Geologic Modelling Using Parametric NURBS Surfaces

Most reservoir modelling/simulation workflows represent geological heterogeneity on a pillar-grid defined early in the modelling process. However, it is challenging to represent many common geological features using pillar grids: examples include intersecting faults, recumbent folds, slumps, and non-monotonic injection structures such as salt diapirs. It is also challenging to represent multi-scale features, because the same number of pillars must be present in all layers so there is little flexibility to adjust the areal grid resolution. We present a surface-based geological modelling (SBGM) workflow that uses NURBS (Non-Uniform Rational B-Splines) surfaces to represent geological heterogeneities without reference to a pre-defined grid. The NURBS surfaces represent a broad range of heterogeneity types, including faults, fractures, stratigraphic surfaces across a range of length-scales, and boundaries between different facies or lithologies. The geological model is constructed using the NURBS surfaces and a mesh created only when required for flow simulation or other calculations. The mesh preserves the geometry of the modelled surfaces. NURBS surfaces are an efficient and flexible tool to model complex geometries and are common in many modelling and engineering disciplines; however, they are rarely used in reservoir modelling. Complex surfaces can be created using a small number of control points; modelling with NURBS surfaces is therefore computationally efficient. We report here a variety of new stochastic approaches to create geological NURBS surfaces, including (1) extrusion of spatially variable cross-sections, (2) parametric 3D geometry templates, and (3) perturbation of control points to yield similar results to some pixel-based geostatistical methods. Surface interactions, such as erosion, stacking or conforming, are enforced to ensure geological relationships are preserved and the boundary representation is watertight. We illustrate our NURBS SBGM approach via a number of examples, including channelized sandbodies, clinoforms, sedimentary cycles, fractures, crosscutting faults, recumbent folds and combinations thereof.

[1]  K. Spitzer,et al.  Electromagnetic methods for exploration and monitoring of enhanced geothermal systems – A virtual experiment , 2015 .

[2]  P. Salinas,et al.  Reservoir Modelling Using Parametric Surfaces and Dynamically Adaptive Fully Unstructured Grids , 2016 .

[3]  Pablo Salinas,et al.  Dynamic unstructured mesh adaptivity for improved simulation of near­wellbore flow in reservoir ­scale models , 2016 .

[4]  Norman L Jones,et al.  Generating MODFLOW grids from boundary representation solid models. , 2002, Ground water.

[5]  Björn Zehner,et al.  Workflows for generating tetrahedral meshes for finite element simulations on complex geological structures , 2015, Comput. Geosci..

[6]  S. Geiger,et al.  Numerical simulation of water injection into layered fractured carbonate reservoir analogs , 2006 .

[7]  Clayton V. Deutsch,et al.  Stochastic surface modeling of deepwater depositional systems for improved reservoir models , 2009 .

[8]  Sebastian Geiger,et al.  The third porosity system , 2012 .

[9]  Matthew D. Jackson,et al.  Three-dimensional modeling of clinoforms in shallow-marine reservoirs: Part 2. Impact on fluid flow and hydrocarbon recovery in fluvial-dominated deltaic reservoirs , 2015 .

[10]  Sebastian Geiger,et al.  What can we learn from high-resolution numerical simulations of single- and multi-phase fluid flow in fractured outcrop analogues? , 2012 .

[11]  Matthew D. Jackson,et al.  Effective flow properties of heterolithic, cross-bedded tidal sandstones: Part 1. Surface-based modeling , 2016 .

[12]  Clayton V. Deutsch,et al.  Stochastic surface-based modeling of turbidite lobes , 2005 .

[13]  Matthew D. Jackson,et al.  Three-dimensional modeling of a shoreface-shelf parasequence reservoir analog: Part 1. Surface-based modeling to capture high-resolution facies architecture , 2009 .

[14]  J. Stewart,et al.  Characterization of stratigraphic architecture and its impact on fluid flow in a fluvial-dominated deltaic reservoir analog: Upper Cretaceous Ferron Sandstone Member, Utah , 2011 .

[15]  Matthew D. Jackson,et al.  Surface-based reservoir modelling for flow simulation , 2013 .

[16]  Guillaume Caumon,et al.  Modeling Channel Forms and Related Sedimentary Objects Using a Boundary Representation Based on Non-uniform Rational B-Splines , 2016, Mathematical Geosciences.