U.S. patent application number 16/891564 was filed with the patent office on 2020-09-17 for systems, methods and computer program products for constructing complex geometries using layered and linked hexahedral element meshes.
The applicant listed for this patent is National Technology & Engineering Solutions of Sandia, LLC. Invention is credited to Moo Y. Lee, Byoung Yoon Park, Barry L. Roberts, Steven R. Sobolik.
Application Number | 20200293705 16/891564 |
Document ID | / |
Family ID | 1000004870155 |
Filed Date | 2020-09-17 |
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United States Patent
Application |
20200293705 |
Kind Code |
A1 |
Park; Byoung Yoon ; et
al. |
September 17, 2020 |
SYSTEMS, METHODS AND COMPUTER PROGRAM PRODUCTS FOR CONSTRUCTING
COMPLEX GEOMETRIES USING LAYERED AND LINKED HEXAHEDRAL ELEMENT
MESHES
Abstract
Systems, methods and computer program products for creating 3D
representations of bodies are disclosed. The systems, methods and
computer program products include the construction of FE meshes
representing complex geometries. The complex geometries may be
artificially or naturally formed or designed geometries. The
techniques reduce the number of elements as much as possible to
save on computer run time while maintaining computational
accuracy.
Inventors: |
Park; Byoung Yoon;
(Albuquerque, NM) ; Roberts; Barry L.; (Edgewood,
NM) ; Sobolik; Steven R.; (Albuquerque, NM) ;
Lee; Moo Y.; (Placitas, NM) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
National Technology & Engineering Solutions of Sandia,
LLC |
Albuquerque |
NM |
US |
|
|
Family ID: |
1000004870155 |
Appl. No.: |
16/891564 |
Filed: |
June 3, 2020 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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15435904 |
Feb 17, 2017 |
10657301 |
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16891564 |
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62296458 |
Feb 17, 2016 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06F 30/23 20200101;
B33Y 30/00 20141201; B33Y 50/00 20141201; B33Y 10/00 20141201 |
International
Class: |
G06F 30/23 20060101
G06F030/23; B33Y 10/00 20060101 B33Y010/00; B33Y 30/00 20060101
B33Y030/00; B33Y 50/00 20060101 B33Y050/00 |
Goverment Interests
STATEMENT OF GOVERNMENT INTEREST
[0002] The United States Government has rights in this invention
pursuant to Contract No. DE-AC04-94AL85000 between the United
States Department of Energy and Sandia Corporation, for the
operation of the Sandia National Laboratories and under Contract
No. DE-NA0003525 awarded by the United States Department of
Energy/National Nuclear Security Administration. The Government has
certain rights in this invention.
Claims
1. A method of performing in a computer a finite element analysis
of a body, comprising: providing a 3D map or representation of the
body; creating a finite element mesh representation of the body by
the steps comprising: dividing the body into slices; and creating
elements within the slices, wherein adjacent layers of elements are
connected by common nodes; performing an action based on the
created finite element mesh representation selected from a group
consisting essentially of analysis, design and fabrication.
2. The method of claim 1, wherein the action is fabricating a part
based on the finite element mesh representation.
3. The method of claim 2, wherein the part is fabricated by a
technique selected from a group consisting of 3D printing,
machining, casting and molding.
4. The method of claim 1, further comprising: creating layers of an
outer body around the body.
5. The method of claim 4, wherein the action is analysis of the
body by selectively removing the layers.
6. The method of claim 1, wherein the action is analysis, and the
analysis is a creep determination of the body.
7. The method of claim 6, wherein the body is a salt geological
formation surrounding a subterranean cavity.
8. A computer program product stored on a non-transitory computer
readable medium, wherein executed by a process, the computer
program product configured to: create a finite element mesh
representation of a body by the steps comprising: dividing the body
into slices; and creating elements within the slices, wherein
adjacent layers of elements are connected by common nodes; wherein
the finite element mesh representation of the body is analyzed by a
processor.
9. The computer program product stored on a non-transitory computer
readable medium of claim 8, wherein the body is analyzed to
determine creep, stress, stain, and fatigue.
Description
RELATED APPLICATIONS
[0001] This application is a divisional of U.S. application Ser.
No. 15/435,904, filed Feb. 17, 2017, entitled "SYSTEMS, METHODS AND
COMPUTER PROGRAM PRODUCTS FOR CONSTRUCTING COMPLEX GEOMETRIES USING
LAYERED AND LINKED HEXAHEDRAL ELEMENT MESHES," which claims the
benefit of U.S. Provisional Application No. 62/296,458 filed on
Feb. 17, 2016, entitled "Systems, Methods and Computer Program
Products for Constructing Complex Geometries," the entireties of
which are herein incorporated by reference.
FIELD
[0003] The present disclosure is generally directed to the field of
finite analysis shape modeling, and more specifically to systems,
methods and computer program products for producing finite element
linked hexahedral element mesh models of bodies for analysis and
fabrication.
BACKGROUND
[0004] In order to analyze, design and/or fabricate structures,
parts and/or components, large-scale three-dimensional (3D)
computational models have been used. These models include finite
element (FE) analysis models to represent the body being analyzed.
It is difficult to accurately represent these irregular geometries
or spaces by a meshed mass in these computational models, and so
the representation of these irregular spaces has been limited to
approximations in the models.
[0005] In addition, to predict the mechanical integrity of
irregular geometries using FE analysis, the 3D geometry of the
structure has been found to be an essential contributor to the
resulting stress conditions and so must be represented in the model
as accurately as possible. For example, complex finite element
analysis models have been used to evaluate the mechanical integrity
of salt surrounding existing petroleum storage caverns. However,
these prior models lack the precision to accurately model the
caverns for some types of analysis.
[0006] The U.S. Strategic Petroleum Reserve (SPR) uses 62 salt
caverns to store crude oil at four sites located along the Gulf
Coast. As of 2016, the reserve contains approximately 700 million
barrels (MMB) of crude oil. Most of the caverns were solution mined
by the U.S. Department of Energy (DOE) resulting in irregular
cavern geometry, spacing, and depth. The irregularity of the shape
may be further compounded if a salt fall occurs within the cavern.
Large-scale, three-dimensional computational models have been used
to model the geo-mechanical behavior of these underground storage
facilities. These models include simplified cylindrical shapes of
the caverns for modeling purposes.
[0007] Additionally, complex shapes or parts may be modeled as
simplified shapes to reduce the number of elements to save on
computer run time. For example, a complex part may be modeled with
less fidelity to save on computer run time, the part may then be
fabricated, and a finishing process may be used to bring the part
into fabrication specification.
[0008] The need remains, therefore, for systems, methods and
computer program products that can more precisely model complex
geometries for analysis, design and fabrication.
SUMMARY OF THE DISCLOSURE
[0009] The present invention is directed to systems, methods and
computer program products that include the construction of FE
meshes representing geometries or shapes. The shapes may be
artificially or naturally formed or designed geometries. The
systems, methods and computer program products utilize techniques
that reduce the number of elements as much as possible to save on
computer run time while maintaining the computational accuracy. The
systems, methods and computer program products include steps and
program command scripts integrated into an automated mesh
generation program for the robust generation of two- and
three-dimensional finite element meshes (grids) representing a
shape. In an embodiment, the shapes may be simple or complex or
irregular, and homogeneous or non-homogeneous. For example, the
shape may be simple, such as, but not limited to a cylinder, sphere
or cube. For another example, the shape may be complex, such as,
but not limited to a gear, piston, or wheel. For another example,
the shape may be irregular, such as, but not limited to a geologic
cavern or formation, and organic body such as, but not limited to a
heart or limb, and a manufactured part such as a drill or auger
bit. As used in this disclosure, the term "irregular shape" means a
non-symmetric 3D shape including irregular cross-sections and
having no planes of symmetry.
[0010] In an embodiment, the disclosed systems, methods and
computer program products may be applied to the analysis and design
of complicated shapes, such as, but not limited to civil and
geological structures such as mines, tunnels, faulted regions, and
underground fluid injection sites; biological applications such as,
but not limited to artificial limbs, bone and artery, and
artificial joints. The complicated shaped masses or geometries may
represent void, solid, and/or semi-solid spaces. Solid spaces are
meant to include solid and liquid masses.
[0011] In another embodiment, the systems, methods and computer
program products may be applied to the analysis, design and
fabrication of complicated shapes, such as, but not limited to
parts and devices. The analysis may be stress, strain, fatigue and
creep analyses. For example, the parts may be, but are not limited
to machine parts, musical instruments, molds, medical devices such
as, but not limited to artificial limbs, and molds. For example,
the devices or articles may be, but are not limited to tools or
machines, works of art, jewelry, deformed structural components and
architectural structures.
[0012] After a mesh model of the shape of a body is made by in
accordance with this disclosure, known fabrication processes may be
provided the model, which then may be used to fabricate the body.
For example, the body may be formed by three dimensional (3D)
printing, machining, tooling, mold formation and casting.
[0013] According to an embodiment of the disclosure, a method of
performing a computer a finite element analysis of a body,
including providing a 3D map or representation of the body,
creating a finite element mesh representation of the body by the
steps including dividing the body into slices, and creating
elements within the slices, wherein adjacent layers of elements are
connected by common nodes, and performing an action based on the
created finite element mesh representation selected from a group
consisting essentially of analysis, design and fabrication.
[0014] According to another embodiment of the disclosure, a system
for fabricating a body including a processor for executing
programming, a non-transitory computer readable storage medium
encoded with the programming for creating a complex geometry. The
non-transitory computer readable medium with programming is
configured to receive a mapping of a body, create a finite element
mesh representation of the body by the steps including dividing the
body into slices, and creating elements within the slices, wherein
adjacent layers of elements are connected by common nodes. The
system further includes a manufacturing system that receives the
finite element mesh representation of the body and manufactures a
part based on the created finite element mesh representation of the
body.
[0015] According to another embodiment of the disclosure, a
computer program product stored on a non-transitory computer
readable medium is disclosed, wherein executed by a process, the
computer program product configured to create a finite element mesh
representation of a body by the steps including dividing the body
into slices, and creating elements within the slices, wherein
adjacent layers of elements are connected by common nodes. The
finite element mesh representation of the body is then analyzed by
a processor.
[0016] One advantage of this disclosure is that its methodology
provides for an accurate transfer of measured solid-body nodal
points to a computational mesh consisting of hexahedral finite
elements that maintains the integrity of the original measured
geometrical data, and constructs hex mesh elements that have the
required characteristics (overall dimensions, aspect ratio, convex
shape, etc.) for efficient, accurate, and stable calculations.
[0017] Another advantage of the present disclosure is to provide
techniques to construct meshes representing artificially and
naturally formed geometries that are more accurate than simplified
approximation.
[0018] Other features and advantages of the present disclosure will
be apparent from the following more detailed description of the
preferred embodiment, taken in conjunction with the accompanying
drawings which illustrate, by way of example, the principles of the
disclosure.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] FIG. 1 shows a sonar image (left) and meshed volume (right)
of Bayou Choctaw (BC) Cavern 20 with one drawdown onion layer
according to an embodiment of the disclosure.
[0020] FIG. 2 shows a calculation of coordinates of a vertex for
the 1.sup.st drawdown onion layer according to an embodiment of the
disclosure.
[0021] FIG. 3 illustrates a work flow for the simulation using FE
mesh capturing realistic, irregular geometries of the BC site
according to an embodiment of the disclosure.
[0022] FIG. 4 shows work flow to create BC Cavern 20 mesh according
to an embodiment of the disclosure.
[0023] FIG. 5 shows work flow to create BC dome mesh according to
an embodiment of the disclosure.
[0024] FIG. 6 shows work flow to create BC surrounding rock (far
field) mesh according to an embodiment of the disclosure.
[0025] FIG. 7 shows BC Cavern 18 cavity with six drawdown onion
layers according to an embodiment of the disclosure.
[0026] FIG. 8 shows cavern columns and dome column are combined
into the dome.
[0027] FIG. 9 shows the images of salt dome and caverns obtained
from the seismic and sonar surveys, respectively (left) and the
hexahedral elements mesh capturing realistic geometries of Bayou
Choctaw Strategic Petroleum Reserve.
[0028] FIG. 10 shows overview of the hexahedral finite element
meshes of the stratigraphy and cavern field at Bayou Choctaw. The
U.S. Strategic Petroleum Reserve stores crude oil in the seven blue
caverns. Green shows privately owned caverns, and grey depicts
abandoned caverns. The cavern ID numbers are also shown.
[0029] Wherever possible, the same reference numbers will be used
throughout the drawings to represent the same parts.
DETAILED DESCRIPTION
[0030] The present disclosure will now be described more fully
hereinafter with reference to the accompanying drawings, in which
preferred embodiments of the invention are shown. This invention
may, however, be embodied in many different forms and should not be
construed as limited to the embodiments set forth herein; rather,
these embodiments are provided so that this disclosure will be
thorough and complete and will fully convey the scope of the
invention to those skilled in the art.
[0031] The present disclosure is directed to systems, methods and
computer program products that include a 3D FE mesh (which may be
referred to simply as "mesh" herein) representations or models of a
complex geometries. The systems, methods and computer program
products include the creation of a computational mesh that
approximates geometries of a space, shape or body. The geometry may
be complex or irregular. The geometries may be initially mapped by
tools such as, but not limited to X-ray, laser scanning,
ultra-sonic, photo-analysis, borehole and well logs, sonic and
seismic measuring technologies. The original mappings are then used
to create a modeling mesh formed of linked, hexahedral elements.
The mesh elements may be tetrahedral, hexahedral and combinations
thereof.
[0032] In an embodiment, systems, methods and computer program
products for the 3D geo-mechanical analyses of large underground
storage facilities using a computational mesh that approximates
their complex geological geometries are disclosed. Such geometries
may be initially accurately mapped using sonic and seismic
measuring technologies. The geometries may be initially of a first
space, which may then be grown to an outer space. For example, the
technique described herein may include creating a combination of
data sets of mapped salt dome and cavern geometries and
constructing a hexahedral element mesh that maintains the accuracy
of the measurements, appropriate aspect ratios for individual
elements. This model represents a first or interior or void space
of the cavern. In an embodiment, adding additional geometries
around caverns ("onion layers") may be added that represent the
salt surrounding the cavern or the cavern walls, that may be
removed by selective layer removal in the future by leaching or
other removal process to expand the void or cavern space.
[0033] The process includes creating horizontal slices of the
mapped geometry, creating elements for that slice, sequentially
adding and assembling additional horizontal slices. The
sequentially added slices include elements that have common nodes.
After the creation of the first horizontal slice of a geometry, the
nodal points (nodes) of that slice are mapped to the adjoining
surfaces of adjacent horizontal slices, thus maintain equal spatial
coordinates on co-located or common nodes. These common nodes are
simplified to a single node at each coordinate location when the
slices are later merged together.
[0034] The disclosed systems and methods include the following
technique: [0035] a. a mapping of a subject space or shape is
performed or provided; [0036] b. the mapped shape or space is
modeled by generating horizontal slices of the mapped geometry,
creating elements for each horizontal slice, and sequentially
adding and assembling the horizontal slice elements. The
sequentially added slices include elements that have common
nodes.
[0037] In an embodiment, the process includes: [0038] a. Inputting
mapping data into a 3D data modeling and manipulation package.
[0039] b. Extracting isolevel lines which represent sample slices
from the 3D data model. [0040] c. Using software algorithms to
resample the extracted isolevel lines. [0041] d. Calculate the
coordinates of onion layers and create additional layers (onion
skin or layers) of material outside the original shape that
qualitatively maintain the original shape while adding thickness
around it. These "onion layers" are important for applications such
as solution mining of caverns, where an original shape of a salt
cavern containing fluid is enlarged by the introduction of fresh
water. The process calculates the coordinates of these onion layers
using layer thicknesses provided by the user. [0042] e. Mesh
generation of caverns and followed of salt dome, interbed, caprock,
overburden, interface between dome and surrounding rock, and the
surrounding rock in order. [0043] f. Check mesh quality. [0044] g.
Assemble each mesh block to form the entire or complete FE
mesh.
[0045] The technique will be discussed below as applied to a cavern
space or geologic formation analysis. However, it should be
apparent to one of ordinary skill in the art that the technique may
be analogously used for any mapped space or body to create a FE
mesh representation of that space or body for analysis, design
and/or fabrication.
[0046] Finite element codes such as Sierra and Adagio, developed by
Sandia Corporation, are designed to conduct simulations with finite
elements that are either tetrahedral or hexahedral. Two
constitutive models, i.e. power law creep (PLC) model and
multi-mechanism deformation (M-D) model, are coded as material
models to represent the salt behavior in Adagio. These two material
models are programmed in Sierra/Adagio assuming eight-node
hexahedral elements.
[0047] Therefore, the mesh for the BC SPR site has to be
constructed with hexahedral elements. Hexahedral elements include
six convex quadrilateral sides, or facets, with the nodes for these
facets being the eight nodes for the element. The cavern boundaries
such as the ceiling, wall, and floor are obtained from sonar
measurements, and the irregular geometries of these boundaries
ultimately require various shapes of facets. Similarly, the
geometry of the flank of the salt dome, obtained from seismic
measurements, also consists of complicated shapes of facets. To
construct a mesh with convex hexahedral elements for a geological
volume keeping the complicated geometry as much as possible, the
following rules were established and followed: [0048] 1. Each
perimeter (cavern and dome) consists of the same number of vertices
[0049] 2. Reference distance between vertices on a perimeter is:
[0050] a. about 20 ft for caverns [0051] b. about 80 ft for dome
[0052] 3. The vertical thickness of an element level is kept
constant at 20 ft [0053] 4. 15% cavern volume increase for each
drawdown leach.
[0054] FIG. 1 shows the meshed volume of BC-20 with the sonar image
as an example. The circumference at each elevation varies. The
average circumference is calculated from averaging the diameter
obtained from the sonar data at each elevation. The number of
intervals on a circumference is calculated to be 90 by dividing the
average circumference by 20 ft, and then kept constant for each
vertical layer. Thus, the interval size between two vertices varies
with elevation. The cavern volume consists of 90 lines from the
ceiling to the floor as shown in FIG. 1. The thickness of each
element level is kept constant at 20 ft. Using this rule,
coordinates of each vertex are resampled from the sonar image.
[0055] Modeling of the leaching process of the caverns is performed
by deleting a pre-meshed block of elements along the walls of the
cavern so that the cavern volume is increased by 15 percent per
drawdown. The 15% volume increase is typical for a standard
freshwater drawdown, although salt quality can vary that amount.
Also, typical leaching processes tend to increase cavern radius
more at the bottom of the cavern than at the top, with very little
change to the roof and floor of the cavern. For the purposes of
this modeling effort for Bayou Choctaw, leaching is assumed to add
15% to the volume of the cavern and is assumed to occur uniformly
along the entire height of the cavern, with no leaching in the
floor or roof of the caverns. Each leaching layer, or onion layer,
is built around the perimeter of the meshed cavern volume using the
same rules stated previously and shown in FIG. 3.
[0056] The X-axis of model is in the E-W (East-West) direction,
Y-axis is in the N-S (North-South) direction, and Z-axis is the
vertical direction. To realize the leaching process in the mesh,
the coordinates of a vertex (X.sub.1, Y.sub.1) in FIG. 2 have to be
calculated for the first drawdown:
[0057] The coordinates of the center at each element level are:
X c = i = 1 N X i N , Y c = i = 1 N Y i N ( 1 ) ##EQU00001##
where, N=number of vertices=90 for BC-20, X.sub.i, Y.sub.i are
shown in FIG. 1.
[0058] The distance between the center point and a vertex (X.sub.0,
Y.sub.0) on the perimeter of original cavern volume:
L.sub.0= {square root over
((X.sub.C-X.sub.0).sup.2+(Y.sub.C-Y.sub.0).sup.2)} (2)
[0059] The distance between the center point and a vertex (X.sub.1,
Y.sub.1) on the perimeter of one drawdown leached volume:
L.sub.1=L.sub.0 {square root over (1+R.sub.v)} (3)
where, R.sub.v=volume increase rate=15% for BC salt
[0060] Then, the coordinate of a vertex (X.sub.1, Y.sub.1) on the
perimeter of one drawdown leached volume are calculated as:
X 1 = X C + ( X 0 - X C ) L 1 L 0 , Y 1 = Y C + ( Y 0 - Y C ) L 1 L
0 ( 4 ) ##EQU00002##
[0061] FIG. 3 shows the overall work flow to construct a mesh
capturing realistic geometries of the Bayou Choctaw geologic site.
The BC 3D seismic data was shot in 1994 for petroleum exploration.
The sonar surveys on BC caverns were performed on the dates as
listed in Table 1.
TABLE-US-00001 TABLE 1 Date of the last sonar survey on BC caverns,
cavern number, top and bottom elevations of the caverns. Date of
the Cavern/Dome Top Bottom ID sonar survey number elevation (ft)
elevation (ft) BC-1 May 30, 1980 001 -1040 -1820 BC-2 Jul. 28, 1983
002 -780 -1520 BC-3 Jul. 13, 1977 003 -1020 -1840 BC-4 Jul. 30,
2013 004 -640 -1660 BC-6 Nov. 01, 2006 006 -1240 -1560 BC-7
Collapsed in 007 0 -1940 1954 BC-8 May 31, 1980 008 -1300 -1940
BC-10 Sep. 13, 1973 010 -1000 -1880 BC-11 Mar. 10, 1978 011 -1120
-1740 BC-13 Aug. 13, 1977 013 -1120 -1860 BC-15 Apr. 15, 2009 015
-2600 -3260 BC-16 Jun. 28, 2004 016 -2620 -3200 BC-17 Apr. 16, 2009
017 -2740 -3960 BC-18 Jan. 06, 2009 018 -2160 -4160 BC-19 Apr. 14,
2009 019 -2980 -4200 BC-20 Dec. 13, 2013 020 -3820 -4180 BC-24 Apr.
16, 1997 024 -3100 -4320 BC-25 Oct. 30, 2007 025 -2580 -5640 BC-26
Oct. 11, 1996 026 -2300 -3320 BC-27 Oct. 28, 2007 027 -5940 -6280
BC-28 Oct. 29, 2007 028 -4700 -6240 BC-J1 Jul. 27, 2006 031 -2860
-3900 BC-N1 Dec. 05, 2003 032 -1920 -3480 BC-UTP Oct. 14, 2006 033
-2380 -3480 BC-101 Apr. 14, 2009 101 -2580 -4780 BC-102 Feb. 22,
2012 102 -2640 -5220 Dome 999 0 -6400
[0062] The cavern numbers are also defined in Table 1 to use in an
input journal of a toolkit for robust generation of two- and
three-dimensional finite element meshes (grids) and geometry
preparation, such as, but not limited to CUBIT Geometry and Mesh
Generation Toolkit by Sandia Corporation, which was used in this
Example. The top and bottom elevations of each cavern are
calculated in the resampling step discussed below. The data from
the surveys are manipulated in a geologic modeling analysis and
visualization software suit or tool, such as, but not limited to
the Mining Visualization System (MVS) by C Tech Development Corp.
This step is necessary to provide a full three-dimensional surface
model of the sonar and seismic data.
[0063] The vertices output for the geomechanical simulations need
to be at specific depth intervals which may not correspond to the
actual sonar sampling locations. Continuous three-dimensional
surface models of the survey data are created, which allows
sampling at any needed depth. This resampling step is performed
through an algorithm coded using Python. Then, the resampled node
coordinates data sets for the dome and caverns are generated as the
output in this step.
[0064] The resampled nodal data are converted into Cubit vertices
data through MS Excel manipulation. 3D hexahedral element meshes
for 26 caverns, salt dome, caprock, overburden, interbed, and
interface between the dome and surrounding rock of BC SPR site, are
constructed using various functions in Cubit. Mesh quality is
checked for each block in Cubit. All meshes are combined into one
hexahedral FE mesh, using a mesh combination program, such as GJOIN
developed by Sandia Corporation. A solver for quasistatic nonlinear
finite element program, such as ADAGIO developed by Sandia
Corporation, will be executed with the mesh to calculate the
geomechanical behavior of caverns, dome and surrounding
lithologies.
[0065] FIG. 4 shows the procedure to create a cavern mesh of BC-20
as a further example. The sonar image of the cavern boundary
including cavern ceiling, wall, and floor is obtained from the
sonar survey. The 3D-coordinates of the vertices are resampled from
the sonar image. Cavern slice block 20 ft thick layers are
generated using the coordinates of vertices. The cavern mesh has to
be composed of hexahedral elements. The hexahedral element shape
has to be translated from the top through the bottom of the model.
Therefore, the upper and lower salt blocks, interbed block, caprock
block, and overburden block are needed.
[0066] The hexahedral element meshes are created in the overburden
layer first. The quadrilateral element shapes on the top surface of
the overburden block translate to the bottom surface of the block.
The element shapes on the bottom surface of the overburden block
transfer to the top surface of the caprock block through merging
the surfaces. In the same manner, the hexahedral element shapes of
the overburden block are translated through the interbed, upper
salt, cavern ceiling, cavern body, cavern floor, and lower salt
blocks. Those meshed blocks are assembled into the cavern column.
The upper salt block leans to the left (west) because the dome
leans to the west. To avoid poor shape elements in the salt between
the dome edge and the upper salt block, the upper salt column needs
to be parallel to the dome edge as much as possible. In the same
manner, the other 26 cavern columns are generated for the remaining
26 caverns.
[0067] FIG. 5 shows the procedure to create the BC dome mesh. The
3D-coordinates of vertices are resampled from the seismic image.
The dome mesh has to be composed of hexahedral elements. The
hexahedral element shape has to be translated from the top through
the bottom of the model. Therefore, the overburden block, caprock
blocks, interbed block, upper salt blocks, and lower salt blocks
have to be generated first. The vertex data for the upper salt
blocks are translated upward from the vertex data of the trimmed
salt dome top. The salt dome leans to the west. The coordinates of
vertices at every 20 ft element level from elevations -1320 ft
through -680 ft are calculated considering the leaning. The vertex
data for the interbed, caprock, and overburden blocks are
translated vertically upward from the vertices data of the top of
upper salt blocks. 283 dome slice blocks with 20 ft thickness are
created using the coordinates of vertices. Finally, the dome column
consists of 286 slice blocks including the overburden block 500 ft
thick, caprock block 160 ft thick, and bottom salt dome block 100
ft thick.
[0068] Each block is punched with 26 cavern columns which were
generated in the previous section. The vertices data of each hole
in the dome layer blocks are transferred from the cavern columns.
The mesh will be created with the vertices of each hole and dome
perimeter.
[0069] The hexahedral mesh in each block will be translated from
over/under block. The cross-section areas of each cavern column and
dome column are varied with depth. Considering the cross-sectional
areas of the pillars between caverns; caverns and dome edge, the
optimum base layer block is selected to avoid creating poor shape
elements, so creating the number of poor shape elements in every
layer block is as little as possible. The hexahedral element meshes
are created at the base slice block which bottom is located at
-2760 ft below the surface with 20 ft thickness. The quadrilateral
element shapes on the top of the base slice block translate upward
through the top of the dome column, and the element shapes on the
bottom of the base layer block translate downward through the
bottom of the dome column. 286 meshed layer blocks are assembled
into the dome column which consists of 320 element levels (the
height of dome column is 6400 ft). The dome leans to the west as
shown in FIG. 5.
[0070] FIG. 6 shows the procedure to create the BC surrounding rock
(far field) mesh. To represent the far field surrounding the BC
dome, a rectangular brick, whose widths in E-W and N-S directions
are two times the maximum widths of dome in the E-W and N-W
directions, respectively, is created at -6400 ft depth. The
rectangular brick is the base surrounding rock slice block whose
thickness and bottom elevation are 100 ft and -6400 ft,
respectively.
[0071] The bottom salt dome block, which was created in the
previous section, is inserted into the base block and punched with
the bottom salt dome block. The vertices data of the dome perimeter
are transferred from the salt dome block. The number of intervals
on E-W and N-S sides of the block is 20 which is selected as a
balance number between the total number of elements and element
shape. The number of intervals is one of key factors to determine
the total number of elements in the model. Larger number of
elements consumes more computer running time but makes better mesh
quality. The hexahedral element mesh is constructed with the
vertices and the intervals. The thickness of each element layer
sets up 20 ft in this model. The mesh has five element levels
vertically because the thickness of the base block is 100 ft.
[0072] In the similar manner, a rectangular block is created right
above the base block. The top surface of the base block becomes the
bottom surface of the new block. The vertices of four corners of
the new block top are calculated considering the dome declination
because the dome leans to the west. New blocks are constructed over
the base block upward to the surface. Each layer block is assembled
as the surrounding rock. As shown in FIGS. 4 and 5, twenty-six
cavern columns and dome column are combined into the BC dome
through the GJOIN process as shown FIG. 8. The dome and surrounding
rock column created as shown FIG. 6 are combined into the entire
mesh as shown FIG. 9 through the GJOIN process.
[0073] Representations of the Bayou Choctaw caverns based on sonar
data were incorporated into the geomechanical model to provide a
more realistic depiction of the caverns. To facilitate this, the
cavern sonar data were resampled to a nodal spacing more
appropriate for the geomechanical model. This process was
implemented using a custom Python script which operated on ASCII
files containing representations of the sonar data. The output from
the script was an ASCII file containing X, Y, and Z locations of
the newly determined nodal sites.
[0074] According to another embodiment of the invention, a computer
program product is disclosed for performing the operations of the
disclosed methods described in this disclosure.
[0075] In an embodiment, a computer program product is disclosed
for performing the operations of the disclosed methods for creating
a mesh representation of an object, body or space. In an
embodiment, the computer program product is embedded within a
non-transitory computer readable storage medium readable by a
processor of a computer and configured to store instructions for
execution by the processor for performing methods as described in
this disclosure. Additional executable steps are as described in
the method descriptions of this disclosure.
[0076] Moreover, the acts described herein may be
computer-executable instructions that can be implemented by one or
more processors and/or stored on a computer-readable medium or
media. The computer-executable instructions may include a routine,
a sub-routine, programs, a thread of execution, and/or the like.
Still further, results of acts of the methodologies may be stored
in a computer-readable medium, displayed on a display device,
and/or the like. The computer-readable medium may be any suitable
computer-readable storage device, such as memory, hard drive, CD,
DVD, flash drive, or the like. As used herein, the term
"computer-readable medium" is not intended to encompass a
propagated signal.
[0077] A computing device can be used in accordance with the system
and methodology disclosed herein. The computing device includes at
least one processor that executes instructions that are stored in a
memory. The memory may be or include RAM, ROM, EEPROM, Flash
memory, or other suitable memory. The instructions may be, for
instance, instructions for implementing functionality described as
being carried out by one or more components discussed above or
instructions for implementing the method described above. The
processor may access the memory by way of a system bus. In addition
to storing executable instructions, the memory may also store
models of other operational elements.
[0078] The computing device additionally includes a data store that
is accessible by the processor by way of the system bus. The data
store may be or include any suitable computer-readable storage,
including a hard disk, memory, etc. The data store may include
executable instructions and/or models. The computing device also
includes an input interface that allows external devices to
communicate with the computing device. For instance, the input
interface may be used to receive instructions from an external
computer device, from a user, etc. The computing device also
includes an output interface that interfaces the computing device
with one or more external devices. For example, the computing
device may display text, images, etc. by way of the output
interface.
[0079] Additionally, while illustrated as a single system, it is to
be understood that the computing device ay be a portion of a
distributed system. Thus, for instance, several devices may be in
communication by way of a network connection and may collectively
perform tasks described as being performed by the computing device.
It is noted that several examples have been provided for purposes
of explanation. These examples are not to be construed as limiting
the hereto-appended claims. Additionally, it may be recognized that
the examples provided herein may be permutated while still falling
under the scope of the claims.
[0080] The invention being thus described, it will be obvious that
the same may be varied in many ways. Such variations are not to be
regarded as a departure from the spirit and scope of the invention,
and all such modifications as would be obvious to one skilled in
the art are intended to be included within the scope of the
appended claims. It is intended that the scope of the invention be
defined by the claims appended hereto. The entire disclosures of
all references, applications, patents and publications cited above
are hereby incorporated by reference.
[0081] In addition, many modifications may be made to adapt a
particular situation or material to the teachings of the disclosure
without departing from the essential scope thereof. Therefore, it
is intended that the disclosure not be limited to the particular
embodiment disclosed as the best mode contemplated for carrying out
this disclosure, but that the disclosure will include all
embodiments falling within the scope of the appended claims.
* * * * *