二维单裂隙-孔隙双重介质的核素迁移数学模型及参数反演  

A Mathematical Model of Nuclide Migration and Its Parameters Inversion in a Two-dimension Single Fracture-Porosity Dual Media

作　　者：张文[1,2] 阮周生[1,2] 邱淑芳[1,2] 何杰[1,2] 

机构地区：[1]东华理工大学放射性地质与勘探技术国防重点学科实验室,江西抚州344000 [2]东华理工大学理学院,江西抚州344000

出　　处：《东华理工大学学报（自然科学版）》2012年第4期422-427,共6页Journal of East China University of Technology(Natural Science)

基　　金：国家自然科学基金(41001320);江西省教育厅科技项目(GJJ11151);放射性地质与勘探技术国防重点学科实验室(2010RGET12)

摘　　要：探讨了二维单裂隙-孔隙双重介质系统中的核素(以90Sr为例)迁移数学模型及其参数反演问题。该核素迁移模型是一个耦合的抛物型方程组定解问题。若已知排污点的核素浓度变化规律,利用傅立叶变换及Saul’yev不对称差分格式,求得了核素迁移模型正问题的解。反之,由下游裂隙中某位置的实测核素浓度,利用遗传算法,反求出核素迁移模型中的地质参数,即裂隙介质水动力弥散系数D1和裂隙平均渗流速度u。最后,给出核素迁移模型的正问题和反问题的数值模拟。数值结果表明,正问题能够刻画核素的迁移规律,也显示出所提反问题方法能有效地反演核素迁移模型中的地质参数。A mathematical model of nuclide （90Sr） migration and its parameter inverse problem for the dual media consist of the two-dimension porosity and the single fracture media is studied. The nuclide migration model is a coupled parabolic system with initial and boundary conditions. If the variation of the nuclide concentration is known at the release point, a set of solution of the nuclide migration model can be obtained by the Fourier trans- form and the Saul＇ yev asymmetric difference scheme. On the contrary, the solution of the inverse problem of the nuclide migration model, i.e. hydrodynamic dispersion coefficient and average flow rate in fracture media, is re- constructed with the Genetic Algorithm derived from the measured data of nuclide concentration at a location. Fi- nally, numerical simulations for the forward and inverse problems are given. Numerical results show that the solu- tion of the forward problem can describe the variation of the nuclide migration, and the method proposed for the inverse problem is also effective to reconstruct the geological parameters of the nuclide migration model.

关 键 词：核素迁移 单裂隙 双重介质 傅立叶变换 遗传算法 参数反演 

分 类 号：O29[理学—应用数学]