报告题目:
About the evaluation of geological shape sensitivities of
subsurface flow simulations using up scaling methods
报告人：Benoit Noetinger
（巴黎中央理工学院化石能源系主任、法国石油研究院“新能源”集团
高级专家、法国巴黎第六大学教授，美国怀俄明州立大学特邀教授）
报告时间：2014年5月13日（周二） 下午 16:00-17:00
报告地点：力学一楼239
组织单位：热科学和能源工程系
Abstract
Most geomaterials possess a multi-scale structure that have a major impact
on large scale transport properties. In particular, the effective
conductivity coefficient associated to thermal, electrical or hydraulic
transfers depends on its microstructure. In practice, it can be determined
using some analytical formula working in limited configurations. More
generally it can be obtained numerically by solving a closure problem that
maps the micro-scale to the macro-scale. The resulting effective coefficient
depends on the local properties, as well on the geometry of the inclusions.
The goal of this work is to give explicit formulae relating the sensitivity
of large scale effective conductivity with respect to local micro-scale
parameters using directly the solution of the mapping problem. The proposed
formula is direct and it does not imply solving any additional adjoint
problem. It needs only evaluation of volume or surface integrals involving
the mapping problem solution. The extra numerical cost is negligible once
the mapping closure problem has been solved. Simple numerical tests of the
formula are presented, as well as possible implementations for solving
geoscience issues. Possible generalizations for applications involving
several injection or production wells are proposed. Practical applications
can be proposed for solving inverse problems, for optimizing a microstructure
shape fulfilling an imposed constraint like maximizing or minimizing the
overall conductivity.
Keywords: Composite media, Porous media, Inclusions, Facies, Level sets,
upscaling, homogenization, Effective conductivity, Variational formulation,
Fréchet derivative