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Solve Solids Flow Problems in Bins, Hoppers, and Feeders1

byJ. Marinelli

andDr. John W. Carson

1 Reprinted with permission from Chemical Engineering Progress, June, 2001. Copyright © 1992 American Institute ofChemical Engineers. All rights reserved. Not to be uploaded to any other site without written permission from the AIChE.Individual downloads are permitted so long as a fee of $15 per article is paid directly to the Copyright Clearance Center,222!Rosewood Drive, Danvers, MA 01923.

Good plant designs provide reliableflow of powders and other bulkmaterials.

Look at these solids flow problems and askyourself what they have in common.

Case History #1. A fiberglass manufacturer inthe Midwest handles glass batch (a mixture ofdry chemical ingredients having a variety ofparticle sizes and densities) in a surge bin justupstream of its furnace. The contents of this binare discharged to the furnace continuously, butthe level in the bin usually does not changemuch because fresh mixtures are beingcontinually produced and conveyed into the bin.Every so often, this mixing and conveyingsystem breaks down and, before the problemcan be corrected, the bin level dropsconsiderably. Operators have found that when

this occurs, the viscosity of the glass in thefurnace changes dramatically, creatingsignificant operational problems.

Case History #2. A coal-fired power plant, alsoin the Midwest, collects fly ash in a bin andmeters it into a conditioner. Periodically, flyash floods uncontrollably through the outlet ofthis bin, overloading the screw feeder and theinclined screw conveyor. The result is lostproduction and significant costs for cleanup.

Case History #3. A chemical manufacturer inthe Southeast stores cellulose acetate in twolarge silos, each having a design capacity ofapproximately one million pounds. Sometimeago plant personnel discovered large regions ofstagnant material when they attempted to emptythe silos, so a contractor was hired to clean themout. After several weeks of work, 600,000 lb of

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flake were removed from one silo and400,000!lb from the other. All of this materialmust be scrapped since it has deteriorated bysitting stagnant in the silos for a prolongedperiod of time.

Case History #4. A pet food manufacturer inthe Southwest has a series of bins to storevarious raw ingredients used to make dog food.Several of these bins have a capacity of100,000!lb of material. However, the actualuseable capacity of these bins is, in severalcases, less than half their design capacity. Thereare large stagnant regions in these bins, whichprevent them from being emptied completely.

What do these case histories have in common?All involve a storage container (bin, silo,bunker), which is exhibiting a funnel-flowpattern. This is characterized by a condition inwhich the walls of the hopper section at thebottom of the container are too shallow or roughfor the bulk material to slide along them. As a

result, material flows preferentially through afunnel-shaped channel located directly abovethe outlet while material outside this flowchannel is stagnant, as shown in Figure 1. Thisresulting first-in last-out flow often leads toparticle segregation and spoilage. Ratholing isa common occurrence, which can lead toflooding of fine powders or reduced useablecapacity.

While the four case histories cited above allinvolve problems with funnel-flow bins andsilos, there is a large class of bulk materialswhich are well-suited to being handled in suchstructures. These generally have the followingcharacteristics:

• coarse particles – usually a quarter inch insize and larger;

• free flowing materials – materials which donot stick to each other;

• non-degrading particles – materials which donot cake, spoil, or oxidize when sitting for

Figure 1. Bulk material flowing down a storage containerbecomes stagnant along the bottom due to either shallowwall angle or wall roughness.

Moving

Stagnant

Figure 2. Mass-flow design in action: all the material ismoving to prevent operations and maintenance problems.

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long periods of time without movement; and• segregation is not a problem – either the

material is non-segregating or, if it doessegregate, it will not affect downstreamprocesses (for example, if operated on a batchbasis).

Provided that the bulk material meets all four ofthese characteristics, a funnel-flow bin or silo isthe most economical storage device. Onereason is that the sloping hopper walls can beshallow which results in savings in overallheadroom for the bin as well as the cost ofelevating material into the bin. In addition, bynot having particles sliding along the hopperwalls, abrasive wear is minimized.

If the bulk material being handled is not coarse,free flowing, non-degrading, and non-segregating, a funnel flow pattern is no longersuitable. Most such materials can be reliablyhandled using a mass-flow design, that is, one inwhich all of the material is in motion wheneverany is withdrawn, as shown in Figure 2. Thiseliminates ratholing and the associated problemsof flooding of fine powders as well as reduceduseable bin capacity. In addition, caking,spoilage, and oxidation of the bulk material isminimized because of the first-in first-out flowpattern. Segregation is also minimized for thesame reason.

Mass flow bins are suitable for fine powders,cohesive (that is, non-free flowing) bulkmaterials, materials that tend to degrade whenstored for extended periods of time withoutmovement, and when segregation is important.Indeed all four problems described in the casehistories above could have been avoided if amass-flow pattern had been used. How canmass flow be achieved?

Hopper slope and smoothness

The first step is to make sure that the hopperwalls are sufficiently steep and smooth to forcethe bulk material to slide along them. Therequired steepness and smoothness isdetermined by first testing to measure wallfriction and then using a set of design charts.

Wall friction measurement. For a bulk materialto slide on a surface, friction between the twomust be overcome. This friction can bemeasured by use of a test apparatus such as theone shown in Figure 3. First, the bulk materialis placed in a retaining ring on a flat piece ofwall material. Then, using weights, variousforces are applied to the material in a directionnormal (perpendicular) to the wall surface.Material in the ring is forced to slide along thestationary wall material, and the resulting shear

Figure 3. Test setup design allows shear stress (see horizontal arrow) to be measured as a result of applied weights (seevertical downward arrow).

(force appliedby direct sheartester)

RingCover

Sample of wall materialBulk material

Bracket

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force is measured as a function of the appliednormal force.

Figure 4 shows the results of a typical wallfriction test. Along the horizontal axis arevalues of normal pressure (force per unit areaacting perpendicular to surface) applied to thematerial, while the vertical axis represents themeasured shear stresses required to overcomefriction with the wall sample.

Wall friction angle, designated as f', is definedas the angle formed by a line drawn from theorigin to a point on the curve. For a given bulkmaterial and wall surface this angle is notnecessarily a constant but often varies withnormal pressure, usually decreasing as normalpressure increases.

Factors that influence wall friction. For a givenbulk material, wall friction can be affected by:

• Wall material. Generally, the smoother thewall surface, the lower the wall friction angle.As a result, less steep hopper angles areneeded to ensure mass flow.

• Temperature. Both the wall temperatureand the bulk material temperature can affectthe wall friction angle that develops.

• Moisture. Changes in moisture of the bulkmaterial can affect wall friction angles. Insome cases, moisture can migrate to the wallsurface when warm material is deposited oncold bin walls.

• Corrosion. If a hopper is fabricated fromcarbon steel, it may corrode, creating a morefrictional surface than anticipated.

• Abrasive wear. As a surface wears, it oftenbecomes polished. Thus, a design based onan unpolished surface is often conservative.In other cases, the surface becomes rougher,which can upset mass flow.

• Time at rest. Some bulk materials adhere towall surfaces while remaining at rest underpressure. As a result, the wall friction anglebecomes larger, and steeper hopper angles areneeded for mass flow.

Once the wall friction angle for a given bulkmaterial and wall surface has been determined,the next step is to determine what hopper anglesare compatible with mass flow. The two typesof hopper geometries that have been studiedmost are cones and wedges.

Figure 4. Typical results of the test setup shown in Figure3 to help engineers determine wall friction angle.

Shearstress,

psf

Normal pressure, psf

f'1

f'2

f' = Wall friction angle, deg

0

0

Figure 5. Design chart for a conical hopper allows thedesigner to know whether mass-flow or funnel-flow willtake place. It has a built-in margin of safety.

Massflow

Funnelflow

Uncertain

40°

30°

20°

10°

0°

50°40°30°20°10°0°

qc

f'

qc

5

Conical hoppers. Design charts were originallydeveloped by Dr. Andrew Jenike and publishedin his classic handbook, "Storage and Flow ofSolids" [1]. These charts indicate allowablehopper angles for mass flow for given values ofwall friction angle. Figure 5 shows a typicalchart. On the horizontal axis are values ofhopper angles (qc) measured in degrees fromvertical while the vertical axis contains wallfriction angles, f'.

There are several ways to use such a chart. Oneway is to determine the type of flow pattern thatwill develop in an existing bin given a certaincombination of wall friction angle and hopperangle. For example, if the wall friction angle is15° and the hopper is 20° from vertical (70°from horizontal), the combination of these twovalues lies within the mass flow region of thedesign chart. On the other hand, a wall frictionangle of 15° and a hopper angle of 35° willresult in funnel flow.

Another way to use such a chart is to determinethe maximum (that is, shallowest) hopper anglethat will allow mass flow for a certain wallfriction angle. To do this, first select ameasured value of f' (wall friction angle), thenread over to the edge of the mass flow regionand down to the appropriate hopper angle. Thisis the shallowest recommended angle for massflow.

Notice that there is a region labeled uncertainwhich lies between funnel flow and mass flow.In actuality, this represents a margin of safety tocover slight differences in material propertiesand hopper design. If the combination ofhopper angle and wall friction angle lies tooclose to the funnel flow line, a switch betweenmass flow and funnel flow can occur causingbin vibrations and other problems.

Wedge hoppers. Different design charts areused for wedge hoppers than for conicalhoppers. Figure 6 shows a typical chart. Valuesof hopper angle (measured from vertical) are onthe horizontal axis (called in this case qp), andwall friction angles f' are on the vertical axis.Notice that there is no uncertain region in thewedge hopper charts. This is because there isno sharp boundary line between mass flow andfunnel flow. In fact, mass flow can occur to theright of the design line, even though this labeledas the funnel flow region. This means that awedge geometry is more forgiving and capableof handling materials with a wider range offlowability than a conical geometry.

This chart is used in the same way as the conicaldesign chart. As an example, if f' is 15°, theresulting maximum wedge hopper angle formass flow is 40° from vertical. This is 12° lesssteep than the required conical hopper angle.Hence, mass-flow wedge-shaped configurationsrequire significantly less headroom than conicalhoppers.

Figure 6. This typical design chart for a wedge hopper isused similarly to the one in Figure 5, except note that an"uncertain" region is not needed.

Massflow

Funnelflow

40°

30°

20°

10°

0°

50°40°30°20°10°0°

qp

f'

60°

qp

6

Other designs. Mass flow can also be achievedby the use of inserts, such as a BINSERT®.The latter can convert a funnel-flow bin to massflow by use of a second hopper inside anexisting hopper. Figure 7 shows a typicaldesign. Material is forced to flow along thewalls of the shallow (formerly funnel flow)outer cone.

Outlet size determination

How large does the outlet of a mass-flow binneed to be? This is the second consideration forproper design of such a bin.

There are two types of flow obstructions thatcan occur with bulk materials, as shown inFigure 8. The first is particle interlockingwhere particles lock together mechanically. Theminimum outlet size required to prevent aninterlocking arch is directly related to the size ofthe particles, provided that the particles are atleast 1/4 in. or larger. As a rule of thumb, acircular outlet must be sized about six to eighttimes the largest particle size. Wedge hoppersmust have an opening width that is at least threeto four times the largest particle size.

If most of the particles are less than about1/4!in. in size, flow obstructions can occur bycohesive arching. Particles can bond togetherphysically, chemically, or electrically. In orderto characterize this bonding tendency (calledcohesiveness of a bulk material), its flowfunction must be determined. This can begenerated in a testing laboratory by measuringthe cohesive strength of the bulk material as afunction of consolidation pressure applied to it.Such strength is directly related to the ability ofthe bulk material to form arches and ratholes inbins and hoppers.

The strength/pressure relationship (flowfunction) is usually measured using a directshear tester. Consolidation values are easilycontrolled, and the cohesive strength of the bulkmaterial is determined by measuringinterparticle shear stresses while theconsolidation pressure is being applied.

Once a flow function has been developed,minimum opening sizes to prevent arching canbe calculated by the use of the hopper's flowfactor. Flow factors can be obtained fromJenike's design charts [1]. Comparing the flowfactor and flow function yields the minimum

Figure 7. Dashed trapezoidal shape indicates the secondhopper inside the existing hopper.

Mass flow hopper

Critical anglefor mass flow

Twice critical anglefor mass flow

Figure 8. Knowing the characteristics of these two types offlow obstructions will help determine outlet size.

Interlocking arch Cohesive arch

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opening required to prevent a cohesive archfrom forming.

Typically, the requirement for a circularopening is about twice that of a slotted opening.For example, if a 12 in. diameter opening isrequired to prevent arching in a cone, theminimum slot requirement would be about 6 in.wide. Note that the length of a slot should be atleast three times its width.

Minimum dimensions to prevent cohesivearches are affected by several parameters,including:

• Particle size and shape. Generally the finerthe particle size the greater its cohesivestrength – hence the larger the outletrequired. Particle shape is less important,but the more irregular the shape, generallythe more difficult to flow.

• Temperature. Many bulk materials aresensitive to the temperature at which theyare handled. This temperature may either beconstant or changing. It is essential thatflow property tests be conducted closelysimulating the environmental conditions towhich the bulk material is (or will be)exposed.

• M o i s t u r e . Moisture can affect thecohesiveness of a bulk material. Typically,as moisture increases, cohesive strength alsoincreases. Only when saturation moisture isapproached, does a solid's strength decrease(becoming slurry-like).

• Time of storage at rest. During continuousflow (flow which is initiated as soon as thebin is filled) many bulk materials flow quiteeasily. However, if flow is stopped becauseequipment is shut down or breaks down, thematerial will sit at rest for a period of time:overnight, a weekend, a month, or even

longer. When this period has elapsed, thematerial is expected to flow but often doesnot because its cohesive strength hasincreased. The test program must simulatethe time of storage at rest that material willexperience so that it can be consideredduring the design stage.

• Relative humidity. Since many bulkmaterials are hygroscopic, the exposure ofsuch materials to humid air causes anincrease in moisture and therefore a gain instrength.

Flow rate considerations

A third consideration when designing a mass-flow bin is the discharge rate required. All bulkmaterials have some maximum rate at whichthey will discharge through a hopper opening ofa given size. Usually this rate is far in excess ofthe required rate, especially if the bulk materialconsists primarily of coarse particles. Finepowders, on the other hand, have considerablylower maximum discharge rates when exitingfrom a bin. This is due to the interactionbetween air (or gas) and solid particles asreflected in the permeability of the material [3].The following are some of the factors that affectflow rates of fine powders:

• Particle size and shape. Generally the finerthe particle size and the greater the range ofparticle sizes, the less permeable it is andhence the lower the flow rate. Shape canalso affect permeability but generally to asmaller extent.

• Level of material in bin. As the level ofmaterial increases, the maximum flow ratewill generally decrease. This is becausemore air or gas within the voids of thematerial is squeezed out in the cylindersection creating more of a vacuum conditionin the lower portion of the hopper.

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• Outlet size. For fine powders, themaximum flow rate increases in directproportion to the area of hopper opening.Thus by increasing the opening, flow-ratelimitations can sometimes be overcome.However, the size of the feeding devicerequired to control the rate of dischargemust also increase.

• Outlet shape. Solids can flow at higherrates through slots because they generallyhave a larger cross-sectional area thancircular outlets.

• Residence time. This can be both helpful aswell as detrimental. Sometimes a minimumresidence time is needed to provide somedeaeration so that the material does notflood through the bin outlet. However, ifthis time is too long, the material maybecome so deaerated that its maximum rateof discharge is dramatically reduced.

Solid/gas interactions are very complex and, inmany cases, counter-intuitive. While trial-and-error methods can be used, the results are oftendisappointing. Proprietary two-phase flowcomputer programs have been developed thatcan reliably predict how solids and gases willinteract. Problems such as settlement andlimiting flow rate can be studied, as well asways to overcome flow-rate restrictions by theintroduction of small, controlled amounts of air.

Outlet area must be fully live

Conditions at and below the hopper outlet arejust as important as the outlet size, and thehopper's slope and smoothness. A cut-off gate,feeder, or both may be used. In a subsequentarticle, we will discuss in more detail how todesign feeders to ensure reliable flow. The keyto gate and feeder design is that material mustbe able to flow uniformly over the entire area of

the outlet. If a gate is used with a mass-flowbin. it is important that it be used either fullyopen or fully closed. Modulation of flow ratemust be done with a feeder, not a gate. It isusually important that the feeder's capacityincrease in the discharge direction, particularlywhen using a screw or belt feeder under aslotted outlet.

We have discussed basic concepts of solids flowin this article. Subsequent articles will dealspecifically with feeder selection and design,and segregation problems and solutions.

Literature cited

[1] Jenike, A. W.: "Storage and Flow ofSolids," Bulletin 123 of the UtahEngineering Experiment Station,(revised March 1970).

[2] Dick, D.S. and Hossfeld, R.J.: "VersatileBINSERT® System Solves Wide Rangeof Flow Problems." Presented at thePowder and Bulk Solids 12th AnnualConference, Rosemont, IL (May 1987).

[3] Royal, T. A. and Carson, J. W.: "FinePowder Flow Phenomena in Bins,Hoppers and Processing Vessels." Bulk2000 (1991).

[4] Carson, J. W. and Dick, D. S.: "HowBin Retrofits Can Correct FlowProblems." Presented at AIChE SpringNational Meeting, Houston, TX (April 4,1989)

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[Published as sidebar to article]

Steep conical hopper may not be the answer

In order to ensure mass flow a steep hopper isrequired to overcome friction and promotematerial sliding on the walls. Hopper steepness,however, is not the only concern. Smoothnessof the wall surface is just as important.

Many people have the mistaken impression thata 70° cone (20° from vertical) ensures massflow. Nothing could be further from the truth!A 70° cone with a rough wall surface or africtional bulk material will more than likelyflow in a funnel-flow pattern. Both steepnessand smoothness of the hopper walls areimportant.

Wedge hoppers are often better than cones

Several advantages to using wedge-shapedconfigurations over conical configurations are[4]:

• Less steep hopper angles. Typically awedge-shaped hopper can be 10° to 12° lesssteep than a conical hopper and still promotemass flow. This can provide significantsavings in hopper height and cost. Inaddition, a wedge hopper design is moreforgiving than a cone in terms of limitinghopper angles and wall friction. Examplesof wedge-shaped hoppers are shown inFigure 9.

• Smaller outlet sizes. In order to overcomea cohesive or interlocking arch, a conicalhopper has to have twice the diameter as thewidth of a wedge-shaped hopper. Thus,cones generally require larger, moreexpensive feeders.

• Higher flow rates. Because of theincreased cross-sectional area of a slottedoutlet, the maximum flow rate is muchgreater than that of a conical hopper.

Other considerations:

• Capital cost. Each application must belooked at individually. While a wedge-shaped hopper requires less headroom or aless expensive liner than a cone, the feederand gate (if used) may be more expensive.

Figure 9. Side and front views of wedge, transition, andchisel hoppers.

Wedge Hopper

Transition Hopper

Chisel Hopper

p

L W

q

p

L W

q

c p

WL

qq

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• Headroom. Here the advantage is clearlywith wedge-shaped hoppers. This isparticularly important when retrofittingexisting equipment in an area of limitedheadroom.

• Discharge point. In many applications, it isimportant to discharge material along thecenterline of the bin, in order to interfacewith downstream equipment. Generally,conical hoppers are better for thesesituations, particularly if only a gate is usedto stop or start flow.

• Mating with a standpipe. If material isbeing fed into a pressurized environment, astandpipe is often used to take the pressuredrop. Either circular or rectangularstandpipes can be used, but circular ones areoften preferred because they are smaller incross-sectional area (resulting in less gasleakage) and structurally more robust.