Transient pressure response in an anisotropic formation

In this paper we study the evolution of pressure of a single-phase, slightly compressible fluid in a porous medium where a non-permeable wellbore is present. The flow is induced by a single probe on the side of an otherwise sealed wellbore which is drilled at an angle to the vertical into the anisotropic rock formation.The formulation is derived by giving a transient correction due to the presence of the wellbore to the time dependent free space source field solution (the probe). Using the divergence theorem and the zero flux condition on the wellbore surface, a boundary element formulation is derived and solved numerically in the Laplace and Fourier transformed domain before being inverse-transformed to give the real time behaviour.