Abstract: In the development of the low permeability reservoir, fluid flow through lowpermeability media deviates from Darcy law and the moving boundary expands outwards constantly. Where moving border does not reach, the reservoir keeps still. All these make strata pressure distribution and bottom-hole pressure distribution different from that of medium-high permeability reservoir, a new moving boundary model with Stefan condition is set up in this paper. After turning the existence and uniqueness of the moving boundary problem into fixed point problem of a integral transformations, Schauder fixed point theorems and extreme value principle are utilized to prove the existence and uniqueness of the model. There are some value to calculation and numerical simulation in the development of low permeability reservoir.

Key words: low-permeability reservoir, Non-Darcy flow, moving-boundary problem, schauder fixed point theorem, extreme value principle