A direct determination of the transient exchange term of fractured media using a continuous time random walk method

In two recent papers, Noetinger and Estebenet, 2000; Noetinger et al., subm itted, we set-up a method allowing to compute both the transient and steady -state exchange terms between the matrix and fractured regions of a natural ly fractured porous medium using continuous time random walk methods (CTRW) . The goal of the present paper is to show that a new version of the CTRW a lgorithm provides a direct determination of the so called transient exchang e function f(t) (or its Laplace transform f(s)) widely used in well test in terpretation. It is shown that this function is directly linked with the pr obability density of the first escape time in the fractured region of a Bro wnian particle launched initially in the matrix region. This new interpreta tion allows relating directly the exchange coefficient alpha (infinity) wit h the mean escape time of brownian particles in the matrix. From a practica l point of view, these new results allow to derive a simpler version of the CTRW method. In addition, we obtain a considerable speed up of the CTRW me thod for up-scaling fractured reservoirs.