Minex 2 d_3d_models

2D and 3D Block Models Jon Barber - Vice President Minex, - Gemcom Software International Inc.

WHITE PAPER

*Gemcom Software was acquired

by Dassault Systèmes, the

3DEXPERIENCE Company, in July

2012. It is now known as GEOVIA.

Gemcom Minex™ – 2D and 3D Models – J. Barber

Copyright © 2011 Gemcom Software International Inc. Page 2 of 10

Abstract Gemcom clients often query the difference between a 3D block model and a 2D gridded model. Gemcom’s Minex is based on 2D grids or surface models, while Gemcom’s Surpac and GEMS systems are is primarily concerned with the 3D block model approach to resource modeling and mine planning.

Most engineers and geologists would agree that 2 < 3, and that 3 > 2. This does not necessarily mean that 3 is better than 2. In family size there are many arguments for more or less children. Two might be better than three and vice versa. It is the same with geological modelling. The advantages and disadvantages of 2D versus 3D modelling are varied and create great discussion. Just because 3 > 2 doesn’t mean 3D modelling is better than 2D modelling.

This paper explores the issues involved in 2D versus 3D modelling, and suggests where each approach will result in resource models that best reflect the true in ground distribution of ore grade and volume. It also goes on to explore the differences in 2D versus 3D mine planning, and which approach will deliver the highest project value for different ore body and mine planning scenarios.

What is a model? A geological model is a representation or an interpretation of a mineral deposit. The deposit could be any commodity, including gold, iron, or coal. Prior to the 1970’s many geologists and engineers would build 3D models of the ore body and mine workings to help visualise or understand the deposit. The model would often be a set of Perspex cross sections hanging in a wooden frame.

Computers have given us the power to build those models electronically, and view them dynamically in 3D or in sections and plans. The models can be updated as new data becomes available and most importantly guide mine planning. Computer models also produce volume and grade reports that reconcile production information and measure mining efficiency and performance.

A software model is a numerical arrangement of data that can readily be displayed and used for volumes. Computer models typically represent geology as so called 2D or 3D models.

Ore bodies can be categorised in many ways, but for this paper we consider three different categories, as shown in Table 1.



TABLE 1. THREE CATEGORIES OF ORE BODIES

1. Ore bodies that are three dimensional in nature, such as porphyry coppers iron ore and many gold deposits. Normally these are best modelled using full 3D methods.

2. Layered ore bodies such as coal that are suited to 2D modelling.

3. Transitional ore bodies where deeper consideration of the characteristics of 2D versus 3D modelling are required in order to determine the modelling approach.

2D Models In a 2D model a square or rectangle grid or mesh is placed over the area of interest. Z values or elevations are then assigned to centres of the mesh. The mesh is a pattern in XY space. So Z is stored at XY locations, hence the term 2D model. The Z value is stored at X and Y locations. The Z values represent attributes of the geology, such as topography (Figure 1), or nickel content or thickness.

Figure 1: Typical 2D model of topography.



3D Models Many Surpac users will be familiar with 3D models. Here the model values or attributes (called Q for quality) are stored at the centroid of a block. The block has a location and size in XYZ space and the Q is stored is 3D space, hence the term 3D model. Figure 2 shows a Surpac block model.

Q values such as gold grade, mill cost or mill recovery are held in each block. In Figure 2 the block colour reflects a block attribute. Block models are ideal for complex ore body shapes. Typically these ore bodies have been formed by intrusion and/or faulting and the ore body interpretation is usually based on rock type, alteration or grade using wire framing. Interpretations are made on sections and these interpretations are then joined in a wire-framed shape. Figures 3 and 4 show such an interpretation.

Figure 2: 3D block model.

Figure 3: Wire frames (blue) connect outlines (white).

Figure 4: Solid display.



In 3D models the wire frame shapes are filled with blocks and sub-blocks to represent the ore body. By selection of a reasonable block size, which trades accuracy and speed, the ore body can be well represented. These blocks are then filled with attribute values (Q) from the drill hole data. Typically this involves detailed variogram analysis and selection of appropriate variogram parameters. Domain control such that the grades within a wire frame are used to determine the blocks in that frame are a key feature of the process. The attribute could be gold, silver or SG. Figure 5 shows a block model in cross section, the colours represent gold values. The ore body has been cut with a barren dyke represented by the grey blocks.

Figure 5: Sub-blocked model showing use of small sub blocks on edges.

2D models are ideal for thin or layered deposits, such as coal, bauxite and phosphate. These deposits are often extensive in area. For example a typical Hunter Valley coal mine would be 8,000 metres by 10,000 metres in lateral extent. While the total Sydney coal basin covers an area from Newcastle to Wollongong and west to Lithgow (approximately 200kms x 300kms). Within a single mine there could be 40 seams, which vary in thickness from 0 metres to 10 or 20 metres.

In modelling these layered deposits, the seams are modelled as a series of linked or associated surfaces. For a coal seam such as the Bayswater a number of individual 2D models or surfaces are created. In Minex a naming convention is used consisting of the seam prefix and an extension suffix. Usually the seam suffixes are kept brief, so Bayswater is abbreviated to BAY. The standard Minex naming convention is shown in Table 2. The common prefix BAY associates all these surfaces together while the standard suffix endings allows Minex to treat the model correctly for volumetric, tonnage or cross section purposes.



TABLE 2: EXAMPLE GRID OR MODEL NAMING CONVENTIONS USED IN MINEX.

Model Suffix Explanation Bayswater seam example

SF Seam Floor BAYSF

ST Seam Thickness BAYST

SR Seam Roof BAYSR

RD Relative Density BAYRD

AS Ash BAYAS

SE Specific Energy BAYSE

SU Sulphur BAYSU

NA Sodium BAYNA

BTU British thermal units

BAYBTU

A 2D model is stored as elevation values (Z) at the centroid of a regular XY grid. Remember that just with 3D models the Z can be quality. So the Z value could be seam ash or nickel or iron content. In Figure 6 the elevation of a coal seam is displayed below a topography surface. Just as in 3D modelling the model dimensions reflect the data distribution. Typically the mesh or grid size in X and Y is between ¼ and 1/5 of the data spacing. For a drill hole spacing of 100 metres a grid size of 25x25 or 20x20 would be appropriate. Just as the 3D block model in Figure 2 is coloured by grade a seam model can also be coloured by grade. Figure 7 shows the seam floor coloured by seam depth. One attribute of the model is seam depth; topography minus seam floor gives depth. Simple (and complex) grid-to-grid arithmetic is just as easy with a 2D model system as with a 3D system.

Figure 6: Floor elevation model for a coal seam (yellow) with topography (green).

Figure 7: Floor of a coal seam coloured by depth with topography (green).



2D Versus the 3D Approach There are several deposit characteristics where the 2D modelling is preferred. These characteristics are:

The thickness of the ore body, seams or veins may necessitate a high-resolution block model (very small or thin blocks) to adequately represent the ore body. Coal, phosphate and laterites are either thin and variable in thickness. Figure 8 shows an example coal seam cross section. This deposit has a typical mixture of thick and thin seams, which vary from 1cm to 3metres in thickness. The seam thickness is typically measured to +/- 1cm accuracy. As thickness is equivalent to tonnage and tonnage is equivalent to dollars, the thickness model must be accurate. Even though computers are steadily increasing in speed, the time required for processing a block model with a very large number of blocks may be impractical. 2D modelling due to its infinitely variable block size is ideal for these deposits.

Figure 8: Typical coal deposit in cross section.

Sedimentary deposits are often large in lateral extent (measured in tens of kilometres) and block models become too large and slow.

Traditional 3D polygon and solids modelling techniques may not be able to adequately project the detailed fault and shear structures through a range of veins or seams. Extending such structures manually through each seam or vein may be tedious and impractical. A seam or vein modelling system has the facilities to define structures and propagate them through the model.

The 2D modelling approach uses rules that ensure that ordering of the seams or veins is rational (stratigraphic). This avoids seams crossing or overlapping. Rules also allow for seam splitting. The rules system also makes automatic modelling of all seams relatively simple. There is no need to manually wire frame borehole-to-borehole data.

The automatic modelling and rules based approach means new data can be efficiently added to the model. In other words the model can be easily maintained.



How Do We Generate the 2D Surfaces or Models? In Minex the seam data is held in the drill holes as intervals or picks. These intervals provide thickness, moisture, ash and seam elevation data at the drill hole location. By compositing quality data (such as ash or moisture) across the interval the average quality is defined. Figure 9 shows a borehole database with the seam intervals in different colours. Various algorithms are used to generate a model from this data. Example algorithms are kriging, inverse distance and trend surface techniques. For example in Figure 9 the light blue data points can be connected into a thickness model or surface.

Figure 9: Borehole database seam data.

In 2D modelling algorithms the seam name in the borehole is critical. If the name is correct then the modelling is virtually automatic. The seam name in the drill hole is analogous to the domain name in a 3D block model. When we determine the block value we only use the correct domain data, we don’t want to use data from another domain. The seam name has the same importance in 2D modelling. We only use seam A data to determine the values in the seam A model. The simplicity of the naming is a major advantage over wire framing. Wire frames are built manually by connecting drill hole data on a series of sections. Typically the wire frame is built in the office after all the analytical data is collected.

In coal however, the lithology is more black and white and often the field geologist can assign the seam name in the field while logging or can assign it from down hole geophysical logs, such as density, which differentiate between coal and waste. Once the seam(s) is defined the model values (elevation, thickness, ash) are estimated by scanning the surrounding drill hole data. Figure 10 shows an area around three drill holes. The model values vary from 0.48 metres at the top of the sheet to 0.35metres at the bottom. Each model value (purple) is stored at the centroid of the grid cell while the borehole data value is sampled at the red drill hole location.

Figure 10: Seam thickness model and drill hole data.



In layered deposits Minex links the various 2D surfaces into a 3D model. For example the seam floor model locates the seam in XYZ space; the thickness model defines the coal volume and the RD model converts volume to tonnes. In a 3D block model, volume is just a count of the cubes inside say a pit. In a 2D model volume is simply a count of the columns inside the pit. However in a 2D model each column has a variable thickness or height. So where a 3D model is based on lots of regular cubes a 2D model is based on a pattern of regular bases or grids with irregular heights or thickness. Thus for thin or large extensive layered geology the 2D model is more accurate then the 3D model.

Vein Models The standard 2D model stores the Z values in planar XY space. That is X is usually measured horizontally from west to east and Y is measured horizontally from south to north. Z (or Q) is stored as an offset from this plane. For thin steeply dipping ores such as nickel or gold veins, vein modelling can be used. Vein modelling uses a coordinate system where X and Y are along a plane parallel to the ore body and Z is perpendicular to the plane. For measuring thickness (and hence tonnage) this orientation is useful as the thickness measured is now true thickness not apparent thickness. Thus variography and other statistics are more robust. Figure 11 shows a vein model system. Here the ore is near vertical and the footwall (orange) and hanging wall (yellow) are modelled as 2D grids. To give reasonable resolution the XY coordinates are rotated to a vertical plane. Both models were created as surfaces from the borehole vein intersects. Careful wire frame digitising was not required. Using these surfaces the vein can be converted to a conventional block model. The footwall and hanging wall are then used as the limit surfaces. Examples of these blocks are shown in Figure 12.

Figure 11: Example Vein Model. Figure 12: Block model based on vein surfaces



Mining Applications Minex uses the 2D models in a number of ways in mine design and scheduling. Minex Apollo is based on mining blocks with volumes of waste and coal in these blocks. Figure 13 shows a set of mining blocks. The individual volumes of the seams are stored in these blocks. The seams are shown in red and are dipping steeply the waste layers include a footwall waste volume (dark blue). Pit optimisation is used widely in metals pit evaluation. Minex has a 2D grid optimiser which uses seam following blocks in the determination of the pit floor. Figure 13 and 14 shows an example of a set of nested optimum pits in a coal application.

Figure 11: Mining blocks in a steep dip deposit. Coal in red waste and coal designed in 10metre benches.

Figure 12: Optimum Pit based on seam following algorithm bottom compared with regular XYZ blocks top.

The regular XYZ blocks use constant Z bock size and mine under burden.

This document gives only a general description of products and services and except where expressly provided otherwise shall not form part of any contract. Changes may be made in products or services at any time without notice. Copyright 2011, Gemcom Software International Inc. Gemcom, the Gemcom logo, combinations thereof, and Gemcom Minex are trademarks of Gemcom Software International Inc. All other names are trademarks, registered trademarks, or service marks of their respective owners.

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