| Title | TETRAHEDRAL FINITE ELEMENTS AND GEOTHERMAL RELATED SUBSIDENCE |
|---|---|
| Authors | J. Pogacnik, P. Franz, and L. Azwar |
| Year | 2017 |
| Conference | New Zealand Geothermal Workshop |
| Keywords | Finite Element Method; Tetrahedral Elements; THM Modeling; Subsidence |
| Abstract | In recent years within the geothermal community, there has been an increase in interest to use numerical methods to represent rock mechanics phenomena such as production-related subsidence, thermal cracking, hydraulic fracturing/shearing, and stress analysis for induced seismicity. These interests require the coupling of the differential equations for heat and mass transport to the differential equation for linear momentum balance of the rock matrix. Heat and mass transport software packages are traditionally based on the finite volume method (FVM), while rock mechanics packages are traditionally based on the finite element method (FEM). Many volumes (cells) used in FVM techniques are inadmissible as finite elements as they do not satisfy the isoparametric element criterion required to guarantee solution convergence. However, any mesh structure can be broken down into a mesh of tetrahedral cells without increasing the number of nodes (vertices). The 4-noded tetrahedron is an admissible finite element type, although it is a notoriously poor performer in stress analyses. In this work, we investigate two techniques (nodal integration and addition of nodal rotation degrees of freedom) in order to improve the performance of standard linear tetrahedral elements. We compare those results to the results of traditional tetrahedral and hexahedral element meshes for a variety of benchmark problems as well as a hypothetical geothermal production related subsidence problem. While tetrahedra are convenient from a mesh construction viewpoint, that convenience comes at the expense of computational time, effort, and accuracy. The finite element user should endeavor to use hexahedral elements when possible. |