The Solution Of Test Model With A Free Boundary

From the well test analysis theory development perspective, each time's progressis inseparable from the seepage models and logging interpretation model research,Especially after the 1980s, The strong foundation in the mathematical has becomethe essential condition of well test research."No solid mathematical foundationcannot grasp the contemporary well test"–it's really frontier contemporary well testbounded a caused resonance. So closely related with well test explain some of theseepage partial di?erential equations of knowledge and establish and problems ofmathematical model handle well test the research technique of great value. In recentyears,A parabolic with a free boundary problem research has also become more andmore.And about the study of well test model with a free boundary problem is alsonot enough. In petroleum reservoir development process, the ?uid ?ow boundarywith the increase of mining the passage of time continuously expand outward free,But in the free boundary did not reach place, reservoir still dormant.Aiming at thisspecial seepage phenomenon, the paper with heterogeneous reservoir as an example,the well test model is established with free boundary of well test model. And byusing the fixed point theorem and integral transform thoughts about the existenceand uniqueness of consideration.Using the method of variable separation considerthe basic model of solution. The author tries to make a qualitative analysis of thespecial solution in a free boundary condition.