Study of the mathematical model of gas percolation flow through low-permeability reservoir and its calculation method

The distribution of the low-permeability gas reservoirs in China is very wide and their reserves amount to 80% of the reserves of the total gas reservoirs in China according to an incomplete statistics. Obviously, developing this kind of gas reservoirs is of an important practical significance, but up to now, the low-permeability data have been interpreted by adopting the conventional gas reservoir theory in general and the ideal results have not been obtained often due to the particularities the low-permeability gas reservoirs have but the conventional ones have not, such as tight rocks, extremely low permeability and gas percolation flow with slippage effect, etc. In view of this situation, a corresponding mathematical model is set up on the basis of investigating and studying a vast amount of the foreign and domestic literatures and the practical calculation and starting from studying the specific property of the gas percolation flow in low-permeability reservoirs. Through special processing of the coefficients and interior and exterior boundary conditions in the equation, a non-linear difference equation which solution is acquired by Newton's iteration method is obtained. The model and the calculation method in the paper can be fit in better with the measured data of the gas well through processing the data of one well in central Sichuan. As a result of this work, an effective method for solving this kind of problems is found out and this achievement is easy to be spread to the multidimension and multiphase model.