Volumetric grid generation in a domain with heterogeneous material properties

A method for generating a model of a material property of a subsurface region for hydrocarbon prospecting or reservoir development, said method comprising:

• generating, using a computer, a mapping from a physical domain of the subsurface region, with faults, to a continuous design space in which all faults are removed;
• describing the material property in the continuous design space as a piecewise smooth implicit or explicit function in three dimensions;
• in the physical domain, constructing grid layering from the function describing the material property, the constructing comprising:
• (i) generating a two-dimensional mesh in a two-dimensional plane of the physical domain;
• (ii) extruding the two-dimensional mesh through the physical domain into the third dimension;
• and
• (iii) building prismatic cell faces based on material property contrasts thereby subdividing the physical domain into prismatic grid cells, wherein the grid cells are truncated at faults, the grid cells are conformed to fault surfaces using a parameterization of a 3D model domain, or a combination of both;
• sampling the material property from the continuous design space and populating the grid cells in the physical domain with material property values;
• in the physical domain, identifying connectivity of the prismatic grid cells across each fault by approaching the fault from both sides, wherein the identifying connectivity comprises computing intersections of cell faces from both sides of the fault;
• and
• using the model of the material property for hydrocarbon prospecting or reservoir development in the subsurface region.