Abstract: The numerical simulation of oil (gas) reservoirs can be described by two-phase penetration dynamic equations, which are high-dimensional, non-linear, singular and time-dependent partial differential equations, subjected to some appropriate initial and boundary conditions.The partial differential equations are discretized by differencing schemes (such as Fully Implicit method, 1MPES,etc.)and produce different non-linear algebraic systems.To solve a non-linear system Newton's method is the most popular method. But it requires calculation of a Jacobi matrix and solving a linear system in each iteration.These will consume huge computing CPU time.For saving the CPU time we have modified the Newton's method with Samanskii's idea and controled the number of iterations in solving the linear systems. The programming is quite simple. We tested our algorithm in a set of ideal data.The results are as accurate as those obtained from the Newton's method and the efficiency is better.

Key words: numerical simulation of gas reservoirs, fully implicit difference schemes, modified Newton's method