LABORATORY METHOD FOR PRODUCING GRANULAR AMMONIUM NITRATE

N. P. KURIN, G. A. ORMAN, and E. T. LABYKINA

In a previous communication by one of us [1], the structure of ammonium nitrate granules obtained by spraying the melt and cooling the resulting drops as they fall in a stream of air was considered, as were the mechanism of caking and possible ways of combating the caking of this important agricultural fertilizer. For various experimental studies in the field of producing non-caking granular ammonium nitrate, it is necessary to have a laboratory method for producing granules similar in their shape, structure, and size to industrial samples. The existence of such a method will enable researchers to study the influence of various factors on the caking of freshly prepared, unmodified granules without carrying out numerous costly experiments on a plant scale.

The methods of granulating ammonium nitrate described in the literature amount to crushing [2] solidified lumps of previously melted nitrate and, with the aid of sieves, separating the required fraction with a granule size of about 1.5–2.5 mm, or to granulating the molten melt [3] in vessels with a steam jacket under gradual cooling and continuous stirring of the melt by means of a slowly moving agitator.

However, in both methods the resulting granules do not have the correct spherical shape and structure characteristic of granules obtained by spraying and cooling the melt in a stream of air.

The main difficulty in creating a laboratory method for granulating ammonium nitrate by the method of spraying in air is the great height of fall of the drops, which for industrial granulation towers is about 35 m.

In developing a laboratory method for obtaining granular ammonium nitrate by spraying, we were guided by the following general considerations.

The production of granules from an ammonium nitrate melt must consist of two processes:

1) the process of forming drops of a specified size,
2) the process of solidifying the drops into granules as they fall in air.

To carry out the first process, it is necessary to expend a certain amount of energy on forming the surface of the drops. This energy is expended in doing work against the forces of surface tension.

If the kinetic energy of the falling ammonium nitrate melt itself is used as the source of energy, then the minimum height \((h)\) of the vessel with melt (9) above the surface of fragmentation (11) (Fig. 1) must be such that the energy reserve of the melt would be equal to the energy necessary for forming the surface of the drops.

Taking into account that the volume of one drop is

\[ V=\frac{1}{6}\pi \cdot d^3, \tag{1} \]

the surface of a drop \((s)\)

\[ s=\pi d^2 \tag{2} \]

and the number of drops \((n)\) formed from \(G\) grams of melt

\[ n=\frac{G}{\gamma \cdot V}, \tag{3} \]

Fig. 1. Schematic of a laboratory setup for producing granular ammonium nitrate.

we find the total surface \((S)\) of all drops

\[ S=n \cdot s=\frac{6 \cdot G}{\gamma \cdot d}. \tag{4} \]

In equations (1), (2), (3), and (4)

\(d\)—drop diameter,
\(\gamma\)—specific gravity of the nitrate melt.

The minimum work \((A)\) required to form the surface of all the drops will be equal to

\[ A=S \cdot a=\frac{6 \cdot G \cdot a}{\gamma \cdot d}, \tag{5} \]

where \(a\)—the minimum work of formation of \(1\ \mathrm{cm}^2\) of drop surface.

On the other hand, the potential energy \((A')\) of the liquid nitrate melt at height \(h\) (Fig. 1) above the plane of disintegration is

\[ A'=G \cdot h. \tag{6} \]

The quantities \(A\) and \(A'\) must be equal, i.e.

\[ A=A'. \tag{7} \]

Hence, if the values of \(A\) and \(A'\) from equations (5) and (6) are substituted into equation (7), we find

\[ h=\frac{6\cdot a}{\gamma\cdot d}. \tag{8} \]

The quantity of work \((a)\) entering into equation (8) for the formation of a unit surface of droplets is numerically equal to the surface tension of the liquid \((\sigma)\). Replacing \((a)\) by \((\sigma)\) in equation (8), we obtain

\[ h=\frac{6\cdot \sigma}{\gamma\cdot d}. \tag{9} \]

From equation (9) it is clear that the height \(h\) of the melt above the disintegration plane required for the formation of droplets is directly proportional to the surface tension and inversely proportional to the specific weight of the melt and the diameter of the droplet. Thus, in order to obtain droplets, and consequently granules, of smaller diameter, it is necessary to increase the height \(h\).

Using equation (9), let us calculate the minimum height of fall \((h)\) of the melt above the disintegration surface for the formation of granules with a diameter of 2 mm.

In granulating a melt with a concentration of 98.5–99% \(NH_4NO_3\) and at a temperature of about \(155^\circ\), the surface tension is approximately \(100 \ \dfrac{\text{dyn}}{\text{cm}}\).

Since \(1\) dyne \(=1.0197\cdot 10^{-8}\) kg, then

\[ \sigma=\frac{100\cdot 1.0197\cdot 10^{-8}}{0.01^2} =1.0197\cdot 10^{-2}\ \text{kgm}. \]

The specific weight of the saltpeter melt under the same conditions is \(1437 \ \text{kg}/\text{m}^3\). Substituting the above values into equation (9), we obtain

\[ h=\frac{6\cdot 1.0197\cdot 10^{-2}}{1437\cdot 0.002} =0.0213\ \text{m}=2.13\ \text{cm}. \]

Thus, if all the kinetic energy of the falling ammonium nitrate melt were used for the formation of droplets with a diameter of 2 mm, it would be necessary for this purpose to pour the melt onto the disintegration surface from a height of 2.13 cm.

It should be noted, however, that equation (9) does not take into account the expenditure of energy for overcoming air resistance during the fall of the melt on the path from the vessel (9) to the disintegration surface (11) (Fig. 1), for overcoming resistance as the melt passes through the openings of surface (11), and for producing rotational and some translational motion of the droplets. Therefore the actual value of \(h\) must be greater than that calculated from equation (9).

In order that a droplet of ammonium nitrate melt, after detaching from the disintegration surface, turn into a solid granule, it must be cooled to a certain final temperature.

The required height of fall of the droplet-granule from the disintegration surface (11) to the receiver (2) \((H)\) will be determined by the conditions of heat transfer, and the latter are closely connected with the velocity and time of flight of the granule in the air.

Rate of Fall of Granules

The rate of fall of spherical particles in air can be found from the following considerations.

The force acting on a freely falling particle will be equal to the force of gravity of this particle, diminished by the force of air resistance, i.e.,

\[ m \cdot \frac{dv}{dt} = m \cdot g - F, \tag{10} \]

where \(m\) is the mass of the particle,

\[ \frac{dv}{dt} \]

is the observed acceleration of the particle’s fall, equal to the first derivative of the velocity with respect to time,

\(g\) is the acceleration due to gravity,

\(F\) is the force of air resistance.

For spherical particles, the force of air resistance [4], according to Newton’s law, will be equal to

\[ F = Z \cdot \frac{\pi d^2}{4} \cdot \gamma_2 \cdot \frac{v^2}{2g}, \tag{11} \]

where \(d\) is the diameter of the granule,

\(v\) is the rate of fall of the granule,

\(\gamma_2\) is the specific weight of air,

\(Z\) is the drag coefficient.

The coefficient \(Z\) depends on the character of the motion, expressed by the Reynolds number.

The Reynolds number for practically possible rates of fall of granules in air at a temperature of \(20^\circ\) can be calculated from equation (12)

\[ Re = \frac{v \cdot d \cdot \gamma_2}{\mu \cdot g}. \tag{12} \]

Under the specified conditions \((\gamma_2 = 1.2\ \mathrm{kg}/\mathrm{m}^3;\ \mu = 1.83 \cdot 10^{-6}\ \mathrm{kg\,sec}/\mathrm{m}^2;\ d = 0.002\ \mathrm{m}\) and \(g = 9.81)\), and at rates of fall from \(0.01\) to \(4\) and from \(4\) to \(10\ \mathrm{m/sec}\), \(Re\) proved to be equal respectively to \(1.3\text{–}530\) and \(530\text{–}1340\).

In the range of possible rates of fall of granules, the character of the dependence of \(Z\) on velocity changes; for velocities up to \(4\ \mathrm{m/sec}\), \(Z\) must be calculated from equation (13),

\[ Z = \frac{18.5}{Re^{0.6}} = \frac{18.5}{\left(\dfrac{v \cdot d \cdot \gamma_2}{\mu \cdot g}\right)^{0.6}}, \tag{13} \]

and at rates of fall above \(4\ \mathrm{m/sec}\) and up to \(Re = 150000\) it should be taken as constant and equal to \(0.44\).

Let us calculate the rate of fall of a granule as a function of time at \(Re = 1\text{–}500\). For this purpose, substituting into equation (11), instead of \(Z\), its value from equation (13), we obtain

\[ F = \frac{18.5 \cdot \pi \cdot \mu^{0.6} \cdot d^{1.4} \cdot \gamma_2^{0.4} \cdot v^{1.4}} {8 \cdot g^{0.4}}. \tag{14} \]

The mass of granules \(m\) is equal to

\[ m = \frac{\pi \cdot d^3 \cdot \gamma_1}{6 \cdot g}. \tag{15} \]

After substituting \(F\) from equation (14) and \(m\) from equation (15) into equation (10), and after some transformations, we obtain

\[ dv=\left(g-\frac{6\cdot 18.5\,\mu^{0.6}\cdot \gamma_2^{0.4}\cdot g^{0.6}}{8\cdot \gamma_1\cdot d^{1.6}}\cdot v^{1.4}\right)dt \]

or

\[ dv=(g-av^{1.4})\,dt, \tag{16} \]

where

\[ a=\frac{6\cdot 18.5\,\mu^{0.6}\cdot \gamma_2^{0.4}\cdot g^{0.6}}{8\cdot \gamma_1\cdot d^{1.6}} \]

is a constant quantity.

To find the dependence of the falling velocity on time, it is necessary to integrate equation (16) within the limits from 0 to \(t_1\), and from 0 to \(v_1\), namely

\[ \int_{0}^{t_1} dt=t_1=\int_{0}^{v_1}\frac{dv}{g-av^{1.4}}. \tag{17} \]

It is not possible to solve integral (17) in general form, and therefore we resorted to graphical integration for the case of the fall of a granule 2 mm in diameter in air having a temperature of \(20^\circ\) and a pressure of 1 atm. Under these conditions, the value of \(a\) in equation (17) is

\[ a=\frac{6\cdot 18.5\cdot 1.83\cdot 10^{-6}\cdot 1.2^{0.4}\cdot 9.81^{0.6}}{8\cdot 1477\cdot 0.002^{1.6}}=0.29878, \]

where the quantity 1477 is the mean apparent specific gravity of the drop and of the granule formed from it at temperatures of 155 and \(85^\circ\). As was noted by one of us [1], at 155 and \(85^\circ\) \(\gamma_1\) proved to be equal, respectively, to 1437 and 1517 kg/m\(^3\); hence

\[ \gamma_1=\frac{1437+1517}{2}=1477\ \text{kg/m}^3. \]

After substituting the value of the acceleration of gravity and the value of \(a\) into equation (17), we obtain

\[ t_1=\int_{0}^{v_1}\frac{dv}{9.81-0.29878\cdot v^{1.4}} =\int_{0}^{v_1} f(v)\,dv. \tag{18} \]

Assigning values to \(v\), we calculated the values

\[ f(v)=\frac{1}{9.81-0.29878\cdot v^{1.4}} \]

and, from the data obtained, plotted a diagram (Fig. 2), where the falling velocities are laid off along the abscissa axis, and the corresponding values of \(f(v)\) along the ordinate axis. The areas bounded by curve (1), the abscissa axis, and any ordinate dropped from curve (1) to the abscissa axis, multiplied by the scale of the diagram (1 square of area is equal to 0.05 sec), give the falling time of the granule required to reach specified velocities up to 4 m/sec.

The areas in Fig. 2 were measured with the aid of a planimeter. The results of the calculations are presented in the upper half of Table 1.

Table

Time required for freely falling drops–granules of ammonium nitrate to acquire specified velocities in air having a temperature of 20° and a pressure of 1 atm
(the initial falling velocity is taken as zero).

When calculating the falling velocity of a granule as a function of time at \(Re = 500\text{–}1200\), it was taken into account that the resistance coefficient \(Z = 0.44\); substituting this value into equation (11), we obtain

\[ F = 0.44 \, \frac{\pi d^2}{4} \cdot \gamma_2 \cdot \frac{v^2}{2g}. \tag{19} \]

Fig. 2. Dependence of \(f(v)\) on falling velocity.

Replacing in equation (10) the air-resistance force \(F\) by its value from equation (19), and expressing the mass \(m\) of the granule through its diameter, specific weight, and the acceleration due to gravity, we find

\[ \frac{dv}{dt} = g - av^2, \tag{20} \]

where

\[ a=\frac{0.33\,\gamma_2^{2}}{\gamma_1\,d}. \tag{21} \]

To find the relation between the falling velocity and the time required for this, equation (20) must be integrated over the time limits from \(t_1\) to \(t_2\) and, correspondingly, \(v_1\) and \(v_2\)

\[ \int_{t_1}^{t_2} dt=\int_{v_1}^{v_2}\frac{dv}{g-av^2}. \tag{22} \]

Integrating and substituting the limits, we find

\[ t_2=t_1-\frac{2.303}{2a\sqrt{\dfrac{g}{a}}}\log \frac{\left(v_2-\sqrt{\dfrac{g}{a}}\right)\cdot\left(v_1+\sqrt{\dfrac{g}{a}}\right)} {\left(v_2+\sqrt{\dfrac{g}{a}}\right)\cdot\left(v_1-\sqrt{\dfrac{g}{a}}\right)}. \tag{23} \]

For granules of diameter \(2\ \mathrm{mm}\), for the given state of the air, according to equation (21)

\[ a=\frac{0.33\cdot 1.5^2}{1477\cdot 0.002}=0.13683 \]

and

\[ \sqrt{\frac{g}{a}}=\frac{9.81}{0.13683}=8.467. \]

The minimum falling velocity at which the force of air resistance begins to be expressed by equation (19) is \(4\ \mathrm{m/sec}\), and this requires \(0.4471\ \mathrm{sec}\). Substituting into equation (23) the values of \(a\), \(\sqrt{g/a}\), \(v_1=4\), and \(t_1=0.4471\), we obtain

\[ t_2=0.4471-0.9939\log\frac{2.7909(8.467-v_2)}{(8.467+v_2)}. \tag{24} \]

Using equation (24), the time required to attain specified falling velocities of a granule in air was calculated. The results of the calculations are given in the lower half of Table 1.

To illustrate how great the influence of air resistance is, the third column of Table 1 also gives the time required to attain the specified velocity in an airless space.

The results of the calculations are shown in Fig. 3, where portions \(OA\) and \(AB\) of curve 1 are plotted according to the data of Table 1, when the coefficients \(Z\) are respectively equal to \(\dfrac{18.5}{Re^{0.6}}\) and \(0.44\). As can be seen from Table 1 and Fig. 3, the falling velocity of the granule in air increases up to a certain limit and subsequently remains constant.

From equation (20) it is seen that the granule acquires the maximum falling velocity when

\[ \frac{dv}{dt}=g-av^2=0, \]

whence the maximum constant falling velocity will be equal to

\[ v_{\max}=\sqrt{\frac{g}{a}}=8.467\ \text{m/sec}. \]

It follows from this that equation (24) is valid only for velocities of \(4\)—\(8.467\ \text{m/sec}\).

Fig. 3. Dependence of the falling velocity of an ammonium nitrate granule on the time of fall. Granule diameter 2 mm. Curve 1 expresses the dependence \(v=f(t)\) for air. Curve 2—for an airless space.

From the analysis of equation (24) follows the necessity of spending an infinite amount of time to attain the maximum falling velocity; however, in reality, to attain velocities close to the maximum, a limited time is required; for example, after \(2.984\) sec of falling a velocity of \(8.45\ \text{m/sec}\) is reached, which is \(99.8\%\) of \(v_{\max}\).

Height of fall of the granule

Curve 1 in Fig. 2 expresses the functional dependence of the falling velocity of a granule on time, and in general form it may be expressed by the equation

\[ v=\frac{dH}{dt}=f(t), \tag{25} \]

where \(H\) is the height of fall.

From equation (25), \(dH=f(t)\,dt\), whence the height of fall of the granule by the time \(t\) will be equal to

\[ \int_{0}^{H} dH=H=\int_{0}^{t} f(t)\,dt. \tag{26} \]

In our case \(f(t)\) is given by curve 1 in Fig. 3, and therefore the height \(H\), equal to integral (26), will be expressed by the area bounded by curve 1, the abscissa axis, and one of the velocity ordinates. To find \(H\) by measurem-

measured with a planimeter from the areas in Fig. 3 were multiplied by the diagram scale, equal to 0.25 m per one square cell. The results of the calculations are given in Table 2 and shown in Fig. 4.

Table 2

Height of fall of a drop-granule of ammonium nitrate
as a function of fall time

Diameter of the drop-granule 2 mm.
Air temperature 20°; \(P = 1\) atm

Fig. 4. Dependence of the height of fall of an ammonium nitrate granule on time.

Curves 1 and 2 correspond respectively to air and to airless space.

Thus, from all that has been set forth above it is evident that, if one is limited by the drop heights available under laboratory conditions from the pulverizing surface (11) to the receiver (2), of the order of \(\sim 8\text{–}12\) m, then the falling time, equal to the cooling time, must not exceed \(1.5\text{–}2\) sec for a granule of diameter 2 mm under the conditions indicated above.

Cooling time of an ammonium nitrate droplet-granule from heat-transfer conditions

The cooling of a droplet, and then of a granule, should be regarded as the cooling of a sphere in air under unsteady conditions. However, this problem is greatly complicated by the liberation of heat during phase transitions (solidification of molten nitrate into crystalline modification I (\(\varepsilon\)) with the liberation of 16.75, transitions of crystalline modifications I (\(\varepsilon\)) to II (\(\delta\)) with the liberation of 12.24 and II (\(\delta\)) to III (\(\gamma_1\)) 4.17 kcal/kg), and by abrupt changes in the heat capacities and thermal conductivities of the newly arising phases. Therefore, as a first approximation, we identified the cooling of the droplet-granule with the cooling of a sphere in which phase transitions and changes in heat capacity and thermal conductivity are absent. As Gröber [5] showed, in this case the final temperature of the sphere is in functional dependence on the initial temperature and is determined by equation (27)

\[ T_o = T_c \Phi_o \left( hR,\ \frac{at}{R^2} \right), \tag{27} \]

where \(T_o\) is the temperature at the surface of the sphere toward the end of cooling,

\(T_c\) is the initial temperature of the sphere, the same at the center of the sphere and at its surface,

\(R\) is the radius of the sphere in meters,

\[ h=\frac{\alpha}{\lambda} \]

is the relative heat-transfer coefficient,

\(\alpha\) is the coefficient of heat transfer from the surface of the sphere to the air, in kcal/m\(^2\)·hr·deg,

\(\lambda\) is the thermal conductivity coefficient of the substance of the sphere, in kcal/m·hr·deg,

\[ a=\frac{\lambda}{c\cdot \gamma} \]

is the thermal diffusivity coefficient,

\(c\) and \(\gamma\), respectively, are the heat capacity and specific weight of the sphere, in kcal/kg·deg and kg/m\(^3\),

\(t\) is the cooling time of the granule in hours.

To calculate the relative heat-transfer coefficient \(h\), it is necessary to know \(\alpha\) and \(\lambda\).

In the literature there are no data on the coefficient of heat transfer from the surface of a sphere to air, and therefore, to calculate \(\alpha\), we used equation (28), valid for cylinders [5],

\[ \alpha = 0.0670 \frac{\lambda_m}{d} \cdot \left( 1273 + \frac{v \cdot d \cdot \rho_m}{\mu_m} \right)^{0.716}, \tag{28} \]

where \(\lambda_m\) is the coefficient of heat transfer of air at the mean temperature of the cylinder wall and the air \(t_m\),

\(d\) is the diameter of the cylinder in m,

\(v\) is the velocity of the air motion in m/sec, in our case the mean velocity of fall of the droplet-granule,

\(\rho_m\) and \(\mu_m\) are, respectively, the density and viscosity of the air at the mean temperature \(t_m\).

In our experiments, the nitrate melt fed to granulation contained \(\sim 1\%\) moisture and had a temperature of \(155^\circ\), close to the temperature of the saturated solution, as a result of which there was no need to spend time removing superheat. The temperature of the granule during its fall in air having a temperature of \(15^\circ\) decreased to \(85^\circ\). The mean temperature of the surface of the droplet-granule was

\[ \frac{155+85}{2}=120^\circ \]

and the mean temperature difference between the temperatures of the granule surface and the air

\[ t_m=\frac{120+15}{2}=68^\circ. \]

At this temperature \(\rho_m=0.105\ \mathrm{kg\,sec^2/m^4}\); \(\mu_m=2.12\cdot 10^{-6}\ \mathrm{kg\,sec/m^2}\). As was shown above, the falling velocity of a granule is a variable quantity, the mean value of which can be determined from the curve in Fig. 3. For this purpose, the falling velocities at the times \(0.25;\ 0.5;\ 0.75;\ 1.0;\ 1.25;\ 1.5\) sec were determined, and the arithmetic mean falling velocity over 1.5 sec, calculated from the data obtained, proved to be \(6\ \mathrm{m}\) per second. The heat-transfer coefficient, calculated from equation (28), for a droplet-granule of diameter \(2\ \mathrm{mm}\), is \(181\ \mathrm{kcal/m^2\cdot hr\cdot deg}\).

There are also no data in the literature on the thermal conductivity of molten and solid ammonium nitrate; therefore, for an approximate calculation of the indicated quantity, equation (29) [4] was used

\[ \lambda=\frac{0.293\cdot \gamma^{2.15}\cdot c^{1.55}\cdot M^{0.119}}{\mu^{0.12}}\ \mathrm{kcal/m\cdot hr\cdot deg}, \tag{29} \]

where \(\gamma=1.434\) is the relative (to water) specific gravity of the liquid,
\(c=0.37\) is the specific heat of the liquid in \(\mathrm{kcal/kg\cdot deg}\),
\(M=80\) is the molecular weight of the liquid,
\(\mu=4.94\) is the viscosity of the liquid in centipoises.

The value of \(\lambda\) calculated from equation (29) proved to be \(0.261\ \mathrm{kcal/m\cdot hr\cdot deg}\).

Taking into account the initial temperature of the droplet, \(155^\circ\), and the air temperature \(15^\circ\), with its diameter \(2\ \mathrm{mm}\), we obtain

\[ \frac{T_0}{T_c}=\frac{155-15}{85-15}=0.50;\qquad h=\frac{\alpha}{\lambda}=\frac{181}{0.261}=693; \]

\[ h\cdot R=693\cdot 0.001=0.693. \]

For the found values of \(\dfrac{T_0}{T_c}\) and \(h\cdot R\), the quantity

\[ \frac{a\tau}{R^2} \]

according to Gröber’s diagram [5] is equal to 0.3. In calculating the coefficient of thermal diffusivity

\[ a=\frac{\lambda}{c\cdot \gamma}=\frac{0.261}{0.4\cdot 2.1477}=0.000221 \]

it was taken into account that, during cooling of the granule, not only the sensible heat of the crystals and of the mother liquor is removed, but also the heat of phase transitions; since these heats are approximately equal in the indicated temperature interval, the mean heat capacity of the crystals and mother liquor, equal to 0.4, was doubled.

The cooling time of the droplet-granule proved to be

\[ t=\frac{0.3\cdot R^2\cdot 3600}{a} =\frac{0.3\cdot 0.001^2\cdot 3600}{0.000221} =4.89\ \text{sec}, \]

which considerably exceeds the value acceptable for laboratory conditions and, as will be shown below, indicates substantial errors in the calculation.

Diagram of the Laboratory Installation

A diagram of the laboratory installation for granulating ammonium nitrate is shown in Fig. 1.

The installation consists of a chamber for melting the nitrate and producing droplets (1), a granule receiver (2), a rheostat (3), and an ammeter (4). The chamber (1) was made of sheet iron and lined inside with asbestos (5) 10 mm thick in order to reduce heat losses to the surrounding space. The chamber was heated by an electric current passed through a coil (6). The temperature was regulated by changing the current strength by means of the rheostat (3), using the readings of the ammeter (4) and thermometer (7) as a guide.

In the upper part of the chamber, on an iron axle (8), a porcelain cup or one made of acid-resistant steel EI1-T (9) was mounted, capable of being turned over by means of a handle (10). In the lower part of the chamber, at a distance \(h = 100\) mm from the cup (9), a sieve (11) of sheet aluminum or steel EI1-T, 110 mm in diameter and 0.5 mm thick, was mounted on supports. The holes in the sieve had a diameter of 1.5 mm and were spaced 3–4 mm apart.

The front wall of the chamber was made in the form of a door, which is closed during operation. In the upper cover of the chamber there are two openings, into one of which a thermometer is inserted for measuring the temperature of the nitrate melt, while through the other (12) the nitrate and, if necessary, water are introduced. In the bottom of the chamber there is an opening closed by a slide gate (13) made of sheet asbestos.

The chamber was mounted on a bracket at a height \(H = 7.5\) m from the floor, for which purpose the stairwell between the first and second floors was used.

The granulation process was carried out as follows.

With the front door and slide gate (13) closed, electric heating of the chamber was switched on, and upon reaching the specified temperature in it, the required amount of crushed ammonium nitrate and, if necessary, the corresponding amount of distilled water were introduced through opening (12) using a funnel and a pipette. Opening (12) was closed with a stopper, and after the nitrate had melted and the specified melt temperature had been established, slide gate (13) was opened. By a rapid turn of handle (10), cup (9) was quickly overturned, and the melt poured onto sieve (11). The droplets of melt formed during the fall from sieve (11) to receiver (2), through heat exchange with the surrounding cold air, gave up part of their heat and turned into solid spherical granules.

The hot granules obtained could be quickly poured out of the receiver into apparatus for studying caking processes and other questions, bypassing the stage of preliminary cooling of the nitrate to room temperature.

Of course, it was also possible to introduce the nitrate and water into cup (9) through the door; however, this disturbed the temperature regime of the chamber much more substantially, and additional time had to be spent regulating it.

As the experiments showed, with the aid of the described apparatus it is possible to granulate pure ammonium nitrate in quantities sufficient for studying caking and certain other questions.

The granulometric composition of the nitrate obtained in the laboratory approaches the granulometric composition of industrial samples [6] and is characterized by the following data.

Granulometric composition of ammonium nitrate obtained on the laboratory apparatus

When the molten nitrate was poured from cup (9), only about 20–30% of it passed through the openings of sieve (11) and was converted into granules, while the remaining part of the melt stayed on the sieve.

Using equation (9), and also knowing the yield of granules \((x)\) as a percentage of the total amount of melt entering granulation, the percentages of granules \((y_1, y_2, y_3 \ldots y_n)\) having diameters respectively \(d_1, d_2, d_3 \ldots d_n\), it is not difficult to show that the degree of utilization of the energy of the falling melt \((a)\) for the formation of the granule surface will be expressed by equation (30)

\[ a=\frac{6 \cdot \sigma \cdot x}{100 \cdot \gamma \cdot h} \left( \frac{y_1}{d_1} + \frac{y_2}{d_2} + \frac{y_3}{d_3} +\ldots \frac{y_n}{d_n} \right). \tag{30} \]

Substituting into equation 30 the values \(y_1, y_2, y_3 \ldots y_n\) and the corresponding mean granule diameters \(d_1, d_2, d_3 \ldots d_n\) from the above table of granulometric composition, we obtain

\[ a= \frac{6 \cdot 1.0197 \cdot 10^{-2} \cdot 30}{100 \cdot 1437 \cdot 0.1} \left( \frac{1}{0.003} + \frac{42.76}{0.0025} + \frac{23.5}{0.00175} + \frac{24.2}{0.00125} + \right. \]

\[ \left. + \frac{6.93}{0.00075} + \frac{1.63}{0.00025} \right) =8.43\%. \]

Thus, only 8.43% of the energy of the falling melt was expended in performing work against the forces of surface tension in forming the surface of the drops. In accordance with the preceding, this can be explained by the considerable expenditure of energy in overcoming the resistance of the sieve openings and in creating rotational and some translational motion of the granules formed.

Variation of the temperature regime during the melting process, together with the introduction into the nitrate of various amounts of water, made it possible under laboratory conditions to obtain nitrate granules with various moisture contents, from 98.5 and higher percent. Overheating and excessively high moisture content of the nitrate must not be abused, since in these cases the drops, falling from a height of 7.5 m, did not have time to acquire sufficient strength and flattened upon striking the bottom of the receiver.

The experiments also showed that with the aid of the described apparatus it is possible to granulate ammonium nitrate with various soluble and solid dust-like additives. This is of especially great importance for fulfil-

of research in the field of developing methods for combating caking without carrying out costly, hard-to-access experiments on a plant scale.

Proceeding from the conditions of heat transfer, the cooling time of a droplet-granule with a diameter of 2 mm should be 4.89 sec; under our conditions it was 1.5 sec. This indicates significant errors in the above heat-engineering calculation.

These errors are associated with a number of assumptions caused by the lack of the necessary exact data on the thermal-conductivity coefficients of aqueous ammonium nitrate solutions and crystalline modifications, by the inaccuracy of accounting for the influence of phase transitions, and, finally, by the absence of data on the heat-transfer coefficients from the surface of the droplet-granule to the air. The error caused by the last reason is apparently the most substantial.

Conclusions

1. A laboratory apparatus has been developed for producing granular ammonium nitrate by the method of spraying the melt and cooling the falling droplets in air.

2. An equation has been derived for calculating the minimum height of fall of the melt to the fragmentation surface in order to convert the ammonium nitrate melt into droplets.

3. Using data from aerodynamics, quantitative relationships observed during the fall of a droplet-granule in air have been derived. The velocity, time, and height of fall of an ammonium nitrate droplet-granule have been calculated, and it has been shown that, at a diameter of 2 mm, the droplet-granule will traverse a distance of 7.5–12 m in 1.5–2 sec, with the falling velocity increasing from 0 to 8.3 m/sec.

4. The developed method for calculating the velocity and time of fall of a droplet-granule in air may be useful in designing various versions of the laboratory apparatus and industrial granulation towers.

5. The apparatus makes it possible under laboratory conditions to obtain granules both from pure ammonium nitrate and from nitrate with various soluble and dust-like inorganic impurities. The granulometric composition of nitrate obtained under laboratory conditions is close to the granulometric composition of industrial samples of this substance.

Literature

1. N. P. Kuryin. Izv. TPI, vol. 71, 25, 1952. Zhurn. Khim. prom., 5, 1, 1953. Zhurn. Khim. prom., 6, 1953.

2. A. M. Dubovitskii and F. T. Martolyas. Zhurn. Khim. prom., 5, 136, 1947.

3. D. Miller and Ind. Eng. Chem. 38, 7, 704, 1946.

4. A. G. Kasatkin. Basic Processes and Apparatuses of Chemical Technology. Goskhimizdat, 1950, p. 120; Part II, 16, 1938.

5. G. Gröber. Introduction to the Theory of Heat Transfer. GTTI, Moscow, 1929.

6. A. M. Dubovitskii and Ya. I. Kilman. Technology of Ammonium Nitrate. Goskhimizdat, 1949.