Models for Thermal Transport Properties of Oil Shale Carl D. Palmer, Earl Mattson, Hai Huang Idaho National Laboratory www.inl.gov 30 th Oil Shale Symposium October 18-22, 2010
Objective: To develop models of the thermal transport properties of oil shale as a function of temperature and grade. Approach: • Combine heat capacity data of oil shale components (minerals, kerogen, coke) • Develop theoretical and empirical approaches for estimating thermal conductivity values as a function of temperature and grade • Compare the thermal conductivity of oil shale with models of binary mixtures
Heat Capacity of Oil Shale • Applied law of additivity of heat capacities: • Heat capacity is a weighted sum of the heat capacities of the minerals and organic fractions in the formation. C p (oil shale) = f(minerals) C p (minerals) + f(kerogen) C p (kerogen) + f(char)C p (Char) • f(kerogen) and f(char) are changing during retorting. This change can simulated with first-order reaction of kerogen and a proportionate increase in char.
Heat Capacity of Oil Shale
Thermal Conductivity -- Theory For insulators above the Debye temperature: 3 4 x k 2 k T x e π ⎛ ⎛ ⎞ ⎞ / T θ D B B dx λ λ = ∫ τ τ ⎜ ⎜ ⎟ ⎟ total 2 2 2 v h 0 π ( ) x e 1 ⎝ ⎝ ⎠ ⎠ − For Umklapp (U) processes: 1 B / T 2 A Te − θ = ω D τ U Therefore: 5 ( B 1 ) x x e + / T θ D 3 T dx λ λ = ξ ξ ∫ 2 0 ( ) x e 1 θ − D
Thermal Conductivity -- Theory Simplify by using the approximations: ( B 1 ) x 2 e 1 ( B 1 ) x (( B 1 ) / ) x 2 + ≈ + + + + x 2 e 1 x ( x / ) 2 − ≈ − ≈ + Substitute the approximations: 3 2 x ( 1 ( B 1 ) x (( B 1 ) ) ) x + + + + + + D T / θ 3 T dx λ λ = ξ ξ ∫ 2 0 ( ) 2 1 x x / 4 θ + + + + D Integrate and Simplify: 1 θ ξ θ ξ D λ = = = = 8 16 T a bT θ + + + + D
Horizontal Thermal Conductivity of Oil Shale 1 3.5 λ = h a bT cG 3 + + + + 2.5 2 r 2 = 0.939 1.5 1 0.5 350 450 Temperature (K) 0 550 20 650 40 60 750 80 850 Grade (gal/ton) 100 Data from: Wang et al. (1979), Pratt and O-Brien (1975), Tihen et al. (1968), Nottenburg et al. (1978), Sladek (1970), Dindi et al. (1989), Wang et al. (1979b), Clauser and Huenges (1995)
Thermal Conductivity -- Theory Ratio of Coefficients: a θ D = b 2 We can there estimate an effective Debye temperature for oil shale: Oil shale 110K Calcite 261K Deines (2004) Crude Oil 98K Singh et al. (2006)
Vertical Thermal Conductivity of Oil Shale 1 3.5 λ = 3 v a bT cG + + + + 2.5 2 1.5 r 2 = 0.911 1 0.5 850 750650550450350 0 20 Temperature (K) 40 60 80 Grade (gal/ton) 100 Data from: Wang et al. (1979), Pratt and O-Brien (1975), Tihen et al. (1968), Nottenburg et al. (1978), Sladek (1970), Dindi et al. (1989), Wang et al. (1979b), Clauser and Huenges (1995)
Anisotropy of Thermal Conductivity of Oil Shale 1.3 1.25 1.2 Anisotropy 1.15 1.1 1.05 1 0.95 80 700 70 60 600 50 500 40 G (gal/ton) 30 400 T(K) 20 300 10 0 200
Fischer Assay versus Density 80 ¡ 291.118 a ρ FA min 291.118 a = − ρ sh ¡ 60 Fischer Assay (gpt) α a = ρ ρ − ρ − min ker 40 r 2 = 0.9496 20 min = 2.676 ±0.039 g/cm 3 r a = 0.350 ±0.020 cm 3 /g 0 1.5 1.7 1.9 2.1 2.3 2.5 2.7 Density (g/cm 3 ) Data from Pratt and O’Brien (1975)
Conversion Factor and Kerogen Density Mass of carbon in oil 0 68 (Palmer & Mattson) . α = ≈ M Mass of carbon in kerogen f Volume of Oil ρ C ,ker ker α α = = α α = = M f Volume of kerogen ρ C oil , oil α a = ρ ρ − ρ ρ min ker Substitute and solve for ρ ker : a ρ min ρ = ker f 1 ⎛ ⎛ ⎞⎛ ⎞ ⎛ ⎞ + ⎞ C ,ker a α ⎜ ⎜ ⎟ ⎟⎜ ⎜ ⎟ ⎟ M ⎜ ⎜ ⎟ ⎟⎝ f ρ ⎝ ⎠ ⎠ ⎝ ⎝ ⎠ ⎠ C oil , oil
Conversion Factor and Kerogen Density f 3 0 900 . 0 012 g/cm . C ,ker 0 941 . ρ = = ± ± = oil f C oil , (based on 4667 measurements, USGS 2009) 3 0.882 g/cm α = 0.693 ρ = ker For Type II Kerogens: Sample Maturity Specific Gravity End of Diagenesis 0.814 Onset of Oil Window 0.995 Vandenbrouke and Largeau (2007)
Kerogen Volume Fraction 1.0 Kerogen Volume Fraction = 0.5 0.8 a 0.6 0.7 0.6 0.8 0.4 V FAa ρ 0.2 ker min = V ( FA 291 118 . a ) α + sh 0.0 0 20 40 60 80 100 Fischer Assay (gpt)
Composition/Structure Models Parallel Model v v λ λ = = λ λ + + λ Flow parallel to layers avg 1 1 2 2 1 Series Model λ = avg v / v / λ λ + λ λ Flow across to layers 1 1 2 2 Maxwell-Eucken 1 3 λ v v 1 λ λ + λ λ Low conductivity dispersed in 1 1 2 2 2 λ λ + λ λ 1 2 λ = continuous high conductivity material avg 3 λ v v 1 + 1 2 2 λ λ + λ λ 1 2 Maxwell-Eucken 2 3 λ v v 2 High conductivity dispersed in λ λ + λ λ 2 2 1 1 2 λ λ + λ λ 2 1 continuous low conductivity material λ = avg 3 λ v v 2 + 2 1 2 λ λ + λ λ Equivalent Media Theory 2 1 λ λ − − λ λ λ − − λ Random distribution of components 1 avg 2 avg v v 0 + + = = 1 2 2 2 λ λ + + λ λ λ + + λ 1 avg 2 avg
Composition/Structure Models 1.0 Parallel Maxwell-Eucken 1 0.8 Maxwell-Eucken 2 Series Effective Media minerals 0.6 Theory avg / l 0.4 l 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 Volume Fraction of Kerogen
Comparison of Fitted and Theoretical Models Parallel to Bedding Perpendicular to Bedding 1.0 1.0 298 K 298 K 0.8 0.8 Fitted Surface Fitted Surface Parallel to bedding minerals minerals Perpendicular to bedding 0.6 0.6 avg / l avg / l 0.4 0.4 l l 0.2 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Volume Fraction of Kerogen Volume Fraction of Kerogen
Summary For oil shale, we have • Developed a simple model for estimating heat capacity, • Demonstrated a theoretical basis for the temperature dependence of thermal conductivity, • Developed a simple equation for estimating thermal conductivity and thermal anisotropy as a function of temperature and grade, • Demonstrated that that the thermal conductivity does not follow simple layered models of minerals and kerogen.
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