APPLICATION OF A WAVE TRANSFORM TO PRESSURE TRANSIENT TESTING IN POROUS-MEDIA

Solutions to the diffusion equation for nonuniform media are difficult to obtain in a form that can be easily evaluated. Often the solutions are written as the inverse Laplace transform of an inverse Fourier tr ansform. In this paper, I show that the wave transform of Bragg and De ttman (1968) coupled with the Cagniard-de Hoop method for solving the wave propagation problem results in simplified solutions to the proble m of pressure transient testing in linear composite reservoirs. The po tential usefulness of an inverse wave transform, which would transform measured pressure data (smooth) into a wave signal propagating at the 'velocity' of the square root of the diffusivity, is demonstrated by a synthetic example. In the example, diffusivity of the source region is estimated from the 'time' of the direct wave arrival, white diffusi vity of a second, higher diffusivity region is estimated from the 'vel ocity' of the head wave. In the wave domain the time-like variable has units of (time)(1/2) which makes the units of 'velocity' equal to LT- ((1/2)). I also demonstrate, using synthetic data, that it is difficul t, but perhaps possible, to invert the wave transform numerically.