Comput Geosci (2014) 18:949–967 DOI 10.1007/s10596-014-9438-7 ORIGINAL PAPER Spline-based reservoir’s geometry reconstruction and mesh generation for coupled flow and mechanics simulation Horacio Florez · Raul Manzanilla-Morillo · Jorge Florez · Mary F. Wheeler Received: 8 June 2013 / Accepted: 15 July 2014 / Published online: 1 August 2014 © Springer International Publishing Switzerland 2014 Abstract In this paper, the geometry of oil reservoirs is reconstructed by using B-splines surfaces. The technique exploits the reservoir’s static model’s simplicity to build a robust piecewise continuous geometrical representation by means of B` ezier bicubic patches. Interpolation surfaces can manage the reservoir’s topology while translational surfaces allow extrapolating it towards its sideburdens. After that, transfinite interpolation (TFI) can be applied to generate decent hexahedral meshes. In order to test the procedure, several open-to-the-public oil reservoir datasets are recon- structed and hexahedral meshes around them are generated. This reconstruction workflow also allows having different meshes for flow and mechanics by computing a projec- tion operator in order to map pressures from the original flow mesh to the generated reference mechanics mesh. As an update respect to a previous version of this research, we already incorporate blending functions to the TFI pro- cedure in order to attract the mesh towards the reservoir, which allows grading the hexahedral meshes in the appro- priate manner. Finally, field scale reservoir compaction and subsidence computations are carried out by using continu- ous Galerkin FEM for both flow and mechanics in order to demonstrate the applicability of the proposed algorithm. H. Florez () · J. Florez Reservoir Dynamics, ConocoPhillips, Reservoir Dynamics, 600 North Dairy Ashford, OF 2068, Houston, TX 77079, USA e-mail: florezg@gmail.com R. Manzanilla-Morillo School of Mathematics, Yachay Tech, Yachay City of Knowledge, 100119-Urcuqui, Ecuador M. F. Wheeler Center for Subsurface Modeling, UT-Austin, 201 East 24th Street, ACE 5.324, Austin, TX 78712, USA Keywords B-splines · Geometry reconstruction · Geomechanics · Finite elements · Mesh generation 1 Background Geomechanics at the reservoir level, i.e., reservoir com- paction and subsidence, usually involves solving flow and mechanics by an iterative coupling technique [15, 22]. This raises the question about what is a valid mesh for mechan- ics. At first glance, one may consider using the same mesh for flow and mechanics, at least in the so-called pay-zone. Meshing only in the pay zone requires the in situ stresses as Neumann boundary conditions, which is limited due to the uncertainties to measure them accurately in the field [4, 31]. Another approach is to extend the reservoir mesh on its surroundings (i.e., non-pay zone), which increases the com- putational cost by generating a larger mesh for mechanics but it allows using simpler boundary conditions for displace- ments instead. This latter approach is more tractable in spite of its additional computational effort [15]. There exists a gap between static model builders pack- ages, such as Schlumberger’s Petrel for instance, and mesh generators. Usually, as a starting point, one may have a corner-point mesh for the pay zone but neither geometri- cal nor analytical description of the reservoir itself [29]. This lack of representation makes generating a mesh in the non-pay zone for mechanics a complicated and tedious task for most users. Another advantage of having such geometry is being able to generate a different mesh for mechanics even in the pay zone, which is quite attractive for several reasons such as having a coarser mesh or non- matching meshes in the non-pay zone. In either approach, an analytical description of the reservoir’s geometry must be obtained.