About the evaluation of geological shape sensitivities of subsurface flow simulations using up scaling methods.

@inproceedings{NoetingerGM2014,
 abstract = { Modern geomodels allow to represent complex subsurface patterns characterized by many irregular frontiers. Simulating flow or heat transfers in such structures imply generally an up scaling step. The engineer is led to estimate an effective conductivity associated to thermal, or hydraulic transfers that depends on the shape of the internal geological bodies. Generally it can be obtained numerically by solving a closure problem that maps the microscale to the macroscale. 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 microscale parameters using directly the solution of the initial up scaling 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 up scaling problem solution. The associated numerical cost is negligible once the up scaling closure problem has been solved. Practical applications can be found for history matching a geomodel with respect to the shape of the geological bodies. },
 author = { Noetinger, Benoît },
 booktitle = { Proc. 34th Gocad Meeting, Nancy },
 title = { About the evaluation of geological shape sensitivities of subsurface flow simulations using up scaling methods. },
 year = { 2014 }
}