Speaker
Description
In the fields of engineering and science, the coupled flow and geomechanics problem is of significant importance in various applications, especially in hydraulic fracturing, CO$_2$ injection and storage, sand production, and wellbore stability prediction. In fractured media, the coupling of flow and geomechanics is particularly critical, as fractures are not only regions of mechanical instability but also have a significant impact on the flow profile. In this talk, we present our recent work investigating the fluid-solid coupling problem in fractured porous elastic media. The geometry of the fractures is explicitly considered as a potentially non-planar interface. The model equations are of mixed-dimensional type, where the flow equations on the $d$−1 dimensional fracture surfaces are coupled with the $d$ dimensional porous matrix. This paper considers a strongly compressible fluid flow model, where the density is chosen as the primary variable, in contrast to the slightly compressible model discussed by Girault et al, which takes pressure as the primary variable. We derive a thermodynamically consistent mathematical model and present its weak formulation. Energy stability is established for both the continuous and semi-discrete (in time) cases. The proposed model and numerical framework provide a solid foundation for simulating strongly compressible flows while maintaining thermodynamic consistency and stability.
| Country | China |
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