Category:Models - Revision history

Alex Doll: /* Theory of Power-based Specific Energy Consumption Models */

2023-08-29T17:41:31Z

Theory of Power-based Specific Energy Consumption Models

← Older revision		Revision as of 17:41, 29 August 2023
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	* "the best fit of experimental data was obtained with exponents close or equal to -1. Therefore, Morrell’s method [exponent -0.3] is not applicable for batch grinding"		* "the best fit of experimental data was obtained with exponents close or equal to -1. Therefore, Morrell’s method [exponent -0.3] is not applicable for batch grinding"

	==Theory of ~~Power-based~~ Specific Energy Consumption Models==		==Theory of Specific Energy Consumption Models==
	Laboratory measurements of the grinding energy required to break rocks are input into ~~emperical~~ formulae, such as Bond's equations, the SGI equations or the "Mi" equations that use results from SMC tests. Different size classes are tested and, in general, the specific energy consumption models use the laboratory parameters to influence the similar size range in the model.		Laboratory measurements of the grinding energy required to break rocks are input into empirical formulae, such as Bond's equations, the SGI equations or the "Mi" equations that use results from SMC tests. Different size classes are tested and, in general, the specific energy consumption models use the laboratory parameters to influence the similar size range in the model.

	Taggart noted (and Bond adopted) several properties of common size reduction processes that allows modelling as a process of energy consumption by and ore<sup>[[Bibliography: Specific energy consumption models#Bibliography of Other Useful Documents \|1,2]]</sup>. The underlying observations (and assumptions) of ~~Power~~ Models are:		Taggart noted (and Bond adopted) several properties of common size reduction processes that allows modelling as a process of energy consumption by and ore<sup>[[Bibliography: Specific energy consumption models#Bibliography of Other Useful Documents \|1,2]]</sup>. The underlying observations (and assumptions) of Specific Energy Models are:

	* Any particle size distribution can be modelled by a single value. Generally, it is the 80% passing size that is used as being indicative of the entire size distribution.		* Any particle size distribution can be modelled by a single value. Generally, it is the 80% passing size that is used as being indicative of the entire size distribution.

Alex Doll: /* History of Power-based Specific Energy Consumption Circuit Models */

2023-08-29T17:38:37Z

History of Power-based Specific Energy Consumption Circuit Models

← Older revision		Revision as of 17:38, 29 August 2023
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	# Knowing the circuit power draw allows the throughput to be calculated: t/h = kW / (kW h/t)		# Knowing the circuit power draw allows the throughput to be calculated: t/h = kW / (kW h/t)

	==History of ~~Power-based~~ Specific Energy Consumption Circuit Models==		==History of Specific Energy Consumption Circuit Models==

	A systematic relationship between energy consumed in grinding and size reduction was proposed by Peter von Rittinger in 1867, yielding the first Power Model and beginning of comminution as a science [[Bibliography: Specific energy consumption models\|<sup>Lynch & Rowland, 2005</sup>]]. This was followed in 1885 by the theory of Friedrich Kick who proposed a much different power model. Instruments of that age did not allow accurate enough measurements to test the theories [[Bibliography: Specific energy consumption models\|<sup>Lynch & Rowland, 2005</sup>]], so the difference between the models was largely of academic interest. Not until instruments for motor power measurement and laboratory grinding mills were standardized in the late 1930's to 1940's were attempts made to bench-mark the theories of von Rittinger and Kick to operating grinding plants (one such attempt was [[Bibliography: Benchmarking\|Myers, Michaelson & Bond, AIME 1947]]). The failure of these rod mill and ball mill bench-mark studies to validate either model led to the development of a "Third Theory" by Fred Bond [[Bibliography: Specific energy consumption models\|<sup>Bond 1952</sup>]].		A systematic relationship between energy consumed in grinding and size reduction was proposed by Peter von Rittinger in 1867, yielding the first Power Model and beginning of comminution as a science [[Bibliography: Specific energy consumption models\|<sup>Lynch & Rowland, 2005</sup>]]. This was followed in 1885 by the theory of Friedrich Kick who proposed a much different power model. Instruments of that age did not allow accurate enough measurements to test the theories [[Bibliography: Specific energy consumption models\|<sup>Lynch & Rowland, 2005</sup>]], so the difference between the models was largely of academic interest. Not until instruments for motor power measurement and laboratory grinding mills were standardized in the late 1930's to 1940's were attempts made to bench-mark the theories of von Rittinger and Kick to operating grinding plants (one such attempt was [[Bibliography: Benchmarking\|Myers, Michaelson & Bond, AIME 1947]]). The failure of these rod mill and ball mill bench-mark studies to validate either model led to the development of a "Third Theory" by Fred Bond [[Bibliography: Specific energy consumption models\|<sup>Bond 1952</sup>]].

Alex Doll: /* Power Models */

2023-08-29T17:37:05Z

Power Models

← Older revision		Revision as of 17:37, 29 August 2023
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	[[File:SAG_AG_milling_models.svg\|frameless]]		[[File:SAG_AG_milling_models.svg\|frameless]]

	==Power Models==		==Power and Specific Energy Models==
	Power models work by estimating the specific energy required to grind an ore (the specific energy consumption) and the mill power available to grind the ore (the mill power draw). These two types of models in SAGMILLING.COM correspond to:		Specific Energy and Power models work together by estimating the specific energy required to grind an ore (the specific energy consumption) and the mill power available to grind the ore (the mill power draw). These two types of models in SAGMILLING.COM correspond to:

	* '''Specific energy consumption models''' are used to estimate the amount of grinding energy required to grind a particular ore, and what throughput can be achieved by passing that ore through a particular set of grinding mills. Examples are the "Optimized Bond/Barratt" models where the circuit specific energy consumption is calculated using the results of Bond work index testing in a laboratory.		* '''Specific energy consumption models''' are used to estimate the amount of grinding energy required to grind a particular ore, and what throughput can be achieved by passing that ore through a particular set of grinding mills. Examples are the "Optimized Bond/Barratt" models where the circuit specific energy consumption is calculated using the results of Bond work index testing in a laboratory.

Alex Doll: /* Comminution Models */

2023-08-29T17:35:00Z

Comminution Models

← Older revision		Revision as of 17:35, 29 August 2023
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	==Comminution Models==		==Comminution Models==
	Computer models are commonly used in comminution can generally be classified into the following ~~three~~ classes:		Computer models are commonly used in comminution can generally be classified into the following four classes:
			* '''Power Models''', such as Nordberg and Morrell C-model, are used to predict the power draw of a tumbling mill with a specified charge geometry rotating at a specific speed.
⚫	* '''~~Power~~ Models''', such as Bond, are used for initial design and for geometallurgy. The mathematics are simple and mostly ''linear'' meaning computers can quickly compute hundreds of these types of calculations. These models assume a "standard" particle size distribution (PSD) that can be represented by a single point on the PSD, typically the 80% passing size.

		⚫	* '''Specific Energy Models''', such as Bond, are used for initial design and for geometallurgy. The mathematics are simple and mostly ''linear'' meaning computers can quickly compute hundreds of these types of calculations. These models assume a "standard" particle size distribution (PSD) that can be represented by a single point on the PSD, typically the 80% passing size.

	* '''Population Balance Models''', such as JK SimMet and MolyCop Tools, are used mostly for optimization and generally work best when a mill already exists so that the model parameters can be fit to it. The mathematics are more complex than the Power Models and the parameter calibration can be both tedious and time-consuming. These models track the mass flow of each size class independently and do not assume a "standard" particle size distribution, making them suitable for detailed analyses of pebble crushing circuits, for example.		* '''Population Balance Models''', such as JK SimMet and MolyCop Tools, are used mostly for optimization and generally work best when a mill already exists so that the model parameters can be fit to it. The mathematics are more complex than the Power Models and the parameter calibration can be both tedious and time-consuming. These models track the mass flow of each size class independently and do not assume a "standard" particle size distribution, making them suitable for detailed analyses of pebble crushing circuits, for example.
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	* '''Discrete Element Modelling''' (DEM) is generally used for detailed design of specific subsystems in an existing plant. Examples are lifter height and face angle design for mill liners, chute design, and SAG mill discharge system design.		* '''Discrete Element Modelling''' (DEM) is generally used for detailed design of specific subsystems in an existing plant. Examples are lifter height and face angle design for mill liners, chute design, and SAG mill discharge system design.

	SAGMILLING.COM implements only Power Models. Other specialized software is needed for population balance or DEM modelling.		SAGMILLING.COM implements only Power and Specific Energy Models. Other specialized software is needed for population balance or DEM modelling.

	[[File:SAG_AG_milling_models.svg\|frameless]]		[[File:SAG_AG_milling_models.svg\|frameless]]

Alex Doll at 16:07, 9 March 2020

2020-03-09T16:07:11Z

← Older revision		Revision as of 16:07, 9 March 2020
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	SAGMILLING.COM implements only Power Models. Other specialized software is needed for population balance or DEM modelling.		SAGMILLING.COM implements only Power Models. Other specialized software is needed for population balance or DEM modelling.

	[[File:SAG_AG_milling_models.svg]]		[[File:SAG_AG_milling_models.svg\|frameless]]

	==Power Models==		==Power Models==

Alex Doll: /* History of Power-based Specific Energy Consumption Circuit Models */

2018-04-04T18:16:28Z

History of Power-based Specific Energy Consumption Circuit Models

← Older revision		Revision as of 18:16, 4 April 2018
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	Fine grinding models, such as the Isamill signature plots, tend to have widely varying exponents, in the range of -1 to -3 depending on the ore. Metso jar mill tests can be interpreted in a way that also gives a signature plot.		Fine grinding models, such as the Isamill signature plots, tend to have widely varying exponents, in the range of -1 to -3 depending on the ore. Metso jar mill tests can be interpreted in a way that also gives a signature plot.

			Hukki (among others) related many of the empirical models back to a more fundamental differential equation form, attributed to Walker et al (1937) or Charles (1957):

			* <i>dE/dx = -C x<sup>-a</sup></i>

			where <i>E</i> is energy consumed; <i>x</i> is particle size; and <i>C</i> and <i>a</i> are empirical ore characteristics.

	A later model by [[Bibliography: Specific energy consumption models\|Stephen Morrell]] attempted to smoothly merge all three of the earlier models into a single continuum that was fitted to surveys conducted (mostly) in Australasia and Africa. However, the exponents derived by Morrell are very different from the exponents predicted by Hukki and, in the finest size classes where the exponent tends to ~-0.30, do not match observed signature plots from tests involving stirred mills (e.g. Isamills and Vertimills where the exponent ranges between -1 and -3).		A later model by [[Bibliography: Specific energy consumption models\|Stephen Morrell]] attempted to smoothly merge all three of the earlier models into a single continuum that was fitted to surveys conducted (mostly) in Australasia and Africa. However, the exponents derived by Morrell are very different from the exponents predicted by Hukki and, in the finest size classes where the exponent tends to ~-0.30, do not match observed signature plots from tests involving stirred mills (e.g. Isamills and Vertimills where the exponent ranges between -1 and -3).

Alex Doll: /* Comminution Models */

2017-08-19T19:53:01Z

Comminution Models

← Older revision		Revision as of 19:53, 19 August 2017
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	* '''Discrete Element Modelling''' (DEM) is generally used for detailed design of specific subsystems in an existing plant. Examples are lifter height and face angle design for mill liners, chute design, and SAG mill discharge system design.		* '''Discrete Element Modelling''' (DEM) is generally used for detailed design of specific subsystems in an existing plant. Examples are lifter height and face angle design for mill liners, chute design, and SAG mill discharge system design.

	SAGMILLING.COM ~~only~~ implements ~~the~~ Power Models.		SAGMILLING.COM implements only Power Models. Other specialized software is needed for population balance or DEM modelling.

	[[File:SAG_AG_milling_models.svg]]		[[File:SAG_AG_milling_models.svg]]

Alex Doll: /* Comminution Models */

2017-08-19T19:51:58Z

Comminution Models

← Older revision		Revision as of 19:51, 19 August 2017
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	SAGMILLING.COM only implements the Power Models.		SAGMILLING.COM only implements the Power Models.

			[[File:SAG_AG_milling_models.svg]]

	==Power Models==		==Power Models==

Alex Doll: /* History of Power-based Specific Energy Consumption Circuit Models */

2016-04-26T16:58:55Z

History of Power-based Specific Energy Consumption Circuit Models

← Older revision		Revision as of 16:58, 26 April 2016
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	A later model by [[Bibliography: Specific energy consumption models\|Stephen Morrell]] attempted to smoothly merge all three of the earlier models into a single continuum that was fitted to surveys conducted (mostly) in Australasia and Africa. However, the exponents derived by Morrell are very different from the exponents predicted by Hukki and, in the finest size classes where the exponent tends to ~-0.30, do not match observed signature plots from tests involving stirred mills (e.g. Isamills and Vertimills where the exponent ranges between -1 and -3).		A later model by [[Bibliography: Specific energy consumption models\|Stephen Morrell]] attempted to smoothly merge all three of the earlier models into a single continuum that was fitted to surveys conducted (mostly) in Australasia and Africa. However, the exponents derived by Morrell are very different from the exponents predicted by Hukki and, in the finest size classes where the exponent tends to ~-0.30, do not match observed signature plots from tests involving stirred mills (e.g. Isamills and Vertimills where the exponent ranges between -1 and -3).

			A recent testing program [http://www.onemine.org/document/abstract.cfm?docid=159709&title=Relationships-between-comminution-energy-and-product-size-for-a-magnetite-ore--Synopsis Jankovic, Dunar & Mehta, 2010] finds von Rittinger's exponent of -1 provides the best fit to a data set of batch grinding magnetite ore ground down to between 80 µm and 20 µm. There is an issue with the experimental data that the authors do not address: the particle size distributions of the feed and product are not completely parallel in log-log space and the feed appears to have a small surplus of fines. This effect probably does not influence the conclusions:
			* "the exponent of the Bond equation (-0.5) is not accurate for prediction of the whole range of test work results [80 µm to 20 µm]. A significantly better fit was obtained using the Rittinger (exponent -1) formula."
			* "the best fit of experimental data was obtained with exponents close or equal to -1. Therefore, Morrell’s method [exponent -0.3] is not applicable for batch grinding"

	==Theory of Power-based Specific Energy Consumption Models==		==Theory of Power-based Specific Energy Consumption Models==

Alex Doll: /* History of Power-based Specific Energy Consumption Circuit Models */

2016-03-19T18:34:21Z

History of Power-based Specific Energy Consumption Circuit Models

← Older revision		Revision as of 18:34, 19 March 2016
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	[[Bibliography: Specific energy consumption models\|R. Hukki in 1962]] showed that all three theories may be special cases of a spectrum of a larger, more generalized, theory where Kick best characterized the coarsest particles (blasting), Bond the middle size ranges (rod and ball milling), and von Rittinger the finest size classes (fine and ultra-fine grinding). Hukki's diagram showing the size spectrum is reproduced below:		[[Bibliography: Specific energy consumption models\|R. Hukki in 1962]] showed that all three theories may be special cases of a spectrum of a larger, more generalized, theory where Kick best characterized the coarsest particles (blasting), Bond the middle size ranges (rod and ball milling), and von Rittinger the finest size classes (fine and ultra-fine grinding). Hukki's diagram showing the size spectrum is reproduced below:

	[[File:Hukki1962-chart.png]]		[[File:Hukki1962-chart.png]]