Workflows for generating tetrahedral meshes for finite element simulations on complex geological structures

Subsurface processing numerical simulations require accurate discretization of the modeling domain such that the geological units are represented correctly. Unstructured tetrahedral grids are particularly flexible in adapting to the shape of geo-bodies and are used in many finite element codes. In order to generate a tetrahedral mesh on a 3D geological model, the tetrahedrons have to belong completely to one geological unit and have to describe geological boundaries by connected facets of tetrahedrons. This is especially complicated at the contact points between several units and for irregular sharp-shaped bodies, especially in case of faulted zones. This study develops, tests and validates three workflows to generate a good tetrahedral mesh from a geological basis model. The tessellation of the model needs (i) to be of good quality to guarantee a stable calculation, (ii) to include certain nodes to apply boundary conditions for the numerical solution, and (iii) support local mesh refinement. As a test case we use the simulation of a transient electromagnetic measurement above a salt diapir. We can show that the suggested workflows lead to a tessellation of the structure on which the simulation can be run robustly. All workflows show advantages and disadvantages with respect to the workload, the control the user has over the resulting mesh and the skills in software handling that are required. HighlightsWe developed, tested and validated three workflows to generate a good tetrahedral mesh from a geological basis model.We used a simulation of a transient electromagnetic measurement as a testcase.We can show that the suggested worklfows lead to a tessellation on which the simulation can be run robustly.

[1]  K. Spitzer.  A 3-D FINITE-DIFFERENCE ALGORITHM FOR DC RESISTIVITY MODELLING USING CONJUGATE GRADIENT METHODS , 1995 .

[2]  Hang Si,et al.  TetGen: A quality tetrahedral mesh generator and a 3D Delaunay triangulator (Version 1.5 --- User's Manual) , 2013 .

[3]  M. Nabighian.  Quasi-static transient response of a conducting half-space; an approximate representation , 1979 .

[4]  A. Bernath,et al.  Geologic Modeling, Upscaling and Simulation of Faulted Reservoirs Using Faulted Stratigraphic Grids , 1999 .

[5]  Christoph Clauser,et al.  Numerical simulation of reactive flow in hot aquifers : SHEMAT and processing SHEMAT , 2003 .

[6]  Erik H. Saenger,et al.  Numerical simulation of ambient seismic wavefield modification caused by pore-fluid effects in an oil reservoir , 2013 .

[7]  Simon Spitz,et al.  A finite-element solution for the transient electromagnetic response of an arbitrary two-dimensional resistivity distribution , 1986 .

[8]  T. Günther,et al.  Three‐dimensional modelling and inversion of dc resistivity data incorporating topography – II. Inversion , 2006 .

[9]  Thomas Bohlen,et al.  Paralel 3-D viscoelastic finite difference seismic modelling , 2002 .

[10]  J. Mallet.  Space–Time Mathematical Framework for Sedimentary Geology , 2004 .

[11]  Jean-Laurent Mallet,et al.  Discrete smooth interpolation , 1989, TOGS.

[12]  Oliver G. Ernst,et al.  A Restarted Krylov Subspace Method for the Evaluation of Matrix Functions , 2006, SIAM J. Numer. Anal..

[13]  Elaine S. Oran,et al.  Numerical Simulation of Reactive Flow , 1987 .

[14]  Olaf Kolditz,et al.  A Dynamic Flow Simulation Code Intercomparison based on the Revised Static Model of the Ketzin Pilot Site , 2013 .

[15]  Christoph Schwarzbach,et al.  Three-dimensional adaptive higher order finite element simulation for geo-electromagnetics—a marine CSEM example , 2011 .

[16]  C. Bennis,et al.  One More Step in Gocad Stratigraphic Grid Generation: Taking into Account Faults and Pinchouts , 1996 .

[17]  C. H. Park,et al.  PET2OGS: Algorithms to link the static model of Petrel with the dynamic model of OpenGeoSys , 2014, Comput. Geosci..

[18]  J. Mallet.  Elements of Mathematical Sedimentary Geology: the GeoChron Model , 2014 .

[19]  G. E. Archie.  The electrical resistivity log as an aid in determining some reservoir characteristics , 1942 .

[20]  Alessandro Tibaldi,et al.  Understanding Etna flank instability through numerical models , 2013 .

[21]  Jens-Uwe Repke,et al.  The impact of CO2 on the electrical properties of water bearing porous media – laboratory experiments with respect to carbon capture and storage , 2013 .

[22]  Shu Hu.  ANALYSIS AND SIMULATION OF THE MAIN ACQUISITION PARAMETERS OF THE SEISMIC IN THE NORTH YELLOW SEA BASIN , 2011 .

[23]  Christophe Geuzaine,et al.  Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities , 2009 .

[24]  W. Gossel,et al.  High-resolution 3D spatial modelling of complex geological structures for an environmental risk assessment of abundant mining and industrial megasites , 2009, Comput. Geosci..

[25]  Rita Streich,et al.  3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: Direct solution and optimization for high accuracy , 2009 .

[26]  Guillaume Caumon,et al.  Topological control for isotropic remeshing of non-manifold surfaces with varying resolution: application to 3D structural models , 2011 .

[27]  Matteo Massironi,et al.  3D modeling of fault-zone architecture and hydraulic structure along a major Alpine wrench lineament: the Pusteria Fault. , 2007 .

[28]  Guillaume Caumon,et al.  Towards Stochastic Time-Varying Geological Modeling , 2010 .

[29]  Thomas Kohl,et al.  Geothermal resource mapping—example from northern Switzerland , 2003 .

[30]  Patrick Jenny,et al.  Implementation of a Flux-Continuous Finite-Difference Method for Stratigraphic, Hexahedron Grids , 2002 .

[31]  D. E. Smylie.  Numerical Earth models , 2013 .