APPLICATION OF THE FINITE HANKEL TRANSFORM TO A DIFFUSION PROBLEM WITHOUT AZIMUTHAL SYMMETRY

The problem treated in this paper concerns calculating the evolution o f the pressure in a single-phase, slightly compressible fluid in a por ous medium consisting of communicating layers. The fluid is produced t hrough a point sink located on the side of an otherwise sealed cylindr ical wellbore. This location of the sink causes the flow around the we llbore to be azimuthally asymmetric. The problem is solved through suc cessive application of Laplace, finite Fourier and finite Hankel trans forms. Although apparently straightforward, this approach leads to ser ious numerical difficulties. The published form of the inversion formu la for the finite Hankel transform leads to inaccurate computation for the higher azimuthal modes even with 128 bit arithmetic. An alternati ve form is developed which enables accurate evaluation of the solution with the more practical 64 bit arithmetic. The technique for two-laye r solution presented here can be directly extended to a problem with a larger number of communicating layers. This is the first instance of successful application of the finite Hankel transform to an azimuthall y asymmetric diffusion problem.