Dilution and ore recovery
As a mining project is developed from conceptual to production phases, there exist a variety of uncertainties and difficulties that affect the operation’s designs and economic value. A notable design parameter to be taken into account is the factor of dilution. Dilution is the waste material not separated from the ore in the stages of mining, and is sent to the processing plant. It is defined at the ratio of tonnage waste mined and sent for processing over the combined ore and waste tonnage milled. The following equation is the expression used for dilution:
Planned and Unplanned Dilution
The following definitions are crucial in the estimations for planned and unplanned percent dilution.
Geological Reserves (Tg): The tonnage of ore above the cut-off grade
Planned Waste (Wp): Rock with a lower mineralization content than the cut-off grade within slope limits
Mining Reserves (Tm): The ore tonnage within the planned stope limits
Unplanned Waste (Wu): Rock with a lower mineralization content than the cut-off grade, coming from beyond the planned stope limits
Total Waste: Rock which includes mineralization below the cut-off grade
Run of mine ore (Tt): The tonnage generally sent to the mill, sum of geological reserves, planned waste, and unplanned waste
Figure 1: Visual representation of the planned and unplanned dilution (DeSouza, 2010) 
Internal and External Dilution
Internal dilution occurs within a mining block in which pockets of waste are unable to be separated and are mined with the block. Degrees of internal dilution can vary within various types of deposits; specifically, lithological and grade distributions significantly influence the degree of dilution. Furthermore, the following four main components govern internal dilution:
- Geology and Mineralogy: Typically fine-grained mineralization with local but relatively small occurrences of mineralization.
- Data Density: Becomes a significant factor once the geology is understood.
- Estimation Method: Manual and automatic estimation methods tend to overestimate grade and underestimate tonnes.
- Cutoff grade and grade control: When cutoff grade is applied to a deposit, the engineer assumes that the grade contacts are definable at any given grade.
External dilution is the waste outside of the orebody that is mined within the block. It varies based on an assortment of parameters and can be controlled using effective equipment and mining practices. The following initiatives can be used to minimize external dilution:
- Defining the contact surfaces of ore and waste
- Selection of the proper equipment to attain desired selectivity
- Mining along the contact surfaces
- Modelling the effects of unavoidable dilution
Figure 2 displays a mining block and bench depicting internal and external dilution.
Figure 2: Mining block in an open pit visualizing internal and external dilution (Ebrahimi, 2013) 
Primary and Secondary Dilution
Estimating dilution prior to mining is a challenging task, demanding the use of an engineer’s best judgement to assess the feasibility and economic value of mining a block, stope, or deposit. An important parameter to consider while doing so is total dilution, a value which can be expressed in the following equation:
In general, primary dilution is found in narrow deposits, as the thickness of the ore zone becomes the main source for dilution. Figure 3 displays the concept of primary dilution within a narrow orebody.
Figure 3: Primary Dilution in a narrow orebody (Crawford, 2004) 
Conversely, secondary dilution is the dilution that occurs beyond the planned stope dimensions. Secondary dilution is caused by a number of factors which include sloughing, drilling and blasting, ground conditions, planar discontinuities, mining method, equipment, and work practices. A visual representation of secondary dilution is shown in Figure 4.
Figure 4: Secondary dilution in an orebody (Crawford, 2004) 
Factors of Dilution
Mine dilution occurs due to the mining method selected and from overbreak during the mining process. There are multiple considerations in terms of dilution. Mining methods such as block caving, sublevel stoping and room-and-pillar have mining methods which are more predictable, where dilution can be modeled using empirically generated equations. The major factors which have a direct effect on dilution are as follows:
- Mine Depth – Methods with greater selectivity exhibit lower dilution
- Rock Competency – More competent rock will be less susceptible to sloughing and overbreaking
- Ore Type – Defines the selective and effective dilution parameters
- Ground Support – Support can be used to maintain ore and waste surfaces, limiting the amount of dilution
Self-supported openings are more selective and have lower dilutions than block caving with typical dilution ranges from 5% to 15%. Additional factors which influence dilution to a lesser extent are as follows:
- Rock Mechanics – Mechanical parameters and technical ability lead to increased dilution to account for
- Ore Geometry – Layout of the ore in skewed orientation leads to increases in unplanned dilution
- Hanging-wall Dip – The likelihood of wall slabbing and release of wedges will depend on wall dip relative to the orientation of lamination and joints
- Geotechnical – Parameters are increased lead to an increase in dilution values
- Stope Span – Larger stope spans are less stable, increasing the risk of wall failure and unplanned dilution
Bulk Mining Methods
Dilution in respects to Block Caving is the percentage of the ore column removed before waste materials are removed from the drawpoint. It is a function of mixing occurring in the drawpoints, with the following input parameters:
- Ore Draw Height
- Ore and Waste Fragmentation Range
- Drawzone Spacing
- Tonnage Drawpoint Range
The model used to estimate dilution for block caving is defined by three parameters: A, draw-column height swell factor, B height of interaction, and C, draw control factor.
Figure 5: Draw control factor (P. Darling, 2011) 
Figure 6: Calculation of dilution entry (P. Darling, 2011) 
(figures and equations and sources)
Ore recovery is based on the material within the model that is left behind to provide structural support, thereby not being recovered. The generalized equation for recovery is given from equation 7:
More specifically, ore recovery can be defined by the percentage of minable reserves extracted in the mining process. The issue of balancing dilution and ore recovery is a challenging one as profitability is to be optimized while not effecting the efficiency of operation. It has been noted that instead of utilizing labour intensive mining methods to high tonnage bulk mining has decreased the ability to control ore recovery. In a practical underground and open pit setting, the ore recovery is affected by three main factors as follows:
- Ore wedges located at the top and bottom sills of the panel are unable to be extracted as they provide access to mined-out areas in backfill and provide support. This is comparable to room and pillar operations in which pillars are also left for support.
- Ore left against backfill, as there exists a certain amount of ore adjacent to the backfill that is unable to be extracted due to irregularities of the ore-backfill contact surface
- Oxidization of ore stuck to the footwall is a direct consequence of the extraction sequence. In this, ore blasted at the beginning of the extraction phase must stay within the stope until the last slice of ore is extracted.
Room and Pillar Example
Viewing a room and pillar operation from a longitudinal cross section given the width of the pillar (wp) and the width of the opening (wo) the recovery is given by the following equation:
Figure 7: Longitudinal view of room and pillar recovery (DeSouza, 2010) 
Viewing a room and pillar operation from a plan view given the width of the pillar (wp) and the width of the opening (wo) the recovery is given by the following equation:
Figure 8: Plan view of room and pillar recovery (DeSouza, 2010) 
Depending on the mining method which is being used, recovery can be estimated by understanding the stope dimensions relative to the mineralization. One must also have an understanding of the geotechnical environment to know if ore will have to be left in place to provide support. Once these characteristics are known the recovery is easily calculated using the generalized equation.
- E. DeSouza, "Underground Mining," Kingston, Ontario, Canada, 2010.
- A. Ebrahimi, "The Importance of Dilution Factor for Open Pit Mining Projects," 2013. [Online]. Available: http://www.srk.com/files/File/papers/dilution_factor_openpit_a_ebrahimi.pdf. [Accessed 7 February 2017].
- G. Crawford, "Dilution and Ore Recovery," 2004. [Online]. Available: http://docslide.us/documents/mining-dilution.html#. [Accessed 7 February 2017]
- P. Darling, "SME Mining Engineering Handbook (3rd Edition) - 18.104.22.168 Layouts. Society for Mining, Metallurgy, and Exploration (SME).," Society for Mining, Metallurgy, and Exploration , 2011.
-  L. Pareja, "Deep Underground Hard-Rock Mining: Issues, Strategies, and Alternatives," April 2000. [Online]. Available: http://www.collectionscanada.gc.ca/obj/s4/f2/dsk1/tape4/PQDD_0011/NQ52844.pdf. [Accessed 7 February 2017].
-  J. Jakubec, "Underground Mining Methods SME," 2001. [Online]. [Accessed 7 February 2017].