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Ind. Eng. Chem. Res. 1999, 38, 4100-4103
Granular Fertilizer Agglomeration in Accelerated Caking Tests G. M. Walker,* C. R. Holland, and M. N. Ahmad School of Chemical Engineering, The Queen’s University of Belfast, Belfast BT9 5AG, Northern Ireland, UK
J. N. Fox and A. G. Kells Irish Fertilizer Industries Ltd., Herdman Channel Road, Belfast BT3 9AP, Northern Ireland, UK
The phenomenon of granular fertilizer agglomeration in storage, known as “caking”, has been investigated and explained via a plastic creep-capillary adhesion model. Experimental investigations were undertaken using accelerated caking test equipment, fitted with a displacement transducer. The shear stress required to break the resultant cake, the creep rate, and the voidage were calculated. The steady-state creep rate for nitrate-based NPK granular fertilizer increased as a function of storage pressure and followed a power law relationship. This indicated dislocation creep as the probable creep mechanism for granular fertilizer in accelerated caking tests. A capillary adhesion-agglomeration model was developed, which took into account the increased granule-granule contact area caused by plastic creep. The model was validated experimentally using a range of granular fertilizer with an acceptable correlation found between experimental and model data. 1. Introduction The agglomeration of fertilizer granules in storage, known as caking or bagset, is a significant quality assurance problem for the fertilizer industry. The agglomeration of fertilizer granules can take place over weeks or months in storage. However, a measure of the future caking propensity can be determined by accelerated caking tests. These accelerated caking tests are of short duration and for this reason are used in fertilizer granulation plants on a quality control basis. Accelerated caking tests used in the fertilizer industry involve the formation of a fertilizer cake in a cylindrical press, with the stress then required to break the cake proportional to the caking propensity of the fertilizer. The caking of fertilizer in storage is often associated with the formation of crystal bonds or bridges between adjacent granules,1 although in our estimation agglomeration due to mobile liquid bridges is a more significant factor. This crystal bonding, caused by the diffusion of saturated fertilizer salts to the granule surface, with subsequent evaporation and crystal formation, is a slow process taking weeks or months to complete. The accelerated caking tests used by fertilizer manufacturers cannot effectively describe this process, as they usually take between 6 and 12 h. It follows, therefore, that most accelerated caking tests, using pressure to accelerate the agglomeration process, define caking as a surface tension and capillary force phenomenon. 2. Agglomeration Theory It is the intention of this paper to illustrate how a combination of plastic creep of fertilizer granules under pressure combined with capillary adhesion between granules leads to the phenomenon known as caking. Capillary Adhesion. Mobile liquid binding results in agglomeration due to interfacial forces and capillary * Corresponding author. Tel: (01232) 274172. Fax: (01232) 381753. E-mail
[email protected].
suction, in which small amounts of liquid are held as discrete lens-shaped rings at the points of contact of the granules. It is postulated in this work that agglomeration caused by liquid binding between fertilizer granules is described by this pendular state with little liquid pore spaces in the agglomerate. An expression of agglomerate strength was proposed by Rumpf2 in which the strength of an agglomerate composed of equal sized particles (i) is given by eq 1
i)
( )
9 1- NF 8 πX2
(1)
where X is the particle diameter, F is the bonding force per point of contact, N is the mean coordination number, and is the voidage fraction. Plastic Creep. Thompson,3 in the only published comprehensive review of caking processes within granular fertilizer, concluded that “the probable cause of caking in ammonium nitrate prills follows a process of deformation due to plastic creep ... (with prills) bound together by the pressure deficiency beneath the curved meniscus of the aqueous film between the prills”. Little or no detailed evidence has emerged in the following years to confirm or deny this theory. When a constant stress is applied over a period of time to a crystalline material, plastic deformation or creep may occur dependent upon the magnitude of the stress and the time period. The first region of creep is known as “diffusion creep”, where the rate of strain is directly proportional to the applied stress [e ∝ σ]. A second region is described by “dislocation creep”, whereby the crystals glide over each other under high stress. Dislocation creep is characterized by e ∝ σ (n > 1).4 3. Materials and Methods The fertilizer granules used in this study were a nitrate-based NPK granular fertilizer, the analysis comprising of ammonium nitrate, ammonium phosphate, and potash, respectively. The particle size dis-
10.1021/ie990204s CCC: $18.00 © 1999 American Chemical Society Published on Web 09/01/1999
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 4101
Figure 1. Caking pressure and granule deformation, d, during accelerated caking tests.
tribution of the granules was between 2.0 and 4.5 mm. For each fertilizer sample the mass mean diameter was calculated using a standardized sieve series, and the bulk density and sample voidage were measured by calculation of the mass, volume, and solid density of the agglomerate. The fertilizer granules were agglomerated in an ICI caking test apparatus5 in which 350 g of fertilizer was compacted in a cylindrical press under pressures of 4-60 psig for between 6 and 72 h. The caking apparatus was airtight and situated in a fertilizer laboratory where the air humidity is maintained below the critical relative humidity of the fertilizer. The fertilizer used in the study was coated in paraffin coating oil, which largely prevents moisture ingress from the surrounding air or moisture diffusion from the core of the fertilizer granules to the surface. The measures described above nullify the effect of relative humidity of surrounding air on the sample. The deformation of the fertilizer cake was measured and voidage calculated continuously by means of a displacement transducer. After a predetermined time the fertilizer agglomerate was then sheared under controlled conditions and the shear pressure noted.
Figure 3. log-log plot of strain versus time in accelerated caking test with variation in storage pressure.
4. Results and Discussion Accelerated Caking and Creep Tests. The characterization of caking propensity by the apparatus developed by Bloom and Sharpe5 has been shown to be an accurate method of determination of the future caking propensity of granular fertilizer and has been used successfully at ICI/IFI for many years. A schematic diagram of the effect on fertilizer granules of this test is illustrated in Figure 1. To verify the plastic creep model, accelerated caking test experiments were conducted over an extended period of time with compression of the sample measured continually by the displacement transducer. In further accelerated caking test experiments the creep mechanism was investigated by variation of the applied stress in a separate set of experiments. A typical experimental plot of displacement (equated to percent strain) versus time is illustrated in Figure 2. The results are comparable with those of previous investigators in that the initial high rate of displacement/creep reduces to a near constant creep rate after a period of time. Thompson3 and other investigators found that this “shrinkage” or creep plot followed a power law relationship with respect to time (eq 2):
creep ) atn
Figure 2. Strain versus time for NPK fertilizer sample during an accelerated caking test.
(2)
The results of these experiments also followed this relationship with linear plots of ln strain versus ln time, as shown in Figure 3 and Table 1. The variation in applied pressure (4, 30, 60 psig) resulted in considerable variation in strain, although the power law relationship still applied. Several researchers have shown that the
Table 1. Constants for the Linearization [Strain ) a(time)n] of log-log Plot of Strain versus Time in Accelerated Caking Test with Variation in Storage Pressure storage pressure (psig)
n
a
r2
60 30 4
0.12 0.18 0.19
1.64 0.13 1.61
0.971 0.998 0.999
Table 2. Rate of Steady State Creep versus Applied Stress for NPK Fertilizer in Accelerated Caking Test storage pressure (psig)
steady-state creep rate (1/min)
60 30 4
0.0155 0.0043 0.0002
exponential constant, n, is an important indicator of fertilizer granule strength and caking propensity. We agree with this hypothesis, but care must be taken when comparing n values from different caking tests, as the results in Table 1 indicate that n is a function of the applied stress. Another analysis of the strain-time plot is the linearization of the latter section of the plot, where an almost constant strain rate is achieved as illustrated in Figure 2 (t ) 1000-4000 linearization results in an r2 value of 0.978). The rate of strain (e) calculated from experiments with variation in applied stress (σ) indicates that e ) f(σ) (see Table 2). This relationship is not linear, but can be modeled with a power relationship (see eq 3).
e ) (const)σ4.14
(3)
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Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999
Figure 4. Plot of force per contact point versus agglomerate strength from Rumpf for NPK fertilizer having a wide distribution of caking propensity.
This result indicates that the creep processes in granular NPK fertilizer under stresses found in accelerated caking tests are due to dislocation glide. Fertilizer stored under normal conditions in storage piles or in palletized bags are under stresses ranging from 4 to 8 psig.1 At these pressures the creep rate is extremely low compared to the accelerated tests with deformation caused by diffusion creep where e ∝ σ. By comparison of the creep rates, accelerated caking tests can be modified by varying applied stress and or time to determine the condition of a fertilizer sample at some future date. An example is shown below. It follows, therefore, that harder granules, less resistant to creep, will remain in good condition for longer periods of time. Example 1 creep rate at 30 psi for fertilizer A time of test creep rate at 4 psi for fertilizer A
3.37 × 10-3/min) 8h 2.40 × 10-7/min)
therefore the condition of the fertilizer after 480 min at 30 psig equates to 3.37 × 10-3/2.40 × 10-7)/8 ) 1755 h (approximately 2.5 months)
Plastic Creep-Capillary Adhesion Model. With plastic creep established as a deformation mechanism in caking tests and under storage conditions, the relationship between creep and caking was then investigated. The relationship between the break strength of the fertilizer cake, i, and the force per unit contact point, F (calculated from eq 1), is illustrated in Figure 4. The relationship between these two parameters is linearized with force per contact point directly proportional to the break strength. This relationship shows an accurate correlation with a regression coefficient of r2 ) 0.949 with fertilizers having a wide distribution in tensile strength and caking propensity. Gillespie and Settineri6 in their work on capillary adhesion proved that an increase in the angle, ψ, which would result in a reduction in capillary pressure, can be caused by an increase in the amount of capillary liquid (in the case of incompressible spheres). In this case, where the granules are compressible and the volume of liquid remains unchanged, an increase in ψ should also take place with compression. However, the liquid in this case is a coating oil which is applied at 0.35% w/w. This results in ψ of approximately 4° for the binding liquid. In the fertilizer caking tests, the maximum strain was calculated at 10%. Although this strain would result in an increase in ψ, it is unlikely that the increase would result in ψ
greater than 10°. From the capillary theory of Gillespie and Settineri,6 an increase in ψ from 4° to 10° would result in a maximum 5% decrease in capillary pressure. From the above discussion the authors conclude that in this case the capillary pressure can be assumed to be constant. As the force per unit contact is the product of capillary pressure and the unit contact area, and as capillary pressure is assumed to be constant, the attractive force between granules is directly proportional to the contact area. Figure 1 illustrates the increase in contact area as pressure is applied to deformable spheres (granules). At t ) 0 and under no external stress the granules (in the caking tester or in storage) are tightly packed, having a voidage of e0. As pressure is applied the spheres deform, causing a displacement difference, d. The contact area between the spheres thus increases, accompanied by a reduction in voidage. In an ideal assembly of rigid, perfectly plastic spheres, compressed uniaxially, Morrison and Richmond7 proposed the following equation 4.
(
A ) 8.45r2 1 -
h D
)
(4)
The rearrangement of this equation using h as strain results in
A ) 4.225rd
(5)
Combining the relationships outlined above we propose the following theory: (1) attractive forces between granules are proportional to agglomerate strength; (2) attractive force is the product of area of contact and capillary pressure; (3) capillary pressure is assumed to be constant for a given system; therefore, the area of contact is proportional to agglomerate strength; (4) the area of contact is proportional to deformation due to plastic creep; (5) therefore, deformation, due to plastic creep, is directly proportional to agglomerate strength; (6) deformation due to plastic creep is proportional to (0 - ); (7) therefore, (0 - ) is proportional to agglomerate strength, leading to the following expression
i ) C(0 - )
(6)
where (0 - ) is a function of the contact area between granules and C is a function of the capillary pressure Equation 6 simplifies the problem of estimating the break strength of an agglomerate, in that once the constant C has been determined experimentally, for a particular grade of fertilizer and fertilizer coating system, the equation will then enable the break strength to be predicted from the change in bulk density alone. The analysis has been used for the agglomeration of granular fertilizer in the accelerated caking test outlined above with the results illustrated in Figure 5 as a plot of experimental and predicted break strengths (i, N mm-2). The plot indicates good correlation for fertilizers varying in caking propensity with a r2 correlation coefficient of >0.95 with Y ) X. It follows therefore that soft weak granules will deform more in storage due to plastic creep and cause caking problems. These results support our previous findings8,9 relating to the compression testing of fertilizer granules, in that fertilizers possessing high compressive strength will resist defor-
Ind. Eng. Chem. Res., Vol. 38, No. 10, 1999 4103 C ) constant (function of capillary pressure) d ) deformation or % strain D ) diameter of sphere (M) e ) creep rate (T-1) F ) bonding force at per pint of contact (M L T-2) i ) tensile strength of agglomerate (M L-1 T-2) n ) power law constant N ) mean coordination number ()π/) r ) mean particle radius (L) X ) particle diameter (L) Greek Symbols ) voidage fraction 0 ) voidage fraction under no external pressure θ ) semiangle subtended by wetted meniscus σ ) stress (M L-1 T-2) ψ ) internal capillary angle6 Figure 5. Experimental versus predicted NPK fertilizer agglomerate strength from eq 6.
mation and caking described by the plastic creepcapillary adhesion model. Conclusions The plastic creep-capillary adhesion model described above can be used to predict the future caking propensity of granular fertilizers. This could prove useful to fertilizer manufacturers where “bag-set”, i.e., a slight caking propensity, is found in otherwise high-quality granular fertilizer. The model assumes that bag-set is entirely due to capillary bonding between granules, rather than crystal bridging, and is based on plastic creep within fertilizer granules when stored under pressure. Acknowledgment This work was funded by Irish Fertilizer Industries and The Industrial Research and Technology Unit for Northern Ireland under grant ST177. Nomenclature a ) linearization constant A ) area of contact between spheres
Literature Cited (1) United Nations Industrial Development Organisation Fertilizer Manual; Development and Transfer of Technology Series No. 13; United Nations: New York, 1980. (2) Rumpf, H. The strength of granules and agglomerates. In Agglomeration, Knepper, W. A., Ed.; Wiley: New York, 1962. (3) Thompson, D. C. Fertiliser caking and its prevention. Proc. Fertilizer Soc. 1972, 125, (4) Narbarro, F. R. N.; de Villiers, H. L. The Physics of Creep; Taylor and Francis: London, 1995. (5) Bloom, M. S.; Sharpe, M. R. British Patent No. 1,005,288, 1963. (6) Gillespie, T.; Settineri, W. J. The effect of capillary liquid on the force of adhesion between spherical solid particles J. Colloid Interface Sci. 1967, 24, 199-202. (7) Morrsion, H. L.; Richmond, O. Sphere flattening with application to the moderate plastic compaction of the regular sphere assemblies. Powder Technol. 1976, 14, 153. (8) Walker, G. M.; Magee, T. R. A.; Holland, C. R.; Ahmad, M. N.; Fox, N.; Moffatt, N. A. Compression testing of granular NPK fertilizers. Nutrient Cycling in Agroecosystems, 1997, 48 3, 231234. (9) Walker, G. M.; Magee, T. R. A.; Holland, C. R.; Ahmad, M. N.; Fox, N.; Moffatt, N. A.; Kells, A. G. Compression testing of granular NPK fertilizers. Ind. Eng. Chem. Res. 1998, 37, 435438.
Received for review March 18, 1999 Revised manuscript received July 13, 1999 Accepted July 13, 1999 IE990204S
