The Application of Numerical Laplace Inversion Methods for Type Curve Development in Well Testing: A Comparative Study

Abstract

In this work the Fourier series and Zakian and Schapery methods are considered to numerically solve the Laplace transform of a pressure distribution equation for radial flow and to generate the type curves for three different boundary conditions. The results show that the Schapery method leads to approximate solutions for small values of dimensionless time. For large values, however, this method is almost accurate and hence is recommended because it is fast to apply compared to other algorithms. It has been found that the accuracy of the Schapery method for early time prediction can be improved to almost a perfect match with analytical results through multiplying the Schapery relation by a proposed constant coefficient. This coefficient, regardless of the condition in the external boundary, is set to 0.58 when the wellbore storage effect and skin factor are considered. For an infinite acting case, when CD and S are included, and also for constant pressure case, all the methods fail to predict the behavior of the derivative plot accurately at late times, whereas other cases showed acceptable accuracy. At middle times, no analytical solution is available to check the accuracy of numerical methods, but because all the methods discussed here showed identical results, it is reasonable to trust in numerical inversion calculations.