# Development of a model on batch grinding characteristics of raw coal.

IntroductionMost of the industrial and domestic operations need size reduction in one form or the other. Crushing, grinding and cuttings are the primary operations to achieve size reduction. Bilgilli et al [1] estimated that of all the energy generated in the world was utilized for the comminution operation. Murthy et al [2] and Satyanarayana et al [3] explained through studies that, for the grinding needs of small quantities of materials, many types of mills are available but ball mill is generally used. Kim et al [4] studied the kinetic theory to cohesive particle flow. Sato et al [5] showed that for the grinding of large quantities, ball, tube, or rod mills are the mostly used. In comminution studies, like any other studies more efforts are needed to optimize parameters of the study which show influence on the operation. Energy supplied to the mill is utilized to the following purposes.

1. to move the various parts of the mill under loading conditions

2. to overcome the friction at the bearings

3. for achieve size reduction

Present study is aim at the identifying the conditions of the mill which can run at lower energy inputs. Baafi et al [6] extended the work to rock mechanics and proved that major part of the energy is dissipated as heat, vibration loss and noise. It is extremely difficult to evaluate the various terms separately and thus obtaining an accurate energy balance on the comminution process. There has been a great controversy over the most suitable measure of minimum energy required for effective size reduction. In view of this, several runs were conducted to obtain optimum operating conditions. In the present study, experiments were conducted to relate the surface area, energy consumption per unit surface area with following parameters namely 1)Time of milling 2)Ball size 3)Feed size 4)Weight of grinding media. Finally a correlation was proposed.

Experimental Setup

A photograph of experimental setup is shown in the figure I. The working of the ball mill was ordinarily closed at one end and the other end was closed by using cover. The cover in turn is provided with a groove and gasket around the periphery and can be fixed to the mill by means of a suitable nut and bolt mechanism such that material does not leak out of the mill while in operation. The inside surface of the mill is smooth except that it is provided with a baffle of rectangular cross section of dimensions 30cm x 5cm along the length of mill fixed firmly and evenly. Material of balls used is mild steel.

[FIGURE I OMITTED]

The essential dimensions of the mill are shown below in Table I.

The mill is supplied with 12 balls of 4.8cm diameter, 12 balls of 3.8cm diameter, 12 balls of 2.8cm diameter with this arrangement the mill can be charged with the required size of balls, cover placed in position, tightened to leak proof and run for required period of time. Other accessories used for the experiment work include a set of ISS sieves, a watch and an energy meter to read the energy consumption.

Results and Discussions

The main objective of the study is to determine the batch grinding characteristics of coal in a cylindrical horizontal ball mill. To know the individual effects of parameters of the study namely time of grinding, feed size and ball size. The study is also contemplated to determine the effect of other parameters namely feed quantity and weight of balls. Further contemplation is to determine surface area generated, energy consumes and energy consumption per unit surface area generated. It is also proposed to correlate the experimental results in terms of grinding rate factor.

Effect of time on grinding

The effect of time of grinding is studied for three different feed sizes by taking 400 gms of feed at constant ball size of 4.8 cm diameter. A graph is drawn specific surface area versus time of grinding for different feed sizes and shown as figure II. Feed quantity and Ball weight are maintained at 400gms and 5080gms respectively. The figure reveals that 6 minutes time is sufficient for obtaining the maximum surface area. Further experimentation is done at 6 minutes. It was found that the specific surface area produced increased with increasing time up to certain value. It was observed that higher specific surface area was generated as the feed size decreased. Specific surface of a ground powder reflects energy consumption. Therefore a graph is drawn Energy consumed versus time and shown as in Figure III. Energy consumption increased with increase in time steadily. At any instant of time Energy consumption increased with feed size. Energy consumption per unit surface area (E/S) has increased with increase in time as shown in figure IV. At any instant of time E/S increases with increase in feed size up to a certain value and then showed decreasing tendency.

[FIGURE II OMITTED]

[FIGURE III OMITTED]

[FIGURE IV OMITTED]

Effect of feed size

To study the effect of feed size on the performance of the mill, energy consumption and E/S for various feed quantities of different sizes by keeping time of grinding and charge of the grinding media at constant. The various feed sizes used in the present study were 4.1mm, 3.1mm and 1.3mm using 12 balls of 4.8 cm, 12 balls 0f 3.8 cm, 12 balls of 2.8 cm at a grinding time of 6 minutes. As the feed quantity increases, effectiveness of the grinding decreases. A graph is drawn as specific surface area versus feed quantity with feed size as a parameter and shown in figure V. Feed size is varied from 1.3mm to 4.1mm. Specific surface area increased with increase in feed quantity up to a certain value and there after recorded a decrease. At any feed quantity specific surface area increases with increase in feed size. The increase is large at lower feed quantities but marginal at higher quantities. This was attributed to the increase of the capacity of the mill. As a result comminution by impact was greatly reduced.

[FIGURE V OMITTED]

Figure VI shows the variation of Energy consumption with feed quantity for various feed sizes by keeping other parameters constant. Energy consumption was found to be higher for the larger size of the feed. It was observed that the Energy consumption increases as the feed quantity increases. This was due to the increase of the capacity of the mill.

[FIGURE VI OMITTED]

Figure VII shows the variation of Energy consumption per unit surface area (E/S) with feed quantity used for various feed sizes by keeping other parameters constant. E/S value increases as the feed size increases. It was also observed that the E/S increases as the feed quantity increases but decreases as the feed quantity further increases. It was true for all ball sizes and all the feed sizes investigated.

[FIGURE VII OMITTED]

Effect of ball size

To study the effect of ball size on the specific surface area of the product, energy consumption and the ratio E/S, various balls of sizes 4.8cm and 3.8 cm having the same number of 12 balls were taken.

The effect of ball size is clearly seen from figure VIII .It is plotted as specific surface area versus feed quantity with ball size as parameter. Ball sizes are varied as 4.8 and 3.8cm. Feed size and time are maintained at 4.1mm and 6 minutes respectively. Specific surface area decreased with increase in feed quantity. The decrease is marginal up to 300gms of feed quantity but it is found to fall rapidly thereafter. Indicating the cushioning effect of fines and reduced friction for attrition between balls. Figure IX shows the variation of specific surface area with feed quantity for feed size 3.1mm.

[FIGURE VIII OMITTED]

[FIGURE IX OMITTED]

Energy consumption has direct relationship with specific surface area of the product. Effect of ball size on energy consumption is demonstrated in the figure X as it is plotted as energy consumption versus quantity feed for ball sizes 4.8, 3.8 and 2.8 cm. The figure reveals energy increases with feed quantity. At any feed quantity energy consumption increases with increase in ball size. As the ball size increases weight of grinding media also increases. Because of increase in load of grinding media power consumption was also found increased. Figure XI and figure XII show the variation of specific energy consumption with feed quantity for feed size 3.1mm and 1.3mm respectively.

[FIGURE X OMITTED]

[FIGURE XI OMITTED]

[FIGURE XII OMITTED]

The variation of the energy consumption per specific surface area generated (E/S) with the feed quantity having same feed size of 4.1mm was shown in the figure XIII It was found that the E/S value increases with increase in the ball size. Figure XIV and figure XV show the variation of E/S value with feed quantity for feed sizes 3.1mm and 1.3mm respectively.

[FIGURE XIII OMITTED]

[FIGURE XIV OMITTED]

[FIGURE XV OMITTED]

Effect of grinding media

The effect of grinding media on the specific surface area and E/S was studied using 4.8 cm, 3.8cm and 2.8cm balls keeping the feed quantity constant at 300 gms and time of grinding at 6 minutes. Grinding media will have a strong effect on grinding. Increase in quantity of grinding media offers higher surface area and can be seen from figure XVI. The figure is drawn as specific surface area versus grinding media with feed size as parameter. Specific surface area increases with increase in grinding media. The increase is low for feed size of 4.1mm and that is found at higher feed size values. At any quantity of grinding media, specific surface area increases with the decrease in feed sizes. Figure XVII and figure XVIII showed the variation of specific surface area with the total load of grinding media for different feed sizes using ball size of 3.8cm and 2.8cm respectively.

[FIGURE XVI OMITTED]

[FIGURE XVII OMITTED]

[FIGURE XVIII OMITTED]

Figure XIX was drawn as E/S value versus grinding media using 4.8cm ball size by keeping feed quantity constant for different feed sizes. It was found that the E/S value decreased with increase in load of the grinding media. This was due to the increase in specific surface area generated. This was true for the other sizes of grinding media. Figure XX was drawn for E/S value vs. total load of the grinding media by keeping feed quantity constant for different feed sizes using ball size of 3.8cm

[FIGURE XIX OMITTED]

[FIGURE XX OMITTED]

Model Development

Results generated out of the study were correlated empirically. The valid generalization of the results of the tests, demands that there should be a complete dynamical similarity between the systems. From the present study it was clear that the specific surface of the product significantly varied with the quantity of feed Q, size of balls Bs, and total load of the grinding media QT and time of milling t. Hence the data were correlated in terms of grinding rate factor, (S * [rho] * Dm)/([n.sub.T] * t) and various other variables of the study as was used in earlier studies.

(s[rho][D.sub.m]/[n.sub.T] * t) = f(Q, [Q.sub.T], [B.sub.s], [F.sub.s], [F.sub.s], [P.sub.s], [D.sub.m]) (1)

By making use of dimension analysis based on the method of similitude, the following correlation is obtained. The dimensionless groups were used to correlate data are defined as S[rho][D.sub.m]/[n.sub.T] x t, Q/[Q.sub.T], Bs/Fs, Fs/Ps, Fs/[D.sub.m].

The final relationship obtained for the entire data is as follows:

(S[rho][D.sub.m]/[n.sub.T] * t) = 0.046 * [(Q/[Q.sub.T]).sup.-0.0107] [([B.sub.s]/[F.sub.s]).sup.0.025] [([F.sub.s]/[P.sub.s]).sup.0.942] [([F.sub.s]/[D.sub.m]).sup.-0.929]

Average Deviation = 4.0, Standard Deviation = 10.8

Correlation plot was shown in figure XXI

[FIGURE XXI OMITTED]

Q/QT--Ratio of feed to grinding media in terms of mass units.

Bs/Fs--Ratio of size of grinding media to size of feed in terms of length units.

Fs/Ps--Reduction ratio.

Fs/[D.sub.m]--Ratio of size of feed to diameter of mill in terms of length units.

Conclusions

Effect of time on batch grinding was studied. Effect of feed size, ball size, quantity of charge and ball charge were studied in terms of surface area, energy consumption and energy consumed per specific surface area. Surface area generated increased with time up to 6 minutes and there after showed constant tendency. Surface area generated increased with feed size and ball size. Surface area generated increased with increase in grinding media and decreased with increase in feed quantity. Energy consumption increased with time steadily while energy consumed per specific surface area also exhibited an increasing tendency. Energy consumption increases steeply with increase in quantity. Energy consumption found to be higher for the larger size feed. Energy consumed per specific surface area versus quantity showed S-shaped curve. Energy consumption recorded an increasing tendency with ball size while energy consumption showed a decreasing tendency with grinding media. Energy consumed per specific surface area recorded an increasing tendency with ball size while energy consumed per specific surface area showed a decreasing tendency with grinding media.

A correlation relating dimension less grinding rate factor with other dimension less parameter was presented as

(S[rho][D.sub.m]/[n.sub.T] * t) = 0.046 * [(Q/[Q.sub.T]).sup.-0.0107] [([B.sub.s]/[F.sub.s]).sup.0.025] [([F.sub.s]/[P.sub.s]).sup.0.942] [([F.sub.s]/[D.sub.m]).sup.-0.929]

Average Deviation = 4, Standard Deviation = 10.7

[Y.sub.1] = Correlation Factor = (S[rho][D.sub.m]/[n.sub.T] * t) / ([([B.sub.s]/F.sub.s]).sup.0.025] [([F.sub.s]/[P.sub.s]).sup.0.942] [([F.sub.s]/[D.sub.m]).sup.-0.929])

The study is useful for predicting specific surface area, energy consumption and energy consumed per specific surface area with geometric parameters covered under the study. The data could be used for optimizing grinding parameter of the study.

Nomenclature

Bs = Ball size, cm

Dm = Diameter of the Ball mill, cm,

Dm = Mean size of product, cm.

E = Energy consumption, w-h.

E/S= Energy consumption per specific surface area,(w-h)/(sq.cm/grams).

Fs = Average size of Feed, cm

Ks = Specific surface Factor (6 for spheres)

[n.sub.T] = Speed of the mill, rpm

Q = Quantity of Feed, gm

[Q.sub.T] = Weight of grinding media, gm

[S.sub.P] = Specific surface area generated, [cm.sup.2]/gm

[S.sub.f] = Specific surface area of Feed, [cm.sup.2]/gm

t = time of milling, minutes.

W = Weight of the mill product retained by a sieve, gm

[rho] = Density of feed, gm/[cm.sup.3]

Ps = Mean size of the product, cm.

References

[1] Bilgilli, E., Arastroopour,H. and Bernstein,B., "Pulverisation of Rubber granulates via Solid State Shear Extension(SSSE) Process", Part1; Process concept and characteristics, Powder Technology journal, 2001, 115(3),265-276.

[2] Murthy.V.V.N., Rajendra Prasad.P., and Sarveswara rao.S., "Energy conservation Studies on Batch Grinding of Quartz with ball clay as an additive", 2004.

[3] Satyanarayana, Ch., 2002, "Studies on the grinding kinetics of feldspar", Masters Thesis, Andhra University College of Engineering (A), Andhra University, Visakhapatnam.

[4] Kim, H., and Arastroopour, H., "Extension of kinetic theory to cohesive particle flow", Powder Technology journal, 2002, Vol. 122, Pg: 83-94.

[5] Sato, K., Meguri, N., Shoji, K., Kanemoto, H., Hasegawa, T., and Maruyama, T., Powder Technology journal, Volume 86, Issue 3. 1996, Pages 275-283.

[6] Baafi, E. Y., and Ramani, R. V., International Journal of Rock Mechanics and Mining Science & Geomechanics, 1979, Volume 16, Issue 2.

B. Niranjana Rao (1) *, M. Gangadhar (1), V. Nageswara Rao (2) and P. Rajendra Prasad (2)

(1) Department of Chemical Engineering, GMRIT-Rajam, AndhraPradesh-532127, India

(2) Department of Chemical Engineering, Andhra University College of Engineering(A), Andhra University, Visakhapatnam-530 003, Andhra Pradesh, India

* E-mail: niranjohnny@yahoo.co.in

Table I Inside Diameter: 30 cm Weight of the balls Inside length: 30cm 4.8cm diameter ball: 480 grams Thickness of mill wall: 0.5cm 3.8cm diameter ball: 295grams Theoretical critical speed 2.8cm diameter ball: 95 grams of the mill: 30 rpm Groove dimensions: 25cm X 10cm

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Author: | Rao, B. Niranjana; Gangadhar, M.; Rao, V. Nageswara; Prasad, P. Rajendra |
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Publication: | International Journal of Applied Environmental Sciences |

Article Type: | Report |

Date: | Dec 1, 2010 |

Words: | 2786 |

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