Well Test Interpretation Using Laplace Space Type Curves

This study presents the mathematical background which justi es the use of Laplace space in well test analysis. It enables us to perform the whole parameter identi cation (CD; Skin; kh; ...) in Laplace space, or at least gives us a powerful tool to treat the pressure data in order to recognize the model to use for the parameter identi cation in real space. It shows a manner in which the Laplace transform can be plotted, showing exactly the same behaviour as the real pressure function so the plots keep their familiar shape. The coe cients of the dimensionless parameters remain the same, too. This enables us to display a new set of characteristic and easily understandable type curves in Laplace space. The mathematical background also sheds light on the use of the Laplace transform to achieve owrate deconvolution, using modi cations of earlier techniques which had been found to be extremely sensitive to noise in the data. The treatments displayed are numerically stable, and it is explained why numerical instability can occur in owrate deconvolution. The e ectiveness of the treatments is explained whenever possible, and the e ect of the latetime extrapolation is discussed as well. The Laplace space approach provides an entirely new way of examining and understanding well test results. It has been succesfully applied to noisy, simulated data where a conventionnal interpretation could not illuminate ambiguities.