Models for Thermal Transport Properties of Oil Shale

Transcription

1 Models for Thermal Transport Properties of Oil Shale Carl D. Palmer, Earl Mattson, Hai Huang Idaho National Laboratory 30 th Oil Shale Symposium October 18-, 010

2 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

3 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.

4 Heat Capacity of Oil Shale

5 Thermal Conductivity -- Theory For insulators above the Debye temperature: 3 4 D / x k T B π kbt θ x e τ 0 total π v h e 1 λ = ( x ) dx For Umklapp (U) processes: Therefore: τ 1 B / T U λ = ξt = 3 Aω Te θ D 5 ( 1) D / B+ x θ T x e 0 θ D ( x e 1) dx

6 Thermal Conductivity -- Theory Simplify by using the approximations: e 1+ ( B+ 1) x+ (( B+ 1) x/ ) ( B+ 1) x x e 1 x+ ( x/ ) Substitute the approximations: λ = ξt 3 θ 3 / x ( 1+ ( B+ 1) x+ (( B+ 1) x) ) D T Integrate and Simplify: ( 1+ x+ x / 4) 0 θ D θξ D 1 λ = = 8θ D + 16T a+ bt dx

7 Horizontal Thermal Conductivity of Oil Shale Grade (gal/ton) Temperature (K) λ h = + + a bt cg r = 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)

8 Thermal Conductivity -- Theory Ratio of Coefficients: a b = θ D We can there estimate an effective Debye temperature for oil shale: Oil shale 110K Calcite 61K Deines (004) Crude Oil 98K Singh et al. (006)

9 Vertical Thermal Conductivity of Oil Shale Grade (gal/ton) Temperature (K) λ v = + + a bt cg r = 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)

10 Anisotropy of Thermal Conductivity of Oil Shale Anisotropy G (gal/ton) T(K)

11 Fischer Assay versus Density Fischer Assay (gpt) FA r = r min =.676 ±0.039 g/cm 3 a = ±0.00 cm 3 /g ρ min = ρ Density (g/cm 3 ) sh a a α a = ρ ρ min ker Data from Pratt and O Brien (1975)

12 Conversion Factor and Kerogen Density Mass of carbon in oil α M = Mass of carbon in kerogen α f ρ C,ker ker = αm = fc, oil ρoil a = ρ min 068. (Palmer & Mattson) Volume of Oil Volume of kerogen α ρ ker Substitute and solve for ρ ker : ρ ker = α M aρ min fc,ker 1 f + Coil, ρoil a

13 Conversion Factor and Kerogen Density f f C,ker C, oil = ρ = ± g/cm oil (based on 4667 measurements, USGS 009) 3 3 ρ ker = 0.88 g/cm α = For Type II Kerogens: Sample Maturity Specific Gravity End of Diagenesis Onset of Oil Window Vandenbrouke and Largeau (007)

14 Kerogen Volume Fraction 1.0 Kerogen Volume Fraction sh Fischer Assay (gpt) a = Vker FAaρmin = V α FA a ( )

15 Composition/Structure Models Parallel Model Flow parallel to layers Series Model Flow across to layers Maxwell-Eucken 1 Low conductivity dispersed in continuous high conductivity material Maxwell-Eucken High conductivity dispersed in continuous low conductivity material Equivalent Media Theory λavg = v1λ1+ vλ λ avg = λ λ v avg avg 1 / λ + v / λ 1 1 3λ1 v1λ1+ vλ λ1+ λ = 3λ1 v1+ v λ1+ λ 3λ v + v1 1 + = 3λ v + v1 λ + λ λ λ λ λ 1 avg Random distribution of components v 1 1 avg 1 1 λ λ λ λavg + v = λ + λ λ + λ avg 0

16 Composition/Structure Models l avg / l minerals Parallel Maxwell-Eucken 1 Maxwell-Eucken Series Effective Media Theory Volume Fraction of Kerogen

17 Comparison of Fitted and Theoretical Models Parallel to Bedding Perpendicular to Bedding K K l avg / l minerals Fitted Surface Parallel to bedding l avg / l minerals Fitted Surface Perpendicular to bedding Volume Fraction of Kerogen Volume Fraction of Kerogen

18 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.