FlowPit - 4D Open Pit Optimization

Open pit mines are typically designed with the help of block models, which represent the material inside the pit using millions of "blocks" of a predefined volume. The calculations required to design an open pit mine that is both safe and efficient can be complex and are typically time consuming. ThreeDify FlowPit is a unique pit limit optimization tool that is an order of magnitude faster than many competing technologies.

The primary purpose of open pit design is to determine the final configuration of the open pit at the end of its economic life, which will optimize ore recovery and total net profit. The mathematical formulation of the problem was solved decades ago (Lerchs and Grossman 1965) and several algorithms on the topic have been published since the event of computer applications in the mineral industry. Not all of these algorithms (typically floating cone based) produce optimum results and hence they are known as heuristic (i.e., non-rigorous optimizing) algorithms. There are basically two rigorous optimizing techniques available for pit shell design, namely, 3D Lerchs & Grossman and network flow algorithms.

Like other algorithms for determination of final pit limit, the network flow algorithm is also based on a block model which is assumed to have been established somehow for the deposit concerned, before the problem of determining the final limit can be attacked.  Lerchs and Grossman (1965) demonstrated that the optimal pit limit problem was equivalent to determining the maximal closure in a directed, weighted graph. They also mentioned that the maximal closure problem is equivalent to finding the maximum flow in a modified network.  Johnson (1968) elaborated on this concept for use in multi-period scheduling for open pits and showed, for the first time, how an equivalent network could be constructed from a block model.

The same result was obtained independently by Picard (1976): "...the problem of finding a maximal closure of a graph is equivalent to solving the maximal flow problem in a network formed by the graph G with infinite capacities on its arcs, a source linked to each node vi of positive value by an arc of capacity (+mi) and a sink linked from each node vi of negative value by an arc of capacity (-mi)."

Very efficient algorithms exist for determining the maximum flow in a network, and thereby determining the optimal pit limit. The network flow algorithm for pit optimization is thus resolved much faster than the L & G when an efficient maximum flow algorithm is used.

Version 2.0 Featuring (see screen-shots at the bottom of the page):

• Further significant speedup and memory reduction: Version 2.0 requires half of RAM and is 2 to 3 times faster than version 1.25 which already featured an outstanding performance. On several real-life block models each with >3.5 million blocks, FlowPit 2.0 consistently completes full optimization within 1 hour 15 minutes on Core 2 Duo commodity laptops with 2gb free ram (compared to 2.5 hours with Version 1.25).
• Ability to rapidly generate multiple nested pits for pit sequencing and/or up-scaled pits for sensitivity analysis in a single FlowPit run. Such an ability is sometimes referred to as 4D in some other expensive open pit strategic planning packages. FlowPit 2.0 does it in an extremely efficient manner again due to the new  performance enhancement: It took 5 minutes to generate 31 (20 nested, 10 up-scaled and 1 final) pits in a single run for a block model of 76x144x62 dimensions.

• new GUI front-end with re-blocking and graphical post processing capabilities, i.e, ability to graphically view stripping ratio graphs, plan and cross sectional views showing nested and/or up-scaled pits in real time.

• Full working demo available upon request.

Version 1.2.5 Capabilities

ThreeDify FlowPit is a program and a VB callable COM object designed to find the optimal final limit of an open-pit mine given an economic block model.  It implements the maximum flow algorithm for determination of the final pit limit. ThreeDify FlowPit offers the following benefits:

Use of bounding techniques:

To speed up the maximum flow algorithm and to reduce memory requirement, ThreeDify FlowPit incorporates a combination of three bounding techniques to an input block model before applying the maximum flow algorithm (bounding techniques are not optimizing algorithms as such but comprise a group of techniques used to limit the search for the optimum pit by defining upper and lower bounds to the optimal pit). These are layer cake (data are introduced layer by layer from top), prepass, and best valued cross sectional bound.

Support for variable pit slope:

The search pattern (or precedence constraints) for a given block is a group of indices, representing the locations of the blocks which must be removed before a given block can be extracted. The pattern is generated by a set of predetermined pairs of azimuths and dips using trigonometry (as opposed to the approximation with a fixed global support pattern used by most other pit limit optimizers). Linear interpolation method is employed in calculating the dips of the blocks to determine whether a block at a specified level should be included in the pattern or not.

Allowance for exclusion regions:

Exclusion region(s), i.e. property lines that must not be crossed, can be specified as polylines in a DXF file.

Use of floating point arithmetic for accurate optimal solution:

ThreeDify FlowPit implements Goldberg and Tarjan's maximum flow algorithm, one of the fastest maximum flow algorithms available today (Table 1 below). Unlike other implementations that use integer approximation, our implementation uses floating point arithmetic for accurate optimal solution without compromising accuracy for speed. 

Also available as VB-callable COM object:

ThreeDify FlowPit is available either as a standalone application or as a COM object that is callable by Visual Basic applications. For instance, an open pit mine scheduling application written in Visual Basic can ask ThreeDify FlowPit to compute (via its COM interface) the optimum pit for each planned phase in order to arrive at a long or medium range mine plan.

Engineered to handle large block models

FlowPit is extremely fast and scalable to handle large block models. On a low-end Dell M1210 Core 2 Duo 2.0ghz laptop with 2.5gb free ram, FlowPit took less than 2 hours to determine the optimial pit limit for a block model of 245x150x125 dimensions. .

Table 1 Efficiency of various maximum flow algorithms (n denotes number of nodes, i.e., blocks, and m number of edges, i.e. arcs in the network formed from a block model).

Key Benefits

• Affordable. ThreeDify FlowPit guarantees optimum pit limit with block sequencing and sensitivity analysis (aka 4D), but costs up to an order of magnitude less than similar products.
• Efficient implementation. FlowPit offers up-to an order of magnitude speed-up over other competing products.

Pricing

ThreeDify FlowPit Screenshots

The screenshots below showcase features of our ThreeDify FlowPit 2.0 product.