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SPE symbols standard
The Society of Petroleum Engineers (SPE) developed standard usage for superscript, subscript, and representational symbols in 1956. While it has been updated and expanded during the ensuing period, many of the symbols and their usage remain unchanged. The Symbols Standard was developed to promote common usage, which would enhance understanding of the literature. A pdf copy of the SPE Symbols Standard can be downloaded from the SPE website.
Principles of symbols selection
Since the original reservoir Symbols Standard was established, the principles used in the selection of additional symbols have been as follows.
- (A) Use single letters only for the main letter symbols. This is the universal practice of the American National Standards Institute (ANSI), the International Organization for Standardization (ISO), and the International Union of Pure and Applied Physics (IUPAP) in more then 20 formal standards adopted by them for letter symbols used in mathematical equations.
(B) Make available single and multiple subscripts to the main letter symbols to the extent necessary for clarity. Multiple letters, such as abbreviations, are prohibited for use as the main symbol (kernel) for a quantity. A few exceptions are some traditional mathematical symbols, such as log, ln, and lim. Thus, quantities that are sometimes represented by abbreviations in textual material, tables, or graphs are required in the SPE Symbols Standard to have single-letter kernels. Examples are gas/oil ratio (GOR), bottomhole pressure (BHP), spontaneous potential (SP), and static SP (SSP), which have the following SPE standard symbols: R, pbh, ESP, and ESSP, respectively.
- Adopt the letter symbols of original or prior author usage, where not in conflict with Principles 3 and 4.
- Adopt letter symbols consistent or parallel with the existing SPE Symbols Standard, minimizing conflicts with that Standard.
- Where pertinent, adopt the symbols already standardized by such authorities as ANSI, ISO, or IUPAP (see Principle 1); minimize conflicts with these standards.
- Limit the list principally to basic quantities, avoiding symbols and subscripts for combinations, reciprocals, special conditions, etc.
- Use initial letters of materials, phase, processes, etc., for symbols and subscripts; they are suggestive and easily remembered.
- Choose symbols that can be readily handwritten, typed, and printed.
Principles of letter symbol standardization
Requirements for published quantity
- Symbols should be standard where possible. In the use of published symbols, authors of technical works (including textbooks) are urged to adopt the symbols in this and other current standards and to conform to the principles stated here. An author should provide a Nomenclature list in which all symbols are listed and defined. For work in a specialized or developing field, an author may need symbols in addition to those already contained in standards. In such a case, the author should be careful to select simple, suggestive symbols that avoid conflict in the given field and in other closely related special fields. Except in this situation, the author should not introduce new symbols or depart from currently accepted notation.
- Symbols should be clear in reference. One should not assign different meanings to a given symbol in such a manner as to make its interpretation in a given context ambiguous. Conflicts must be avoided. A listed alternative symbol or a modifying subscript is often available and should be adopted. Any symbol not familiar to the reading public should have its meaning defined. The units should be indicated whenever necessary.
- Symbols should be easily identified. Because of the many numerals, letters, and signs that are similar in appearance, a writer should be careful in calling for separate symbols that in published form might be confused by the reader. For example, many letters in the Greek alphabet (lower case and capital) are practically indistinguishable from English letters, and the zero is easily mistaken for the capital O.
- Symbols should be economical in publication. One should try to keep the cost of publishing symbols at a minimum: no one work should use a great variety of types and special characters; hand¬writing of inserted symbols, in copy largely typewritten and to be reproduced in facsimile, should not be excessive; and often a complicated expression appears as a component part of a given base. Instead, one may introduce, locally, a single non-conflicting letter to stand for such a complicated component. An explanatory definition should then appear in the immediate context.
Subscripts and superscripts are widely used for a variety of conventional purposes. For example, a subscript may indicate the place of a term in a sequence or matrix; a designated state, point, part, time, or system of units; the constancy of one independent physical quantity among others on which a given quantity depends for its value; or a variable with respect to which the given quantity is a derivative. Likewise, for example, a superscript may indicate the exponent for a power, a distinguishing label, a unit, or a tensor index. The intended sense must be clear in each case. Several subscripts or superscripts, sometimes separated by commas, may be attached to a single letter. A symbol with a superscript such as prime (′) or second (″) or a tensor index should be enclosed in parentheses, braces, or brackets before an exponent is attached. So far as logical clarity permits, one should avoid attaching subscripts and superscripts to sub¬scripts and superscripts. Abbreviations, themselves standardized, may appear among subscripts. A conventional sign or abbreviation indicating the adopted unit may be attached to a letter symbol or corresponding numeral. Reference marks, such as numbers in distinctive type, may be attached to words and abbreviations, but not to letter symbols.
Multiple subscripts—position order
The wide variety and complexity of subject matter covered in the petroleum literature make it impossible to avoid use of multiple subscripts with many symbols. To make such usage less confusing, the following guides were used for the order of appearance of the individual letters in multiple subscripts in the symbols list. Use of the same rules is recommended when it becomes necessary to establish a multiple-subscript notation that has not been included in this list.
- When the subscript r for "relative" is used, it should appear first in subscript order. Examples: kro and krg.
- When the subscript i for "injection," "injected," or "irreducible" is used, it should appear first in sub¬script order (but after r for "relative"). Examples: Big, formation volume factor of injected gas, and cig, compressibility of injected gas.
- Except for Cases 1 and 2 above (and symbols kh and Lv), phase, composition, and system sub¬scripts should generally appear first in subscript order. Examples: Bgi, initial or original gas FVF; Boi, initial or original oil FVF; CO2i, initial or original oxygen concentration; Bri, initial or original total system formation volume factor; ρsE, density of solid particles making up experimental pack; and FaF, GLp, Gwgp, and GFi.
- Abbreviation subscripts (such as "ext," "lim," "max," "min"), when applied to a symbol already subscripted, should appear last in subscript order and require that the basic symbol and its initial subscript(s) be first enclosed in parentheses. Examples: (ia1)max and (Shr)min.
- Except for Case 4, numerical subscripts should appear last in subscript order. Examples: qoD3, dimensionless oil-production rate during Time Period 3; pR2, reservoir pressure at Time 2; and (ia1)max, maximum air-injection rate during Time Period 1.
- Except for Cases 4 and 5, subscript D for "dimensionless" usually should appear last in subscript order. Examples: ptD, qoD, and (qoD3)max.
- Except for Cases 4 through 6, the following subscripts usually should appear last in subscript order; regions such as bank, burned, depleted, front, swept, and unburned (b, b, d, f, s, and u); separation, differential, and flash (sp, d, and f); and individual component identification (I or other). Examples: EbD, Rsf, and npj.
When appearing as lightfaced letters of the English alphabet, letter symbols for physical quantities and other subscripts and superscripts, whether upper case, lower case, or in small capitals, are printed in italic (slanted) type. Arabic numerals and letters of other alphabets used in mathematic expressions are normally printed in vertical type. When a special alphabet is required, boldface type is preferred over German, Gothic, or script type. It is important to select a typeface that has italic forms and clearly distinguished upper case, lower case, and small capitals. Typefaces with serifs are recommended.
Quantity symbols may be used in mathematical expressions in any way consistent with good mathematical usage. The product of two quantities is indicated by writing ab. The quotient may be indicated by writing a/b, or ab–1. If more than one solidus (/) is used in any algebraic term, parentheses must be inserted to remove any ambiguity. Thus, one may write (a/b)/c, or a/bc, but not a/b/c.
- When the mobilities involved are on opposite sides of an interface, the mobility ratio will be defined as the ratio of the displacing phase mobility to the displaced phase mobility, or the ratio of the upstream mobility to the downstream mobility.
- Abbreviated chemical formulas are used as subscripts for paraffin hydrocarbons: C1 for methane, C2 for ethane, C3 for propane…Cn for CnH2n+2.
- Complete chemical formulas are used as subscripts for materials: CO2 for carbon dioxide, CO for carbon monoxide, O2 for oxygen, N2 for nitrogen, etc.
- The letter R is retained for electrical resistivity in well logging usage. The symbol ρ is to be used in all other cases and is that preferred by ASA.
- The letter C is retained for electrical conductivity in well logging usage. The symbol σ is to be used in all other cases and is that preferred by ASA.
- Dimensions: L=length, m=mass, q=electrical charge, t=time, T=temperature, M=money, and n=amount of substance.
- Dimensionless numbers are criteria for geometric, kinematic, and dynamic similarity between two systems. They are derived by one of three procedures used in methods of similarity: integral, differential, or dimensional. Examples of dimensionless numbers are Reynolds number, NRe, and Prandtl number, NPr. For a discussion of methods of similarity and dimensionless numbers, see "Methods of Similarity," by R.E. Schilson, Journal of Petroleum Technology (August 1964) 877–879.
- The quantity x can be modified to indicate an average or mean value by an overbar.
Distinctions between and descriptions of abbreviations, dimensions, letter symbols, reserve symbols, unit abbreviations, and units
Confusion often arises as to the proper distinctions between abbreviations, dimensions, letter symbols, reserve symbols, unit abbreviations, and units used in science and engineering. SPE has adhered to the following descriptions.
For use in textual matter, tables, figures, and oral discussions. An abbreviation is a letter or group of letters that may be used in place of the full name of a quantity, unit, or other entity. Abbreviations are not acceptable in mathematical equations.
Dimensions identify the physical nature or the general components of a specific physical quantity. SPE uses seven basic dimensions: mass, length, time, temperature, electrical charge, money, and amount (m, L, t, T, q, M, and n).*
For use in mathematical equations. A letter symbol is a single letter, modified when appropriate by one or more subscripts, used to represent a specific physical or mathematical quantity in a mathematical equation. A single letter may be used to represent a group of quantities, properly defined. The same letter symbol should be used consistently for the same generic quantity, with special values being indicated by subscripts or superscripts.
A reserve symbol is a single letter, modified when appropriate by one or more sub¬scripts or superscripts, that can be used as an alternative when two quantities (occurring in some specialized works) have the same standard letter symbol. These conflicts may result from use of standard SPE symbols or subscript designations that are the same for two different quantities, or use of SPE symbols that conflict with firmly established, commonly used notation and signs from the fields of mathematics, physics, and chemistry.
To avoid conflicting designations in these cases, use of reserve symbols, reserve subscripts, and reserve-symbol/reserve-subscript combinations is permitted, but only in cases of symbols conflict. Author preference for the reserve symbols and subscripts does not justify their use.
In making the choice as to which of two quantities should be given a reserve designation, one should at-tempt to retain the standard SPE symbol for the quantity appearing more frequently in the paper; otherwise, the standard SPE symbol should be retained for the more basic item (temperature, pressure, porosity, permeability, etc.). Once a reserve designation for a quantity is used, it must be used consistently throughout a paper. Use of an unsubscripted reserve symbol for a quantity requires use of the same reserve symbol designation when sub¬scripting is required. Reversion to the standard SPE symbol or subscript is not permitted with a paper. For larger works, such as books, consistency within a chapter or section must be maintained. The symbol nomenclature, which is a required part of each work, must contain each reserve notation used, together with its definition.
A unit abbreviation is a letter or group of letters (for example, cm for centimeter), or in a few cases a special sign, that may be used in place of the name of a unit. The International Organization for Standardization (ISO) and many other national and international bodies concerned with standardization emphasize the special character of these designations and rigidly prescribe the manner in which the unit abbreviations shall be developed and treated.
Units express the system of measurement used to quantify a specific physical quantity. In SPE usage, units have "abbreviations" but do not have "letter symbols." See the SI Metric System of Units and SPE Metric Standard.
- Electrical charge is current times time. ISO uses Mass (m), Length (L), Time (T), Temperature (θ), Electrical current (T), Amount of substance (n), and Luminous Intensity (J).