EA045746B1 - SYSTEM OF FRACTURE DENSITY MODEL, METHOD AND DEVICE - Google Patents

Description

Technical field

The present invention generally relates to explosion technology. More specifically, the present invention relates to methods, systems and apparatus for predicting the size of rock fragmentation from an explosion.

Brief description of drawings

To easily identify the description of any particular element or action, the most significant digit or digits in the number designation refer to the drawing number in which the element was first introduced.

Fig. 1A illustrates stresses applied to a rock element by a shock wave emitted from a borehole in accordance with one embodiment of the invention.

Fig. 1B illustrates a resulting radial fracture or fracture in a rock element in accordance with one embodiment of the invention.

Fig. 2A illustrates a three-dimensional model of a portion of a blast site in accordance with one embodiment of the invention.

Fig. 2B illustrates a three-dimensional model segmented into multiple volume elements in accordance with one embodiment of the invention.

Fig. 3A illustrates a top plan view of a three-dimensional model in front of any simulated explosions in accordance with one embodiment of the invention.

Fig. 3B illustrates a plan view of a three-dimensional model after simulated blasts from a first borehole and a second borehole in accordance with one embodiment of the invention.

Fig. 4 illustrates vector mechanics equations that can be used in fracture density modeling (FDM) to calculate distance functions and detect charge positions relative to a rock element in a blast, in accordance with one embodiment of the invention.

Fig. 5 illustrates a top plan view of an explosion model with ghost holes for determining fractures and fracturing intensity due to reflected shock waves in each element of the explosion model in accordance with one embodiment of the invention.

Fig. 6 illustrates a top plan view of a ghost hole explosion model with a dynamic free surface in accordance with one embodiment of the invention.

Fig. 7A illustrates a plan view of a blast model and fracture angles from a first blast hole in accordance with one embodiment of the invention.

Fig. 7B illustrates a plan view of a blast model and fracture angles from a ghost hole corresponding to a first blast hole, in accordance with one embodiment of the invention.

Fig. 8 illustrates a side view of a blast hole in accordance with one embodiment of the invention.

Fig. 9A illustrates a three-dimensional model that includes rock type properties that can be used to more accurately predict fracture rates in accordance with one embodiment of the invention.

Fig. 9B illustrates a cross section of a multi-layer vertical blast hole.

Fig. 10 illustrates a simulation of an underground mine face model using FDM in accordance with one embodiment of the invention.

Fig. 11 illustrates a flow diagram of a method for predicting the size of rock fragmentation resulting from a blast in accordance with one embodiment of the invention.

In fig. 12 illustrates a block diagram of an FDM system in accordance with one embodiment of the invention.

Fig. 13A illustrates a three-dimensional FDM contour plot of the fracture intensity of a three-dimensional explosion model with multiple discrete elements in accordance with one embodiment of the invention.

Fig. 13B illustrates a two-dimensional particle size distribution curve in accordance with one embodiment of the invention.

Fig. 14 illustrates a top plan view of the explosion model.

Carrying out the invention

Explosives are widely used in the mining, quarrying and excavation industries to destroy rocks and ores. Typically, a hole called a blast hole is drilled into a surface such as the ground. Explosives can then be placed into the blast hole

- 1 045746 substances. Typically, multiple blast holes are used to destroy large volumes of rock and ore. The use of multiple blast holes introduces complexity into blast planning. For example, blasting may vary depending on a variety of factors, including blasthole spacing, blasthole loading, blasthole depth, blasthole location, number of blastholes, geologic properties, type of explosive, amount of explosive, and time to initiate blastholes. The number of possibilities makes blast planning difficult even for a highly trained blast engineer.

Explosion simulations performed by simulation systems can be used to predict the outcome of an explosion. For example, some modeling systems can predict the size distribution of explosion fragmentation. The fragmentation size distribution can predict the size of rocks after an explosion. Rock fragmentation from blasting is one of the key results in mining. Optimizing fragmentation can significantly improve all downstream mining and grinding processes. Accurately predicting the fragment size distribution based on all relevant blast inputs helps in the optimization process.

Embodiments of the invention herein generate a three-dimensional (3D) rock fragmentation model. The model may be called a fracture density model (FDM). The modeling system can generate FDM by segmenting the blast site model into multiple elements, simulating explosions, and tracking the fragmentation that occurs in each of the multiple elements. In some embodiments of the invention, the simulation system can handle complex physical scenarios, including pre-existing separations, burnout, dynamic free surfaces, changing blast parameters, and wave reflections on free surfaces. Additionally, in some embodiments of the invention, FDM can also be extended to simulate rock blasting in a subterranean environment.

In this context, 3D FDM elements are elements of a 3D FDM model. Three-dimensional FDM elements are referred to herein as finite elements, volume elements, multiple volume elements, discrete elements, multiple discrete elements, multiple elements, multiple individual elements, elements, and rock elements. Each of these terms refers to the 3D FDM elements of a 3D FDM model.

It will be readily understood that the components of the embodiments, as generally described below and illustrated in the figures herein, can take a variety of different arrangements and implementations. For example, the steps of the method need not be performed in any particular order or sequentially, and the steps need not be performed once. Thus, the following more detailed description of the various embodiments, as described below and illustrated in the figures, is not intended to limit the scope of protection of the present invention, but merely represents the various embodiments. Although various aspects of embodiments of the invention are depicted in the drawings, the drawings are not necessarily to scale unless specifically stated otherwise.

Embodiments and implementations of the systems and methods described herein may include various steps that may be implemented in computer-executable instructions to be executed by a computer system. The computer system may include one or more general purpose or special purpose computers (or other electronic devices). A computer system may include hardware components that include special logic for executing steps, or may include a combination of hardware, software, and/or firmware.

Embodiments of the invention may be presented as a computer program product including a computer-readable medium containing instructions that can be used to program a computer system or other electronic device to perform the processes described herein. Machine-readable media may include, but are not limited to, hard disks, floppy disks, optical disks, CD-ROM, DVD-ROM, ROM, RAM, EPROM, EEPROM, magnetic or optical cards, solid-state storage devices, or other types of media/computer-readable media suitable for storage of electronic instructions.

Computer systems and computers in a computer system can be connected through a network. Suitable networks for configuration and/or use as described herein include one or more local area networks, wide area networks, metropolitan area networks, and/or Internet or IP networks such as the World Wide Web, private Internet, secure Internet, value-added network, virtual private network, extranet, intranet, or standalone machines that communicate with other machines through the physical transport of media. In particular, a suitable network may be formed from parts or combinations of two or more other networks, including networks using disparate hardware and network communication technologies.

One suitable network includes a server and several clients; other suitable networks may contain other combinations of servers, clients and/or peers, and a given computer system may function as either a client or a server. Each network includes

- 2 045746 includes at least two computers or computer systems, such as a server and/or clients. The computer system may include a workstation, a laptop computer, a disconnected mobile computer, a server, a mainframe, a cluster, a so-called networked computer or thin client, a tablet, a smartphone, a personal digital assistant or other portable computing device, a smart device, or a consumer electronics device, medical device or combination thereof.

Suitable networks may include communications or networking software, such as those available from Novell®, Microsoft®, and other vendors, and may operate using TCP/IP, SPX, IPX, and other protocols over twisted pair, coaxial, or fiber optic cables; telephone lines; radio waves; satellites; microwave relays; modulated AC power lines; physical data transfer; and/or other data wires known to those skilled in the art. The network may include smaller networks and/or may be connected to other networks through a gateway or similar mechanism.

Each computer system includes one or more processors and/or storage devices; computer systems may also include various input devices and/or output devices. The processor may include a general purpose device such as an Intel®, AMD®, or other off-the-shelf microprocessor. The processor may include a specialized processing device such as an ASIC, SoC, SiP, FPGA, PAL, PLA, FPLA, PLD, or other custom or programmable device. The memory may include static RAM, dynamic RAM, flash memory, one or more flip-flops, ROM, CD-ROM, disk, tape, magnetic, optical, or other computer storage medium. The input device(s) may include a keyboard, mouse, touch screen, light pen, tablet, microphone, sensor or other hardware with accompanying firmware and/or software. The output device(s) may include a monitor or other display, a printer, a speech or text synthesizer, a switch, a signal line, or other hardware with associated firmware and/or software.

Computer systems may be capable of using a floppy disk, tape disk, optical disk, magneto-optical disk, or other means for reading storage media. A suitable storage medium includes a magnetic, optical or other computer readable storage device having a particular physical configuration. Suitable storage devices include floppy disks, hard disks, tape, CD-ROM, DVD, PROM, RAM, flash memory and other computer system storage devices. Physical configuration represents data and instructions that cause a computer system to operate in a specific and predetermined manner as described herein.

Suitable software to assist in the implementation of the invention is readily available to those skilled in the art using the information provided herein and programming languages and tools such as Modern Fortran, Java, Pascal, C++, C, PHP, .Net, database languages, APIs, SDK, build, firmware, microcode and/or other languages and tools. Suitable signal formats may be implemented in analog or digital form, with or without error detection and/or correction bits, packet headers, format-specific network addresses, and/or other supporting data readily available to those skilled in the art.

Aspects of some embodiments of the invention may be implemented as software modules or components. As used herein, a program module or component may include any type of computer instruction or computer-executable code located within or on a computer-readable storage medium. A software module may, for example, contain one or more physical or logical blocks of computer instructions, which may be organized as a program, object, component, data structure, etc., that performs one or more tasks or implements particular abstract data types. A particular software module may contain disparate instructions stored in different locations on a computer-readable storage medium that together implement the described functionality of the module. Indeed, a module may contain a single instruction or many instructions and may be distributed across several different code segments, among different programs, and among several computer-readable storage media.

Some embodiments may be practiced in a distributed computing environment where tasks are performed by a remote processing device coupled through a communications network. In a distributed computing environment, program modules may be located on local and/or remote computer-readable media. In addition, the data linked or visualized together in a database record may be on the same computer-readable medium or on multiple computer-readable media and may be linked together in fields of the database record by

- 3 045746 networks. According to one embodiment of the invention, a database management system (DBMS) allows users to interact with one or more databases and provides access to data contained in the databases.

Fig. 1A and 1B illustrate stresses on rock element 102. In particular, FIG. 1A illustrates the stresses created on rock element 102 by a shock wave emitted from blast hole 104, and FIG. 1B illustrates a resulting radial fracture 110 or fracture in rock element 102. Explosive rock fragmentation is a complex physical process that includes many different physical phenomena, such as the generation and propagation of shock waves, the attenuation of shock waves into stress waves, the formation of cracks and the mechanism of crack growth in rocks, explosive gas loading, and rock movement. etc. This happens dynamically within a fraction of a second. As a result, it is very difficult to capture these physical aspects of blasting using a single closed-form analytical equation. Many numerical models have been proposed to represent rock blast fragmentation. Some of the models were more successful than others in predicting fragmentation.

When a shock wave impacts the borehole wall, the force of the wave far exceeds the compressive strength of the rocks and thus damages and crushes the rock on the surface of the borehole wall. As the shock wave propagates further away from the blast hole 104, the intensity of the shock wave decreases and the shock wave is converted into stress waves. The stress wave exerts a compressive stress 106 in the radial direction and a tensile stress 108 in the tangential direction. In the illustrated embodiment of the invention, the tangential strength of the rock element 102 is less than the compressive strength. As a result, the rock breaks due to tensile stress 108 in the tangential direction and a radial fracture 110 is formed. The high pressure explosive gas penetrates the radial fracture 110 and further increases/promotes rock failure.

Fig. 2A illustrates a three-dimensional model 202 of a portion of a blast site. The three-dimensional model 202 includes a blast hole at each corner (eg, a first blast hole 206, a second blast hole 208, and a third blast hole 210). While the illustrated embodiment of the invention shows blast holes at the corners of the 3D model 202, multiple blast holes may be included throughout the blast site model. The blastholes of the 3D model 202 do not extend all the way to the surface 212 to model the stope for each blasthole.

To generate the three-dimensional model 202, the modeling system may receive multiple inputs. Input data can be obtained from various sources. For example, input data may be obtained from one or more of a human-machine interface (HMI), a previous model stored in the simulation system, a blast site scanning system, or default values stored in the simulation system. Input data may include blast hole data and blast site data. Blasthole data may include blasthole parameters such as blasthole spacing, blasthole load, blasthole depth, blasthole diameter, blasthole location, number of blastholes, stope information, blasting properties, blasthole angle, position blast hole, row offsets, triggering, front row load, top blast hole coordinates, bottom blast hole coordinates, underdrilling information and loading information.

The blast site data may include formation information and geological properties of the blast site. Non-limiting examples of formation information include surface angle, formation height, formation inclination angle, shaft inclination angle, free surface location, and waste angle. Non-limiting examples of geological properties include mineralogy (elemental and/or mineral), lithology (primary, secondary, and/or texture), porosity, hardness, attenuation, Young's modulus, shear modulus, bulk modulus, Poisson's ratio, P-wave velocity, S-wave velocity, rock density, rock type, rock strength, rock conditions, rock description, pullout condition, pullout angle, pullout orientation, standard deviation of pullout interval, cohesion, vertical pullout spacing, horizontal pullout spacing, unlimited strength at compression (UCS), sonic speed, drilling standard deviation, impact velocity, rock fracture toughness, rock reflectivity, rock tensile strength, angle of internal friction, Hugoniot data (e.g. Up min, Up max, Us min, Us max), and soil stresses (σ1, σ2, σ3, stress orientation, DIP, tilt and rotation). Texture refers to the size, shape and arrangement of interlocking mineral crystals that form a rock or other material. Geological properties can be used to determine additional geological characteristics such as abrasion and fragmentation.

Fig. 2B illustrates a three-dimensional model 202 segmented into a plurality of volume elements (eg, element 204). The 3D model 202 can be segmented into as many or as few elements as desired. A large number of elements can provide better resolution for the simulation, while a smaller number of elements can use less computational resources.

The simulation system can track cracks from a simulated explosion within each element. The resulting FDM can predict the intensity of fracturing within each element. Fracture intensity refers to the number of cracks within a given area (e.g., element). The cracks can be either natural detachments or cracks caused by the shock wave from the explosion. Fracture intensity can also be called fracture frequency. By monitoring the fracture intensity of each element, the modeling system can predict the size of the fragment.

Fig. 3A illustrates a top plan view of the 3D model 202 before any simulated explosions. As illustrated, the three-dimensional model 202 includes a first blast hole 206, a second blast hole 208, a third blast hole 210, and a fourth blast hole 302. In addition, the three-dimensional model 202 includes natural breakout groups 304 in the rock. Natural detachment groups 304 are pre-existing detachment fractures that are part of the geological properties of the rock. In some embodiments, natural tear groups 304 may extend uniformly downward through the 3D model 202, while in other embodiments, natural tear groups 304 may vary in location and orientation throughout the 3D model 202. For example, different rock layers can be modeled with different group of natural separations.

Fig. 3B illustrates a plan view of the three-dimensional model 202 after simulated blasts from the first blast hole 206 and the second blast hole 208. As shown, the blasts result in fractures (ie, blast cracks 306) that extend from the blast holes.

The FDM modeling system predicts the size of rock fragments based on fracture-fracture interactions from natural fracture groups 304 present in the rock and caused by blast fractures (ie, blast fractures 306) from blastholes. Fractures from blastholes interact with each other and with groups of 304 natural fractures in the rock. These interactions can be used by the modeling system to determine the equivalent crack intensity.

As shown, regions near blast fractures 306 impact the geology, causing multiple fractures within that region. Blast cracks 306 propagate and become less dense the further they extend from the blast holes. In the area between blastholes, fracture interactions between natural detachment groups 304 and blast fractures 306 have a greater impact on rock fragmentation. In these areas, the modeling system can account for the combined effects of natural fragmentation and post-blast fragmentation, and even overlapping fragmentation from adjacent blastholes.

In some embodiments of the invention, the modeling system may take into account cracks from previous explosions when determining the intensity of fracturing. For example, when blasting formations, a new free surface is created after the explosion of a series of blast holes. While the blasthole row now no longer exists, the modeling system can store blast-induced cracks that are within the new free surface. Previous explosion cracks can be added to naturally occurring fragments and fragments from the next explosion.

The intensity of the resulting blast cracks can be predicted by an empirical equation that takes into account the physical aspects of the problem, such as: i) blast properties, ii) rock properties, iii) blast geometry and iv) blast time. One advantage of the fracture intensity concept is that the intensities (defined as fractures per unit length) can be added if their angles to the free surface are similar. This addition may be valid regardless of the source of the equivalent crack.

In some embodiments of the invention, the intensity of explosion-induced fracturing may be as follows:

where k is a site-specific calibration parameter which may be based on i) blast properties ii) rock properties and iii) blast geometry;

r is the distance from the well in feet.

As shown, the intensity of fracturing decreases rapidly depending on the distance from the blast hole. For example, at a distance of one foot from the well, the fracture frequency may be 4,000 fractures per foot. At 16 feet, the frequency of cracks can be reduced to one crack per foot.

In some embodiments of the invention, the intensity of blast-induced fracturing can be calculated using the following equation:

- 5 045746

F = K *F1 *F2 *F3 (EQUATION 2) where

F1 corresponds to rock and explosive properties, F2 gives the shape of the particle size distribution curve (eg the geometric term for a cylindrical charge), and F3 creates an intensity effect based on the element's distance from the charge;

K is the calibration parameter for a specific area. The K parameter may depend on the rock fracturing properties of a particular area. The functions in equation (2) are shown below in detailed equations: / N*

F1 ₌ —| i pp*pp / \y (EQUATION 3)

GNao / 1 nmh .XMSW

F2= tan ^-1 ——- + tan ¹ —— ) I

L i\R R/J (EQUATION 4)

(EQUATION 5) where where F1, the numerator is the rock strength described by the strain energy density, and the denominator is the available explosive energy;

R ₀ corresponds to the well radius;

R is the radial orthogonal distance of the element from the well;

BR is the distance of the element from the blast hole. (BR differs from R in the stopping zone);

HMX and XMS are distance functions estimated for different blasthole orientations using vector distance equations; and NMX is the distance from the bottom of the charge to the center of the element (measured along the direction of the blast hole). XMS is the distance from the top of the charge to the center of the element (measured along the direction of the blast hole).

Indicators α, Υ and δ are calibrated using test blasts of the formation.

PF - powder factor.

EE is the energy of explosives.

As can be seen from Equations 1-5, these functions are dimensionless, which may allow embodiments to more flexibly use different unit systems such as: SI, CGS, etc. Arctangent F2 functions can create the desired shape of the fragment size distribution.

To calibrate the equations and find the best set of parameters (K, α, Υ, δ), the root mean square error (RMSE) between the experimental and numerical data sets can be calculated. In some embodiments of the invention, multiple optimization iterations may be performed to minimize the RMSE error and find the best set of parameters to represent the explosion. In some embodiments, the FDM system can adapt a fracture density model to the blast region using RMSE. For example, a site RMSE study can be performed by repeatedly running fracture density models many times (eg, 1000 simulations) while gradually varying the FDM fitting parameters (eg, K, α, Υ, δ). To study RMSE, the system can compare FDM results with actual blast results at a specific site. The system can attempt to optimize the FDM parameters (K, α, γ, δ) to match the actual blast data by performing thousands of RMSE iterations. Using simulations, the system can obtain optimized RMSE fitting parameters for the FDM (for that specific region). The result of the RMSE study can be tuned fitting parameters that can accurately predict fragmentation caused by future blasting operations.

The fracturing intensities from blast fractures 306 and natural rupture groups 304 may be combined to determine the overall fracturing intensity for each of the elements making up the 3D model 202. For example, for each element of the 3D model 202, the modeling system may add the blast fractures 306 and natural rupture groups 304, located in the element to determine the overall intensity of fracturing for each element.

In some embodiments of the invention, the interaction between cracks can be combined using a combination rule for FDM. The modeling system can predict the fracturing intensity in a volume element using Equation (2), and then combine the result with previous fracturing intensities using the following Equation 6.

It = (Ze + Zn). cos ² (Ae - An) + max(Ze, C. In). sin ² (Ae - A _n ) (EQUATION 6) where

I _r is the resulting intensity of fracturing in a volume element. Ie and _Ae are the existing intensity of fracturing and the angle of fracturing, respectively. Similarly, In and An correspond to the new fracture intensity and fracture angle. C is the fault intersection coefficient, which is essentially a factor reducing the fracturing intensity for orthogonal fracturing intensities.

As a rule, parallel cracks can add up and increase intensity. On the other hand, orthogonal cracks tend to reduce the intensity of fracturing in the volume element. The crack angle with higher intensity can be considered dominant and saved for the next iteration. Determination of the crack angle is discussed with reference to FIG. 7A and FIG. 7B.

Using the overall fracture intensity, the modeling system can determine the size of the fragmentation. In some embodiments of the invention, the fragment size for each element can be determined by calculating:

Fragment Size = V ^Y /F (EQUATION 7) where F is the total intensity of fracturing.

In fig. 4 illustrates vector mechanics equations 404 that can be used by an FDM system to calculate distance functions and detect charge positions relative to a rock element in a blast. The vector mechanics equations 404 use the angle between the blast hole 410 and the rock feature 402 at the bottom 406 of the hole, and the angle between the blast hole 410 and the rock feature 402 at the top 408 of the hole. The vector mechanics equations 404 in the illustrated embodiments of the invention are as follows:

I.ST = |H| |ST| cos θ where H is a vector with the length and direction of the blast hole from the base of the hole to the top of the hole;

SB - vector drawn from the base of the well to the center of the element;

ST is a vector drawn from the center of the element to the top of the well.

Vector mechanics equations 404 can be used to solve the distances HMX 416 and XMS 418. HMX and XMS are distance functions that can be used in FDM. NMX is measured as the distance from the base of the well to the intersection point 420. XMS is measured as the distance from the well top 408 to the intersection point 420. The intersection point 420 is the intersection between a perpendicular line drawn from the center of the rock element 402 and the blast hole line represented by the vector H. The FDM system may use H.SB and H.ST to calculate the angles β and θ. The system can then use these angles (β and θ) and direction cosines to mathematically calculate the distances HMX and XMS.

In some embodiments of the invention, the FDM modeling system can use these vector mechanics equations 404 to accurately process rock in different subzones of the model. Using dot products and direction cosines, the modeling system can predict the intensity of fracturing in different areas without explicitly defining blast parameters such as load, spacing, stoppage, auxiliary drilling, etc.

In some embodiments of the invention, the FDM modeling system can deal with any blast hole orientation and variable blast parameter using vector mechanics equations 404. Using vector mechanics equations 404, the modeling system may be able to accurately predict charge distance and location functions regardless of the size, position, or orientation of the blast hole. For example, vector mechanics equations 404 may be used to process calculations for blasts with inclined blast holes and variable charge lengths/positions.

Fig. 5 illustrates a top plan view of a ghost hole blast model 500 for determining fractures and fracturing intensity due to reflected shock waves in each element of the blast model in accordance with one embodiment of the invention. The blast model 500 is a formation blast model with a free surface 506. Similar to the three-dimensional model 202 of FIG. 2B, the explosion model 500 may be three-dimensional and include multiple individual elements. Reflected shock waves 502 occur when the shock wave from the explosion reaches the free surface 506 and the top surface. In some embodiments of the invention, the variable reflectivity of the free surfaces can be set to 100%.

The ghost boreholes 504 may be spaced equidistant from the free surface 506, like a series of test blast boreholes 510. The test boreholes 510 are boreholes currently undergoing a simulated blast. Test wells 510 are located from the free surface 506 at a distance from the load 508. Accordingly, in the illustrated embodiment, ghost wells 504 are located outside the free surface 506 at a distance from the load 508. Since the ghost wells 504 are located outside the free surface 506, the ghost wells 504 are located in the free space and do not have direct contact with any explosive Model 500 rock elements.

To simulate an explosion from test blast holes 510, the simulation system can initiate an explosion from both test holes 510 and ghost holes 504 simultaneously. As a result of the simultaneous initiation and placement of ghost holes 504, when shock waves from test blast holes 510 reach the free surface 506, shock waves from ghost holes 504 act as reflected shock waves 502 to simulate an explosion. Thus, the modeling system may use reflected shock waves 502 to simulate shock waves from ghost wells 504. In some embodiments of the invention, the modeling system may assume that the reflectivity of the free surfaces is 100%. Thus, the shock wave from ghost wells 504 may be equivalent in magnitude to the shock wave from test wells 510. In other words, the equations discussed with reference to FIGS. 3B can be used to calculate the fracture intensity from each of the test blast holes 510 and each of the ghost holes 504.

The ghost wells 504 may have the same shape as the test wells 510. For example, the ghost wells 504 may have the same diameter and depth as the test wells 510. In some embodiments, the ghost wells 504 may be simulated to emit a shock wave length charge test wells 510. In other embodiments, ghost wells 504 can be simulated to emit a shock wave with the length of the charge and plug test wells 510.

In some embodiments of the invention, additional ghost boreholes can be used to simulate reflection from the top surface of the explosion model, for example, ghost boreholes can be placed at a distance from the top surface equal to the length of the stope area. These ghost boreholes may be called ghost boreholes and can generate reflected shock waves in the borehole area. These ghost holes simulate the reflection of shock waves on the top surface of explosions.

In some embodiments, test holes 510 may be located based on actual scan or GPS data from an already drilled blast site. In some embodiments, test blastholes 510 may be based on a previously blasted area and account for blastholes that were overcharged, undercharged, failed to detonate properly, were partially filled with water, or otherwise had abnormal detonations. This data can be fed into a model to predict post-blast fragmentation.

The reflected shock waves 502 that are generated in the ghost wells 504 may have a different angle than the shock waves from the test wells 510. For example, in one embodiment of the invention, the reflected shock waves 502 from a plurality of ghost wells 504 are modeled as a first angle tensile wave, and the shock wave from the plurality of test wells 510 is modeled as a compression wave at a second angle.

Ghost wells 504 can also be used by the modeling system to create dynamic free surfaces, as described in connection with FIG. 6 (see Fig. 6).

Fig. 6 illustrates a planar top view of a blast pattern 600 with ghost holes 608 and a dynamic free surface 604. The blast pattern 600 contains multiple rows of blast holes (ie, row R5 612 and row R6 610). The blast holes in Row R5 612 had previously been blasted. Before the blast holes of row R5 612 were blasted, a dynamic free surface 604 was positioned in front of row R5 612 to incorporate row R5 612 into the formation. The modeling system has moved the dynamic free surface 604 to the back row R5 612, representing rock elements broken off from the formation during the explosion of row R5 612. Moving the dynamic free surface 604 allows the modeling system to more accurately determine the effects of reflected shock waves. In this example, t0 is the ignition time and Ri is the ignited rows (i=1, 2,...n).

As each row fires during the simulation, the simulation system dynamically moves the dynamic free surface 604. Moving the dynamic free surface 604 can help avoid strapping and incorporate reverse rupture effects into the explosion model 600. When a row fires, a firing 606 and a new free surface occurs, as shown by dynamic free surface 604. Dynamic free surface 604 will move as additional rows fire over time.

Trigger 606 represents the distance between the previously ignited row and the new location of the dynamic free surface 604. Whenever a row is ignited, rock elements located in line with the row and between the row and the previous free surface are displaced. Additionally, in some embodiments, some rock elements behind the row (eg, rocks further from the previous free surface than the blasted row) are also displaced. For example, the distance between row R5 612 and dynamic free surface 604 is actuation 606. In some embodiments, actuation 606 may be one third of the load. In some embodiments of the invention, the dynamic free surface 604 may be modified such that the load of the plurality of blastholes changes at different Y-axis heights of the model.

Trigger 606 changes the load for the next row to be fired. Effective on

- 8 045746 load 602 is the row spacing minus actuation 606. The effective load 602 is used to determine the placement of ghost wells 608. The ghost wells 608 are located at a distance equivalent to the effective load 602 from the dynamic free surface 604. In other words, the row spacing 618 R6 610 and dynamic free surface 604 is equal to the distance 620 between dynamic free surface 604 and ghost wells 608. Ghost wells 608 are located on the opposite side of dynamic free surface 604 relative to row R6 610.

The ghost holes 608 initiate shock waves at the same time as the shock waves from the R6 series blast holes 610. The shock waves from the ghost holes 608 reach the dynamic free surface 604 at the same time as the shock waves from the R6 series blast holes 610 and simulate shock waves reflected from dynamic free surface 604. Accordingly, the ghost holes 608 follow the same timing as row R6 610. That is, whenever one of the blast holes in row R6 610 is ignited, the corresponding ghost well is ignited. For example, when the first blast hole 614 is ignited for 200 milliseconds (ms) and a wave is emitted, a shock wave is simultaneously emitted from the first ghost hole 616. Likewise, in the illustrated embodiment of the invention, the remaining pairs of blast holes and ghost holes are ignited for 225 ms, 250 ms, 275 ms and 300 ms.

Dynamic free surface 604 can be created for any blasting pattern or timing sequence. Additionally, by using dynamic free surface 604, the modeling system can avoid strapping when simulating a large problem with multiple rows and wells.

Fig. 7A and 7B illustrate how the modeling system can determine crack angles. The crack angles are defined as the angle of the actual shock waves and the reflected shock waves. Fig. 7A illustrates a planar top view of blast pattern 702 and fracture angles from the first blast hole 704. The angle of the shock wave from the first blast hole 704 can be determined by the modeling system by finding the angles between the free surface 708 and the direction of the incident shock wave. More specifically, the angles for the incident shock wave are the angles between the inside of the free surface 708 and the direction of the incident wave.

Similarly, FIG. 7B illustrates a top plan view of the blast pattern 702 and fracture angles from the ghost hole 706 corresponding to the first blast hole 704. As shown, the reflected shock wave angles of the ghost hole 706 can also be calculated from the inside of the free surface 708 and the direction of the reflected wave.

In some embodiments of the invention, angles are considered positive. In addition, if the position of the blast hole changes in the vertical direction (Y direction), the modeling system can use direction cosines to accurately determine the location of the charge in the plane (X-Z plane). The system can use the calculation and storage of dominant fracture intensity angles. For example, parallel cracks interact, while orthogonal cracks interfere with each other. The system can recognize the order in which fractures appear and takes into account the interaction of newly created fractures with existing fractures in each volume element for each well that is fired.

Fig. 8 illustrates a side view of a borehole 802. As shown, the blast hole 802 includes a stopper 804 and an explosive charge 806. In some embodiments, the modeling system may use illustrated elliptical fracturing intensity contours 808 with dual ArcTan functionality to determine fragment sizes for each element of the 3D model and obtain a fragmentation size distribution. Fracture intensity contours 808 may be centered around the explosive charge 806.

In some embodiments of the invention, the FDM modeling system may integrate FDM with multiple geological layers and multiple reservoirs. Geological layers and multiple strata can be input to an FDM modeling system.

Fig. 9A illustrates a three-dimensional model that incorporates rock type properties to more accurately predict fracturing severity. Each rock layer (also called a geologic layer) can be associated with rock properties, including density, fracture toughness, and modulus. These rock properties can influence how cracks form in the elements in each rock layer. For example, less dense rock may allow a crack to propagate further than denser rock.

Input data to the FDM modeling system, representing the geological layers in the hole or blasting pattern, can be applied to the FDM analysis. Geological layers can be layers with different geological properties (such as rock type, porosity, hardness, etc.) An FDM modeling system can use geological properties to adjust how cracks form in rocks based on geological properties, so that cracks in different geological layers may appear differently. For example, blast cracks in each of a plurality of volume elements depend on which geological layer the plurality of volume elements are located in.

- 9 045746

Non-limiting examples of geological properties include mineralogy (elemental and/or mineral), lithology (primary, secondary and/or texture), porosity, hardness, rock strength and density. Texture refers to the size, shape and arrangement of interlocking mineral crystals that form a rock or other material. Geological properties can be used to determine additional geological characteristics such as abrasion and fragmentation. Geological properties can be determined directly or indirectly from sources such as seismic data, drilling data, drill cuttings, core samples, or combinations thereof. For example, drill cuttings and/or core samples can be analyzed using x-ray or gamma fluorescence, scanning electron microscopy and other spectroscopy and/or microscopy techniques. Geologic data may include information on an incremental basis, such as per foot.

In some embodiments of the invention, geological properties of subsurface layers can be obtained from drilling data. Drilling data can be obtained by sensors on the drilling machine using artificial intelligence. Drilling data may include information such as drill bit size, drill bit rotation speed, drill bit torque, rate of penetration, bit vibration, drop pressure, deformation air pressure, hole location, hole number, and hole length or depth . Drilling data can be correlated with geological properties along the entire length of the blast hole. Thus, drilling data can be used to create hardness values along the length of the blast hole (i.e., hardness profile).

Fig. 9B illustrates a cross section of a multi-layer vertical blast hole 910. Layers can be segments with different explosion energies. For example, each segment may have a different emulsion density or ANFO energy density. Vertical blast hole 910 may be filled with an explosive article 61 (eg, a sensitized product) comprising a first explosive article 61a delivered at a first blast energy A, a second explosive article 61b delivered at a second blast energy B, a third explosive article 61c delivered at a third blast energy C, and a fourth explosive article 61d delivered at a fourth blast energy D. It will be understood that the explosive article 61 may also include additional segments delivered at a different blast energy. The explosion energy in each layer can be set according to the hardness of the rock in that layer. The hardness of a rock layer can be in any random order with depth. Thus, the formation energy of the explosion can be distributed in any order inside the blast hole. The blast energy may be filled in a manner that attempts to match the geologic properties to an adjacent explosive article with a blast energy that matches the geologic properties.

Fig. 9B illustrates the relative blast energy distribution along blast hole 910 with a histogram E on either side of blast hole 910. Although the explosive article 61 is illustrated with four different feed densities, the relative blast energy distribution in some embodiments of the invention may vary gradually from the top part of the explosive article 61 to the bottom of the explosive article 61. In some embodiments, the distribution of explosion energy within each formation may remain constant or nearly constant, and each formation may include an explosion energy selected based on the geological properties within that formation.

The FDM modeling system can use blast layering as input to prepare fracture models. Explosive layering may be layering of emulsion densities or layering of explosive energy from an explosive article (eg, ANFO).

In some embodiments of the invention, the FDM modeling system can use both blast layering and geological layers in preparing fracture models. In some models, geological layers and explosion energy layers may coincide. In other models, the geological layers and the explosion energy layers do not coincide.

Fig. 10 illustrates a simulation of a mine face model 1000 using FDM. As shown in the illustrated example, the modeling system can simulate angled blast holes with different charge lengths using FDM. As can be seen, physical parameters such as charge length, stoppage and spacing can vary in different subzones of the model.

To determine fragmentation size and fragmentation intensity, the modeling system can generate explosion parameters by reading the top and bottom coordinates of the charge and calculating other parameters using vector distance equations, as described with reference to FIG. 4. Fracture intensity can then be calculated as described here.

Fig. 10 also illustrates a graph 1002 of fragment size distribution. Near blast holes, the explosion produces very small sized rock particles. Fragment size distribution plot 1002 shows fragmentation in various subzones of the model. Larger particles may be shown with a gradient. The fragment size distribution plot 1002 can be used to validate the model and to add more precision to the two-dimensional distribution plot.

- 10,045,746 particles in size.

Fig. 11 illustrates a flow diagram of a method for predicting the size of rock fragmentation resulting from an explosion. The modeling system using method 1100 will use a model of the explosion site. The blast site model may include blast hole data and blast site data. Blasthole data may include blasthole parameters such as blasthole spacing, blasthole load, blasthole depth, blasthole diameter, blasthole location, number of blastholes, stope information, blasting properties, blasthole angle, position blast hole, row offsets, triggering, front row load, top blast hole coordinates, bottom blast hole coordinates, underdrilling information and loading information. In some embodiments, method 1100 may include selecting the type of explosive to be used, selecting the length of the charge, and placing the charge in a plurality of blast holes.

The blast site data may include formation information and geological properties of the blast site. Non-limiting examples of formation information include surface angle, formation height, formation inclination angle, shaft inclination angle, free surface location, and waste angle. Non-limiting examples of geological properties include mineralogy (elemental and/or mineral), lithology (primary, secondary, and/or texture), porosity, hardness, attenuation, Young's modulus, shear modulus, bulk modulus, Poisson's ratio, P-wave velocity, S-wave velocity, rock density, rock type, rock strength, rock conditions, rock description, pullout condition, pullout angle, pullout orientation, standard deviation of pullout interval, cohesion, vertical pullout spacing, horizontal pullout spacing, unlimited strength at compression (UCS), sonic speed, drilling standard deviation, impact velocity, rock fracture toughness, rock reflectivity, rock tensile strength, internal friction angle, Hugoniot data (e.g. Up min, Up max, Us min., Us max), and soil stresses (σ1, σ2, σ3, stress orientation, DIP, tilt and rotation). Texture refers to the size, shape and arrangement of interlocking mineral crystals that form a rock or other material. Geological properties can be used to determine additional geological characteristics such as abrasion and fragmentation.

The modeling system may segment the explosion site model 1102 into multiple volume elements. The modeling system can track fracturing intensities in each volume element throughout the simulated explosion. For example, the modeling system can identify 1104 pre-existing tensile cracks in multiple volume elements. The modeling system can simulate 1106 explosions from each of a plurality of blast holes and identify 1108 blast cracks (blast cracks) in a plurality of volume elements. Explosions can be simultaneous or sequential. For successive after each explosion, the modeling system can record the intensity of fracturing created by the explosion.

In some embodiments, the modeling system may simulate 1110 shock wave reflection on the free surface of the model by simulating explosions at a plurality of ghost wells outside the free surface to identify reflective cracks in a plurality of volume elements. The modeling system can integrate 1112 pre-existing rupture cracks, explosion cracks, and reflective cracks to determine the overall intensity of fracturing across multiple volume elements. The modeling system can convert the overall fracture intensity associated with each volume element to determine the fragmentation size for each volume element and provide 1114 a predicted fragmentation size distribution for the model based on the overall fracture intensity across multiple volume elements.

In some embodiments, the modeling system may use a dynamic free surface. The modeling system can move the dynamic free surface after the row is blasted. For example, the system may move the free surface after the first row has exploded to a position behind the first row to account for the trigger. In some embodiments of the invention, the free surface may move beyond the first row by one third of the load. The new location of the dynamic free surface can then be used to blast the next row. A moving free surface can cause differences in the placement of ghost wells. For example, in some embodiments, the ghost holes are located at a distance from the free surface equal to the distance between the blast holes and the free surface. Thus, ghost holes can be considered mirror blast holes, where the blast holes are on the first side of the free surface and the ghost holes are on the second side of the free surface.

Method 1100 may be used before blast holes are drilled, after blast holes are drilled, or after an explosion has occurred. For example, method 1100 may be used to plan a blast that has not yet been executed, or it may be used to estimate the extent of fragmentation of a blast that has already been executed. For example, after an explosion has completed, but before the equipment has begun removing dirt, the system can run a simulation based on knowledge of how

- 11 045746 there was actually an explosion. This way, holes that were overcharged, undercharged, did not detonate properly, partially filled with water, etc. can be entered into the simulation and the mine engineer will receive an updated prediction of what fragmentation was caused by the explosion. In some embodiments of the invention, the system may also predict blast ejection and predict fragmentation size areas in the broken rock. In some embodiments of the invention, prediction of the size of the broken rock and fragments can be used to calculate the cost and time of removing material from the blast site, as well as the time and costs associated with crushing the ore.

Fig. 12 is a block diagram of an FDM modeling system 1200 in accordance with one embodiment of the invention. The FDM modeling system 1200 may perform the methods and use technologies described with reference to other figures in the application materials. The FDM simulation system 1200 may include a memory 1203, one or more processors 1204, a network interface 1206, an I/O interface 1208, and a system bus 1209.

One or more processors 1204 may include one or more general purpose devices such as an Intel®, AMD®, or other standard microprocessor. One or more processors 1204 may include a special purpose processing device such as an ASIC, SoC, SiP, FPGA, PAL, PLA, FPLA, PLD, or other customizable or programmable device. One or more processors 1204 may perform distributed (eg, parallel) processing to perform or otherwise implement the functionality of the embodiments disclosed herein. One or more processors 1204 may run a standard operating system and perform standard operating system functions. It is envisaged that any standard operating systems can be used, such as, for example, Microsoft® Windows®, Apple® MacOS®, Disk Operating System (DOS), UNIX, IRJX, Solaris, SunOS, FreeBSD, Linux®, ffiM® OS /2® and so on.

Memory 1203 may include static RAM, dynamic RAM, flash memory, one or more flip-flops, ROM, CD-ROM, disk, tape, magnetic, optical, or other computer storage media. Memory 1203 may include a plurality of program modules 1210 and program data 1220. Memory 1203 may be local to the FDM simulation system 1200, as shown, or may be distributed and/or remote relative to the FDM simulation system 1200.

Data generated or used by FDM modeling system 1200, such as program modules 1210 or other modules, may be stored in memory 1203, such as stored program data 1220. Data 1220 may be organized as one or more databases.

The data 1220 may include blast site model 1222, fracture intensity 1224, and contact, fragment size 1226 data. The blast site model data 1222 may be input by the user through the input/output interface 1208 or received from other sources such as an artificial intelligence drilling machine and a computer-aided blast design system. In some embodiments, blast site model data 1222 may include blast hole data, formation information, explosive information, natural lift information, and geology input data. In some embodiments, the FDM modeling system 1200 may be coupled to an artificial intelligence drilling machine containing sensors to obtain rock properties for subsequent fragmentation modeling. Geological properties of volumetric features can be based on drilling machine data using artificial intelligence. Geological properties can influence how each volume element fragments. In some embodiments, the FDM modeling system 1200 may be coupled to a computer-based blast design system to create charge arrangements for subsequent fragmentation modeling. In some embodiments, the FDM modeling system 1200 may read blast properties from each well using individual blast hole analysis data. Fracture intensities 1224 may include fractures for each of a plurality of volume elements of the blast site model. In some embodiments, fracturing intensities 1224 are stored in groups for each volume element, with each group containing natural lift-off intensity, fracturing intensity from each simulated blasthole explosion, and reflected shock wave fracturing intensity from each simulated blasthole explosion. Fragment size data 1226 may record the fragment size associated with each volume element based on fracture intensities 1224.

Software modules 1210 may include all or parts of other elements of the FDM modeling system 1200. Software modules 1210 may perform multiple operations simultaneously or in parallel through or on one or more processors 1204. In some embodiments of the invention, portions of the disclosed modules, components, and/or means are implemented as

- 12 045746 non-volatile instructions implemented in hardware or firmware, or stored on a non-volatile computer-readable storage medium. Executable instructions may comprise computer program code that, when executed by a processor and/or computing device, causes a computing system to implement certain processing steps, procedures and/or operations as described herein. The modules, components and/or means disclosed herein may be implemented and/or implemented as a driver, library, interface, API, FPGA configuration data, firmware (eg, stored in EEPROM) and/or the like. In some embodiments, portions of the modules, components, and/or means disclosed herein are implemented as machine components, such as general and/or dedicated devices, including, but not limited to: circuits, integrated circuits, processing components, interface components, hardware controller(s), storage controller(s), programmable hardware, FPGAs, ASICs and/or the like. Accordingly, the modules disclosed herein may be referred to as controllers, layers, services, engines, means, drivers, circuits, subsystems, and/or the like.

Modules 1210 may include a fracture simulator 1212, a fracture combination calculator 1214, and a fragmentation size converter 1216. Fracture simulator 1212 can simulate explosions from each blast hole and reflected shock waves from a plurality of associated ghost holes. The fracture simulator can also track fracture intensities 1224 from simulated explosions. The fracture combination calculator 1214 can combine fracture intensities. The fragmentation size converter 1216 may convert the overall fracture intensity of each volume element into a fragment size 1226. In some embodiments, modules 1210 of FDM modeling system 1200 may be used to perform detailed explosion analysis. Detailed blast analysis can include: 2D PSD plot, 3D PSD, and predict the location of large boulders. In some embodiments, modules 1210 of FDM modeling system 1200 may be used to optimize blast design/charge placement (eg, load, interval factors, borehole diameter, blast energy, etc.) to obtain a desired fragmentation profile. For example, the FDM simulation system 1200 may receive inputs characterizing the desired fragmentation size and perform many different simulations using multiple blast designs to determine the final blast design (e.g., row load, well spacing, well diameter, blast energy, etc. ...), which results in the desired fragmentation size. The final blast design can be displayed on a graphical user interface (GUI). In some embodiments of the invention, the final blast design may be used to control one or more of blasthole drilling, blasthole loading, and/or detonation sequencing.

The input/output interface 1208 may facilitate user interaction with one or more input devices and/or one or more output devices. The input device(s) may include a keyboard, mouse, touch screen, light pen, tablet, microphone, sensor or other hardware with accompanying firmware and/or software. The output device(s) may include a monitor or other display, a printer, a speech or text synthesizer, a switch, a signal line, or other hardware with associated firmware and/or software. For example, in one embodiment of the invention, input/output interface 1208 includes a display for providing a graphical user interface (GUI) illustrating potential ablation perimeters. The input/output interface 1208 may receive user input 1222. In some embodiments of the invention, the input/output interface 1208 is a touch screen, and the size input is received through the touch screen. In some embodiments, the I/O interface 1208 may overlay target ablation perimeters onto the tissue image.

Network interface 1206 may facilitate communication with other computing devices and/or networks and/or other computing and/or communications networks. In some embodiments of the invention, the network interface 1206 may communicate with one or more of an artificial intelligence drilling machine, a blast design system, and an explosive delivery vehicle. Network interface 1206 may be provided by conventional network connectivity means, such as, for example, Ethernet (IEEE 1102.3), Token Ring (IEEE 1102.5), Fiber Distributed Datalink Interface (FDDI), or Asynchronous Transfer Mode (ATM). However, the network interface 1206 may be configured to support various network protocols, such as, for example, Internet Protocol (IP), Transmission Control Protocol (TCP), Network File System over UDP/TCP, Server Message Block (SMB), Shared File System Microsoft® Internet Services (CIFS), Hypertext Transfer Protocols (HTTP), Direct Access File System (DAFS), File Transfer Protocol (FTP), Real Time Publishing Subscription Protocols (RTP), Open Systems Interconnection Protocols (OSI), Transfer Protocol Simple Mail (SMTP), Secure Shell (SSH), Secure

- 13 045746

Socket Layer (SSL) and so on.

The system bus 1209 may facilitate communication and/or interaction between other components of the FDM simulation system 1200, including one or more processors 1204, memory 1203, I/O interface 1208, and network interface 1206.

Example

The following example illustrates the disclosed methods. In light of this disclosure, those skilled in the art will appreciate that variations on these examples and other examples of the disclosed method will be possible without undue experimentation.

Example 1: Test results using US Bureau of Mines data.

The United States Bureau of Mines (USBM) conducted a series of 29 blasts at the Rolla Experimental Site at the University of Missouri and screened the blasted rocks to obtain a fragment size distribution plot (Otterness et al., 1991). The blasts had 3 or 4 blast holes, with a delay of 1-4 ms per foot of load. Other design parameters were formation height, load, interval, bottomhole and well diameter. In table Figure 1 shows the range of parameters that were used in the USBM test (all units are in inches). The strata used for the explosions were in a massive dolomite formation and the charges used were ammonia dynamite with a density of 1.12 g/cm ³ . FDM was created to simulate these 29 USBM formation explosions.

Table 1. Range of physical parameters used in the test

USBM 29 (Otterness et al, 1991)

A three-dimensional (3D) mesh with approximately 20,000 discrete volume elements was created to represent the blast geometry of the USBM formation. Equations 2-5 were used to predict the intensity of fracturing at each volume element. Fracture intensities were then converted to an equivalent size assigned to each element. Numerical bins were used to select sizes and create a fragment size distribution curve. To calibrate Equations 2-5 and find the best set of parameters (K, α, Υ, δ), the root mean square error (RMSE) between the experimental and numerical data sets can be calculated. Several thousand optimization iterations were performed to minimize the RMSE error and finally find the best set of parameters to represent the 29 USBM explosions.

Fig. 13A illustrates a three-dimensional FDM contour plot 1302 of the fracture intensity of a three-dimensional explosion model with multiple discrete elements. In particular, in FIG. 13A shows a 3D FDM contour plot of fracture intensity for one of the 29 USBM blasts. As can be seen, very high crack intensity is observed near the blast holes. This high intensity corresponds to the very small size of the rock near the blast holes. Further from the wells, the intensity weakens and, consequently, the size of the rock increases.

Fig. 13B illustrates a two-dimensional particle size distribution curve 1304. The two-dimensional particle size distribution curve 1304 is in good agreement with the USBM experimental data. To produce a two-dimensional particle size distribution curve 1304, the modeling system used fracture intensities and converted them to an equivalent size assigned to each element. The modeling system used numerical bins to select sizes and plot the fragment size distribution curve. A two-dimensional particle size distribution curve 1304 illustrates the percentage of rocks capable of passing through various filter sizes.

The two-dimensional particle size distribution curve 1304 includes a predicted fragment size distribution curve 1306 using FDM and an actual fragment size distribution curve 1308 . As can be seen, the predicted fragment size distribution curve 1306 matches the actual fragment size distribution curve 1308 well.

Fig. 14 illustrates a plan view of an explosion model 1400. In the illustrated embodiment, the three-dimensional blast model 1400 includes three blast holes, shown as circles (first blast hole 1402, second blast hole 1404, and third blast hole 1406), and a plurality of rock features, shown as boxes with dotted boundaries (e.g., feature FDM 1408). As shown, three fractures emerge from the blast holes (eg, first fracture 1410, second fracture 1412, and third fracture 1414). Breaks are illustrated by zigzag lines with an arrow at the end representing the direction in which the break occurred.

Time is an important parameter in explosion design. Time between wells in a row and

- 14 045746 time between rows can significantly affect rock fragmentation. In general, a short delay time (simultaneous ignition) or a very long delay time can lead to poor fragmentation. The delay time may be optimal, which may result in better fragmentation for the explosion. In FDM, the system can handle the effect of delay time as described below.

The timing of fracture occurrence from various blastholes on an element of interest (eg, FDM element 1408) can be calculated using Equation 8. Then, using a combination rule, the fracture frequencies can be combined in the sequence in which they appeared on the element of interest. This gives the resulting crack frequency and fragmentation data for each element of interest. In Equation 8, represents the well ignition time (NH), which is known from the delay time among wells in a row and the delay time among rows. t ₀ (NH)

Time (the appearance of a gap) = --------sorrow p„р.,„. (v _c) --------- ⁺ « ^ΝΗ ' (EQUATION 8)

As shown in FIG. 14, the faults reach the element of interest from the blast holes (NH=1, NH=2 and NH=3), passing distances BR1, BR2 and BR3, respectively. Fracture velocity (can be estimated as 30% of the speed of sound in the rock _Vc ) These variables can be used to calculate the time at which a fracture occurred in an element (using Equation 8), after which the system can combine the fracture intensities in the sequence in which they appeared on the element from different wells.

In some embodiments of the invention, the system can change fracture intensities based on the delay time between wells. In this case, the system can combine fracture intensities in a sequence (as described above) to obtain the resulting FDM fracture intensities. Modifications of fracture intensities can reflect the quality of fragmentation based on lag time. For example, a very short delay is likely to result in poor fragmentation, while an optimal delay is likely to result in good fragmentation.

Any methods described herein include one or more steps or actions for carrying out the described method. The steps and/or steps of the method may be interchangeable with each other. In other words, if a particular order of steps or actions is not required for proper operation of an embodiment of the invention, the order and/or use of the specific steps and/or actions may be modified.

While specific embodiments of systems and methods for simulating explosion processes have been illustrated and described, it should be understood that the disclosed invention is not limited to the precise configuration and components disclosed. Various modifications, changes and variations obvious to those skilled in the art having the advantage of these materials can be made in the layout, operation and details of the disclosed methods and systems using the present materials.

It is understood by default that one skilled in the art can use the foregoing description to utilize the present invention to its fullest extent. The examples and embodiments of the invention disclosed herein are to be construed as illustrative and exemplary only and not as limiting the scope of the present invention in any way. It will be apparent to those skilled in the art that changes may be made to the details of the above-described embodiments without departing from the spirit of the invention.

Claims (44)

1. A method for modeling an explosion, comprising segmenting a model of at least part of the explosion area into a plurality of volume elements, wherein the model contains a plurality of blast holes and a free surface; identifying pre-existing tensile cracks in each of the plurality of volume elements; simulating explosions from each of a plurality of blast holes; identifying blast cracks in each of the plurality of blast volume elements from each of the plurality of blast holes; simulating shock wave reflection on the free surface of the model by simulating explosions at a plurality of ghost wells outside the free surface to determine reflective cracks in each of the plurality of volume elements; combining pre-existing detachment cracks, explosion cracks and reflective cracks to determine the overall fracturing intensity in each of the plurality of volume elements and determining fragmentation sizes for each of the plurality of volume elements based on the overall fracturing intensity. 2. The method according to claim 1, in which the explosions are sequential and explosion cracks and reflections - 15 045746 crushing cracks are determined after each explosion. 3. The method of claim 1, wherein the plurality of blast holes comprise rows that are to be blasted sequentially, the method further comprising creating a new free surface for the model after each row is blasted. 4. The method of claim 3, wherein the new free surface is located one third of the load distance from the previously blasted row. 5. The method according to claim 1, in which the model is an underground fan explosion, and a plurality of blast holes are located at an angle. 6. The method of claim 1, wherein at least some of the plurality of blast holes are angled and the model is a surface blast model. 7. The method of claim 1, wherein blast cracks and reflective cracks are determined using rock properties, blast properties, and distance from the blast hole. 8. The method of claim 1, wherein a plurality of ghost holes are located at equal distances from the free surface as the next blast hole to be blasted. 9. The method of claim 1, wherein the force from the plurality of ghost holes is modeled as a tensile wave at a first angle, and the force from the plurality of blast holes is modeled as a compression wave at a second angle. 10. The method of claim 1, wherein the simulated explosions at the plurality of ghost wells and the simulated explosions at the plurality of blastholes occur simultaneously. 11. The method according to claim 1, in which determining the size of fragmentation for a plurality of volume elements contains the solution: 1/total intensity of fracturing. 12. The method of claim 1, further comprising summing the total number of different fragmentation sizes to obtain a predicted fragmentation size distribution for the model; 13. The method of claim 1, wherein the pre-existing tensile fractures include natural fractures that are a geological feature. 14. The method of claim 1, wherein the pre-existing pullout cracks comprise different cracks on different planes along the Y-axis of the model. 15. The method according to claim 1, further comprising selecting the type of explosive used; selection of charge length and charge positioning in multiple blast holes. 16. The method of claim 1, wherein the blast cracks are determined by solving the following equations for each of the plurality of volume elements: F = #*F1*F2*F3 / ^- ² \ ^δ Fl = I —— I \ PF*EE ) [Ro Λ ^HMX _t ^XMSXV [R\R R/J where F1, the numerator is the rock strength described by the deformation energy density, and the denominator is the available energy of explosives; R ₀ corresponds to the well radius; R is the radial orthogonal distance of the element from the well; BR is the distance of the element from the blast hole (BR differs from R in the blast hole zone); HMX and XMS are distance functions estimated for different blasthole orientations using vector distance equations; and the α, Υ and δ indices are calibrated using test blasts of the formation. 17. The method of claim 1, wherein the free surface is varied such that the load of the plurality of blast holes varies at different heights of the Y axis of the model. 18. The method according to claim 1, in which the average interval and average load are not used to determine the intensity of fracturing. 19. The method of claim 1, wherein the plurality of blast holes are located based on actual scan or GPS data of an already drilled blast site. 20. The method of claim 1, wherein the plurality of blast holes are based on a previously blasted area and blast holes that have been overcharged, undercharged, not detonated properly, or partially filled with water are introduced into the model. 21. A method of modeling an explosion, comprising segmenting a model of at least part of an explosion area into a plurality of volume elements, the model containing rows of blast holes; identification of pre-existing separations in multiple volume elements; - 16 045746 sequential simulation of explosions for each row of blast holes; determining the intensities of explosive fracturing in a variety of volume elements from explosions, and the cracks from explosions are determined after the detonation of each of the rows of blast holes; simulate the reflection of a shock wave from explosions on the free surface of the model to determine the intensities of reflective cracks in a variety of volume elements, wherein the location of the free surface is shifted after the detonation of each of the rows of blast holes, and the cracks from the reflection of the shock wave are determined after the detonation of each of the rows of blast holes using the location free surface; combining pre-existing detachments, explosive fracturing intensities, and reflective fracturing intensities to determine the overall fracturing intensity across multiple volume elements, and predicting fragmentation sizes for multiple volume elements based on the overall fracturing intensity. 22. The method of claim 21, wherein the shock wave reflection simulation comprises simulating explosions at a plurality of ghost wells beyond the free surface. 23. The method of claim 22, wherein a plurality of ghost holes are arranged at equal distances from the free surface as the next blast hole to be blasted. 24. The method of claim 22, wherein the force from the plurality of ghost holes is modeled as a tensile wave at a first angle and the force from the plurality of blast holes is modeled as a compression wave at a second angle. 25. The method of claim 22, wherein the simulated explosions at the plurality of ghost wells are synchronous with the simulated explosion of the next row of wells. 26. A non-transitory computer-readable storage medium, wherein the computer-readable storage medium contains instructions that, when executed by a computer, cause the computer to segment a model of at least a portion of a blast site into a plurality of volumetric elements, the model comprising rows of blast holes; identify pre-existing tensile cracks in multiple volume elements; sequentially simulate explosions for each row of blast holes and for each simulated explosion: identify explosion cracks caused directly by an explosion in a variety of volume elements; determine the location of the dynamic free surface for the model, with the location of the dynamic free surface shifting after each simulated explosion; simulate the reflection of a shock wave on the dynamic free surface of the model to determine reflective cracks in a variety of volume elements; combine pre-existing detachment cracks, explosion cracks, and reflective cracks to determine the overall fracturing intensity in multiple volume elements, and predict fragmentation sizes for multiple volume elements based on the overall fracturing intensity. 27. The non-transitory computer readable storage medium of claim 26, wherein the shock wave reflection simulation comprises a simulation of explosions at a plurality of ghost wells beyond the dynamic free surface. 28. The non-transitory computer readable storage medium of claim 27, wherein a plurality of ghost holes are disposed equidistant from the dynamic free surface as the next row of blast holes to be blasted. 29. The non-transitory computer readable storage medium of claim 27, wherein the force from the plurality of ghost holes is modeled as a tensile wave at a first angle and the force from the series of blast holes is modeled as a compression wave at a second angle. 30. The non-transitory computer readable storage medium of claim 27, wherein the simulated explosions at the plurality of ghost wells are synchronous with the simulated explosion of the next row of blast holes. 31. A method for modeling an explosion, comprising segmenting a model of at least part of an explosion area into a plurality of volume elements, wherein the model contains a plurality of blast holes and a free surface; identification of pre-existing tensile cracks in each of the many volume elements; simulating explosions from each of a plurality of blast holes; identifying blast cracks in each of the plurality of volume elements from explosions from each of the plurality of blast holes; simulating the reflection of a shock wave on the free surface of the model to determine reflective cracks in each of the many volume elements; combining pre-existing rupture cracks, explosion cracks, and reflective cracks to determine the overall intensity of fracturing in each of multiple volume elements; - 17 045746 determining fragmentation sizes for each of a plurality of volume elements based on the overall intensity of fracturing and predicting fragmentation size areas in the resulting broken rock. 32. A method of modeling an explosion, comprising segmenting a model of at least part of the explosion area into a plurality of volume elements, wherein the model contains a plurality of blast holes and a free surface; identification of pre-existing tensile cracks in each of the many volume elements; simulating explosions from each of a plurality of blast holes; identifying blast cracks in each of the plurality of volume elements from explosions from each of the plurality of blast holes; simulating the reflection of a shock wave on the free surface of the model to determine reflective cracks in each of the many volume elements; combining pre-existing rupture cracks, explosion cracks, and reflective cracks to determine the overall intensity of fracturing in each of multiple volume elements; determining the size of fragmentation for each of a number of volume elements based on the overall intensity of fracturing and calculating the cost and time of removing material from the blast site based on the size of the fragmentation and available equipment. 33. The method of claim 32, further comprising calculating the time and cost of grinding the ore based on the size of the fragmentation. 34. A method of modeling an explosion, comprising segmenting a model of at least a portion of an explosion site into a plurality of volume elements, the model comprising one or more blast holes and a plurality of geological layers; identification of pre-existing tensile cracks in each of the many volume elements; simulating explosions from one or more blast holes; identifying blast cracks in each of the plurality of volume elements from explosions from each of the one or more blast holes, wherein the blast cracks in each of the plurality of volume elements are affected by in which of the geological layers the plurality of volume elements are located; combining pre-existing detachment cracks and explosion cracks to determine the overall fracturing intensity in each of the plurality of volume elements; and determining fragmentation sizes for each of the plurality of volume elements based on the overall fracturing intensity. 35. The method of claim 34, wherein the geological layers contain rock properties for different sections of the blast hole or blast pattern. 36. The method of claim 35, wherein rock properties are obtained from drilling data. 37. The method of claim 34, wherein the model further comprises an explosive layer, wherein the explosive layer comprises an explosive product with varying blast energy within one or more blast holes, wherein the blast cracks in each of the plurality of volume elements are based on the explosive layer. 38. A method of modeling an explosion, comprising segmenting a model of at least part of an explosion area into a plurality of volume elements, wherein the model contains one or more blast holes and a plurality of blast layers representing an explosive product with varying explosion energy within one or more blast holes; identifying pre-existing tensile cracks in each of the plurality of volume elements; simulating explosions from one or more blast holes; determining blast cracks in each of the plurality of volume elements from explosions from each of the one or more blast holes, wherein the blast cracks in each of the plurality of volume elements are affected by varying explosion energy; combining pre-existing detachment cracks, explosion cracks and reflective cracks to determine the overall fracturing intensity in each of the plurality of volume elements and determining fragmentation sizes for each of the plurality of volume elements based on the overall fracturing intensity. 39. A method for simulating an explosion, comprising receiving input data from sensors located on a drilling machine; determination of geological properties based on input data; segmenting a model of at least a portion of the blast site into a plurality of volume elements, the model comprising one or more blast holes, each of the plurality of volume elements comprising geological properties; identification of pre-existing tensile cracks in each of the many volume elements; simulating explosions from one or more blast holes; identifying blast cracks in each of the plurality of blast volume elements from each one or more blast holes, wherein the blast cracks in each of the plurality of blast volume elements are based on geological properties; combining pre-existing detachment cracks and explosion cracks to determine the overall fracturing intensity in each of the plurality of volume elements; and determining fragmentation sizes for each of the plurality of volume elements based on the overall fracturing intensity. 40. The method of claim 39, further comprising obtaining the location of the charges from a computer-generated explosion design. 41. The method of claim 39, further comprising performing a detailed blast analysis, wherein the detailed blast analysis includes one or more of a two-dimensional plot, a three-dimensional plot, and large boulder location prediction. 42. The method of claim 39, further comprising reading blast properties from each of the one or more blast holes using analysis data from the individual blast holes. 43. A method for simulating an explosion, comprising receiving input data characterizing the desired size of fragmentation; segmenting the model of at least part of the explosion area into a plurality of volume elements; identifying pre-existing tensile cracks in each of the plurality of volume elements; performing a plurality of explosion simulations, each of the plurality of simulations associated with a different explosion design; identifying blast cracks in each of a plurality of volume elements from a plurality of blast simulations; combining, for each of a plurality of simulations, pre-existing tensile and blast cracks to determine the overall intensity of fracturing in each of the plurality of volume elements; determining fragmentation sizes for each of the plurality of volume elements based on the overall intensity of fracturing for each of the plurality of simulations; determining a final blast design from multiple simulations that produces a fragmentation size that is closest to the desired fragmentation size; and rendering the final blast design onto a graphical user interface (GUI). 44. A method for modeling an explosion, comprising segmenting the model of at least part of the explosion area into a plurality of volume elements; identifying pre-existing separation cracks in each of the plurality of volume elements; performing a root mean square error (RMSE) study to determine the fitting parameters of the fracture density model for the site; simulating explosions from one or more blast holes; determining blast cracks in each of a plurality of blast volume elements from each of the one or more blast holes, wherein the blast cracks in each of the plurality of blast volume elements are based on fitting parameters of a fracture density model for the area; combining pre-existing detachment cracks and explosion cracks to determine the overall fracturing intensity in each of the plurality of volume elements; and determining fragmentation sizes for each of the plurality of volume elements based on the overall fracturing intensity.