ORIGINAL ARTICLE Hex-dominant mesh generation for subterranean formation modeling Longmin Ran • Houman Borouchaki • Abdallah Benali • Chakib Bennis Received: 12 February 2010 / Accepted: 14 June 2011 / Published online: 8 July 2011 Ó Springer-Verlag London Limited 2011 Abstract Under the context of subterranean formation modeling using finite volume methods, the computational domain is a basin, a reservoir, or an underground CO 2 storage site. Such a domain has a layered structure and is geometrically described by its layer limits called horizons and random disruption of layers called faults. Horizons and faults are both numerically represented by 3D triangulated surface meshes. Respecting the interface formed by hori- zons and faults, the volume mesh of the subterranean for- mation is required to be mainly hexahedral, with a few tetrahedrons, prisms or pyramids allowed along the faults, where mesh non-conformity is tolerated. A ‘‘constrained grid’’ approach is proposed to generate the so-desired mesh. Firstly, each horizon surface is unfolded with fault traces being sewn. Then, for each unfolded horizon, a regular grid with the same topology is generated from its boundary. Subsequently, node relocation and conditional grid refinement are applied to constrain fault traces to the grid. Afterwards, each grid is mapped back to its corre- sponding 3D horizon surface with fault nodes being split. Finally, a hex-dominant mesh is generated by connecting consecutive grids along corresponding nodes, with some elements cut into two by faults and degenerated into prisms, tetrahedrons, and pyramids. An optimization pro- cedure is then applied to enhance the shape quality of the resulting 3D mesh. Keywords Subterranean formation modeling  Hex-dominant mesh generation  Mesh optimization  Mesh refinement 1 Introduction In the petroleum exploration field, in particular in its three major sub-domains of basin modeling, reservoir simula- tion, and CO 2 injection simulation, fluid flow is studied by means of a system of partial differential equations (PDEs) resolved via finite volume methods, based on a mesh describing the geometry of relevant porous subterranean formation [1]. Automatic construction of the corresponding 3D mesh is hence the first step and the basis for such fluid flow study. Let us take a quick look at the aforementioned three sub- domains. Basin modeling aims at reconstructing the geo- logical history of a sedimentary basin and its oil system so as to locate the hydrocarbon traps (i.e. the reservoirs), to estimate their quantity and quality, and to evaluate the risk encountering pressure excess during drilling. Reservoir simulation studies the evolution of water, gas and oil proportions in the reservoir in order to judge its profit- ability, to validate or optimize well positions ensuring the functioning of reservoir exploitation. In an era of durable development and environment protection, a third major study associated to petroleum exploration is to execute simulations to inject excessive CO 2 into the underground L. Ran (&)  A. Benali  C. Bennis IFP, 1 and 4 Avenue du Bois Pre ´au, 92852 Rueil-Malmaison, France e-mail: Longmin.Ran@gmail.com A. Benali e-mail: Abdallah.Benali@ifp.fr C. Bennis e-mail: Chakib.Bennis@ifp.fr H. Borouchaki Universite ´ de Technologie de Troyes (UTT), BP 2060, 10010 Troyes Cedex, France e-mail: Houman.Borouchaki@utt.fr 123 Engineering with Computers (2012) 28:255–268 DOI 10.1007/s00366-011-0234-x