Combined Free and Forced Convection in Porous Media

Abstract

Abstract An experimental study of thermal convection in a horizontal porous layer bounded by isothermal planes has been performed with and without a mean flow of the saturating fluid phase. The temperature distribution and heat transfer resulting from convection have been determined. The theoretical criterion for the onset of convection (Rayleigh number NRa > 4p2) has been verified. For low values of NRa (< 260) a regular pattern of convective cells has been observed which may be motionless or moving depending on the experimental conditions. For NRa values higher than 260, another convective state has been found that is mainly unstable. Numerical computations have been worked out that confirm the experimental results on the heat transfer and size of convective cells. INTRODUCTION Thermal convective currents may exist in a porous medium when the vertical component of the temperature gradient runs in the same direction as the gravity vector. Such a configuration is possible in some cases during a real in-situ combustion test4 or during hot fluid injection. A general understanding of convection is also of interest for analyzing the abnormal temperature gradients sometimes observed in oil and gas reservoirs.22 From the phenomenological standpoint a distinction must be made between the natural or free convection occurring in a closed volume and the mixed or combined free and forced convection arising when there is a mean flow of the fluid phase. Natural convection in porous media has been the subject of numerous experimental attempts to determine a convection criterion, e.g., by using a linear theory,1,2,9 and to measure the mean heat transfer.3,7 Numerical studies8,10,15,19,20 have also been made, and their results are not always in good agreement with experimental observations. However, no thorough study of mixed convection has been made except for a theoretical analysis of the convection onset criterion5 and some qualitative experimental observations.4 This paper presents some findings concerning both the natural and mixed convection of an incompressible fluid in a homogeneous horizontal porous layer bounded by two parallel impervious isothermal surfaces. The temperature for the cooler upper surface is T1 and that of the lower surface is T2=T1+?T. THEORETICAL ANALYSIS The effect of pressure on specific gravity is assumed to be negligible with regard to the effect of thermal expansion. So the relationship between density and temperature may be expressed as:Equation 1 In addition to complying with equations for motion and continuity, velocity and temperature distributions obey the heat transfer equation:Equation 2 By taking into account the additivity property of enthalpy, M may be expressed asEquation 3 On the contrary, khR is not just a simple function of khj and khs and must be measured or calculated with different kinds of models.6