Geostatistical approaches on the thermal conductivities of rocks

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rocks Byoung Ohan Shim, Jeongmin Park, Hyoung Chan Kim, Youngmin Lee

1 H: Workshop Geothermal Studies: Instruments, Measurements, and Interpretation Geostatistical approaches on the thermal conductivities of rocks Byoung Ohan Shim, Jeongmin Park, Hyoung Chan Kim, Youngmin Lee Korea Institute of Geoscience and Mineral Resources, Republic of Korea,

2 Objective and background Interpretation of the measured thermal properties of rocks in KIGAM geothermal D/B system Statistical investigation and geostatistical analysis of the thermal conductivity of rocks Demands of thermal conductivity data have been increased from geothermal heat pump industries

3 From geostatistical analysis on the thermal conductivity of rocks Characterization of the spatial structure of collected data To increase the reliability of estimated data Generation of the best thermal conductivity distribution maps

4 Geological map of the Rep. of Korea

5 Measurements of rock properties Thermal diffusivity density, porosity, specific heat, thermal diffusivity, thermal conductivity (dry, saturated): 560 specimens Density

6 Principle of flash method (LFA 447) λ = αρc p λ α ρ Cp : Thermal diffusivity : Thermal conductivity : Density : Specific heat

Thermal conductivity distribution of total samples 5645 44600 tm5y 39974 Saturated Thermal conductivity below.50.5-3.50 3.5-4.50 4.5-8.

7 Thermal conductivity distribution of total samples tm5y Saturated Thermal conductivity below (max) tm5x Total : 560 ea Igneous rocks: 647 ea Metamorphic rocks: 494 ea Sedimentary rocks: 9 ea Volcanic rocks: 8 statistics minimum maximum Mean (W/m-K) SD Variance Skewness Kurtosis on Transformed Log Transformed

8 relationships between property variables

9 Thermal conductivity ranges of igneous rocks (o. of data: 647) granite diorite feldspar porphyr y quartz porphyr y felsite granite porphyr y acidic dike syenite silicate rock basic dike rock felsoph yre felsic dike gabbro anortho site quartz halloysi te Minimum Maximum Mean

10 Thermal conductivity ranges of metamorphic rock (o. of data: 494) gneiss schist phyllite quartzite h o rn fe ls quartz schist am phibolite andesitic porphyry Minium Maximum M ean dolom ite 3

11 Thermal conductivity ranges of sedimentary rocks (o. of data: 9) sandstone lim estone breccia m udstone silts to n e conglom erat e 8 shale sandic rock chert Minimum Maximum Mean

12 Thermal conductivity ranges of volcanic rocks (o. of data: 8) andesite tuff rhyolite basalt trachyte Minimum M aximum M ean

General statistical analysis on thermal conductivity of granite 4544.9 44078. uym_y 4099.06 Saturated Thermal conductivity below.50.5-3.50 3.5-4.50 4.5-7.

13 General statistical analysis on thermal conductivity of granite uym_y Saturated Thermal conductivity below (max) utm_x statistics minimum maximum mean SD on Transformed Transformed

14 Characterization of spatial patterns: Seimvariogram Measure of: average dissimilarity between observations as a function of separation distance + direction (h) γ(h) = [ ρ m (u α ) ρ m (u α + (h) α = h)] (stationary case)

15 Semivariogram analysis on the saturated thermal conductivity of granite rocks Semivariance Saturated Thermal conductivity Separation Distance (h) Actual thermal conductivity (W/m-K) Estimated thermal conductivity (W/m-K) Variogram model type ugget variance (Co) Regression coefficient = (SE = 0.065, r =0.98, y intercept = 0.9, SE Structural variance Sill (Co+C) Range (A) Spherical

16 kriging (BLUE) of the thermal conductivity of granite rocks with semivariogram model

General statistical analysis Gneiss 467789 454377 Saturated Thermal

0 (max) Statistics on Transformed Transformed 397555 356 356 38443

17 General statistical analysis Gneiss Saturated Thermal conductivity (W/m-K) uym_y below (max) Statistics on Transformed Transformed minimum utm_x maximum mean SD

18 Semivariogram analysis on the saturated thermal conductivity of gneiss 8 Semivariance Saturated Thermal conductivity Exponential model (Co = ; Co + C = ; Ao = ; r = 0.04; RSS = 6.35E-03) Separation Distance (h) Actua thermal conductivity (W/m-K) Estimated thermal conductivity (W/m-K) Variogram model type ugget variance (Co) Regression coefficient = (SE = 0.6, r =0.5, y intercept = 0.86, SE Structural variance Sill (Co+C) Range (A) Exponential

19 kriging of the thermal conductivity of gneiss rocks with semivariogram model

20 Semivariogram analysis on the saturated thermal conductivity of total sampled rocks 0.0 Saturated Thermal conductivity 8 Semivariance Actual tthermal conductivity Separation Distance (h) Estimated thermal conductivity Variogram model type Exponential ugget variance (Co) 0.0 Regression coefficient =.00 (SE = 0.04, r =0.69, y intercept = 0.08, SE Structural variance Sill (Co+C) Range (A) 6000

21 Thermal conductivity distribution map of total rocks by kriging

22 Thermal conductivity distribution maps Granite Gneiss Total

23 Statistical equations for cross validation tests * ) ( ) ( k x Z x Z RE σ = 0 ] ) ( ) ( [ * = = i i k x Z x Z MRE σ = = i i MRE RE VRE ) ( SDRE = VRE MSE SRMSE = = = i i k MKV ) ( σ = = = i MKV ME Error VE ) (

24 Cross validation test results statistics granite gneiss total rock ME MSE SRMSE MKV MRE VE VRE SDRE

25 Conclusions Histograms of the thermal conductivity of granite, gneiss and total rocks show lognormal distributions. Most of the porosity of rock specimens are less than 0%, and shows weak relationship with thermal conductivities. The semivariograms of the thermal conductivities of granite, gneiss and total rocks shows weak stationarity. In cross validation tests of estimated thermal conductivities, each scatter plot and statistics show similar agreements between actual and estimated values.

CEE 437 Lecture 10 Rock Classification. Thomas Doe

CEE 437 Lecture 10 Rock Classification Thomas Doe Igneous Origins Intrusive Batholithic or plutonic: phaneritic Dikes or sills that chill rapidly: aphanitic Extrusive deposition as melt (lava) pyroclastic