CA1337190C - Process for beneficiating particulate solids - Google Patents

Abstract

The present invention provides a method for selecting magnetite to form a dense media for benefi-ciation of fine particulate solids such that the par-ticulate solids are as buoyant with respect to the dense media as if the solids were in a true liquid having a specific gravity equal to that of the dense media. The method involves determining a magnetite particle diameter such that the diameter ratio of par-ticulate solid to magnetite lies above a diameter ratio partition curve. The invention is also directed toward using magnetite having a particle diameter less than about 0.005 mm and a mean particle diameter of about 0.0025 mm. Such magnetite is formed from a gas phase pyrohydrolysis reaction on an aqueous iron (ferrous) chloride solution. The present invention is further directed towards a method for determining the ef-ficiency of separation of a dense media separation pro-cess. This method includes determining an apparent distance a particle must travel in a dense media cyclone to be correctly beneficiated. From this ap-parent distance, an apparent velocity a particle must achieve to be correctly beneficiated is calculated.
This apparent velocity is used, along with cyclone geo-metry and operational parameters to calculate a diver-gence value which indicates the efficiency of separa-tion. The present invention also includes a method for selecting cyclone geometry and operating parameters which includes determining separation efficiency and adjusting geometry and parameters in a manner to obtain improved efficiency.

Description

I 337 1 ~0 P~OC~SS FOR 3ENEFICIATING PA~TICULATE SOBI~S
Fleld Of The Invention The present invention relates to an improved process for beneficiating coal fines and for predicting 05 the efficiency of separation of density separation processes.

Background Of The Invention The burning of fossil fuels, including coal, is necessary to meet the energy requirements of our soclety. However, the combustion of coal, and in par-ticular, many lower grades of coal, produces sulfur oxides which are emitted to the atmosphere. The release of these compounds produces many detrimental environmental effects. Respiration of these pollutants can cause human health problems ranging from mild respiratory irritation to more serious chronic dis-eases. Sulfur oxides can also react with other com-positions in the atmosphere to form acid preciDitation which has the effect of acidifying bodies of water and destroying the wildlife which live in such habitats.
Acid precipitation also can destroy manmade structures such as buildings and statues.
Industry has sought to burn coal with low sulfur content to avoid the problems associated with sulfur oxides emissions. However, such fuel is not always readily available and the costs to recover and trans-port such high quality coal is in many cases prohibi-tive. Therefore, to meet the objective of environmen-tally acceptable coal combustion, effective methods areneeded to remove sulrur compounds from the coal before, during, and arter combustion.
Recent revisions in the Federal Clean Air Act require a ninety percent reduction in pounds of sulfur dioxide per million Btu for high sulfur coal before release to the ~tmosphere of combustion byproducts for new sources or air pollution. Some states have applled stringent reauirements for reduc~ion of sulfur dioxide to existing facilities. Federal and state legislation, ! (l 337 1 ~0 there~cre, make it necessary to achieve high reductlons in the amount or sulfur compounds emitted during the combustion of coal.
A method of reducing the sulfur content of coal 05 before combustion includes~ grinding the coal to a small particle size to liberate the inorganic sulfur containing compounds and other ash forming minerals from coal; and (2) separating the inorganic material bearing sulfur from the organic portion, coal. A major limitation in this technique is that when coal is ground fine enough to liberate substantial quantities of sulfur minerals and ash-forming minerals, separation of the coal from the unwanted material and subsequent recovery of the coal become difficult.
The grind size required to enable a ninety percent pyrite reduction and eighty-five percent Btu recovery for most coals is less than 0.5 mm and frequently flner than 0.1 mm. At these sizes, reported beneficiation techniques are not consistently effective in separating coal at acceptable efficiencies.
Jigs, hydrocyclones and tables are inefficient for separation of minus 0.5 mm coal. Froth flotation is ineffective when applied to o~idized coals because their surface character is not sufficiently hydrophobic to be activated by collecting reagents. For unoxidized coals, good Btu recovery is attainable by froth flota-tion, but pyrite rejection is difficult because of the relative ease with which pyrite floats.
Ergun, U.S. Patent No. 3,4~3,310 discloses a method of cleaning fine coal material (0.400 mm - 0.037 mm) by subjecting a mi~ture of coal and pyrite to electro-magnetic radiation which selectively magnetizes pyrite. Pyrite is then removed by magnetic means.
This process is limited to magnetizable refuse material such as pyrite. Other materials frequently found in coal, such as silica, canr.ot be removed by this method.
Dense media cyclones are efficient devices for separating coal in the quarter inch to O.S mm range from refuse material on the basis of coal and refuse material having different densities. A mixture of the two materials is suspended in a dense media to form a sink product and a float product. A dense media, or a psuedo-heavy liquid, is necessary because the specific gravities ofcoal and refuse material are greater than one, and therefore, cannot be separated by water alone. A media with an effective media specific gravity between that of coal and of refuse material is required. A common media useful for coal beneficiation is a suspension of magnetite particles in water. By introducing coal-refuse material mixture into a magnetite media, clean coal floats and refuse material sinks. Separation of these materials is hastened by using a dense media cyclone which increases the nominal gravitational acceleration on the mixture.
The use of dense media cyclone separations for beneficiating coal is well known. For example, Miller, et al., U.S. Patent No. 3,794,162, is directed toward a heavy medium beneficiating process for coal particles greater than 150 mesh (about 0.1 mm). Horsfall, U.S. Patent No.
4,140,628, is also directed toward a dense medium separation process. Horsfall discloses the use of magnetite particles less than 0.100 mm for beneficiation of coal fines having a particle size less than 1.000 mm and, in particular, less than 0.500 mm. This process involves separation of materials in a suspension with a dense media to form two fractions and a series of subsequent screenings and washings of magnetite from the two fractions. Horsfall, however, does not address the question of efficiency of separation of the two products.
Previous attempts to extend the performance of dense media cyclones below 0.5 mm have generally met with limited success and, in particular, have been unsuccessful in terms of teaching a general method for efficient separation. One parameter which is useful in assessing the effectiveness of separation of coal fines ~ ;

- ~ 33Zl 90 and refuse material by dense media and cther separation technicues is the Ecar~ P-obable (Ep). The Ep ~alue is defined as the difference between the particle density of that f action of the cyclone feed having a 75~
05 chance of reporting to the overflow minus the particle density of that fraction of the cyclone feed having a 25% chance of reporting to the overflow divided by two.
~ The separation gravity is defined as the specific gravity of a small increment of the feed which reports fifty percent to the clean coal overflow and fifty per-cent to the refuse underflow. The Ep value is a measure of the sharpness cr efficiency of the separa-tion, while the separation gravity defines the specific gravity at which the separation occurred. This separa-tion gravity is different for different size fractlonsof feed coal even though all size fractions are cle~ned in the same dense media cyclone. Generally, a smaller size ft~ction has a higher separation gravity. Also, the specific gravity of the dense media is generally less than the separation gravity.
A typical dense media is a suspension of magnetite particles in water. The magnetite can be natural mag-netite which has been milled. Magnet~te is also recoverable from fly ash. For e~ample, Aldrich, U.S.
Patent No. 4,432,868 discloses that magnetite particles less than 325 mesh in diameter, having 90% magnetics, and a specific gravity between 4.1 and 4.5, can be ob-tained from fly ash. Aldrich further discloses that such magnetite contains a high proportion of round par-ticles which are desirable for heavy medium separationbecause round particles reduce the viscosity of the heavy medium and facilitate separation.
Fourie, et al., The Beneficiation of Fine Coal by Dense-Medium Cyclone, J. S. African Inst. Mining and Metallurgy, pp. 357-61 (October 1980), discloses dense media cyclone separ~tion of a 0.5 mm - 0~075 mm coal ~ action in a heavy medium cyclone with milled ~ag-netite with at least fifty percent less than 0.010 mm `~ using z 150 mm diameter cyclone. E~ val~es from 0.020 to 0.031 were achieved. While accepta~le ~eparation efflciences were achieved by Fourie, et al., the reference does not address cleaning the minus 0.075 mm os coal fraction or provide a general method for determin-ing operational parameters necessary to achieve accept-able efficiences.
Extending the capability of density separation beyond reported limits to effectively separate coal fines smaller than 0.5 mm and particularly smaller than 0.075 mm is highly advantageous. Substantial reduc-tions in sulfur content and high Btu recovery can be achieved with such coal sizes. The ability to clean such fine coal is also economical because waste coal fines which were previously unrecoverable can ncw be used as an additional fuel source. Accordingly, there is a need for an improved procsss for the beneficiation of minerals to effectively recover fine coal.

Brief Desc-iption Of The Drawings Fig. 1 is a graph of coal to magnetite diameter ratio values at differing specific gravities using a specific gravity for coal of 1.3 and a specific gravity for magnetite of 5.1;
Fig. 2 illustrates the relationship between prob-able error (Ep) and divergence (difference between par-ticle specific gravity and effective media specific gravity);
Fig. 3 illustrates the relationship between par-ticle size and divergence of actual data from the pub-lished works of Deurbrouck; and Fig. 4 illustrates the relationship between cyclone diameter and apparent distance (as defined in the specification) as determined by the data in the published wor~s of Deurbrouc~.

` 1 337 1 ~0 Fig. 5 illustrates a flowchart detailing the steps followed in one embodiment of the invention using a diameter ratio deter-ination //

~ 337 1 ~0 ~ Summ2ry O The Tnvention One aspect of the presen~ in~entio~ involves a method ~or selecting magnetite to form a dense media for a dense media separation to benefic ate particulate 05 solids. Particulate solids are provided having a pre-determined minimum particle size and a known specific gravity. The method involves calculating a diameter ratio value applicable to the particulate solids, mag-netite and the dense media. A diameter ratio value represents a particulate solid to magnetite particle diameter ratio for particles having equal but op-positely directed settling velocities in dense media of a given specific gravity. The method further involves selecting magnetite having a particle diameter such that the actual particulate solid to magnetite diameter ratio is greater than the diameter ratio value. This method is particularly useful for beneficiating coal having a particle size less than about 0.15 mm.
The present method is also direc'ed toward using magnetite having a particle diameter of less than about 0.005 mm and a mean particle diameter of about 0.0025 mm. Such fine sized magnetite is particularly useful for beneficiating fine coal particles at low media specific gravities. Magnetite of this size can be pro-duced by a process which involves providing an aqueousiron (ferrous) chloride solution. A gas phase pyro-hydrolysis reaction is then conducted on the solution to form a mixture of magnetite and hematite. By con-ducting the reaction in an oxygen restricted atmos-phere, substantially only magnetite is produced. If thepyrohydrolysis reaction is conduc~ed in an atmosphere with unrestricted oxygen, a substantial portion of the product is hematite. For such mixtures, the method further includes chemically reducing sufficient hema-tite in the mixture to obtain a mixture comprisin~ atlezst about ~5 percent magnetite.
Another aspect of the present ~nvention invclves determining the efficiency of separation of a de~se - media seoaratlon process for beneficiating particulate solids. This method uses, as an indication or effi-ciency, a "divergence value". This term indicates the difference between the specific gravity of the particle 05 to be separated and the effective media specific gravity. This method involves determining an apparent distance a particle must travel within a dense media cyclone or centrifuge to be c~rrectly beneficiated.
From the apparent distance and the residence time of particles in the cyclone or centrifuge, an apparent velocity a particle must achieve to be correctly bene-ficiated is calculated. Using the apparent velocity and other known cyclone geometry and operational para-meters, a divergence value is calculated to indicate the efficiency of separation of the system.
A further aspect of the invention involves a method for selecting cyclone geometry and operating parameters for improved efficiency of separation in a dense media cyclone separation process. This method involves determining a proposed separation efficiency in terms of a prcposed divergence value. A set of Cyclone geometry and operating parameters are selected.
A divergence value for the selected cyclone geometry and operating parameters is determined and compared with the proposed divergence value. If the selected divergence value is greater than the proposed diver-gence value, a new set of cyclone geometry and opera-tional parameters are selected and a new divergence value determined. This process is iterated until the selected divergence value is less than the propose~
divergence value. The step of selecting new cyclone geometry and operating parameters includes selecting greater cyclone length, smaller inlet diameter and greater inlet velocity at constant flow rate, decreased dense media viscosity, larger particle size and lower _pec-~ic gr~vity.
A still further aspect of the invention involves a method for beneficiating particulate solids. This ~ metho~ involves providing magnetite having a diameter such that the par~iculate solids h~ve a buoyancy with respect ~o the dense media. Cyclone geometry and operating parameters are then selected and a divergence 05 value for the geometry and parameters is determined.
The particulate solids are then beneficiated in a cyclone having the cyclone geometry and operating parameters with dense media formed from the provided magnetite.
Detailed Description Of The Invention The present invention is directed toward an im-proved method for beneficiating particulate solids from refuse material in a dense media cyclone. By practice of the invention, particulate solids, and in parti-cular, coal, can be effectively cleaned down to a par-ticle size on the order of tens of microns. When cleaning coal at such fine particle sizes, more than 60 percent of the pyrite and more than 60 percent of the ash can be removed, while retaining more than 60 per-cent of the heating value.
In one aspect of the present method, e.Ytremely fine magnetite is used to form a dense media for beneficiating coal in a dense media cyclone. Magnetite is selected having a particle size such that the buoyant force of the coal with respect to the dense media is great enough to provide effective separation.
It has been recognized that effective separation of small coal particles requires the use of magnetite fine enough so that the coal particle to magnetite diameter ratio is greater than a diameter ratio value. Magnetite having about a 2.5 micron mean diameter is generally effective for cleaning coal fractions down to 0.015 mm.
In another aspect of the invention, a method for predicting the efficiency of separation in a dense media c-~clone is provided. This method involves the use of three equations which have been derived that re-late divergence values (difference between specific ~3371-qO

grav~ty cf a p2rticle and effective media specific gravity) to a number of terms including cyclone g~o-metry factors and operating parameters. Divergence values have been recognized to be a measure of the ef-05 ficiency of seoaration of a system. One of the terms ineach of the equations is V, apparent velocity that a particle must travel to be correctly beneficlated. To solve the three divergence equations, a value for V
must be obtained.
V, however, cannot be directly measured. To determine V for a given system, the following procedure is used. Using the divergence equations, the term V is calculated from known data, such as that published by Deur~rouck, at an arbitrarily selected cyclone radius lS for sets of data corresponding to different size cyclones. These velocity terms represent actual radial particle velocities at the selected radius. However, for the purpose of simplification o. analysis, radial part-cle ve~oclty is assumed to be constant and is as-sumed to be represented by the actual velocities at theselected radius. These velocities are termed "apparent velocities" and can be determined at ar.y radius as long as the same radius is used consistently throughout any analysis. These apparent velocities from Deurbrouck are used along with particle residence time to calcu-late an "apparent distance" a particle must travel to be correctly beneficiated. For coal, "correct bene-ficiation" is to the overflow, and for refuse material, "correct beneficiation" is to the underflow. The ap-parent distances thus calculated have been found to belinearly related to cyclone diameter. From this linear relationship, an "apparent distance" a particle must travel to be correctly beneficiated can be determined for any diameter cyclone. From the apparent dlstance, an apparent velocity can be determined for any given sys~e~. In conjunction with known parameters of the given sys.~m, a di~Jergence value, representing ef-- -- 13~7190 ~ ficiency, can be calculated and can be used in a com-parative analysis of pro~osed or existing systems.
Grinding coal to a small particle si~e is neces-sary for ef~ective liberation and separation of coal 05 from refuse material with a density separation method.
Density separation operates by suspending an admi~ture of coal and refuse material in a dense media of a par-ticular spec~fic gravity which has an effective media specific gravity between the specific gravities of the coal and refuse material. Particles in the suspension having a specific gravity of pure coal or pure re~use are most likely to report correctly to the overflow or underflow because such particles have specific grav-ities which are either much greater or much less than the effective media specific gravity. Particles in the suspension having specific gravities about equal to that of the effective media specific gravity are e~ually likely to report to the overflow with the coal or to the underflow with the refuse. The specific gravity of particles which include coal and refuse material physically bound together is between that of coal and refuse material, and are, therefore, less likely to report to either the overflow or underflow than coal and refuse material, respectively. In either case, the mixed particle will either carry some refuse to the overflow or some coal to the underflow, thereby reducing the separation efficiency. By grinding coal to a small particle size, a high percentage of par-ticles comprising coal and refuse material are broken apart into seoarate particles of only coal and only refuse material. Such separate particles are likely to report correctly to the overflow and underflow, respec-tively, because the specific gravity of each is suffi-ciently different from that of the effective media specific gravity to form either a float or sink par-ticle w,th respect to the dense medium.
A primary difficulty with grinding coal to a small particle size, however, is efficient separation of coal 1 3'37 1 90 ~ frsm re~use material. As used herein, "refuse mater-ial" or "refuse" means any non-car~onace~us substance entrapped in coal deposits or inadvertently added to the coal during mining, including, but not llmited to, 05 clays, shales, pyrite, and other precursors to ash.
Coal which is sufficiently fine to obtain accept-able levels of refuse material rejection can be produced by grinding coarser coal by conventional means. The grind size required to enable at least about a ninety percent by weight pyrite reduction and at least about ninety percent Btu recovery for most coals is less than abc~t 0.6 mm and frequently finer than about 0.1 mm. The present invention is par-ticularly directed toward cleaning of coal ground fine enough to allow at least about sixty percent by weight pyrite rejection with at least about si~ty percent Btu recovery, more preferably at least about eighty percent by weight pyrite rejection with at least about eighty per-ent Btu recovery, and most preferably at least about ninety percent by weight pyrite rejection with at least about ninety percent Btu recovery. Alternatively, fine coal can be obtained from other sources. For e~-ample, coal found in silt ponds of conventional coal preparation systems is generally less than about 0.5 mm. Most coal preparation plants currently operating dense media cYclone separation circuits produce a minus 0.5 mm raw coal slimes product which can be used in the present process. Additionally, coal derived from co~-minuting e~isting coal preparation plant refuse, i.e., aob or culm bank material, can be used. A substantial portion of any such coal source will consist of fine coal material having particle sizes less than about .150 mm.
The present invention involves the separation of particulate solids ~rom refuse ma~érials by a density separation method. ~he preferred em~odiment of the in-vention discussed herein is the separatlon of fine co~l particles from refuse material in a dense medium with -~- 1 3373-90 dense media cyclone. It is ccntempl2ted that the in~Jen-tion is a~plicable to beneficiati~n ~f par~icuiate solids other than coal. It is also contemplated that the present method is applicable to beneficiation by 05 other types of separating systems which employ cent-rifugal force including devices not normally considered to be gravity separators, such as centrifuges.
While magnetite dense media is discussed herein as a preferred embodiment, it should be recognized that the general principles discussed herein are equally ap-plicable to other types of dense media. For example, dense media can be formed from suspensions of sand, barites and ferrosilicon. For e~ample, with ferro-silicon, dense media can be formed having specific gravities which cannot be formed with magnetite dense media.
One aspect of dense media separation is that the light (or float) particles must ke less dense than the effective media specific gravity for separation to oc-cur. That is, the specific gravity of the float par-ticles must be less than the effective media specific gravity. The buoyant force on a particle is a runction of the difference between the specific gravity of the particle and the specific gravity of the media. Rela-tively large coal particles displace dense media, i.e.,a suspension of magnetite in water. As coal partlcles become smaller and approach the size of magnetite, they increasingly displace primarily water. Since coal is not buoyant in water, separation will not occur for such small particles.
The present invention provides a method for deter-mining an acceptable magnetite diameter for forming dense media for the beneficiation of particular c~l size distributions down to a minimum particle size.
3s More particularly, the present method is useful for determining the size of magnetite required to ~roduce a dense media in whicn a particular coal fracticn is buoyant. This method has the following theoretical ~ basis. To be buoyant, a coal particle must have a velocity in the direction of the center of a cycione.
Such a velocity is a result of a buoyant force, acting toward the center of the cyclone, minus a resistance 05 force. Particle velocity is a function of the particle diameter, the difference between its specific gravity and the specific gravity of the fluid it displaces and the "g" acceleration arising from rotation of the coal and media in the cyclone. Accordingly, the velocities of coal, refuse and magnetite particles can be written as follows:

[ 1 ] Vc o a 1 = K ( SpGrC o a 1 ~ SpGrf d ) D~: o a 1 m [Z] Vrefuse = K (SpGrrefuse ~ SpGrfd ) Drefusem [3~ Vmagneti te = K (SPGrmacne~i te ~ SpGrfd ) Dmagneti te~

where V = terminal velocity K = term including components for acceler-ation and viscosity SpGrf d = specific gravity or the fluid displaced SPGrcO a 1, r e f u s e o r = specific gravity of the m a g n e t i t e coal, refuse and magnetite D = diameter of the particles m = exponent ranging from 2 under laminar flow conditions to 1 for turbulent conditions It is known that in dense media systems using centrifugal force, particles which form the dense media, e.g., magnetite, have a component of velocity in the direction of centrifugal force. For the present invention, the assumption is made that, at a minimum, the velocity of coal in the direction oppcsite the centrifugal force is equal to the component of veloci.y of magnetite particles ccmprising the dense media in the direction of centrifugal force. For refuse material, a similar assumption is made eYcept that refuse material moves in the same direction as mag-netite. Addition~ , for refuse material having a buoyant fGrce equal to that of coal, the refuse material enccunters less resistance force than coal be-cause it moves in the same direction as magnetite, and ~ consecuently, has a higher velocity. As a li~it ng case, nowever, refuse mat~_ial velocity must be ~t least as great as ~agnetite velocity. The ollowing equalities can be established based upon the above 05 discussion:

[4] V~oa~ 1) Vmagneti te [ ~i ] Vr e f u 5 e = Vm a g n e t i t e By substitution of Equations 1, 2, and 3 into the above e~ualities, the following ratios are derived D o a 1 SpGrr, a g n e t i t e ~ SPGrw a t e r 1 / m [6] = (-1) Dmagnet1 te SpGr~:oal ~ SpGrfd - _ Drefuse ~SpGrmagneti te ~ SPGrwater l/m t7i Dmagneti te SpGrrefuse SpGrfd These equations, with the exception of the negative factor in equation 6, are the same as the equal set-tling relation given by Gaudin, A.M., Principles of Mineral Dressing, McGraw-Hill Book Co., Inc., New York, N.Y., p. 186 (1939).
A value for m in the equations 6 and 7 depends upon the applicable flow regime: turbulent, transi-tional or laminar. The Reynolds number of a particle is a criterion which indicates whethe~ the flow regime is laminar or turbulent. For Reynolds numbers greater than 500, flow is turbulent; between 500 and 2, transitional; and less than 2, laminar. Reynolds num-ber depends directly upon a particle's diameter, its veloclty, specific gravity of the fluid it displaces and inversely upon the fluid viscosity.
To calculate the Reynolds number of a particle, its ter~inal settling velocity must be known. S.okes iaw, modified wi~h correction factors for the slmul-taneous movement of many particles, may be used.
Gaudin, A.M., Principles of Mineral Dressing, McGraw-ook Co., Inc., New YorX, ~.Y., p. 188 (1939).

[8] Vpar~ ~ s2~3) (1 - s) (1 - 2 5s) 05 g(SpGrp a r t ~ spGrf 1 u i d ~ D2 U
where s = volume fraction of solids u = viscosity of the fluid Reynolds number is given by the following equation:
D V SpGrflui d [9] Re Equations 6 and 7 provlde limiting particle diameter ratios for coal and refuse to be correctly beneficiated in magnetite heavy media. For particle dizmeter ratios less than that given by equations 6 and 7, beneficiation cannot occur. The ratios provided by Equations 6 and 7 are termed "diameter ratio values".
For coal or refuse particles to have the same buoyancy as though they were immersed in a true liquid having the same specific gravity as the media, the coal or refuse to magnetite particle diameter ratios must be greater than diameter ratio values given by equations 6 and 7. Equations 6 and 7 can be used to construct Diameter Ratio Partition Curves which plot diameter ratio values for a range of media specific gravities.
For example, with reference to Fig. 1, a Diameter Ratio Partition Curve is illustrated wherein the specific gravity of the dense media is on the abscissa and the ratio of coal to magnetite particle diameter is cn the ordinate. Diameter ratio values forming the curve indicate coal-to-magnetite particle diameter ratios for coal and magnetite particles having equal al.h~ug:~ oooosi'e'y dir~cted velocities in a dense medium of a particular spec7fic gravity for a given flow regime. If coal partlcles have a velocity in the 1 3371 9~

_ dense medium toward the cyclone center less than mag-netite particle velocLty in ~he opposite direction, ef-fective separation of coal by the magnetite dense medium is not possible because the coal will not 05 "float" with respect to the dense medium.
Two curves are shown in Fig. 1. The upper curve 1 represents the theoretical minimum coal to magnetite particle diameter rat os for separation in dense media of given specific gravities for turbulent flow. The lower curve 2 represents the same information for lam-inar flow in the cyclone. The graph in Fig. 1 defines three important regions relevant to effective coal beneficiation: (1) the region above the turbulent curve I; (2) the region between the laminar and turbulent curves II; and (3) the region below the laminar curve III. Points on the graph in region I allow efficient separation, while points in region III are ineffective for coal separation. Points occurring in region II
produce separation efficiencies which are difficult to predict precisely, but in general depend on the flow regimes of the particles.
Fig. 1 illustrates the relationship that as the dense media specific gravity decreases, the ratio be-tween the coal and magnetite particle diameters must increase asymptotically for effective separation. In view of this relationship, processes using dense media with low specific gravities should have high particle diameter ratios, i.e. small magnetite with respect to the coal, for the diameter ratio points to be greater than diameter ratio values.
Equal settling curves similar to those depicted in Fig. 1 can be generated by selecting appropriate values for coal specific gravity and coal size and solving for magnetite particle size diameter according to Equations 6 or 7. The turbulent curve of Fig. 1 was generated using a specific g av~ty for magnetite of 5.1 and for coal of 1.3 for various dense media specific gravities.
For e~ample, in a dense media having a specific gravi~y -~6-of 1.6, a coal/magnetite diameter ratio value is approximately 14:1. Accordingly, to effectively clean coal particles having a 0.14 mm diameter, a dense media comprising magnetite particles less than 0.01 mm in diameter is required.
The use of a Diameter Ratio Partition Curve in the manner described above is useful for beneficiation of coal from refuse material with magnetite dense media.
While the process is particularly useful for separation of fine coal, it is applicable to any density separation for cleaning coal. The present process is also useful for any separation of solid materials generally on a density separation principle.
A flowchart for one embodiment of the invention using a diameter ratio is shown in Fig. 5. Feed material (1), contains particulate solids to be beneficiated and refuse particles to be removed. The particulate solids and refuse particles are of known size and specific gravity. A fluid (2) and suspension material (3) are to be used to prepare dense media (4).
The dense media is prepared by first selecting a minimum particle size (5) of particulate solids to be beneficiated. A diameter ratio is then determined (6) for the ratio of particle diameter of particulate solids to be beneficiated to particle diameter of suspension material particles required for the particulate solids to be buoyant in the dense media. Based on the determined diameter ratio, a maximum particle size for suspension material is selected (7) corresponding to the minimum particle diameter to be beneficiated. Suspension material particles having a particle diameter no larger than the maximum particle diameter (8) are mixed with the fluid (2) to prepare the dense media (4), which is then used for dense media separation (9) of feed material (1), resulting in beneficiated particulate solids (10) and refuse (11).

A ~

Acceptable separation efficiencies in dense media cyclone systems depend on the economics of a given process. However, an Ep value of 0.035 or less generally indicates a separation efficiency acceptable for economical recovery of coal, while an Ep value of 0.10 or more is generally unacceptable for effective recovery of coal.
The present invention is particularly effective for coal beneficiation systems in which a low specific gravity of separation is desired. The specific gravity of separation (or separation gravity) is the specific gravity of that portion of the feed reporting fifty percent to the underflow and fifty percent to the overflow. The separation gravity is related, but not equal, to the specific gravity of the dense medium. If, for example, it is desired to operate a beneficiation process with a low separation gravity to clean a specific size coal fraction, the present process is useful for determining the magnetite particle size necessary for effective separation. Over a small change in dense media specific gravity, the coal to magnetite particle diameter ratio for effective separation can vary greatly.
In accordance with the present invention, 1~

, .
A

~ partlcle size. While t~e present process is appiicaDle to beneficiation or coal of all sizes, the proce~s be-comes more critical at smaller coal si~es. For such coal, correspondingly smaller magnetite is required for 05 effective beneficiation. It is contemplated that minus 0.010 mm magnetite can be used for cleaning down to small coal particle diameters. conventional grinding of magnetite to such small particle sizes for purposes of coal beneficiation by dense media cyclone separation processes is prohibitively e~pensive. Grinding costs rise e~ponentially as magnetite particle size decreases.
Magnetite of the present invention can be produced by the oxidative pyrohydrolysis of iron (ferrous) chloride according to the following reaction:

[10] 3 FeCl2 + 3 H2O + 1/2 2 _, Fe3O~ + 6HCl magnetite Production of fine magneti'e in this manner avoids high costs of grinding larger size magnetite. An iron chloride solution is sprayed into a reaction chamber or roaster at elevated temperatures and oYygen is supplied for the reaction to produce magnet te. Such magnetite has a particle diameter less than about 0.010 mm, and substantially all of such magnetite has a particle diameter less than about 0.005 mm. "Substantially", as used above, means at least about ninety percent and more preferably about ninety-five percent.
A suitable source of iron (ferrous) chloride solu-tion can be obtained by dissolving scrap ferrous metalwith hydrochloric ac~d. The hydrochloric acid can be recovered from the pyrohydrolysis reaction and can be recycled to dissolve additional scrap. Spent steel making liquors are also a convenient source of iron (ferrous) chloride. Additionally, iron (ferrous) chlor de can be -ecovered from the dissolution of il-menite wlth hydrochlorlc acid. It should be recognized, however, that any of various solutions containing iron 1 337 1 qO
- (ferrous) chLoride c~n be use~ in this inventlcn.
If the oxygen content in the pyr~hydrolYsis rezc-tion is not controlled, the product mi;~ture contains largely hematite particles with some magnetite, accord-05 ing to the following reaction:

[11] 2 FeCl2 + 2 HzO + 1/2 02 ~ Fe203 + 4HClhematite However, by subjecting the mixture to reducing condi-tions, the iron oxide particles can be converted toprimarily magnetite. For e~ample, the product mixture can be heated in a carbon monoxide ~r a hydrogen atmos-phere to reduce hematite to magnetite at relatively low temperatures of between about 300C and about 400OC.
An acceptable magnetite content in such a mixture depends upon the economics of a system. However, for example, it is contemplated that such a mixture have at least about 85% magnetite and more preferably at least about 95% maanetite.
Initially, magnetite particles formed by this process may be fused together into aggregates. Such fused particles are broken apart into separate par-ticles as they are initially run through a separation circuit.
Production of magnetite by these gas phase pyro-hydrolysis reactions produces substantially rounded magnetite particles because the temperature of forma-tion of the particles is close to the fusion tempera-ture of magnetite or hematite. Rounded magnetite par-ticles are more efficient for dense media separation because they create a lower effective dense media vis-cosity for a given particle size and concentration than does angular magnetite produced by, for example, grind-ing. A lower viscosity is more efficient because the cleaned coal and refuse material move more easily th oush the heavy medium. Ancther benefit of lowered viscosl y is that the medium is less cos.ly to pump.
Rounded magnetic particles are also more easily washed .

free from coal than are angular particles because coa_ particLes themselves have ~lat an~ular surraces.
Rounded particles are also much less abrasive to the internal components of the system, such as pumps, 05 cyclone, and magnetic separators.
It is also contemplated that more effective separ-tion between coal and refuse material can be achieved by treating the magnetite particles in the heavy medium suspension with a surfactant to decrease the effectiJe viscosity of the heavy medium. Surfactants should be added to the dense media in the dense media sump prior to introduction into the cyclone. It is believed that both coal and refuse material particles move more freely in the suspension in the presence of a surfac-tant and are thus more likely to report to the overflowand underflow, respectively.
The concept of buoyancy discussed above is nec-essary to achieve separation between particulate solids and refuse material. Particulate solids must approach the buoyancy they would have if they were immersed in a true liquid of the same speclfic gravity as the dense media to be correctly beneficiated, and refuse material must have a negative buoyancy with respect to the media to correctly report to the underflow. Positive or negative buoyancy, however, only indicates the direc-tion of particle velocity. For a given system, dense media separation methods also have a time limitation in that a given particle has a limited residence time.
Therefore, the forces acting upon the given particle must cause it to travel far enough in the medium to be correctly beneficiated during the residence time.
Poor separation efficiencies are often encountered due to a lac~ of understanding of factors involved in dense media separation processes. Another aspect of the present invention includes a method for predicting the separation efficiency of a given system or propcsed system for the purpose of achieving improved separati~n effic encies. While this method is discussed in terms ~ of a masnetite dense media Frocess, it should be recog-ni ed that other types of ~edia can be used equally well. For example, other types of dense media, such as suspensions of sand, barites, or ferrosilicon, c~n be OS used. The method is also applicable to true heavy liq-uids, such as solutions of halogenated hydrocar~ons or aaueous salt solutions.
The present method uses, as a measure of effic-iency of separation, the difference between the par-ticle specific gravity (SGp) and effective mediaspecific gravity (SG.m). SGe~ is defined as the lowest specific gravity of separation of any size fraction treated. For practical purposes, SGem is slightly higher than the specific gravity of the media. This measure of efficiency, the difference between SGp and SGem, is termed "divergence".
It has been found that a direct relationship e~ists between divergence values and Ep values (a widely recognized measure of efficiency). Data have been taken from two published works by Deurbrouck, and divergence values have been plotted against Ep values in Fig. 2. For the 20" and 24" cyclones, each data point represents an average of four actual data points.
Deurbrouc~, A.W., "Washing Fine Coal In A Dense-Medium Cyclone", U.S. Dept. of Interior, U.S. Bureau of Mines, Report of Investigation 7982, 1974, six pages.
Deurbrouck, A.~., "Performance Characteristics of Coal Washing Equipment-Dense-Medium Cyclones", U.S. Dept. of Interior, U.S. Bureau of Mines, Report of Investiga-tion" 7673, 1972, 34 pages. As seen in Fig. 2, as divergence values increase, Ep values increase (less efficient se~aration). Therefore, by minimizing diver-gence values, efficlency of separation is increased.
Data from the Deurbrouck wor~s, much of which is used in the following discussion are shown in Tables 1, 2, and 3.

O r~ ~ ~ ,1~ ~ 1' O Ul ~, Q o ~ ~ ~ ~ tn 1-- ID H~
rt 1-- : ~ 1-' r~ ~ ' O O U~ n C 3 -- O O rt W 1-- tt 1- 3 ,.
. )D (D C
~ ~ It c tn :~ ~ O, n ~ .
t~ C
Z Q
C (D` (D tD
O ID ID O O O O O ~ Pl O
~ r~ C - . . . . . . 3 ~ 3 a~ 1-- 1-- ~ ~ ~ 0 1-- 3 tD
~D O O V O
n cn -~ o o ~ 1-- It I
7' N H

~ ~ tn n w ~ 1-3 ~
O ~ ~D ~n Q C~ ~
- O 1'- . . . . . D c r W 1~ 1~ N ~Jl Ul >~ ~ W W t 1'- --~ rt rD _l w ~ I-- ~ w )D rt ~ H
_. rt~C 1'- Z t1 D l-h O O O !Z -3 tl ~) 3 I-h cn rn - n ~ ~-- H
'D ~ 3 ts~
)D t~ 3 ~I C~
rt O P~ D 3 3 rt ~ (D D n 1'- :I rt o o o o o o rt rt ~
o ~ t ~ r C~ 3 ~- ~ N I--` O O 0 1~ 0 n ~ o ~ ~ W o ~ ~ 3 o r!
'~ I~ )~ 3 C 3 ,r ~3 C~ 1'- (D rt C -' ~ C )11 ~ t~
n ~ 3 3 n 1l ~ n ~ ~ ~Z
rt _l ~1 ~ 1-- ~ ~ W ~ 3 - ~ 3 tD ~1-- _~ ~ a~ ~_rl rJ~ O ~ ~ rt 1--. . . . . I tn ~ ~ 3 a~ ~ r~ -- n c ~5 ~ 0 ul n rt 1--3 ~C ` '`C tD
~ r .
C t~ -pJ :r r rt O O O O O O W 1-1'- . . . . . . ~ -O ~ 1~ 0 0 0 0 0 ~ 5 3 (D O a~ w ~ ~ ~ o ~
~ w .P a~ t 5 t~ rt ~D

1337~90 .
~J ~_ ' N
W OO C t~
~o nn ~
tJ 3 ~-tD C
~a ~t o ~ ~ u, 3 ~
n ~ o O
~1 ~D~3 3 ~ G~
r ~
p~~h ~ O 1' ~D ~ O
O~S O ~D ~P CO ~~ ~n rt 3 1~ t O
N IJ~ I
O ~D n ~ X
Il ~ Ul ~D ~
w ~ n W -o o - ~ n _~ ~ o ~,t ~
T) ~t Ul Vl o O ~- Q t~
O O ts n- It 3 ~h -U.
tD~ rn t:
~ r~
o n w rn G~ u~
)-- o o OO ~
Q rt o o O O~ rt ~ ~Q K
~ O ~ -G~- ~ Y- O O O O
--~ 1- n a~ w ~ o~ ~ 30 n o ~ ~ 3 rr z:
~W ~ ~ ~n ~ O ~- ~ ~ W
rt ~
n n~ s 3 t~
pl~!:) 3 n D1 3 ~3 103 tSI ~ 1--` ~ N ~ O ~t 1--~ ~ w Ir~ n -- 3 _~ ~. . tD IJ- ~ 5 ~
a~ IJ- ~ ~ o n r~ - 3 Q
_~
~ww 3 a~ I N Q
pJ~O-- ~T
o o o o~ ~
a ~ o O - ~ o o o o~ ~r ; Ul ~ ~ ~O ~' w r o ~ J
a~ ~ w ul --/o ~ :
_. r~
,t ~ ~
5~ ~.
rn .

r ~_ O
~Q (D

. .
~ ~ Ul --rD
W (~1 0 C ~ 1~~: 1~ t k 5D ~h ~ N) ~ ~ I-t 00 CD ~P o ~D
C~
~ 3 1--ID ~ 111 C tD O
t'~ 3 'D
~ O
0~ ~ ~h ~
a~ ~ O ~ ~:

~r Hl (D O ~ w O~ O
g r~ O ~ ~ 3 3 3 O 1~ 0 (D ~ C~
3 I t It1~ t' 1-1 ~ .
N ~
n 1-- 1_ 0 ID O H
It~ 3 C 3 Il 1~ U~ tl) 3 W
W~
;n C u~
O O t~
_ D ~' ~
,~--- pJ _1 W ~0 CO D r~ -h 2 ~ ~t U7 ~ O w 1-- n IDn tD o O
n~ ~t 3 ~h Z
n Y- r~
~D~ rn rD~ Y- '3 ~tO n W w IDt rn C~ 3 t~ C~ rn ~ ~
~ ~ rD ~ ~- H
1'~ 0 0 ~ 3 ' (D C D tl) tD D n ~- t ~-Q rt O O O O rt ~t ID UD t ~ O ~t C~
C~ Y~ o o O O
n ~o Ul ~ o C rD 3 0 n r,l '3 w w w ID~ D rD ~ _ 1-- 1- n ID ~: n ~
S ~ Q

~ ~ ,3 H
Y ~ n ~D ID Y- Q
ttO ~ ~ ~ t~ 3 ~ ~t 3 e~3 ~D3 ~3 w ~ ~1 ~ ~ ~
I rn n Y- 3 _~ C~ o ~ ~ rD -- n ~;
tJ~y- o o W ~D n ~1-3 --~ ~ O ~: tD
W ~ ¦ N
t~ ` tD ~
ID

~ _~ O O O 0 O ' tD O O O O It w t:n w ~ ~ tt ~ ~n ~ ~ o ~
-- 'D
~ ~C .
S (D Y-Ul ~

Q
<: n, ~;l'f )D 3 ~n rn - The Deur~rouck data have als~ ~e~ plotted as dlvergence values versus par_icle size in Eig. 3. I' is apDarent that for smaller size particles, divergenco values increase. Given the direct relationship between 05 divergence values and Ep, it would be expected and is borne out by data that smaller particle sizes have higher divergence values since it is widely known that efficiency deteriorates at smaller size frac~ions.
The present method involves the use of three equa-tions which have been derived relating divergencevalues to a number of factors (referred to as "diver-gence equations"). These factors include the followinq:
1. V--Velocity for a given size cyclone that a particle must achieve in the direction of buoyancy to be correctly beneficiated;

2. D~--Particle Diameter;

3. G--Acceleration;

4. u--Dense Media Viscosity; and 5. S&em--Effective Media Specific Gravity Each of the three equations is applicable to a different flow regime, turbulent, transitional, or laminar, which depends upon particle Reynolds Number.
These three eauations are shown immediately below. The derivation of the equations is shown before the Ex-perimental Section.

- 1 337 1 90 ~
,` W

H v A Z v 0 ~3 0 ::~
O H O Z

O O O
'Q 'Q
c Q ~ C tl Il 11 11 11 11 11 11 1~ 1 o ~
hi C ~ ~ 3 ~ ~ o C Ul r~ O O
~- n ~
n c ~c C C C
;n ~ 1--3 n o ~ o n ~ O O "~1 ~t O O Q
O ~ ~ +
O
+ + O
''D ~ O

Y
n ~R
c o o o ~ o O O cn Q ~I Q
u~ cn Q
Q Q
Q Q
+ + ~

O O O
~Q 'Q w I-- W
W
O C~

2(~

1 337 1 ~0 For any given cyclone/coal system, the Particle Diameter, Viscosity, and Fluid Specific Gravity terms are constant. The Velocity (V) and Acceleration (G) terms vary as a particle moves within a cyclone. Since the particles accelerate, particle velocities change. Moreover, the G
term varies as particles are at different radii. It is contemplated that the divergence equations can be used to determine divergence values by accounting for this variability. However, such mathematical precision is not required for effective use of the divergence equations.
Instead, the present method involves using the concepts of apparent distance and apparent velocity to predict separation efficiency. As discussed below in more detail, apparent velocity is calculated from apparent distance which is calculated on the basis of actual data using an arbitrarily selected radius of interest. Accordingly, when apparent velocity is used to calculate a divergence value from equations 12, 13, and 14, the acceleration term, G, for that divergence value must be calculated at the same radius of interest.
The present method involves assuming that apparent velocity is a constant velocity throughout the entire residence time in the cyclone. Apparent velocity is a function of residence time and apparent distance travelled by a particle. Of the terms residence time and apparent distance, residence time can be directly calculated from the cyclone geometry and the media flow. The apparent distance, however, cannot be directly calculated because the flow dynamics and actual paths that particles travel within a cyclone cannot be accurately determined. It is noted that the apparent distance a particle must travel to be separated is the same for particles of any size and that the apparent distance is a function of the diameter of the cyclone.
To overcome the limitation of not being able to directly determine either apparent distance or apparent ~' veloc-ty, the present method includes deter~lning an apoarent distance based u?on known da~a, such 2S that reported by Deurbrouck. The apparent d s.ance is ~hen used to calcuLat~ apparent velocity for use in the oS divergence e~uations. The acceleration term in the divergence equations must then be determined at a radius of interest corresponding to the selected radius of interest used in conjunction with the known data to provide the basis for determining apparent distances, as described below. In this manner, divergence values for separation systems can be determined. These pre-dicted divergence values can be analyzed to determine whether the efficiency of a proposed system is accept-able.
Apparent distances are determined from the ~eur-brouck data in the following manner. Initially, the as-sumption is made that the distance travelled by a par-ticle in a cyclone is a function of cyclone diameter.
Then, from the Deurbrouc~ data, divergence and fluid specific gravity are known and viscosity is assumed to be 1 centipoise, for each particle fraction. Accelera-tion varies with radius, but for present purposes is determined at an arbitrarily selected radius of inter-est of 1/3 the cyclone radius. With this information, the divergence equations are solved for V, and average values for V are calculated for the 8", 20", and 24"
cyclones. These values are actual velocities of par-ticles at one-third the radius of the cyclones. These values are also termed apparent velocities and are as-sumed to represent a constant velocity a particle musttravel to be correctly beneficiated.
The apparent distance that particles travel in each of the three cyclones is then calculated by multi-plying V by the residence time. The apparent distances calculated in this manner are then plotted against cyclone diame~er as sh~wn in Fig. 4. The three data points on this graph rorm an approximately st-aisht line. This relationship suggests that the starting as-~ 337 1 90 sumpt7on was cor-ect, and that a linear relationshi?
e~ists between cyclone di~met~r ~nd the apparent dis-tance particles, regardless of size, must traveL to ~e separated. By conducting a linear regression of the 05 data points in Fig. 4, the following e~uation for determining apparent distance from cyclone diameter was calcllated .

[15] y = 3.05 x + 42.07 where y = apparent distance, centimeters x = cyclone diameter, inches According to the present method, the efficiency of separation of a dense media cyclone for each partlcle size fraction can be predicted in the following manne-.
The residence time of a particle is calculated by dividing cyclone volume by flowrate. The apparent dis-tance a particle must travel to be correctly bene-ficiated is calculated by applying the cyclone diameter to Equation 15. A value for apparent velocity is then detenmined by dividing the apparent distance by the residenc~ time. G is determined at a radius of inter-est or 1/3. The appropriate equation, depending on Reynoids number, of Equations 12, 13, and 14 is then solved using the value for V and other knowh values. A
value for the logarithm of the divergence value ap-plicable to the cyclone for a given particle size and its operating conditions is then obtained.
The divergence value thus obtained can be used in a comparative analysis with divergence values appli-cable to cyclones having different geometry or operat-ing conditions.
The effect of proposed changes in a separation system on efficiency of the system can be detèrmined by the above method. Any changes in cyclone geometry and operat_ng raramete-s in a separation system for im-proved ef-iciency wiil normally be selectea on the basis of efficiency improvement per cost. Various 1 337 1 qO
separaticn systems having di~ferent cyclone geomet~v and cpe~~ting paramet~r, have ~een analyzed ~or pre-dicted e-ficlency as measured by divergence values by the present method. The results of these anal~ses are 05 desc-ibed in the E:~perimental Section. By examining the amount of efficiency improvement from each of the changes analyzed and relative cost, it has been ~eter-mined that certain changes for improving efficiency are more cost effective.
Increasing residence time by using longer cyclones or decreased cone angles has been found to be a cost effective manner for improving efficiency of separa-tion. As seen in Example 2, substantial decreases in divergence values are achieved by increased residence time. The cost associated with this change is simply the capital cost for buying longer cyclones. This cost is minimal in terms of efficiency improvement per ton of coal. It should be noted that residence time can also be inc~eased by using larger diameter cyclones.
However, any benef ts from this method of increasing residence time are virtually completely offset by lower efficiency frcm dec~eased accelerati~n.
Another cost effective -hange in a separation sys-tem is to increase acceleration, without at the same time dec~easing residence time. While acceleration can be increased by smaller cyclone diameters, residence time is reduced by such a change. Ac^eleration, hc~J-ever, can be increased without decreasing residence time by some combination of decreasing the inlet dia-meter and increasing the inlet velocity, while keepingflowrate constant. The additional cost of such changes includes costs of equipment modification and increased pumping costs to achieve higher inlet pressures. The improvements in divergence values from smaller inlet diameter at constant flowrate are shown in Example 4.
Re~ucing dense media viscosity is another cost ef-fective method for imDroving separat-on efficLency.
The effect of reduc-ng the media viscosity on dLver-gence values s illustrated in Example 3. As d-scusse~
above, viscosity reduction can ~e ach~eved by a~diticn of a su-fac~ant, such as Lomar D,* p:oduced by Diamcnd Shamroc~. In this manner, magnetite particles move os more freely with respect to each other. The use of rounded magnetite particles also reduces viscosity, as discussed above. Viscosity reduction can also ~e achieved by heat~ng the dense media. For e~ample, by raising the temperature of the media in a heated cir-cuit from 680F to 140F reduces the viscosity of water from about 1 to about 0.47 centipoise. Moreover, the use of a heated circuit has other benefits, such as reduced drying time of filtered coal. The cost of achieving viscosity reductions by these methods is ac-ceptable in view of the improvements in efficiencies.
These methods of viscosity reduction can be used alone or in combination.
Particle size also has a strong effect on separa-tion efficiences. As seen in all of the Examples, much lower divergence values are achieved for larger par-ticle sizes. Accordingly, coal should be ground only to as small a size as is necessary for acceptable libera-tion. Moreover, grinding methods which generate the least amount of extreme fines should be used, such as rod rather than ball mills.
The general principles disc-~ssed above and equa-tions 12, 13, and 14 relating to the use of cyclones for dense media separation (separation of solids based on different specific gravities) arE also applicable to the use of cyclones as thickeners (separation of solids from liquid) and classifiers (separation of solids based on size). These principles and equations are also useful for other mineral processing systems which use ce~trifugal force, such as spirals and hydro-cyclones. These principles and equations are also ap-piicable t~ mineral processing systems which do not use cen.riEusal force for processing. Such systems include the use of vertical currents, e.g., jigs, the use of * Trade-mark - :

streaming currents, e.g., tables, and the use cf launde-s. These princi31es c~n be ~sed to predict per-formance ef~ectiveness or such systems and to select operational parameters for improving performance.
05 Equations 12, 13, and 14 can be used directly for such other systems. Howeverl instead of using Deurbrouc~'s data, similar data for the appropriate system would be used to determine apparent distance and apparent velocity. In the case of systems not using centrifugal force, acceleration would simply be gravitational acceleration.
After the coal is separated from refuse material in the dense media cyclone, the overflow portion con-taining clean coal is separated from the magnetite par-ticles by magnetic separation. Coal particles having adiameter less than about 0.6 mm are typically separated from magnetite particles using magnetic separators.
The underflow portion containing refuse is typically fed to a separate magnetite recovery circuit where the dense media is separated, for eY~mple, by magnetic separators and recycled.
The reductions in ash forming material by the present invention are highli advantageous and economi-cal for coal combustion processes. For example, foul-ing and slagging of furnaces caused by ash is decreasedwith a decrease in ash forming materials in the fuel.
Additionally, ash removal costs are reduced when the total ash burden is reduced. Costs are also associated with the transportation of ash forming material to a utility and movement of ash forming material and ash through the combustion process. Such costs are reduced by use and combustion of clean coal.
A clean coal from the present process is par-ticularly advantageous for mixing with various addi-tives and forming aggLomerations prior to combustion.Such coal is suited 'o agglomeration because of its fine size. As used herei~, "agglomeration" refers to methods for forming fine particles of coal into larger 13371~0 size units, such as pelletizing, comDaction, or agita-tlon. Advantages of agslomer~tLon include impro~ed nandling of coal material, particularly during the transpor~ation of fuel products. Agglomerations are o5 particularly advantageous for coal-fired utilities which use pulverized coal (PC) boilers in which coal material is pulverized before combustion to a particle si~e less than about 0.075 mm. Energy savings in this pulverizing process are made by using agglomerations or clean coal from the process because agglomerated coal is more easily pulverized than solid coal pieces and a large percentage of the coal particles in the pellets already meet the size requirements for the crushing process.
There are additional advantages to using clean coal from the present process when additives are incor-porated with the coal material. Such additives can in-clude materials for air pollution reduction, such as alkaline sorbents for sulfur capture, sulfation pro-moters, catalysts for intermeaiate reactions in air pollution reduction processes, or anti-slagging agents.
While such additives can form ash u~on combustion, the overall ash burden is sufficiently reduced by the present process that ash formed from additives is ac-ceptable. Additionally, because of the fine size ofthe coal particles, additives are partlcularly effec-tive due to ease of dispersion of ad~itives and in-t-mate mixture with the fine coal particles.

Derivation of Divergence Eauations The force acting on a coal particle in a cyclone system in the direclion of the interior of the cyclone is te~med the "~uoyant force" and is provided by E~ua-tion A.

[A~ F~ = Volp (SGp - SGfd) G

1 3~371~9 whe-oin, F = buoyznt force Volp = part cle volume SGp = art-cle specific gravi~I
SGf d = specific gravity of fluid displaced G = G acceleration The G acceleration is a radial acceleration which is caused by the circular motion or the coal/refusejmedia stream inside the cyclone. This ac-celeration is a function of tangential velocity of the stream. As can be seen from Equation A, to increase the buoyant force on a given particle in a given dense media, the G acceleration must be increased.
Bradley, D., The Hydrocyclone, Pergamon Press Ltd., London, 1965, discusses cyclones and provides two equations which, solved simultaneously, give the fol-lowing e~uation for G acceleration.
~3.7 R. 2 Rc Vj 2 Rc 2 n +
[B] G = V~ang /r = _______________ ___ Rc ~ r 20 wherein, R~ = radius of in7et, ft R~ = radius of cyclone, ft Vj = velocity of feed in inlet, ft/sec r = radius of in~erest, ft Vt a n ~ = tangential velocity of stream inside cyclone, ft/sec For purposes of the present discussion, the radius of interest, i.e., the radius within the cyclone at which acceleration is determined has been selected as 1/3. As mentioned previously, selec~ion of this ~alue for r is not critical to the present invention and other values work equally well The term n is an ex-ponent, the value of which depends on cyclone geometry.
A value of 0.8 is typical and will be used in this derivation.
In opposition to the buoyant force, is a resis-tance force. The resistance force is a func'ion ofmany varia~',es and deDends! in part, upon the flcw regime of partlcles inside the cyclone. As is known, particles can have turbulent, transitional, or laminar flow regimes. The particular flow regime for a par--3~--ticle depends upon the properties of fluid in which the particle is travelling, viscosity and specific gravity, as well as on the particle's velocity and diameter. The Reynolds number of a particle is the criterion which determines flow regime. For Reynolds numbers less than 2, particles will travel in laminar flow. For Reynolds numbers between about 2 and about 500, flow will be in a transitional phase. For Reynolds numbers greater than about 500, turbulent flow occurs. The formula for Reynolds number is provided in Equation C.
Dp Vp SGf d [C] Re =
u wherein, Re = Reynolds number Dp = particle diameter Vp = particle velocity SGf d = specific gravity of fluid displaced u = viscosity of fluid displaced The coefficient of resistance of a particle is a measure of resistance experienced by a particle as it travels through a fluid. The formula for coefficient of resistance is provided in Equation D.

25 [D] Q = 4 Dp (SGp - SGf d) G
3 Vp2 ( SGf d ) whereQ = coefficient of resistance Dp = particle manner SGp = particle specific gravity SGf d = specific gravity of fluid displaced G = G acceleration Vp = particle velocity The relationship between coefficient of resistance and Reynolds number can be described by three equations, one for each flow regime.
[E] Turbulent (Re >500) log Q = log 0.44 [F] Transitional (500 ~Re >2) log Q = log 18.5 - 3/5 log Re [G] Laminar (Re ~2) log Q = log 24 - log Re -The partic'e velocity can oe determined in the following manne~ uations C ~nd 3 3re sol~ed for the velocit-~ term and then set equal. The following rela-tionship is derived f,om this procedure.

4 Dp ~SG;, - SGfd ) G
[H] log Q = log ______ +
3 SGf d Dp SGf d 2 log _ - 2 log Re u The log ~ term in Equations E, F, and G can be substituted into E~uation H and the resulting Reynolds number may then be solved for particle velocity in tenms which are generally known. These equations for each of the three flow regimes are provided in Equa-tions I, J, and K.

4 D? (SG;, - SGFd ) G
[I] (Re >500) 2 log Vp = log ___________________ - log 0.44 3 SGf d 4 Dp (SGp - SGf d ) G
[J] 500>Re>2 1. 4 log Vp = log - ----------3 SGf d Dp SGf d + 0.6 log _ - log 18.5 u 4 Dp (SGp - SGf d ) G
tK] Re<2 log Vp = log _______ _____ +
3 SGf d Dp SGf d log _______ - log 24 u Equations I, J, and K can be algebraically manipu-lated to the form of Equations 12, 13, and 14.

~ EXP~RIMENTAL

E:~ample 1 Observed divergence values for difrerent size 05 fractions of coal from DeurbroucX's work with an 8 inch cyclone are compared with divergence values predicted by the present method using the actual test parameters of Deurbrouc~'s worX. The actual conditions of DeurbroucX's test are shown in Table l-A.

Table l-A
Value Value Parzmete{ (Actual Conditions) (New Conditions) Cyclone Diameter 8 inches 8 inches Inlet Diameter 1.5 inches 0.75 inches Cyclone Length 8 inches 32 inches Cone Angle 12 degrees 12 degrees Flowrate 110 gpm 141.6 gpm Viscosity 1 centipoise 0.4688 centipoise (assumed) Effective Media 1.33 1.33 Gravity Based upon the actual conditions in Table l-A, predicted divergence values were calculated according to the present method. These predicted values are com-pared with observed divergence values for each size fraction considered by DeurbroucX. This comparison is shown in Table l-R.

-~able 1-3 Predicted Predicted Divergence Divergence Size Observed (Actual (New 05 Fraction Divergence Conditions) Conditions) 0.814 mm 0.03 0.017 0.001 O.420 mm O.08 0.053 0.002 O.250 mm O.11 0.121 0.006 0.177 mm 0.20 0.210 0.010 0.105 mm 0.24 0.483 0.022 O.074 mm -- 0.846 0.039 0.037 mm -- 2.565 0.119 A new set of test conditions, varying four factors from Deurbrouc~'s 8 inch cyclone data, were selected for improved separation. These new conditions were analyzed according to the present invention to deter-mine predicted divergence values to illustrate the potential for improved ef.iciency of separation. The values for the new corditions are shown in Table 1-A
and the predicted divergence values under the new con-ditions are shown in Table 1-B. The improvement in predicted divergence values from the modifications in the four changed conditions is substantial. Acceptable cleaning efficencies, represented by a divergence value of 0.119, are obtained for particles even as small as 37 microns (400-mesh).

Example 2 For Examples 2-8, a series of simulated separation runs were conducted using Equations 12, 13, and 14, to ~ ;ne the effect on separation efficiency, as indi-cated ~y divergence values, cf variations in different parameters.

ln ~xample Z. four s mulatlon runs we~e c~nducted with the residence tL~e ~i ng varied ~y up t~ a ,ac~r of 6. The results of this comparison and the effects on divergence values are shown in Table 2-A. It should os be noted that this simulation illustrates an increase in residence time by either an increase in the length of the cyclone or by a decrease in the cone angle. If the residence time increase had been achieved by in-creased cyclone diameter, the acceleration value would have dec-eased at higher cyclone diameters.

Table 2-A
Run 1 2 3 4 lS Cyclone Diameter, inches 8 8 8 8 Inlet Velocity, ft/sec 68.4 68.4 68.4 68.4 Alpha, 3.7 Dj n 1 e t /Dc y c 1 o n e O . 60 0.60 0.50 0.60 Flowrate, G~M 281.8 282.0 282.0 282.0 Acceleration, g's 2735 2735 2735 2735 Residence Time 0.939 1.409 2.817 5.635 Residence Time Factor, 1 1.5 3 6 x std cyc.
Minimum Vel. for 70.8 47.2 23.6 11.8 Se?aration, cm/sec Viscosity, Centipoise 1.0 1.0 1.0 1.0 Specific Gravity of 1.5 1.5 1.5 1.5 Fluid Displaced Divergence at 0.074 mm (200-mesh) 0.383 0.217 0.082 0.031 O.037 mm (400-mesh) 1.2 0.65g 0.250 0.095 O.0185 mm 3.5 2.0 0.757 0.287 Example 3 The effect of viscosi~y on efficiency of separa-t on, as measured by divergence values, was e~amined in simulation runs 1-4. All other factors were held con-stant with viscosity being varied from 1.0 to 0.3565 centipoise. The media temperatures represented by the simulated changes in viscosity are approximately 20C, 40C, 60C, and 80C. The results of these test runs and effects on divergence are shown in Table 3-A.
Table 3-A
Run 1 2 3 4 Cyclone Diameter, inches 8 8 8 8 Inlet Velocity, ft/sec 68.4 68.4 68.4 68.4 Alpha, 3.7 Dinlet/Dcyclone 0.60 0.60 0.60 0.60 Flowrate, GPM 281.8 282.0 282.0 282.0 Acceleration, g's 2735 2735 2735 2735 Residence Time 0.939 0.939 0.939 0.939 Residence Time Factor, x std cyc.
Minimum Vel. for 70.8 70.8 70.8 70.8 Separation, cm/sec Viscosity, Centipoise 1.0 0.656 0.468 0.3565 Specific Gravity of 1.5 1.5 1.5 1.5 Fluid Displaced Divergence at 0.074 mm (200-mesh) 0.383 0.298 0.243 0.206 0.037 mm (400-mesh) 1.2 0.902 0.737 0.626 0.0185 mm 3.5 2.7 2.2 1.9 Example 4 The effect of varying the term alpha on particle separation efficiency, as measured by divergence values, was examined in simulation test runs 1-4. The alpha value is equal to 3.7 (Dinlet/DCyclone). Since cyclone diameter was held constant, only the inlet diameter was varied in each of the runs. The effect of making the inlet diameter smaller, given a constant flowrate, is to increase inlet velocity and, therefore, acceleration. As can be seen from the results in Table a-A~ divergenc values were significantly decreased by dec-eases in the value of ~lFha.

Table 4-A
~5 Run 1 2 3 4 Cyclone Diameter, inches 8 8 8 8 Inlet Velocity, ft/sec 20 30.4 54.1 121.7 Alpha, 3.7 Dj n 1 e ~ /Dc y c 1 o n e 74 0.60 0.45 0.30 Flowrate, GPM 125.3 125.3 125.3 125.3 Acceleration, g's 356 541 961 2163 Residence Time 2.11 2.11 2.11 2.11 ~esidence Time Factor, x std cyc.
Minimum Vel. for 31.5 31.5 31.5 31.5 Separation, cm/sec Viscosity, Centipoise 1.0 1.0 1.0 1.0 Specific Gravity of 1.5 1.5 1.5 1.5 Fluid Displaced Divergence at 0.074 mm (200-mesh) 0.948 0.623 0.351 0.156 0.037 mm (400-mesh) 2.9 1.9 1.1 0.472 0.0185 mm 8.7 5.7 3.2 1.4 E~ample 5 The effect of increased inlet velocity at constant inlet diameter on particle separation efficiency, as measured by divergence values, was ~x~mi ned with the results shown in Tables 5-A, 5-B, 5-C, and 5-D. As can be seen from the following results, the increased ac-celeration has a beneficial effect on divergence values.

-Table 5-A
Run 1 2 3 05 Cyclone Diameter, inches8 8 8 Inlet Velocity, ft/sec20 45 70 Alpha, 3.7 D1nle~/Dcyclone 0.74 0 74 Flowrate, G~M 125.3 282.0 438.7 10 Acceleration, g's 356 1800 4357 Residence Time 2.11 0.939 0.603 Residence Time Factor, x std cyc.
15 Minimum Vel. for 31.5 70.9 110.2 Separation, c~/sec Viscosity, Centipoise 1.0 1.0 1.0 S~ecific Gravity of 1.5 1.5 1.5 Fluid Dispiaced Divergence at 0.074 mm (200-mesh) 0.948 0.583 0.447 0.037 mm (400-mesh) 2.9 1.8 1.4 0.0185 mm 8.7 5.4 4.1 _a7-Table 5-3 Run 1 ~ 3 05 Cyclone Diameter, inches 8 8 8 Inlet Velocity, ft/sec 30.4 68.4 106.5 - Alpha, 3.7 D~nlet/Deyclone 0.60 0.60 0.60 Flowrate, GPM lZ5.3 282.0 438.7 Acceleration, g's 541 2739 6678 Residence Time 2.11 0.939 0.603 Residence Time Factor, x std cyc.
Minimum Vel. for 31.5 70.9 110.2 Separation, cm/sec Viscosity, CentiDoise 1.0 1.0 1.0 Specific Gravity of 1.5 1.5 1.5 Fluid Displaced Divergence at 0.074 mm (200-mesh) 0.623 0.383 0.294 0.037 mm (400-mesh) 1.9 1.2 0.891 0.0185 mm 5.7 3.5 2.7 Table 5-C
Run 1 2 3 05 Cyclone Diameter, inches 8 8 8 Inlet Velocity, ft~sec 54.1121.7 189.3 - Alpha, 3.7 Din~et/Dcyclone 0.45 0-45 Flowrate, G~M 125.3Z82.0 438.7 Acceleration, g's 961 4869 11,783 Residence Time 2.110.939 0.603 Residence Time Factor, x std cyc.
Minimum Vel. for 31.570.9 110 2 Separation, cm/sec Viscosity, Centipoise 1.0 1.0 1.0 Specific Gravity of 1.5 1.5 1.5 Fluid Displaced Divergence at 0 074 mm (200-mesh) 0.351 0.216 0.165 0.037 mm (400-mesh) 1.10.653 0.501 0.0185 mm 3.2 2.0 1.5 Table 5-9 Run 1 2 3 o5 Cyclone Diameter, inches 8 8 8 Inlet Veloc t-~, ft/sec 121.7 273.8 425.9 Alpha, 3.7 Di n 1 e t /D~y c 1 ~ n e 30 0.30 0.30 Flowrate, G~M 125.3 282.0 438.7 Acceleration, g's 2163 10,955 26,511 Residence Time 2.11 0.939 0.603 Residence Time Factor, x std cyc.
Minimum Vel. for 31.5 70.9 110.2 Separation, cm/sec Viscosity, Centipoise 1.0 1.0 1.0 Specific Gravity of 1.5 1.5 1.5 Fluid Displaced Divergence at 0.074 mm (200-mesh) 0.1560.096 0.073 0.037 mm (400-mesh) 0.4720.290 0.223 O.0185 mm 1.4 0.880 0.675 Example 6 The effect of increased flowrate, at constant in-let velocity, was ~x~mined in Table 6-A. ~s can be seen from the following results, in contrast to Example 5, divergence values increased as flowrate increased.

Table 6-~
Run 1 2 05 Cyclone Diameter, inches 8 8 8 Inlet Velocity, ft/sec 45 45 45 Alpha, 3.7 D1nl~t/D~yclone0.493 0 74 0.923 Flowrate, GP~ 125.3 282.0 438.7 Accelerationl g'S 800 1800 2801 Residence Time 2.11 0.939 0.603 Residence Time Factor, x std cyc.
Minimum Vel. for 31.5 70.9 110.2 Separation, cm/sec Viscosity, Centipoise 1.0 1.0 1.0 Specific Gravity of 1.5 1.5 1.5 Fluid Displaced Divergence at 0.074 mm (200-mesh) 0.421 0.583 0.696 0.037 mm (400-mesh) 1.277 1.8 2.180 0.0185 mm 3.872 5.4 6.4 Example 7 The effecL of varying cyclone diameter on effi-ciency, as measured by divergence values, was ~x~mi ~ed in simulation runs 1-6. The results of these runs are provided below in Table 7-A. It can be seen that at smaller cyclone diameters, which have an included cone angle of 12, there is, for all practical purposes, no effect on divergence values. For c-~clones having a cone 1 33~-1 90 angle of 20O, some small improvements in diver~ence .~aLues is obser~ed at smaller cyclon2 diameters. The lack of substantial improvements is due to decreased residence time.

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( E~amDle 8 The effect or media spe~ific gravity on e~ iency of se?aration, as measured by divergence vaiues, was Q~mined. Litlle effect W25 observed on diver~ence 05 values by variations in this factor.

Table 8 Run 1 2 3 10 Cyclone Diameter, inches 8 8 8 Inlet Velocity, ft/sec 68.4 68.4 68.4 Alpha, 3.7 Dinl~t/Dcyclone 0.60 0.60 0.60 Flowrate, GPM 281.8 282.0 282.0 Acceleration, g's 2735 2735 2735 Residence Time 0.939 0.939 0.939 Residence Time Factor, x std cyc.
Minimum Vel. for 70.8 70.8 7C.8 Separation, cm/sec Viscosity, Centipoise 1.0 1.0 1.0 Specific Gravity of 1.5 1.4 1.3 Fluid Displaced Divergence at 0.074 mm (200-mesh) 0.383 0.373 0.362 0.037 mm (400-mesh) 1.2 1.1 1.1 0.0185 mm 3.5 3.4 3-3 While various embodiments of the present invention have been described in detail, it is apparent that modific~tions and adaptaticns of those embodiments will occur to those skilled in the art. ~owever, it is to be exDressly understood that such modifications and adap-tations are within the scope of the present invention, as set forth in the foilowing claims.

Claims (8)

1. A method for beneficiating particulate solids comprising:

(a) providing a feed material comprising particulate solids of known particle diameters and specific gravity and refuse particles of known particle diameters and specific gravity;
(b) selecting a minimum particle diameter for particles in said particulate solids to be beneficiated;
(c) selecting a fluid of known specific gravity;
(d) selecting a suspension material of known specific gravity, particles of which are to be mixed with said fluid to form dense media of known specific gravity;
(e) calculating a diameter ratio, said diameter ratio being the ratio of said minimum particle diameter in said particulate solids to the maximum particle diameter of said suspension material particles that if mixed with said fluid to form dense media would result in said minimum particle diameter particles of said particulate solids being buoyant in said dense media;
(f) mixing suspension material particles having a particle diameter smaller than maximum particle diameter of suspension medium particles with said fluid to prepare said dense media of known specific gravity; and (g) beneficiating said particulate solids by dense media separation of at least a portion of said particulate solids from said refuse particles using said dense media of known specific gravity prepared in step (f).

2. A method as claimed in Claim 1, wherein said suspension material is selected from a group consisting of magnetite, sand, barites, ferrosilicon, and mixtures thereof.

3. A method as claimed in Claim 1, wherein said particulate solids comprises coal and said suspension material comprises magnetite.

4. A method as claimed in Claim 3, wherein said coal has a maximum particle size of about 0.6 mm.

5. A method as claimed in Claim 3, wherein said refuse particles comprise pyrite and wherein at least about 60 percent by weight pyrite in said feed material is removed from said feed material during said dense media separation and at least about 60 percent of the heating value of the feed material is retained in said particulate solids following removal of said refuse particles from said feed material during said dense media separation.

6. A method as claimed in Claim 5, wherein said magnetite particles are substantially rounded.

7. A method as claimed in Claim 3, wherein the particle diameter of said magnetite is less than about 0.010 mm.

8. A method as claimed in Claim 5, wherein said fluid comprises water and wherein said calculating in step (e) comprises calculating said diameter ratio according to the equation:

where DA = Diameter of minimum particle size particles in said particulate solids DB = Diameter of maximum particle size particles of magnetite particles SGA = Specific gravity of particulate solids SGB = Specific gravity of magnetite SGS = Specific gravity of dense media SGW = Specific gravity of water 1<m<2.