Technical Notes - The Conduction of Heat Incident to the Flow of Vaporizing Fluids in Porous Media

Problems relating to thermal methods of oil recovery have been given increasing attention during the past year. The nature of the physical and chemical processes underlying thermal recovery are not yet well understood. The need for pertinent basic information is recognized generally. One of the processes involved is the transfer of heat by conduction in oil reservoir rocks containing moving reservoir fluids. This technical note deals with heat conduction in a laboratory sand column filled with a moving hydrocarbon and therefore should be contributory to the presently inadequate fund of knowledge on thc over-all subject. In an analysis of the flow of vaporiziny propane through a horizontal column of sand, one of the present author9 demonstrated correspondence between thc measured values of pressure along the length of the column and those predicted by a theory which postulated that the enthalpy of the propane was invariable along the length of the column. This postulate way implied as a deduction from the principle of conservation of energy but the details of the deduction were not given. The specific purpose of this technical note is the presentation of these details both as an adjunct to the earlier analysis and to supply some additional details on the processes involved in this type of flow. Results disclose that rates of heat transfer by conduction, in the direction of fluid motion, generally would be small for systems of the type studied. FUNDARIENrAI. ENERGY EiQUAI-[ON The principle of conservation of energy may be applied to a section of the porous material on the basis that heat transfer, like fluid flow, is possible in the x direction only. Transfer of heat in the y and z di'rections is prevented by suitable insulation or by taking the medium as infinite in directions perpendicular to the x axis. For steady state heat conduction and conditions of steady fluid flow the principle of conservation of energy specifies that any reduction in the enthalpy rate increases the flow of heat in the same proportion. Stated mathematically, dH KA 87 —- = - — - — U) * dx W dx........ Lvhere is the flow of heat in the positive x W dx direction. TEMPERATURE DISTRIBUTION IN DIRECTION OF FLOW The column of sand used in the previoi~sly described research is divisible into three different flow regimes. each of which may be analyzed independently. In the entrance region the liquid approaches the saturation state. A transition region is postulated following the transverse section at which the saturation state of the liquid is attained. In this transition region gas and liquid phases are both envisioned as present, with no vaporization occurring and with fluid movement restricted to the liquid. The upstream end of the exit region is at the transverse section of the column where the fraction of the pore space occupied by gas first becomes great enough for gas flow and where vaporization of the liquid begins. Fig. 1 indicates schematicaHy the thermodynamic processes undergone hv the fluid in the three flow regimes.