1、JPY PROYID0器API#27INSTORICAL PURPOSES OULY195243H35331i31H41133111LIBRARYAMERICAN PETROLEUM INSTITUTEAPI RP 27Third EditionSeptember,1952Reissued August,1956RECOMMENDED PRACTICEforDETERMINING PERMEABILITYofPOROUS MEDIAThis publication is distributed as isand is no longer acurrent publication of the
2、American Petroleum Institute.Itis fumnished soiely for historic purposee and some or all ofthe information may be outdated.API MAKES NOWARRANTY OF ANY KIND.EXPRESS OR IMPLED,AND SPECIFICALLY THERE IS NO WARRANTY OFMERCHANTABIUTY OR FITNESS FOR A PARTICULARISSUE.AMERICAN PETROLEUM INSTITUTENew York,N
3、.Y.0Issued byAMERICAN PETROLEUM INSTITUTEDivision of ProductionDallas,TexasPrice:75 CentsCopyright 1956 by the American Petroleum Institute.2American Petroleum InstituteRECOMMENDED PRACTICE FOR DETERMININGPERMEABILITY OF POROUS MEDIATABLE OF CONTENTSPageForewordSection I:Definitions3Section II:Theor
4、y.5Section III:Measurements and Calculations.10Section IV:Summarized Laboratory Procedure.12Section V:Sample Calculations17Appendix A:Addenda.25Appendix B:Permeability References25Appendix C:Contemplated American Standard Unit of Permeability.270NotThis edition supersedes the 2nd edition dated April
5、,1942.Adoptedin May,1935,Standard Procedfor符e品ility of Porousaapr7 D8ar器a0of PorousCOPY PROVIDED FORMISTORICAL PUIRPOSES6器YRecommended Practice for Determination of PermeabilityAPI RECOMMENDED PRACTICE FORDETERMINING PERMEABILITY OF POROUS MEDIAForewordb.The purpose of this recommended practice is t
6、oa.This revised Recommended Practice has beenfacilitate comparisons and coordination of perme-prepared by the Special Project Committee on Per-ability measurements on porous media asmade inmeability.It is published under the auspices of thevarious laboratories by the adoption of uniform no-Central C
7、ommittee on Drilling and Production Prac-tation and dimensionally equivalent units.It is thetice,as were the original*and previously revisedffurther purpose to define the conditions of test andeditions.to point out sources of error commonly encountered,not with the view to standardize the detailed t
8、ech-*Adopted May,1935,after formulation by the Topical Committee on Development and Production Researeh.nique of measurement but rather to insure that re-fAmendments of May and Nov.,1941,ineorporated in a revi-ported values are free from inaccuracies caused bydby the Toplcal Commitee on Production T
9、echfaulty methods and improper conditions of test.SECTION IDEFINITIONSIntroductionsquare centimeter of cross-sectional area under a1.Permeability is a property of a porous mediumpressure or equivalent hydraulic gradient of oneand is a measure of the capacity of the medium toatmosphere(76.0 cm of Hg)
10、per centimeter.“Condi-transmit fluids.The measurement of permeability oftions of viscous fowshall mean simply that theuid smductivi he paricuiar materonserate of flow be sufficiently low to be directlypro-portional to the pressure or hydraulic gradient.Con-quently,permeability represents the recipro
11、cal of thesideration of this definition indicates that the unit ofresistance which the porous medium offers to fluidpermeability(the darcy)as a coefficient of propor-flow.Reference to the relation of the resistance andtionality betweenpertinent,althoughadmittedlyconductance properties of electrical
12、conductors to thearbitrary,physical quantities possesses dimensions.flow of electrical current and of the resistance andSpecificallythe permeability,so defined,has the di-conductance properties of thermal conductors to themensions of length squared(L),or those of an area.flow of heat suggests an ana
13、lagous interpretation ofIt should be emphasized that the permeability co-the phenomena of fluid flow.The permeability of aefficient has these dimensions because it is desiredhomogeneous medium is considered to be the samethat it represent a property or attribute of theeverywhere,although in a hetero
14、geneous medium themedium alone and not of the fluid except asherein-permeability may be anisotropic.after qualified,and that the selection of a definitionand hence of the dimensions has been done through2.The experiments and studies of Darcy1o manychoice.For convenience the following sub-unit mayyea
15、rs ago led to an empirical expression of the rela-be used:tionship among the variables involved in the fowofliquids through porous media.This expression isMillidarey 0.001 darcy.(1)known now as Darcys law.Briefly,Darcys workshowed that the volume rate of flow of a liquid er5.The use of other sub-uni
16、ts such as the centi-unit cross-sectional area of permeable mediumdarey or microdarcy is not recommended becausewasdirectly proportional to the pressure gradient andpractical considerations eliminate the necessity foradditional sub-multiples of the standard unit.Theinversely proportional to the visc
17、osity of the liquidfor a condition of flow which customarily is calledsame statement can be made for multiples of theviscous flow.The coefficient of proportionalityisdarcy.The spelling of the plurat form of the unitthe permeability(see Appendix B for further de-has been standardized and established
18、in the litera-tails).ture as“darcys”and“millidarcys.TerminologyUnit of Permeability6.Symbols.A complete list of symbols,with defi-3.In order to make practical use of the generalnitions as used herein,has been prepared(Table 11).concept that porous media possess the measurableproperty of permeability
19、,an arbitrary standard unit7.Permeability.The definition of the standardmust be defined.For the purpose for which this rec-unit of permeability requires that the porous mediumommended practice is intended,the standard unit ofcontain only one homogeneous,single-phase fluid.permeability shall be the d
20、arey,the definition andAlthough the property of the medium so determineddiscussion of which follow.properly might be termed the specific permeabilityfor practical reasons sanctioned by custom,it shall4.A porous medium has a permeability of onedarcy when a single-phase fluid ofbe called simply permea
21、bility,and shall be denotedone centipoiseby the symbol k.It should be emphasized that by thisviscosity that completely fills the voids of the mediumwill flow through it underconditions of viscous flowdefinition the unqualified term,permeability,becomessolely the property of the porous medium;and the
22、at a rate of one cubic centimeter per second perparticular numerical value of the permeability isAmerlcan Petroleum Instituteconstant and independent of the fluid used in themedium to water when the percentage fuid satura-measurement.It is to be realized,however,that when-tion is 50 per cent oil,40
23、per cent water,and 10 perever certain minerals and fluids are brought in contactcent gas is(millidarcys or darcys).Take note thatand interaction results or material is deposited fromkg(o:o),which is effective permeability to gas,ordi-the fluid,this phenomenon,in effect,produces a newnarily would be
24、expected to equal the permeabilitymedium the permeability of which may differfromand hence could just as well be written k.that of the unaltered medium.This phenomenon in noway vitiates the application of the principles herein10.As more experimental data are obtained,evi-stated(cf.Ref.2,12,and 23).W
25、henever this phe-dence is increasing of the importance of the immedi-nomenon is experienced,the fact should be indicatedate past history in arriving at a particular saturationclearly by appropriate references to both medium andand distribution of fluids in a porous medium onparticular fluid,e.gthe p
26、ermeability of Woodbinewhich it is desired to conduct flow studies.For ex-sand to salt water(fresh water,crude oil,heptane,ample,a particular gas saturation may be arrived atair,nitrogen,as the case may be).bydynamic methods,4capillarypressuremeth-ods,5,i8,29 or by pressure depletion from a gas-satu
27、-8.Effective Permeability.The effective permeabil-rated liquid phase.For each methodthefinal gasity34 of a porous medium is a measure of the con-saturation may be the same,but the distribution ofductance of the medium to one fluid phase of a multi-the gas within the porous medium may be quite dif-ph
28、ase fluid system existing in the medium.Theferent.In some regions of saturation a pronouncedmedium can have a distinct and measurable efectivehysteresis develops in the measurement ofeffectivepermeability to each such fuid phase present.Inpermeability,depending upon the method of changingaddition to
29、 being a function of the porous medium,the saturation.The reproduction within a core of thethe effective permeability to each fluid phase clearlysame condition of saturation and distribution of fluidsis a function of the quantity or percentage saturawhich mayprevail in an underground reservoir oftio
30、n and of the distributiont ofeach phase in theequal percentage saturation is essential to successfulmedium.The effective permeability to a particu-experimental work and interpretation of results;thislar phase has a constant value only for“certainsame condition to be brought about bythe use ofnecessa
31、ryconditions of flowand for a constantmethods and mechanisms which approximate thosepercentage saturation and a unique distributionby which fluid saturation becomes changed in under-the fluid phases present(see Sect.III).The possiblegroundreservoirs by theproduction ofreservoirrange for values of ef
32、fective permeability lies,there-fuids.No specific nomenclature applicable to thisfore,between the limit of zero at some definite per-problem is suggested here,but the suggestion is madecentage of the phase under consideration andthethat when reeporting efective permeability data thepermeability of t
33、he medium.The effective perme-methods used in experimentation be stated clearly.ability to a particular fluid phase at 100 percentsaturation of the medium will be equal to the per-11.Relative Permeability.The relative permeabilmeability(except as pointed out in Par.7).The fluidity of a porous medium
34、 to one fluid phase of a multi-phases of major significance to the petroleum produc.phase fluid system existing in the medium at anytion industry and hence properly the concern of thisdefinite percentage saturation of the fluid phases isrecommended practice are oil,water,and gas.Thedefined as the ra
35、tio of the effective permeability to theamount or saturation of each phase present in apermeability.In accordance with the discussion underporous medium shall be expressed as a percentage ofPar.7,8,and 9,the terminology required is illustratedthe total pore volume.and defined with the following exam
36、ples:9.The effective permeability should beexpressedk。(50.30)in standard units and can be denoted symbolically as.(2)ko,kwo,or kg.If the percentage saturation ofthekr0(50,30)kvarious phases is known,it is suggested that the per-centage saturation of oil and water(always in thisk.(50.30)order of succ
37、ession)be indicated by an appropriatekrW(50,301.(3)designation.For example,o(eo,13)is read:keffective permeability of the medium to oil when thepercentage fluid saturation of the medium is 60 perkg(50,30)cent oil,13 per cent water,and 27 per cent gas(mil-kg(50,30)=.(4)lidarcys or darcys).The gas con
38、centration(27 percent)obviously isderived by difference.Likewise12.As a practical expedient,any effective per-(50.40)is read:The effective permeability of themeability e.g.,k(o,100)can be used as a referenceor base permeability instead of the permeability k,solong as the particular one used is state
39、d clearly.In。招ring onh r8e5gD6rme5.the medium hasreporting relative permeability the effectiveper-2.the upper limit.see Appendis B.referencesmeability also should be reported so that any desiredconversion of relative permeability base can be made.Recommended Practice for Determination of Permeabilit
40、ySECTION IITHEORYSummarized Theory of Permeability Determinationuv13.Darcys law for the viscous flow of fluidsk=一.(9)through permeable media may be stated in generaldpterms asdxB.Vertical flow:一Pg(5)dzwherein:s洲-2：，=1(10）dss=distance along the direction of flow.(a)Free downward flow(see Fig.1):Ve=vo
41、lume flux(rate of flow)across a unitarea of the porous medium in unit time.dp=0.z vertical coordinate directed downward.ds(11)p=the density of the fluid.本V=一pg(12)g acceleration of gravity.dpAVk=-(13)=pressure gradient along s at the point todswhich v.refers.Pgviscosity of the fluid.k permeability o
42、f the medium.Take note thatVa三.(6)Awherein:Q=volume rate of flow.FIG.1A average cross-sectional area perpendicularto lines of flow.See B(a)14.The convention adopted here and that which is(b)Downward flow with a driving head“h”(seethe basis for placing the minus sign in front of theFg.2):right side o
43、f Equation(5)is that v.should be positiveif the fluid is flowing toward increasing values of thedppghcoordinate s(see Par.18).88.(14)LLiquidskCh15.Special Cases for Steady State Flow of Incom-L五+1三一(15)pressible Liquids.Equation(5)may be reduced tosimpler forms under special conditions of flow.SomeA
44、Vof the more important of these are as follows.k=.(16)(NOTE:The absolute value of de/ds as a de-+1rivative always is used together with the defini-L length of flow column.tion of s as given in Par.18 and Table 11 todetermine the algebraic sign,plus or minus,inequations.)A.Horizontal flow:dz8洲X:，,=0.(7)dsk dp=-(8)FIG.2adxSee B(b)