Transient, Radial Temperature Distribution in a Porous Medium During Fluid Injection

摘要

Analytical and numerical solutions are presented for the transient, radial temperature distribution in a porous medium which is subjected to a constant-rate injection of an incompressible fluid from a wellbore. The formulation includes energy transfer by conduction and convection, and the Danckwerts boundary condition is applied at the finite-radius wellbore. At late times, the numerical solutions approach a self-similar form which can be described in terms of the incomplete Gamma function. In typical petroleum and geothermal applications, convergence to the asymptotic similarity solutions occurs on a time scale of roughly one hour. The results are generally applicable to a broad range of convection-diffusion phenomena which are best described in radial coordinates. (ERA citation 07:048275)