Rotary Dryer

7

Rotary Drying Magdalini Krokida, Dimitris Marinos-Kouris, and Arun S. Mujumdar

CONTENTS 7.1 7.2 7.3 7.4

Introduction ........................................................................................................................................... Types of Rotary Dryers ......................................................................................................................... Flight Design ......................................................................................................................................... Residence Time Models ......................................................................................................................... 7.4.1 Cascade Motion........................................................................................................................ 7.4.2 Kiln Action ............................................................................................................................... 7.4.3 Bouncing ................................................................................................................................... 7.5 Heat and Mass Transfer in Rotary Dryers ............................................................................................ 7.6 Energy and Cost Analysis ...................................................................................................................... 7.7 A Model for the Overall Design of Rotary Dryers................................................................................ 7.7.1 Burner ....................................................................................................................................... 7.7.2 Dryer......................................................................................................................................... 7.7.3 Drying Kinetics......................................................................................................................... 7.7.4 Residence Time ......................................................................................................................... 7.7.5 Geometrical Constraints ........................................................................................................... 7.8 Case Study 1 .......................................................................................................................................... 7.9 Case Study 2 .......................................................................................................................................... 7.10 Conclusion ........................................................................................................................................... Nomenclature ................................................................................................................................................. References ......................................................................................................................................................

7.1 INTRODUCTION Rotary drying is one of the many drying methods existing in unit operations of chemical engineering. The drying takes place in rotary dryers, which consist of a cylindrical shell rotated upon bearings and usually slightly inclined to the horizontal. Wet feed is introduced into the upper end of the dryer and the feed progresses through it by virtue of rotation, head effect, and slope of the shell and dried product withdrawn at the lower end. A simplified diagram of a direct-heat rotary dryer is presented in Figure 7.1. The direction of gas flow through the cylinder relative to the solids is dictated mainly by the properties of the processed material. Cocurrent flow is used for heatsensitive materials even for high inlet gas temperature due to the rapid cooling of the gas during initial evaporation of surface moisture, whereas for other materials countercurrent flow is desirable in order to

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151 151 153 155 156 156 156 159 163 164 164 165 165 165 166 166 167 170 170 171

take advantage of the higher thermal efficiency that can be achieved in this way. In the first case, gas flow increases the rate of solids flow, whereas it retards it in the second case [3,19,20,35].

7.2 TYPES OF ROTARY DRYERS Rotary dryers are classified as direct, indirect–direct, indirect, and special types. This classification is based upon the method of heat transfer being direct when heat is added to or removed from the solids by direct exchange between gas and solids, and being indirect when the heating medium is separated from contact with the solids by a metal wall or tube. There is an infinite number of variations, which present operating characteristics suitable for drying, chemical reactions, mixing, solvent recovery, thermal decompositions, sintering, and agglomeration of solids [35].

Quench air

Combustion air

Atomizing air

Wet feed

Fuel

To cyclone and fans

Dry product

FIGURE 7.1 Simplified diagram of direct-heat rotary dryer.

The main types of rotary dryers include the following: .

.

.

.

.

Direct rotary dryer. It consists of a bare metal cylinder with or without flights, and it is suitable for low- and medium-temperature operations, which are limited by the strength characteristics of the metal. Direct rotary kiln. It consists of a metal cylinder lined in the interior with insulating block or refractory brick, in order to be suitable for operation at high temperatures. Indirect steam-tube dryer. It consists of a bare metal cylindrical shell with one or more rows of metal tubes installed longitudinally in its interior. It is suitable for operation up to the available steam temperature or in processes requiring water-cooling of the tubes. Indirect rotary calciner. It consists of a bare metal cylinder surrounded by a fired or electrically heated furnace and it is suitable for operation at temperatures up to the maximum that can be tolerated by the metal of the cylinder, usually 800–1025 K for stainless steel and 650–700 K for carbon steel. Direct Roto-Louvre dryer. It is, perhaps, the most important of the special types, as the solids progress in a crosscurrent motion to the gas, and it is suitable for low- and medium-temperature operations.

The rotary dryers can perform batch or continuous processing of the wet feed, and the discharged product should be solids relatively free flowing and granular. If the material is not completely free flowing in its feed condition, a special operation is necessary, which includes recycling a portion of the final product, a premixing with the feed or maintaining a bed of


free-flowing product in the cylinder at the feed end. The direct-heat dryers are the simplest and most economical and are used when the contact between the solids and gases or air is not harmful. However, if the solids contain extremely fine particles, excessive entrainment losses in the exit gas stream is possible, due to the large gas volumes and high gas velocities that are, usually, required. The indirect types require only sufficient gas flow through the cylinder to remove vapors, and have the advantage to be suitable for processes requiring special gas atmospheres and exclusion of outside air. The auxiliary equipment of a direct-heated rotary dryer includes a combustion chamber for operation at high temperatures, while steam coils are used for low temperatures. Gases are forced through the cylinder by either an exhauster (especially when a low-pressure drop heater is employed) or an exhauster–blower combination, which is suitable for maintaining precise control of internal pressure even in the case of high-pressure drop in the system. The material characteristics determine the method of feeding of the rotary dryer, which can be done by a chute extending into the cylindrical shell or by a screw feeder for sealing purposes or if gravity feed is not convenient. The feedrate should be controlled and uniform in quality and quantity. In the exit end of the dryer, cyclone collectors are usually installed for the removal of the dust entrained in the exit gas stream. Bag collectors in case of expensive materials or extremely fine product may follow cyclone collectors. Wet scrubbers may be used when toxic solids or gases are processed, the temperature of the exit gas is high, the gas is close to saturation or there is recirculation of the gas. Insulation and steam tracing usually required for cyclones and bag collectors, and an exhaust fan should be used downstream from the collection system.

For the reduction of heat losses the dryer (especially cocurrent direct-heat dryers) and its equipment should be insulated, except when brick-lined vessels or direct-heat dryers operating at high temperatures are employed. In the last case, heat losses from the shell cause a cooling of its material and prevent overheating. The rotary dryers (direct-heat dryers and kilns) are controlled by indirect means, e.g., by measuring and controlling the gas temperatures in their two ends, whereas shell temperature is measured on indirect calciners, and steam pressure and temperature as well exit gas temperature and humidity are controlled on steam-tube dryers. It is not possible to achieve control by measuring the product temperature because not only this is difficult but also its changes are slowly detected, although the product temperature is used for secondary controls. External shell knockers are often used for removing solids sticking on flights and walls. In case of large cross section, internal elements or partitions can be used to increase the effectiveness of material distribution and reduce dusting. For systems operating at temperature higher than 425 K and are electrically driven, the existence of auxiliary power sources and drivers is necessary, as loss of rotation will cause sagging of the cylinder. Representative materials dried in direct-heat rotary dryers are sand, stone, ilmenite ore, sodium sulfate, sodium chloride, and fluorspar, for which high temperatures are used, cellulose acetate, sodium chloride, styrene, copperas, cast-iron borings, and ammonium sulfate, for which medium temperatures are required, and urea prills, vinyl resins, oxalic acid,

(a) straight

(d) Semicircular

FIGURE 7.2 Common flight profiles.


(b) angled

(e) EAD

urea crystals, and ammonium nitrate prills, that are dried at low temperatures [35].

7.3 FLIGHT DESIGN Of all types of rotary dryers the ones that have been studied more extensively are the direct-heat rotary dryers equipped with peripheral flights, while very little scientific work has been published for the other types. Their purpose is to lift and shower the solid particles through the gas stream promoting intimate contact between wet solids and hot gases. The flights are usually offset every 0.6–2 m and their shape depends upon the characteristics of the solids. Radial flights with a 908 lip are used for free-flowing materials and flat radial flights without lip for sticky ones. It is a common practice to employ different flight designs along the dryer length to accommodate with the changing characteristics of the material during drying. In the first meter or so at the feed end spiral flights are used for better distribution of the material under the feed chute or conveyor. The flights most commonly used are presented in Figure 7.2 [35]. Flights a, b, c, and d of Figure 7.2 are frequently used in cascading rotary dryers; the first one is suitable for sticky solids in the wet end of the dryer, while the fourth one, which has a semicircular shape, has been proposed by Purcell [45], because it is supposed to be formed easier in comparison with types b and c. The last two designs have been proposed on the basis of theory for improving dryer’s performance, but their profile is rather complex. They have been studied by Kelly [19] and include the equal angular distribution (EAD) flight and the centrally biased distribution

(c) right-angled

(f) CBD

(CBD) flight, which is shown in Figure 7.2e and Figure 7.2f, respectively. To ensure that the dryer is loaded close to optimal it is important to know the amount of solids that can be held up in the flights. If they are underfilled, the dryer will be performing inefficiently, below its capacity. Excessive overload of the shell will result in a proportion of the material transported by kiln action, and the contact with the hot gases is limited. The residence time of the solids will be reduced and the quality of the product may be unacceptable. The quality of solids retained on a flight is a function of its geometry and angular position and the angle w formed between the horizontal and the free surface of the solids, as shown in Figure 7.3. Schofield and Glikin [49] determine this angle from an equilibrium balance of the forces acting on a particle, which is about to fall from a flight. Gravitational force wg, centrifugal force wc, and frictional force wf act on the particle, which is the product of the dynamic coefficient of friction g as it slides down the surface of like particles by the normal reaction of this surface on the particle wn. The force balance yields the following equation: tan w ¼

g þ n( cos u g sin u) 1 n( sin u þ g cos u)

(7:1)

where u is the angle subtended by the flight lip at the center of the drum, and n ¼ re v2/g is the ratio of the centrifugal to the gravitational forces acting on the particle. Rotary dryers are usually operated in the range 0.0025 n 0.04, therefore the above equation gives accurate results over the range of practical importance, considering that Kelly [19] and Purcell [45] found that it is valid for values of n up to about 0.4. It has to be mentioned that this equation was tested for free-flowing solids having a constant moisture content. In practice the moisture content decreases

as the particles move to the exit end, furthermore the feed enters wet and may adhere to the flights. Since the angle, w, is given by Equation 7.1, the design value of the solids holdup per unit length of flight h* can be calculated from the geometry of the system. Glikin [11] expressed the following relationships for right-angled flights as u increases from zero: 1. For u < w, h* ¼ ll 0

j−b

l

l⬘

b j q re

x

FIGURE 7.3 Loading of flights in the first quadrant.


(7:2)

2. For u > w, if u w b < 0, then h* ¼ ll 0

r (1=2)l 1 2 l tan (w u) rl 2

(7:3)

and if u w b 0 and tan (u w b) < l0 /l, then h* ¼ ll 0

r (1=2)l 1 2 l [ tan b þ tan (u w b)] (7:4) rl 2

3. For u > w, if u w b > 0 and tan (u w b) l 0 =l, then h* ¼

l 02 2 tan (u w b)

(7:5)

The flight becomes empty for u w b ¼ 908 where b is the angle subtended by the flight at the center of the drum and is given by the relationship b ¼ tan

1

l0 rl

(7:6)

The maximum loading occurs at u ¼ 08 and is equal to h*0 ¼

r

r (1=2)l 1 2 þ l tan (w u) rl 2

ll 0 (r (1=2)l) 1 2 þ l tan w0 rl 2

(7:7)

where tan w0 ¼ ( (g þ n) / (1 ng)). Analogous analysis has been done for other common flights, for example, Baker [3] described in the same way for the angled- and extended-circular flights. The total amount of solids contained in the drum is about 10–15% of its volume. It has been proved empirically that this loading gives the most efficient performance, therefore a sufficient number of flights must be provided to contain and distribute these solids. Assuming that there are nf flights in the shell, the spacing between each will be

ui ¼ 360 =nf

(7:8)

In the case of right-angled flights, it has been proved by Glikin [11] that the minimum spacing between them must be such as to satisfy the equation re tan (ui b) > l tan w0

(7:9)

in order for the flights to load completely at u ¼ 08. The holdup of any particular flight, in the upper section of the drum, decreases, as the cylindrical shell rotates, from its maximum value h*0 to zero at a value of u equal to or, usually, less than 1808. According to Glikin [11], the loading on any flight in the bottom half of the drum is the mirror image of the flight positioned vertically above it in the upper section, and if the number of flights is even, the total holdup in the flights in a design-loaded drum will be H* ¼ 2

X

h* h*0

(7:10)

In this equation, the sum includes the holdup of each flight in the upper half of the shell, thus for 08 u 1808. A revised equation suggested by Kelly and O’Donnell [22], which has the form

H* ¼

h*0 (nf þ 1) 2

(7:11)

This relationship is more accurate when the particles cascade across the whole upper region. Nevertheless, in most practical cases cascading ceases for u much less than 1808 [19], and then that equation gives a value of H* much higher than the correct one. Glikin [11] proved that the discrepancy could get up to 80% or more. The design of the flights, not only determines the holdup of the dryer, but also the manner in which solids are shed from them. Kelly [19] has published many data about the distribution of cascading solids across the drum for right-angled, semicircular, and angled flights, but did not give detailed information on the geometry of them. It is not easy to determine which flight profile is the most efficient. Of course, particles cascading down the center of the shell will present the longest contact time with the hot gases, but the fact that the cascading is concentrated in a particular area, will cause considerable shielding of the particles by their neighbors, resulting in inefficient heat and mass transfer. The average length of fall depends on characteristics of the shell, flights, and particles and is given by the equation


R0 h Y dh* Y ¼ R00 h0 dh*

(7:12)

where h0 is the actual holdup in the flight at u ¼ 08 and h* the design holdup at any other value of angle q. h0 may be less or equal to the design holdup h0*. Kelly [19] proposed the expression Y ¼ De (sinu/ cosa) for underloaded and design-loaded drum; therefore ¼ De Y cos a

R0

sin udh* R0 h0 dh*

h0

(7:13)

In general, the solution of the above equation requires numerical integration; only in a few special cases there is an analytical solution, like for EAD flights that was presented by Kelly [19]. Thus, for a designloaded drum the following simple equation may be used: ¼ 2De Y p cos a

(7:14)

In an overloaded drum cascading commences at u ¼ 08, while in an underloaded one cascading only starts at some angle between 08 and 1808 at which the actual holdup becomes equal to the design one. The following revised expression gives the average distance of fall in an overloaded drum: ¼ Y

2De Mp cos a

(7:15)

where M ¼ H/H* 1. The next general expression gives the average distance of fall in cascading rotary dryers: ¼ Y

k0 De M cos a

(7:16)

The constant k0 depends upon the flight geometry and its value for different design-loaded flights are given in Table 7.1 [19].

7.4 RESIDENCE TIME MODELS A rotary dryer is a conveyor of solid material and at the same time promotes heat and mass transfer between the drying material and the hot gas. The particles move through the dryer by three distinct and independent mechanisms, and are described as follows.

TABLE 7.1 Values of k 0 for Different Design-Loaded Flights k0

Flight Profile Semicircular Equal angular distribution (EAD) Right-angled Equal horizontal distribution (EHD) Centrally biased distribution (CBD)

0.570 0.637 0.760 0.784 0.902

7.4.1 CASCADE MOTION This is the result of the lifting action of the flights and the slope of the dryer. The advance of a particle per cascade is equal to De (sin u / tan a) assuming that the descent path of the particle is vertical when there is no gas flow. With cocurrent gas flow there is increased advance of the particle due to the drag on the cascading solids, while the reverse action occurs with countercurrent flow.

7.4.2 KILN ACTION It is the motion of the particles as they slide either over the metal surface in the lower half of the shell, or over one another. Due to the slope of the dryer the particles proceed to its exit. This movement can also appear in horizontal drums as a result of the ‘‘hydraulic gradient’’ of the solids. Kiln action is always present, but is of major importance for overloaded dryers.

7.4.3 BOUNCING

Most of the studies referred to particles residence time, consider average holdups and residence time. To determine the distribution of residence times, Miskell and Marshall [31] used closely sized 496-mm sand containing a radioactive tracer in a 0.14-m diameter flighted drum, and found that the residence time is normally distributed. Fan and Ahn [8] showed that an axial dispersion model could describe the above results. Porter and Masson [43] concluded that deviations from plug flow are not large after examination of two cocurrent industrial dryers. However, it is not safe to assume plug flow of the particles in industrial dryers, because only narrowly sized materials were studied; furthermore just two dryers were studied. In practice there is a wider size distribution and a wider range of residence times. Moreover, if the operating criterion is the maximum moisture content of any particle instead of the bulk average value, it is logical to consider that there will be deviations from plug flow. In order to express residence time as a function of dryer’s characteristics Johnstone and Singh [16] proposed the equation t ¼

t ¼

H F

(7:17)

Theoretically, holdup can be measured directly. Nevertheless, in an industrial dryer this measurement is inconvenient, because the system must shut down and its content has to be discharged and weighed. In order to avoid that, a radioisotope or a small amount (0.5–1.0 kg) of an inert detectable solid may be added to the feed and analyzed in the product. The time required for the maximum concentration to occur represents the average time of passage [35].


(7:18)

where t is the residence time (min), L is the length, D is the diameter, N is the rotational speed (r/min), tan a is the slope of the dryer, and n is the dynamic angle of repose of the solids (degrees). This formula is derived from the equation t ¼

This motion occurs when a falling particle rebounds from the shell surface or from the settler layer of particles, instead of come to rest, and results in the particle progress because of the dryer slope. The average residence time (or, time of passage) t is defined as holdup H divided by the solids feedrate F, thus

0:0433(Ln)1=2 DN tan a

0:0310(Ln)1=2 DN tan a

(7:19)

which is known as the ‘‘Bureau of Mines,’’ proposed by Sullivan et al. [52] and refers to the passage of solids through a rotary kiln not equipped with flights or retaining dams. The modified constant in Equation 7.18 stands for the action of the flights. A much more extensive experimental study on rotary dryer holdup was done by Prutton et al. [44], who correlated their data of a design-loaded shell by the following empirical expression: t ¼

kL mu þ DN tan a 60

(7:20)

where k is a dimensionless constant, depending on the number and design of the flights and varies from 0.275 for 6 flights to 0.375 for 12 flights and m is a factor depending on the size and density of the particles and the direction of the airflow varies (in the range of the particular study) from 177 to 531 s2/m

for cocurrent flow and from 236 to 945 s2/m for countercurrent flow. This equation does not express m as a function of particle properties and, furthermore, is not considered to give accurate results at air velocities much higher than those used in the study, because, although it implies a linear relationship between residence time and gas velocity, it has been proved that there is a curvature in the plots between those two parameters, especially in the case of countercurrent flow at high gas rates. Perry and Chilton [35] proposed the following equation: t ¼

0:23L DN 0:9 tan a

(7:21)

based on the experimental data obtained by Friedman and Marshall [9] who present a wide-ranging study on residence times and recognized that the dryer holdup is affected by the number of flights, particularly at low feedrates, even though most of their data refer at values lower than those of industrial dryers. The following equation: Xa ¼ X0 KG

(7:22)

expresses the effect of air velocity for values up to 1 m/s, where Xa is the holdup with airflow, X0 is the holdup without airflow, G is the gas flow rate (kg/ hm2), and K ¼ 16.9/dp1/2rb is a dimensional constant in which rb is the bulk density (kg/m3) and dp is the weight average particle size (mm). For cocurrent flow the negative sign stands and for countercurrent the positive. The constant K has not been proven quite sufficient. Saeman and Mitchell [47] proposed the following expression, based on a theoretical analysis of the material’s transport through the dryer taking into account the incremental transport rates associated with individual cascade paths t ¼

L f (H )DN ( tan a m0 u)

(7:23)

where f (H) is the cascade factor varied between 2 for lightly loaded dryers and p for heavily loaded ones with small flights. The exact value seems to be affected by the cascading pattern. The positive sign stands for cocurrent flow and the negative sign for countercurrent flow; m0 is an empirical constant depended on the material. Saeman [48] developed a model for the estimation of that constant, but concluded that it is easier to measure it, due to the parameters required for the estimation, which are difficult to obtain.


Schofield and Glikin [49] analyzed the fluid mechanics of falling granules and proposed the relationship L 1 þ t t ¼ f Y ( sin a K 0 u2=g) sN

(7:24)

where Y is the average height of fall of the particle given by Equation 7.16, g is the acceleration due to gravity, K0 ¼ 1.5 f rf /dp rp is a constant related to the drag coefficient f, rf is the air density, rp is the particles density, 1/sN is the time spent by a particle on Ð the flights, where s ¼ 180/ and ¼ (1/h0) 0h0 u dh is the angle that the particle is carried in the flights, and tf ¼ (2 Y /g)1/2 is the average time of fall of the particles, assuming that the vertical component of the air drag is negligible as was proved by Kelly [21]. Generally, tf 1/sN A critical point in the analysis of the above residence-time equations is that residence time is calculated from the velocity of the average particle L/ t, whereas the residence time calculated from the average velocity L=t is much higher, because the particles progress through the dryer not by a simple kiln action, but there is a cascade motion of them. This observation was made by Glikin [11] who showed that for EAD flights the following expression stands: (L= t ) 0:69(L=t)

(7:25)

The average particle velocity is Z (L=t) ¼ * h0

ð h* 0

0

sin u dh* u

(7:26)

where Z ¼ pNDe [(sin a + K0 ur2/g)/cos a] and the relative velocity between the particles and the gas is ur ¼ u + (1/2) sin a(2gY )1/2. In these equations the plus sign applies for countercurrent flow and the minus sign for cocurrent flow. Glikin showed that for cocurrent flow the residence time t increases with particle size dp while the reverse relationship seems to exist for countercurrent flow. In order to explain the discrepancies between his equation of the form Leff 1 1 1 m 0 þ tf Z¼ 2 Y sin a f (u) N

(7:27)

which stands for EAD flights and experimental results, Kelly [20] proposed that a rapid forward movement as a result of kiln action, which should be taken into account, follows the cascade motion of the particles.

Therefore, the effective length in that equation is Leff instead of L, where Leff is the length of the shell over which the average granule progresses due to the cascade motion only and is given by the expression Leff ¼ kc L

(7:28)

The constant kc is a function of the loading and rotational speed, but it is independent of the slope of the drum, as Kelly’s experimental procedure proved. He proposed the following empirical expression for that constant: kc ¼ bM þ b0

(7:29)

in which b and b0 are functions of the rotational speed N. The values of these constants are presented in Table 7.2. Kiln action becomes important in overloaded drums as proved by experimental data and supported by the model of Kelly and O’Donnell [23]. In underloaded drums, particle bouncing, especially on the exposed metal surface of the shell, has an important contribution to their motion. Kelly and O’Donnell [23] present the most advance study of the particles motion through rotary dryers that have flights. Their work includes an extensive experimental procedure as well as a theoretical analysis of the behavior of the particles. They measure the cycle time and the advance per cycle for a single average particle, which was compared to the predictions of the model that incorporates cascade motion, kiln action, and bouncing. The basic features of their model are the following. The Schiller and Naumann equation was used for the estimation of the drag coefficient and the pressure drop of the air flowing through the curtain of the falling solids to that of air flowing through the free cross section of the drum for estimation of the effect of the particle shielding. The movement of the particles after bouncing from the shell, a flight or a bed of particles was taken into consideration. This effect is not important

TABLE 7.2 Values of b and b0 in Equation 7.29 N (r/min)

8 24

0.4 < M < 1.0

1.0 < M < 1.6

b

b0

b

b0

0.530 0.719

0.124 0.178

0.280 0.426

0.672 0.932


because, after contact, the particle loses most of its velocity in the direction normal to the surface and, in practice, the advance of the particle after the second bounce is very limited. There are three varieties of kiln action; the first refers to the sliding motion of the particle inside the shell after its bounce has stopped, the second occurs if the particle moves contrary to the direction of rotation of the drum and slips backward into the flight, and the third, appears only for overloaded drums, for which the holdup ratio M > 1, because there is a rolling load of solids in the bottom of the drum and the average particle bypasses one or more flights before being arrested by a flight. The particle advances with each bypass due to the slope. The above features were included in a computer simulation for the calculation of the advance and time for the average particle in a single cascade, as well as the average residence time. It was proved that cascade motion and bouncing are very important in the pilot dryer; bouncing has a major effect in underloaded kilns. Under these conditions, in a pilot and an industrial dryer, about 50 and 22%, respectively, of the particle advance was due to bouncing. At the same time, kiln action accounted for less than 10% of the advance, while it was becoming important for overloaded drums. The computed values of the residence time given by the model are greater than the measured ones, and the error becomes greater as the air velocity increases. Although the model proposed by Kelly and O’Donnell is quite advanced as long as it concerns the mechanisms of particle transport in rotary dryers, it is quite complex to be used for industrial design purposes. The kiln equations of Sullivan et al. [52] and of Johnstone and Singh [16], which are experimentally based, predict low values of the residence time in case of zero gas flow. When gas flow is applied, these relationships are inadequate, as there is no term to express that flow and, furthermore, give the same result for both cocurrent and countercurrent flow. So, these equations are unreliable for gas velocity greater than 1 m/s. The equations of Prutton et al. [44], Saeman and Mitchell [47], and Friedman and Marshall [9], which are also experimentally based, give comparable results at zero and low gas velocities, although the first and second seem to predict rather wide ranges of residence time. Their application requires judgment and experience, whereas their theoretical basis is not solid. These expressions have been formed for gas velocity less than 1.5 m/s. The standard deviation between their predictions is about 25% for gas velocities up to 1 m/s, but exceeds 100% at 3 m/s, so the extrapolation seems rather invalid. The disagreement between real and calculated values is

80 (1) 70

Residence time (min)

(2) 60

(3)

50

(4) (5)

40

(6) 30 (7) 20

(8)

10

Mean

0 0

1

2

3

4

5

6

Dryer slope (degrees) FIGURE 7.4 Residence time prediction versus dryer slope for zero airflow. 1, Sullivan et al. [52]; 2, Johnstone and Singh [16]; 3, Prutton et al. [44]; 4, Friedman and Marshall [9]; 5, Saeman and Mitchell [47]; 6, Schofield and Glikin [49]; 7, Kelly [20]; 8, Glikin [11].

expected to be greater in the range of industrial importance, which is 3–5 m/s. The equations proposed by Schofield and Glikin [49], Kelly [20], and Glikin [11] have theoretical basis and seem to be the most accurate for zero gas flow. Under these circumstances, Kelly’s model presents the best agreement with the experimental data. To some degree this occurs because of the presence of the empirical constant kc, which has been evaluated by fitting the model to those data. The models of Schofield and Glikin [49], and Glikin [11] predict residence times much higher than the experimental ones. Kelly and Glikin used the equation of Schiller and Naumann for the estimation of the friction factor. However, this expression refers to a single particle and it cannot predict sufficiently the effect of the raining curtain of the solids as they drop from the flights, particularly at high gas velocities. If fact, Kelly [19] rejected his model in favor of an empirical method. Figure 7.4 presents the effect of dryer slope to the residence time for zero airflow according to the above-mentioned equations, while Figure 7.5 shows the residence time versus airflow velocity for cocurrent flow.

7.5 HEAT AND MASS TRANSFER IN ROTARY DRYERS During drying, heat is supplied to the solids for the evaporation of water or, in a few cases, some other volatile component, and the removal of the corresponding vapor from the dryer.


The heat transferred in direct-heat rotary dryers is expressed by the following equation: Q ¼ Uv aV (Dt)m

(7:30)

where Q is the rate of heat transfer, J/s, Uva is the volumetric heat transfer coefficient, J/(sm3K) or W/ (m3K), V is the dryer volume, m3, and (Dt)m is the true mean temperature difference between the hot gases and the material. Miller et al. [30], Friedman and Marshall [9], and Seaman and Mitchell [47] have done considerable amount of research for the evaluation of Uva. The volumetric coefficient Uva is the product of the heat transfer coefficient Uv based on the effective area of contact between the gas and the solids, and the ratio a of this area to the volume of the dryer. When a considerable amount of surface moisture is removed from the solids and their temperature is unknown, a good approximation of (Dt)m is the logarithmic mean between the wet-bulb depressions of the drying air at the inlet and outlet of the dryer [35]. Miller et al. [30] present the first extensive study of heat transfer in rotary dryers and conclude that the total rate of heat transfer is affected by the number of flights. It is given by the following equations: Q ¼ 1:02LD

(nf 1) 0:46 G Dtlm 2

Q ¼ 0:228LD

for 6 flights (7:31)

(nf 1) 0:60 G Dtlm for 12 flights (7:32) 2

25 (1) (2)

Residence time (min)

20

(3) (4)

15

(5) (6)

10

(7) (8)

5

Mean 0 11

0.5

2

2.5

3

Air velocity (m/s) FIGURE 7.5 Residence time prediction versus drying air velocity for cocurrent flow. 1, Sullivan et al. [52]; 2, Johnstone and Singh [16]; 3, Prutton et al. [44]; 4, Friedman and Marshall [9]; 5, Saeman and Mitchell [47]; 6, Schofield and Glikin [49]; 7, Kelly [20]; 8, Glikin [11].

Comparing the above two relationships to the general equation (Equation 7.30), we can express the volumetric coefficient as Uv a ¼ 0:652(nf 1)D1 G0:46

for 6 flights

Uv a ¼ 0:145(nf 1)D1 G0:60

for 12 flights (7:34)

(7:33)

They also note that the rate of heat transfer is independent of the slope and the rotational speed of the shell, and therefore of the residence time, as well as of the flight size. The increase of the gas flowrate increases the efficiency of the dryer. Furthermore, they study a number of dryers having diameters up to 2.13 m and propose that the equations for 6 flights are more representative for the design of industrial dryers. This proposal is in agreement with the study of Prutton et al. [44]. Friedman and Marshall [9] noted that in practice the number of flights is in the range 6:56 (nf =D) 9:84

(7:35)

In case that nf 1, the following simple equation can be used: Uv a ¼ Ks G0:46 where 4.3 Ks 6.4.


(7:36)

Friedman and Marshall concluded that the above analysis has three major simplifications and cannot predict the heat transfer quite accurately. First, the heat losses from the dryer have not been taken into account, second the use of the logarithmic mean temperature difference Dtlm is not correct, as the temperature of the solids does not vary linearly with the gas temperature, and third, they express doubts for the correlations between the rate of heat transfer and the number of flights, due to the fact that Miller et al. [30], although they proposed the above equations based on experimental data, accepted that the one for 12 flights in not representative for industrial dryers. For their experiments, Friedman and Marshall [9] used an extensively insulated dryer to reduce heat losses to around 15%. They used advanced methods to achieve accurate measurements of the gas, solids, and shell along the length of the dryer, although due to circulation patterns within the dryer they obtain erratic results for the gas temperature, and had to calculate it by heat balances. From the analysis of their data they concluded that the use of coefficients based on the terminal temperature differences does not properly predict the performance of pilot dryers, which have a large shell-area-to-volume factor, although the estimations are a lot better in commercial dryers, which have relatively much smaller heat losses. Therefore, the scale-up of heat transfer data requires caution and experience. They found that Uva varies proportionally with the solids holdup (as a percentage of drum volume) X0.5 and increases with G0.16,

therefore is affected by gas rate in two independent ways. The holdup increases with G for countercurrent flow causing an increase in the effective contact area between the solids and the gas, which is expressed by parameter a. Friedman and Marshall [9] also suggested that the heat transfer coefficient Uv increases with gas rate, although this is not generally accepted. The rate of rotation has little effect on Uva, as it has opposing effects on the holdup and the cascade rate. They examined the effect of the number of flights on Uva and concluded that the major increase occurs. The simplest and rather conservative equation has the form Uv a ¼ KGn=D

(7:37)

where K is a proportional constant, G is the gas mass velocity (kg/m2h), D is the dryer’s diameter (m), and n is a constant. Based on the data of Friedman and Marshall [9] the constants are: K ¼ 44 and n ¼ 0.16 [35]. According to McCormick [29], the constant K determines flight geometry and shell speed. These parameters in addition to the number of flights seem to affect the overall balance, although there are no available data for evaluating these variables separately. As long as it concerns the gas velocity it seems that its increase breaks up the showering curtains of solids more effectively and exposes more solids surface, therefore there is an increase of a in Ua rather than U. Saeman and Mitchell [47] suggested a more advanced approach to the heat transfer mechanism in rotary dryers (and coolers). The heat transfer takes place mainly between the cascading solids and air entrained by them. This mass of air attains thermal equilibrium with the particles surface in a very short period and when it reaches the bottom of the dryer it diffuses into the main horizontal airflow, which confines to the voids between the cascades. To support this theory, they measure the air temperatures in the voids near the bottom of the shell, which were higher than those at the top. Also, the bulk of the heat transfer occurs within about 0.3–0.6 m of the origin of the cascade, as it was proved by temperature measurements in the cascading streams. Therefore, the heat transfer rate is a function of the cascade rate, which depends on the flights number and size, the rate of rotation, and the holdup, and the ratio of air– material entrainment in the cascading streams, which depends mainly on flight size. Other parameters, such as the surface area of the particles, have less influence. They employ a heat transfer coefficient based on unit length of the dryer, thus


Q ¼ UL aLDtm

(7:38)

where ULa is in W/(mK). The two coefficients Uva and ULa are related by the equation UL a ¼

pD2 Uv a 4

(7:39)

For modern commercial dryers that have a flight count per circle of 2.4 to 3.0 D and operate at shell peripheral speeds of 60–75 ft/min, the following equation has been proposed: Q ¼ (0:5G0:67 =D)V Dtlm ¼ 0:4LDG0:67 Dtlm

(7:40)

where Q is in Btu/h, L is the dryer’s length in ft, D is in ft, G is in lb (h ft2 of cross section), and Dtlm is the log mean of the drying gas wet-bulb depressions at the inlet and outlet of the dryer. A different method for the estimation of heat transfer during drying can be obtained by dimension0 0 less equations of the type Nu ¼ a0 Rem Prn , which can be transformed as jH ¼ aRen

(7:41)

thus the heat transfer factor correlates to Reynolds number. This analysis can be done for two reasons. First, it is a very simple expression and the Reynolds number is easy to be estimated in most cases, through three parameters that can be measured quite easily, the particles diameter, the velocity of the drying medium, and its temperature. The second reason is that using this equation, we calculate directly the heat transfer factor that is important when we use analogies among momentum, heat, and mass transport. The most common is the well-known Chilton– Colburn analogy (or simply Colburn analogy) that is based on empirical correlations, and not on mechanistic assumptions that are only approximations. Thus, it represents the experimental data extremely well over the range in which the empirical correlations are valid. This analogy stands for both laminar and tubular flows and for Prandtl and Schmidt numbers between 0.6 to 100 and 0.6 and 2500, respectively. The Chilton–Colburn analogy can be expressed as jH ¼ jD ¼

f 2

(7:42)

where f is the friction factor, jD is the mass transfer factor, and jH is the heat transfer factor, given by the expression jH ¼ StPr2=3 ¼

h ru1 Cp

Pr2=3

(7:43)

Figure 7.6 presents the heat transfer factor versus Reynolds number for rotary drying processes and various materials, Figure 7.7 shows the ranges of variation of the heat transfer factor versus Reynolds number for the rotary drying process in comparison with other thermal processes, and Figure 7.8 presents the estimated equation of heat transfer factor for the rotary drying versus Reynolds number, in comparison with other thermal processes. The inlet gas temperature in a direct-heat rotary dryer is generally fixed by the heating medium, i.e., 400–450 K for steam and 800–1100 K for oil- and gasfired burners. Lower temperatures should be used only if there are limitations by the shell’s material. The exit gas temperature, which is a function of the economics involved, may be determined by the relationship

TABLE 7.3 Constant of Equation 7.41 and the Corresponding Reynolds Number Range for Some Products Product/Reference

a

n

min Re

max Re

Fish Shene et al.

0.00160

0.258

80

300

Soya Alvarez et al. Shene et al.

0.00960 0.00030

0.587 0.258

10 20

100 80

Sugar Wang et al. Rotary

0.805 0.001

0.528 0.161

1 500 10

17 000 300

where St ¼ h/ru1 Cp is the Stanton number, h is the heat transfer coefficient, r is the air density, u1 is the air velocity, and Cp is the specific heat of the air. Note that the second equaivalence, f/2, in Equation 7.42 stands only in the case of flow around relatively simple shapes, like flat surfaces or inside tubes. Knowing the heat transfer factor we know the mass transfer factor, as well, and can calculate parameters concerning mass transfer, like the diffusion coefficient. This is important considering that rotary drying includes both heat and mass transfer, as the material receives heat and losses moisture, simultaneously. Data retrieved from the literature for the drying of some materials in rotary dryers are shown in Table 7.3, which presents the constants of equation jH ¼ aRen, and the range in which it is valid. A general expression for the process is also given.

Nt ¼ (t1 t2 )=(Dt)m

where Nt is the number of heat transfer units based on the gas, t1 is the initial gas temperature (K), and t2 is the exit gas temperature (K), allowing for heat losses. The most economical operation of rotary dryers can be achieved for Nt in the range 1.5–2.5 as it has been found empirically. The diameter of a rotary dryer may vary from less than 0.3 m to more than 3 m whereas the length-todiameter ratio, L/D, is most efficient between 4 and 10 for industrial dryers. In a dryer design the value of Nt may change until the ratio mentioned above fall within these limits. The volume of the dryer that is filled with material during operation is 10–15%. Lower fillage is insufficient to utilize the flights, while a greater one causes a shortcircuit in the feed of solids across the top of the bed [35]

1 Rotary drying

0.1

Non food material jH = 0.877Re−0.5281

jH 0.01

Sugar

0.001

0.0001 1

10

100

1,000

10,000

100,000

Re

FIGURE 7.6 Heat transfer factor versus Reynolds number for the rotary drying process and various materials.


(7:44)

1

0.1

jH

0.01

Rotary

0.001 1

10

100

1,000

10,000

100,000

Re FIGURE 7.7 Ranges of variation of the heat transfer factor versus Reynolds number for the rotary drying process in comparison with other thermal processes.

u¼

0:23L BLG 0:6 0:9 SN D F

(7:45)

B ¼ 5(Dp )0:5

(7:46)

7.6 ENERGY AND COST ANALYSIS The power required to drive a dryer with flights may be calculated by the following equation, proposed by the CE Raymond Division, Combustion Engineering Inc., bhp ¼

N(4:75Dw þ 0:1925D0 W þ 0:33W ) 100,000

Drying constant (1/h)

50

(7:47)

u = 3 m/s Y = 0.01

40

u = 5 m/s Y = 0.01

u = 3 m/s Y = 0.03

30

u = 2 m/s Y = 0.01

20

10

0 50

150

250 350 Air temperature (8C)

FIGURE 7.8 Typical drying curves.


450

550

where bhp is the break horsepower required (1 bhp ¼ 0.75 kW), N is the rotational speed (r/min), D is the shell diameter (ft), w is the load of the material (lb), W is the total rotating load (equipment plus material) (lb), and D0 is the riding-ring diameter (ft), which for estimating purposes can be considered as D0 ¼ (D þ 2). The estimated cost of a steam-heated air rotary dryer, including auxiliary subsystems such as finned air heaters, transition piece, drive, product collector, fan and duct, ranges from about $100,000 for a dryer size 1.219 m 7.62 m to $320,000 for a dryer size 3.048 m 16.767 m. Their evaporation capacity is 136 and 861 kg/h, respectively, whereas they have a discharge value ranging from 408 kg/h for the smaller dryer to 2586 kg/h for the bigger one. In case that combustion chambers and fuel burner are required for operation at higher temperatures the cost is higher. The total installation cost that includes allocated building space, instrumentation, etc., is 150– 300% of the purchase cost. Operating costs include fuel, power, and 5–10% of one worker’s time, the yearly maintenance cost is 5–10% of the installation cost, and the power required for fans, dryer drive, and feed and product conveyors ranges from 0.5D2 to 1.0D2. The above prices are referring to carbon steel construction; when 304 stainless steel has to be used the prices are increased by about 50%. High-temperature direct-heat rotary dryers present thermal efficiency in the range 55–75%, which is reduced to 30–55% for dryers that employ steamheated air as heating medium.

7.7 A MODEL FOR THE OVERALL DESIGN OF ROTARY DRYERS One way to estimate the time for the material to be dried is through the drying constant, kM, that can be determined experimentally using an apparatus in which air passes through the drying material and air temperature, humidity, and velocity are controlled, while the material moisture content is monitored. A number of experiments have to be carried out for different temperatures, humidities, and velocities. The application of these methods proved that the drying constant depends on those parameters of the drying air and that it can be expressed as a function of them through a general equation of the type kM ¼ f (TA ,YA , uA )

(7:48)

7.7.1 BURNER

A derived analytical correlation that can be produced by fitting the above equation to experimental data is given by the following equation: 0

kM ¼ k0

T T0

k01

Y Y0

specifications by minimizing the total drying cost. The specifications include the solids feedrate Fs (kg/h db), and the inlet and outlet moisture content of the material, X0 (kg/kg db) and Xs (kg/kg db). Among the characteristics of the dryer are its diameter D (m), the length-to-diameter ratio L/D, the totalholdup-to-volume ratio H/V, the number of flightsto-diameter ratio nf/D, and the slope of the cylindrical shell s (%). The drying conditions include the inlet temperature TAC (8C) and the gas velocity u (m/s) at temperature TA (8C). A simplified diagram of the dryer is shown in Figure 7.9. The mathematical model of the process consists of two parts, the model of the burner and the model of the dryer.

k02 k03 u u0

(7:49)

where T0, Y0, u0 are the parameters which express the mean values of the intervals of air temperature, humidity, and velocity that are used for the experi0 0 0 0 ments, and k0 , k1, k2 , and k3 are parameters. Figure 7.8 presents typical curves, which express the drying constant versus temperature for various air humidities and velocities. Krokida et al. [28] proposed a model for the design of a rotary dryer, based on the estimation of the drying kinetics of the material that express data from laboratory experiments, and the calculation of residence time of the dryer from empirical equations. The dryer size and characteristics as well as the operating conditions can be calculated for given process

Assuming that the fuel is hydrocarbon with heat of combustion DHf (kJ/kg) and fraction of hydrogen CH (kg/kg) and that the combustion reactions are C þ ! CO2 and H2 þ 1/2O2 ! H2O, then 9 CH kg of water vapor are produced per kg of fuel. Thus Rw ¼ 9CH Z

where Rw is the production rate of water vapor (kg/h) and Z is the feedrate of fuel (kg/h). The total and moisture balances over the burner are given by the following equations, which describe the combustion process: FAC (1 þ YAC ) ¼ FAO (1 þ YO ) þ Z FAC YAC ¼ FAO YO þ Rw

Burner

Flue gas (FAC, TAC, YAC) Wet material (Fs, XO)

Rotary dryer

Exhaust air (FAC, TA, YA) Dried material (Fs, Xs)

FIGURE 7.9 Simplified diagram of the dryer and burner constituting the drying process unit.


(7:51)

(7:52)

where FAO and FAC are the inlet and outlet flowrate of gases at the burner (kg/h db), and YO and YAC are

Air (FAO, TO, YO)

Fuel (Z)

(7:50)

the inlet and outlet humidity of the gases at the burner (kg/kg db), respectively. Assuming that the gases have the same thermophysical properties as air, the corresponding energy balance over the dryer is given by the following relationship: FAC (1 þ YAC )CPA (TAC T0 ) ¼ ZDHf

(7:53)

where TAC is the outlet gas temperature at the burner (8C), T0 is the ambient temperature (8C), and CPA is the specific heat of the gases (kJ/kg K).

7.7.2 DRYER The following equations describe the mass and energy balances upon the dryer. Mass balance on water FAC (YA YAC ) ¼ FS (XO XS )

(7:54)

where YAC is the inlet humidity of the gases at the dryer (equal to the outlet humidity of the gases at the burner) (kg/kg db), and YA is the outlet humidity of the gases at the dryer (kg/kg db). Energy balance (simplified)

where T, Y, u are the temperature (8C), humidity 0 (kg/kg db), and velocity of the drying gas, and k0 , 0 0 0 k1, k2 , and k3 are parameters, which express the effect of various factors on the drying constant. The equilibrium moisture content of the solids, as a function of water activity and temperature of the surrounding air, can be calculated by the following correlation: XSE ¼ b1 exp (b2 =TA )[aw =(1 aw )]b3

(7:58)

where aw is the water activity of the gas stream and b1, b2, and b3 are characteristic constants. The absolute humidity of the drying airstream can be evaluated by the relationship Y ¼ m[aw P0 (TA )]=[P aw P0 (TA )]

(7:59)

where m ¼ 0.622 is the water-to-air molecular ratio and P0 (TA) is the water vapor pressure at temperature TA. The water vapor pressure at temperature TA can be obtained from the Antoine equation ln P0 (TA ) ¼ A1 A2 =(A3 þ TA )

(7:60)

where A1, A2, and A3 are constants. FAC CPA (1 YAC )(TAC TA ) þ FS DHV (XO XS ) ¼ 0 (7:55) where CPA is the specific heat of the air–vapor mixture (kJ/kg K), DHV is the latent heat of vaporization of water at the reference temperature (kJ/kg), and TA is the mean air–vapor temperature at the dryer output.

7.7.3 DRYING KINETICS The following well-known first-order kinetic model is selected to express the drying kinetics: (X XSE ) ¼ exp ( kM t) (X0 XSE )

(7:56)

where X is the material moisture content (kg/kg db) after a time interval t (h), kM is the drying constant (per hour), and XSE is the equilibrium material moisture content. The drying constant is a function of gas conditions and the following empirical equation can be used: 0

0

0

0

kM (T,Y , u) ¼ k0 T k1 Y k2 uk3


(7:57)

7.7.4 RESIDENCE TIME The residence time ( t ) is defined by the equation t ¼ M=FS

(7:61)

where M is the total product mass in the dryer, which relates to the product holdup of the dryer (H) by the following expression M ¼ (1 «)rP H

(7:62)

where rp is the density of the material (kg/m3) and « is its porosity. Generally, the residence time in a rotating dryer is a function of its length, diameter, slope, and rotating velocity. An empirical equation can be used [24] for this correlation as follows: t ¼

kL NDs

(7:63)

where k is an empirical constant. An empirical equation is also used by Kelly to correlate the total holdup to the flights load per unit length. This relationship underestimates the true

holdup value as it ignores the particles cascading through the gas. The equation can be written as

The electrical power hp for the cylinder rotation is given as follows (Kelly [24]):

H ¼ 0:5(nf þ 1)h0 L

hp ¼ qND(M þ W 0 )

(7:64)

where h0 is the holdup per meter (m2).

7.7.5 GEOMETRICAL CONSTRAINTS The following geometrical constraints should be added to the mathematical model: 5% < H =V < 15% 2 < L=D < 20 5 < nf =D < 10 Cost estimation The process unit cost of wet product ($/kg wb) has to be minimized Cp ¼

CT FS (1 þ XS ) top

(7:65)

where CP is the cost of the product due to the drying process, top is the operating time per year (h/y), and CT is the total annual cost of the drying process that can be expressed by the following equation: CT ¼ eCeq þ Cop

(7:66)

where eCeq is the yearly capital cost ($/yr), Cop is the operating cost ($/yr), and e is the capital recovery factor that is given by the equation e¼

i(1 þ i)N (1 þ i)N 1

(7:67)

where i is the annual interest rate and N is the time of the loan (yr). The equipment cost is affected by the size of the dryer and the consumption rate of fuel, assuming that a furnace is used for heat supply. Thus, Ceq ¼ aD AnD þ anZ Z nZ

(7:68)

where aD, aZ are unit costs and nD, nZ are scaling factors for the dryer and burner, respectively. The operating cost involves electrical energy and fuel cost: Cop ¼ hp Ce top þ ZCZ top

(7:69)

where Ce and Cz are the electricity and fuel cost, respectively.


(7:70)

where q is an empirical constant and W 0 is the dryer weight (kg). The calculation of the dryer weight is based on its geometrical characteristics and is given by 2pD2 þ pDL dx W ¼ rM 4

(7:71)

where dx is the dryer wall thickness (m), and rM is the metal density (kg/m3). A degree of freedom analysis suggests that five design variables are available for the design problem described above. It can be proved that an effective solution algorithm can be based on the following selection of design variables: TAC, u, H/V, L/D, and nf/D, where the first and second express the operating conditions and the rest the dryer shape.

7.8 CASE STUDY 1 The solution of a typical dryer problem for an industrial olive cake rotary dryer is presented. The data required for process design calculations are given in Table 7.4. The results of calculations using the model proposed by McAdams [28] are presented in Table 7.5, and are obtained by minimizing the process unit cost, and evaluating the design variables. A sensitivity analysis of the process unit cost is achieved by changing the two significant decision variables: the drying air temperature and the velocity. As the air-drying temperature is allowed to vary, air velocity is maintained constant and each time all other variables are calculated. It must be noted that as the air temperature increases and thus the operating cost increases, whereas the size of the equipment and, consequently, the cost of equipment decreases. For a given air velocity, the total cost reaches a maximum at a specific air temperature (see Figure 7.10). In Figure 7.11 the total unit cost is presented as function of air temperature for different air velocities. The model was adapted to an industrial rotary dryer with the following characteristics: length 22 m, diameter 2.5 m, and number of flights 24. The drying conditions are 6508C inlet drying air temperature, 2.4 m/s mean gas–vapor velocity, and the fuel consumption rate is 1500 kg/h. The operating conditions obtained from process design calculations are close to the real ones.

TABLE 7.4 Data for Process Design Calculations

TABLE 7.5 Results of Process Design Calculations

Process specifications Solids flow rate Input material moisture content Output material moisture content

Fs X0 X

5000 1.00 0.10

kg/h kg/kg db kg/kg db

Fresh air characteristics Temperature Humidity

T0 Y0

25 0.01

8C kg/kg db

Thermophysical properties Water to air molar fraction Air specific heat Water specific heat Heat of combustion Latent heat of vaporization of water Porosity

m CPA CPV DHf DH0 «

0.622 1.18 1.98 15 2500 0.48

— kJ/kg 8C kJ/kg 8C MJ/kg kJ/kg —

k q

0.003 1

— —

aD nD aZ nZ N i top Ce Cz

8 0.62 200 0.4 10 8 2000 0.07 0.05

Empirical constants Empirical constant in Equation 7.14 Empirical constant in Equation 7.24 Economic data Dryer unit cost Dryer scaling factor Burner unit cost Burner scaling factor Lifetime Interest rate Operating time Electricity cost Fuel cost

k$/m2 — $/kg — yr % h/yr $/kW h $/kg

7.9 CASE STUDY 2 For the drying of catalyst pellets, the engineers of a certain industry decided that a direct rotary dryer will be appropriate, and studied the performance of a pilot plant rotary dryer in order to obtain data for the scale-up. The production F will be 350 kg/h on a dry basis. The pellets have cylindrical shape, about 1 cm long and 1 cm in diameter, their bulk density rb is 570 kg/m3, the specific heat Cps is 1 kJ/kg K, and the initial moisture content X0, as a result of the previous unit operation, is 0.65 kg/kg db. The final product, in order to be stable, must have moisture content X no more than 0.05 kg/kg db. It is nonsticking, but it is sensitive at high temperatures. Therefore, cocurrent operation has to be used and the initial air temperature T1 will not exceed the range of 150–1708C. The heating medium will be hot air. A steam-air heat exchanger is going to be used for the heating. The air velocity has to be limited to avoid entraining of the material by the air. Table 7.6 presents the values of the operating parameters of the pilot plant rotary dryer. The following calculations aim at a preliminary design of the dryer.


Design variables Input air temperature Mean air–vapor velocity Total holdup to volume fraction Length-to-diameter fraction Number of blades to diameter fraction

700 2.4 15 20 10

TAC u H/V L/D nf/D

8C m/s % — 1/m

Drying air characteristics Mean air temperature Humidity outlet

TA Y

298 0.37

8C Kg/kg db

Operating characteristics Residence time Total holdup Rotating velocity

t H N

0.3 8.4 8.6

h m3 rpm

Dryer characteristics Diameter Length Blade number

D L nf

1.5 30.6 15

m m

Utilities Fresh air flow rate Fuel rate

FA0 Z

15,048 1066

kg/h kg/h

Economics Electricity cost Fuel cost

Ce Cz

6286 106,606

$/yr $/yr

Operating cost Cost of equipment Total cost Unit cost

Cop Ceq CT Cp

112,891 55,619 168,510 0.00843

$/yr $/yr $/yr $/kg wb

—

The overall material mass (kg/h) that is fed is F1 ¼ F (1 þ X0 )

(7:72)

whereas the mass (kg/h), which exits the dryer is F2 ¼ F (1 þ X )

(7:73)

Therefore, the evaporating water mw (kg/h) is mw ¼ F1 F2

(7:74)

The heat supplied by the hot air is used for five different operations: 1. To evaporate the water, that leaves the material Q1 ¼ mw DHw

(7:75)

2. To heat the vapor from the initial wet-bulb temperature of the air to the exit air temperature

0.018

Total unit cost ($/kg)

TABLE 7.6 Data Obtained by the Pilot Plant Dryer

u = 2. 4 m/s

0.016 0.014

Ctot

Inlet temperature of drying air Exit temperature of drying air Wet-bulb temperature of inlet air Exit temperature of product Permitable air mass velocity Retention time of product

0.012 0.010 Ceq

0.008 0.006 0.004

T1 T2 Tw T2 uperm t

160 65 40 45 3 0.35

8C 8C 8C 8C kg/m2s h

Cop

0.002 0.000 0

200

400 600 800 Air temperature (⬚C)

1000

FIGURE 7.10 Total unit cost versus air temperature for air velocity 2.4 m/s.

Q2 ¼ mw Cpv (T2 Tw )

(7:76)

3. To heat the water that evaporates, from its initial temperature, as it enters the dryer, to the inlet wet-bulb temperature of the air, in order to evaporate Q3 ¼ mw Cpw (Tw Tm1 )

(7:77)

4. To heat the dry solid from its inlet temperature to its exit temperature Q4 ¼ FCps (Tm2 Tm1 )

(7:78)

5. To heat the water that remains in the final product from the inlet to the exit temperature of the material Q5 ¼ FXCpw (Tm2 Tm1 )

0.015

Total unit cost ($/kg)

0.014 0.013 u = 5 m/s u = 2.4 m/s

0.011 u = 4 m/s

0.010 0.009 0.008 0

200

400 600 Air temperature (8C)

800

1000

FIGURE 7.11 Total unit cost versus air temperature for three different air velocities.


Q ¼ (1 þ a)(Q1 þ Q2 þ Q3 þ Q4 þ Q5 )

(7:80)

where a is a factor that represents the heat losses due to the conduction between the outer surface of the dryer and the atmospheric air and especially, because of radiation. These losses are estimated to be about 7.5–10% of the heat consumption for the reasons mentioned above. The largest amount of heat is used for the evaporation of moisture content and is expressed by the ratio b ¼ Q1 =Q

(7:81)

The air mass rate G required in order to transfer sufficient amount of heat for the drying is

(7:79)

where DHw is the latent heat of vaporization (kJ/kg), Cpv, Cpw, Cps, are the specific heat of vapor, water,

0.012

and solid (kJ/kg 8C), respectively, Tw is the inlet wetbulb temperature of the drying air, T2 is the outlet temperature of the air (8C), and Tm1, Tm2 are the inlet and exit temperature (8C) of the material (dry solid and moisture content), respectively. The overall heat transferred to the product is given by the correlation

G¼

Q Cp,air (T1 T2 )

(7:82)

where T1 is the inlet air temperature (8C) and Cp,air is the specific heat of air (kJ/kg 8C). For the estimation of the diameter D of the dryer (m) two points have to be examined. First it must be large enough so that the air mass velocity u (kg/m2s) will not exceed the value that causes entrainment of the product, and second we must assume that only a percentage of the dryer cross section represents a free area for the air to pass. This percentage is about 85% ( j ¼ 0.85), as can be estimated by operating rotary dryers. Therefore the diameter of the cylindrical shell is calculated by the following equation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4G (7:83) D¼ 3600pju where 3600 is a factor for the arrangement of the units.

The humidity of the exit air should be checked for not exceeding the maximum mass of vapor the air can hold under the specific condition on the exit (for %RH ¼ 100). The initial air humidity Y1 is about 0.01 kg/kg dry air (for T1 ¼ 1608C and Tw ¼ 408C). The humidity of the exit air Y2 is Y2 ¼ Y1 þ

mw G

(7:84)

3

The volume V of the dryer (m ) is calculated by the expression V¼

tF2 Hrs

(7:85)

where t is the retention time of the product (h), and H is the dryer holdup, that is assumed to be about 0.07– 0.08 of the dryer volume, as values in this range give good performance in industrial dryers. The retention time could be calculated by the geometric characteristics of the dryer, but it is desirable to obtain it by experiments rather than through theoretical calculations. In this case study it is estimated on the basis of pilot plant data, and the volume is calculated by the above expression. The length L of the dryer (m) is given by the correlation 4V L¼ pD2

T1 Tw T2 Tw

(7:88)

Steam at temperature Tst (8C) will be used as heating medium in the exchanger. The consumption of steam is Fst ¼


Qhe DHst

F X0 X Tm1

350 0.65 0.05 25

Kg/h db kg/kg db kg/kg db 8C

Thermophysical properties Evaporation heat of water Specific heat of product Specific heat of water Specific heat of vapor Specific heat of air Bulk density

DHw Cps Cpw Cpv Cp,air rb

2350 1.0 4.18 1.88 1.01 570

kJ/kg kJ/kg 8C kJ/kg 8C kJ/kg 8C kJ/kg 8C kg/m3

Properties of air Atmospheric air temperature Humidity of inlet air

T0 Y1

15 0.01

8C kg/kg db

Constants Dryer holdup Factor Factor

H a j

0.075 0.1 0.85

— — —

The thermal efficiency of the dryer is nth ¼

Q1 þ Q2 þ Q3 þ Q4 þ Q5 Qhe

(7:90)

Table 7.7 presents the specifications, thermophysical properties, and factor j for the design of the dryer, and Table 7.8 shows the values of the parameters calculated by the above equations.

(7:87)

and should be in the range 1.5 to 2.5 [35]. These ranges have been estimated through practical experience by the study of industrial direct rotary dryers in order for efficient operation to be achieved. For the heating of the air, a steam-air heat exchanger is to be used. Its energy load should be sufficient for the heating of the airstream from the initial atmospheric temperature T0 (8C) to the inlet air temperature in the dryer T1, and given by the equation Qhe ¼ GCp,air (T1 T0 )

Product specifications Production rate (dry basis) Initial moisture content Final moisture content Inlet product temperature

(7:86)

In practice the ratio L/D should be within the range 4 to 10, for optimum performance. The number of heat transfer units NT is defined by the equation NT ¼ ln

TABLE 7.7 Data for Process Design Calculations

(7:89)

TABLE 7.8 Results of Process Design Calculations Overall inlet material Overall exit material Evaporating water Overall heat consumption Heat for evaporation Heat for vapor Heat for liquid Heat for product solid Heat for product water Air mass rate Diameter Volume Length Number of heat transfer units Heat load of exchanger Heat consumption Thermal efficiency

F1 F2 mw Q Q1 Q2 Q3 Q4 Q5 G D V L NT Qhe Fst nth

578 368 210 577,500 493,500 9,870 13,167 7,000 1,463 6,019 0.9 3.0 4.6 1.6 881,447 316 0.60

kg/h kg/h kg/h kJ/h kJ/h kJ/h kJ/h kJ/h kJ/h kg/h m m3 m — kJ/h kg/h —

7.10 CONCLUSION Until recently, the design of the industrial dryers was based on the experience of manufacturers and suppliers of these units, who used both data obtained in pilot plant rotary dryers and operating characteristics from units already installed. Because of the variety in drying equipment and solid materials that are processed, little consideration was given to mathematical models and theoretical approaches. It was common practice for the dryer to be built a bit oversized and inefficient, but mechanically sound and well proven in operation, instead of an optimization process to be followed, even if the capital and operating costs were larger. In resent years, many models and simulation techniques have been published, which can be useful for the design of dryers, especially when the drying material is the same or similar to the one the model refers to. Nevertheless, the development of a universal model of the rotary dryer, that combines the cascading motion of the particles with the heat and mass transfer, is questionable. The mathematical expressions and models that have been described can promote the understanding of the individual processes that take place during drying and the particular effect of each design parameter to the drying process.

NOMENCLATURE A1 A2 A3 aD aZ b b0 bhp b1 b2 b3 Ce Ceq CH Cop CP CT CZ D D0 De dp dx e F

constant in Equation 7.60 constant in Equation 7.60 constant in Equation 7.60 unit cost for the dryer, $/m2 unit cost for the burner, $/kg constant in Equation 7.29 constant in Equation 7.29 break horsepower constant in Equation 7.58 constant in Equation 7.58 constant in Equation 7.58 electricity cost, $/kW h equipment cost, $ hydrogen mass fraction, kg/kg operating cost, $/yr process unit cost, $/kg wb total annual cost, $/yr fuel cost ($/kg) drum inside diameter, m riding-ring diameter, ft effective drum diameter, m particle diameter, mm dryer wall thickness, m capital recovery factor solids mass feedrate, kg/s


f f( ) G g H H* h* h*0 h0 hp i j jD jH K K K0 Ks k k k0 kc kM k00 k10 k20 k30 L l l0 Leff M M m m m0 m0 mw N N Nt n n n0 nD nf nth nZ

drag coefficient, or friction factor function of parameter indicated in parentheses gas flowrate per unit area of dryer cross section, kg/hm2 acceleration due to gravity, m/s2 actual volumetric holdup of drum, m3 design volumetric holdup of drum, m3 design volumetric holdup of solids per unit length of flight, m3/m value of h* at u ¼ 08 actual volumetric holdup in the flight of solids per unit length of flight at u ¼ 08, m3/m electrical power, kW annual interest rate percentage of the dryer cross section represents a free area for the air to pass mass transfer factor heat transfer factor constant in Equation 7.22 proportional constant in Equation 7.37 constant in Equation 7.24 constant in Equation 7.36 dimensionless constant in Equation 7.20 empirical constant in Equation 7.63 constant constant drying constant, per hour constant in Equation 7.49 constant in Equation 7.49 constant in Equation 7.49 constant in Equation 7.49 drum length, m radial flight depth, m height of flight lip, m length of drum over which particle travels by cascade motion, m ratio of actual drum holdup to the design holdup total material mass in the dryer, kg constant in Equation 7.20 constant in Equation 7.59 empirical constant in Equation 7.23 ratio of actual flight holdup to the design holdup at u ¼ 08 rate of water vaporization, kg/h period of the loan, y rotational speed, rpm number of heat transfer units based upon the gas dynamic angle of repose of the solids (degrees) constant in Equation 7.37 and in Equation 7.41 constant scaling factor for the dryer number of flights thermal efficiency scaling factor for the burner

P0 Q Qi q r re Rw s T0 T tf top UL Uv u uperm ur V w W W0 X X0 Xa Y Y Y Z Z

water vapor pressure, kPa rate of heat transfer between gas and solids, J/s partial rates of heat transfer in Case Study 2, kJ/h empirical constant in Equation 7.70 drum inside radius, m effective drum radius production rate of water vapor in burner, kg/h slope of the cylindrical shell, % ambient temperature, 8C temperature, 8C average falling time of the particles annual operating time, h/yr overall heat transfer coefficient based on dryer length overall heat transfer coefficient based on dryer volume gas velocity, m/s permitable air mass velocity, kg/m2s relative velocity between particles and gas drum volume, m3 load of the material, lb total rotating load, lb dryer weight, kg material moisture content, kg/kg solids holdup expressed as percentage of drum volume without airflow solids holdup expressed as percentage of drum volume with airflow absolute humidity of air, kg/kg db particle length of fall, m average particle length of fall, m parameter in Equation 7.25 flowrate of fuel, kg/h

GREEK SYMBOLS a a a a0 aw b b g DHf DHV (DT)m DT1m

«

ratio of the effective area to the volume of the dryer constant in Equation 7.80 and Equation 7.41 drum slope (degrees) constant water activity of airstreams angle subtended by flight at center of the drum factor in Equation 7.81 dynamic coefficient of friction of particle heat of combustion of fuel, kJ/kg latent heat of vaporization of water, kJ/kg true mean temperature difference between the hot gases and the material, 8C logarithmic mean temperature difference between the wet-bulb depressions of the drying air at the inlet and outlet of the dryer, K porosity


u ui n r rb rM rp s t w w0 wc wf wg wn v

angle subtended by flight lip with horizontal at center of the drum angle to which average particle is carried in flights before cascading angular spacing between flights ratio of centrifugal to gravitational forces acting on particle air (or gas) density, kg/m3 bulk density of solids, kg/m3 metal density, kg/m3 particles density, kg/m3 parameter in Equation 7.24 residence time of average particle (or, time of passage) angle between horizontal and free surface of solids angle between horizontal and free surface of solids at u ¼ 08 centrifugal force on particle, N frictional force on particle, N gravitational force on particle, N normal reaction of surface on particle angular speed of drum

SUBSCRIPTS a air he s st AC A0 SE v w 1 2

gas air heat exchanger solid steam drying airstream fresh airstream at equilibrium vapor wet-bulb inlet outlet

DIMENSIONLESS NUMBERS Nu Pr Re St

Nusselt number Prandtl number Reynolds number Stanton number

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Rotary Dryer

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