Upscaling on Fracture Flow Models

Abstract

Fractures have a great impact on the quality of a porous media. The understanding of the fractures is important to describe the challenges linked to flow of geothermal heat, the transport of groundwater or transport of hydrocarbons in a porous media. The understanding of fracture can help to increase the energy production, or the extraction of clean drinkable groundwater. In this study we will investigate the effects of fractures in a porous medium by incorporate fractures as a lower dimensional geometric objects embedded in the porous matrix. Our approach here is to consider the fracture permeability as a diagonal tensor with the permeabilities scaled as an exponent of the width of the fracture. This thesis provides a rigorous approach towards derivation of upscaled model in a fracture. The quality of upscaling is further illustrated through extensive numerical examples that have been studied.