R, r
gas constant, kcal/kmol-”K distance from center, inside a catalyst particle of spherical shape, m ,S = external surface of catalyst particles, per volume unit, m2/m3 T = temp, OK I- = overall heat transfer coefficient in nonadiabatic layer, kcal/m2-hr-”K V = reaction volume, m3 11- = flow rate, kmol/hr X = molar fraction Y = molar ratio y , 5 = integration variables @ = void fraction of catalyst particles p b = bulk density of the catalytic bed, kg/m3 CAT = density of catalyst particles, kg/ma = =
literature Cited
Cappelli, A,, Dente, AI., Chzm. Ind. (Milan), 47, 1068 (1965). Carberry, J. J., AIChE J., 7 , 350 (1961). Clayton, J. O., Gianque, W. F., J . Amer. Chem. SOC.,54,2610 (1932). Dente, >I., Biardi, G;: Ranzi, E., Ing. Chzm. Ital., 5, 122 (1969). Hamming, It. W., Sumerical Methods for Scientists and Engineers,’’ p 352, NcGraw-Hill, New York, S.Y. (1962). Ragatz, R. A., “Chemical Process Hougen, 0. A,, Watson, K. M., Principles,” Vol. 2, p 593, Wiley, New York, X.Y. (1959). Kramers, H., Westerterp, K. R., “Elements of Chemical Reactor Design and Operation,” p 161, Chapman and Hall Ltd., London, England (1963). ru’atta, G., Pino, P., Mazzanti, G., Pasquon, I., Cham. Ind. (Milan), 35, 705 (1953). Natta, G ,“Catalysis,” P. H. Emmet, Ed., Vol. 3, p 345, Reinhold, New York, S . Y . (1955). n’atta, G., Nazzanti, G., Pasquon, I., Chim. Ind. (Milan), 37, 1015 i l S 6 . i ~
Newtonj-R., Ind. Eng. Chem., 27, 302 (1935). Pasquon, I., D a t e , ll.,J . Catal., 1, 508 (1962). Lapidus, L., Digital Computation for Chemical Engineers,” p 88, McGraw-Hill, Sew York, S . Y . (1962). Weeler, A., Arlnan. Catal., 3 , 249 (1957). Weiss, P., Prater, C., {hid.,6, 143 (1954). Weiss, P., Prater, C., zhid., 9, 957 (1957). RECEIVED for review September 24, 1970 ACCEPTEDOctober 28, 1971
SUBSCRIPTS
i G
= =
component i gas inside tubes in nonadiabatic layer
SUPERSCRIPTS
0
=
inlet conditions
s = external surface of catalyst particles
Influence of Adsorption on Industrial Grinding Friedrich Wilhelm Locher and Hans Michael v. Seebach Forschungsinstitut der Zementindustrie, Diisseldorf, Germany
In grinding of cements, organic liquids are used as grinding aids. In general it is supposed that they act as antiagglomerants. O n the other hand, various investigations have revealed that plastic deformation is influenced by adsorption of organic molecules. To find whether this effect would be utilized in cement grinding, abrasion and grinding tests were carried out with cement clinker and other materials in the presence of vapors. Besides, the tensile strength of clinker powder ground in various vapors and the adsorption behavior were measured. The results reveal that breakage of brittle material in ball mills is not influenced by adsorption owing to the fact that plastic deformation rarely occurs in such mills. Accordingly, the effectiveness of vapor grinding aids is limited to reduction of adhesion forces in the material. The tendency of the clinker particles to agglomerate is reduced only by vapors chemisorbed on the clinker surface.
G r i n d i n g represents a n important cost factor in the production of cement. I n Germany the cost of energy expenditure of electric energy and of fuel energy amouiits to approximately 50% of the production costs. On the average, about 7% of this amount is required for grinding of the raw material, 30y0 for burning of the clinker, 2% for dust removal from the furnace waste gases, the transport routes and the mills, and 11% for grinding of the cement clinker with a n addition of 6 4 % gypsum to cement. There are, therefore, continuing efforts to reduce the costs of grinding by improving the grinding processes. A possibility of promoting the grinding process is provided by the use of organic liquids as grinding aids. These are added to the material in amounts of up to 0.1%. By this means, with the consumption of electric energy per unit of time remaining constant, the capacity of the mill is increased, and consequeiitly the utilization of the energy, that is to say, the 190 Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972
amount of the new surface produced per unit of work, is greater. Grinding aids thus favorably affect the grinding process. Ziegler (1956) was the first to study the principles of the use of vapor grinding aids in the grinding of cement. Esperimenting in a small laboratory vibration mill, he established that the vapors of ryater and acetone are particularly effective. continuation of these tests revealed that the vapors of ethylene glycol, propylene glycol, and butylene glycol are effective to a considerably higher degree and that with these vapors the capacity of technical mills can also be increased by up to 4070. Since then these materials, as well as triethanolamine, have been used for the grinding of cement. The relative increase in capacity obtained is greater, as the cement is ground finer. For this reason, grinding aids are a t present only used in the production of the finer ground cements 15 ith high early strength, which, however, only amounts
t o about 10-157G of the total cement production in Germany.
It is a n important question, therefore, whether and under what conditions grinding aids can also be economically used with coarser ground cements. To this end, investigations have been carried out to obtain information on the mode of action of this type of grinding aid. Basic Principles
Background. If a solid material is mechanically stressed it is deformed. If the elastic region is exceeded in the process, permanent' deformations take place; plastic deformations occurring in ductile materials fracture in brittle materials. Plastic deformation is caused by slip processes which begin when the critical shear stress is exceeded and then run p i marily in t'he crystals along definite planes of the crystal lattice. The plast'ic deformation is first recognizable by dislocations-Le., by slip b y definite amounts that are typical for the crystal lattice concerned, and leads in the extreme case to a slip fracture and disintegration of the crystal. An ideally brittle solid cannot undergo plastic deformation. It fractures as sooii as tensile stress caused by the elastic deformation exceeds the tensile strength. I n this case, the fracture always starts from pre-existing cracks or defects. I n the grinding of real solid materials it is necessary to consider t'he pos4bility that brittle fracture is preceded by plastic deformation. The extent of the plastic deformation depends not only on the kind of material to be ground but also on the duration of the stress. The more slowly the stress is applied aiid the longer its action lasts, the greater is the extent of deformation. Ciider the stress coiiditions of technical grinding the load times are less than 10-l see. It is expected, therefore, that with materials like cement clinker which usually break by britt'le fracture, practically no plastic deformations take place in industrial grinding. For d r y grinding, not only the deformation and fract'ure behavior of the solid material a r e important, but also the behavior of the fine material in the mill. The finer a solid material is ground, the greater is its tendency to form agglomerates and to adhere to the balls and to the liners. This greatly increases the difficulty of further grinding. Accordingly, the behavior of a solid material in grinding is determined by three overlapping processes, namely, plastic deformation, brittle fracture of single particles, and formation of particle agglomerates. I n principle, therefore, it can be postulated that the vapors of the organic liquids which are used as grinding aids may influence one or more of these processes. Influence of Adsorption on Plastic Deformation. I n t h e opinion of v. Eiigelhardt and Haussuhl (1965) the Vickers hardness may be taken as a criterion for the plastic deformability. Various reports are available on the influence of enviroiimeiit on the hardness of some inorganic noiimetallic solid materials. The influence of n-ater on the hardness of t'itaiiiuin carbide, established by Kestbrook and Jorgensen (1968) is show1 in Figure 1. (Xll figures published with perrnksioii of Hauverlag GmbH, Kiesbaden.) The hardness in an ailhydrous eiivironineiit does not depeiid on the duration of the load and, on the other hand, it decreases in a wet environmeiit with an increasing duration of load. Further observutioiih were made by Kestbrook and Jorgensen (1968) and 3150 by Kestn-ood (1966, 1968) aiid ST'estwood and Goldheim (1970) oil the influence of environment on .ingle crystals of silver chloride, lithium fluoride, fluorspar, periclase, and corundum in investigations carried out in water, hydrous salt solutions, and various organic liquids aiid liquid mixtures.
I
2 700
1
2000 1
I
5
7
70
50
700 duraiion of loadlns
1
500
Figure 1. Microhardness of titanium carbide TIC as function of duration of load, Westbrook and Jorgensen (1 965)
It was shop\-nthat, environment can also increase the hardness, as, for instance, in fluorspar and periclase (Westwood and Goldheim, 1970). According to them, the change in the hardness of ionic crystals results from the fact that electron transfer takes place between the adsorbed molecules and the surface defect structure of the crystalline solid. Influence of Adsorption on Strength. -in ideally brittle solid when mechanically stressed only undergoes elastic deformation aiid fractures as soon as the stress thus caused exceeds its tensile strength. The fracture always starts from existing cracks or from defects. According to Rumpf (1959), on the basis of the physical fracture theory of Griffith, the following equation is valid for the tensile strength F , of a brittle solid : F,
=
d4 E?/&
(1)
where F , is the tensile strength of the solid, E is the modulus of elasticiby, y is the surface energy, and 1, is the crack length. As the surface energy decreases when molecules are adsorbed a t the surface, the tensile strength must also decrease. The variation in the surface energy due to adsorption results from the integration of the Gibbs adsorption equat'ion: dy =
RTpd In p
(2)
where R is the gas constant, T is the absolute temperature, i3 is the number of adsorbed moles per surface unit, and p is t h e equilibrium pressure. p can be replaced from
p
=
(3)
K/MO,
where K is the adsorbed mass of sorbate per mass unit of adsorbent, X is the molecular weight of sorbat'e, and 0, is the specific surface of adsorbent. Thus, by
=
(RT/VO,)
SP
xd
111
0
p
(4)
In the case of a n ideally brittle solid, the decrease in surface energy caused by adsorption can be calculated from Equation 4 and, consequeiitly, t.he decrease in strength from Equation 1. Similar calculations are in the literature for the adsorption of vapors of organic liquids and of steam on quartz and baryte (Boyd and Livingston, 1942) and for the adsorption of steam 011 a- and y--11203 (Hardie aiid Petch, 1965). .kcording to these figures, the surface energy of the indicated solids can only be decreased by a maximum of 250 erg/cm2. According to I-. Seebach (1969), adsorption of cyclohexane on cement clinker gives similar values. As the surface energy of anhyInd. Eng. Chem. Process Des. Develop., Vol.
11, No. 2, 1972
191
drous silicates lies in the range betffeen 500 and 4000 erg/cm* (Hardie and Pet,ch, 1965; Surse, 1968; Hammond and Ravitz, 1963), this would be equivalent to a decrease in the surface energy by a maximum of 30% and in the tensile strength by a maximum of 20%. However, ideally brittle fracture behavior cannot be assumed even in the case of the so-called brittle materials. Plastic deformat'ions will play a part, both in the formation of the Griffith cracks from which the brittle fractures start, and also in the progress of the fractures. This applies also to the investigations on the influence of steam and of vapors of some organic liquids on the tensile strength of various glasses (Hammond and Ravitz, 1963; Irwin, 1966; Schoiiert et al., 1969; Wiederhorn, 1967) and of the single crystals of cy- and y-A1203 (Hardie and Petch, 1965). I n every case in which the velocity of the load increase was taken into account as a factor, the result was that with a very rapid increase of the load the adsorbed materials no longer influence the strength. I n the case of slow fractures, on the other hand, a decrease of strength was established which, however, did not always correspond to the results from Equation 1. According to v, Engelhardt and Haussuhl (1965), the resistance to abrasion can also be considered as a relative crit'erion for the strength. During abrasion, the particles of the abrada n t produce many little fractures which split up the surface areas into small fragments that' ultimately separate from the solid. I n this kind of stress, also, plastic deformations may play a by no means negligible role. The abrasion tests in liquids showed that the resistance to abrasion largely depends on environment and that it was always decreased by an addition of a polar organic compound (e.g., alcohol, acids, amines) to a nonpolar abrasive fluid (e.g., benzene, xylene). I n view of these test results, it is assumed by v. Engelhardt and Haussiihl (1965) that it is less the plastic properties of the crystal that are influericed by enrironment but rather the strength, as only the latter depends essentially on the surface energy of the solid material. A different conclusion from this, however, was reached by Robinson (1967) from teats with calcium carbonate which '\vas saturated with various brines. The behavior of the calcium carbonate under three-dimensional compressive stress and the results of drilling tests suggested that the slip fracture-Le., the plastic deformation, can be aided or retarded by various liquids, but not the brit,tle fracture. This is in accordance with the results of drilling experiments carried out by Kestxood and Goldheim (1970). .Us0 in line with this is the fact' established by Irwin (1966) and b y Schonert et al. (1969) that with higher stress velocities steam no longer promotes the fracture of glass. With increasing speed of stress application, the relative effect of plastic deformation that can be influenced by environment is decreased while the relative effect of the brittle material properties that cannot be influenced is increased. Influence of Adsorption on Agglomeration. The adhesion of the part'icles of fine ground material to each other and to balls and liners is caused by Van der Waals and electrostatic forces of the newly created surface (ICrupp, 1967; Pietsch and Rumpf, 1967; Rumpf, 1958). Practical experience and the work of Schiieider (1969) would appear to suggest that the vapors of the organic liquids used as grinding aids considerably reduce the forces of adhesion. Thus the tendency to formation of agglomerates aiid accretions is decreased aiid flowability is increased (Fischer, 1967). I n this way grinding is promoted, aiid the separation of the adequately fine particles from the material is facilitated. 192
Ind. Eng. Chem. Process Des. Develop., Vol. l l , No. 2, 1972
vapor
dry c/:o
air drying
vu:, whting ?ontainws Figure 2. Apparatus for abrasion tests in various vapors, v. Eichborn ( 1 968)
fime of abrasion in min
Figure 3. Rate of abrasion during abrasion of quartz in various vapors, v. Eichborn ( 1 970)
Conclusion. I t has thus been shown in the existing literature that adsorption layers primarily influence plastic deformation and correspondingly the slip fracture. The longer the action of the deforming force lasts, the more clearly evident is this effect. The influence on the brittle fracture has not yet been entirely clarified. It would appear, however, that an influence of the adsorption layers has always been established only in such investigations in which plastic processes were important. It n-ould be reasonable to conclude, therefore, that the brittle fracture behavior cannot be influenced by the adsorption of foreign molecules. By comparison, however, adsorption layers reduce the forces of adhesion in the ground material to a considerable degree. They thus prevent the formation of agglomerates and layers in the mill and in this way promote the grinding process. The reduction of strength by adsorbed materials is generally termed the Rebinder effect (Rebinder and Kalinkovskaya, 1932), aiid the cause was originally assumed to be the decrease of surface energy. This term would accordingly only be applicable to the effect on the brittle fracture. It is also used, however, by Kestwood (1966, 1968) and Westwood and Goldheim (1970) for the influencing of the plastic deformation. As a n exact separation of the two processes is seldom possible, it would seem reasonable to apply the term Rebinder effect generally to the influencing of the fracture behavior and of the plastic deformation of solids by adsorption layers. Experiments and Results
Aim of Investigations. I n the industrial grinding of cement clinker it is expected that brittle fracture is the pri-
mary process. The use of vapor grinding aids might thus also be of economic advantage for coarser ground cement if it facilitated brittle fracture, whereas it would be restricted to the finer ground cement if it' were only possible to influence the forces of adhesion bet'ween small part'icles. T o clarify this, work was undertaken by v. Eichborn (1968, 1970) with the financial support of the Arbeitsgemeinschaft Industrieller Forschungsvereiiiigungeii e.V. (Community of Industrial Research Associations) to investigate the behavior of cement clinker, quartz, aiid steatite during abrasion in saturated vapors of various liquids. This type of mechanical treatment was chosen because, in the opinion of v. Engelhardt and Haussiihl (1965), it, was to be expect'ed that strength was of prime iniportaiice and that no essential part Tvas played by agglomeration processes. I n a second series of tests, v. Seebach (1969) studied the influence of vapor grinding aids on the grinding behavior of cement clinker in a small ball mill. The stress conditions occurring here are about equivalent t o those in technical mills. They were chosen to permit direct conclusions to be drawn from the laboratory tests for comniercial scale cement grinding. The third series of tests, which were also carried out by v. Seebach (1969), dealt with the influence of grinding aids on the forces of adhesion between particles of the cement powders. I n connection with this study, t h e adsorption of the vapors i\-as also investigated to permit a n interpretation of the differences in effectiveness established in the measurements of the adhesive forces. Abrasion Tests. For t h e abrasion tests, a twin centrifugal mill was used. This mill consists of tn-o cont'ainers each of which is moving 011 a circle without rotating arouiid its own axis. I n the containers, definite vapor atmospheres could be maintained. The scheme of the testing arrangement is shon-n in Figure 2. I n the containers 6-10-mm spheres of cement clinker, quart,z, or st,ea,titewas centrifuged a3 the material to be abraded while corundum was used as abrasive. The progress of abrasion was taken as a criterion of the strength in the various vapors-Le., the weight loss per unit of time; this was determined by JTeighing the abraded spheres after sieving out the abrasive. Figure 3 shows the rate of abrasion vs. the time of abrasion determined from abrasion experiments on quartz in dry air and in the vapors of water, benzene, and acetone. The figure s h o w that the rate is always greater, and the abrasive strength accordingly always lower, in the vapors than in dry air. I n the dipolar vapors of 11-aterand acetolie and also iii d r y air, the velocity of abrasion is constant for up to 10 min and only then slows domi, while in the nonpolar benzene vapor it decreases immediately. Electron microscopic investigations showed that after n short period of abrasion, very small particles were already adhering to the surface of the spheres owing to their rougliness; they could not be removed by sieving. This means that the abrasion process is influenced by the adhering particles and therefore the rate of abrasion, shown in Figure 3, is a superposition of abrasion and re-adhering of small particles t o the spheres. For this reason: in further esperiments with steatite, the spheres TTere washed with water in a n ultrasonic bath after sieving. The results of the tests carried out in tliimanlier in dry air and in acetone vapor are shon-n in Figure 4. Uot'h for abrasion in acetone vapor aiid for abrasioii in dry air, a considerably greater rate of abrasion as obtaiued than when dry sieving only was used. In these tests, too, the rate of abrasion decreased with increasing abrasion time, though clearly less in acetone vapor than in dry air. Therefore, it must be assumed that immediately after abrasion starts,
Y 06087
2
Y
6 8 70
20
Figure 4. Rate of abrasion of steatite in acetone vapor, v. Eichborn ( 1 970)
7
Figure 5. Ball mill for grinding of cement clinker in various vapors
small particles begin to adhere to the clean, Le., dtrasonicbathed surface thus reducing the rate of abrasion. The fact that the rate of abrasion in acetone vapor is still greater than in dry air d o w i to abrasion times of about 1 niin &show$that the acetone vapor primarily prevents adhesion of the fine particles to the rough surface of the spheres being abraded. Hence the vapor has a similar effect during the ahrasion process as the washing with ultrasonic treatmelit after the abrasion. I t very short abrasion times of 0.75 miii or less, n-hen interference of the abrasion process by small particles can be neglected, the acetone vapor does not promote the abrasion. -\ccordingly, the promotive action of adsorbed vapors in abrasion of solids must be attributed principally to the fact that they prevent the adhesion of small abraded part'icles t o the surface of the ground material and of the abradant. aliiy effect on the hardness or strength of the solid due to adsorption of the acetone vapor, if present a t all, is very sinal1 a i d caiiiiot be confirmed for this kind of niechaiiical treatment. Grinding Tests. T h e grinding tests w r e carricd oiit n-it11 cement clinker in a ball mill under similar inecliaiiical conditions to those present in technical millq. Figure 5 .slion.s a diagram of the testing apparat,us. It, consisted of a griritliiig tube and a vaporizer which rail on a roller-bench and could be coiiriected with each other by a needle valve aiid a ballcock. The central tube was attached through a rotary flange to a vacuum equipment. The grinding tube and the vaporizer could be heated iiidependently of each other to different temperatures which were controlled by re eters. I n this way it was possible to adjuat temperature and Ind. Eng. Chem. Process Des. Develop,, Vol. 1 1,
No. 2, 1972
193
in Figure 6 for t'he size fraction 1.25 t'o 1.41 mm and in Figure 7 for the size fraction 0.125 to 0.160 mm. According to Nempel (1965) and Schulz (1968), the grinding rate in a ball mill can be described by the equation AG/At = -k
7
IO 7
702 -
703
mass of clinker G in g Figure 6. Dependence of grinding rate on mass of material in grinding of clinker fraction 1.25-1.41 mm
I
M7 702 mass of clinker Ging
703
Figure 7. Dependence of grinding rate on mass of material in grinding of clinker fraction 0.125-0.1 60 mm
vapor pressure in the grinding tube independently of each other. Testing and heating currents were transmitted over slip rings. The grinding tube is 200 mm long and 150 mm in diameter. It was filled with 361 steel balls of 18-mm diameter. The speed of the mill was 85 rpm. The energy needed to break a particle was used to describe the grinding and fracture behavior in different atmospheres of the ground material. This factor is called apparent fract'ure energy. It was determined for both the two fractions 1.25 to 1.41 mm aiid 0.125 to 0.160 mm from the grinding rates according to the method described by Xempel (1964, 1965). This method is based 011 the fact t'hat the grinding rate depends on the strength of the material to be grouiid and on the average energy transferred from the ball charge to the material. The grinding rate was calculated from the mass of the ground material and the grinding time. Material was defined as ground when it became smaller than the initial fractionLe., when it passed the 1.25-mm and the 0.125-mni sieve, respectively. The grinding rate AG/At was plotted vs. the average mass (? of initial size fraction in the mill before and after each grinding experiment. As grinding times were very short (10-50 sec), and, accordingly, the portion of ground nearly mat'erial did not exceed 20%) the average mass equals the total mass, G, of material. The dependence of the grinding rate AG/At on the mass of clinker a is demonstrated
e
194 Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972
'
en
15)
which is formally equivalent to the equation by which the kinetics of the change in concentration of a homogeneous chemical reaction can be described. Therefore, n represents the order of the disappearance of the feed size in dependence on the average mass of feed size in the mill, and k represents the rate constant. Bot'h these values can be calculated from the curves shown in Figures 6 and 7 . During the grinding experiments, all geometric values of the mill were kept constant by using hollow steel balls with the same diameter but with different masses. In this way, only the average energy transferred from the balls t o the material was changed. Therefore the change of k-values, shown in Figures 6 and 7 , are due to changes of masses of the balls-Le., of energy transferred from the balls t'o the materiaI. From these results, the minimum mass of balls can be calculated a t which grinding-Le., fracturing begins. The energy which under these conditiolis is transferred to the material equals the apparent' fracture energy of the material. This energy can be calculat'ed from an equation found empirically by Mempel (1965) and Schulz (1968). In this manlier, t'he apparent, fracture energy of the two clinker fractions ITas determined in dry air a t various temperatures between 20" and 12OoC, in vacuum (5 X lo-* torr), and in the vapors of water, cyclohexane, ethylene glycol, and n-bubylamine a t various relative vapor pressures. These test,s gave a t 20°C a mass-related apparent fracture energy of 9.0 =t 1 J/g for the fraction 1.25-1.41 mm and of 14.3 i. 3 J j g for the fraction 0.125-0.160 mm in dry air. These values of apparent fracture energy result from the mechanical treatment of the particles under ball milling conditions. The result of the clinker fraction 1.25-1.41 mni is also in agreement with the results of fracture tests carried out with the impact apparatus described by Hildinger (1968) at' a fracture probabilit,y of 90-95yo. The coefficient of variation of repeated griiiding experiments was 15%. Wit,hin these limits no influence of temperature, pressure, or environmeiit on the apparent fracture energy could be detected. In addition, the newly created surface was calculated from the particle size distributions of the material that passed the 1.25-mm sieve aiid the 0.125-mm sieve, respectively, after being ground in the various vapors. The newly created surface was the same after the grinding of a fraction in dry air as after the grinding of the fraction in cyclohexane, ethylene glycol, or butylamine vapors. According to this result, the fragments of the clinker particles which occur in grinding in the ball mill in air or in various vapors are, on t'he average, of approximately the same size. It, emerges from the grinding tests, therefore, that fracture of material like cement clinker is not facilitated by vapor grinding aids. Similar conclusions were also reached by Iiiesskalt and Dahlhoff (1965) who, in interpreting this finding in wet grinding, stated that with the stresses occurring in vibration mills, the fracture velocities are considerably greater than t,he spreading velocities of the adsorption layer,^. -ICcording to this aiid to the results of Westwood and Goldheim (19iO), a reduction in strength by adsorption layers is only possible for materials in n-hich plastic deformations pia? a major role in the fracture process. Furthermore, a necessary condition is that the deforming force is effective for a con-
Figure E. Apparatus for measuring tensile strength of powders siderable length of time. I n ball mills, therefore, due t o the very short duration of the stress, even with plastic deformable materials a strength-reducing effect of the vapor grinding aids is unlikely. An improvement of the grinding effect can thus only be effected by a reduction of the forces of adhesion between the particles of the ground material. Measurement of Forces of Adhesion and of Vapor Adsorption. The forces of adhesion between the particles of cement clinker were measured by the tensile strength of a loose powder bulk. For this purpose, the device shown in the diagram Figure 8 was used similar t o the apparatus described by Ashton et al. (1964) and by Farley and Valentin (1968). The cylindrical powder cell, with a diameter of 49.5 mm and a height of 15 mm, filled homogeneously with the powder t o be investigated, was divided in the middle. With the help of a calibrated spring and a geared motor, the mobile half was subjected to a gradually increasing force. Following the failure of the powder bed, the tractive force was recorded and the bulk density of the powder bed determined. The effect of ethylene glycol vapor on the forces of adhesion of clmker powder is shown in Figure 9 and t h a t of butylamine vapor in Figure 10. The figures show the connection between tensile strength and bulk density for clinker powders of similar particle size distributions ground a t 120OC in dry air and also a t various relative vapor pressures. The dependence 'of the adhesive force on the bulk density is about linear in the investigated range, thoug:h this does not quite correspond to the correlation indicated by Pietsch and Rumpf (1967). The figures show t h a t the ethylene glycol and butylamine w p o r s clearly reduce the tensile strength of the clinker powder and thus the adhesive forces between the clinker particles. The effect of relative vapor pressure is pronounced with the ethylene glycol vapor, hut with the butylamine vapor a relative vapor pressure p / p . of 0.1 greatly reduces the adhesive forces; then increase of the vapor pressure has only slight additional effect. On the other hand, the tensile strengths of clinker powders are not much changed by the vapors of cyclohexane and of water. For the interpretation of these differences, adsorption measurements with these vapors were carried out a t the same temperatures a t which the clinker powders were ground for the tensile strength measurements. To minimize preadscrption, the clinker powders for the adsorption studies were ground in a vacuum (5 X 10-2 torr) and then, as quickly as possible, transferred to the adsorption apparatus. After being
bulk density ps in &m3
Figure 9. Influence of ethylene glycol vapor on tensile strength of clinker powders
Figure 10. Influence of butylamine vapor on tensile strength of clinker powders transferred the powder was degassed again for 12 hr a t 98'C and 5 X 10-6 torr. For the adsorption measurements which were carried out with a recording electromagnetic microbalance the carrier gas method was used. Therefore, after degassing, the apparatus was filled with N, t o atmospheric pressure. Then a stream of Nz with addition of definite amounts of vapor was led through the apparatus. For desorption the system was evacuated to 10-4 torr again. The adsorption measurements revealed t h a t the cyclohexane is adsorbed reversibly and that, with a certain vapor pressure, the adsorbed amount decreased with a rising temperature. Ethylene glycol and butylamine, on the other hand, a r e deposited irreversibly-i.e., they are chemisorbed, and the amount is increased with increasing temperature. I n connecInd. Eng. Chem. Pmcerr De%Develop., Vel. 11, No. 2, 1972
195
For the economic use of grinding aids, therefore, it must be concluded that they should be distributed in the mill as far a s possible where the grinding process is particularly obstructed by the adhesive forces of the material. This is primarily the case in the fine grinding compartment of a tube mill grinding clinker. From the investigations of v. Seebach (1969), however, the influence of t'he adhesive forces can be confirmed in the case of cement clinker, even in lower finenesses, that is, in specific surface areas of about 1000 cm2/g (Blaine). I n such cases, therefore, the use of grinding aids can also be economically acceptable in these ranges of fineness. Summary
Figure 1 1. Adsorption of ethylene glycol vapor and butylamine vapor to clinker powder and their influence on tensile strength a t constant bulk density
tion with the measurements of the forces of adhesion, therefore, the conclusion is reached that' the adhesive forces of a cement clinker powder are only reduced by those vapors chemisorbed on the surface. The relationship bet'ween the quantity of vapor chemisorbed and the reduction of the adhesive forces is illustrated in Figure 11, in which the adsorption isot'herms of ethylene glycol and butylamine and the tensile strengths of the clinker powders with constant bulk density (for two bulk densities) a r e shown as a function of the relative vapor pressure. A close relationship exists between the reduction of tensile strength and the amount of the chemisorbed vapor. The greater the amount of chemisorbed ethylene glycol, the lower is the tensile strength. I n the case of butylamine vapor, there is no further change in the tensile strength with relat'ive vapor pre2.-cures p / p s above 0.1, since the aniouiit of chemisorbed butylamine also remains constant,. This relationship between chemisorption and forces of adhesion between particles is not valid in the grinding of clinker in the presence of steam, as hydrabe phases are formed which interlock with each other and thus increase the forces of adhesion between particles. Conclusions for Industrial Grinding in Ball Mills
The investigations have revealed that t'he fracturing of brittle materials cannot be promoted by organic vapor grinding aids. From the literature, it is concluded that the grinding of materials in which plastic deformation plays a major part in the fracture can be influenced by environment. Plast'ic deformation, however, is unlikely when short, durations of stress occur a s found in ball mills. Therefore, it is expected that even the fracturing of ductile materials in ball mills cannot be influenced by vapor grinding aids. For the improvement of the grinding effect of mills, therefore, only such materials can be considered \$-hose vapors reduce the forces of adhesion between the small particles of the ground material; that is t o say, materials that are chemically bound to the surface of the particles. 196 Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972
The finer t'he ground material is, the better is the promotion of dry grinding by grinding aids. It is assumed, therefore, bhat their effectiveness must be primarily attributed to their properties of dispersion. I n various investigations it was proved, however, that plast'ic deformation is facilitated by adsorption layers. This finding is not generally applicable to the fracturing of brittle materials, especially in view of the high stress velocities in mills. I n order to clarify these relationships, abrasion and grinding tests lvere carried out' with cement clinker and other materials in various vapors, and measurements were taken of adhesive forces and adsorption with clinker powders. The abrasion tests showed that adsorbed vapors promote the abrasion process. Their effectiveness must be primarily attributed to the fact that they prevent' the adhesion of the abraded particles to the ground material and to the abrasive. Grinding tests carried out with cement clinker in a ball mill showed that the brittle fracture is not influenced to a measurable extent by the vapors of the organic liquids. By the measurement of the tensile strength of a loose bulk of ground cement clinker accompanied by adsorption measurements, it was proved that the forces of adhesion between the clinker part,icles could only be reduced by those vapors that are chemisorbed on t,heclinker surface. The tests have led t o the conclusion that adsorption layers do not facilitate brittle fracture. The grinding of materials in which plastic deformations play a major part in the fracture can be influenced by environment; hon-ever, as this effect only becomes evident with a long duration of stress and since stresses are applied rapidly in ball mills, a strength-reducing effect of adsorbed vapors is not to be expected in ball mills, even in the case of plastic deformable materials. Accordingly, the effectiveness of vapor griiidiiig aids in industrial grinding in ball mills is limited to the reduetion of the adhesive forces in the material and consequently to the prevention of the formation of agglomerates and coat'ings on the balls and liners. literature Cited
Aahton, 11,I),, Farley, R., Valentin, F. H. H., J . Sci.Instru~n., 41, 763-.i (1964).
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Eichborri, J. L. v., Chcm. Ztg. Chem. I p p . , 92, 803-13 (1968). Eichborn, J. L. v., unpublished (1970). Engelhardt, FV. v., Hauxsuhl, S.,Fortschr. Mineralog., 42, j-49 (1965).
Farley, R . , Valentin, F. H. H., Powder Techno(., 1, 322-34 (1968). Fischer, W., Zem. Kalk,Gips, 20, 138-9 (1967). Hammond, AI. L., Ravitz, S.F., J . dmer. Ceram. Soc., 46,329-32 (1963).
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Hildinger, P., PhU thesis, Univerbitat Karlsruhe (T.H.), Karlsruhe, Germany, 1968. Irwin. (2..U.S. Saval Research I,aboratories, Memorandum Rept. 1678, 1966.
Kiesskalt, S.. Dahlhoff, B., Chem. Ing. Tech., 37, 277-83 (196,5). Krupp, H., Adcun. Colloid Interface Sci., 1, 111-239 (1967). bIempel, G., PhD thesis, T. 11. Munchen, Munchen, Germany, 1964. Mempel, G., Chem. Ing. Ti,ch., 37, 933-9, 1146-53, 1259-63 ilQ6.i) ,_” -- ,.
Surse, R. W., Proc. 9th Coni. of Silicate Ind., pp 129-41, Publ. House Hung:. Acad. of Science, Budapest, Hiingaria, 1968. Pietsch, W., Rumpf, H., Chcm. Ing. Tech., 39, 885-93 (1967). Rebinder, P. A Kalinkovskaya, S . A , , J . Tc ch. Phys. (U.S.S.R.), 2. 726-.55 113321 E n d . Trana. Robinson, L:j1:, j.8;. Petrol. Eng., 7, 2 9 5 4 (1967). Rumpf, H., Chem. Ing. Tech., 30, 144-58 (19d8). Rumpf, H., ibhd., 31, 697-70.5 (1959). Schneider, H., Zein. Kalk Gips, 22, 193-201 (1969). Schonert. K.. Umhauer. 11.. Klemm. \T., “The influence of temperature and environment o n the slow crack propagation in elass.” Presented at 2nd Conference on Fracture. Briehton. Eniland, April 16-18, 1969. Schulz, St., PhD thesis, T. H. Munchen, Munchen, Germany, 1968. .)
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Seebach, H. 11. v., “Schriftenreihe der Zernentindustrie,” No. 35, Beton-Verlag, Dusseldorf, Germany, 1969. Seebach, H. l f . v., Zem. KaIk Gips, 22,202-11 (1969). Westbrook, J. H., Jorgensen, P. J., A r n e r . Jfineral., 53, 18991909 (1968). Westbrook, J. H., Jorgensen, P. J., Trans. M e t . Soc. A I M E , 233, 425-8 (1965). Westwood, A. R. C., “Environnient-sensitive mechanical behavior,” 11etallurgical Soc. Coni., 5’01. 35, pp 1-65, Gordon and Breach Science Publishers, New York, N.Y., 1966. Westwood, A. 11. C., Research Institute for -4dvanced Studies, LIartin Marietta Corp., Baltimore, USA, Annual Hept. pp 1.5-17 f1F)GXi. ~ ~ - ._ , Westwood, A. R. C., Goldheim, D. L., J . A m e r . Ccram. Soc., 53, 142-7 (1970). Wiederhorn, S. M., ibid., 50, 404-14 (1967). Ziegler, E., “Schriftenreihe der Zementindustrie,” X o . 19, S’erein l_)eutscher Zementwerke, Dusseldorf, Germany, 1936. RECEIVED for review September 29, 1970 ACCEPTEDAugust 30, 1971
Statistical Test and Adjustment of Process Data Shunsuke Nogita Hitachi Research Laboratory of Hitachi, Ltd., Oniika, Hitachi, Ibaragi, Japan
Based on statistical consideration, a test criterion of data inconsistency i s introduced which detects the existence of erroneous measurements and process disorders. The sensitivity of the proposed test criterion i s discussed as well. Further, a data adjustment technique i s developed. The algorithm eliminates suspect measurements, producing a reliably consistent set of data from a set of measured data. No special knowledge i s required about the particular process except for knowing the variances and correlation coefficients of measurements. The presumption adopted i s that there might b e a few systematic errors in the experimental data, the others being small random errors.
A set of heat’ and material balance data from a chemical process does not usually satisfy the heat and material balance equations. This brings about many difficulties in the analysis and control of a chemical process. The inconsistency results from three sources; unsteadystate operation, erroneous measurements! and process disorders or unexpected efflux from and influx to the process. For desirable operation aiid control, first of all, t’he process engineer must distinguish wliet’her the inconsistency is significant or not. If it is significant in spite of the fact that the operator’s experience tells him that the process is in a steady state, he should examine the process and the entire data-gathering system. For this purpose a test criterion of data inconsistency is introduced in this article. Another problem of process analysis and control is t o obtain a reliably consistent set’ of data Y---closing the heat and material balances exactly-from a set of measured data X. This is especially necessary when there are erroneous measurements and process disorders. The determination algorithm of Y is also proposed. Here it is assumed that there might be a few systeniatic errors in the experimental data, aiid that each of the other measurements is a random sample from a normal population with unknown correct value (mean) p t , known variance ui2, and known correlation coefficient p g j . The last two
values, ut2 and p z j , can be easily obtained for a particular proces.? from the piles of the daily operation data, or from the experiments desigued for them. Adjustment Technique of Experimental Data
A technique for adjusting data containing only small random errors caused by steady-state operation and measurement has been proposed by Kuehn and Davidson (1961). They introduced the least-squares criterion Equation 1 to predict a consistent set of data Y from a set of measured data X. This set X is for a single ruu, that is, a single fixed operating condition.
5 (--)- xg yt
@
= i=l
where u t 2 is the previously given error variance of the it11 measurement, z t is the i t h measurement as actually observed, yE is the i t h measuremeiit when corrected, and n is the number of meaburements. In the analysis, the elements of Y are assumed to be linearly connected to one another by the heat and material balance equations. n +J
ujtyg =
=
0
(J =
1, 2,
*
. ., m)
(2)
2=1
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972
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