An empirical relationship between thermal conductivity and elastic wave velocities in sandstone

Zamora, Maria; Vo-Thanh, Dung; Bienfait, G.; Poirier, Jean

doi:10.1029/92gl02460

Cited by 24 publications

(11 citation statements)

References 9 publications

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“…Since no clear systematic difference for velocities measured in parallel and perpendicular directions was found, all acoustic data are used for the correlation. The resulting linear relation between velocities and thermal conductivity is in accordance with similar empirical relations for different rocks (Schoen 1996;Zamora et al 1993). In the present case, this is mainly due to a similar dependence of both parameters on porosity, which is the dominant influencing factor.…”

Section: S U P P L E M E N T a R Y P E T Ro P H Y S I C A L P Ro P E supporting

confidence: 85%

Physical properties of rocks from the upper part of the Yaxcopoil‐1 drill hole, Chicxulub crater

Popov

Romushkevich

Bayuk

et al. 2004

Meteorit & Planetary Scien

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Abstract-Physical properties were determined in a first step on post-impact tertiary limestones from the depth interval of 404-666 m of the Yaxcopoil-1 (Yax-1) scientific well, drilled in the Chicxulub impact crater (Mexico). Thermal conductivity, thermal diffusivity, density, and porosity were measured on 120 dry and water-saturated rocks with a core sampling interval of 2-2.5 m. Nondestructive, non-contact optical scanning technology was used for thermal property measurements including thermal anisotropy and inhomogeneity. Supplementary petrophysical properties (acoustic velocities, formation resisitivity factor, internal surface, and hydraulic permeability) were determined on a selected subgroup of representative samples to derive correlations with the densely measured parameters, establishing estimated depth logs to provide calibration values for the interpretation of geophysical data. Significant short-and long-scale variations of porosity (1-37%) turned out to be the dominant factor influencing thermal, acoustic, and hydraulic properties of this post impact limestone formation. Correspondingly, large variations of thermal conductivity, thermal diffusivity, acoustic velocities, and hydraulic permeability were found. These variations of physical properties allow us to subdivide the formation into several zones. A combination of experimental data on thermal conductivity for dry and water-saturated rocks and a theoretical model of effective thermal conductivity for heterogeneous media have been used to calculate thermal conductivity of mineral skeleton and pore aspect ratio for every core under study. The results on thermal parameters are the necessary basis for the determination of heat flow density, demonstrating the necessity of dense sampling in the case of inhomogeneous rock formations.

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Section: S U P P L E M E N T a R Y P E T Ro P H Y S I C A L P Ro P E supporting

confidence: 85%

Physical properties of rocks from the upper part of the Yaxcopoil‐1 drill hole, Chicxulub crater

Popov

Romushkevich

Bayuk

et al. 2004

Meteorit & Planetary Scien

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“…This indicates that at the applied boundary conditions, the solid heat transfer cross section is equal to that of the grain contacts ( Figure 10). This justifies the applicability of using material stiffness for prediction of thermal conductivity as was proposed by, e.g., Horai and Simmons (1969), Zamora et al (1993) (2006), Gegenhuber andSchoen (2012), andPimienta et al (2014), but with the use of empirical relations or empirical parameters. The weak grain contacts found in outliers of Fontainebleau samples (Figures 8a, 9a, and 10), illustrate the discrepancy between the boundary conditions at which the thermal conductivity is measured, respectively, modeled.…”

Section: Discussionmentioning

confidence: 72%

“…However, because the sizes of pores and solids are typically smaller than a representative volume, emphasis should be on describing the cross sections between single pores and single solids, respectively. Relating physical properties such as electrical resistivity (e.g., Revil, 2000) and elastic wave velocity (e.g., Horai and Simmons, 1969;Zamora et al, 1993;Kazatchenko et al, 2006) to thermal conductivity indirectly relates the cross sections between single pores and single solids, respectively. Because the thermal conductivity of the solid constituents found in most sandstones is typically several orders of magnitude larger than that of the saturating fluid, which for most practical applications is water, the cross section governing heat transfer is presumably that of the solid and this should hence be quantified.…”

Section: Introductionmentioning

confidence: 99%

“…We introduce Biot's coefficient (Biot, 1941) derived from mineralogy, bulk density, and elastic wave velocities as a measure of the solid heat transfer cross section, so we follow the conceptual idea of relating material stiffness to thermal conductivity (Horai and Simmons, 1969;Zamora et al, 1993;Kazatchenko et al, 2006;Gegenhuber and Schoen, 2012;Pimienta et al, 2014). As a measure of the cross section governing heat transfer through the pore space, we introduce a geometric factor modeled from porosity according to Mortensen et al (1998), quantifying the proportion of the pore space that is open for fluid flow in a given direction and we assumed it to be identical to the pore space open for heat transfer.…”

Section: Introductionmentioning

confidence: 99%

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Thermal conductivity of sandstones from Biot’s coefficient

et al. 2018

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Thermal conductivity of rocks is typically measured on core samples and cannot be directly measured from logs. We have developed a method to estimate thermal conductivity from logging data, where the key parameter is rock elasticity. This will be relevant for the subsurface industry. Present models for thermal conductivity are typically based primarily on porosity and are limited by inherent constraints and inadequate characterization of the rock texture and can therefore be inaccurate. Provided known or estimated mineralogy, we have developed a theoretical model for prediction of thermal conductivity with application to sandstones. Input parameters are derived from standard logging campaigns through conventional log interpretation. The model is formulated from a simplified rock cube enclosed in a unit volume, where a 1D heat flow passes through constituents in three parallel heat paths: solid, fluid, and solid-fluid in series. The cross section of each path perpendicular to the heat flow represents the rock texture: (1) The cross section with heat transfer through the solid alone is limited by grain contacts, and it is equal to the area governing the material stiffness and quantified through Biot's coefficient. (2) The cross section with heat transfer through the fluid alone is equal to the area governing fluid flow in the same direction and quantified by a factor analogous to Kozeny's factor for permeability. (3) The residual cross section involves the residual constituents in the solid-fluid heat path. By using laboratory data for outcrop sandstones and well-log data from a Triassic sandstone formation in Denmark, we compared measured thermal conductivity with our model predictions as well as to the more conventional porosity-based geometric mean. For outcrop material, we find good agreement with model predictions from our work and with the geometric mean, whereas when using well-log data, our model predictions indicate better agreement.

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“…This consistency between inclusion-based approximations and poroelasticity is a desirable property that is not possessed by all inclusion-based approximations. Furthermore, this connection allows poroelastic behaviour to be related to other physical properties that can be described in terms of inclusion-based formulations, such as dielectric permittivity (Endres & Knight 1991) or thermal conductivity (Zamora, Cattin & Bienfait 1994).…”

Section: Discussionmentioning

confidence: 99%

Geometrical models for poroelastic behaviour

Endres

1997

Geophysical Journal International

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S U M M A R YPoroelasticity implicitly incorporates pore structure information through the use of empirically determined macroscopic parameters; hence, quantitative analysis of pore geometry effects on poroelastic behaviour cannot be performed. Analogues for poro-. elastic parameters with explicit dependence on pore structure are derived here by using an inclusion-based model where inclusions represent individual pores. The inclusionbased formulation used in this paper permits uniform pore fluid pressure throughout the pore space, a requirement of poroelasticity. When specific inclusion-based approximations resulting from different descriptions of inclusion interactions were considered, it was found that the analogue quantities obtained from the dilute volumetric average, Kuster-Toksoz and equivalent inclusion-average stress approximations replicated the relationships between poroelastic parameters predicted by poroelasticity. This equivalence implies that pore geometry information can be consistently incorporated into poroelastic parameters with an inclusion-based model when one of these approximations is used.This connection is used to examine pore geometry effects on poroelastic behaviour by considering a simple model with identically shaped pores. The results of this modelling study show that variations in pore shape significantly affect poroelastic parameters and that the nature of these effects is controlled by the specified applied stress-strain and fluid pressure conditions. The following observations were made about specific poroelastic quantities. The Skempton ratio is relatively insensitive to porosities below 0.1. Its minimum value for a given solid matrix, pore fluid and total porosity level is obtained when all pores are spherical; this value can be significantly greater than the theoretical lower limit of zero. Specific storage terms increase by several orders of magnitude as pores become more crack-like. The difference between the traditional definition of specific storage and that proposed by Green & Wang ( 1990) for 'normal' aquifer conditions grows as the pore aspect ratio decreases.

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An empirical relationship between thermal conductivity and elastic wave velocities in sandstone

Cited by 24 publications

References 9 publications

Physical properties of rocks from the upper part of the Yaxcopoil‐1 drill hole, Chicxulub crater

Physical properties of rocks from the upper part of the Yaxcopoil‐1 drill hole, Chicxulub crater

Thermal conductivity of sandstones from Biot’s coefficient

Geometrical models for poroelastic behaviour

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