1、Designation: D 4612 08Standard 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 () 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 prima
5、ry 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-inclu
6、sive.1.2 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are mathematicalconversions to inch-pound units that are provided for informa-tion only and are not considered standard.1.3 The practice is intended to apply to isotropic samples;that is, sample
7、s 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 associated with the samedirection as that utilized in the conductivity measurement.1.4 The
8、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.1.5 The generally inhomogeneous nature of geologic forma-tions precludes the unique specification of a thermal diffusivitycharacteriz
9、ing 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 important limitations arisefrom the following factors:1.5.1 Variable MineralogyIf the mi
10、neralogy 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 calculateddiffusivity for a given set of specimens will be dependent onthe precise locations from whi
11、ch these specimens were ob-tained.1.5.2 Variable PorosityThe thermal properties of porousrock are highly dependent on the amount and nature of theporosity. A spatially varying porosity introduces problems of anature similar to those encountered with a spatially varyingcomposition. In addition, the c
12、haracter of the porosity maypreclude complete dehydration by oven drying.1.6 All observed and calculated values shall conform to theguidelines for significant digits and rounding established inPractice D 6026.1.7 This standard does not purport to address all of thesafety concerns, if any, associated
13、 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 Documents2.1 ASTM Standards:2C 177 Test Method for Steady-State Heat Flux Measure-ments and
14、Thermal Transmission Properties by Means ofthe Guarded-Hot-Plate ApparatusC 518 Test Method for Steady-State Thermal TransmissionProperties by Means of the Heat Flow Meter ApparatusC 642 Test Method for Density, Absorption, and Voids inHardened ConcreteD 3740 Practice for Minimum Requirements for Ag
15、enciesEngaged in Testing and/or Inspection of Soil and Rock asUsed in Engineering Design and ConstructionD 4611 Test Method for Specific Heat of Rock and Soil1This practice is under the jurisdiction of ASTM Committee D18 on Soil andRock and is the direct responsibility of Subcommittee D18.12 on Rock
16、 Mechanics.Current edition approved July 1, 2008. Published July 2008. Originally approvedin 1986. Last previous edition approved in 2003 as D 4612 03.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStan
17、dards volume information, refer to the standards Document Summary page onthe ASTM website.1*A Summary of Changes section appears at the end of this standard.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.D 6026 Practice for Using Sig
18、nificant Digits in Geotechni-cal Data3. Terminology3.1 Parameter Definitions: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,
19、cp5 dh/dT!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 th
20、ermal diffusivitythe 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
21、 areobtained. 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 the
22、rmal diffusivity 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 t
23、his practice.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 di
24、ffuse througha 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
25、, and cpare 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
26、, r, cp)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 stateme
27、nts on precision 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 com
28、petent and 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 d
29、ata for k, r, and cpas a function oftemperature using the appropriateASTM 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
30、 morphology 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,on
31、ananalytical 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 foll
32、ows,r5ms/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 a
33、t temperatures 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 he
34、at using 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
35、 analysis technique is not intended topreclude the use of other methods of data analysis which may be moreD4612082suitable 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
36、uncertainties in each parametermay be estimated. The results of the calculations for the temperaturedependent parameters will be in a form which is useful for most thermalanalysis computer programs.7.2 Description of the MethodThe parameter data for anassociated set of specimens will usually be in t
37、he form 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 b
38、e performed using ordinary least squarestechniques.3The value of Nshould 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
39、 5 1MgTi! 2giTi!#21/2(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
40、for 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 Es
41、timate 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
42、-dures 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 the
43、se methods. 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
44、 theparameter 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 t
45、o 7.4 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 tem
46、perature, 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.
47、1.4.1 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
48、parametermeasurement 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; i
49、sotropiccontent; porosity; rock; temperature tests; thermalanalysis-diffusivity3Beck, J. V., and Arnold, K. J. Parameter Estimation in Engineering andScience, John Wiley, NY, 1977, pp. 234237.D4612083SUMMARY OF CHANGESCommittee D18 has identified the location of selected changes to this standard since the last issue(D 4612 03) that may impact the use of this standard. (Approved July 1, 2008.)(1) Inserted Section 1.2ASTM International takes no position respecting the validity of any patent rights asserted in connection with any item
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