Abstract: According to the practice of exploitation and well testing in low permeability reservoirs, the fluid flow had the starting pressure gradient in low permeability reservoirs. The well test curves are not easy to show the radius flow straight lines. a feature of pressure propagation with low velocity nondarcy percolation is that the fluid flowing boundary extends outwards continuously. In views of this situation, a fixed boundary mathematical model based on the pattern of low velocity non-darcy percolation with wellbore storage and skin effect was presented, and solutions of wellbore pressure in Laplace domain was solved with Green’s function. The radiuses of flowing boundary corresponding to the different time were determined in accordance
with the starting differential pressure by fluid from static to flowing condition, analytical solution of fixed boundary model was then used to calculate the correction of wellbore pressure varied with time, which was regarded as a numerical approximation of flowing boundary model. The curves of the wellbore pressure varied with time were developed by Stehfest reverse
method, and the influences of flowing boundary, starting pressure gradient, storage ratio, inter porosity flow coefficient and difference between darcy percolation and non-darcy percolation were discussed in details.

Key words: low permeability reservoir, pressure gradient, boundary, well test interpretation, wellbore storage and skin effect