Abstract: With finite difference method and Laplace transform,a Laplace transform difference method for well-test problem with one-dimensional seepage flow is proposed.Firstly,time variable is eliminated by Laplace transform.Then the mathematics model is solved with finite difference method.Finally the wellbore pressure or production is obtained with numerical inversion algorithm.A comparison with finite difference method solution and analytic solution shows that the calculating error of Laplace transform difference method is smaller than that of finite difference method,though it consumes more time in each step.Laplace transform difference method has advantages in well-test application since any moment simulation does not rely on other moment result and space grid.

Key words: Laplace transform, finite difference method, well-test, error