CA1327342C - Process for beneficiating particulate solids - Google Patents

Abstract

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

:: . 1 3 2 7 3 ~ 2 `: P!~(OC_SS FOR 3E~EFICI~TI~IG ?A~TIC'JLi~T~ S;:)LIDS
Field Of The Invention ~ he present invention relates to an improved process for beneficiating coal fines and for predicting 05 the efficiency of separation of density separat cn processes.

BacXaround Of The Inventlon - The burning of fossil fuels, including coal, is necessary to meet the energy re~uirements of our society. 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 enviror,mental effe~ts. Respiration of these pollutants can cause human health problems ransing from mild resoiratory irritation to more serious chronic dis-~ eases. Sulfur oxides can also react with other com-.~positions in the atmosphere to form acid preclpitation which has the effect of acidifying bodies of water and destroying the wildlife which live in such habitats.
Acld p e~ipitation also can destroy manmade structures such as buildings and statues.
Indust.y 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 reco~er 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 sulfur compounds from the coal before, during, and after 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 rele~se t~ the atmosphere of COmDUstion byproducts for new sollrces or air pollution. Some states have ao~l-ed str_ngent requirements for reduction of sulfur dio.Ylie to eYisting faciliti e5. Feder~l and state legislation, 1 3 2 7 ~ ~ 2 there_cre, make it necessar~ to achieve high reductions ~ in the amount of sulfur c~mFo~ncs em Lted during the ,~, combustion of coal.
A method of reducing the sulfur content of coal ' 05 before combustion includes: (1) 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 c~al is ground fine enough to liberate substantial quantities of sulfur minerals and ash-for.~ing minerals, separation , of the coal from the unwanted material and subse~ue~t '- recovery of the coal become difficult.
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' 15 The grind size required to enable a ninety percent pyrite reduction and eighty-five percent 8tu recovery for most coals is less than 0.5 mm and frequently finer .~ than 0.1 mm. At these sizes, reported beneficlation .~ techniques are not consistently effec_ive in separating coal at acceptable efficiencies.
Jigs, hydrocyclones and tables are inefficient for separation of minus 0.5 mm ~oal. Froth flotation is ~:~ ineffective when applied to o~idized coals because their surface character is not sufficiently hydrophobic ~, 25 to be activated by collecting reagents. For unoxidized coals, good Btu recovery is attainable by froth flota-tion, but pyrite rejection is difficul,t because of the ~;,, relative ease with which pyrite floats.
, Ergun, U.S. Patent No. 3,463,310 discloses a method of cleaning fine coal material (0.400 mm - 0.037 mm) by subjecting a mixture of coal and pyrite to electro-magnetic radiation .inich selectively magnetizes pyrite. Pyrite is then removed by magnetic means.
This process is limited to magnetizable re~use material such as pyrite. Other materials frequently found in , coal, such as silica, carr.ot be removed by this method.
Dense media cyclones are efficient de~r~ces for '~ ~eparating coal in the quarte- inch to 0.5 mm range . .-. .

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f-_m -e~use mate~al on the basis or coal and r~fuse mat~rial having differ~nt ~ens ~ ~s. A m~:s~~~~ o- the ~;two mate~ials is suspended in a dense media t~ form a .sink produc- and a float product. A dense media, or a os psuedo-heavy liquid, is necessary because the speciflc gravities of coal and refuse material are greate{ than one, and therefore, cannot be separated by water ~lone.
A media with an effective media specific gravity be-:~tween that of coal and of refuse material is reauired.
;t'10 A common media useful for coal beneficiation is a ~;suspension of magnetite particles in water. By intro-duoing a coal-refuse material mi~ture into a magnetite ~media, clean coal floats and refuse material sinks.
-~Se~aration of these materials is hastened by using a dense media cyclone which inc.eases the nominal gravit tional acceleration on the mixture.
`The use of dense media cyclone separations for beneficiating coal is well known. For exampLe, ~iller, ~,~et al., U.S. Patent No. 3,794,162, is directed toward a heavy medium beneficiating process for coal par1icles greater than 150 mesh (about 0.1 mm). Horsfall, U.S.
Pa_ent 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 bene-ficiation of coal fines having a particle si2e less ~;than 1.000 mm and, in partic~llar, less than 0.500 mm.
This process involves separation of materials in a sus-pension with a dense media ~o form two fractions and a `series of subsequent screenings and washings of mag-neti~e 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 un-sur~essful ir. _e~s of teachinc a general metAod for :efricient se~aration. One parame~er which is usefll in assessing the effectiveness of separation of coal fines ,,~

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and reflse material by dense media and other separat_cn techniques is the Ecart P.obable (F?~. ~he ~ ;alue is defined as the difference between the particle density of that f.action of the cy~lone 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 repcr's 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 e~ iciency of the separa-$ tion, while the separation gravity defines the specific s~ gravity at which the separation occurred. This separa-lS tion gravity is different for different size fract-ons of feed coal even though all size fractions are cleaned in the same dense media cyclone. Gene_ally, a smaller ~; si~e fraction 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 magr.etite ~' particles in water. The magnetite can be natural mag ?' netite which has been milled. Magnetite is also ':. recoverable from fly ash. For example, Aldrich, U.S.
~; 25 Patent N~. 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 separation because round particles reduce the viscosity of the : heavy medium and facilitate separation.
~. Fourie, et al., The ~eneficiation of Fine Coal by Dense-Medium Cyclone, J. S. African Inst. Mining and ~, ~ 35 Metallurgy, p~. 357-51 (October 1980), discloses dense '~ media cyclone separation of a 0.5 ~m - ~.075 mm coal ~; frac~ion in a heavy medium oyclone with milled mag-netite with at least fifty percent less than 0.010 mm ,.~
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i 13273~2 using a 150 mm diamete- cy~lone . ~ values ~ o.020 t~ 0.031 were ac~ie~ed. While ~~e~3~1~ seoa~
effic~ences 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 reoorted limits to efrectively separate c~al -10 fines smaller than 0.5 mm and particularly smaller than O.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 co~l fines which were previously unrecoverable can now be used as an additional fuel source. Accordingly, the~e is a need for an improved process for the beneficiation of minerals to erfectively recover fine c~al.

Brief Desc-iption Of The Drawings Fig. 1 is a graph of coal to magnetite diameter ralio valu~s at dirfering specific gravities usins 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 gravit~);
Fig. 3 illustrates the relationship between par--f30 ticle size and divergence of actual data from the pub-~lished works of Deurbrouc~; and `~^Fig. 4 illustrates the relationship between -~cyclone diameter and apparent distance (as defined ~n the specification) as determined by the data in the published works of Deurbrouc~.
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Summary Of The Inven~ion One aspect of the present -n~-ent-on ~n-olves i~
method for select-ng magnet~te to form a dense media for a dense media separation to bene~iciate particulate 05 solids. Particulate solids are provided having a pre-determined minimum particle size and a known specifi~
.gravity. The method involves calculating a diameter rat o value applicable to the particulate solids, mag-netite and the dense media. A diameter ratio value lo represents a particulate solid to magnetite particle diameter ratio for particles having equal but op-positely direcled 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 directed toward using magnetite having a particle diameter of less than about O.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-~25 duced by a process which involves providing an aqueous ,.iron (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-,~ducling the reaction in an oxyge~ restricted atmos-phere, substantially only magnetit- is produced. If the .pyrohydrolysis reaction is conduc_ed in an atmosphere ,with unrestricted oxygen, a substantial portion of the .`product is hematite. For such mixtures, the metho~
further includes chemically reducing sufficient hema-`35 tite in the mixture to obtain a mixture comprisina at '`i2as', aDou~ 35 pe-cent magnetite.
Another asDec_ of the present in~ention invci~es determining the ef_iciency of separation of a dense :

13273 ~2 medi~ seoaration process for be~efi~at ng particuiate solids . This method uses, as ~r. ~d~c~ on or e''i-cie~cy, a "divergence value". This term indicates the differenc2 between the specific gravity of the particle 05 to be separated and the effective media specif,c gravity. This method involves determining an apparent distance a particle must travel within a dense media -c-~clone or centrifuge to be correctly beneficiated.
From the apparent distance and ~he residence time of -10 particles in the cyclone or centrifuge, an apparent .velocity a particle must achieve to be cor-ectly bene-ficiated is calculated. Using the apparent velocity and other known cyclone gecmetry and operational para-meters, a divergence value is calculated to indicate lS the efficiency of separation of the system.
A further aspec~ of the invention involves a method for selecting cyclone geometry and operating -parameters for improved efficiency of separation in a dPnse media cyclone separation process. This method ~0 involves determining a proposed separaticn efficiency in terms of a proposed divergence value. A set of cyclone geometry and operating parameters are selected.
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~A divergence value for the selected cyclone geometry 'J,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 dlvergence ;~value determined. / This process is iterated until the 30 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 ::35 dense media viscosity, larger particle size and lowe~
~peci' c gr~vi.y.
A still further aspec~ of the invent on invol~res a method for beneficiating particulate solids. This ,;'; :
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~L~273~2 method involves providing magnetite hav-ng a ai~mete~
such that the particulate solids hav~ yar.~
respect to 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.
'~ 10 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 63 percent or the pyrite and more than 60 percent of the ~; 20 ash can be removed, while retaining more than 60 per-~ cent of the heating value.
'i In one aspect of the present method, e~tre.~ely ~j fine magnetite is used to form a dense media for -~ benefic-ating coal in a dense media cyclone. Magnetite is selec'ed 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 par~icle to magnetite diameter ratio is greater than a diameter ratio value. Magnetite having about a 2.5 micron mean diameter is generally ~i effective for cleaning coal fractions down to 0.015 mm.
~ In Another aspect of the invention, a method for s~ 35 predicting the efficiency of separation in a dense modia -~clone is ~rovided. Th~s method involves the use of three equatior.s which have oeen derived t~at re-late divergence values (diffierencs bet~een s~e~ific ~, . --8--.~

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13~73-i~2 gravity of a Far_~clQ and ef~ect-ve media scee~ f ic ~ravit~) to a number or ! erms inc~ n~ cI~ne g~-metry factors and operating paramet~rs. Dive~gence values have been recognized to be a measure of the ef-05 ficiency of separation of a system. One of the terms in each of the equations is V, apparent velocity that a particle must travel to be correclly beneficiated. To solve the three divergence equations, a value for V
. must be obtained.
: 10 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 Deurbrouck, at an arbitrarily selected cyclone radius for sets of data corresponding to different size cyclones. These velocity terms represent ac'ual radial particle velocities at the selected radius. However, for the purpose of simpli'ication o~ analysis, r~dial ~; particle veloc-ty is assumed to be constant and is as-sumed to be represented by the actual velocities at the s selected radius. These velocities are termed "ap~arent s~ velocities" and can be determined at any radius as long as the same radius is used consistently throughout any ' analysis. These apparent veloc-ties from Deurbrouck are used along with particle residence time to ~alcu-~ late an "apparent distance" a particle must travel to `` be correctly beneficiated. For coal, "correcl 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 ke linearly related to cyclone diameter. From this linear relationship, an "apparent distance" a particle must - travel to be correctly bene'iciated can be determined for any diameter cyclone. From the aFDarent d stance, an apparent velocity can be dete ~ined for any givQn sye'em. In conjunct on with known paramete-s of the given sys.em, a divergence value, reDresen~-ng e--~ _g_ i:

7 3 ~ 2 .iciency, can be calculated and can be used in a com-oarative analysis of proposed or ex:st~na sY~ s.
Grinding coal to a small particle size is neces-sary for ef_eclive 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 specific 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 refuse `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 .`15 the effective media specific gravity. Particles in the suspension having specific gravities about equal to ~;that of the effective media specific gravity are equally likely to report to the overflow with the coal or to the underflow w~th the reruse. The specific .;.20 gravity of particles which include coal and refuse .~;mater-al physically bound together is between that of coal and reruse material, and are, therefore, less ~;likely to report to either the overflow or underflo~
than coal and refuse mate-ial, respectively. In ei~her ~ase, the mixed particle will either carry some refuse 'i~to the overflow or some coal to the underflow, thereby reducing the separation efficiency. By grinding coal to a small par~icle size, a hign percentage of par-ticLes comprising coal and refuse material are broken apart into se~arate particles of only coal and only refuse material. Such separate particles are likely to report correctly to the overflow and underflow, respee-tively, because the specific gravity of each i5 suffi-ciently differ2nt from that of the effective me~ia ~:35 specific gravity to form either a float or sink par-ticle tJith respec_ to the dense medium.
A ?r_mary dif'icul~I with gr nding coal to a sm~ll par'icla size, however, i5 efficlent separation of coal s~

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i` ~3273i~2 fr^m _efuse material. As usen .e_Qir., llrQ~ISe ~ater-;ial" or "refuse" means ~n~- ncn-o~ r._c~c~c s~s.anc~
entrapped in coal deposits or inadvertently a~ded to -the coal during minin~, including, but not limited 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 ooal by conventicnal means. The grind size required to enable at least about a ninety percent by weight pyrite reduc'ion and at least about ninety percent Btu recovery for mos.
coals is less than abcut 0.6 mm and frequently finer than about 0.1 mm. The present invention is par-ticularly directed toward cleaning of coal ground fine ~15 enough to allow at least about sixty percent by weight '.-pyrite rejec_ion with at least about sixty percent Btu recovery, more preferably at least about eighty percent by weight pyrite rejection with at least about eight-~
percent Btu recovery, and most pre erably at leas~
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 s-~stems 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 com-minuting e~isting coal preparation plant refuse, i.e., aob or culm bank material, can be used. A su~stantial ~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 par~iculate solids from refuse materials by a derlsit separation me ho~. The preferred emDodiment of the in vention discussed here~n is the separat~on or fine co~l parti_les fro.~ refuse material in a dense medium ~ h ~
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dense media cfclcne. It is ccntemplated .hat the ln~Jen-tion is applicable to beneficlat_cn or pa-~ C'112~ Q
solids other than coal. It is also contemplated that the present method is applicable to beneficlation by 05 other types of s~parating 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 recogni~ed that 10 the general principles discussed herein are equally aD-' pllcable to other types of dense media. For e~ample, 'r dense media can be formed from suspensions of sand, barites and fersosilicon. ~or example, with ferro-silicon, dense media can be formed having specific ' 15 gravities which cannot be formed with magnetite dense . media.
~- One aspec' of dense media separation is that the light (or float) particles must be less dense than the ef'ective media specific gravity for separation to oc-'. 20 cur. That is, the speciflc gravity of the float par-~i tic!es must be less than the effective media specific s grav:ty. The buoyant force on a particle is a ~iunction of the difference between the speciiic gravity of tlle particle and thc specific gravity of the media. Rela-25 tively large coal particles displace dense media, i.e., ` a suspension of magnetite in water. As coal particles become smaller and approach the size of magne~ te, thev inc-easingly displace primarily wate-. Since coal is not buoyant in water, separation will not occur for '.. - 30 such small particles.
The present invention provides a method for derer-x; mining an aoceptable magnetite diameter for forming dense media for the benefic-ation of particular co l ~ size dist,ibutions down to a minimum particle size.
: 35 More particularly, the pre~ent method is useful for det~rmining the , ze of magnetite requi~ed to ~roduce a '~ dense media in which a Darticular c~al f-~c~icn lS
buoyant. This method has the following theorQ~-cal :
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3~7~
basis. To be buoyant, ,~ coal particle must have a eloc L y in the di~~c.ion of the c_~o~ of a c-~clcne.
Such a velocity is a result of a buoyant force, acting toward t~e center of the cyclone, minus a resistance os 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 ar~sing from rotation of the coal and media in the cyclone. Accordingly, the velocities of coal, refuse and magneti~e par_icles can be written as follows:
., [1] Vcoal = K (SpGr~ ,a~ ~ SpGrfd ) D-oalm V~efu~e = K (SpGrrefuso ~ S~Gr~d ) Dref~lse [3~ V~-agneti te = K (SPGrmacne~i te ~ SpGrfd ) D~ag~et where V = terminal veloclty : ~ = te~m including comFonents for ac_eler-ation and viscosity SDGrfd = specific gravi'y or the fluid dlsplaced SpGr~0 a ~ ~ ~ f u ~ ~ o ~ = speclfic gravitv of the magneti te coal, refuse and magnetite D = diameter of the particles m = ex~onent ranging from 2 under laminar flow conditions to l 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 veloclt-~ in the direction of centrifugal force. For the present ~ invention, the assumption is made that, at a minimum, t~ 3Q the velocity of coal in the direction opposite t~e centrifugal force is equal to the component of velocity ' of magnetite particles ccmDrising the dense media in ; the direction of centrifugal force. For refuse ~i material, a similar assumption is made e~cept that refuse materiai moves in the same direction as mag-~, netite. Additicn~ , for refuse mater1a1 having a ~ buoyant 'cr_e equal to that of coal, the ref~se - ma~erial encounters less resistanco force than .~al be-:.:
. cause it mo~es in the same dlrec~ion as maanetite, and .

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11 3273~2 consecuently, has a higher velocity. As a li.~i'ing c~se, however, refuse material veioc:.y mus. ~e ~t least as great as magnetite velocity. The follo~Jing equalities can be established based upon the above `~ 05 discussion:

~ [ 4 ] V~ o a 1 = (--1 1 Vm a g n e t i t e ~ S ] V r e f u 9 e Vm a g n ~ ~ i t e ~Y, By substitution of Equations 1, 2, and 3 into the . above e~ualities, the following ratios are derived:
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~ [6] D^oal = SpGr~agn~ti te ~ SPGr~ater I/m D:T~agnet1te SpGrcoa1 ~ SpGrfd [7j _ 1' SpGrm a g n e . i t .. ~ SPGrw a t ~ r 1 1 ,' m ~, Dm a 3 n e t i t e l - -- SDGrf ~ ¦
.,~.
These equations, with the e~ception of the negalive 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 (193~).
>~ A value for m in the equations 6 and 7 depends c 25 upon the applicable flow regime: turbulent, transi-tional or laminar. The Reynolds number of a particle is a criterion which indicates whether the flow regime is laminar or turbulent. For Reynolds numbers greater than 500, flow is turbulent; between 500 and 2, 30 transitional; and less than 2, laminar. Reynolds num-ber depends directly uDon a particle's diameter, its velocity, specific gravity of the fluid it displaces and inversely uoon the fluid viscosity.
To calculate the Reynolds numDer of a particle, 35 its terminal set~ling velocity must be known. Stokes iaw, modif-e~ wi.h cor-ect on factors for the s.mul-t~neous movement of many F~rticles, may be lsPd.
~ Gaudin, A.M., Princ ~les of Mineral Dressing, McJraw-r. ~

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~3273~2 ~Hill ~ook Co., Inc., New vor~, N.Y., p. 188 (13~).

: 1 [8] V~ar ~ s2i3) (1 - s) (1 - 2.5s) :" 05 ~g-(SpGr,ar~ - SpGrflujd)D2 ~
:~ ~ u where s = volume frac~ion of solids u = viscosity of the fluid 10Reynolds number is given by the following equation:
D V SpGrclui d [9] Re u 15Equation~ 6 and 7 provide limiting particle diameter ratios for coal and refuse to be correctly beneficiated in magnetite heavy media. For particle diameter ratios less than that given by equations 6 and : 7, beneficiation cannot occur. The ratios provided by ~20 Equations 6 and 7 are termed "diameter ratio values".
.~ For coal or refuse particles to have the same buoyancy s~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 construc' "Diameter Ratio Partitlon Curves which piot diameter ratio values for a r~nge of media specific gravities.
For example, with reference to Fig. 1, a Diameter 30 Ratio Par~ition Curv~ is illustrated wherein the specific gravity of the dense media is on the abscissa x~ssand the ratio of coal to magnetite particle diameter is on the ord nate. Diameter ratio values forming the .curve indicate coal-to-magnetite particle diameter 35 ratios for coal and magnetite particles having equal although oo~o~i'e'y dir cted velocities in a dense :.
~medium of a par_icular spec .ic gravity Lor a given ;~flow regime. If coal particles have a veloci~f in t~e ~ 's `~ -15-.

1 3 2 7 r~ ~ 7 dense medium toward the cyclcne cent~r less than maa-neti-e particle veloc~ty in .he -~-cs ~e ~ir~-_ C!~, ef-. fective separation of coal by the magn~tite 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 ccal to magnetite particle diameter ratios for separation in dense media of given specific gravities for turbulent flow. Th~
10 lower curve 2 represents the same information for lam-` inar flow in the cyclone. The graph in Fig. 1 defines three important regions rele~Jant to effective coal beneficiation: (1) the region above the turbulent curve I; (2) the region between the laminar and turbulent `~ 15 curves II; and (3) the region below the laminar curve III. Points on the graph in region I allow efficient 3; separation, while points in region III are ineffective for coal separation. Points oc-urring in region II
,;
produce separation efficiencies which are difficult to 20 predict precisely, but in general depend on the flow : regimes of the particles.
Fig. 1 illustrates the relationship that as the s dense media specific gravity decreases, the ratio be-~ tween the coal and magnetite particle diameters must s`~ 25 increase asymptotically for effective separation. In ~; view of this relationship, processes using dense media ::~ with low specific gravities should have high part cle :~ diameter ratios, i.e. small magnetite with respecl to ~$~ the coal, for the diameter ratio points to be greater than diameter ratio values.
Eaual settling curves similar to those depicted in Fig. 1 can be generated by selecting aporopriate values for coal sDecific gravity and coal size and solving for magnetite particle size diameter according to Equations . 35 6 or 7. The turbulent curve of Fig. 1 was generated using a s~ecific g.avit~I for magnetite of 5.1 and for .~ coal of 1.3 for ~arious dense media s~ecific gra~ es.
Eor e~ample, in a dense media having a specific gravity - ` 13273~2 or 1.5, a coal/magnet te diameter r t~o valle is a?-p_ox~ma-ely 14:1. Accordingly, ~o _f-ect vely clean coal pa-ticles having a 0.14 mm diameter, a dense med a comprising magnetite particles less than 0.01 mm in 05 diameter is required.
The use of a Diameter Ratio Par~ition Curve in the manner described above is useful for beneficiation of coal from refuse material with magnetite dense media.
While the process is particllarly useful for separation of fine coal, it is applicable to any density separa-tion for cleaning ^oal. The present process is also useful for any separation of solid materials generally ;on a density separation principle.
.Acceptable separation efficiencies in dense med.ia cyclone systems depend on the economics of a given pro-cess. However, an Ep value of 0.035 or less generally .;indicates a separation efficiency acceptable for econo-.mical 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 ~s~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 over-flow. 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 beneficia-,~30 tion process with a low separation gravity to clean a specific size coal fraction, the present process is useful for determining the magnetite particle si-e necessary for effective separation. Over a small change in dense media specific gravity, the coal to magnetite particle diameter ratio for effective separa-tion c~n vary grea'iy.
In ac~ordance with the present invention, maa-ne_ite for the dense media is selected havin~ a small .
. -~7-.
;

13273~2 par icle s ze. While the pr~sent process is applicable to beneficiation of coal or a'l s_~es, ~e ~rocess be-comes more critical at smaller coal ~izes. For such coal, correspondlngly smaller magnetite is required for 05 effective beneficiation. It is contemplated that minus o.o1o 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 separatlon ~` 10 processes is prohibitively e~pensive. Grinding costs rise exponentially as magnetite particle si e ~- decreases.
Magnetite of the present invention can be produced by the oxidative pyrohydrolysis of iron (ferrous) r 15 chloride according to the following reaction:

. ~10] 3 FeCl2 + 3 H20 + 1/2 O2 ~ ~ Fe30~ + 5~Cl s~ magnetite ~; Production of fine magnetile in this manner avoids high i¢ 20 costs of grinding large' size magnetite. An iron r~ chloride solution is sprayed into a reaction chamber or roaster a~ elevated temperatures and oxygen is supplied ~ for the reac'ion to produce magnet_te. Such magnetite r~',`` has a particle diameter less than about 0.010 mm, and ~; 25 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 tferrous) chloride solu-30 tion can be obtained by dissolving scrap ferrous metal . with hydrochloric acid. 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 recovered from the dissolution of il-menite with hydroc~loric ac d. It should be rec~gnized, however, that any of various solutions containing iron .,.

.
:

., ~3~73~2 (ferrous) chlcride c~n be used 1~ this ~n~ention.
If the oxi~gen conten- i~ th~ D','~ o~ydr3~ysis reac-tion is not controlled, the product mi;cture ccnt~l~.s largely hematite particles with some magnetite, accord-05 ing to tne following reaction:

- [11] 2 FeCl2 + 2 H20 + 1/2 0z ~ Fe203 + 4HCl - hematite However, by subjecting the mixture to reducing c~ndi-tions, the iron oxide particles can be converted to primarily magnetite. For e~ample, the product mixture ~:- can be heated in a carbon monoxide or a hydrogen atmos-phere to reduce hematite to magnetite at relatively low ~ temperatures of between about 3000C and about 4000C.
,~ 15 An acceptable magnetite content in such a mi~ture .. 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 leas about 95% magnetite.
~ 20 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 s~ circuit.
. 25 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 tempe~a-ture of magnetite or hematite. Rounded magnetîte par-ticles are more efficient for dense media separation because they create a lower effec'ive dense medi~ ~lis-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,ousn ~;ne heavy medium. Anc.her benef~t of lowered ,` viscosity is that the medium is less cos~ly t~ pUmD.
~ Rounded magnetic par'icles are also more easily washed i~, c~ -L?-''~

', : 13~73~
free from coal than are angular particles because coa_ -particles themselves have ~'at ar.~- ~r ;ur-aces.
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 bet~een coal and refuse material can be achieved . by treating the magnetite particles in the heavy medium -' suspension with a surfacS~ant to decrease the effectl~e .~lo 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 tha.
both coal and refuse material particles move more j.~freely in the suspension in the presence of a surfac-.`15 tant and are thus more likely to report to the overflo~
.and underflow, respectively.
-.The concept of buoyancy discussed above is nec-sessary to achieve separation between particulate solids and refuse material. Particulate solids must approach .20 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 u~derflow. 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 ~e correctly benef ciated during the residence time.
Poor separation efficiencies are often enco-tntered due to a lack of understanding of factors involved in dense media separation processes. Another aspect of the present invention inc!udes a method for predicting 'tthe sepa-at-on effic ency of a given sys-em or propcse~
.~syste~ for the purpose of achieving improved separ~ri-~
~ef.icienc es. While this method is discussed in ter~s r '.,~

13273i~2 ' o~ a magnetite dense media process, it should be rec~g nized that othe~ types ~f ~edi~ -~n be i~se~ all~
` well. For example, other types of der.se media, such as `~. suspensions of sand, barites, or ferrosilicon, can be oS used. The method is also applicable to true heavy liq-uids, such as solutions of halogenated hydrocarbons or aqueous salt solutions.
The present method uses, as a measure of effic-, iency of separation, the difference between the par-ticle specific gravity (SGC) and effective media ~ specific gravity (SGem). SG~m is defined as the lowes~
.. specific gravity of separation of any size fraction treated. For practical purposes, SG~m is slightly higher than the specific gravity of the media. This 15 measure of efficiency, the differen~e between SGp and SG~m, is termed "divergence".
It has been found that a direct relationship exists between divergence values and Ep values (a widely recognized measure of efficiency~. Data have x 20 been taken from two published works by Deurbrouc~, and `- divergence values have been plotted against Ep values J~ in Fig. 2. For the 20" and 24" cyclones, each data point reoresents an average of four actual data points.
Deurbrouck, A.W., "Washing Fine Coal In A Dense-Medium ;~ 25 Cyclone", U.S. Dept. of Interior, U.S. Bureau of Mines, - Report of Investigation 7982, 1974, six pages.
`~ Deurbrouc~, A.W., "Performance Characteristics of Coal :~j Washing Equipment-Dense-Medium Cyclones", U.S. Dept. of Interior, U.S. Bureau of Mines, Report of Investiga-tion" 7673, 1~72, 34 pages. As seen in Fig. 2, as . divergence values inc-ease, Ep values increase (less !, efficient separation). Therefore, by minimizing diver-: gence values, efficiency of separation is increased.
. Data ~rom the Deurbrouck works, much of which is used ? 35 in the following discussion are shown in Tables 1, 2, and 3.
.,~
s `~ -21-. . .

'`:
h~

, ,.

~3273~2 ., ,;
.
~.
.,. ~ V
.: ~a o ~, " ~ 0 ~ O ~ c . ~ ~ O O ~, O O ,, a o ~ O O ~ O O V
., ~ .

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u~ u~ D tD C
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~ o C 3 ~ ~ v ~ ~ ~ h a) ~ ~
a ~ v o o o o o o ~ m ~
h ,1 U ~ a) C JJ C:
O ~ ~
a~ ,( v .;~ H g ~ cn ~ ~3 t~ L~

r ~ H ~LI G ~ ~ U
a ~; a ~;^ H ~ N C ~ t~ C
~ ¢~ O 1~ 0 0 0 C E ~ I 3 ~
~: O ~ O O O O 0 1~ o 3 ~

' c ~a :~ h ~ 1--, ~ E
U Ll el~ tD a~ O g ~ H i~ r , 1~1 o ~

lo ~ ~ O ~ 3 .4 ~ ~ ~ R ~
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;~

.
, 1327~2 a3 ~
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.;. ,~~ I ~ E ~`
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E
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E O
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O U ~ O ~ D U
~-1 C-~ LlO O O O ~1 la c ~:1 )a) ~ :~-~1 ~ ~ O H
1 JJ ~ O O O O V t.) 1 U ~ U) ~
a~-,l E ~ o o o o ~1 a C~ 0 u o ~ 0 ~
U
o o a~
o ~1 o o u u~ ~ a 1 ~ ~ u~ or~
,,: ~4~ ~ ~ co o ~ ~ la , ~ V O O
:;~' c a~
C-~ 6 S~ Z h ~
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; Irl N ~/ ` G
'' o~-~1 ,~
~cs~ 0 Ll O
aJ E ~ ~ ~D ID G
C E .. . . - h C
~:' O ~ ~ ~1 0 a~
a~ a ~ C ~
,~ ~ ~1 0 ~ ~D
:~ o ,~, ' 0 1 r: _ Ql ,~,i O JJ ~
U~ O
o ~
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~" t~ ~ ~ ~ U
': ~ O et~
h ~ C) ~1 111 L 0 ~J ~ ~ O t.) . C ~ ::~
U? ~ .
. ~ N U = ~1:1 ~,~

~3~7~'~2 ~ 0 O h .~ a :' U
' ~ ~

., ~. ~ ~
G IC ,-Q) r~ o1~ i GJ ~ a:
,: la o ~ r~
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O
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U O~ ~ O O rl U ,1 ~ .~ ~ 3 r--E rl u ~o ~ .. .
i: _ j ~1 ~ O ~ I r ~1 ~ ~ G~
. ~c ~_1 e ~ ~ ~ ~ o U ~.rl 0 HE~ p~ ;> -.-1 ~ 5 ,~ ~ ~ ~ D~
.~ ~ ~ ~ a) 0 ~ ~
1 a~ ~ ~ 5' 3 U~ U
:~: ~ C-~ :~
U O ~ ~ ~ ~ ~ U ~ ~ --Z.rl ~:> Ll OO O G ~r! 0 ~ ~
~ o ~ _ ~~ ~ V ~ O OO O J~ V
", p~ ~ 4~ C
-,, e ~ o o ., ~~ ~0~ o o rl Hrl 11) Ll 4-1 O tl) ~ V
'` 1~) ~ U O Ll m u~ ~ u Z~ ~ ~ ~ U
~ E~ ~O O
': i ~V ~1 ~ ou~
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~ 0-~
'.; E~ U
.,. ~~ ~ ~ ~,~,~, ~, s ; æ ~ ~,o o ;-: C ~ ~ ~I 11 ~,............... $ ~ ~ V
~ z ~m 0 ~
HV a~ O --I ~ o -1 N 41 ~
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~ O ~ O ~
CD ~ a~ 1 c ~, O C ~ _ ~ O v ~1 ,.,, t~ 5~ c ~ O ~ ~
~Cww ~o i ~' C u~ U C ~ ~.
~: O ~ O Q~
., ~ ~ ~ ~ ~:
., V ~ ~ U u . Ia O ~ ~ ~ 3 u~
Q ~ ~ O
~; U
rl~ _~

,., :, -24 j, 1 3 6~ r7 ~

: The Deur~rouc.~ data have also been plotled ~5 : d-~Je gence values ve-sus pa._~cle s e in r i g . 3 . I t i3 aoparent that for smalier size par~icles, divergenc~
~: values increase. Given the d-rec~ relationship between . 05 divergence values and Ep, it would be expected and is borne out by data that smaller particle sizes have higher diver~ence 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 fac~ors include the followina:
~' 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. SG~m--Efrectlve Media Specific Gravity Each of the three equations is applicable to a .~ 20 different flow regime, turbulent, transitional, or laminar, which depends upon particle Reynolds Number.
. These three equations are shown immediately below. Ihe derivation of the equations is shown before the Ex-perimental Sec'ion.

., , ~ 30 h , 35 :

. .

~327~2 ,., ~

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., ,.
. .
~V o o o . ~
o + +
. ~
+ ~ .
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~" O
' ,_, + a . +
'' ~ tn .,~
': :5 0 0 U
,~, o ~D ~ C
~ o + + m O
;, ~ o :,., ~ o o _~ .rl o Q ~ ~
:~, I a a ~ ~
O O ~I J~
U
O ~ -O U
'5" ~ U ~4 ~ ~ a~
C
E ~J--I 0 ~5 D) O O C h U

~ O

c~ ~ a ~
:~: :n rn D) ,~' O O O

!.', E--I

0~ O0;
:~ ~,q æ
Z v A~ ~' h C~ G

~ 1~273~

~or anv given cl~clone/ccal sys'ern, the Partis~ e Di2mete-, visc~sity, ~ Spec ~ :,.avitv ter~s are c~nstant. The Velocity (V) and Acceleration (G) terms vary as a part cle moves within a cyclone. Since 05 the particles accelerate, par.icle velocities change.
Moreover, the G term varies as particles are at dif-ferent radii. It is contemplated that the divergence equations can be used to determine divergence values by accounting for this variability. However, such mathe-10 matical precision is not required for efrec'ive 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 15 calculated from apparent ~istance which is c~lculated J~ on the basis of actual data using an arbitrarily selec~ed radius of interest. Ac-ordingly, when ap-parent velocity is used to calculate a divergence value from eauations 12, 13, and 14, the acceleration term, 20 G, for that divergence value must he calculated ~t the same radius of interest.
. -~ The present method involves assuming that aDparent velocity is a constant velocity throughout the entire ,r` residence time in the cyclone. Apparent velocity is a 5. 25 function of residence time and ~pparen~ distanee travelled by a particle. of the terms residence time and ~pparent distance, residence time can be directly .- calculated from the cyclone geometry and the media 7 flow. The apparent dis~ance, however, cannot be 30 direc_ly calculated because the flow dynamics and ac-i tual paths that particles travel within a cyclone can-;. not be accurately determined. It is noted that the ap-parent distance a particle must travel to be separated is the same for particles of any size and that the ap-35 parent distance is a function of ~he diameter of the cyc!one.
To overcome the limi_ation of not being able to direc~ly dete-mine either apDarent dis.~nce or apparent 13273~
velocltf, the present me~hod inc'udes detQrmi~ins an aD~arent dist~nce based ~?on ~nown data, such zs tha~
repor~ed by Deurbrouck. The apparent d s.ance is ~hen used to calculate ap~arent velocity for use in the 05 divergencQ equations. The accelerat.on te~m in the divergence equations must then be determined at a radius of interest corresponding to the selected ra~ius of interest used in conjunction with the known data ~o .provide the basis for determining apparent distances, .10 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 acceDt-. able.
`~ 15Apparent distances are determined from the Deur-brouck data in the following manner. Initially, the as-`~ sump~ion is made that the distance travelled by a par-~ ticle in a cyclone is a function of cyclone diameter.
s. Then, from the Deurbrouck data, divergence and fluid .20 speciric gravity are known and viscosity is assumed to be 1 centipoise, for each particle f-action. Accelera-'jtion 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 Far-ticles at one-third the radius of the cyclones. ~hese 'values are also termed apparent velo~ities and are as-sumed to represent a constant velocity a particle must travel to be correctly benef ciated.
The apparent distance that particles travel in ~each of the three cyclones is then calculated by multi-'.~plying V by the residence time. The ap~arent distances calculated in this manner are then plotted against cyclone di~meter as ~hown in Fig. 4. The three data polnts on this graoh orm an apprcximately s.raigh' line. This relationship suggests that the star~ing as--2~-13273L~2 sumpt on was cor-ec~, and .hat a linear raiat onship e~is., between cyc e..e ~lamet~- ~nd l~e apparent dis-tance particles, regardless of si7e, must t-3ve to ~e separated. ~y conaucting a linear regression of the -05 data points in Fig. 4, the following equation for -determining apparent distance from cyclone diameter was calc~lated.
:`' [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 particle size fraction can be predicted in the following manner.
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-ficiat~d is calculated by applying the cyolone diameter to E~uation 15. A ~alue for apparent velocity is then determined by dividing the apparent distance by the residence time. G is determined at a radius of nter-~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 knowr, 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 dif.erent geomet-y or operat-ing conditions.
~ The effect of proposed changes in a separation :. system on e$ficiency or the system can be determined by the above ~ethod. Any changes in cyclone geometry and oper~t-ng ~aramete-s in a seDaration system for im-proved efficienc-~ will ncrmally be selec'ed on the basis of efficiency improvement per cost. Var ous ; -29-.

7 ~ '~ 2 separat on systems having di _erent cyclone geomel~v and operating parameT~ra h~ve Deer. ~na_-!zed ~or ~re-dicted e-ficiencl as measured by divergence values bv the present method. The results of these anal~ses are 05 described in the Experimental Section. ~y examining the amount of efficiency improvement from each of the ch~nges analyzed and relative c~st, it has been deter--~ mined that certain changes for improving effic encf 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 separ~-~- tion. As seen in Example 2, substantial decreases in divergence values are achieved by increased residence ~ 1~ time. The cost associated with this change is simply the capital cost for buying longer cyclones. This cost is minimal in ter~s of efficiency improvement per ton , of coal. It should be noted that residence time c~n ;~ also be increased by using larger diameter cyclones.
However, any benefits f_om this method of increasing residence time are virtually completely offset by lower s~ efficiency frcm dec~eased acceleratinn.
Another cost effective shange in a separation sys-. tem is to increase acceleration, without at the same time decreasing residence time. While acceleration can ~ be increased by smaller cyclone diameters, residence ,~ time is reduced by such a change. Ac-eleration, hcw-ever, can be increased without decreasing residence time by some combination of dec_easing the inlet dia-,i 30 meter and inc-easing the inlet velocity, while keeping flowrate cons~ant. The addi~_onal cost of such changes includes costs of e~uipment modlfication 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.
Reducin~ dense media viscosity is another cost ef-fective method fo~ improv-ng separat on ef-^iciencf.
The er ec~ of reduc ng the media viscosi~f on diver-,- ~L327~2 ~ gence values is illustrated in Example 3. As discussed - above, viscosity reducticn can ~e ac`~.ieved ~y addition of a sur,actant, such as Lomar D,* producQd by Diamcnd Shamroc~. In this manner, magnetite particles move 05 more freely with respect to each other. The use of rounded magnetite particles also reduces YiscOSity, as discussed above. Viscosity reduction can also be achieved by heating the dense media. For e:~ample, by raising the temperature of the media in a heated cir-10 cuit from 68F to 140F reducQs 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-~` 15 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 20 lower divergence values are achieved for larger par-ticle sizes. Accordingly, coal should be ground only to ~r' 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 25 rod rather than ball mills.
The general principles discussed abo~e and equa-tions 12, 13, and 14 relating to the use of cyclones i~ for dense media separation (separation of solids based on different specific gravities) ar~ also applicable to 30 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 centrifugal force, such as spirals and hydro-` 3S cyclones. These principles and equations are also ap-piicable to miner~l processin~ systems which do not use centr-fugal force for processing. Such systems include the use of vertical currents, e.g., jigs, the use of * Trade-mark .

13~7~
:` st-_aming cur-ents, e.g., tables, and ~he use of launders. These principles can be use~ o ~re~ic~ per-~ formance effect-veness of such systems and to selec .~ operational parameters for improving performance.
05 Equations 12, 13, and 14 can be used directly for such other systems. However, instead of using DeurbroucX'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 ~` 10 centrifugal force, acceleration would sim~ly 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-1c ticles by magnetic separation. Coal particles having a ~ diameter less than about 0.6 ~m are typically separated ~ from magnetite particles using magnetic separators.
'~''t''~ The underflow portion containing refuse is typicallv fed to a separate magnetite recovery circuit where the dense media is separated, for e~ample, by magnetic !~' .
i~ separators and recycled.
The reductions in ash forming material by the present invention are highl-~ advantageous and economi-cal for coal combustion processes. For example, foul-ing and slagging of furnaces caused by ash is decreased ~ with a decrease in ash forming materials in the fuel.
; Additionally, ash removal costs are reduced wnen 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 ashthrough 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 rorming agglomerations prior to combustion.
~- Suc:~ coal is suitet 'o agglomeration because of itq : fine size. As used here n, "agy~omeration" ~erers to me~hods for forming fine particles of csal into la_~e_ ~32-.:

~273~2 .~
size units, suc:~ as pelleti_ing, compac_ion, or agita-.ion. Advantagea of agglcme~e on -nc_~de m~-~ved handling of coal material, particularly during t~e transporlation or fuel products. Agglomerations are . 05 particularly advantageous for coal-fired utilities which use pulverized coal (PC) boilers in which coal material is pulverized before combustion to a particle ~ size less than about 0.075 mm. Enersy savings in this ,~ pulverizing process are made by using agglomerations of 10 clean coal from the process because agglomerated coal . is more easily pulver~zed than solid coal pieces and a large percentage of the coal particles in the pellels , already meet the size requirements for the c-ushing process.
15 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-`'.7`~'~ c!ude materials for air pollution reduction, such as alkaline sorbents for sulfur -apture, s~lfation pro-moters, catalvsts for intermediate reactions in air pollution reduction processes, or anti-slagging agents.
While such additives can form ash upon combustion, the overall ash burden is sufficiently reduced by the present process that ash formed from additives is ac-z5 ceptable. Additionally, because of the fine size of ~ the coal particles, additives are particularly effec-ii tive due to ease of dispersion of a~itives and in-~ timate mixture with the fine coal particles.
';
Derivation of Dive~gence Eauat ons The force acting on a coal particle in a cyclone system in the direction of the interior of the cyclone is te-med the "buoyant force" and is provided by Equa-tion A.
~A3 ~, = Vol~ ~SGD - SG.~) G

.~
,~
~ -33-,.~
. ' , ~32`
where-n, F~ = buoyant force . Vol~ = particle -~olume SG? = partlcle spec-fic c~avi~y SGf d = specific gravity or fluid displaced . G = G acceleration .~ The G acceleration is a radial acceleration whic~
$~ iscaused by the circular motion of the ~coaltrefusejmedia stream inside the cyclone. This ac-'~cele-ation is a func ion of tangential velocity of the `~10 stream. As can be seen from Equation A, to inc~ease .he buoyant force on a given particle in a given dense ..media, the G acceleration must be inc_eased.
.~radley, D., The Hydrocyclone, Pergamon Press ~:Ltd., London, 1965, discusses cyclones and provides two `15 equations which, solved simultaneously, give the fol-:.lowing equation for G acceleration.
[B] G = Vtlng /r = ~ ___~ _______ ~ ~ 2 n + 1 wherein, R1 = radius of inlet, ft R~ = radius of cyclone, ft .V; = velocity of feed in inlet, ft/sec r= radius of interest, ft 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 ac 1/3. As mentioned previously, selection of this ~.~alue for r is not critical to the present invention and other values work equally well. The term n is an e~-ponent, the value of which depends on cycione geomet~v.
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~-on of many qa-iables and depends. in part, upon the flcw regime or ?ar'ic'es inside the c~clone. As is ~no~n, par_icles can have turbulent, transitional, or lamina~
flow regimes. The par'icular flow r~gime for a par-., .~ -3~-.
' `~ ' ,, .

.. .

1~27~
t~cle de~ends uoon the properties of fluid in wh~ch the par~icle is tra~tell ng, v~ccsi~. ~nd s?esi~-- ~ra~lt~, as well as on the part~cle's veloc ty and diamecer.
The Reynolds numoer of a particle is the criterion 05 which determines flow regime. For Reynolds numbers less than 2, particles will travel in laminar flow. For Reynclds numbers bet~een about 2 and about 500, flow will be in a transi~ional phase. For Reynolds numkers greater than about 500, tur~ulent flow occurs. The formula for Reynolds number is provided in Eauation C.
....
-'s [ ] Dp V~, SG~ d `,' U
wherein, Re = Reynolds number D~ = particle diamete-' Va = particle velocity :~ SGf d = specific gravity of rluid displaced u = viscosity of fluid displaced ,~ The coefricient of resistance of a particle is a measure of resistance e~perienced by a particle as it .; t-avels ~hrough a fluid. The for3ula for coefficient .~ of resistance is provided in Equation D.
,s, [D] Q = 4 D~ (SG - SG~ d ) G

' where Q = coefficient of resistance Do = particle diameter SG~ = particle specific gravity SGf d = specif~c gravity of fluid displaced G = G acceleration Vp = particle velocity The relationshio between coefficient of resistance and Reynolds number can be desc-ibed by three equa-, ~ tions, one for each flow regime.

~E] Turbulent (Re >500) log Q = log 0.44 . 35 ~'. [~J Transi_~onal (500 >Re >2) lcS Q = log 18.5 - 3/5 loa ~e [G] Laminar (Re <~) log Q - log 24 - log Re . .
' . .

.~

~ 13273~2 . The particIe ~elocity c~n De de~ermine~ in t~e ;- foilowing manner. Equ-.io~s c ~nd D ~r~ so ~e~ 'c ~e velocity term and then set equal. The following rela-tionship is derived from this procedure.
,~ 05 .~ 4 Dp (SGp - SGc d ) G
` [H] log Q = log -----------_---___- +
3 SGf d Dp SG~ d .:- 2 log _______ - 2 log Re ~" 10 u , The log Q ~erm in Equations E, ~, and G can be ~: substituted into Equation H and the resulting Reynolds '~ number may then be solved for particle velocity in terms 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~ - SG~) G
[I] (Re >500) 2 log Vp = log ________ _~ log 0.44 3 SGc d 4 Dp (SGp - SG~d ) G
.~ [J] 500>Re>2 1.4 log Vp = log ______---_---------3 SG~ d Dp SGf d - + 0.6 log -----_- - lo~ 18.5 ~5u . 4 Dp (SGp - SG~d) G
~R] Re<2 log Vp = log ------------------- +
3 SG~ d Dp SGf d . 30 log --__--- - log 24 u Equaticn~ I, J, and K can be algebraically manipu-lated to the form of Equations 12, 13, and 14.
~`
' 35 c .~ :

:

,,:

~327~'~2 E:~B~IMENTAL
i '. E,Yample 1 ~; Observed divergence values for di~ferent si-e OS fractions of coal from DeurbroucX's work with an 8 inc:~
cyclone are compared with divergence values predicted .- by the present method using the ac'ual test parameters s or Deurbrouck's wor.~ he ac~ual conditions of ~. Deurbrouck's test are shown in Table 1-A.
`,'` 10 ~ Table 1-A
;.," Value Value -~ Parameter (Actual Conditions) (New Conditions) ~;
Cyclone Diameter 8 inches 8 inches :. 15 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 `: 20 Viscosity 1 centipoise 0.4688 centipoise (assumed) ,~ Eff eclive Media 1.33 1.33 ~, Gravity Based upon the actual conditions in Table 1-A, :~i 25 predicted divergence values were calculated according to the present method. These predicted values are com-~ pared with observed divergence values for each sise :~ fraction considered by Deurbrouck. This comparison is ~: shown in Table 1-B.
.,x 30 s, ~. 35 . ~.
;'`

. ~37-.

' :
, .

1~7~3~

_aDle 1-3 Predicted Predicted Diver~ence Divergenc~
Size Observed (Actual (New s 05 Fraction Divergence Conditions) Conditions) 0.814 mm 0.03 0.017 0.001 0.420 mm 0.08 0.053 0.002 O.250 mm O.11 0.1~1 0.006 10 0.177 mm 0.20 0.210 O.Olo ~` O.105 mm O.24 0.483 0.022 0.074 mm ~- 0.846 0.039 0.037 mm -- 2.565 0.119 A new set of test conditions, varying four factors from Deurbrouck's 8 inch cyclone data, were sele~ted for improved separation. These new conditions we-e analyzed according to the present invention to deter-mine predicted divergence values to illustrate the potential for improved efficiency of separation. The ~ values for the new corditions are shown in Table 1-~
:.~ and the predicted divergence values under the new con-ditions are shown in Table 1-B. The improvement in predi~ted 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 ~` 30 37 mic-ons (400-mesh).
:' Example 2 X For Examples 2-8, a series of simulated separation runs were conducted using Equations 12, 13, and 14, to e~amine the effect on separation efficiency, as indi-cated by diver~ence valuPs, cf variations in diff2rent parameters .

,` -38-7~
In rxample 2. four simulation runs were c~nduct with the residence :m~ oin~ va-ie~- ~v u~ ~ a fa~ ^_ of 6. The results of this comparison and the effec's on divergence values are shown in Ta~le 2-A. It should 05 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 accele-ation value would 10 have dec_eased at highe- cyclone diameters.

Table 2-A
Run 1 2 3 4 , - Cyclone Diameter, inches 8 8 8 8 Inlet Velocity, ft/sec 68.4 68.468.4 68.~
Alpha, 3.7 Dinlet/Dcyclone 0.60 0.60 0 50 0.60 Flowrate, GPM 281.8 282.0282.0 282.0 ' 20 ~ Acceleration, g's 2735 27352735 2735 : Residence Time 0.939 1.409 2.817 5.635 s~ Residence Time Factor, 1 1.5 3 6 x std cyc.
:~ 25 Minimum Vel. for 70.8 47.223.6 11.8 '~ Separation, cm/sec Viscosity, Centipoise 1.0 1.01.0 1.0 Specific Gravity of 1.5 1.51.5 1.5 Fluid Di~placed Divergence at ` 0.074 mm (200-mesh) 0.383 0.217 0.082 0.031 , 0.037 mm ~400-mesh) 1.2 0.6;9 0.250 0.095 O.0185 mm 3.5 2.00 757 0.287 Ex~mole 3 The effect of viscosi~y on efficiency of separa-t on, as measured by divergence values, was e~amlned in simulatlcn runs 1-4. All o.her fac~ors wer2 heid con-stant with viscosity being varied from 1.0 to 0.~5O5 `
-3~-" _ I,36?73L1~
cent Doise. The media temper~tures represented by the simulated changes _n risc~s -~ are a~pr~ ~atel-~ 20~(, 40C, 60C, and 80C. The results or these test runs ` and effects on divergence are shown in Table 3-~.
-.` 05 Table 3-A
Run 1 2 3 4 .
- Cyclone Diameter, inches 8 8 8 8 .~ 10 Inlet Velocity, ft/sec 68.4 68.4 6a.4 68.4 Alpha, 3.7 Djnlet/D y~lone 0.60 0.60 0.60 0.50 Flowrate, GPM 281.8 282.0 282.0 282.0 15 Acceleration, g's 2735 2735 2735 2735 Residence Time 0.939 0.939 0.939 0.939 ; Residence Time Factor, -' ~ std cyc.
Minimum Vel. for 70.8 70.8 70.8 70.8 ~'^ 20 Se~aration, cm/sec Viscosity, Centipoise 1.0 0.6560 0.4688 0.3565 Specific Gravity of 1.5 1.5 1.5 1.5 .~. Fluid Displaced 25 Divergence at .~ 0.074 mm (200-mesh) 0.3~3 0.298 0.243 0.06 0.037 mm (400-mesh) 1.2 O.90Z 0.737 0.626 0.0185 mm 3.5 2.7 2.2 1.9 ~ Exam~le 4 :~.The effect of varying the term alpha on particle ~:30 separation e_ficier.cy, as measured by divergence values, was examined in simulation test runs 1-4. The alpha value is equal to 3-7 (Dinl~t/D yclone)- Since ~.cyclone diameter was held constant, only the inlet dia ;:~meter was varied in each of the runs. The effect of ~35 making tne inlet diameter smaller, given a constant :~flowra-e, is :~ inc-ease inlet velocity and, there~ore, acceleration. As can ~e seen from the results in T~ole ~40~

a 13~7~'~2 - 4-A, dive_~ence values were sianiricant'y dec_eased by dec-eases in the value a- - ?r-a-Table 4-A
~5 Run 1 2 3 4 _ ~ Cyclone Diameter, inches 8 8 8 8 .~ Inlet Velocit~, ft/sec 20 30.4 54.1 121.7 Alph2, 3.7 Djnle /D~yclone 0 74 0.600.45 0.30 Flowrate, GPM 125.3 125.3 125.3 1~5.3 Acceleration, g's 356 541 961 2163 Re-idence Time 2.11 2.112.11 2.11 Residence 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 : 20 ~ S~ecific 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. lSo ~. 0.037 mm (400-mesh) 2.9 1.9 1.1 0.472 ;; 25 0.0185 mm 8.7 5.7 3.2 1.4 ExamDle 5 The effect of inc~eased inlet velocity at constant inlet diameter on particle separation efficiency, as measured by diver~ence values, was examined with the results shown in Tables 5-A, S-B, 5-C, and 5-D. As can be seen from the following results, the inc-eased ac-celeration has a beneficial effect on divergence . values.

:

1327~
TaD1e 5 - ' Run 1 2 3 OS Cyclone Diameter, inches 8 8 8 Inlet Velocity, ft/sec 20 45 70 Alpha, 3.7 Dtnlet/Dcy~lone 0.74 0.74 0-74 Flowrate, GPM 175 . 3282 . O438 . 7 Acceleration, g's 356 1800 4357 . Residence ~ime 2.110.939 0.603 ~ Residence Time Factor, .j~ x std cyc.
Minimum Vel. for 31.5 70.9 110.2 Separation, c~/sec Viscosity, Centipoise 1.0 1.0 1.0 ~, SDecific 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 ,~'''' ' .
~. 25 "Y, ~
:, -~;' :~.
:: 3 O
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:~ -az-:"
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Table 5-3 Run 1 2 3 .
05 Cyclone Diameter, inches 8 8 8 , Inlet Velocity, ft/sec 30.4 6a . 4 106.5 :.;. Alpha, 3.7 D1nlet/D~y~lone 0.60 0.60 0.60 - Flowrate, G~ 125.3 282.0 438.7 10 Acceleration~ g's 541 2739 6678 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, cm/sec Viscosity, Centipoise 1.0 1.0 1.0 ,~Specific Gravity of 1 . 5 1 . 5 1.5 ~:'i'Fluid Displaced -20 Divergen~e at A, 0.074 mm (200-mesh) 0.623 0.383 0.29~
0.037 mm (400-mesh) 1.9 1.2 0.891 0.0185 mm 5.7 3.5 2.7 ~; 25 ~:-:~, ~ 30 ,`', :~
.
. 35 , ~ 3-,~., `

.

13273 ~

Table 5-C
Run 1 2 3 .
05 Cyclone Diameter, inches 8 8 8 ~ Inlet Velocity, ft/sec 54.11~1.7 189.3 ~ Alpha, 3.7 Dinl~t/D~yclone 0.45 0.45 0-45 Flowrate, GP~ 125.3282.0 438.7 10 Acceleration, g's 961 4869 11,783 Residence Time 2.110.939 0.603 . Residence Time Factor, . x std cyc.
; 15 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) 0.3510.216 0.165 .037 mm (400-mesh) 1.1 0.653 0.501 0.0185 mm 3.2 2.0 1.5 .
~.~
` 35 ., .

13273l~

- _~ble 5-3 Run 1 2 3 05 Cyclone Diameter, inches 8 8 8 ;~ Inlet Veloc ty, ft/sec 121.7 273.8 425.9 Alpha, 3.7 Dlnl~t/D-yclone 0.30 0.30 Flowrate, G~M 125.3 282.0 438.7 10 Acceleration, g's 2163 10,95526,511 ~ 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, cmJsec -. Viscosity, Centipoise 1.0 1.0 1.0 Specific Gra~ity of 1.5 1.5 1.5 : Fluid Displaced ~; 20 Divergence at 0.074 mm (200-mesh) 0.156 0.096 0.073 :~ O.037 mm ~400-mesh) 0.472 0.290 0.223 `. 0.0185 mm 1.4 0.880 0.675 .
~ Exam~le 6 : 25 The effe~t of increased flowrate, at constant in-let velocity, was examined in Table 6-A. As ean be seen from the following results, in contrast to Example s 5, divergence values increased as flowrate increased.
. .
~ 30 :.,.

S, ,.

, `t,~

., .~' . .

~ - ` 13~7~2 Table ~-a . Run 1 2 05 Cyclone Diameter, inches 8 8 8 . Inlet Velocity, ft/sec45 45 45 Alpha, 3.7 D~nlet/D-yclon~ 0.493 0 74 0.923 Flowrate, GPM 125.3 282.0 438.7 ~. 10 Acceleration~ g's 800 180~ 2801 J`: 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 O.074 ~un (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 25 The effect of varying cyclone diameter on ef.i-ciency, as measured by divergence values, was examined 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 30 angle of 12, there is, for all practical purposes, no effect on divergence values. For cyclones having a cone r i .
~' ~` `" 132~
angle of 20O, some small improvements in divergence .~ va_-es is observed at s~alle_ -y~lor.e diameters. The r lack of substantial improvements is due to decr ased ,~ residence time.

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`; 15 , ` 13273~
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., Ec2~le The effect of medi~ spesiS_c gr2vi'I on e- c:enc~
of separation, as measured ~v divergence vaiues, wzs e~am ned. Lit~le effecl was observed on diveraenc~
; 05 values by variations in this factor.

t Table 8 Run 1 2 3 10 Cyclone 3iame~e-, inches 8 a 8 Inlet Veloc ty, ft/sec 68.4 68.4 68.4 Alpha, 3.7 Dinl~t/D~yclon~ 0.60 0.60 0.60 ' Flowrate, GPM 281.8 282.0 282.0 15 Acceleration, g' 5 2735 2735 2735 Residence Time 0.939 0.939 0.939 Residence Time Factor, x std cyc.
Minimum Vel. for 70.8 70.8 70.8 Separation, cm/sec , Viscosity, Centipoise 1.0 1.0 1.0 !~ S~ecific Gravity of 1.5 1.4 1.3 Fluid Displaced Divergence at -~ ~ 0.074 mm (200-mesh) 0.383 0.373 0.362 .0~7 mm (400-mesh) 1.2 1.1 1.1 ~ O.0185 mm 3 5 3 4 3 3 ,~While various embodiments of the present invent~on have been described in detail, it is apparent that `30 modifications and adaptations of those embodiments will ;occur to thosé skilled in the art. However, it is to be expressly understood that such modifications and adap-tations are within the scope of the present invention, as set forth in the following claims.

:' ~":

Claims (14)

1. A method for beneficiating particulate solids suspended in a media, comprising:
a) selecting a first divergence value;
b) selecting particle beneficiation apparatus geometry and operating parameters;
c) determining an apparent distance a particle must travel to be correctly beneficiated for the apparatus geometry selected in step b;
d) calculating an apparent velocity a particle must achieve to be correctly beneficiated using said apparent distance; and e) calculating a second divergence value for the particle beneficiation apparatus geometry and operating parameters selected in step b using said apparent velocity;
f) comparing said second divergence value calculated in step e with said first divergence value from step a;
g) repeating steps b through f until said second divergence value calculated in step e is less than said first divergence value from step a;
h) beneficiating particulate solids in a process comprising particle beneficiation apparatus geometry and operating parameters resulting in said second divergence value being less than said first divergence value in step g.

2. A method as claimed in Claim 1, wherein said process comprises applying centrifugal force to said media by causing said media to travel in a circular path and wherein said step of determining an apparent distance comprises using the equation:
D = a M + b where D = apparent distance, centimeters M = diameter of said circular path, inches a = about 3 b = about 42

3. A method as claimed in Claim 1, wherein said step of calculating an apparent velocity comprises calculating a residence time for said particulate solids and dividing said apparent distance by said residence time.

4. A method as claimed in Claim 1, wherein calculation of said divergence values comprises determining a flow regime applicable to said particulate solids and using an equation to calculate said divergence value for said flow regime, which equation is selected from among Equations 12, 13, or 14, as described below:
[12] Turbulent log Div = 2 log V - 1 log Dp - 1 log G +
0.0 log u + 1.0 log SGfd + log 0.33;
[13] Transitional log Div = 1.4 log V - 1.6 log Dp - 1 log G +
0.6 log u + 0.4 log SGfd + log 13.875;
[14] Laminar log div = 1.0 log V - 2.0 log Dp - 1 log G +
1.0 log u + 0.0 log SGfd + log 18.0;

where Div = Divergence V = Minimum Particle Velocity to be Beneficiated Dp = Particle Diameter G = Acceleration u = Viscosity SGfd = Fluid Specific Gravity.

5. A method as claimed in Claim 2, wherein said step of determining an apparent distance comprises calculating an actual particle acceleration from known data for a cyclone separation at a given fraction of the cyclone radius; and further comprising calculating a particle acceleration of said separation process at said given fraction of the radius of the circular path used to apply said centrifugal force.

6. A method as claimed in Claim 5, wherein said particle acceleration of said separation process is calculated by the formula:
G = Vtang/r where G = particle acceleration Vtang = tangential particle velocity r = given fraction of radius

7. A method for separating solid particles in a dense media cyclone, comprising:
a) determining a first separation efficiency in terms of a first divergence value said first divergence value representing the difference between the specific gravity at which particles are to be separated and the effective specific gravity of dense media with which the particles are to be separated;
b) selecting cyclone geometry and operating parameters;
c) determining a second divergence value, said second divergence value representing a prediction of the difference between the specific gravity at which particles would separate and the effective specific gravity of said dense media for said selected cyclone geometry and operating parameters;
d) comparing said first divergence value with said second divergence value;
e) iterating steps b, c, and d until said second divergence value is less than said first divergence value; and f) separating solid particles in a dense media cyclone with geometry and operating parameters that result in said second divergence value being less than said first divergence value in step e.

8. A method as claimed in Claim 7, wherein said step of iterating step b includes selecting new cyclone geometry and operating parameters selected from the group consisting of greater cyclone length, smaller inlet diameter and greater inlet velocity at constant flowrate, decreased dense media viscosity, larger particle size and lower specific gravity of separation.

9. A method as claimed in Claim 8, wherein decreased dense media viscosity is achieved by a process selected from the group consisting of using rounded magnetite particles, adding a surfactant to the dense media, heating the dense media, and combinations thereof.

10. A method for beneficiating particulate solids of known size and specific gravity distribution down to a predetermined minimum particle size from refuse at a predetermined efficiency, comprising:
a) providing magnetite having a diameter such that particulate solids of said minimum particle size have a buoyancy substantially equal to the buoyancy said particulate solids would have in a true liquid having a specific gravity equal to that of said dense media;
b) identifying a desired efficiency in terms of a threshold divergence value;
c) selecting a set of values for:
minimum particle velocity to be beneficiated (V) particle diameter (Dp) acceleration (G) viscosity (u) fluid specific gravity (SGfd);
d) determining a flow regime and calculating a the divergence value (Div.) for the selected set of values using a divergence value equation for the appropriate flow regime selected from the group consisting of turbulent, transitional and laminar wherein said equations are:
Turbulent log Div = 2 log V - 1 log Dp - 1 log G +
0.0 log u + 1.0 log SGfd + log 0.33;
Transitional log Div = 1.4 log V - 1.6 log Dp - 1 log G +
0.6 log u + 0.4 log SGfd + log 13.875 Laminar log Div = 1.0 log V - 2.0 log Dp - 1 log G +
1.0 log u + 0.0 log SGfd + log 18.0;
e) comparing said calculated divergence value with said threshold divergence value;
f) selecting a new value for at least one of V, Dp, G, u or SGfd when said calculated divergence value is greater than said threshold divergence value and repeating step d to obtain a new calculated divergence value;
g) repeating step f, when necessary, until a calculated divergence value is obtained which is less than said threshold divergence value; and h) beneficiating said particulate solids in said cyclone with dense media formed from the provided magnetite when said calculated divergence value is less than said threshold divergence value.

11. A method as claimed in Claim 10, wherein said particulate solids comprises coal and said refuse material comprises pyrite.

12. A method as claimed in Claim 10, wherein said magnetite particles have a diameter less than about 0.010 mm.

13. A method as claimed in Claim 11, wherein said coal has a particle diameter of less than about 0.6 mm.

14. A method for beneficiating, thickening or sizing particulate solids suspended in a media, comprising:
a) selecting a first divergence value;
b) selecting processing apparatus geometry and operating parameters for separation processing selected from the group consisting of beneficiating, thickening and sizing;
c) determining an apparent distance a particle must travel to be correctly separated for the apparatus geometry selected in step b;
d) calculating an apparent velocity a particle must achieve to be correctly separated using said apparent distance;
e) calculating a second divergence value for the separation process apparatus and operating parameters selected in step b using said apparent velocity;
f) comparing said second divergence value calculated in step e with said first divergence value from step a;
g) repeating steps b through f until said second divergence value calculated in step e is less than said first divergence value from step a;
h) separation processing particulate solids in a process comprising apparatus geometry and operating parameters resulting in said second divergence value being less than said first divergence value in step g.