“Thermal Conductivity of Sandstones from Biot’s Coefficient”
Abstract:
We propose a theoretical model for prediction of effective thermal conductivity with application to sandstones and input from standard downhole logging campaigns.
Provided known or estimated mineralogy from e.g., drill cuttings, the proposed model exclusively utilizes parameters derived through conventional log interpretation, so to be applicable within petroleum and geothermal reservoir engineering.
Derived parameters are used to quantify the rock texture from which we construct a simplified rock model and we propose that a one-dimensional heat flow passes through three parallel heat paths: solid, fluid, and solid-fluid in series.
Cross sections for heat transfer in single constituent heat paths are proposed quantified from the conceptual ideas that 1) heat transfer through a grain contact area is equal to the area governing the material stiffness and is quantified through Biot’s coefficient, 2) the pore space open for fluid flow in one direction is equal to the pore spore open for heat transfer in the same direction and quantified by a factor derived from porosity and envisaged in the same way as Kozeny’s factor is for permeability.
Enclosing 1) and 2) within the physical boundaries of a unit volume we derive remaining solid-fluid heat path by arranging residual constituent volumes in series. For a series of different sandstones, we measured thermal conductivity in the dry and the water saturated state and in both cases we find good agreement with model predictions from both laboratory and well log data.