Permeability Gas Percolation Mathematical Model And Its Solution

With a gradually increasing of demand of natural gas in the world, the production and reserve-production radio of conventional gas reservoir appearing a gradual decline, unconventional gas resource is considered as the most hopeful resource supplement. Thus accelerating the exploration and development of low-permeability gas reservoir becomes an inevitable trend of the energy indunstrial development in the century.It is also an important strategic direction of the industrial development of petroleum of our coumtry to develop scientifically and rationally low-permeability gas reservoir. It can be known from the development and well testing practice of low-permeability gas reservoir that fluid flow through low-permeability media exist threshold pressure gradient and present the special phenomenon that the moving boundary expands outwards constantly. Namely, the pressure is not spreading to infinite instantly. In place that moving border does not reach, the gas reservoir keep still. In addition, a large number of tests verify low-permeability fluid will deviate from Darcy flow. All these make low-permeability gas reservoir, stratum pressure distribute, bottom-hole pressure distribute and the differential of pressure are different from that of medium-high permeability and have their own characteristics, Worthy of our discussion deeply,in order to guide practice of developing better.In view of this, on the foundation of some supposed condition, the paper set up a moving boundary model with Stefan condition on low-permeability gas reservoir flow. The difference of explicit forcastion and impbicit correction has been set up and used Newton method to solute the nonlinear equations on the foundation of utilize the Schauder fixed point theorems and extreme value principle to prove the existence and uniqueness of the model. Then we analysis Relatedly Conclusion.The paper discuss the following content mainly:1. Research the percolating mechanism in low-permeability gas reservoir, on the foundation of some supposed condition, Using the general method to set up fluid flow through low-permeability media mathematics model and considering the influence of threshold pressure gradient, we set up a moving boundary model with Stefan condition.