Fracture density model system, methods, and apparatuses
A fracture density model (FDM) system may predict the fragmentation size distribution for a blast. The FDM system may generate a model comprising a plurality of volume elements. The FDM system may determine pre-existing joint fractures in the volume elements. The FDM system may also simulate blasts and track fractures, for each of the volume elements, caused by the shock wave of the blast and a shock wave reflected off of a free face of the model. The FDM system may combine the pre-existing joint fractures and the blast induced fractures to determine a predicted fragmentation size for the distinct elements.
1 . A method for explosive blast modeling, the method comprising:
segmenting a model of at least a portion of a blast site into a plurality of volume elements, wherein the model comprises a plurality of blastholes and a free face;
determining pre-existing joint fractures in each of the plurality of volume elements;
simulating blasts from each of the plurality of blastholes;
determining explosive fractures in each of the plurality of volume elements from the blasts from each of the plurality of blastholes;
simulating a shock wave reflection at a free face of the model by simulating blasts at a plurality of ghost holes beyond the free face to determine reflective fractures in each of the plurality of volume elements, wherein the ghost holes are positioned in free space and not in direct contact with rock elements of the model;
combining the pre-existing joint fractures, the explosive fractures, and the reflective fractures to determine a total fracture intensity in each of the plurality of volume elements;
determining fragmentation sizes for each of the plurality of volume elements based on the total fracture intensity; and
controlling, in response to the fragmentation sizes meeting a desired fragmentation size, one or more blasting equipment based on the model.
2 . The method of claim 1 , wherein the blasts are sequential and explosive fractures and reflective fractures are determined after each blast.
3 . The method of claim 1 , wherein the plurality of blastholes comprises rows that are to be blasted sequentially, and wherein the method further comprises generating a new free-face for the model after each row is blasted.
4 . The method of claim 3 , wherein the new free face is positioned one third of a burden distance from a previously blasted row.
5 . The method of claim 1 , wherein the explosive fractures and the reflective fractures are determined using rock properties, explosive properties, and distance from a blasthole.
6 . The method of claim 1 , wherein the plurality of ghost holes are positioned an equal distance from the free face as a next blast hole to be blasted.
7 . The method of claim 1 , wherein force from the plurality of ghost holes is modeled as a tensile wave with a first angle and force from the plurality of blastholes is modeled as a compressive wave at a second angle.
8 . The method of claim 1 , wherein the simulated blasts at the plurality of ghost holes and the simulated blasts at the plurality of blastholes occurs at the same time.
9 . The method of claim 1 , further comprising summing a total of different fragmentation sizes to achieve a predicted fragmentation size distribution for the model.
10 . The method of claim 1 , wherein the explosive fractures are determined by solving the following equations for each of the plurality of volume elements:
F
=
K
⋆
F
1
⋆
F
2
⋆
F
3
F
1
=
(
σ
c
2
2
E
PF
⋆
EE
)
δ
F
2
=
[
R
0
R
(
tan
-
1
HMX
R
+
tan
-
1
XMS
R
)
]
α
F
3
=
(
BR
R
0
)
γ
where F1 corresponds to rock and explosive properties;
F is an explosive induced fracture intensity;
K is a site-specific calibration parameter;
F2 is a shape of a particle size distribution curve;
F3 is an intensity effect;
EE is an explosives energy;
PF is a powder factor;
E is energy available from explosives;
σ c corresponds to a rock strength described by a strain energy density;
α, γ, and δ are variables calculated using test bench blast shots;
Ro corresponds to the hole radius;
R is the radial orthogonal distance of an element from the hole;
BR is the distance of an element from the blasthole, (BR differs from Rin stemming zone);
HMX and XMS are distance functions evaluated for blasthole orientation using vector distance equations; and the exponents a, Y, and 6 are calibrated using test bench blast shots.
11 . The method of claim 1 , wherein the free face is varied such that a burden of the plurality of blastholes varies at different y-axis elevations of the model.
12 . A method for explosive blast modeling, the method comprising:
segmenting a model of at least a portion of a blast site into a plurality of volume elements, wherein the model comprises rows of blastholes;
determining pre-existing joint fractures in the plurality of volume elements; sequentially simulating blasts for each of the rows of blastholes; determining explosive fracture intensities in the plurality of volume elements from the blasts, wherein fractures from the blasts are determined after each of the rows of blastholes is detonated;
simulating a shock wave reflection from the blasts at a free face of the model by simulating blasts at a plurality of ghost holes beyond the free face to determine reflective fracture intensities in the plurality of volume elements, wherein the ghost holes are positioned in free space and not in direct contact with rock elements of the model, and wherein the free face location is shifted after each of the rows of blastholes is detonated and fractures from the shock wave reflection are determined after each of the rows of blastholes is detonated using the location of the free face;
combining the pre-existing joint fractures, the explosive fracture intensities, and the reflective fracture intensities to determine a total fracture intensity in the plurality of volume elements;
predicting fragmentation sizes for the plurality of volume elements based on the total fracture intensity; and
controlling, in response to the fragmentation sizes meeting a desired fragmentation size, one or more blasting equipment based on the model.
13 . The method of claim 12 , wherein the plurality of ghost holes are positioned an equal distance from the free face as a next row of blastholes to be blasted.
14 . The method of claim 12 , wherein force from the plurality of ghost holes is modeled as a tensile wave with a first angle and force from the rows of blastholes is modeled as a compressive wave at a second angle.
15 . The method of claim 12 , wherein the simulated blasts at the plurality of ghost holes are synchronous with a simulated blast of a next row of blastholes.
16 . A method for explosive blast modeling, the method comprising:
segmenting a model of at least a portion of a blast site into a plurality of volume elements, wherein the model comprises one or more blastholes and multiple geologic layers;
determining pre-existing joint fractures in each of the plurality of volume elements;
simulating blasts from the one or more blastholes;
determining explosive fractures in each of the plurality of volume elements from the blasts from each of the one or more blastholes, wherein the explosive fractures in each of the plurality of volume elements are affected by which of the geologic layers the plurality of volume elements is located within;
determining reflective fractures based on blasts from virtual holes positioned in free space on an opposite side of a free face of the model relative to the one or more blastholes;
combining the pre-existing joint fractures and the explosive fractures and the reflective fractures to determine a total fracture intensity in each of the plurality of volume elements;
determining fragmentation sizes for each of the plurality of volume elements based on the total fracture intensity; and
controlling, in response to the fragmentation sizes meeting a desired fragmentation size, one or more blasting equipment based on the model.
17 . The method of claim 16 , wherein the geologic layers comprise rock properties for different portions of in a borehole or a blast pattern.
18 . The method of claim 17 , wherein the rock properties are obtained from drilling data.
19 . The method of claim 16 , wherein the model further comprises explosive layering, wherein the explosive layering comprises an explosive product with varying explosive energy within the one or more blastholes, and wherein the explosive fractures in each of the plurality of volume elements is based on the explosive layering.