Thermal Conductivity of Standard Sands II. Saturated Conditions

Abstract

A non-stationary thermal probe technique was used to measure the thermal conductivity of three saturated standard sands (Ottawa sand C-109, Ottawa sand C-190, and Toyoura sand) in a range of soil porosities (n) from 0.32 to 0.42, and temperatures (T ) from 25 • C to 70 • C. The sand thermal conductivities at full saturation (λ sat ) increased with decreasing n (increasing compaction, 1 − n). In addition, a declining λ sat (T ) n=const trend was observed. The peak λ sat values and highest decreasing rate of λ sat with T were observed at the heaviest compaction and lowest tested T . This trend gradually diminished with increasing T and expanding volume of water (larger n) due to the markedly lower ability of water to conduct heat than quartz. A series-parallel model, containing three parallel paths of heat flow (through continuous solids, continuous fluid, and solids plus fluid in series), was successfully applied to predicted λ dry and λ sat data. The model by de Vries, with new fitted grain shape values, also closely followed measured λ sat data. The corresponding square root of the relative mean squared errors varied from 2.9 % to 3.4 % for C-109, from 1.9 % to 3.0 % for C-190, and from 2.3 % to 2.4 % for Toyoura sand. The use of a weighted geometric mean model also provided good λ sat estimates with errors ranging from 3.1 % to 3.5 % for C-109 and C-190 and 8.3 % for Toyoura sand. This paper also discusses a successful attempt to model λ sat as a product of thermal conductivity of the solid fraction (quartz plus other minerals) and a thermal conductance factor of water.

Characterisation of Ground Thermal and Thermo-Mechanical Behaviour for Shallow Geothermal Energy Applications

“…In saturated conditions, the guarded hot plate apparatus measured a maximum discrepancy of 5.2% lower than the reference data by Reference [78] at 25 • C. The variations do not seem significant, falling within the expected uncertainties of the methods. However, when in Reference [34] guarded hot plate and thermal needle probe measurements were compared for a range of temperatures from 25 • C to 70 • C, the steady-state method provided higher thermal conductivities than the ones reported by References [33,71]: 2.7%, 10%, and 17.5% at 25 • C, 50 • C, and 70 • C, respectively. This misfit is attributed to the water movement driven by a temperature gradient, i.e., buoyancy-driven water flow.…”

“…However, there is a trend to utilise steadystate methods for rocks (solid mineral matter) and transient methods for soils (e.g., see Reference [40]). [20,33,34,47,66,[70][71][72][73][74]; Sr: degree of saturation, n: porosity.…”

“…Tarnawski and collaborators [33,71,72], who used the thermal needle probe, and Nikolaev et al [34], who employed the guarded hot plate, constitute the most recent and complete studies on the dependency of the thermal conductivity of standard sands at different degrees of saturation over a temperature range. For dry sands, in Reference [34] agreement was demonstrated, with a maximum discrepancy of 5.7%, between the measurements performed with the guarded hot plate and the thermal needle probe, as reported by References [33,73,77,78] (see Figure 8).…”

Design of a laboratory borehole storage model

“…Another important feature of the simulating ground is its interchangeability, which is why saturated sand is chosen as simulating ground. The thermal properties assumed for the simulated and simulating ground are as follow: = 3.5 W•m -1 •K -1 , = 1.58•10 -6 m 2 ·s -1 and = 3.0 W•m -1 •K -1 , = 7.00•10 -7 m 2 ·s -1 , respectively (Arkhangelskaya & Lukyashchenko, 2017;Sundberg, 1991;Tarnawski et al, 2011). The thermal properties of the simulating ground should be well characterized before experiments are to be performed.…”

Canadian Field Soils II. Modeling of Quartz Occurrence

“…Proper preparation of saturated soil samples is essential for obtaining reliable λ sat data [18]. First, a mass of dry soil, equivalent to the assumed dry bulk density, was added to a known volume of a cylindrical container.…”