On fluid flow in a heterogeneous medium under nonisothermal conditions
Published Web Locationhttps://doi.org/10.1029/2010wr009571
An asymptotic technique, valid in the presence of smoothly varying heterogeneity, provides explicit expressions for the velocity of a propagating pressure and temperature disturbance. The governing equations contain nonlinear terms due to the presence of temperature-dependent coefficients and due to the advection of fluids with differing temperatures. Two cases give well-defined expressions in terms of the parameters of the porous medium: the uncoupled propagation of a pressure disturbance and the propagation of a fully coupled temperature and pressure disturbance. The velocity of the coupled disturbance or front depends upon the medium parameters and upon the change in temperature and pressure across the front. For uncoupled flow, the semianalytic expression for the front velocity reduces to that associated with a linear diffusion equation. A comparison of the asymptotic travel time estimates with calculations from a numerical simulator indicates reasonably good agreement for both uncoupled and coupled disturbances.