly, depending on the data and the area of specialty.

API has opted for 15°C because it is close to 60°F. ASME has used 20°C in some of its metric guides. The bulk of continental European data used for gas and oil correlations is at O”C, although 15°C is used sometimes.

The SPE Subcommittee feels that the choice between 0°C and 15°C is arbitrary. Tentatively, a standard of 15°C has been adopted simply to conform to API stan- dards. It may be desirable to have a flexible temperature standard for various applications.

Standard Pressure To date. some groups have opted for a pressure reference of 101.325 kPa, which is the equivalent of I std atm. The Subcommittee considers this an unacceptable number. Its adoption possesses some short-term conve- nience advantages but condemns future generations to continual odd-number conversions to reflect the change of pressure on properties. It also violates the powers- of-10 aspect of the SI system, one of its primary advantages.

The current SPE standard is 100 kPa and should be used until further notice. It is our hope that reason will prevail and others will adopt this standard.

Gauge and Absolute Pressure There is no provision for differentiating between gauge and absolute pressure, and actions by international bodies prohibit showing the difference by an addendum to the unit symbol. The Subcommittee recommends that gauge and absolute be shown using parentheses follow- ing p:

p=643 kPa, p(g)=543 kPa

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-25

[p is found from p(g) by adding actual barometric pressure. (100 kPa is suitable for most engineering calculations.)]

In custody transfer the standard pressure will be specified by contract. Unless there is a special reason not to do so, the standard pressure will be 100 kPa to preserve the “multiples of ten” principle of the metric system.

Standard pressure normally is defined and used as an absolute pressure. So, psc = 100 kPa is proper notation. Absolute pressure is implied if no (g) is added to denote gauge pressure specifically.

Standard Volumes Cubic meters at standard reference conditions must be equated to a term with the standard “SC” subscript. For example, for a gas production rate of 1 200 000 m3/d, write

qx,y,=1.2x IO6 m3/d or 1.2 (E+06) m3/d read as “1.2 million cubic meters per day.”

If the rate is 1200 cubic meters per day, write

q,,Yc=1.2x103 m3/d.

For gas in place, one could write

G,,=11.0x10’* m3.

Notes for Table 2.2 1. The cubem (cubic mile) is used in the measurement

of very large volumes, such as the content of a sedimentary basin.

2. In surveying, navigation, etc., angles no doubt will continue to be measured with instruments that read out in degrees, minutes, and seconds and need not be converted into radians. But for calculations in- volving rotational energy, radians are preferred.

3. The unit of a million years is used in geochronology. The mega-annum is the preferred SI unit, but many prefer simply to use mathematical notation (i.e., X 106).

4. This conversion factor is for an ideal gas. 5. Subsurface pressures can be measured in

megapascals or as freshwater heads in meters. If the latter approach is adopted, the hydrostatic gradient becomes dimensionless.

6. Quantities listed under “Facility Throughput, Capacity” are to be used only for characterizing the size or capacity of a plant or piece of equipment. Quantities listed under “Flow Rate” are for use in design calculations.

7. This conversion factor is based on a density of 1.0 kg/dm 3

8. Seismic velocities will be expressed in km/s. 9. The interval transit time unit is used in sonic log-

ging work.

10. See discussion of “Energy, Torque, and Bending Moment,” Part 1.

11. The permeability conversions shown in Table 2.2 are for the traditional definitions of darcy and millidarcy.

In SI units, the square micrometer is the preferred unit of permeability in fluid flow through a porous medium, having the dimensions of viscosity times volume flow rate per unit area divided by pressure gradient, which simplifies to dimensions of length squared. (The fundamental SI unit is the square meter, defined by leaving out the factor of IO-‘* in the equation below).

A permeability of 1 pm* will permit a flow of 1 m3/s of fluid of 1 Pa. s viscosity through an area of 1 m2 under a pressure gradient of lo’* Pa/m (neglecting gravity effects):

I pm2 = lo-‘* Pa.s [m3/(s.m2)](m/Pa) = 10 ~ I2 Pa. s(m/s)(mlPa) = lo-‘* m2

The range of values in petroleum work is best served by units of 1O-3 pm2. The traditional millidarcy (md) is an informal name for 10 -3 pm*, which may be used where high accuracy is not implied.

For virtually all engineering purposes, the familiar darcy and millidarcy units may be taken to be equal to 1 pm2 and 10 -3 pm*. respectively.

12. The ohm-meter is used in borehole geophysical devices.

13. As noted in Sec. 1, the mole is an amount of substance expressible in elementary entities as atoms, molecules, ions, electrons. and other par- ticles or specified groups of such particles. Because the expression “kilogram mole” is inconsistent with other SI practices, we have used the abbrevia- tion “kmol” to designate an amount of substance which contains as many kilograms (groups of molecules) as there are atoms in 0.0 12 kg of carbon 12 multiplied by the relative molecular mass of the substance involved. In effect, the “k” prefix is merely a convenient way to identify the type of en- tity and facilitate conversion from the traditional pound mole without’violating SI conventions.

Notes for Table 2.3 1. The standard cubic foot (scf) and barrel (bbl) rem

ferred to are measured at 60°F and 14.696 psia; the cubic meter is measured at 15°C and 100 kPa (1 bar).

2. The kPa is the preferred SPE unit for pressure. But many are using the bar as a pressure measurement. The bar should be considered as a nonapproved name (or equivalent) for 100 kPa.

3. See discussion of “Torque and Bending Moment , ” Part I.

58-26 PETROLEUM ENGINEERING HANDBOOK

Quantity and SI Unit

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS

Metric Unit Customary SPE Other

Unit Preferred Allowable

Conversion Factor’ Multiply Customary

Unit by Factor to Get Metric Unit

Length m

SPACE:’ TIME

naut mile km 1.852’ E+00

mile km 1.809 344* E + 00

chain m 2.011 68 E+Ol

link m 2.011 68 E-01

fathom m 1.828 8’ E+OO

m m 1 .O’ E+OO

yd m 9.144’ E-01

fl m 3.048’ E-01 cm 3.048’ E+nl

in. mm 2.54’ E+Ol cm 2.54’ E+OO

cm mm 1 .O’ E+Ol cm 1 .O’ E+00

mm mm 1 .O’ E+OO

Length/length

Length/volume

Length/temperature

Area

Area/volume

Area/mass

Volume, capacity

m/m

m/m3

m/K

m2

m2/m3

m2/kg

m3

mil pm micron (f.~) bm fUm+ m/km

fUU.S. gal m/m3

ftw m/m3

ft/bbl m/m3

see “Temperature, Pressure, Vacuum”

sq mile km2

section km2

acre m2

ha m2

sq yd m2

sq fl m2

sq in. mm2

cm2 mm2

mm2 mm2

ft?in? m21cm3

cm2ig m*/kg mYg

cubem km’

acre-ft m3

m3 m3

2.54’ E+Ol

1 .O’ E+OO

1.893 939 E-01

8.051 964 E+Ol

1.078 391 E+Ol

1.917 134 E+OO

2.589 988 E +00

2.589 988 E +00 ha 2.589 988 E+O2

4.046 858 E+03 ha 4.046 856 E-01

1 .o Ec04

8.361 274 E-01

9.290 304’ E - 02 cm2 9.290 304’ E + 02

6.451 8’ E+O2 cm2 6.451 6’ E+OO

1.0 Et02 cm2 1.0 Et00

1.0 E+OO

5.699 291 E-03

1.0 E-01 1.0 E-04

4.168 182 E+OO””

1.233 489 E+03 ham 1.233 489 E-01

1 .o E+OO

cu vd m3 7.645 549 E - 01

bbl (42 U.S. aal) m” 1.589 873 E-01

cu R m3 2.831 685 E-02

U.K. gal

dm3

m3 dm3

L 2.831 685 E+Ol

4.546 092 E-03 L 4.546 092 E+OO

U.S. gal

liter

U.K. qt

11s nt

U.S. pt

m3 .-tm3

dm3

dm3 rim3

dm3

3.785 412 E-03 I 37A‘iAl7 F+rul

-

L 1.0’ E+OO -

L 1.136 523 Finn _ -,-I

I Q AR7 5X _.._-__ J E-01

L 4.731 765 E-01

‘An asterisk cdcates that the conversion factcf IS exact using the numbers shown. all subsequent numbers are zeros

“Conversion factors for length. area. and volume (and related quanblles) I” Table 2.2 are based on the intemabonal foot See Footnote 1 of Table 1 7. Part 1

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-27

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Conversion Factor’ Metric Unit Multiply Customary

Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unrt

SPACE,” TIME

Volume, capacity m3 U.K. fl oz cm3 2.841 308 E+Ol

U.S. fl oz cm3 2.957 353 E+Ol

cu in. cmJ 1.638 706 E+Ol

mL cm3 1 .O’ E+OO

Volume/length (linear displacement)

m31m bbliin. m31m 6.259 342 Et00

bbl/H m3/m 5.216 119 E-01

H3/H m31m 9.290 304’ E - 02

Volume/mass

Plane angle

Solid angle

Time

m3ikg

rad

sr

S

U.S. gal/H m31m dm31m Urn

see “Density, Specific Volume, Concentration, Dosage”

rad rad deg (“1 rad

0

min (‘) rad

set (“) rad n

sr sr

million years (MY) Ma

v a

wk d

d d

hr h min

min S

h min

1.241 933 E-02 1.241 933 E+Oi

1 .O’ E+OO 1.745 329 E -. 02 121

1 .O’ E+OO

2.908 882 E - 04 12’ 1 .O’ E+OO

4.848 137 E - 06 ‘2’ 1 .o E+OO

1 .o E+OO

1 .o E + 00 ‘W

1.0 E+OO

7.0 E+OO

1 .o E+OO

1 .o E+OO 6.0 E+Ol

6.0 E+Ol 1.666 667 E-02 1 .O’ E+OO

S S 1 .o E+OO

millimicrosecond ns 1.0 E+OO

Mass

MASS, AMOUNT OF SUBSTANCE

U.K. ton (long ton) Mg US. ton (short ton) Mg U.K. ton kg

U.S. cwt kg

kg kg ibm ka

t 1 ,016 047 E+OO

t 9.071 847 E-01

5.080 235 E+Ol

4.535 924 E+Ol

1 .o E+OO

4.535 924 E-01

Mass/length

Masslarea

Mass/volume

Mass/mass

Amount of substance

kg/m

kg/m2

kg/m3

‘Wkg mol

oz (troy) 9

oz (av) 9

9 9

grain m9

m9 m9 9 9

see “Mechanics”

see “Mechanics”

see “Density, Specific Volume, Concentration, Dosage”

see “Density, Specific Volume, Concentration, Dosage”

Ibm mol kmol

g mol kmol std m3 (WC, 1 atm) kmol

std m3 (15”C, 1 atm) kmol

std ft3 (6O”F, 1 atm) kmol

3.110 348 E+Ol

2.834 952 E + 01

1 .o E+OO

6.479 891 E+Ol

1 .o E+OO

1 .O’ E+OO

4.535 924 E-01

1 .O’ E-03 4.461 58 E - 02 II 131

4.229 32 E - 02 II 131

1.1953 E - 03 II 131

58-28 PETROLEUM ENGINEERING HANDBOOK

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Conversion Factor’ Metric Unit

Customary Multrply Customary

SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

CALORIFIC VALUE, HEAT, ENTROPY, HEAT CAPACITY

Calorific value (mass basis)

Calorific value (mole basis)

Calorific value (volume basis - solids and liquids)

J/kg

Jimol

J/m3

Btuilbm

Cal/g

caklbm kcalig mol

Btu/lbm mol

therm/U.K. gal

BtuiUS. gal

Btu!U.K. gal

BtuifP

kcal/m3

MJikg kJ/kg

kJ/kg

J/kg kJ/kmol

MJikmol kJ/kmol

MJlm3 kJ/m3

MJlm3 kJ/m3

MJlm3 kJ/m3

MJlm3 kJ/m3

MJlm3 kJ/m3

2.326 E-03 J’g 2.326 E+OO (kW.h)/kg 6.461 112 E-04

J’g 4.184’ E+OO

9.224 141 E+OO

4.184’ c+o3’3

2.326 E-0313 2.326 E + OOt3

kJ/dm3 2.320 80 E+04 2.320 80 E+07

(kW.h)/dm3 6.446 660 E+OO

kJ/dm3 2.787 163 E-01 2.787 163 E+02

(kW,h)/m3 7.742 119 E-02

kJ/dm3 2.320 8 E-01 2.320 8 E+02

(kW.h)/m3 6.446 660 E-02

kJidm3 3.725 895 E-02 3.725 895 E+Ol

(kW.h)/m3 1.034 971 E-02

kJidm3 4.184’ E-03 4.184’ E+OO

cal/mL MJ/m3 4.184’ E+OO

Jim3

J1kg.K

J/kg.K

Jlmo1.K

Specific entropy

Calorific value (volume basis - gases)

Specific heat capacity (mass basis)

Molar heat capacity

ft-1bfiU.S. gal

cal/mL

kcalim3

BtuiH3

Btu/(lbm-“R)

cali(g-“K)

kcal!( kg%)

kW-hr/(kg-“C)

Btu/(lbm-“F)

kcal/(kg-“C)

Btui(lbm mol-“F)

cal!(g mol-“C)

kJ/m”

kJ/m3

kJlm”

kJ/m”

kJi(kg.K)

kJi(kg.K)

kJi(kg.K)

kJ/(kg.K)

kJ/( kg.K)

kJ/( kg.K)

kJI(kmo1.K)

kJI(kmo1.K)

J/dm3

J/dm3

Jldm3 (kW. h)/m 3

J/b. N J/b. K) J/h. W J4g ’ K) J/h. K) J/b. to

3.581 692 E-01

4.184. E+03 4.184’ E+OO

3.725 895 E+Oi 1.034 971 E-02

4.186 8’ E+OO 4.184’ E+OO

4.184’ E+OO

3.6’ E+03

4.186 8 E+OO 4.184’ E+OO

4.186 8’ E+00r3

4.184’ E - 0013

TEMPERATURE, PRESSURE, VACUUM

Temperature (absolute)

Temperature (traditional)

Temperature (difference)

Temperature/length (geothermal gradient)

Length/temperature (geothermal step)

Pressure

K

K

K

K/m

m/K

Pa

“R K 519 “K K 1 .O’ E+OO “F “C (“F - 32)/l .8

“C “C 1 .O’ E+OO “F K “C 5i9 E+OO “C K “C 1 .O’ E+OO “F/100 ft mWm 1.822 689 E+Ol

ft/‘F m/K 5.486 4’ E-01

atm (760mm Hg at 0°C or MPa 1.013 25’ E-01 14.696 (Ibfiin.2) kPa 1.013 25’ E+02

bar 1 ,013 25’ E+OO bar MPa 1 .O’ E-01

kPa 1 .O’ E+02 bar 1.0 E+OO

at (technical atm., kgf:cm*) MPa 9.806 65’ E-02 kPa 9.806 65’ E+Ol

bar 9.806 65’ E-01

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-29

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Quantity and SI Unit Customary

Unit

Metric Unit SPE Other

Preferred Allowable

Conversion Factor’ Multiply Customary

Unit by Factor to Get Metric Unit

TEMPERATURE, PRESSURE, VACUUM

Pressure

Vacuum, draft

Liquid head

Pressure drop/length

Density (gases)

Density (liquids)

Density (solids)

Specific volume

(gases) Specific volume (liquids)

Specific volume (mole basis)

Specific volume (clay yield)

Yield (shale distillation)

Concentration (mass/mass)

Concentration (mass/volume)

Pa Ibflin.2 (psi) MPa 6.894 757 E - 03 kPa 6.894 757 E+OO

bar 6.894 757 E - 02

in. fig (32’F) kPa 3.386 38 E+OO

in. Hg (60°F) kPa 3.376 05 E+OO

in. Hz0 (39.2”F) kPa 2.490 82 E-01

in. Hz0 (60°F) kPa 2.408 4 E-01

mm Hg (0°C) = torr kPa 1.333 224 E-01

cm Hz0 (4°C) kPa 9.806 38 E-02

Ibf/A* (psf) kPa 4.788 026 E 02 -

v Hg (0°C) Pa 1.333 224 E-01

pbar Pa 1 .O’ E-01 dyne/cm2 Pa 1 .O’ E-01

Pa in. Hg (60°F) kPa 3.376 85 E+OO

in. Hz0 (39.2-F) kPa 2.490 82 E-01

in. Hz0 (60°F) kPa 2.488 4 E-01 mm Hg (0°C) = torr kPa 1.333 224 E-01

cm HZ0 (4°C) kPa 9.806 38 E-02 m R m 3.048’ E-01

in. mm 2.54’ E+Ol cm 2.54’ E+OO

Pa/m psi/ft kPa!m 2.262 059 E + 01

psi/l 00 ft kPa/m 2.262 059 E - 01 w

DENSITY, SPECIFIC VOLUME, CONCENTRATION, DOSAGE

kg/m3 IbmW kg/m3 1.601 846 E+Ol g/m3 1.601 846 E +04

kg/m3 1bmiU.S. gal kg/m3 1.198 264 E+02 g/cm3 1.198264 E-01

Ibm/U.K. gal kg/m3 9.977 633 E + 01 kg/dm3 9.977 633 E - 02

IbmlfP kg/m3 1.601 846 E+Ol g/cm3 1.601 846 E-02

g/cm3 kg/m3 1 .o* E+03 kgidm3 1 .o E+OO

“API g/cm3 141.5!(131.5+“API) kg/m3 IbmW kg/m3 1.601 846 E+Ol ma/kg R3/lbm m31kg 6.242 796 E - 02

m31g 6.242 796 E - 05 m%g fWlbm dm3/kg 6.242 796 E + 01

U.K. galilbm dm31kg cmYg 1.002 242 E+Ol

U.S. galilbm dm3/kg cm3/g 8.345 404 E+OO m3/mol Ug mol m3/kmol 1 .O’ E + 00’3

fWbm mol m3ikmol 6.242 796 E 0213 - m31kg bb1iU.S. ton m% 1.752 535 E-01

bbl/U.K. ton m% 1.564 763 E-01 m3/kg bbliU.S. ton dm% ut 1.752 535 E+02

bb1iU.K. ton dm% Lit 1.564 763 E+02 U.S. gal/US. ton dm311 ut 4.172 702 E+OO U.S. ga1lU.K. ton dm3/t Lit 3.725 627 E+OO

Wb wt % Wkg 1 .O’ E-02 @kg 1.0’ E+Ol

w mm w/kg 1 .O’ E+OO kg/m3 lbmibbl kg/m3 gidm3 2.853 010 E+OO

g/US. gal kg/m3 2.641 720 E-01

gIU.K. gal kg/m3 9’L 2.199 692 E-01

58-30 PETROLEUM ENGINEERING HANDBOOK

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Conversion Factor’ Metric Unit Multiply Customary

Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Gel Metric Unit

Concentration (mass/volume)

Concentration (volume/volume)

kg/m3

m31mJ

DENSITY, SPECIFIC VOLUME, CONCENTRATION, DOSAGE

lbmilOO0 U.S. gal g/m3 mg/dmJ

IbmilOOO U.K. gal glm3 mg/dmJ

grains/US. gal gimJ mg/dm3

grains/W mg/m3

IbmilOOO bbl g/m3 mg/dm3

mg1U.S. gal g/m3 mgldm3

grains000 ft3 mgim3

bbllbbl m31m3

ftw m31m3

bbl/acreft m31m3 ma/ham

vol % m3/m3

U.K. aal/W dm3/m3 L/m3

1.198 264 E+02

9.977 633 E + 01

1.711 806 E+Ol

2.266352 E+O3

2.853010 E+OO

2.641 720 E-01

2.266 352 E+Ol

1 .O’ E+OO

1 .O’ E+OO

1.288 923 E-04 1.288 923 E+OO

1 .O’ E-02 1 .m=l4R7 F+fP

Concentration (mole/volume)

mol/m3

U.S. aaW

mL/U.S. aal

mL/U.K. aal

vol ppm

dm3/m3 Urn3 i .336 An8 F+n7

dm3/m3 L/m3 2.841 720 F-n1

dm31m3 L/m3 2.199 Is2 F-01

cm3im3 1 .O’ E+OO

I

J.K. gal/l000 bbl

J.S. gal11000 bbl

J.K. pti1000 bbl

Ibm mo1iU.S. gal Ibm moliU.K. gal

Ibm mol/fP

std H3 (6o”F,

dm31m3

cm31m3

cm3im3

cmYm3

kmollm3 kmol/m3

kmol/m3

kmol/m3

L/m3 1 .O’ E-03

2.859 406 E+Ol

2.380 952 E+Ol

3.574 253 E+OO

1.198 264 E+02

9.977633 E+Ol

1.601 846 E+Ol

7.518 18 E-03

Concentration (volume/mole)

m3/mol

1 atm)/bbl

U.S. gall1000 std W (6O”Fi6O”F)

bbl/million std ft3 f60”Fi60°F)

dm3ikmol

dm3/kmol

Ukmol

Ukmol

3.166 93 E+OO

1.330 11 E-01

FACILITY THROUGHPUT, CAPACITY

Throughput (mass basis)

kg/s 4.535 924 E+02

1.016 047 E+OO

m3/s

million Ibm/yr

U.K. toniyr

US. toniyr U.K. ton/D

U.S. ton/D

U.K tonlhr U.S. tonlhr

lbmlhr

bbl/D

W/D

bbllhr

113/h

U.K. gallhr

U.S. gallhr

U.K. gal/min

U.S. galimin

ffa

t/a

t/a

Vd

t/d

t/h t/h

kg/h

t/a

m3/h m3/h

mJ/h

m31h

m3/h

m31h

m31h

m3/h

Mg/a

Mgla

Throughput (volume basis)

Mgla

Mgid t/h, Mgih

tih, Mg/h

Mg/h Mglh

maid

m31d

L/s

US

US

US

9.071 847 E-01

1.016047 E+OO 4.233 529 E-02

9.071 847 E-01 3.779 936 E - 02

1.016 047 E+OO

9.071 a47 E-01

4.535 924 E-01

5.603 036 E+Ol “I 1.589 a73 E-01 6.624 471 E-03

1.179 869 E-03 2.831 685 E-02

I.589 a73 E-01

2.831 685 E-02

4.546 092 E-03 1.262 803 E-03

3.785 412 E-03 1.051 503 E-03

2.727 655 E-01 7.576 819 E-02

2.271 247 E-01 6.309 020 E ~ 02

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Conversion Factor” Metric Unit Multiply Customary

Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

FACILITY THROUGHPUT, CAPACITY

Throughput (mole bass)

Pipeline capacity

Flow rate (mass basis)

Flow rate (volume basis)

Flow rate

(mole basis)

molis

m31m

kg/s

m%

mol/s

Ibm mol!hr kmolih 4.535 924 E - 01 kmolis 1.259 979 E-04

FLOW RATE 16,

bblimile mVkm 9.879 013 E-02

U.K. tonimin kg/s 1.693412 E+Ol

U.S tonimin kg/s 1.511 974 E+Ol

U.K. tonihr kg/s 2.822 353 E-01

U.S. tonihr kg/s 2.519 958 E-01

U.K. ton/D kg/s 1.175980 E-02

U.S ton/D kg/s 1.049 982 E-02

million lbmiyr kg/s 5.249 912 E+OO

U.K. ton/yr kg/s 3.221 864 E-05

US toniyr kg/s 2.876 664 E-05

lbmls kg/s 4.535 924 E-01

lbmlmin kg/s 7.559 873 E-03

Ibm/hr kg/s 1.259 979 E-04

bbl/D m3id 1.589 873 E-01 US 1.840 131 E-03

ftVD m’ld 2.831 685 E-02 US 3.277 413 E-04

bbl/hr mJls 4.416 314 E-05 US 4.416 314 E-02

RVhr m% 7.865 791 E-06 US 7.865 791 E-03

U.K. galihr dmVs US 1.262 803 E-03

U.S. galihr dm% US 1.051 503 E-03

U.K. gal/min dmVs US 7.576 820 E-02

U.S. galimin dmVs US 6.309 020 E - 02

ftVmin dm3!s US 4.719 474 E-01

ftVS dm% US 2.831 685 E+Ol

Ibm molis kmolis 4.535 924 E-01=

Ibm mol/hr kmolis 1.259 979 E 04’5 -

million scWD kmolis 1.363 449 E - 02’3

Flow rate/length (mass basis)

kgism Ibmi(s-ft) kg/(sm)

Ibm/(hr-ft) kg/(sm)

1.488 164 E+OO

4.133 789 E-04

Flow rate/length

(volume basis)

m2is U.K. gal!(min-ft)

U.S. gal!(min-ft)

U.K. gali(hr-in.)

US. gali(hr-in.)

U.K. gali(hr-ft)

m% mV(sm) 2.485 833 E - 04

m2is mV(sm) 2.069 888 E 04 -

m2/s mV(sm) 4.971 667 E-05

mVs mV(sm) 4.139 776 E-05

m*/s mV(sm) 4.143055 E-06

US. gali(hr-ft) m’ls m3/(sm) 3.449 814 E-06

Flow rate/area (mass basis)

Flow rate/area (volume basis)

kg/sm*

m/s

lbm/(s-ft’)

lbmi(hr-ft2)

W(S4t~)

Wlmin-ftz)

kg/sm2

kg/sm2

mis

m/s

4.882 428 E+OO

1.356 230 E-03

m’(sm*) 3.048 E-01

mV(sm*) 5.08’ E-03

U.K. gaV(hr-tn2)

U.S. gal!(hr-rn2)

m/s mV(sm*) 1.957 349 E-03

m/s m3/(smz) 1.629 833 E-03

Flow rate/ pressure drop (productivity index)

mYsPa

U.K. gal!(mm-ft’)

US. gal!(mmW)

U.K. gali(hr-ft’)

U.S. gal!(hr#)

bbli(D-psr)

mls

mis

mls

m/s

mV(d.kPa)

m’/(sm*) 8.155 621 E-04

mV(sm*) 6.790 972 E - 04

mV(sm*) 1.359 270 E-05

m31(sm2) 1.131 829 E-05

2.305 916 E-02

58-32 PETROLEUM ENGINEERING HANDBOOK

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Conversion Factor* Metric Unit Multiply Customary

Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

ENERGY, WORK, POWER

Energy, work

Impact energy

WorWlength

Surface energy

Specific impact energy

Power

Power/area

J

J

Jim

J/m2

J/m2

W

W/m2

quad

therm

U.S. tonf-mile

hp-hr

ch-hr or CV-hr

kW-hr

Chu

f3tu

kcal

cal

ft-lbf

Ibf-ft

J

Ibf-ftz/s2

erg kgf-m

Ibf-ft

U.S. tonf-mileift

erg/cm2

kgf.m/cm*

Ibf+t/in.*

quadiyr

erg/a

million Btu/hr

ton of refrigeration

ml/s kW

hydraulic horse- power - hhp

hp (electric)

hp (550 ft-lbfis)

ch or CV

Btuimin

ft*lbf/s kcalihr

Btuihr

Albfimin

Btuis.ft?

cal/hrcm?

Btuihrft?

MJ TJ EJ

MJ kJ

MJ

MJ kJ

MJ N

MJ kJ

kJ

kJ

kJ

kJ

kJ

kJ

kJ

kJ

J

J

J

MJlm

mJlmZ

J/cm’

J/cm2

MJia TJia EJia TW GW

MW

kW

kW

kW

kW

kW

kW

kW

kW

kW

W

W

W

kWlmz

kWlm2

kW/m2 .-

1.055 056 E+12 1.055 056 Et06 1.055 056 E+OO

MW*h 2.930 711 Et08 GW.h 2.930 711 Et05 TWh 2.930 711 Et02

1.055 056 E+02 1.055 056 E+05

kW.h 2.930 711 E+Ol

1.431 744 E+Ol

2.684 520 E+OO 2.684 520 E+03

kW.h 7.456 999 E-01

2.647 796 Et00 2.647 796 E+03

kW.h 7.354 99 E-01

3.6’ E+OO 3.6’ E+03

1.899 101 E+OO kW.h 5.275 280 E-04

1.055 056 E+OO kW.h 2.930 711 E-04

4.184’ E+OO

4.184’ E-03

1.355 818 E-03

1.355 818 E-03

1 .O’ E-03

4.214 011 E-05

1 .O’ E-07

9.806 650’ E + 00

1.355818 E+OO

4.697 322 Et01

1 .O’ E+OO

9.806 650’ E - 00

2.101 522 E-01

1.055 056 E+12 1.055 056 Et06 1.055 056 E+OO 3.170 979 E-27 3.170979 E-24

2.930 711 E-01

3.516 853 E+OO

1.055 056 E+OO

1 .O’ E+OO

7.460 43 E-01

7.46’ E-01

7.456 999 E-01

7.354 99 E-01

1.758 427 E-02

1.355 818 E-03

1.162222 E+OO

2.930 711 E-01

2.259 697 E-02

1.135653 E+Ol

1.162222 E-02

3.154 591 E-03

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-33

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Quantity and SI Unit Customary

Unit

Metric Unit SPE Other

Preferred Allowable

Conversion Factor’ Multiply Customary

Unit by Factor to Get Metric Unit

ENERGY, WORK, POWER

Heat flow unit - hfu (geothermics)

Heat release rate, mixing power

Heat generation unit - hgu (radioactive rocks)

Cooling duty (machinery)

Specific fuel consumption (mass basis)

Specific fuel consumption (volume basis)

W/m3

WAN

kg/J

m3/J

~calls’cm2

hpift3 cal/(hpcm3) Btu/(sft3)

Btui(hrW)

cal/(s-cm3)

Btu/(bhp-hr)

Ibm/(hp-hr)

mJ/(kW-hr)

U.S. gal/(hp-hr)

mWlm2

kWlm3

kW/m3

kW/m3

kWlm3

pWlm3

W/kW

mg/J

dm31MJ

dm3/MJ

kg/MJ kg/(kW-h)

mm3/J dm?(kW.h)

mm3/J

4.184’ E+Ol

2.633 414 E+Ol

1.162 222 E+OO

3.725 895 E+Ol

1.034 971 E-02

4.184’ E+12

3.930 148 E-01

1.689 659 E-01 6.082 774 E-01

2.777 778 E + 02 1.0 E+03

1.410089 E+OO

MECHANICS

Velocity (linear), speed

Velocity (angular)

Interval transit time

Corrosion rate

Rotational frequency

Acceleration (linear)

Acceleration (rotational)

Momentum

m/s

radls

s/m

m/s

rev/s

m/s*

rad/s2

kg.m/s

knot

mileihr

m/s

fUS

ftlmin

ftihr

ft/D

in.&

in./min

revlmin rev/s degree/min

S/ft

in./yr (ipy) miliyr

rev/s

revimin

revimin

ftk*

gal(cm@)

radls2

rpmis

Ibm.ftJs

km/h

km/h

m/s

m/s

m/s

mm/s

mm/s

mm/s

mm/s

radls rad/s radls

s/m

mmla mmla

rev/s

rev/s

radls

m/s2

mls2

rad/s2

lad/s2

kg.m/s

cm/s mfms

cm/s

cm/s

m/d

cm/s

cmls

KS/m

cm/s2

1.852 E+OO

1.609 344’ E + 00

1 .O’ E+OO

3.048’ E-01 3.048’ E+Ol 3.048’ E - 04@’

5.08’ E-03 5.08’ E-01

8.466 667 E-02 8.466 667 E - 03

3.527 778 E - 03 3.048’ E-01

2.54’ E+Ol 2.54 E+OO

4.233 333 E-01 4.233 333 E ~ 02

1.047 198 E-01 6.283 185 Et00 2.908 882 E-04

3.280 840 E + OO@

2.54’ E+Ol 2.54’ E-02

1 .O’ E+OO

1.666 667 E-02

1.047 198 E-01

3.048’ E-01 3.048’ E+Ol

1 .O’ E-02

1 .O’ E+OO

1.047 198 E-01

1.382 550 E-01

58-34 PETROLEUM ENGINEERING HANDBOOK

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Conversion Factor’ Metric Unit Multiply Customary

Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

MECHANICS

LI S. tonf kN 8.896 443 E+OO

kgf (kp) Ihf

N 9.806650’ Et00

N 4.448 222 E+OO

N N 1 .O’ E+OO

ndl mN 1.382 550 E+02

Bending moment, torque

N.m

dyne

US. tonf-ft

kgf-m

mN

kN.m

N.m

1 .o E-02

2.711 636 E + OO”O’

9.806 650’ E + 00”01

Ibf-ft N.m 1.355 818 E + OO”o

Ibf-in. N-m 1.129848 E - ,,,“O’

odl-ft N.m 4.214011 E- 021’0’

Bending moment/ length

Elastic moduli (Young’s, Shear bulk)

Moment of inertia

Moment of section

Section modulus

Stress

N.m/m

Pa

kqm*

m4

m3

Pa

(Ibf-ft)/in.

(kgf-m)/m

(Ibf-in.)/in.

Ibf!in.’

Ibm-ft2

in.4

cu in. cu fi

U.S. tonf/in.2

kgWmm2

US. tonf/ft2

IbWin.? (osi)

Ibf/ft2 (psf)

dyne/cm2

Ibf/lOO ft2

Ibm/ft

U.S. ton/ft2

Ibm/ft2

In./(in.-“F)

(N.m)/m

(N.m)/m

(N.m)/m

GPa

kg.m2

cm*

cm3 cm3

MPa

MPa

MPa

MPa

kPa

5.337 866 E + Ol”O1

9.806 650’ E + OO”O1

4.448 222 E + OO”O’

6.894 757 E-06

4.214 011 E-02

4.162 314 E+Ol

1.638 706 E+Ol 1.638 706 E+04

mm3 2.831 685 E+04 m3 2.831 685 E-02

N/mm2 1.378 951 E+Ol

N/mm2 9.806 650’ E + 00

N/mm2 9.576 052 E - 02

N/mm2 6.894 757 E-03

4.788 026 E-02

Pa 1 .O’ E-01

Yield point, gel strength Ldrillina fluid)

Mass/length

Mass/area structural loading, bearing capacity (mass basis)

Coefficient of thermal expansion

kg/m

kg/m2

m/(m.K)

Pa

kg/m

Mgim2

kg/m2

mm/(mm.K)

4.788 026 E-01

1.488 164 E+OO

9.764 855 E+OO

4.882 428 E+OO

5.555 556 E-01

TRANSPORT PROPERTIES

Diffusivity m21s fV/S

cm2’s

ft2/hr

(“C-m2.hr)/kcal

(“F-ft2 hr)iBtu

Btu/(hr-R*)

(Cal/s-cm2-%)/cm

Btu/(hr-ft-“Fift)

mm2/s 9.290 304’ E + 04

mm21s 1 .O’ E+02

mm2/s 2.580 64’ E+Ol

Thermal resistance (k.m*)/W (K.m2)/kW

(K.m2VkW

8.604 208 E +02

1.761 102 E+O2

Heat flux

Thermal conductivity

Wlm2

W/(m.K)

kW/mz

W/(m.K)

W/(m.K)

3.154 591 E-03

4.184* E+02

1.730 735 E+OO

-

kcali(hr-mz-“Cim)

Btu/(hr-R2-“Fiin.) cal/(hr-cm’-“C/cm)

kJ.m/(h.m2.K) 6.230 646 E+OO

W/(m.K) 1.162 222 E+OO

W/(m.K) 1.442 279 E-01

W/(m.K) 1.162222 E-01

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-35

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Metric Unit SPE

Preferred Other

Allowable

Conversion Factor’ Multiolv Customarv

Unii dy Factor to’ Get Metric Unit Quantity and SI Unit

Customary Unit

TRANSPORT PROPERTIES

Heat transfer coefficient

W/(m2.K) cal/(s-cm?-“C)

Btu/(s-ft2-“F)

cal/(hr-cm2-“C)

Btu/(hr-ft2-“F)

Btu/(hr-f&OR)

kcal/(hr-m2-“C)

Btui(s-ft3-“F)

Btu/(hr-f13-“F)

dyne/cm

(Ibf-s)iin.2

(Ibf-s)ift2

(kgf-s)/m*

Ibm/(ft-s)

(dyne-@/cm2

cP

4.184’ E+Ol

2.044 175 E +Ol

1.162 222 E-02

Volumetric heat transfer coefficient

Surface tension

Viscosity

(dynamic)

W/(m3.K)

N/m

P&S

kWi(m2.K)

kW/(m*.K)

kWi(m*.K)

kW/(m3.K)

kW/(m3.K)

mN/m

Pas

Pas

Pas

Pas

Pas

Pa.s

5.678 263 E - 03 kJ/(h.m>.K) 2.044 175 E+Ol

5.678 263 E-03

1.162222 E-03

6.706 611 E+Ol

1.862 947 E-02

1 .O’ E+OO

(Ns)im2 6.894 757 E + 03

(N.s)/m’ 4.788 026 E+Ol

(Ns)/m2 9.806 650’ E + 00

(Ns)/m* 1.488 164 E+OO

(Ns):m2 1 .O’ E-01

(Ns)/m* 1 .O’ E-03

Ibm/(ft.hr) Pas (N+m2 4.133 789 E-04

Viscosity m21s ft% mm% 9.290 304’ E + 04

(kinematic) in.*/s mm% 6.451 6 E+02

m2/hr mm2is 2.777 778 E+O2

cm21s mm2/s 1 .o E+02

ft*/hr mm2is 2.580 64’ E+Ol

Permeability m2

cst mm%

darcy km2 millidarcy km2

ELECTRICITY, MAGNETISM

1 .O’ E+OO

9.869 233 E -01’“’

9.869 233 E - 04’“’ 10m3 pm2 9.869 233 E-O,‘“,

Admittance

Capacitance

Capacity, storage battery

Charge density

Conductance

Conductivity

Current density

Displacement

Electric charge

Electric current

Electric dipole

S

F

C

C/m3

S

S/m

A/m2

C/m2

C

A

C*m

S

CLF A-hr

C/mm3

S

U (mho)

S/m

u/m

mu/m

Almm’

C/cm2

C

A

C.m

S

)LF kC

C/mm3

S

S

S/m

S/m

mS/m

A/mm2

C/cm?

C

A

C.m

1 .O’ E+OO

1 .O’ E+OO

3.6’ E+OO

1 .O’ E+OO

1 .O’ E+OO

1 .O’ E+OO

1 .O’ E+OO

1 .O’ E+OO

1 .o E+OO

1 .O’ E+OO

1 .o E+OO

1 .O’ E+OO

1 .o E+OO

1 .o E+OO moment

Electric field strength

Electric flux

Electric polarization

Electric potential

Electromagnetic moment

Electromolive force

Flux of displacement

V/m Vim V/m 1 .O’ E+OO

C C C 1 .O’ E+OO C/m2 C/cm2 C/cm2 1 .O’ E+OO V V V 1 .O’ E+OO

mV mV 1 .O’ E+OO A.m2 A.m2 A.m2 1 .O’ E+OO

V V V 1 .O’ E+OO

C C C 1 .O’ E+OO

58-36 PETROLEUM ENGINEERING HANDBOOK

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Conversion Factor’ Metric Unit Multiply Customary

Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

Frequency

Impedance

Interval transit time

Linear current densitv

HZ

n

slm

Aim

ELECTRICITY, MAGNETISM

cycles/s HZ

n n

@ft t&m

A/mm Aimm

1 .O’ E+OO

1 .O’ E+OO

3.280 840 E+OO

1 .O’ E+OO

Magnetic dipole moment

Wbsm Wb.m Wbm 1 .o E+OO

Magnetic field strength

A/m A/mm

oersted

gamma

mWb

mT

gauss

mT

A-m2

mT

A

Wbimm

A/mm

S

Aim

Aimm

Aim

mWb

mT

T

mT

A.m2

mT

A

Wblmm

A/mm

S

7.957 747

1 .O’ E+OO

E-04

7.957 747 E+Ol

1 .O’ E+OO

1 .O’ E+OO

1 .o* E-04

1 .O’ E+OO

1 .o* E+OO

1 .O’ E+OO

1 .O’ E+OO

1

1

1

Magnetic flux

Magnetic flux density

Magnetic induction

Magnetic moment

Magnetic oolarization

Magnetic potential difference

Magnetic vector potential

Magnetization

Modulus of admittance

Wb

T

T

A*mZ

T

A

Wb/m

Aim

S

Modulus of R n n 1 impedance

Mutual inductance H H H 1

Permeability H/m pH/m PHim 1

Permeance H H H 1

Permittivity F/m WFlm kF/m 1

Potential difference V V V 1

Quantity of C C C 1 electricitv

Reactance

Reluctance

Resistance

n cl n 1

H-’ H-1 H-’ 1

n R R 1

Resistivity Darn @cm fkm 1

Dm Drn 1 W,

Self inductance

Surface density of charge

Susceptance

Volume density of charae

H mH mH 1

C/m* mClm* mClmz 1

S S S 1

C/m3 C/mm3 C/mm3 1

ACOUSTICS, LIGHT, RADIATION

Absorbed dose GY rad GY 1 .o E-02

Acoustical enerav J J J 1

Acoustical intensity Wfm2 W/cm2 Wlm* 1 .o E+O4

Acoustical Dower W W W 1

Sound oressure N/m* Nim2 N/m2 1

llluminance

Illumination

lrradiance

lx

lx

Wlm*

1x3

cd/m*

footcandle

footcandle

W/m2

lx 1.076 391 E+Ol lx 1.076 391 E+Ol

Wlm* 1

Light exposure footcandles 1x.s 1.076 391 E + 01

Luminance

Luminous efficacv

cd/m2 cd/m2 1

ImiW ImiW ImiW 1

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-37

TABLE 2.2-TABLES OF RECOMMENDED SI UNITS (continued)

Conversion Factor’ Metric Unit Multiply Customary

Customary SPE Other Unit by Factor to Quantity and SI Unit Unrt Preferred Allowable Get Metric Unit

Luminous exitance Im/mz

Luminous flux Im

Luminous intensity cd

Quantity of light I’m.s

Radiance W/(m%r)

Radiant energy J

Radiant flux W

Radiant intensity Wisr

Radiant power W

Wave length m

Capture unit mm’

ACOUSTICS, LIGHT, RADIATION

lmim2 lm/mZ 1

Im Im 1

cd cd 1

talbot t’m.s 1 .O’ E+OO - Wl(m%r) W/(m%r) 1

J J 1

W W 1

Wlsr W/sr 1

W 1

r nm 1 .O’ E-01 lo-km 1 m-1 1 .O’ Et01

10.“cm-’ 1

Radioactivity curie 3.7’ E+lO

58-38 PETROLEUM ENGINEERING HANDBOOK

TABLE 2.3~SOME ADDITIONAL APPLICATION STANDARDS

Conversion Factor’ Metric Unit Multiply Customary

Customary SPE Other Unit by Factor to Quantity and SI Unit Unit Preferred Allowable Get Metric Unit

Capillary pressure Pa ft (fluid) m (fluid) 3.048' E-01

Compressibility of Pa-’ psi-’ Pa-’ 1.450 377 E-04 reservoir fluid kPa ’ 1.450 377 E-01

Corrosion allowance m in. mm 2.54' E+Ol

Corrosion rate mls miliyr mm/a 2.54' E-02 hw)

Differential orifice Pa in. f-l,0 kPa 2.488 4 E-01 pressure (at 60°F) cm Hz0 2.54' E+OO

Gas-oil ratio m3/m’ scfibbl “standard” 1.801 175 E -0,“‘” m3/m3

Gas rate mYs sci/D “standard” 2.863 640 E-02"' m31d

Geologic time S Yr Ma

Head (fluid mechanics) m fl m 3.048' E-01 cm 3.048' E+Ol

Heat exchange rate W Btu/hr kW 2.930 711 E-04 kJ/h 1.055 056 E+OO

Mobility m?Pas dicp ~m*/mPas 9.869 233 E-01 km21Pa.s 9.669233 E+02

Net pay thickness m fl m 3.048 E-01

Oil rate m3ls bbl/D m31d 1.589 873 E-01 short toniyr Mgla Va 9.071 847 E-01

Particle size m micron w 1.0’

Permeability-thickness m3 md-ft md.m pm2.rn 3.008 142 E-04

Pipe diameter (actual) m in. cm 2.54 E-c00 mm 2.54' E+Oi

Pressure buildup Pa psi kPa 6.894 757 E + OO’*’ per cycle

Productivity index m3iPes bbli(psi-D) mY(kPad) 2.305 916 E - 0212’

Pumping rate m% U.S. galimin m3/h 2.271 247 E-01 US 6.309 020 E-02

Revolutions per minute

Recovery/unit volume (oil)

Reservoir area

radls

m31m3

m2

vm

bbl/(acre-ft)

sq mile

acre

rad/s

m3/m3

km*

radlm

mYha*m

ha

1.047 198 E-01 6.283 185 E+OO

1.286 931 E-04 1.288 931 E+OO

2.589 988 E+OO

4.046856 E-01

Reservoir volume

Specific productivity index

m3

m3/Pasm

acre-ft

bbl/(D-psi-R)

m3 1.233 482 E+03 hem 1.233 482 E-01

mY(kPa-d.m) 7.565 341 E - 02’>’

Surface or interfacial tension in reservoir caoillaries

N/m dyne/cm mN/m 1 .O’ E+OO

Torque N.m

Velocity (fluid flow) m/s

Vessel diameter m

Ibf-ft

ws

Nom 1.355 818 E + 0013’

m/s 3.048' E-01

l-100 cm in. cm

above 100 cm ft m ‘An asterisk mdlcates the cowersum lactor IS exact wng the numbers shown, all subsequent numbers are zeros

“See Notes 1 through 3 on page 58-E

2.54' E+OO

3.048' E-01

THE SI METRIC SYSTEM OF UNITS & SPE METRIC STANDARD 58-39

TABLE 2.4-FAHRENHEIT - CELSIUS TEMPERATURE CONVERSION CHART

- 459.67 to - 19 -1ato53 54 to 350 360 to 1070 1990t01790 1990 to 3000

(“C) (“F) WI (“F) (“Cl (“F) (“Cl (“F)

-11, II -0P 0

-16, JO -‘,n -10 77 -‘*a -7jbbJ -410 -75, I, -470

--1‘S 56 -410 -740 a0 -400 --I,, ‘I --I90 -7,n 69 --In0 -,,I I, -310

-717 7) --I60 --211 17 -150 -7u 61 -113 -701 II --lx -19% lb --1x

-190 00 --I13 -,M ‘4 --loo --lin 6J -m

--II, II -783 --I69 I, -,I, I, -‘IV ‘I

-169 BP 477 -‘II 6

-‘b, :* -1JQ -‘I‘ a

-I61 ?7 -163 -416 0 -1 j‘ ‘J -710 218 a

-,jl II -740 400 a

--111 56 -710 --In7 a -1‘0 03 -170 -,b‘ 0 --II“‘ -710 -1‘6 0 -179 09 200 -128 a --17,x -100 -,,a 0

--11J 711 -I110 -?Sl a -,\I 12 -IJO -77‘0

--ID, 67 -160 -7% 0

-,a1 I/ -110 -718 0 - PI 16 -ILO -710 0

- 9000 -110 -7070 - 8“‘ -170 --II‘0

- ,880 -110 -1660

- II I, -100 -1‘10 - 70 I‘ - OS --I,90

- 6, IO - 90 -1,OQ

- bl 00 - II -17, 0

- 67 77 - 110 -I170

- ,P ‘5 - II --1a,a - 1667 - JO - 9‘0

- to 00 - ‘0 - ‘00

- ,'I ‘I - 19 - 167 - 18 BP - ,R - 36‘

- 1a 14 - Ii - II 6 - II JO - 36 - I7B

- II 71 - II - II a

- ,661 - Ii - 79 7 - 16 17 - I, - 7, 4

- II I* - II - 7i6 - II 00 - 31 - 11 6

- 1‘ 4‘ - ,Q - 770

- II IP - 79 - 707 - 11 11 - 111 - ,114

- 17 7n - ,7 - lb6 - II 72 - 76 - ,411

- II ‘I ~ II - I,0 --III, -,‘ - I, 7

- IQ lb - 71 - P‘

- ,000 - 72 - 76 - 7) ‘5 - 71 - IO

- 7II8P - IQ - ‘0 -76:: -,P - I7

-17 II --II -a ‘ --I, I, -1J I ‘ -76bJ --I6 11

~ -**17 --II SO

-75 IL --I‘ 4 I

-,1bQ -11 I6

4“‘ -11 10 4

-,I OP --II 111 -71 I, -10 I‘ 0

-77 16 - 9 IS 6

-7777 -8 IJb -7, 6J - J I9 1

-7, 1, - 6 21 7

-70 5) - I no

-7000 --I 716

--IP“ --I 766

--1nn9 - I 76‘

-IS31 - 1 IQ I -27 n Q 320

--I,7 I 11 6

-16 J J 316 -,b 1 I 37‘ -15 6 I 317

-,\a I ‘IQ

--I“ 6 176

--1,P 7 ‘4 6

--II I a ‘6‘

--I?B ? ‘9 7

-17 7 16 500

-,,I II $1 I

-II I 17 II 6 -10‘ 1, II ‘

-10 0 I‘ 111

- 9 4‘ Ii IV0 -860 1* *a &

--II,, 11 67 * - J I8 111 6‘1

- 1 12 10 661 - 6 6J 10 60 0 - ‘ I, 71 *(I

- I 16 27 Jl 6

- 100 7, II‘ - ‘ I‘ I‘ 75 7

- I 89 7, 770 - I II 76 786

- 7J6 7J IO*

- 177 76 671

I BP IV 107 1 1 ‘4 ‘0 IQ‘ a

10 0 II I?7 a IO 6 II 1736

77 7 I7 lbl 6

776 II lb,‘

711 I‘ 1617 7,P J5 1610

7 1 J6 1616 750 JI 1736

lid 18 1;71

76 I Jl II2 7

76, 80 lJ60

777 81 illI

IJB 87 II96

I6 I 81 111 ‘

*I P 0‘ 1617

29‘ II 1850

100 a* leda JO 6 81 166 6 II I 88 IPQ 4

II J IP IV7 I 17 7 PO lS‘0

,“ PI 701 7

II 0 PI 7010

II 6 Pb 704 8 ,&I PI 1066 16 I 98 700 4

I, 7 PP 710 7

II 6 100 717 D

‘I 1 110 ?I00 ‘8 D 170 7111 0 I“ 110 JhbQ

60 0 I‘0 7610

616 IS0 1070 II I 160 17Qo

76, 110 IIBQ 677 180 ,160

nJ 0 IPP ,140 P, 1 100 197 a

PBP 710 ‘lb0

IQ“ 770 478 a ,lbQ 710 “LO

iI56 710 ‘6‘0

171 I 710 ‘670

176 J 7bQ 1000

1317 7JQ II80

111 I 780 116 o

1‘31 790 II‘0

I‘8 9 JO0 $77 0 II“ 110 IPQQ

IbQ 0 170 606 Q

161 6 110 b?bo

,,I 1 ,‘b 64‘0 116 7 150 6670

1171 160 ,110 a 11118 110 (98 0 191 1 ,110 'I60

lPll I 190 I,‘ a 10‘ ‘ ‘00 7110

710 Q ‘IQ 110 Q

tll b 170 JOB 0

771 I 410 806 Q 776J “0 674 6

717 7 ‘la 6‘7 0

711 II 00 lb0 a

I‘,1 110 6180

7‘8 9 ‘80 IV6 a 711‘ ‘TO 91‘0

J‘QQ 100 P,? 0

765 6 510 P19 a

7JI I 170 968 0

776J 110 VBb 0

767 I 5‘0 I0040 76J II II0 IQ710

79, I 560 IQ‘00 790 P 110 IO580

IQ‘ 1 580 1 QJb?

110 0 $90 I 0% 0 ,llb 100 11170

171 1 610 I ~100

116 J 670 1.146 0

117 7 610 l,lbbb I,78 6‘0 11810 I‘, I ,I0 1,101 0

746 P 660 I,7700 11“ 670 17160

,600 680 Ill60

,656 690 I.1740 311 I JO0 I1970

,JbJ 110 1.1100

387 7 770 T.378 Q

18J II 110 I,,460

,931 1‘0 I ,b‘Q

198 9 1SQ \ ,670

‘0“ I60 I.‘000

,100 JJQ 1.4160

‘II 6 780 1.4160 ‘71 I JPQ I ‘;!o

,767 000 I‘,*0

‘II 7 610 I‘900

‘IJ a 170 I 106 a

“I I 010 1 116 a “8 9 1‘0 1 1‘40 ‘5“ 010 II670

‘60 0 1160 I I80 0 ‘616 810 I 118 0

‘II I 880 I6160 ‘lb J BP0 I b,(L)

‘62 I 900 1.6170

‘178 910 I6JOQ

“)I 1 970 1.bR.Q ‘98 9 P,Q I.Jo6Q

IQ‘ 4 P‘b 1.71‘0 110 a PI0 1 1‘70

$15 6 960 I.?600 III I PJQ LJJ80

$76, (10 lJSbQ

III I PVQ 1 1140 III II 1.000 I 8170

,‘I I I a,0 1.1500 ,‘8 T , 070 W8Q

I$‘ ‘ I.010 1 II6 0 lb00 1.0‘0 l.?Q‘Q $65‘ I.050 1.912 0

,I\ I 1.060 1.9‘00

IJb? I.010 1,956 Q

161 I UP0 I.P9‘0

5911 I.100 l.Ol?O IPB D I.110 7.0100

60“ 1.110 1.0‘10

610 0 1.110 1.0660

615 b l.t‘O 2.01‘0 6711 I.150 ?.16?0 676, 1 I60 1.1700

617 2 1 113 I.1110

6110 ,180 ?.I~60

6‘11 LIP0 11160

611 P 1.100 2.11?0 ,I“ 1710 I.1100

660 0 I ?70 17760

6616 1130 7.7460

bJ1 I 1 740 ?.?blC 6JbJ 1710 ??6?0

667 f t 760 2100 a 6816 IPJO 11180

69, I I lb0 I ,,*a 08 P 1790 7 3i‘O 711‘ II00 7lJ7 Q

710 c 1110 7,"OQ

7llb 1170 2‘080

,711 1110 2‘760

,767 11‘0 I“‘0

112 I 1150 ?.66?0 ?lJ 8 I lb0 I ‘IQ0

7‘1 I 1.310 I‘980

7‘8 9 1180 1.1160

II“ IHO 1 ,,‘Q

760 0 1 400 1 II?0 JhI 6 I ‘IO IS100

Jib 7 1‘10 ? 6060 I67 7 I,‘10 7 6,4 Q

76JI 1110 ? 6‘10 7V33 IWO ? Lb0 0 790 P 1.110 ?.6JI 0

no4 1 1 ‘IO 2 bPb0 llOQ I‘(0 1,140 8lS ‘ ,500 11110 811 1 1 510 1.1~00 8761 I I7Q ,,I‘60

),I I 1,110 ?.?I* 0 811 * 15‘0 1.10‘ 0 8‘3 I 1 II0 78770 I‘8 P 1 560 ?.6tQO

111 I 1600 19110 8161 1610 29100 O(ll? I.670 19480

BSJll Id,0 19160 IIPI 3 I 6‘0 two BOB9 lb!0 lQO?O PO“ I 660 1.0700 9100 ,610 10110

9116 I.680 ,bUQ 971 1 i 600 107‘0

976 ? ,100 I bP?O 9177 1JlQ 11100 v3rn ,770 31780

9‘11 ,?,b II‘60

9‘19 l.J‘o I l6‘0

PI“ 1.750 11170

Pbbb L?LQ IZQQQ 9656 1.710 17190

PII I 1,611 11160

Vb I 1 ?90 Ill‘0

I llll 1,100 ,7?7Q

967 I I.110 3 290 0

9911 I I20 113ao (PIT I I10 I ,I, 0

100“ I I‘0 I I“ a

10100 I 110 I lb! 3 1011 b 1.8LO I.100 0 1.071 1 1810 l.JU 0 1076J 1110 1‘160

1 all I 1,aoa 1‘1‘ a

I QIJ I I PO0 ,117 6

1.0‘1 1 I 910 1,410 0 ,041 1 LP?b , ‘81 0 1QI4 4 I,?,0 ,106 0 ,060 0 I 9‘0 1.17‘ ‘i

1.06, ‘ I.750 I I‘7 0 1,071 I 1 960 1160 Q

1.016 7 1110 1.116 Q

WI I 7.WQ ,617 :

1096 9 2 010 1610 C

I IO‘ ‘ 1070 1661 0 lilO0 7010 IbOb'

11116 20‘0 ,.Jo‘C

I 171 I tOI0 3.777 C

! 176 7 1060 I.?‘0 ?

II)?? 1070 37Iaa

1 II? I 1010 l.JJ6 C 1.1‘1 I ?.OPQ ,.,rr 0

I.l‘d, :.100 1,lIIC

1.15‘ 4 I.110 I.,,6 0

1160 0 1.110 1.1‘1 0 1.M ‘ 2.110 11bb 0 1,1J1 I 1.1‘0 ,ll‘Q

I.176 7 I150 3.907 0 1,111 I I.160 1.910 0 I.1118 1.110 I.9190 LIT1 I 1110 3.T16 0 1.10 9 ?.llO 1.91‘0

I.10“ 1100 1.9v1 0

,710 a I.110 4.OIOO

1,211 ‘ ?.??Q ‘028 0

1271 1 2110 ‘ 0410 117‘J 1.1‘0 ‘Ob‘P

1 111 I 1.150 ‘,O#? 0 I II? I I260 4.100 Q I?‘,, ??JO ‘lllQ I ?‘a T l?OQ ‘.IIb Q 1.71‘ 1 2.790 ‘15‘0

1.164 0 I IW 4,112 0

1265 1 2.110 ‘190 0 I,??\ I 2 170 ‘7010 1 276 7 2 110 4.116 0 1.11, 1 2 1‘0 4.1“ 0

l.llJ* 1,111 ‘.I*:0 1.193 I 7 1‘0 4.m 0 1.191 1 ?.I70 ‘,?Tl 0 1 IQ‘ 1 2.110 4.316 0 ,,I00 IV0 ‘11‘0

1.1‘1, 1.416 ‘ 10 0 1.311 I 2 500 4.117 0 l,,Pb 9 I.SIO ‘LIZ a I.‘?, J 1.600 4,117 0

I ‘5‘ 1 2 650 ‘,M7 0

1.‘61 I *.?a0 4.197 6 1.110 0 1.116 4.w 6 I.,,1 6 I600 I.011 6

1.16, 1 2 150 1.147 0 1.191 I ?.TaQ US? 0

I ,I1 1 1.910 I341 0

I “6 9 l.WQ 1‘37 0