Heat transfer characteristics of porous rocks

TLDR

Equations are derived to predict the effective thermal conductivity of beds of unconsolidated particles containing stagnant fluid, depending on solid and fluid conductivities, void fraction, and, when radiation is significant, emissivity, mean temperature, and particle diameter. The study aims to extend this theory to beds of consolidated particles by assuming they form through partial clogging and cementing of unconsolidated beds. The authors extend the packed‑bed equations to include consolidated materials such as sandstone and porous metals, introducing a consolidation parameter that captures heat transfer across contact surfaces between cemented or clogged particles. The resulting equations accurately predict how void fraction and solid and fluid thermal conductivities affect heat transfer in sandstones and sintered metal systems, and they agree satisfactorily with experimental data for both high and low conductivity fluids and solids.

Abstract

Abstract Equations are derived for predicting the effective thermal conductivity of beds of unconsolidated particles containing stagnant fluid. The effective thermal conductivity at these conditions, called the stagnant conductivity , is a function of the thermal conductivities of the solid and fluid phases, the void fraction, and, if radiation is important, the emissivity, mean temperature, and diameter of the solid particles. Comparison with the available experimental data indicates that the equations are satisfactory for fluids and solid particles of both high and low thermal conductivities. To extend the theory to beds of consolidated particles, it is supposed that consolidated beds are formed by partial clogging and cementing of beds of unconsolidated particles. With this assumption the theoretical equations for packed beds are extended to include such materials as sandstone and porous metals. The resulting expressions for the stagnant conductivity involve a consolidation parameter characteristic of the solid material. This quantity accounts for the heat transfer across the contact surfaces between cemented or clogged particles. The equations correctly predict the effect of void fraction and solid and fluid thermal conductivities on the heat transfer properties of sandstones and sintered metal systems.