Impacts of Different Boundary Conditions on Dirac Pulse from a Well into Aquifer

For a partially penetrating well, a Dirac pulse can be generated by sudden charge of water from the well end into the contiguous rock, and subsequently the pulse diffuses away in terms of slow P-wave. This process is described by the Green's function for the initial-value problem. The Green's functions subject to three boundary conditions (BC) are compared mutually, that is, no BC, zero Neumann BC and zero Dirichlet BC for infinitely far boundary, the confining unit and unconfined aquifer, respectively. The well end is set at 10 m below the boundary, and the mass of water suddenly injected is prescribed as 1 kg. Both intact Berea sandstone and fractured Berea sandstone are used for illustration. The spatial distribution and breakthrough curve of the fluid pressure disturbance (p_f) are calculated. The results indicate that zero Neumann BC increases p_f whereas zero Dirichlet BC decreases p_f. For slow and fast P-waves in the regime of low frequency, it is rigorously shown that the ratios (between the confining pressure disturbance and fluid pressure disturbance) are lower than and higher than unity, respectively. This theoretical study suggests that the technique of Dirac pulse may be used for acquisition of small-scale permeability, thus helpful for resolving the heterogeneity of in situ permeability.