1、Designation: D 4612 03Standard Practice forCalculating Thermal Diffusivity of Rocks1This standard is issued under the fixed designation D 4612; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in
2、parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope*1.1 This practice involves calculation of the thermal diffu-sivity from measured values of the mass density, thermalconductivity, and specific heat
3、 at constant pressure. It isapplicable for any materials where these data can be deter-mined. The temperature range covered by this practice is 20 to300C.NOTE 1The diffusivity, as determined by this practice, is intended tobe a volume average value, with the averaging volume being $ 2 3 105m3(20 cm3
4、). This requirement necessitates the use of specimens withvolumes greater than the minimum averaging volume and precludes use offlash methods of measuring thermal diffusivity, such as the laser pulsetechnique.NOTE 2This practice is closely linked to the overall test procedureused in obtaining the pr
5、imary data on density, specific heat, and conduc-tivity. It cannot be used as a “stand alone” practice because the thermaldiffusivity values calculated by this practice are dependent on the natureof the primary data base. The practice furnishes general guidelines butcannot be considered to be all-in
6、clusive.1.2 The practice is intended to apply to isotropic samples;that is, samples in which the thermal transport properties do notdepend on the direction of heat flow. If the thermal conductiv-ity depends on the direction of heat flow, then the diffusivityderived by this practice must be associate
7、d with the samedirection as that utilized in the conductivity measurement.1.3 The thermal conductivity, specific heat, and mass den-sity measurements must be made with specimens that are asnear identical in composition and water content as possible.1.4 The generally inhomogeneous nature of geologic
8、forma-tions precludes the unique specification of a thermal diffusivitycharacterizing an entire rock formation. Geologic media arehighly variable in character, and it is impossible to specify apractice for diffusivity determination that will be suitable forall possible cases. Some of the most import
9、ant limitations arisefrom the following factors:1.4.1 Variable MineralogyIf the mineralogy of the forma-tion under study is highly variable over distances on the sameorder as the size of the sample from which the conductivity,specific heat, and density specimens are cut, then the calculateddiffusivi
10、ty for a given set of specimens will be dependent onthe precise locations from which these specimens were ob-tained.1.4.2 Variable PorosityThe thermal properties of porousrock are highly dependent on the amount and nature of theporosity. A spatially varying porosity introduces problems of anature si
11、milar to those encountered with a spatially varyingcomposition. In addition, the character of the porosity maypreclude complete dehydration by oven drying.1.5 All observed and calculated values shall conform to theguidelines for significant digits and rounding established inPractice D 6026.1.61.7 Th
12、is standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documen
13、ts2.1 ASTM Standards:C 177 Test Method for Steady-State Thermal TransmissionProperties by Means of the Guarded Hot Plate2C 518 Test Method for Steady-State Thermal TransmissionProperties by Means of the Heat Flow Meter2C 642 Test Method for Specific Gravity, Absorption, andVoids in Hardened Concrete
14、3D 3740 Practice for Minimum Requirements for AGenciesEngaged in the Testing and/or Inspection of Soil and Rockas Used in Engineering Design and Construction4D 4611 Test Method for Specific Heat of Rock and Soil4D 6026 Practice for Using Significant Digits in Geotechni-cal Data53. Terminology3.1 Par
15、ameter Definitions:1This practice is under the jurisdiction of ASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.12 on Rock Mechanics.Current edition approved June 10, 2003. Published August 2003. Originallyapproved in 1986. Last previous edition approved in 199
16、6 as D 461286(1996).2Annual Book of ASTM Standards, Vol 04.06.3Annual Book of ASTM Standards, Vol 04.02.4Annual Book of ASTM Standards, Vol 04.08.5Annual Book of ASTM Standards, Vol 04.09.1*A Summary of Changes section appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor
17、 Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.1.1 mass densitythe mass of the sample per unit volumeof sample, r(kg/m3).3.1.2 instantaneous specific heatthe rate of change ofspecimen enthalpy per unit mass, h, with respect to tempera-ture, T, at constant pressure,p, cp5 dh/d
18、T!p3.1.3 thermal conductivitythe constant of proportionality,k, relating the vector heat flux, F expressed in watts persquare metre, to the temperature gradient, T, F =kT.The thermal conductivity may be a function of the direction of F and the temperature, T. The units of k are W/mK.3.1.4 thermal di
19、ffusivitythe thermal diffusivity, a,isaderived parameter. It is related to r, cp, and k by the relation,a5k/rcpThe units of a are m2/s.3.2 Definitions of Terms Specific to This Standard:3.2.1 samplea sample is a large piece of rock from whichthe specimens used in the k, r, and cpmeasurements areobta
20、ined. Usually the samples are obtained in the form of coresfrom a drilling operation.3.2.2 specimensthe specimens are pieces cut from thesample for the k, r, and cpmeasurements. Their sizes andshapes are governed by the applicable ASTM standards listedin 2.1.4. Summary of Practice4.1 The thermal dif
21、fusivity is determined from the equationin 3.1.4. The data for k and cpmust be available over thetemperature range of interest. For density, r, a single measure-ment at room temperature may be used because the density isapproximately constant over the 20 to 300C temperaturerange covered by this prac
22、tice.4.2 The measurements of k, r, and cpare to be performedusing the test methods in Section 6.5. Significance and Use5.1 The thermal diffusivity is a parameter that arises in thesolution of transient heat conduction problems. It generallycharacterizes the rate at which a heat pulse will diffuse th
23、rougha solid material.5.2 The number of parameters required for solution of atransient heat conduction problem depends on both the geom-etry and imposed boundary conditions. In a few special cases,only the thermal diffusivity of the material is required. In mostcases, separate values of k, r, and cp
24、are required in addition toa. This practice provides a consistent set of parameters fornumerical or analytical heat conduction calculations related toheat transport through rocks.5.3 In order to use this practice for determination of thethermal diffusivity, all of the required parameters ( k, r, cp)
25、must be determined under as near identical specimen condi-tions as possible.5.4 The diffusivity determined by this practice can only beused to analyze heat transport in rock under thermal conditionsidentical to those existing for the k, r, and cpmeasurements.NOTE 3Notwithstanding the statements on p
26、recision and bias con-tained in this test method; the precision of this test method is dependenton the competence of the personnel performing it, and the suitability of theequipment and facilities used. Agencies that meet the criteria of PracticeD 3740 are generally considered capable of competent a
27、nd objectivetesting. Users of this test method are cautioned that compliance withPractice D 3740 does not in itself assure reliable testing. Reliable testingdepends on many factors; Practice D 3740 provides a means of evaluatingsome of these factors.6. Procedure6.1 General:6.1.1 Obtain the data for
28、k, r, and cpas a function oftemperature using the appropriate ASTM standard for the giventest as qualified below. If possible, make all measurements withspecimens obtained from the same general location in thesample in order to ensure that the specimens are as nearidentical in composition and morpho
29、logy as possible.6.1.2 To minimize water content variation among speci-mens, vacuum dry all specimens at 105C until mass loss isconstant to 60.5 %.6.2 Parameter Test Procedures:6.2.1 Measure the specimen density in one of the twofollowing ways:6.2.1.1 Determine the mass of the specimen, ms,onananaly
30、tical balance and the volume, Vs, by measurement ofsample dimensions or by water displacement (immersion). Ifthe volume is measured by immersion, the specimen must beencapsulated in a waterproof flexible container of negligiblevolume compared to the specimen volume. Record the density,as follows,r5m
31、s/Vs(1)where:ms= specimen mass, andVs= specimen volume.Also estimate the accuracy of the r determination from theuncertainties associated with the msand Vsmeasurements.6.2.1.2 Measure the specimen bulk specific gravity usingTest Method C 642. In situations where the measurement is tobe made at tempe
32、ratures near or above the boiling point ofwater, a suitable oil working fluid may be substituted for waterin this procedure. Determine the density, r, by multiplying thebulk specific gravity by the density of the working fluid at theimmersion temperature.6.2.2 Measure the specimen specific heat usin
33、g Test MethodD 4611.6.2.3 Measure the specimen conductivity using Test MethodC 518 or Test Method C 177.7. Calculations7.1 GeneralThe following method of calculation is rec-ommended for deriving the temperature dependent diffusivity,a(T), from data from k, r, and cp.NOTE 4The recommended data analys
34、is technique is not intended topreclude the use of other methods of data analysis which may be moresuitable in certain cases. It does provide a method by which a consistentset of temperature dependent parameters may be derived from the primarydata base, and also a method by which the uncertainties i
35、n each parametermay be estimated. The results of the calculations for the temperaturedependent parameters will be in a form which is useful for most thermalD4612032analysis computer programs.7.2 Description of the MethodThe parameter data for anassociated set of specimens will usually be in the form
36、 of tablesgiving the measured parameter value versus the measurementtemperature. Each parameter should be fit to an equation of thefollowing form:gT! 5(n 5 oNcnT 2 To!n(2)where:g = parameter (k, r,or,cp),To= 293 K,T = temperature (K), andN = maximum power used in the fit.7.2.1 The fit shall be perfo
37、rmed using ordinary least squarestechniques.6The value of N should be as small as possible,consistent with obtaining a reasonable fit to the data. The resultof this fit will be a set of coefficients, ( cn), and the estimatedstandard error in the parameter, given by the following equa-tion:sg$(i 5 1M
38、gTi! 2giTi!#2%1/2(3)where:M = number of temperatures at whichg is measured, andgi= measured value of the parameter at temperature Ti.NOTE 5In the case of density, a measurement is usually available onlyat room temperature, To. In this situation, take r(T)=r(To), correspondingto co= r(To), cn= 0 for
39、n 0. The associated error, sr, is the estimatederror for the single measurement.7.3 Calculate the diffusivity from the curve fit relationdetermined in 7.1 and 7.2 as follows:aT! 5 kT!/rT!cpT!#or aT! 5 kT!/rTo!cpT!#7.4 Fit a(T) to an equation of the form of Eq 2, and calculatesafrom (Eq 3).7.5 Estima
40、te the error in a, da, caused by measurementerrors in k, r, and cpfrom the equation,da/a!25 dk/k!21 dr/r!21 dcp/cp!2(4)7.5.1 The relative parameter errors; dk/k, dr/r , and dcp/cp,are determined or estimated, or both, in each of the separateparameter measurements where the appropriate ASTM proce-dur
41、es are used.8. Report8.1 The report shall contain the following information:8.1.1 Data base used for the diffusivity calculation giving k,r, and cpversus the temperatures at which each parameter wasmeasured.8.1.2 The methods used to obtain the data and any devia-tions from ASTM procedures in these m
42、ethods. If one or moreof the parameters was determined from literature values in lieuof direct measurement, then a complete reference should begiven and, in addition, the following information should bequoted directly from the cited references:8.1.2.1 Raw parameter versus temperature data unless the
43、parameter was determined from a recommended curve.8.1.2.2 The estimated relative error in the reported value,dg/g, where g = k, r,orcp, and the method of determining thiserror, if reported.8.1.3 The method used to derive the diffusivity from thedata in 8.1.2.1. If the recommended method in 7.2 to 7.
44、4 is notfollowed, a complete description of the alternate method usedshould be given. In the case where the recommended method isemployed, the following calculated results should be reported:8.1.3.1 The coefficients, cn; n = 0, 1, ., N characterizingthe fit of each parameter as a function of tempera
45、ture, Eq 2, andthe estimated standard error for each fit, sg, from Eq 3.8.1.3.2 The coefficients characterizing a( T) from 7.4 andthe estimated standard error of the fit sa.8.1.3.3 The estimated relative error in a, as found in 7.5.8.1.4 Sample identification and characterization informa-tion.8.1.4.
46、1 Identification of block or core sample from whichthe specimens were cut, including geographic location anddepth from which the sample was obtained.8.1.4.2 Qualitative description of sample mineralogy, mor-phology, isotropy.8.1.4.3 Sample dimensions.8.1.4.4 Dimensions of specimens used in each para
47、metermeasurement and location relative to the sample from whicheach specimen was taken.8.1.4.5 Specimen porosity, if measured, and method ofdetermination.8.1.4.6 Specimen residual saturation, if measured, andmethod of determination.9. Keywords9.1 density; heating tests-specific heat; enthalpy; isotr
48、opiccontent; porosity; rock; temperature tests; thermalanalysis-diffusivity6Beck, J. V., and Arnold, K. J. Parameter Estimation in Engineering andScience, John Wiley, NY, 1977, pp. 234237.D4612033SUMMARY OF CHANGESIn accordance with Committee D18 policy, this section identifies the location of chang
49、es to this standard sincethe last edition (86(1996) that may impact the use of this standard.(1) Added caveat for Practice D 6026to Section 1 and caveatfor Practice D 3740 to Section 5.Added Practices D 3740 and D 6026 to Referenced DocumentsSection.ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such righ
