Modeling subsurface flows

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CO2 trap in a caprock

The modelling of subsurface flow in complex heterogeneous and fractured media is relevant for several applications like oil recovery, CO2 sequestration, thermal energy storage, geothermy.

In the compgeo activity group of the MOX Laboratory we have investigated various numerical techniques to tackle this complex phenomena: eXtended finite elements, mimetic finite differencing, embedded discrete fracture networks and  numerical upscaling techniques.  All the methods share a model reduction process where the fracture network is modeled as a network of one co-dimensional manifolds.

A major issue has been to identify physically consistent and mathematically sound reduced models and proper coupling conditions. The techniques have been implemented in specialised software code.

 

 

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Comparing different numerical techniques

 

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Numerical upscaling in a complex fracture network

D’Angelo, C., Scotti, A.: A mixed finite element method for Darcy flow in fractured porous media with non-matching grids. ESAIM Mathematical Modelling and Numerical Analysis 46,2, 465-489 (2012)

Fumagalli, A, and Scotti A. A numerical method for two-phase flow in fractured porous media with non-matching grids. Advances in Water Resources 62 (2013): 454-464.

Antonietti, P. F., Formaggia, L., Scotti, A., Verani, M., & Verzotti, N. Mimetic finite difference approximation of flows in fractured porous media. ESAIM: Mathematical Modelling and Numerical Analysis, 50(3), 809-832, 2016.

A. Fumagalli, S. Zonca, L. Formaggia, Advances in computation of local problems for a flow-based upscaling in fractured reservoirs, Mathematics and Computers in Simulation, 137: 299-324, 2017

B. Flemisch, I. Berre, W. Boon, A. Fumagalli, N. Schwenck, A. Scotti, I. Stefansson, A. Tatomir, Benchmarks for single-phase flow in fractured porous media, Advances in Water Resources 111: 239-258, 2018

Formaggia L. and Scotti, A. An analysis of mimetic finite difference approximation of flows in fractured porous media, ESAIM Mathematical Modelling and Numerical Analysis (to appear), 2018