低渗透非达西渗流动边界模型理论解的几个命题

Several Propositions about Theory Solution of Moving Boundary Model Non-darcy Flow through Low Permeability Reservoir

建立了低渗透非达西渗流带Stefan条件的动边界模型并且将动边界问题理论解的存在性转化为某一积分变换的不动点问题;然后提出几个重要命题,最后利用不动点定理和极值原理进行证明,这几个命题为证明模型理论解的存在惟一性,并进一步讨论模型数值解奠定了基础.

A moving boundary model of non - darcy percolation in low permeability reservoir with Stefan condition is set up ; meanwhile, the problem of existence of the theory solution of the moving boundary is changed into a problem of the fixed point of an integral transformation. Several propositions are given and based on the fixed point theorems and extreme value principle, they are proved. It enables us to prove the existence of the theory solution of the model unique, and it also can lay the foundation for further discussion about the numerical solution of the model.