Heat Transfer Perpendicular to Fluid Flow In Porous Rocks
Authors: Willhite G.P. , Dranoff J.S. , Smith J.M. 
Published: December 2007

Abstract
Heat transfer rates were measured in sandstones with flow of gases perpendicular to the direction of energy transfer. Effective thermal conductivities keg ranged from 0.7 to 1.7 Btu/(hr)(ft)(F). The contribution of the solid phase appeared to be the most important in these consolidated materials, although the thermal conductivity of the gas had some effect. The velocity of the gas through the pores of the sandstones had no influence upon ker up to values of 168 lb/(hr) (sq ft) in agreement with data obtained for unconsolidated beds of glass beads. The present results indicated that gas mixing, and hence heat transfer by convection in the pores, is less for perpendicular transfer of energy than when fluid flow and energy transfer are in the same direction.

Heat Transfer Perpendicular to Fluid Flow in Porous Rocks
Heat transfer in porous media with pore sizes in the micron range depends upon the fluid in the pores and the geometry of the solid phase. The best characterized system is a bed of solid spherical particles. Heat transfer in this system has been studied extensively (Ref. 8 summarizes the literature up to 1959) when the pores contain stagnant fluid. When the fluid is in motion the directions of flow and energy transfer have an effect on the heat transfer rates, as demonstrated by comparing the work of Willhite, et al,13 for perpendicular flow and that of Kunii and Smith for parallel flow of energy and fluid. For perpendicular flow, no increase in effective thermal conductivity ke was noted up to mass velocities G of 77 lb/(hr) (sq ft). In contrast, for parallel flow ke increased with G in the same range of flow rates. These higher values of k in the direction of flow also have been observed in beds of larger particles, 0.1- to 0.5-in. diameter. For beds of consolidated materials, such as porous rocks, data are not available for these comparisons, although Adivarahan reported results for the parallel case. Hence the primary objective of this work was to measure ke values for perpendicular flow of fluid and energy in porous rocks. Of interest also was the variation in effective conductivity with fluid velocity.

Apparatus and Procedure
In the experimental method, a constant heat flux was applied to the inner surface of an annular section of the porous rock. By cooling the outer wall, a temperature gradient through the annular sample was established and measured with thermocouples placed within the sample at various radial positions, and at three elevations (A, B, C).The location of the 2-in. O.D., 3.75-in. long sample in the apparatus is shown in Fig. 1. Fluid entered the bottom (1) of the 3-in. I.D. (approximate) steel shell, flowed upwards through the sample and out at the top (3). Pressure taps (2,4) were used to check the permeability of the sample. The energy flowed radially from the centrally-located electric heater through the sample and was absorbed in the water-cooled jacket. The samples studied were naturally occurring sandstones from different locations with the properties given in Table 1. These materials are identical with those used by Adivarahan for the parallel flow of energy and fluid. Prior to use they were refluxed with toluene to remove hydrocarbons and leached with distilled water to remove soluble salts. Each sample was visually examined and discarded if large nonhomogeneities, such as cracks or stone particles, were noted.