Aziz S Odeh
Lewis L Raymer
Senior Scientist President
 
@Copyright 1987 by the Society of Petroleum Engineers. Printed in the
United States of America. All rights reserved. This book or parts thereof
cannot be reproduced in any form without written consent of the publisher.
Third printing Feb. 1992 incorporating minor changes on Pages 22-3 30-3
30-4 33-2 and 51-52.
ii
  reface
The 1962 edition of the Petroleum Production Handbook filled a need at that time for a comprehensive compilation
of practical information and data covering production equipment and reservoir engineering. This 1987 edition updates
the original 48 chapters and adds 11 new ones. N ew technology, developed over the past 25 years, resulted in im-
proved equipment, materials, and methods. They are described and discussed in the revised original chapters and
in the new ones. The 11 new chapters are the following:
Chapter 7-Electric Submersible Pumps
Chapter 1 &Offshore Operations
Chapter 52-Mud Logging
Chapter 58-SI Metric System of Units and SPE Metric Stand ard
Chapter 59-SPE Letter and Computer Symbols Standard
This 1 987 edition, now called the Petroleum Engineering Handbook provides a current and worthwhile addition
to the industry’s literature for students and experienced professionals working in the petroleum industry.
The handbook is again divided into three sections: Sec. 1, Mathematics (one chapter); Sec. 2, Production Engineer-
ing (18 chapters); and Sec. 3, Reservoir Engineering (40 chapters). There are 57 chapters written by professionals
who are recognized as authorities in their fields of expertise. Chap. 58 is a revised version of the 198 2 SI Metric
System of Units and SPE Metric Standard, and Chap. 59 is the 1986 revision of the 1984 Standard SPE Letter and
Computer Symbols for Economics, Formation Evaluation and Well Logging, Natura l Gas Engineering, and Petrole-
um Reservoir Engineering.
The Mathematics section presents the basic tables and calculation procedures required by persons engaged in petro-
leum production. The Production Engineering section covers basic types of materials, methods, and tools available
for use in petroleum operations, including their capabilities and proper applications. The Reservoir Engineering sec-
tion treats gas, oil, condensate, and formation water properties and correlations; reservoir rocks and traps; primary,
secondary, and tertiary recovery data and methods; oil and gas reserves; formation evaluation, including well logging
methods; and well treating methods. The what, why, how, and now-what aspects of each topic are emphasized. Also,
at the end of the appropriate chapters, key equations are presented with SI metric units.
Special acknowledgmen t is due the SPE staff for their immeasurable help and advice, the associate editors for their
avid dedication to the technical-editing task, and all the authors who contributed much time and effort to provide
the timely and excellent information included within each chapter. We are much indebted to the editor-in-chief of
the 1962 edition, Thoma s C. Fricke. and to the original group of authors for their arduous 3-year job of developing
the origina l edition of the Petro/eum Production Handbook. Special thanks are due Ed Mayer of THU MS and B.J.
Dotson of Mobil Oil Corp. (now retired) for their advice an d helpful discussions on the proper use of the 198 6 SPE
standard letter symbols throughout the handbook and for their editing of Chap. 59, the SPE Letter and Computer
Symbols Standard.
Our hope is that by proper application of the updated information contained within the second edition of this hand-
book, the petroleum-industry professional will be led to more efficient production and use of the world’s petroleum-
energy resources.
The Society of Petroleum Engineers sincerely thank\ the following organizations and individuals for permission to use the
cited material.
Chap. 2
Figs. 2.1 through 2.3 and 2.6 through
2.8, from Casino, Tubi,l~, and Drill Pipe, API Spec. 5A, 38th edition. API. Dallas
(1985).
Fig. 2.9, from Line Pipe, API Spec. 5L, 35th edition. API. Dallas (1985).
Figs. 2.10A, 2.10B, 2.11, 2.12, and 2.14 through 2.18, from 7hrt&inR, &g;,lg, and 7’hveud hl.~fcct;or2, API Spec SB.
1 Ith edition, API. Dallas (1985).
Table
Spec. 5A, 37th edition, API, Dallas (1984).
Tables 2.2, 2.5 through 2.7, and 2.25 through 2.27,
“Casing, Tubing, and Drill Pipe,“
Bull.,
(1972).
Tables 2.3, 2.4, and 2.24, modified from “Performance Propertics of Casing, Tubing, and Drill Pipe,” Apf Bu//. 5~2,
API. Dallas (1983).
Tables 2.8 through 2.11 and 2.28, from “USS Seamless Casing. Tubing, and Drill Pipe,” Bu//, , USS. Pittsburgh, PA
(1972).
Table 2.14, Bull. 664. National Supply Co.. Houston.
Tables 2.31 through 2.33, 2.36, and 2.37, from Line Pipe, API Spec. 5L. 34th edition. API, Dallas (1984).
Tables 2.38 through 2.43,
from “Formulas and Calculations for Casing, Tubing. Drill Pipe. and Lint Pipe Properties.”
API
Bull. 5C3, third edition with Supplement No. 1. API. Dallas (1983).
Tables 2.44 through 2.54, from Thrrudit~~. Gaging, und thread Inspection. API Spec. 5B, 10th edition with Supplement
No. 4. API. Dallas (1983).
Chap. 3
Figs, 3.1 and 3.3, and Tables 3.1 through 3.33, from Speci’carionsfor Wellhcad and Chrisrtnas Tree Eyuipment. API
Spec. 6A. 14th and 15th editions, API. Dallas (April 1. 1986).
Fig. 3.2, courtesy McEvoy Co., General Catalog 58-59 (Jan. 1959).
Fig. 3.5, from Eichenberg, R.,
“Design Consideration for AWHEM 15,000 psi Flanges,” ASME Paper 57.PET-23, Sept.
22, 1957.
Chap. 4
Figs. 4.1 through 4.11, from Patton, L.D. and Abbott, W.A.: Well Completions and Workovers: The Systems Approuth.
second edition, Energy Publications, Dallas (1985) 57-67.
Tables 4.1 and 4.2, from Pucker Culculations Handbook, Baker Oil Tool Div. (1971).
Chap. 5
Fig. 5.1, from Winkler. H.W.: “How to Design a Closed Rotativc Gas Lift System-Part I: Proccdurc,” World Qj/ (July
1960) 116-19.
Figs. 5.2, 5.5, 5.6, and 5.18, from Gus Lij?, Book 6 of API Vocational Training Series, revised edition. API. Dallas (1984)
65.
Fig. 5.3, from Winkler. H.W.: “Here’s How to Improve Your Gas Lift Installations-Part I : Pressure at Depth
Determinations.”
Figs. 5.4 and 5.29,
Fig. 5.7, from King, W.R.: “Time and V
0 umc Control for Gas Intermitters,”
U.S. Patent No. 2.339.487 (Jan. 1944).
Fig. 5.21, from Kirkpatrick. C.V.:
“Advances in Gas-Lift Technology,”
API Drill. and Prod. Pruc. (I 959) 24-60.
Fig. 5.25, from Gas Lt”, Book 6 of API Vocational Training Series. API. Dallas (1965) 109.
Fig. 5.33, from CLlmco Cornplere Service Cuialog, Cameo Inc. (1962) 42.
Chap. 6
Figs. 6.1, 6.5, 6.7, 6.12, 6.13, 6.31, 6.40, 6.44, 6.47, 6.49, and 6.51, and Table 6.18, courtesy Trico Industries.
Gardena. CA,
Figs. 6.2, 6.3, 6.6, 6.8, 6.11, 6.14, 6.15, 6.19 through 6.24, 6.26 through 6.29, 6.32 through 6.39, 6.41 through 6.45,
6.48, 6.50, 6.52, 6.53, and 6.55, and Table 6.1, from National-Oilwell. Los Nietos. CA.
Fig. 6.9, courtesy Otis Engineering Corp., Dallas.
Figs. 6.17 and 6.52, and Tables 6.3, 6.12, and 6.17, courtesy Dresser Industries, Dallas.
Fig. 6.18 and Table 6.4,
courtesy of Highland Pump Co. Inc.. Midland. TX.
Fig. 6.56, from Si;ing und Selecrion of Electric Submersible Pump Installations, API RP I IU, second edition, API. Dallas
(May 30, 1986).
Chap. 7
Figs. 7.1 through 7.18 and 7.20 through 7.32, and Table 7.1, courtesy TRW Energy Products Group, Reda Pump Div.,
Bartlesville. OK.
Chap. 8
Fig. 8.1, from Subsurface Pumps and Fitrings, API Spec. 11 AX, seventh edition, API, Dallas (June 1979).
Figs. 8.3, 8.5, and 8.7, courtesy Oilwell Div. of U.S. Steel Corp., Garland, TX.
V
from Sucker
API Spcc. 119, 2lst editmn. API, Dallas (May 1985).
Figs. 9.5 and 9.9, and Table 9.9, from Cure und Hundling of Sucker Rod.,, API RP 1 IBR. seventh edition. API. Dallas
(May 30, 1986).
Fig. 9.10 and Tables 9.10 and 9.11, from Reir@ced Plu~fic Sucker Rods, API Spec. 1 IC, first edition. API, Dallas (Jan,
I, 1986).
Table 9.7, from Design Culrulurions for Sucker Rod P~inpini:
Systems
PI RP I 1L. third edition, API, Dallas (Feb. 1977)
Chap. IO
Figs. 10.1, 10.3, 10.6, 10.7, 10.9 through 10.12, and 10.14 pumping unit), courtesy Lufkin Industries Inc., Lufkin. TX.
Fig. 10.8,
API RP 1 IL. third edition.
API. Dallas (Feb. 1977).
Figs. 10.13, 10.16 through 10.20, and 10.24 through 10.28, and Tables 10.5, 10.7, and 10.9, from Sargent Oil Well
Equipment Co., Odessa, TX.
Fig. 10.14 engine), from Arrow Specialty Co., Tulsa, OK.
Fig. 10.15, from Waukesha Engine Div.. Dresser Industries Inc., Waukesha. WI.
Fig. 10.21, from Mom-s and Generators, MG l-1978. Natl. Electrical Manufacturers Assn.. Washington. DC (1978).
Figs. 10.29 through 10.31, from Ronk Electrical Industries Inc., Nokomis. IL.
Figs. 10.32 and 10.33, from Classijcnlion o Areas or Electrical lnstullations at Drilling Rigs and Production Facilities on
Land and on Marine Fixed and Mobile
Platform,
API RP 5009, second edition, API, Dallas (July 1973) 8.
Tables 10.2 and 10.3, from lnsrullation and Luhrimtim of Pumping Units, API RP 1 IG, second edition. API. Dallas (Feb.
1959) and Supplement (Jan. 1980).
Tables 10.6 and 10.10, from Motor Application and Muintenunce Hundbook, second edition, R.W. Smeaton (ed.),
McGraw-Hill Book Co. Inc.. New York City, Table 1 on Page 3-7 and Table 3 on Page I l-3.
Chap. 11
Figs. 11.1 and 11.3, from C-E Natco, Tulsa. OK.
Fig. 11.4, from Design and Fuhricution o Gulvunixd Products, American Hot Dip Galvanizer Assn. and the Zinc Inst.
(Nov. 1983).
Fig. 11.7, from CBI Industries Inc. (Chicago Bridge and Iron Co.), Oak Brook, IL.
Figs. 11.9 and 11.10,
from Fenix & Scisson Inc., Tulsa. OK.
Table 11.1, from Bolted Production Tanks, API Spec. 129, 12th edition, API Div. of Production, Dallas (Jan. 1977).
Tables 11.3 and 11.4, from Venting Atmospheric cmd LowPressure Storage Tunk.7, API Std. 2000, third edition, API,
Dallas (Jan. 1982).
Fig. 12.2, courtesy Jaragua S.A. Industrias Mechanicas. Sao Paula, Brazil.
Figs. 12.7 and 12.8, courtesy Fisher Controls Co., Marshalltown. IA.
Figs. 12.16 and 12.19, courtesy ACS Industries Inc., Woonsocket, RI.
Fig. 12.18, courtesy Peerless Mfg. Co., Dallas.
Fig. 12.20, courtesy Plenty Metrol. Newbury. England.
Fig. 12.21, courtesy Vortec. Inc.. Woodside. CA.
Fig. 12.22, courtesy Porta-Test Systems, Ltd., Edmonton, Alta., Canada.
Figs. 12.24, 12.26, and 12.40, courtesy C-E Natco, Tulsa, OK.
Tables 12.9 and 12.10, courtesy Cornsign Computer Program, Ellis Engineering Inc., Houston.
Tables 12.11 and 12.17, from KWIC Index of Intl. Standards, Intl. Organization for Standardization. Geneva.
Tables 12.12, 12.18, and 12.19, from ASME Boiler and Pressure Vessel Code, Sec. VIII, Div. 1, New York City (1984).
Tables 12.13 and 12.14, from Megyesy, E.F.: Pressure Vessel Handbook, Pressure Vessel Handbook Publishing Inc.,
Tulsa, OK.
Table 12.15, from Kimmell, G.O.: “Stage Separation,” paper 48.PET-15 presented at the ASME Annual Meeting.
Oklahoma City, Oct. 1949.
Chap. 13
Fig. 13.2,
Fig. 13.3, from Ori’ce Constunt Tub/es. American Gas Assn.,
Report No. 3, revised (1969). Also, ANSI/API 2530.
Fig. 13.4 and Tables 13.2a, 13.2b, and 13.4, from GPSA Engineering Dutubook, Gas Processors Suppliers Assn., Tulsa,
OK (1972).
Table 13.1, courtesy American Meter Co.. Inc.
Chap. 14
Fig. 14.5, from GPSA Engineering Dutuhook, ninth edition. fifth revision, Gas Processors Suppliers Assn., Tulsa, OK
(1981).
Fig. 14.14, from NGSMA Handbook.
Figs. 14.19 through 14.21, and Tables 14.1 and 14.2 from Campbell, J.M.: “J.M. Campbell Gas Conditioning and
Processing.” Campbell Petroleum Series, Norman, OK (1962) 2.
vi
Figs. 15.1 through 15.3, and Table 15.9, from Desl,qn and
hstd/don of O&how P~C~CY;OH ~l+t~~ Pip;~ ~~~~~~~~~~~
API RP l4E, third edition, API, Dallas (1981) 22.
Figs. 15.4 through 15.6, and Tables 15.2 through 15.5, from GPSA
Engineerirlg Durchx~k, @IS Processors Suppliers
Assn.. Tulsa, OK (1980).
Fig. 15.8, courtesy Paragon Engineering Services Inc.. Houston.
Fig. 15.11 and Table 15.10, courtesy Perry Equipment Co., Mineral Wells, TX.
Fig. 15.12, courtesy C-E Natco, Tulsa. OK.
Fig. 15.13, courtesy U.S. Filter. Fluid System Corp.. Whittier, CA.
Figs. 15.15 and 15.19, from “Oil-Water Separator Process Design.” API Manual on Disposal of Refinery Wastes. Volume
on Liquid Wastes, API. Dallas (1975) Chap. 5.
Fig. 15.20, Engineering Spccialtiea Inc.. Covington. LA.
Tables 15.6 and 15.7, from Am~r ic r~~ ~ tr iiov7d .bmk~rd Pp / mg .s a zd Fm& Frtir rRs ANSI B26.5. ASME, New
York City (1981).
Fig. 18.32, courtesy CanOcean Resources Ltd., New Westminster, B.C., Canada.
Fig. 18.36, courtesy Fluor Subsea Services. Irvine. CA.
Fig. 18.38, courtesy Hamilton Bros. Oil Co., Denver.
Fig. 18.40, from Lagers, G.H.C., Gusto, B.V., and Bell, C.R.: “The Third Generation Lay Barge.”
Proc., Offshore
Fig. 18.41, courtesy Apache, Santa Fe Intl. Corp., Alhambra. CA.
Fig. 18.43, courtesy Swan Wooster Engineering Ltd., Vancouver, B.C., Canada.
Fig. 18.44, from Willits. K.L.: “Well Completions in the Prudhoc Bay Field.” Pet. Eng. (Feb. 1976).
Fig. 18.45, courtesy Brian Watt Assocs., Houston.
Chap. 19
Figs. 19.1, 19.3, and 19.6 through 19.8, courtesy Shell Development Co., Houston.
Figs. 19.4, 19.5, 19.9, and 19.10, courtesy Baker Performance Chemicals Inc., Santa Fe Springs, CA
Fig. 19.12, courtesy ASTM, Philadelphia. PA.
Fig. 19.17, courtesy Chemineer-Kenics. Dayton. OH.
Fig. 19.18, courtesy Modular Production Equipment Inc., Houston.
Figs. 19.19, 19.29, and 19.30, courtesy C-E Natco Inc.. Tulsa, OK.
Figs. 19.20 and 19.32, courtesy Hydrocarbon Research Inc.. Long Beach, CA.
Figs. 19.21, 19.22, and 19.28, courtesy Energy Recovery Div., Daniel Industries Inc.
Chap. 20
Figs. 20.2A and 20.3, from Katz, D.L. ef (il.: Hcr rdhook of Nutuuu/ Gus
Eng;nrcr;ng,
York City (1959).
Figs. 20.2B and 20.2C, from Brown, G.G. ~1 nl.: “Natural Gasoline and the Volatile Hydrocarbons.” Natural Gas Assn.
of America. Tulsa OK (1948).
Fig. 20.4, from Wichert, E. and Aziz. K.:
“Compressibility Factor for Sour Natural Gases,” Cdn. J. C zerrr. Gl,q. (1972)
49, 269-75.
Figs. 20.8 and 20.9, from Stiel. L.I. and Thodos, G.: “The Viscosity of Non-Polar Gases at Normal Pressures.”
AICIfE J.
(1961) 7, 61 l-20.
Fig. 20.10, from Matthews, T.A.. Roland. C H.. and Katz, D.L.:
“High Pressure Gas Measurement.”
A$sn. of America (1942) 41-51.
Fig. 20.14 and Table 20.1, from Perry. R.H. and Chilton, C.H.: C/~cwicz/ 0tgin~er.s ffmdbook. fifth edition. McGraw-
Hill Book Co Inc., New York City (1975).
Table 20.2, from GPSA
ninth edition. fifth revision. Gas Processors Suppliers Aasn.. Tulsa. OK,
Chau. 21
Gq~~/ oymic~
c$ C/ic,n~ic,tr/ T~~c~/tno/o,e~,The Interscicnce Encyclopedia Inc. ( 1953) 10, 1 17.
Fig. 21.3, after N&on. W.L.: Parrnlertr?~ Rc$rrrj:v ~ri,t~irt~~~ri/t~, fourth edition, McGraw-Hill Book Co Inc., New York
City (1958) 910-37.
Fig. 21.4, courtesy Hansen. D.N. and Hurd. C.O., Shell Devolopmcnt Co ,
Prtrd~wrn Rc wr
(Aprtl 1945).
Figs. 21.7 through 21.21, from ASTM Slcrf&rcl.c 011 Pt,/ro/c~trfi P,.oc/lrc~f.s crnd
Lubricants.
Fig. 21.22, from Matthews. T.A.. Roland. C.H.. and Katz. D.L:
“High Prcssurc Gas Measurements.”
Figs. 21.23 and 21.24. from Standing.
M. B. : l’r~lrr/tif,/rrc, t/rid Phcrsr Bhcr~~io~ r f’ Oil Fir/t/ Hwlrr,c&~orr S\stc~rns, Reinhold
Publtshing Corp.. New York City (1952).
Fig. 21.25, from Standing. M.13.: “A Prcssurc-Volulnc-Tcmpcraturc Correlation for Mixtures of California Oil and Gases.”
Drill. curd Prod. Pm ,
Fig. 21.26, courtesy Calitornia Rcjcarch Corp., 1947.
‘Fable 2 I .7, from Nelson. W. L. : Pr~f-oic,lr ~r Rc:/iucy\ En,g;n~criyy, fourth edition, McGrawHill Book Co. Inc.. New York
City (11)5X) 910-37.
Oil & Gtrv J.
Table 21.11, courtesy Bartlcavillc Energy Technology Ccntcr. Bartlc~ville. OK.
vii
Chau. 22
Figs. 22.1 through 22.3, from Standing, M.B.: Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, Reinhold
Publishing Corp., New York City (1952).
Fig. 22.4, from Katz, D.L.: “Prediction of the Shrinkage of Crude Oils,”
Drill. and Prod. Prac., API (1942).
Figs. 22.5, 22.9, and 22.13, courtesy California Research Corp.
Figs. 22.19 and 22.20,
“Finding Surface Tension of Hydrocarbon Liquids,” Oil & Gas
1. (Jan. 2, 1956).
Fig. 23.9 from GPSA Engineering Databook, Gas Processors Suppliers Assn.,
ninth edition, Tulsa, OK (1972).
Figs. 23.12 and 23.13 from Reamer, H.H., Fiskin, J.M., and Sage, B.H.:
“Phase Equilibria in Hydrocarbon Systems,”
lnd. Eng. Chem. (Dec. 1949) 41, 2871.
Chao. 24
Fig. 24.3, from Hoke, S.H. and Collins, A.G.: Mobile Wellhead Analyzerfor the Determination of Unstable Constituents in
Oil-Field Waters, ASTM STP 735 (1981) 34-48.
Fig. 24.9, from Burcik: Properties o Petroleum Reservoir Fluids, John Wiley & Sons Inc., New York City (1957).
Figs. 24.11 and 24.12, from PI-Petroleum Information,
Chap. 25
Figs. 25.3 and 25.4, from Kobayashi, R.: “Vapor-Liquid Equilibria in Binary Hydrocarbon-Water Systems,” PhD
dissertation, U. of Michigan, Ann Arbor (1951).
Figs. 25.5, 25.10, 25.21, 25.23, and 25.24, and Table 25.4, from Katz, D.L. et al.: “Water-Hydrocarbon Systems,”
Handbook o Natural Gas Engineering,
McGraw-Hill Book Co. Inc., New York City (1959) 189-221.
Figs. 25.6, 25.8, and
“Vapor-Liquid Equilibria for Binary Hydrocarbon-Water
Systems,”
Fig. 25.7, from Alder, S.B. and Spencer, C.F.:
“Case Studies of Industrial Problems, Phase Equilibria and Fluid Properties
in the Chemical Industry,” Proc., Equilibrium Fluid Properties in the Chemical Industry (1980) 465-95.
Fig. 25.14, from von Stackelberg, M.: “Solid Gas Hydrates,”
Natunvissenschaften (1949) 36, 327-33, 359-62.
Figs. 25.17 through 25.20,
from Sloan, E.D.: “Phase Equilibria of Natural Gas Hydrates,” paper 67f presented at the
1983 AIChE Summer Natl. Meeting, Denver, Aug. 28-31.
Fig. 25.22, from Song, K.Y. and Kobayashi, R.:
“Measurement and Interpretation of the Water Content of a Methane-
Propane Mixture in the Gaseous State in Equilibrium with Hydrate,”
Ind. Eng. Chem. Fund. (1982) 21, No. 4, 391-95.
Fig. 25.25, from Deaton, W.J. and Frost, E.M.: Gas Hydrates and Their Relation to the Operation of Natural Gas Pipe
Lines,
Monograph 8, USBM, Washington, DC (1946).
Fig. 25.30, from Saito, S., Marshall, D.R., and Kobayashi, R.L: “Hydrates at High Pressures: Part II. Application of
Statistical Mechanics to the Study of the Hydrates of Methane, Argon, and Nitrogen,” AIChE J. (1964) 10, No. 5,
734-40.
“Pressure-Volume-Temperature and Solubility Relations for Natural
Gas-Water Mixtures,” Drill. and Prod. Prac., API, Dallas (1944) 173-79.
Figs. 25.34 through 25.36, from Peng, D.-Y. and Robinson, D.B.:
“Two- and Three-Phase Equilibrium Calculations for
Coal Gasification and Related Process,” Thermodynamics o Aqueous Systems with Industrial Applications, S.A. Newman
(ed.), Symposium Series 133. ACS (1980) 393-414.
Figs. 25.37 and 25.41, from Scauzillo, F.R.: “Inhibiting Hydrate Formations in Hydrocarbon Gases,” Chem. Eng. Progr.
(1956) 52, No. 8, 324-28.
Figs. 25.38 through 25.40, from Gas Conditioning Fact Book, Dow Chemical Co., Midland, MI (1962) 69-71,
Table 25.5, from Dharmawardhand, P.B.: “The Measurement of the Thermodynamic Parameters of the Hydrate Structure
and Application of Them in the Prediction of Natural Gas Hydrates,”
PhD dissertation, Colorado School of Mines,
Golden (1980).
Chap. 26
“Systematic Packing of Spheres-With Particular Relation to Porosity and
Permeability,” J. Geol. (Nov.-Dec. 1935) 785-909.
Figs. 26.3 and 26.30, courtesy Core Laboratories Inc., Dallas.
Fig. 26.5, 2 6.24, and 26.25, from Stevens, A.B.: A Laboratory Manual or Petroleum Engineering 308, Texas A&M U.,
College Station (1954).
Fig. 26.7, from Krumbein, W.C. and Sloss, L.L.: Stratigraphy and Sedimentation, Appleton-Century-Crofts Inc., New York
City (1951) 218.
Fig. 26.27, from Klinkenberg, L.J.: “The Permeability of Porous Media to Liquids and Gases,” Drill. and Prod. Prac.,
API, Dallas (1941) 200-13.
“Saturation Determination of Rotary Cores,” Pet.
Eng. (Jan. 1954) B.52-B.64.
Table 27.12, courtesy Alaska Oil & Gas Conservation Commission, Anchorage.
Tables 27.13 through 27.15 and 27.17, courtesy Core Laboratories Inc., Dallas.
 
Chap. 28
Figs. 28.3 and 28.4, from Rose. W.: U.S. Patent No. 4,506,542 (1985).
from Rose. W.: “Permeability and Gas Slippage Phenomena.”
Drill. and Prod. Pruc., API. DalIah (1948)
127-35.
Fig. 28.8, from Stone. H.L.: “Probability Model for Estimating Three-Phase Relative Permeability.” J. Ccl,z. P<,t. Tech.
(Oct. 1973) 53-59.
Fig. 28.12, from Panteleev. V.G. et ctl.: “Influence of Carbon Dioxide on Three Phase Permeability by Oil and Water,”
Nej?eprom.wlowe de10 (1973) No. 6. I l-13.
Fig.
28.16, from Ashford. F.E.: “ Determination of Two Phase and Multiphase Relative Permeability for Drainage and
lmbibition Cycles Based on Capillary Pressure Measurement,”
Revisru Tecnicu Intevep (198
Fig. 28.19, from Lin, C. and Slattery. J.C.: “Three-Dimensional. Randomized, Network Model for Two-Phase Flow
Through Porous Media.”
Chau. 29
Figs. 29.1 through 29.3, from Galloway, T.J.: Bull. 118, California Div. of Mines, Sacramento (Aug. 1957).
Fig. 29.6, from Sams. H.: “Atkinson Field. Good Example of ‘Subtle Stratigraphic Trap,’ ” Oil & Gas .I. (Aug. 12. 1974)
145-63.
Fig. 29.7, from Hoyt. W.V.: “Erosional Channel in the Middle Wilcox Near Yoakum. Lavaca County. Texas,” Trrlrt~.
Gulf Coast Assn. of Geological Societies (Nov. 1959) 9, 41-50.
Fig. 29.8, from Pirson, S.J.: Oil Reservoir EnRinerring, second edition, McGraw-Hill Book Co. Inc., New York City
(1958).
Figs. 29.9 and 29.10, from “Occurrence of Oil and Gas in Northeast Texas,” F.A. Herald (ed.). Bureau of Economic
Geology and East Texas Geological Sot. (April 1951).
Fig. 29.11, from An Infrod~rction to Gulf‘ Cousf Oil Fields, Houston Geological Sot., Houston (1941).
Fig. 29.12, from A Guide Book, Houston Geological Sot.. Houston (1953).
Chap. 30
High Performance Pressure
Chao. 31
Fig. 31.1, from Clijnutu/ogicul Dutu in the United Slates. U.S. Weather Bureau, Washington, DC
Chap. 32
Fig. 32.1, from the Railroad Commission of Texas, Austin.
Figs. 32.2 and 32.3, from Calhoun, J.C. Jr.: Fundamentals of Reservoir Engineering, revised edition, U. of Oklahoma
Press. Norman (1953).
of
Petroleum Measurement Standurd.T, Chap. 5. Sec. 3.
Fig. 32.12, from API Measurement of Perroleum Liquid Hydrocarbons by Positive Displuccment Meter, API Std. IlO1, first
edition (Aug. 1960).
Chap. 33
Table 33.7, from Rawlins, E.L. and Schellhardt. M.A.: “Back-pressure Data on Natural Gas Wells and Their Application
to Production Practices,”
Chap. 34
Fig. 34.2, from Moody, L.F.: “Friction Factors for Pipe Flow,” Trans., ASME (1944) 66, 671.
Fig. 34.3, from Brown. G.G. et al.: Nutural Gusohe and the Volatile Hydrocarbons, Natural Gas Assn. of America
(1948).
Fig. 34.4, from Nisle, R.G. and Poettmann, F.H.: “Calculation of the Flow and Storage of Natural Gas in Pipe,” Per Enx.
(1955) 27, No. I. D-14; No. 2, C-36; No. 3, D-37.
from Griffith, P. and Wallis, G.B.: “Two-Phase Slug Flow,”
J. Heur Transfer
(Aug. 1961) 307-20:
Trans., ASME.
Figs. 34.11 and 34.12, from Poettmann, F.H. and Carpenter, P.G.: “Multiphase Flow of Gas, Oil, and Water Through
Vertical Flow Strings with Application to the Design of Gas-Lift Installations,”
Drill. und Prod. Pruc., API (1952)
257-3 17.
Figs. 34.13 through 34.17, from Davis, G.J. and Weidner, C.R.: “Investigation of the Air Lift Pump,” Bull., Eng. Series,
U. of Wisconsin (191 I) 6, No. 7.
Figs. 34.23 through 34.25, from Poettmann, F.H. and Beck, R.L.: “New Charts Developed to Predict Gas-Liquid Flow
Through Chokes,”
World Oil (March 1963) 95-101.
Table 34.7, from Rawlins, E.L. and Schellhardt, M.A.: “Back-Pressure Data on Natural Gas Wells and Their Application
to Production Practices,”
Chap. 36
Gulf of Thailand-A Case History.”
GeophvJics (Feb. 1982) 149-76.
Chap. 37
Fig. 37.6 and 37.7, from Tarncr, J., “How Different Sire Gas Caps and Pressure Maintenance Programs Affect Amount ot
Recoverable Oil.”
Oil Week \~June 12. 1944) 32-44.
Figs. 37.16 through 37.24, and Tables 37.1 and 37.2, from Singh. D. and Guerrero. E.T.: “Material Balance Equation
Sensitivity,”
“Evaluating Producing Volatile Oil Reservoirs.” Workl Oil (April 1979)
159-66 and 246.
Chao. 39
Figs. 39.1 through 39.3, and Table 39.1, after Eilerts. K.C. er ~1.: Phusr Rr/ution.s of Gas-Co,l~lenscite F1ui~l.s. American
Gas Assn., New York City (1957).
Figs. 39.4 through 39.6, and Tables 39.2 through 39.10, courtesy Core Laboratories Inc., Dallas (1985).
Fig. 39.7,
“Some Uses and Limitations of Model Studies in Cycling.” Trcrns.,
AIME (1948) 174, 67-87.
Fig. 39.8, after Stelzer, R.B.: “Model Study vs. Field Performance, Cycling the Paluxy Condensate Reservoir,” Drill. trrrrl
Prod. Pruc., API (1956) 336-42.
Fig. 39.9, data derived from Stelzer, R.B.:
“Model Study vs. Field Performance, Cycling the Paluxy Condensate
Reservoir.” Drill. and Prod. Prac., API (1956) 336-42.
Table 39.12, from Miller, M.G. and Lents. M.R.: “Performance of Bodcaw Reservoir, Cotton Valley Field Cycling
Project. New Methods of Predicting Gas-Condensate Reservoir Performance Under Cycling Operations.” Drill. wzd Prod.
Prac., API (1946) 128849.
Table 41.11, courtesy Republic Bank of Dallas.
Table 41.14. from Wilson. W.W. and Boyd. W.L.: “Simplified Calculations Determine Loan Payout.” World Oil (May
1958).
Chao. 44
Figs. 44.6 through 44.8 and Table 44.2, from Craft, B.C. and Hawkins, M.J. Jr.: Applied Pc~troleum Reservoir
Engineering,
Prentice-Hall Inc., Englewood Cliffs, NJ (1959) 107, 357, 412-13.
Figs. 44.58 through 44.61, from Guerrero. E.T. and Earlougher, R.C.: “Analysis and Comparison of Five Methods Used
to Predict Waterflooding Reserves and Performance,”
Drill. and Prod. Prac., API, Dallas (I 961) 78-95.
Fig. 44.62, from Higgins, R.V. and Leighton. A.J.: “Computer Techniques for Predicting Three-Phase Flow in Five-Spot
Waterfloods,” RI 7011. USBM (Aug. 1967).
Chap. 45
et
al.: “Natural Gasoline and the Volatile Hydrocarbons,” Natural Gasoline Assn. of
America (1948).
Fig. 45.5, from Hutchinson, C.A. Jr. and Braun, P.H.: “Phase Relations of Miscible Displacement in Oil Recovery.”
AIChE J. (1961) 7, 64.
Fig. 45.7, modified from Slobod, R.L. and Koch, H.A. Jr.: “High Pressure Gas Injection-Mechanism of Recovery
Increase,”
Drill. and Prod. Prac., API, Dallas (1953) 82.
Fig. 45.8, modified from Sage B.H and Lacey, W.N.: Some Properties of the Lighter Hydrocarbons, Hydrogen Suljde, and
Carbon Dioxide, Monograph Research Project 37, API, Dallas (1955).
Chap. 46
Fig. 46.1, from Farouq Ali, S.M.: “Steam Injection, Secondary and Tertiary Oil Recovery Processes,” Interstate Oil
Compact Commission, Oklahoma City (Sept. 1974) 148.
Fig. 46.2, from McNeil, M.S. and Moss, J.T.: “Oil Recovery by In-Situ Combustion,”
Pet. Eng. (July 1958) B-29-B-42.
Fig. 46.5, from Smith, R.W. and Perkins. T.K.: “Experimental and Numerical Simulation Studies of the Wet Combustion
Recovery Process,” J. Cdn. Pet. Tech. (July-Sept. 1973) 44454.
Fig. 46.34, from Mace. C.: “Deepest Combustion Project Proceeding Successfully,” Oil & Gus J. (Nov. 17, 1975) 74-81.
Fig. 46.59, from Poettmann. F.H. and Mayland, B.J.: “Equilibrium Constants for High Boiling Hydrocarbon Fractures of
Varying Characterization Factors,”
Pet. Refiner (July 1949) 101ll2.
Tables 46.1 through 46.6, from “Steam Dominates Enhanced Oil Recovery,” Oil & Gas J. (April 5, 1982) 139-59.
Table 46.31, from “1967 ASTM Steam Tables,” ASME. New York City (1967).
Chap. 47
Figs. 47.1, 47.12, and 47.26, from U.S. DOE: drawing by J. Lindley, Bartlesville, OK.
Fig. 47.3, from Mungan, N.: Rev. Inst. Fr. Pet., Editions Technip, Paris (1969) 24, 232.
Fig. 47.4, from Tsaur, K.: “A Study of PolymeriSurfactant Interactions for Micellar/Polymer Flooding Applications,” MS
thesis. U. of Texas, Austin (1978).
Fig. 47.5, from Martin, F.D., Donaruma, L.G., and Hatch, M.J.: “Development of Improved Mobility Control Agents for
SurfactantiPolymer Flooding,” second annual report, Contract No. DOEiBCiOCO013, U.S. DOE (Oct. 1980).
Fig. 47.8, from Overbeck, J.Th.G.: “Colloids and Surface Chemistry. A Self-Study Subject Guide. Part 2, Lyophobic
Colloids,” Bull., Center for Advanced Engineering, Massachusetts Inst. of Technology, Cambridge, MA (1972).
Fig. 47.9, from Khan. S.A.: “The Flow of Foam Through Porous Media,”
MS thesis, Stanford U., Stanford, CA (1965).
 
Fig. 47.19, from Recd. R.L. and Healy, R.N.: “Some Physico-Chemical Aspects of Microemulsion Flooding: A Review.”
Improved Oil Recovery by Sutjticttmt and Polwner Flooding, D.O. Shah and R.S. Schechter (eds.), Academic Press,
New
Recovery.” PhD dissertation, U. of Texas, Austin (1983).
Fig. 47.23, from Lake, L.W. and Pope, G.A.: “Status of Micellar-Polymer Field Tests,” Pet. Eng. Intl. (Nov. 1979) 51,
38-60.
Fig. 47.27, from Minssieux, L.: “Waterflood Improvement by Means of Alkaline Water,” Enhunced Oil Recovery by
Displacement wifh Saline Solutions, Kogan Page Ltd., London (1979) 75-90; courtesy BP Trading Co. Ltd.
Table 47.1, from Manning, R.K., Pope, G.A., and Lake, L.W.: “A Technical Survey of Polymer Flooding Projects,”
Contract No. DOE/BETC/l0327-19, U.S. DOE (Sept. 1983).
Table 47.2, from Akstinat, M.H.: “Surfactants for WOR Process in High-salinity Systems: ‘Product selection and
evaluation,’ ” Enhanced Oi/ Recovery, Elsevier Scientific Publishing Co., New York City (1981).
Chap. 49
Figs. 49.9, 49.10, 49.19 through 49.22, 49.25 through 49.30, and 49.34, from Log Interpretation Principles, Vol. 1,
Schlumberger Well Services, Houston.
Figs. 49.42 through 49.44 and Table 49.2, from Calver, J:C.. Rau, R., and Wells, L.:
“Electromagnetic Propagation-A
New Dimension in Logging,”
Schlumberger Well Services, Houston.
Figs. 49.46 and 49.47, from Best, D.L., Gardner. J.S., and Dumanoir, J.L.:
“A Computer-Processed Wellsite Log
Computation,”
paper presented at the 1978 SPWLA Annual Logging Symposium, June 13-16.
Fig. 49.48, from Coates, G.R., Schulze, R.P., and Throop, W.H.: “VOLAN*-An Advanced Computational Log
Analysis,”
paper presented at the 1982 SPWLA Annual Logging Symposium, July 6-9.
Tables 49.1 and 49.3 through 49.6, from Bateman. R.M., Log Qunlir?, Control, IHRDC, Boston, 1984.
Chap. 50
Figs. 50.5 and 50.6, from Evans, R.D.: 7’he Aromic Nucleus, McGraw-Hill Book Co. Inc., New York City (1967) 426-38.
Figs. 50.9, 50.21, 50.30, 50.32 through 50.34, 50.40, 50.43, 50.50, and 50.51, courtesy Schlumberger Well Services.
Houston.
Fig. 50.18, from Tidman, J.: “Geophysical Well Logging.” excerpts from Methods in Experimental Phyic.\: Physics,
Academic Press (1986) 24.
Figs. 50.22 and 50.36, from Schlumberger Log Interpretation Charts, Schlumberger Well Services, Houston. 1984.
Figs. 50.23, 50.24, and 50.26,
from Edmundson, H. and Raymer, L.L.:
“Radioactive Logging Parameters for Common
Minerals.” paper presented at the 1979 SPWLA Annual Logging Symposium, Tulsa, June 3-h.
Fig. 50.29, from Hertzog, R.C. and Plasek, R.E.: “Neutron-Excited Gamma-Ray Spectrometry for Well Logging.” IEEE
Trms. NM. Sti. (Feb. 1979) NS-26, No. 1,
Fig. 50.46, Arnold, D.M. and Smith, H.D. Jr.: “Experimental Determination of Environmental Corrections for a Dual-
Spaced Neutron Porosity Log,” paper W presented at the 1981 SPWLA Annual Logging Symposium, Mexico City, June
23-26.
Fig. 50.47, from Schlumbergcr Chart Book, Schlumberger Well Services, Houston (1977).
Table 50.3, from Bcrtuzzi. W., Ellis. D.V., and Wahl. J.S.: “The Physical Foundation of Formation Lithology Logging
with Gamma Rays,” Geophy.siu (Oct. 1981) 46, No. 10.
Chap. 51
Fig. 51.2, from Sears, F.W. and Zemansky, M.W.: Unirwsi@ Physics, Addison-Wesley Publishing Co. Inc., Reading. MA
(1955) 1031.
Figs. 51.3 and 51.4, from Krautkramer, J. and Krautkramer, H.: Ultrasonic Testing ofA4ateriais, Springer-Verlag. New
York City (1969) 521.
Figs. 51.6 and 51.71, from Timur. A.: “Rock Physics,” The Arabian J. Sri. Eng. Special Issue (1978) 5-30.
Figs. 51.7 and 51.15,
from Timur. A.: “Temperature Dependence of Compressional and Shear Wave Velocities in Rocks,”
Groph~sics (1977) 42, 950-56.
Figs. 51.8 and 51.9 and Table 51.2, from Jones, S.B., Thompson, D.D., and Timur. A.:
“A Unified Investigation of
paper presented at the Rock Mechanics Conference, Vail, CO (1976).
Fig. 51.10, from Johnston. D.H., Toksoz. M.N., and Timur, A.:
“Attenuation of Seismic Waves in Dry and Saturated
Rocks: Part II: Theoretical Models and Mechanism.”
Grophvsics ( 1979) 44, 69 l-7 1 I
Fig. 51.11, from Wyllie, M.R.J.. Gardner, G.H.F., and Gregory, A.R.: “Studies of Elastic Wave Attenuation in Porous
Media.” Geophysics (1962) 27, 269.
Figs. 51.12 through 51.14, from Gardner. G.H.F., Gardner, L.W.R., and Gregory, A.R.: “Formation Velocity and
Density-The Diagnostic Basics for Stratigraphic Traps,” Geophysics 1974) 39, 770-80.
Fig. 51.16, from Timur, A.: “Velocities of Compressional Waves in Porous Media at Permafrost Temperatures,”
Geophysics (1968) 33, 584-96.
Figs. 51.17, 51.19, and 51.21, from Toksoz, M.N., Cheng. C.H., and Timur, A.: “Velocities of Seismic Waves in Porous
Rocks,” Geoph?sirs ( 1976) 41, 62 l-45.
Fig. 51.17, from King, M.S.: “Wave Velocities in Rocks as a Function of Changes in Overburden Pressure and Pore Fluid
Saturants.” Geophysics (1966) 31, 50-73.
Fig. 51.18, Gregory, A.R.: “Fluid Saturation Effect\ on Dynamic Elastic Properties of Sedimentary Rocks.” Geophysics
1976) 41, 895-921.
Fig. 51.20, from Timur. A.. Hempkins. W.B., and Weinbrandt. R.M.: “Scanning Electron Microscope Study of Pore
Systems in Rocks.”
xi
 
Figs. 51.22, 51.37, 51.50, and 51.94, from Gcycr. R.L. and Myung, J.I.:
“The 3-D Velocity Log: a Tool for In-Situ
Determination of the Elastic Moduli of Rocks.”
Dynamic Rock Mechanics, Proc., Twelfth Symposium on Rock
Mechanics (1971) 71-107.
Figs. 51.23 and 51.24, from Minear, J.W. and Fletcher, C.R.:
“Full-Wave Acoustic Logging,” Tr0n.c.) SPWLA (1983)
paper EE.
“Elastic Wave Propagation in a Fluid-Filled Borchole and Synthetic
Acoustic Logs,” Geophysics (1981) 46, 1042-S3.
Fig. 51.26,
from Cheng. C.H. and Toksoz. M.N.: “Generation, Propagation and Analysis of Tube Waves in a Borehole,”
Trans., SPWLA (1982) paper P.
Figs. 51.27, 51.28, 51.31, and 51.46, from Thomas, D.H.:
“Seismic Applications of Sonic Logs,” The Log Analwt (Jan.-
Feb. 1977) 23-32.
Figs. 51.29 and 51.33, from Lynch, E.J.: Forrnutiorz Evu/uurwn, Harper and Row, New York City (1962) 422.
Figs. 51.36 and 51.77, from Ausburn, J.R.: “Well Log Editing in Support of Detailed Seismic Studies,” Trans., SPWLA
(1977) paper F.
Figs. 51.39 and 51.42, from Goetz, J.F., Dupal. L., and Bowler, J. :
“An Investigation into Discrepancies Between Sonic
Log and Seismic Check Shot Velocities, Part I,” APEA J. (1979) 19, 131-41.
Fig. 51.40, from Ransom, R.C.: “ Methods Based on Density and Neutron Well-Logging Responses to Distinguish
Characteristics of Shaly Sandstone Reservoir Rock,”
The Log Analyst (May-June 1977)
18, 47-62.
Figs. 51.41, 51.43, 51.44, and 51.48, from “The Long Spaciflg So&,”
Schlumberger technical pamphlet (1980).
Fig. 51.45, from Misk, A. ef a/.: “Effects of Hole Conditions on Log Measurements and Formation Evaluation,” SAID,
Third Annual Logging Symposium (June 1976).
Figs. 51.47 and 51.49, from “The Long Spacing Sonic,”
Schlumberger technical pamphlet (1982).
Fig. 51.56, from Parks. T.W., McClellan, J.H., and Morris. C.F.:
“Algorithms for Full-Waveform Sonic Logging,” paper
presented at the 1983 IEEE-ASSP Workshop on Spectral Estimation.
Fig. 51.58, from Wiley. R.: “Borehole Televiewer-Revisited.”
Trans., SPWLA (1980) 21, paper HH.
Fig.
Trans.,
Fig. 51.63, from “Log Interpretation Charts.” Schlumberger (1979).
Fig. 51.65, from “Evaluaci6n de Formaciones en la Argentina,” Schlumberger (1973) 9455.
Fig. 51.66, from Raymer, L.L.. Hunt, E.R., and Gardner, J-S.: “An Improved Sonic Transit Time-To-Porosity
Transform.”
Trms.,
Empirical Correlations Between Velocities and Porosities,”
Tram, SPWLA (1981) paper PP.
Figs. 51.70 and 51.72, from Nations, J.F.:
“Lithology and Porosity from Acoustic Shear and Comprcssional Wave Transit
Time Relationships,” Trms., SPWLA 18th Annual Logging Symposium (June 1974).
Fig. 51.73 and 51.74, from Gardner. G.H.F. and Harris, M.H.:
“Velocity and Attenuation of Elastic Waves in Sands.”
Trans.. SPWLA (1968) 9, paper M.
Fig. 51.75, from Arditty. P.C.. Ahrens, G., and Staron, Ph.:
“EVA: A Long Spacing Sonic Tool for Evaluation of
Velocities and Attenuation.”
paper presented at the 1981 SEG Annual Meeting, Los Angeles.
Fig. 51.76, from Domenico. S.N.:
“Effect of Brine-Gas Mixture on Velocity in an Unconsolidated Sand Reservoir.” Thr
Log A~~nl~st (1977) 18, 38-46.
Figs. 51.78 and 51.79, from Kithas. B.A.: “Lithology, Gas Detection, and Rock Properties from Acoustic Logging
Systems,” Trcrns., SPWLA (1976) 17, paper R.
Figs. 51.80 and 51.81, from Laws. W.R.. Edwards. C.A.M., and Wichmann, P.A.:
“A Study of the Acoustic and Density
Changes Associated with High-Amplitude Events on Seismic Data.” Trans., SPWLA (1974) 15, paper D.
Figs. 51.83 and 51.84, from Herring, E.A.:
“North Sea Abnormal Pressures Determined from Logs,” Per. Eng. (1973)
45, 72-84.
Dresser Atlas technical pamphlet (I 979) 20.
Figs. 51.90 and 51.92, from “Cement Bond Evaluation in Cased Holes Through 3-D Velocity Logging,” Birdwell technical
pamphlet (1978) 12.
Fig.
51.96, from Walker. T.: “Acoustic Character of Unconsolidated Sand,” Welcx paper (1971).
Fig. 51.97, from Myung. J.I. and Baltosser. R.W.:
“Fracture Evaluation by the Borehole Logging Method.” Stuhi& Rock
Sloprs. Thirteenth Symposium on Rock Mechanics (1972) 31-56.
Figs. 51.98 and 51.99, from Taylor, T.J.:
“Interpretation and Application of Borehole Televicwer Surveys.” Tram.,
SPWLA (1983) 24, paper QQ.
Fig. 51.100, from Williams. D.M. et (II.:
“The Long Spacing Acoustic Logging Tool,”
Trans.,
Table 51.1, from Timur. A.:
“Application of Acoustic Wave Propagation Methods to Evaluation and Production of
Hydrocarbon Rcscrvoirs,” Pm-, IEEE Ultrasonic Symposium, Dallas (1984).
Table 51.3, from Guyod. H. and Shane. L.E.: Geophysical Well Logging, Hubert Guyod, Houston (1969) I, 256; and
Wyllic, M.R.J.. Gregory, A.R.. and Gardner. G.H.F.: “Elastic Wave Velocities in Heterogeneous and Porous Media,”
Geophysic~s (1956) 21, 41-70.
Chap. 52
Figs. 52.1 and 52.2, from MS-196, Exploration Logging Inc., Sacramento, CA (1979).
Figs. 52.3 through 52.12 and 52.22 and Table 52.1, courtesy Exploration Logging Inc., Sacramento, CA.
Figs. 52.13, 52.14, 52.16, 52.17, and 52.19 through 52.21, from MS-156, Exploration Logging Inc.. Sacramento, CA
(1981).
Figs.
Fig.
xii
Anadrill Logging Unit, Schlumherger.
Fig. 53.7 and Table 53.2, from Log Qualify Conrrol Munurri. Vizilog Inc., Houston.
Figs. 53.9 through 53.11, from Dipme/er InferpretLltion~Vol. I, Fundamentals, Schlumberger, Houston (1981).
Fig. 53.12 and 53.15, from Gilbreath. J.A.: “Dipmeter Interpretation Rules,”
Schlumberger Offshore Services, New
Orleans.
Figs. 53.13 and 53.14, from “Open Hole Log Analysis and Formation Evaluation.” Vizilog Inc.. Houston.
Figs. 53.16 through 53.18,
Fig. 53.23 through 53.25, from Dresser Atlas Production Senlices Catalog, Dresser Atlas.
Fig. Analyst
Fig. 53.27 through 53.32, from “Well Evaluation Developments 1982,” Schlumherger.
Table
Fig. 53.5, from EXLOG Flyer GA 817-A. EXLOG (June 1983).
Table 53.3 and Figs. 53.21 and 53.22, from Dia-Log flyer, The Dia-Log Co., Houston.
Chap. 54
‘ ‘Acidizing-State-of-the-Art,”
Figs. 56.1 through 56.8, courtesy Dowell Schlumberger Technical Brochure TSL45 19,
“Dowell Sand Control Techniques
 
Acknow ledgmen ts . . . . . . . . . . . . . . . . . . ..~......................___.____._. v
1. Mathematical Tables and Units and Systems of Weights and Mea sures
Mathem atical Tables . .
...............
Casing..
...............
Introduction .
Other Flow-Control Devices
............... 4-l
............... 4-l I
Gas Lift Valve Mechanics
6. Hydraulic Pumping
Introduction
Conclusions ...................
.
.
.. ................ ..
10. Pumping Units and Prime Movers for Pumping Units: Part l-Pumping Units
Introduction ............................................................
Counterbalance .........................................................
Sizing .................................................................
Installation .............................................................
Lubrication ............................................................
8-l
8-2
8-4
8-5
8-6
8-7
8-7
8-8
8-8
8-9
8-9
8-9
8-10
8-10
9-l
9-l
9-10
IO-I
IO-I
IO-4
IO-5
IO-6
IO-7
IO-7
IO-12
IO-13
Pumping Units and Prime Movers for Pumping Units: Part 2-Prime Mo vers for Pumping Units
Introduction
.......................................................
Tank Corrosion Protection .............................
Mate rials of Cons truction ..............................
Production Equipment .................................
Unde rgroun d Storag e ..................................
12. Oil and Gas Separators
Summary..
Methods Used To Remove Oil From G as in Separators ......
Mist Extractors Used in Oil and Gas Separators
............
......
Classification of Oil and Gas Separators
...................
Illustrations of Oil and Gas Separators
....................
Estimating the Sizes and Capacities of Oil and Gas Separators.
xvi
.............................
Capacity Curves for Vertical and Horizontal Oil and Gas Separators
........ 12-27
.................
......................................
....................
..........................
12-38
Controls, Valves, Accessories, and Safety Features for Oil and Gas Separators
12-39
....... 12-40
Introduction
Introduction...............................................
Gas-Treating Systems for Removal of Water Vapor, CO,, and H,S
15. Surface Facilities for Waterflooding and Saltwater Disposal
Introduction
..................
..................
Introduction
Typical Automatic-Control Installations
Introduction
......
.................................
........
.
.
. .
. .
.
. .
19-6
19-6
19-16
19-28
19-32
Molecular Weight. . . . .
Ideal Gas . .
Specific Gravity (Relative Density) . . .
Specific Gravity of Gas Mixtures . . . .
Dalton’s Law . . . . . . . . .
Amagat’s Law.
Formation Volume Factor . .
Introduction
Oil FVF Correlations . . .
Total FVF’s
Oil Viscosity Correlations .
Introduction and History
Inorganic Constituents . . . . .
Interpretation of Chemical Analyses . .
Recovery of Minerals From Brines . . . . . .
. .
. .
Introduction
.....................
.............................................................
Determining the Water Content of Gas (or Hydrocarbon-Rich Liquid) in Equilibrium With Hydrates
...
........................
.........................
.........................................................
.................................
Introduction . .
Porosity . . . . . . . . . . . . . . . . . . . . .
Permeability . .
27. Typical C ore Analysis of Different Formations
Introduction
Introduction
Texas Allowable Rule
Backpressure Testing
.........
........
Production Rate
.............
.......
Introduction.
Basic Data Required.
 
Material Balance as Equation of Straight Line for Determination of OIP and of Gas-Cap Size
37-6
37-7
37-10
37-10
. 37-13
37-17
37-21
.......................................
Introduction ...........................
Definitions.
Gas-Condensate Well Tests and Sampling .......................
Sample Collection and Evaluation .............................
..................
Economics of Gas-Condensate Reservoir O peration ...............
40. Estimation of Oil and Ga s Reserves
Estimating Reserves ...........................
........................................................
Saturated Depletion-Type Oil Reservoirs-Volumetric Methods ................................
API Estim ation of Oil and Gas Reserve s. ..................................................
Undersaturated Oil Reservoirs W ithout Water Drive Above the Bubblepoint-Volumetric Method ...
Volatile Oil Reservoirs-Volumetric Methods
Oil Reservoirs W ith Gas-Cap Drive-Volumetric Unit Recovery Computed by Frontal-Drive Method
Oil Reservo irs Under Grav ity Drain age. ...................................................
Oil Reservoirs W ith Water Drive-Volumetric Methods
......................................
Production-Decline Curves ................
Valuation . . .
Development and Operating Costs . .
42. Injection Operations
Analysis of a Reservoir for Injection Operations
43. Gas-Injection Pressure Maintenance in Oil Reservoirs
Introduction. . . . . . .
Methods of Evaluating Unit-Displacement Efficiency.
Methods of Evaluating Conformance Efficiency . .
Methods of Evaluating Areal Sweep Efficiency .
Calculation of Gas Pressure-Maintenance Performance
.
Appendix B-Selected References Containing Equations, Calculation Procedures, and Example
Calculations Related to Gas-Injection Performance Predictions . . . . . .
Appendix C-Data Requirements for Engineering Analysis of Gas-Injection Operations
44. Water-Injection Pressure Maintenance and Waterflood Processes
Introduction
Determination of Residual Oil After Waterflooding ......................
Predicting Water Injection Oil Recovery and Performance
Wate r-Injection We ll Beha vior .......................................
Wate r-Injection Case Histories .......................................
Water Source and Requirements ......................................
45. Miscible Displacement
Engineering Study . . . .
Appendix-Engineering Examples
Three Forms of In-Situ Combustion. ....
Historical Development ...............
Current Status. ......................
Theoretical Considerations.
Numerical Simulation. ................
Laboratory Experimentation ...........
Field Projects .......................
Project Design ......................
.................
Validity of Simulation Results.
................
............
Acoustic Wave Propagation Methods
51-l
51-l
51-4
The Mud Log . . . . . . .
Petroleum Engineering Services .
Drilling Engineering Services . .
Standards for and Status of Services
52-l
. 52-l
52-2
52-11
52-11
52-16
52-27
52-28
52-30
Introduction...................................................
Reperforation ___.,..,,,..._..___.,,.,..,,,._.._..,._____._.._.
The Landowner’s Interest .........
Assignments by the Landowner ....
Assignments by the Lessee ........
Offshore Leasing ................
58. The SI Metric System of Units and SPE Metric Standard
Preface ..................................
Introduction ...................................................
Application of the Metric System
.................................
Special Terms and Quantities Involving Mass and Amount of Substance
Men tal Guid es for Using Me tric U nits .............................
Appendix A-Terminology ..............
.
Part 2: Discussion of Metric Unit Standards
..........................
Symbols in Alphabetical Order..
Quantities in Alphabetical Order.
Index .
Philip Franklin, Massachusetts nst. f Technol ogy*
L. E. Barbrow U. S. Nat] .Bureau of Standards
Contents
Numbers
Tabl e 1. 3- Square Roots . i - i i
Tabl e 1.4-Cube Roots
Tabl e 1.6- - Reci procal s 1-21
Ci rcl es
Tabl e 1.8-Areas by Hundredths
. I -26
l - 28
I - 30
Tabl e 1.12- Segments. Gi ven
h/D ................ 1-32
Tabl e 1 14- Vol umes by Hundredths . . . . . . . . . . . . . . 1- 34
Table 1 . I 5-Regular Pol ygons
. . . . . . . . . . . . . . . . . .
Tabl e 1 16-- Bi nomal Coeff i cients . . . . . . . . . . . . . . 1-37
Tabl e 1, 17-Common Logari thms (1 OO to 2. 00)
1-38
I - 40
. . . . . . .
l - 42
Tabl e 1 20- - Radi ans i n Degrees . . . . . . . . . . . . . . . 1- 43
Table 1.21- Natural Si nes and Cosi nes l - 44
Table 1.22- Natural Tangents and Cotangents l - 46
Table 1.23- Natural Secants and Cosecants l - 48
Table 1.24- Tri gonometr i c Functi ons
. . . . . . . . . . . I - 50
. . . . . . . . . . . . . . . . . . . . . . 1- 55
I - 56
Cosi nes : : : : :
1-59
I - 60
Tabl e 1. 30- Mul t i pl es of 0.4343
l - 60
Tabl e 1. 31- Mul t i pl es of 2.3026
Tabl e 1.32-Standard Di stri but i on f Resi dual s :
I - 60
I - 61
Table 1.33- Factors f or Computi ng Probabl e Error
1-61
‘This chapter I” the 1962 edMn was written by Ph,l,p Franklm and Laws ”
Judson (both deceased)
Compound I nterest
Table 1.34- Amount of a Gi ven Pri nci pal
Tabl e 1.35- Amount of an Annui ty
Table 1. 36- Pri nci pal Amounti ng to a Gi ven Sum
Annui t i es
Tabl e 1.37- Amounti no to a Gi ven Sum
(Si nki ng Fund) y. ,
Tabl e 1.38- Present Wort h
Table 1.39- Provided f or by a Gi ven Capi tal
Table 1.40- Deci mal Equival ents
Uni ts and Syst ems of Wei ghts
and Measures
Table 1. 43-Common Fract i onsof an I nch
to M l l i meters
Tabl e 1.44- Deci mal s of an I nch to M l l i meters
Table 1.4%M l l i meters to Deci mal s of an I nch
Table 1.46- Area Equivalents
Tabl e 1.47-Vol ume and Capaci ty Equi val ents
Table1. 48- Areas
Tabl e 1. 49- Vol umes or Cubi c Meters
Table 1.50- Vol umes or Capaci t i es :
Table 1.51- Mass Equivalents
Tabl e 1.53- Vel oci ty Equi val ents
Tabl e 1.54- Li near and Angul ar Vel oci t i es :
Tabl e 1.55- - Pressures
Tabl e 1. 57- Energy or Work Equi val ents
Tabl e 1. 58- Energy, Work, Heat
Tabl e 1. 59- Pow& Equi val ents
Tabl e 1.60- Power . ‘ ,
Table 1.62- Thermal Conduct i vi ty
Tabl e 1. 63- Thermal Conductance :
Table 1.64- Heat Fl ow
Tabl e 1.65- Rel ati ve Densi t i esCorrespondtng to
OAPI and Wei ghts per U. S. Gal l on
I - 62
l - 63
l - 64
l - 65
l - 66
TABLE 1 .I -SQUARES OF NUMBERS
1 2 3 4 5 6 7 8 9
Average
1.081 1.083 1. 065
1.05
1.08
1.07
1.08
1.09
1.102
1.124
1.346 1. 348
1. 503
1.553 1. 555 1. 558 1.560
1. 583 1.585 3
1. 606 1. 610
1. 833 1. 838
1. 659 1. 862
1. 685 1. 887
1.39
1.839
1.841
1.893
1.949
1.952
1.968
1.43
1.44 2. 074 2.076 2.079 2. 082
1.977
2.062
2.091 2. 094
2. 111
2.120 2. 123 2.126
2.238 2. 241 2.244
2.372
2.412 2.415 2. 418 2.421
2.424 2.427 2. 430
2.443
2.455 2. 459 2. 462
1.57 2. 465 2.488 2.471 2.474 2.477 2.481 2.484 2.487 2.490 2. 493
1.58 2. 496 2.500 2.503 2.506 2.509
2.512 2. 515
2.547
Exol anati on of Tabl e of Souares
Thi s t abl egi vesthev lue of N2 f orval ues of N f rom1 to 10, correct o f our i gures. I nterpol atedal ues may be i n err or
by 1 i n the f ourt h i gure. )
To f i ndthe square of a number N outsi de the range from1 to 10, note that movi ng t he deci mal poi nt one pl ace i n
Col umn N i s equivalent to movi ng i t two places i n the body of the tabl e. For example, (3.217)' =10. 35,
(0.03217)' =0.001035, and (3,217)'=10, 035,000.
 
MATHEMATICAL TABLES & UNI TS & SYSTEMS OF WEI GHTS & MEASURES 1- 3
TABLE l . l - SQUARES OF NUMBERS(cont i nued)
7 8
2. 589
2.996 3.000 3.003 3. 007 3.010 3. 014 3.017
3.045 3.049 3. 052
3.080 3.084 3. 087
3.151
3.222
3.226
3.229
3.276
3.301 3. 305
3.338 3. 342
3.386
3.415
3.441
3.486 3. 489
3.512 3.516 3. 519
3.549 3.553
3.557 3.561 3. 565
1.89 3.572 3.578 3. 580 3.583 3.587 3.591 3.595 3.599 3.602
1.90
1.91
1.92
1.93
1.94
3.888
3.725
3.784
3.713
3.752
3.791
3.640
3.679
3.717
3.758
3.795
3.729 3. 733 3.738 3.740
3.744
3.748
3.846 3. 849 3.853
3.901
3.905
4.012
2.03
2.04 4.162 4.186
4.235
4.268
4.372
4.378
4.461 4.465 4. 469
4.439 4. 444 4.448
4.653 4. 857
2.18 4.886 4.670 4.674 4.679 4. 683 4.887 4. 692 4.696 4.700
2.17
4.709
4.739
4.783
4. 831
3.094 4
4.239
4.281
4.322
4.364
4.406
4.661
4.705
4.748
4.792
4.836
r =9.66960; l/r2 =0.101321, e2 =7.38906. x2 =9.669w; (T/z)* =2.46740; l/n2
=0.101321.
4
Average
0
4.884
4.928
4.973
5.018
5. 062 5.067 5. 072 5.076 5.081 5.085 5.090 5.094
5. 108
5.171
5.290 5. 295
5.355
5.807 5. 612
5.855 5.660
5.698 5. 703 5.707
5.746 5. 750 5.755
5.794
5.842
5.890
5.939
5.988
2.45
2.48
2.47
2.48
2.49
8.101 6. 108 6.111 6.116 6.121 6.126
5. 789
5. 837
5. 885
5. 934
5. 983
6.180 6. 185
6.200 6. 205 6. 210 6.215 6.220 6.225 6.230 6.235
2.50 8.250
6.280 6. 285
2.51 8.300 6. 305 6.310 8.315 6.320 6.325 6.330 6.335
2.52
2. 53 6.401 6.406
2.56 6.554 8.559 6.564 6.569 8.574 6.579 8.584
6.589
2.57
2. 58 6.656
6.687 8. 693
2. 59 6.708 8.713 6.718 6.724 8.729 6.734 6.739 8.744
2.60
2.61
2.62
2.63
2.64
 
MATHEMATICAL TABLES & UNI TS & SYSTEMS OF WEI GHTS & MEASURES l - 5
N
0
2.80
2.81
2.82
2.83
2.84
7.840
7.896
7.952
8.009
8.066
7 8
7.874
7.902 7.907 7.913 7.919 7.930 7. 935 7.941
7.958 7.964 7.969 7.975 7. 981 7.986 7. 992 7. 998
8.015 8.020 8. 026 8.032 8. 037 8.043 8. 049 8. 054
8.071 8. 077
8. 128 8. 134
8. 185 8. 191 8.197
8.202
8.254 8.260 8. 266 8. 271 8.277 8.283
8.300 8.306 8. 312 8. 317 8. 323 8.329 8. 335 8. 341
8.358
8.384 8. 369 8.375 8. 381 8.387 8. 393 8.398
8.416
8.433 8. 439 8. 445 8.451 8.456
8. 474 8.480 8.486 8.491 8. 497 8.503 8. 509 8. 515
8.532 8. 538
8. 544 8. 550 8. 556 8. 561 8.567 8.573
8.591 8.597 8.602
8.606 8. 614 8. 820 8.626 8.632
8.649 8.655 8. 661 8. 667 8. 673 8.679 8. 885 8. 691
8.708
8.714 8. 720 8.726 8. 732 8.738 8. 744 8.750
8.768
8.773 8.779 8.785 8. 791 8.797 8. 803 8.809
8.827 8.833 8. 839 8.845 8. 851 8.857 8.863 8. 868
8.886
8.946 8. 952
8. 958 8. 964 8. 970 8. 976 8. 982 8. 988
9.006 9.012 9. 018
9.102
9.108
9.187 9.193 9.199 9.205
9.248 9.254 9.260 9.266
9.370 9. 376
9.413
9.493 9.499 9.505
9.554 9. 560 9.567 9.573 9.579 9.585 9.591 9.598
9.616 9. 622
9.678 9. 685
9.691 9. 697 9. 703 9. 709 9. 716 9.722
9.741 9. 747 9.753 9.759 9.766 9.772 9.778 9.784
9.803 9. 809
9.866
9.929
9.992 9. 998 10. 005
9.99 10. 05 10. 11
10. 30 10. 37 10. 43
10. 50 10. 56 10.63
10. 69 10. 76
10. 96 11. 02 11. 09 11. 16 11. 22
11. 29 11. 36 11.42
11. 63
12. 11
12. 60 12.87 12. 74 12.82
13. 03 13. 10 13. 18 13. 25 13. 32
13. 40 13. 47 13.54
13. 76 13. 84
14. 29
14. 90 14. 98 15.05
15. 29 15. 37 15. 44 15. 52
15.60 15. 68 15. 76
15. 84
16. 48 16. 56 16.65
16. 89 16. 97 17. 06 17. 14 17.22 17. 31 17.39 17. 47
17. 72 17. 81 17. 89 17. 98
18.06 18. 15 18.23 18. 32
18. 58 18. 66 18. 75 18. 84 18.92 19. 01 19.10 19. 18
19. 45 19. 54 19. 62
19. 71
19.80 19. 89
19.98 20. 07
20. 34 20. 43 20. 52 20. 61 20. 70 20. 79
20. 88 20. 98
21. 25
21.34 21. 44 21. 53 21. 62 21. 72 21. 81
21. 90
22. 85
23. 14 23.23 23. 33 23. 43 23. 52 23. 62 23. 72
23. 81
24. 60
24. 70
24. 80
25. 40 25. 50 25. 60 25.70
2581
26. 73 26. 83
28. 20 28. 30
28. 52 28.62 28.73
28. 84 28. 94
29. 27 29. 38 29. 48 29. 59 29. 70 29.81 29. 92
30. 03
r2 =986960. l/r2
=o 101321
TABLE l.l-SQUARES OF NUMBERS (continued)
Average
5.6 31.36
31. 47
32.72
33.87
6.0
47. 89
49. 28
57. 30 57. 46 57.61
57. 91 58. 06 58. 22
58. 37 58.52 58. 68 58.83
58. 98 59. 14
59. 44 59. 60
59. 75 59. 91 60.06 60. 22 60. 37 60.53
60. 68
61. 31 61. 47 61.62 61. 78 61. 94 82.09
62. 25
6257 62.73
62. 88 63. 04 63. 20 63. 36 63. 52
83. 68 63. 84
64. 16 64. 32 64. 48 64. 64 64. 80 64. 96 65. 12 65. 29 65.45
65. 77 65. 93
66. 10 66. 26 66. 42 66.59 66.75 66.91 67.08
67. 40
67. 57 67. 73 67. 90 68. 06 68. 23 68. 39 68. 56 68.72
69. 06 69.22 69. 39
69. 56 69. 72 69. 89 70.06 70.22 70.39
70. 73 70. 90 71. 06
71. 23 71. 40 71.57 71.74 71.91 72.08
72. 42
79. 39
79. 57
79. 74
9.0 81.00
9.3 86.49
9.5
9.6
9.7
9.8
9.9
8
9
40. 32 40. 45 40.58 40.70 40.83
41. 60 41. 73 41.86 41.99 42.12
30. 58 30. 69
43.43
46. 10
51. 27
52. 71
54. 17
55. 65
54. 61
56. 10
72. 93 73. ' 10 73. 27 73. 44 73.62 73. 79
74. 65 74. 82 75. 00 75.17 75.34 75.52
76. 39
81. 54
83. 36
85. 19
87. 05
88. 92
90. 82
92. 74
79. 92
80. 10
87. 24 87.42 87. 61 87.80 87.98 88.17
89. 11 89. 30 69.49 89. 68 89.87 90.06
91. 01 91.20 91.39 91.58 91.78 91.97
92. 93
93.12 93.32
96. 83
97.81
r2=966960.(r12)2=246740. l/r2
 
MATHEMATICAL TABLES & UNI TS & SYSTEMS OF WEI GHTS & MEASURES 1- 7
TABLE1. 2- CUBESOFNUMBERS
Average
0
1.00
1.01
1.02
1.03
1.04
1.000
1
1.030 1. 033
1.061 1. 064
2.000 2. 005
1.40
1.41
1.42
1.43
1.44
1.015
1.046
1.077
2.715 2.721
2.774 2.779
2.833 2.839
3.533 3.540 3. 547 3.554 3. 561 3.568 3.575
3.603 3. 610
3.674 3. 681
3.746 3. 753
3.818 3. 826
3.892 3. 900
3.967 3. 974
4.042 4. 050
Expl anati onof Tabl e of Cubes
Thi s t abl egives the value of N3 f orval ues of Nf rom 1 to 10, correct o f our fi gures. I nterpol atedal ues may be i n err or
by 1 i n the f ourt h i gure. )
To f i nd he cube of a number Noutsi dethe range f rom1 to 10, notethatmovi ngthe deci mal poi ntone pl ace i nCol umn
Ni s equival ent o movi ng i t hreeplaces i n the body of thel abl e. For example, (4.852)3 = 114. 2,(0.4852)3=0. 1142, and
(485.2)3=114,200. 000.
Thi s tabl e al so can be used i nversel y o give cube roots.
(continued on next page)
4.844
12. 17
14. 35 14.53
6. 677 6. 687
1-9
Average
16. 39 16. 58 16. 78 16. 97 17. 17
18. 19 18.40 18. 61 18. 82
19. 03
19. 25
17. 37
19. 47
21. 72
24. 14
26. 73
22. 67 22. 91 23. 15
23. 39
25. 93
28. 65
31. 55
43. 99
44. 36
44. 74
45. 12
50. 65
53. 16
54. 87
59. 32
64. 00
68. 92
74. 09
79. 51
85. 18
91. 12
97. 34
192. 1 193. 1
212. 8
213.8 214.9
561. 5 583. 6 565.6
567.7 569.7
603. 4 605. 5 607.6
609.8 612.0
 
N
8.5
614.1
618.5
640.5
663.1
686.1
709.7
733.9
758.6
783.8
809.6
835.9
3
4
6 7
629. 4
651. 7
674. 5
697. 9
721. 7
8 9
 
1-11
9 Di f f erence
1.044 5
1.131
1.175
1.619
1.640
1.709
1.723
1.726
1.729
1.382
1.308
1.418
1.453
1.345
1.487
1.520
1.552
1.584
1.616
1.646
1.676
1.706
1.735
1.764
1.738
2.249 2. 252
2.400
2.410
2.412
2. 520 2. 522 2. 524 2.526 2. 528
2. 540 2. 542 2. 544 2.546 2. 548
2.557 2. 559 2.561 2. 563 2.565 2. 567
2.577
2.596 2. 598 2.600 2. 602 2.604 2. 606
2.615
2.617
2.619
2.621
2.551 2.553 2. 555
2.571 2.573 2. 575
Exol anati on of Table of Sauare Roots
Thi s tabl e gi ves the val ue of f i f orvaluesof Nf rom 1 to l OO, corr ectt of ourf i gures. ( l nterpol atedal ues maybe i nerror
by 1 i n the f ourt h i gure) .
To f i nd he square root of a number N outsi de the range f rom1 to 100, di vi de he di gi ts f the number i ntobl ocks
oft wo(begi nni ng w th thedeci mal poi nt) , and note thatmovi ngthedeci mal
l ace i n the square root of N. For example, &% 8=1.648,
ointtwo pl acesi n N i sequi val ent o movi ng
i t ne
( cont i nuedon next page)
 
TABLE 1. 3- SQUARE ROOTS OF NUMBERS(conti nued)
7
2.668 2. 670
2.672 2. 674
2.676 2. 678
2.706
2.724 2. 728
2.778 2.780 2.782 2.784 2.786
2.787
2.814
2.816
2.818
2.832 2.834 2.835 2.837
2.867 2. 869
2.884 2. 886
2.902 2.903 2.905
2. 944
3.069
3.085 3.087 3.089
3.102 3.103 3.105 3.106 3.108 3.110
3.118 3.119 3.121
3.150
3.151
3.153
3.347 3. 362
3.493
3.507
3.521
3.899
3.912
4.025
4.147 4. 159
4.712 4.722 4.733 4. 743 4.754 4. 764
4.817 4.827 4.837 4. 848 4.858 4. 868
4.919 4.930 4.940 4. 950 4.960 4. 970
5.020 5.030 5.040 5.050 5.060 5. 070
5.119
5.215 5.225 5.235
5.404 5. 413
5.495
5.586 5.595 5.604 5.612 5.621 5. 630
5.675 5. 683 5.692 5. 701
5.710 5. 718
5.848 5. 857
5.933 5. 941 5.950 5. 958 5.967 5.975
6.017 6. 025 6.033 6. 042 6.050 6.058
6.099 6.107 6.116
6.221
2.680 2. 681
2.698 2. 700
2.717 2. 718
6. 317
Vr=i.77245+. l/V'*=O.56419, V,*/Z=l 253 31, and ~e=,.64872
Average
MATHEMATI CALTABLES& UNI TS& SYSTE SOFWEl GHTS& MEASURES 1- 13
TABLE 1. 3- SQUARE ROOTS OF NUMBERS(cont i nued)
N
0 1 2 3 4 5 6 7 8 9
Average
6.380 6. 387 6.395
8
6.411 6.419 6.427 6.434 6.442 6.450 6. 458 6.465 6. 473
6.488 6.496 6.504 6.512 6.519 6.527 6. 535 6.542 6. 550
6.565 6.573 6.580 6.588 6.595 6.603 6. 611 6.618 6.626
6.641 6.648 6.656 6.663 6.671 6.678 6. 686 6.693 6. 701
45. 0
46. 0
47. 0
48. 0
49. 0
50. 0
51. 0
52. 0
53. 0
54. 0
74. 0 8.602 8.608
8.503 8.509 8. 515 8. 521 8. 526 8.532 8.538
8.562 8.567 8.573 8. 579 8. 585
8.620 8.626 8.631 8. 637 8. 643
75.0 8.660 8.666
76. 0
8.741
8.798 8.803 8 809 8. 815
78. 0 8.832 8.837
79. 0 8.888
80. 0
85. 0
86. 0
67. 0
88. 0
89. 0
9. 381
9.618 9.623 9. 628 9. 633 9.638
9.670 9. 675 9.680
9.721 9. 726 9.731
9.808 9.813 9. 818 9.823 9.829 9.834
97. 0
9.874 9.879 9. 884
99. 0
6.768
6.841
6.914
6.986
7.057
7.127
7.197
7.266
7.335
7.403
7.470
7.537
7.603
7.668
7.733
7.797
7.861
7.925
7.987
8.050
8.112
8.173
8.234
8.295
8.355
N
& N J i i N v% N J - N f i N - J %
0.7071- %
- _ _ -
/ 2 0. 7746 % 0. 7559 ' / 9 0. 3333 - 0. 64559/ rs-/ 1* 0. 7500
' / a 0. 5774 a/5 0. 8944 % 0.8452 2/ 0. 4714 y,p 0. 7638 "A6 0. 8292
v3 0. 8165 ' / 6 0. 4082 % 0. 9258 % 0. 6667 1%~ 0. 9574 ' 3/ G 0. 9014
' / 4 0.5000 5/ s 0.9129 ' / A 0.3536 =/ g 0.7454 ' h6 0.2500 ' 5/e 0.9662
v4 0. 8660 ' / $ 0. 3780 % 0. 6124 ' / g 0. 8819 3/ l s 0. 4330 ' / 32 0. 1768
' / s 0. 4472 2/ 7 0. 5345 % 0.7906 8/ s 0. 9428 %s 0. 5590 ' / 6* 0.1250
75 0.6325 3/7 0.6547 ' / a 0.9354 ' / ' 2 0.2887
‘/,s
TABLEl . 4- CUBEROOTSOFNUMBERS
1.029 3
1. 016
1. 048
1. 077
1. 105
1. 132
1.179 1. 182 1.184
1. 186 1.189 1.191
1.203 1. 205 1. 207 1. 210 1. 212 1. 214
1.225 1. 228 1. 230 1. 232 1. 234
1.236
1.289 1. 291 1.293
1.308 1. 310 1.312
1.346 1. 348 1.350
1.382 1. 384
3.1 1. 458
3.2 1.474 1.475 1.477 1. 478 1.480 1.481 1.483
3.3
1. 508 1.510 1. 511 1. 512
3.5
3.9
1.574
1.575
1.577
1.524
1.538
1.552
1.566
1.579
1.663 1. 664
5.3
1.744
5.4
1.754
1. 713 1. 715 1. 716 1. 717 1. 718 1.719
1.720
1.729 1.730 1. 731
1.753
1.763
1.764
5.5
5.6
5.7
5.8
5.9
6.0
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
1.765
1.776
1.779 1.780 1. 781
1.797 1.798 1.799 1.800 1.801 1.802
1.807 1.808
1.809 1.810
1. 837 1. 838
1.821
1.831
1.841
1.851
1.860
1.812
1.822
1.832
1.842
1.772
1.782
1.793
1.803
1.813
1.823
1.833
1.843
1.852
1.853
1.875
1.882 1.883 1. 884
1.890
1. 895 1.895 1.896 1.897
1.898 1.899 1. 900
1.901 1. 902 1.903
1904 1.905 1. 906 1.907 1.907 1.908 1. 909 1.910
1.911
1.912
1.057
1.060
1.086
1.089
Explanati on of Tabl e of Cube Roots
Thi s t abl egi ves the val ue of f i f or val ues of N fr om1 to 1,000,corr ect o f our fi g res. i nterpol atedal ues may be i n
errorby 1 i n the f ourt h i gure) .
To f i nd he square root of a number N outsi de the range fr om1 to 1, 000, divi dethe digi ts f the number i ntobl ocks
of three (beginni ng w th the deci mal poi nt) , nd note that moving t he deci mal poi nt f hree l aces i n col umn N i s
equival ent o movi ng i tone
6. 477 tb- ?% =13. 96
l ace i n the cube r oot of N. For exampl e, %%%? = 1. 396,
& i i 6 =30. 07, m =64. 77,
Ki t = 3.007 ?/ zi x=
and m =0. 06477.
 
1-15
TABLE 1. 4- CUBE ROOTS OF NUMBERS (cont i nued)
1. 920
1.921 1
1.964
1.972
1.984 1.985 1.986 1.987 1.987
1.992 1.993 1.994 1. 995 1.996
1.954
1.963
1.971
1.980
1.988
1.997
2.005
2.013
2.021
1.981
1.989
1.997
8.0
2.003
2.004
2.007 2. 007
2.015 2. 016
2.023 2. 024
2.031 2. 032
2.039 2. 040
8.5 2. 041
2.046
2.047
2.046
8.6 2.049 2. 050 2.050 2.051 2.052 2.053 2.054 2.054 2.055 2.056
8.7 2.057 2. 057 2.058 2.059
2.060 2. 061 2.061
2. 062 2. 063 2. 064
8.8 2.065 2. 065 2.066 2.067 2.068 2. 068 2.069 2. 070 2.071 2.072
8.9 2.072 2. 073 2.074 2.075 2.075 2. 076 2.077 2. 078 2.079 2.079
9.0 2.080 2.081
2.082 2. 082
9.3
2.450
2.455
35. 0
36. 0
37. 0
38. 0
39. 0
3.305
3.308 3. 311 3.314 3.317 3.320 3. 323 3.326 3. 329
3.335 3.338 3. 341
3.365 3.368 3.371
3.394 3. 397
3. 400 3.403 3. 406 3. 409 3.411 3.414 3. 417
-=14&%59aI nd /
TABLE 1.4- CUBE ROOTS OF NUMBERS (cont i nued)
3
3.428
3.457
5
3.711
3.782 3. 784
3.915 3. 917
65. 0
66. 0
67. 0
68. 0
69. 0
4.230 4. 232 4.234
4.252
4.258
4.260 4. 262 4. 264 4. 265 4.267 4.269 4.271
4.278 4.278 4.280 4.282 4.284 4.285 4.287 4.289
4.294 4.296
4.312 4.314 4.316 4.318 4.320 4.321 4.323
4.325
4.344 4.346 4. 348
4.362 4.364 4. 366
4.380 4.381 4. 383
88. 0
95. 0 4. 563
98. 0 4. 610
3.487
3.514
3.541
3.567
3.593
3.619
3.565
3.591
3.616
3.642
3.644
2
3.682
3.699
3.723
3.747
3.992
4.033
4.053
4.074
4.094
4.113
4.343
4.360
4.370
4.395
4.402 4. 404
4.419 4. 421
4.436 4. 438
4.453 4. 455
4.555 4. 556 4.558
4.587 4. 588 4. 590 4.592
4.59
4. 607 4. 609
4. 623 4. 625
4.634 4. 635 4.637
4. 638 4. 640
 
MATHEMATI CAL TABLES & UNI TS & SYSTEMS OF WEI GHTS & MEASURES
1-17
0 1
- -
- -
- -
Cube roots of numbers from 100.0 to 499.0
4.642 4.657 4. 672 4.688 4. 703 4.718 4.733 4.747 4. 762 4.777
4. 791
5.313 5. 325 5.337
5.429 5.440 5. 451
5.104 5.117 5. 130 5. 143
5.155 5.168 5. 180
5.540
7.275
7.281
7.714
7.769
7.824
7.878
7.932
50
7.937
7.942
7.948
51
7.990
55 8. 193
8. 208 8.213 8. 218 8.223
8. 257 8.262 8.267
8. 354 8.359 8. 363 8.368 8. 373
8. 335
8. 448 8.453 8.458 8.462 8. 487
8.472
8. 476
8. 495 6. 499 8. 504 8.509 8.513 6.518 8. 522
8. 541 8. 545 8. 550 8.554 8.559 8.564 8. 568
8.573
8.631 8. 636 8.640 8. 645 8.649 8.853 8. 658
65 8. 662
8.720 8.724 6. 729 8. 733 8.737 8.742 8. 746
67 8. 750
8.785 8. 789
68 8. 794
8.798 8. 802 8.607 8.811 8. 815 8.819 8.824 8. 828 8. 632
69 8.837 8.841 8.845 8. 849
8.854 8.858 8. 862 8. 866 8. 871 8.875
?-i= 1 46459 and l/x= 0.662764
(contmed on next page)
TABLE 1.4- CUBE ROOTS OF NUMBERS (conti nued)
N
1
8.904
6.955 8. 959
6. 975 6.979 8. 984 8.968 8. 992 6.996 9. 000
9.016 9.021 9. 025 9.029
9.033 9. 037
75
76
77
76
79
9.205
9.114
9.118
9.178
9.182
9.217
9.221
9.256 9. 260 9. 264 9. 268 9.272 9.275
9. 122
9.318
81
9.341 9. 345 9.348
9.364 9.366 9.371 9.375 9.379 9.383 9.366 9.390 9. 394
83 9. 396
64 9. 435
9.439 9. 443 9.447 9.450 9.454 9.456 9.462 9.465 9.469
85
86
87
88
69
9. 517
9. 554 9. 557
9. 590 9.594 9.597 9.601 9.605 9.608 9.612
9. 626 9.630 9.633 9.637
9.641
9. 726
9.789 9.792
9.634 9. 637 9.841 9.844 9.846 9.651 9.655 9. 858
9.861
9.902 9. 906 9.909
9.913 9.916 9. 919
9.930
9.936 9.940 9.943 9. 946 9.950 9. 953 9.956 9. 960
9.963
9.970 9.973 9.977 9.980 9.983 9. 987 9.990 9. 993
9.997
100
%N% N% N% N
. 7937 3/ 5 0. 8434 % 0. 8296 ' / 9 0.4807 %2
0.6934 % 0.9263 % 0.6939 2/ 9 0.6057 %?
0. 6355 "/ l j 0. 6826
0.9714 ' 3/16 0.9331
0.3969 ' s6 0.9767
0.5724 ' / a2 0.3150
. ' -
0.9086 ' / , 0.5226 %6 0. 7211 x3 0.9196
%6
0. 5648 +$ 0. 6566 6/S 0. 8550 Y9 0. 9615 %6
0. 7368 % 0. 7539 X8 0.9565 ' A2 0. 4368 %6
K=
 
MATHEMATI CAL TABLES & UNI TS & SYSTEMS OF WEI GHTS & MEASURES
l - 19
2.626 3. 043 3.263 3.466 3. 718 3.953 4. 192
5.196 5.458 5.724 5.995 6. 269 6.546 6. 831
8.000
4.437
7.117
106.0 106. 7
113.2 113. 9
121.3
132.6 133. 3
148.2 149.0 149.8 150. 5
151.3 152. 1
101.8
108.9
116.1
123.5
131.0
138.7
183.6 184.4 185. 3
209.7 210. 6
237.0 238. 0
52. 0 375.0 376. 1 377.1 376.2 379.3
380.4
54. 0 396.8
397.9 399.0 400.1
371. 7
404.6 405. 7 406.8
411.2 412. 3 413.5 414. 6 415. 7 416.8
418.0
56. 0
419.1 420. 2 421.3 422.4 423. 6 424.7 425.8 426.9 428. 1 429. 2
57. 0 430.3 431. 5 432.6
433.7 434. 9 436. 0 437. 1 436. 3 439.4 440.6
58. 0
441.7 442.9 444.0 445.1 446. 3 447.4 446.6 449.7 450. 9 452. 0
59. 0 453.2 454.3 455.5 456.6
457. 8 459. 0 460. 1 461. 3 462.4
463.6
Average
10
10
10
11
11
11
11
11
11
11
11
11
11
12
Thi s t abl egi ves N3” f romN= 1 to N= 100. Movi ng t he deci mal poi nt two pl aces i n N r equi resmovi ng i t hree places i n body of
tabl e. For exampl e, (7.23)3’ ” 19. 44, (723.)3”= 19, 440, (0.0723)3’2 0.01944, (72. 3)3’2614.8, ( 7,230)3’ =614,800, and
(0. 723)3' 20.6148.
Used i nversel y, hi s abl e gwes M2’3
f romM= 1 to M=l , OOO. For exampl e, (0 6148)z3 =0. 7230.
(conhnued on
N 0
8
9
491.7 492. 9 494.1
602.1 603. 3 604. 6 605.9
614.8 616. 0 617. 3 618.6
627.6 628. 8
686.5 867.8 669. 1 670.4
679.6 680.9 682. 3 683.6
692.9 694.2 695. 5 696.8
706.2 707. 5 708. 8 710.2
719.6 720.9
760.3 761.6
801.7 803. 1
804.5 805. 9
829.7 831. 1 832. 6 834. 0
843.9 845. 3 848. 7 848. 1
858.1 859. 5 860. 9 862. 4
872.4 873.8 875. 2 876. 7
886.8 888. 2 889. 6 891. 1
901.2 902. 7 904. 1 905. 6
915.7 917. 2 918. 6 920. 1
930.3 931. 8 933. 3 934. 7
945.0 946. 5
989.5 991. 0
AND THREE- HALVES POWERS
(to assist in locating the decimal point)
For complete tabl e of three- hal vespowers, see precedi ng. That
tabl e, sed i nversel y,rovi desa compl etetableof twc- thi rdsowers.
N
464.16 1,000,000.0
 
MATHEMATI CAL TABLES & UNI TS 8 SYSTEMS OF WEI GHTS & MEASURES
l - 21
1 ABLE
0.9891 0.9881
0.9699 0.9690 0.9681
0.9251
0.9242
0.9234
0. 9470
0. 9381
0.9066 0.9058 0.9050
0.8985 0.8977
0.8969 0.8961
0.8811
0.8803
1.19 0.8403 0. 8398
0.7782
0. 7628 0.7822 0.7616 0. 7610 0.7605
0.7570 0.7564 0.7559 0.7553
0.7962 0.7955 0.7949
0.7899 0.7893 0.7886
0.7716 0.7710
0.7943
0.7880
0.7819
0.7758
0.7898
0.7639
0.7582
0.7524
0.7468
0.7413
1.36 0.7407 0. 7402 0.7396 0. 7391 0.7386 0.7380 0.7375 0. 7369 0.7364
0.7358
0.7348 0.7342 0. 7337 0. 7331 0.7326 0.7321 0. 7315
0.7310 0.7305
1.37 0.7299 0.7294 0.7289 0. 7283 0.7278 0. 7273 0.7267 0. 7262 0.7257 0.7252
1.38
0.7205 0.7199
1.39 0.7194 0. 7189 0.7184 0. 7179 0.7174 0.7168 0.7163 0. 7158 0.7153
0.7148
1.40
1.41
1.42
1.43
1.44
0.7143
0.7092
0.7042
0.6993
0.6944
0.6897
0.6849
0.6803
0.6757
0.6711
0.6667
0.6623
0.7138
0.7087
0.7037
0.6988
0.6940
0.6892
0.6845
0.6798
0.6752
0.6707
0.6662
0.6618
0.7133
0.7082
0.7032
0.6983
0.6935
0.6954
0.6906
0.6859
0.6812
0.6766
0.8720
0.6676
0.6631
0.8588
0.6553 0.6549 0.6545
Expl anati on of Tabl e of Reci procal s
Thi s t abl e gi ves the values of i / N forval ues of N f rom1 to 10, corr ect o f our f i gures. I nterpol atedal ues may be in
errorby 1 i n the f ourt h i gure. )
To f i nd he reci procal f a number N outsi de the range fr om1 to 10, note that movi ng t he deci mal poi ntany number
of pl aces in ei ther i rect i on n Column N i sequi val ent o movi ng i t he same number of pl aces in the
opposite
di recti on
i n the body of the tabl e.For exampl e, l / 3.217=0.3109, 1/ 3,217=0.0003109, and 1/ 0. 003217=310.9.
( cont i nuedon
TABLE 1. 6- - RECI PROCALS OF NUMBERS(cont i nued)
0 1
Average
- -
0.6396 0.6394 0. 6390 0.6366 0.6362
0.6357 0.6353 0. 6349 0.6345 0. 6341
0.6317 0.6313 0. 6309 0.6305 0. 6301
0.6285 0.6277 0.6274 0.6270
1.63 0.6135 0.6131
0. 6227
0. 6168
1.76 0.5682 0.5679 0.5675
0.5656
0.5624
1.78
1.79
0. 5587 05583 0. 5580 0. 5577 0. 5574 05571 0. 5568 0. 5565 0. 5562
1.80
1.81
1.82
1.83
1.84
0.5525 0.5522
0.5534
0.5504
0.5473
0.5444
0.5414
0.5531
0.5501
0.5470
0.5441
0.5411
1.85
1.86
1.87
1.88
1.89
0. 5035 0.5033
0.5030 0. 5028
2.0
2.1
2.2
2.3
2.4
0.5000
0.4762
0.4545
0.4348
0.4785
0.4255 0. 4237 0. 4219 0.4202 0. 4184
0.4082 0.4065 0.4049
0.4032 0. 4016
0.3774 0. 3759 0.3745 0.3731
0.3636 0. 3623 0. 3610 0.3597
0.3546
0.3425 0.3413
3.0
3.1
3.2
3.3
3.4
0.3226
0.3236
0.3106 0.3096 0.3086
0.2924 0.2915 0.2907 0.2899 0.2890 0.2882
0.2974
0.2865
0.3030
 
1-23
: ont i nue
3.7
0.2703
0.2660 0.2653
3. 6 0.2632 0.2625 0.2618 0. 2611 0.2604 0.2597 0.2591 0. 2584
3. 9 0.2564 0.2558 0.2551 0. 2545 0.2538 0. 2532 0.2525 0. 2519
4.0 0.2500
4.1 0.2439
0.2415 0.2410 0.2404
5.9 0.1695 0.1692
6.0
6.1
6.2
6.3
8.4
0.1667 0.1664 0. 1661 0.1656 0.1656 0. 1653 0.1650 0. 1647 0.1645
0.1639
0.1618
0.1610
6.5
6.6
6.7
6.8
6.9
0.1350 0. 1348
0.1029 0.1028
0.2786
0.2710
0.2639
0.2571
0.2506
0.2445
0.2387
0.2331
0.1980
0.2101
0.2058
0.2016
0.1976
0.1938
0.1901
0.1866
0.1632
0.1706 0.1704 0. 1701
0.1949 0.1946 0. 1942
0.1166
0.1152
0.1139
0.1126
0.1114
0.1083 0. 1082 0. 1081 0.1080 0. 1079 0.1078
0.1072 0. 1071 0. 1070 0.1068 0.1067 0. 1066
0.1060 0. 1059 0. 1058 0.1057 0.1056 0. 1055
0.1045 0. 1044
0.1034 0. 1033
0. 1024 0.1022
 
3 4 6 7
3. 424 31
10. 24
10. 56
10. 87
11. 18
11. 50
11. 81
12. 13
12. 44
10. 27
10. 30
12. 00 12. 03 12. 06
12. 10
4.0
12. 57 12. 60 12. 63 12. 66 12. 69 12. 72 12. 75
12. 79 12. 82
13. 01 13. 04 13.07 13. 10 13.13
4.2 13. 19 13. 23 13. 26 13. 29 13. 32
13. 35 13.38 13. 41 13.45
4.3 13.51
4.4
13. 98 14. 01 14. 04 14.07
10. 34
10. 65
10. 96
11. 28
11. 59
11. 91
12. 22
12. 53
12. 85
13. 16
13. 46
13. 79
14. 11
4. 5 14. 14 14. 17 14. 20 14. 23 14. 26 14. 29
14. 33 14. 36 14.39 14. 42
4.6 14. 45 14. 48 14. 51
14. 55 14. 58
4.7 14. 77 14. 80 14. 83 14. 86
14. 89
15. 05
4.8 15. 08 15. 11 15. 14 15. 17 15. 21 15.24 15. 27
15. 30 15. 33 15.36
4.9 15. 39 15. 43 15. 46 15. 49 15. 52 15.55 15. 58 15. 61
15. 65 15. 68
5. 0 15. 71 15. 74 15. 77 15. 80 15. 83
5.1 16. 02 16. 05 16. 06 16. 12 16. 15
5.2
16. 34 16. 37 16. 40 16. 43 16. 46
5.3 16. 65 16. 68 16. 71 16. 74 16. 78
5.4
Exotanat i onof Tabl e of Ci rcumerences
Thi s t abl e gives the product of % t i mes any number
d
(di ameter) rom1 to 10; i . e., t s a tabl e of mul ti pl es01 r.
Movi ng the deci mal poi nt one pl ace i n Col umn
d
i s equi va entto movi ng i tone place i n the body of the tabl e
Ci rcumerence=ax
 
Average
0 1 2 3 4 5 6 7 6 9 Di f f erence
- 17. 317.28 17. 34 17.37 17. 40 17. 44- 17.47 17. 50- 17.53 17. 56 3
17.59 17. 62 17.66 17. 69 17. 72 17 75 17. 78 17. 81 17. 84 17. 88
5.5
5.7
5.8
5.9
18.54
18. 13 18. 16
18. 44 18. 47
18. 76 18. 79
6.2 19.48
19. 51
6.4 20.11
20. 14
6.7
21.05
19. 23
19. 26
19. 29
19. 54
19. 57
19. 60
20.17 20. 20
21.74 21. 77
19. 07
19. 38
19. 70
20. 01
20. 33
20. 64
20. 95
21. 27
21. 58
21. 90
19. 10
19. 42
19. 73
20. 04
20. 36
20. 67
20. 99
21. 30
21. 99 22. 02 22. 05 22. 09 22.12 22. 15 22. 18
22. 31 22. 34 22. 37 22. 40 22. 43 22. 46 22. 49
21. 61
21. 93
22. 62
22. 93
23. 25
22. 65 22. 68 22. 71 22. 75 22. 78 22. 81
22. 97
23. 00 23. 03 23. 06 23. 09 23. 12
23.28
23.59
23. 75
24. 38
23. 47
23. 50
23. 78
23. 81
25. 23
25. 26
25. 29
25. 32
25. 60 25. 64 25. 67
25. 70
8.2 25.76
26. 14 26. 17
26. 30 26. 33
8.4 26. 39 26. 42 26. 45 26. 48 26. 52 26. 55 26. 58
26. 61 26. 64
26. 92
27. 02 27. 05 27. 08 27. 11 27. 14 27.17 27. 21
27. 24
27. 33
27. 65
27. 96
27. 36 27. 39 27. 43 27. 46 27. 49
27. 68
27. 80
27. 99 28. 02 28. 05 28. 09 28. 12
28. 31 28. 34 28. 37 28. 40 28.43
28. 62 28. 65 28. 68
28. 71
27. 55
27. 87
28. 18
28. 49
28. 81
29. 12
29. 44
27. 52
27. 83
28. 15
28. 46
28. 78
29. 09
29. 41
29. 72
29. 91 29. 94 29. 97
30.00 30. 03
9.6
30. 16 30. 19 30. 22 30. 25 30. 28 30. 32 30. 35
9.7 30. 47 30. 50 30. 54 30. 57 30. 60 30. 63 30. 66
9.8 30. 79 30. 82 30. 85 30. 88 30. 91 30. 94 30. 98
9.9 31.10
31. 13
Average
10. 87 10. 93 10. 99
11. 04 11. 10
11. 46 11. 52 11. 58 11. 64 11. 70
12. 07 12. 13 12. 19 12. 25 12. 32
12. 69
13. 33
13. 99
14. 66
15. 34
17. 35 17.42 17. 50 17.57 17. 65
11. 16 11. 22
11. 76 11. 82
19. 63 19.71 19. 79 19. 87
20. 43
21. 24 21. 32 21. 40 21. 48
22. 06
18. 40
19. 17
19. 95
20. 75
21. 57
22. 40
18. 78
19. 56
23. 24
23. 33
23. 41
23. 50 23. 59 23.67 9
Expl anati on of Tabl e of Areas of Ci rcl es
Movi ng the deci mal poi ntone pl ace i nCol umn d (di ameter) Sequival ent o movi ng i t wo places i n the body of the tabl e.
 
MATHEMATI CAL TABLES & UNI TS 8 SYSTEMS OF WEI GHTS & MEASURES
l - 27
Average
26. 42 26.51 26. 60 26.69 26. 79
28.88
29. 42 29. 51 29. 61 29. 71
30.39
31. 37 31. 47 31. 57 31. 67
32. 27
33. 29
34. 32
35. 36
36. 42
37. 50
38. 59
39. 70
40. 83
41. 97
43. 12
44. 30
45. 48
46. 69
47. 91
49. 14
50. 39
51. 66
52. 94
54. 24
55. 55
56. 88
58. 22
59. 58
32. 37
32. 47
33. 80 33.90 34. 00 34.11
34. 42 34. 52 34. 63 34. 73 34. 84
34. 94 35. 05 34.15
35. 47
36. 53
37. 61
38. 70
39. 82
40. 94
42. 08
43. 24
44. 41
39. 04 39. 15
42. 43
44. 65
45. 84
47. 05
48. 27
49. 51
44. 77
45. 96
47. 17
48. 40
49. 64
50. 90
52. 17
53. 46
54. 76
56. 08
54.89
56.21 56 35 56. 48 56.61
57. 15 57. 28 57.41 57.55
57. 68 57. 82
59. 86 59.99 60. 13
60. 27 60.41 60. 55
36. 21
37. 28
38. 37
39. 48
40. 60
41. 74
42. 89
44. 06
45. 25
46. 45
47. 66
48. 89
50. 14
57. 95
59. 31
60. 68
62. 07
63. 48
64. 90
66. 33
67. 78
60. 96
62. 35 62.49 62. 63 62.77 82. 91
63.05 63 19 63. 33
63. 76 63.90 64. 04 64.18
64. 33
65. 18 65.33 65. 47 65.61 65. 76 65. 90
68. 62 66.77 66. 91 67.06 67. 20 67