Skeleton-Based Volumetric Parameterizations for Lattice Structures

Lattice structures with excellent physical properties have attracted great research interest.In this paper,a novel volume parametric modeling method based on the skeleton model is proposed for the construction of threedimensional lattice structures.The skeleton model is divided into three types of nodes.And the corresponding algorithms are utilized to construct diverse types of volume parametric nodes.The unit-cell is assembled with distinct nodes according to the geometric features.The final lattice structure is created by the periodic arrangement of unit-cells.Several different types of volume parametric lattice structures are constructed to prove the stability and applicability of the proposed method.The quality is assessed in terms of the value of the Jacobian matrix.Moreover,the volume parametric lattice structures are tested with the isogeometric analysis to verify the feasibility of integration of modeling and simulation.

Stretch-Minimizing Volumetric Parameterization

Not many methods for parameterization guarantee bijectivity or local injectivity, which is essential for foldover- free mappings. Stretch-minimizing parameterization which is widely used for surface parameterization, provides foldover-free mappings and is capable of trading off between angle and area distortions. We extend its usage to volumetric parameterization in this paper by deriving a 3D version of stretch-distortion energy and incorporating fixed boundary conditions. Our energy definition includes a naturM barrier term which effectively prevents elements from collapsing and folding over. It saves the effort in other methods of formulating additional energy or constrains to ensure the local injectivity. We propose to minimize the overall energy integrated over the whole mesh with a relaxation-enhanced solver and optimize the energy globally. This is different from the conventional approach of surface parameterization where mesh nodes are optimized individually. Compared with other volumetric parameterizations, method, being foldover-free and offering a good trade-off between our approach bears the advantages of stretch-minimizing angle and volume distortions.

An Integrated Mass Balance Approach for Assessing Hydrocarbon Resources in a Liquid-Rich Shale Resource Play:An Example from Upper Devonian Duvernay Formation,Western Canada Sedimentary Basin

Petroleum resource assessment using reservoir volumetric approach relies on porosity and oil/gas saturation characterization by laboratory tests.In liquid-rich resource plays,the pore fluids are subject to phase changes and mass loss when a drilled core is brought to the surface due to volume expansion and evaporation.Further,these two closely related volumetric parameters are usually estimated separately with gas saturation inferred by compositional complementary law,resulting in a distorted gas to oil ratio under the circumstances of liquid hydrocarbon loss from sample.When applied to liquid-rich shale resource play,this can lead to overall under-estimation of resource volume,distorted gas and oil ratio(GOR),and understated resource heterogeneity in the shale reservoir.This article proposes an integrated mass balance approach for resource calculation in liquid-rich shale plays.The proposed method integrates bulk rock geochemical data with production and reservoir parameters to overcome the problems associated with laboratory characterization of the volumetric parameters by restoring the gaseous and light hydrocarbon loss due to volume expansion and evaporation in the sample.The method is applied to a Duvernay production well(14-16-62-21 W5)in the Western Canada Sedimentary Basin(WCSB)to demonstrate its use in resource evaluation for a liquid-rich play.The results show that(a)by considering the phase behavior of reservoir fluids,the proposed method can be used to infer the quantity of the lost gaseous and light hydrocarbons;(b)by taking into account the lost gaseous and light hydrocarbons,the method generates an unbiased and representative resource potential;and(c)using the corrected oil and gas mass for the analyzed samples,the method produces a GOR estimate close to compositional characteristics of the produced hydrocarbons from initial production in 14-16-62-21 W5 well.