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Modelling and Dynamic Simulation of an Industrial Rotary Dryer.

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Dev. Chem. Eng. Mineral Process., 5(3/4),pp.155-182. 1997.
Modelling and Dynamic Simulation of an
Industrial Rotary Dryer
C. Duchesne', J. Thibault' * and C. Bazin2
D e p a m n t of Chemical Engineering and 2Departmentof Mining and
Metallurgy, Lava1 University, Sainte-Foy (Quebec) CANADA GlK 7P4
Rotary dryers are widely used in chemical and mineral processes due to theirflexibility
and simplicity of operatwn. Nevertheless, the comprehension of the basic phenomena
taking place in this type of dryer is still of grea interest. f n order to bener understand the
phenomenological behavwur of the process and to assess product moisture control
strategies, a complete dynamic simulator of a mineral concentrate dryer hus been
developed ;Ilte simulator is calibrated with industrial &a and consists of a furnace
model, a solidr traaportaion model and a gas model, including the heat and m s
transferphenomena. The dryer simulator was shown to adequately represent the dynamic
behavwur of an industrial rotary dryer.
In mineral processing plants, grinding and flotation circuits require water to perform
the separation of the valuable minerals from the ore. The product, a wet concentrate
sold for its metal content, has to be de-watered to satisfy smelting specifications.
Although it tends to be replaced with more efficient equipment, the combination of a
vacuum filter followed by a rotary dryer is still widely used. Rotary dryers are simple
to operate and are versatile units, but the solids transportation as well as the heat and
mass transfer in the rotary drum are very complex phenomena that are influenced by
a large number of parmeters. The modelling of these phenomena is still attracting
considerable attention in order to operate rotary dryers more efficiently. Therefore,
an experimental investigation has been initiated to develop a complete dynamic
* Authorfor correqondence.
C. Duchesne, J. Thibault and C. Bazin
simulator for an industrial dryer, in order to optimise the operating conditions as
well as to assess various moisture control strategies.
The solids transportation as well as the heat and mass transfer in rotary dryers
and kilns has spurred the interest of many researchers for decades. The first
significant contributions were experimentally oriented (Friedman and Marshall,
1949; Saeman and Mitchell, 1954; McCormick, 19621, in order to understand the
effect of the operating conditions on two important variables, which are the average
residence time of solids and the volumetric heat transfer coefficient. Those works
contributed to the development of several correlations, which are still being used
today. More theoretical approaches were used by Myklestad (1963) and Kamke and
Wilson (1986). These authors used differential equations to describe the drymg
process and to develop static simulators which were validated on both small and
large-scale rotary dryers. Later, more elaborate one-dimensional (Barr et al., 1989;
Perron et al., 1992) and three-dimensional (Bui et al., 1995) rotary kiln simulators
have been developed for troubleshooting and to solve design problems. Recently,
some dynamic rotary dryer simulators have become available (Douglas et al., 1992a
and 1992b; Wang et al., 1993). which consist of a set of differential equations
combined with correlations for the calculation of the residence time and the
volumetric heat transfer coefficient. Even though these models take into account the
dynamic behaviour of a rotary dryer, they were only validated on static industrial
The present paper reports a different approach for the dynamic simulation of an
industrial rotary dryer. A solids transportation model has been successfully
developed in a previous work (Duchesne et al., 1996). This solids transportation
model consists of a series of perfectly mixed interacting tanks with dead volumes,
instead of using an empirical correlation. This model was calibrated on an industrial
dryer residence time distribution (RTD) and takes into account the effect of lifters,
air drag and rheology of the material. These three factors are difficult to model
theoretically and are rarely considered in the literature. The heat and m a s transfer
phenomena were modelled with differential equations and the heat and mass transfer
coefficients were adjusted in order to represent the industrial data as closely as
Modelling and dynamic simulation of an industrial rotan d n e r
This paper includes the industrial rotary dryer and the data acquisition procedure,
followed by the mathematical description of the complete dryer simulator. Finally,
the calibration of the model is considered and both dynamic and static performance
evaluation, and a sensitivity analysis of the simulator is performed.
Equipment and Experimental Procedure
The industrial data used for the model calibration and validation was provided by
Brunswick Mining and Smelting, New Brunswick, Canada. The company processes
ore from a massive sulphide ore-body in New Brunswick and operates a lead
sulphide smelting plant at the same location. Four marketable concentrates are
produced: zinc, lead, copper and bulk lead-zinc sulphides. These concentrates are
thickened and de-watered in vacuum filters, followed by rotary dryers, than shipped
to various smelting plants.
(a) Concentrate Dryer
Brunswick Mining and Smelting operates five concentrate rotary dryers. Figure 1
presents a schematic view of one of the concentrate dryers. Horizontal Enertec or
Bigelow-Liptak furnaces (2 m outside diameter and 3.50 m long) are connected to
the rotary cylinder. The furnace walls consist of 11 cm of refractory bricks and 11 cm
of insulation blocks. The outer shell is made of 1.3 cm of carbon steel. Air is blown
into the furnace by two fans and is heated by burning No. 6 fuel oil (Bunker C). The
prlmary air and oil are preheated to 50 and 120°C respectively in order to facilitate
the combustion.
The slope and the speed of the Ruggles-Coles rotary cylinder (2 m outside
diameter and 15 m long) are 5 degrees and 5.8 rpm respectively. Straight 15 cm
lifters are bolted to the internal surface of the 1.3 cm thick carbon steel rotary drum
to facilitate the solids axial displacement and to enhance the air-solid contact. The
dryer feed is produced by thickening and filtering the concentrate. The filter
discharge is conveyed to the dryer by a belt and a screw conveyor at a rate varying
from 15 to 40 metric tonnes per hour. The feed moisture content varies from 15 to
17% by weight and the discharge product moisture content ranges from 7 to 8% by
weight. A fan takes the exhaust damped gas to a wet scrubber where dust is
recovered and recycled back to the process.
C. Duchesne, .
Thibault and C. Bazin
(b) Industria1 Data
The data used for the model calibration was obtained during two days of operation,
kom zinc dryers #1 and #3, and each day will be referred to as Day 1 and Day 2 data
files. Data consists of time series of measurements listed in Table 1. The primary and
secondary air flow rates to the furnace and the dryer feed moisture were measured
manually for Day 1 only. All the other measurements were provided each minute by
sensors installed on the process as indicated in Figure 1. The manual measurements
were obtained during the 8 hour test, and some appropriate averages were used as
inputs for calibrating and validating the simulator. A ratio controller adjusts the ratio
of primary air flow rate to oil flow rate in a proportion that is approximatelyequal to
the stoichiometric ratio. The addition of the secondary air provides complete
combustion within the furnace, ensures a better control of the gas temperature
entering the rotary dryer, and leads to the desired gas flow in the rotary cylinder.
Model Development
The rotary dryer simulator consists of three sections : a furnace model, a solids
transportation model and a gas model. The furnace is an essential part of the
complete simulator because two of its inputs are the main manipulated variables of
the system. The solids transportation model, which has been developed and discussed
in a previous paper (Duchesne et al.,1996) is of utmost importance, because the
residence time of the solids within the dryer has a major impact on the drying
performance, and the prediction of many important process variables is sensitive to
its value (Douglas et al., 1993). A pseudo-stationary gas model was used to simulate
the drying medium. Finally, the heat and mass transfer between the solid phase and
the gas phase were considered.
(a) Furnace Model
The furnace provides the hot gas that flows through the rotary dryer and is primarily
to evaporate the water. It has three inputs : the primary and secondary air flows and
the fuel oil mass flow rate. Preheated air and oil are mixed and burned. As a result of
the fuel oil analysis, the stoichiomeuic reaction is described by the following
equation based on the assumption of complete combustion :
Modelling and dynamic simulation of an industrial rotary dryer
Figure 1. Schematic representation of the industrial rotary dryer.
Table 1. List of industrial measurements and respective sensors.
Process variable
Dryer feed rate
T / h (meuic)
Dryer discharge rate
T / h (meuic)
Exhaust gas temperature
Feed moisture content
Furnace temperature
Ib I h
Corriolis type mass flow meter
Hot wire anemometer
Hot wire anemometer
Oil mass feed rate
Primary air flow rate
Product moisture content
Secondary air flow rate
C. Duchesne, J. Thibault and C. Bazin
The overall heat and mass balances used to calculate the mass flow rate and the
temperature of the gas mixture within the furnace are given by the following two
mpa +msa +mf = m,
The residence time of the hot gas in the furnace is small. Indeed, the gas spends
approximately0.7 second in the furnace enclosure. It was therefore assumed that the
dynamics of the gas in the furnace is negligible. However, to consider the dynamics
of the furnace per se, a total heat exchange term has been included in Equation (3) to
account for the heat transferred between the gas and the furnace enclosure by
convection and radiation. For simplicity, in the calculation of the dynamics of the
furnace, the temperature of the refractory walls was lumped and its variation with
time was represented by the following first order differential equation :
Equations (3) and (4) represents the variation of the gas temperature when
changes in the air and oil flow rates occur. For instance, if the oil flow rate is
suddenly cut to zero, the gas temperature would drop progressively instead of
assuming the temperature of the inlet air. The total heat transfer coefficient was
obtained by calibrating with industrial data and is given by the following simple
correlation :
...(5 )
where 8 and y were determined to be equal to 1 . 4 8 ~ 1 0and
~ 0.613 respectively. This
heat transfer coefficient accounts for all heat transfer mechanisms within the
furnace. The heat lost to the environment (Qm) has been calculated by considering
individual thennal resistances and the overall temperature gradient according to the
following equation :
Modelling and dynamic simulation of an industrial rotary dryer
The total heat coefficient (convection and radiation) at the external surface of the
furnace was calculated using available correlations (Incropera and DeWitt, 1990).
The thermal conductance (kbJof the insulation layer, between the refractory wall
and the steel shell, is not known. In addtion, in a Bigelow-Liptak furnace, the
secondary air flows through the narrow cavity between the refractory brick and the
insulation block walls. Therefore, its value was estimated so that the outside
temperature of the steel shell, under normal operating conditions, would equal the
experimentally measured value. The inside refractory wall temperature (Tw) is
calculated r
fom Equation (4). It is important to point out that this temperature was
lumped in Equation (4) in order to account for the dynamics of fhe furnace, and was
used as the refractory surface temperature for the calculation of the heat loss. The
conduction resistance due to the refractory block insulation is by far the dominant
The enthalpy of a material flow (H)is defined as the weighted sum of the specific
enthalpies of all flow components :
The exit furnace gas is composed of five species : carbon dioxide (COz), nitrogen
(N9, oxygen ( 0 2 ) , sulphur dioxide (SOz) and water vapour (H20). The variation of
the heat capacity with temperature for each species was obtained from Smith and
Van Ness (1987). To calculate the furnace exit gas temperature, the energy balance
given in Equation (3) is solved using Newton's method.
(b) Solids Transportation Model
The solids transportation model is described in detail in Duchesne et al. (1996). The
modified Cholette-Cloutier arrangement, as shown in Figure 2, represents the
C. Duchesne, J. Thibault and C. Bazin
residence time distribution (RTD) of the solids within the industrial dryer. This
model is composed of a series of interactive perfect mixers. The volume occupied by
the solids in a cell is divided into two zones : an active zone which contributes to the
axial transportation of solids along the dryer and a dead zone where the solids are
not exchanged with neighbouring cells but only with the corresponding active
portion of the cell, as depicted in Figure 3. In passing through the rotary dryer, some
portion of the solids is delayed a various number of times by flowing into the dead
zones which leads to the extended tail of the residence time distribution curve. The
model is described with four parameters that were calibrated using the results of a
tracer test (Duchesne et al., 1996). These parameters are : the number of perfect
mixers N ; a conductance coefficient k ; the fraction a of the total volume of solids
that is occupied by the active zone ; and a parameter b which corresponds to the
steady-state ratio of solids exchange rate between active and dead zones to cell mass
feed rate. The values of these parameters are summarised in Table 2. The total wet
solids and water mass balances for the i" mixer are :
...( 1 1 )
where the flow between two adjacent cells is taking place only through the active
zones and is proportional to the difference between the total masses of wet solids in
the active zones of the two cells, as expressed by the following equation :
Modelling and dynamic simulation of an industrial rotary dryer
(i-2) k
Figure 2. Schematic representation of the modified Cholette-Cloutier model.
k fs-')
0.75 1
Figure 3. Mass exchangesfor cell i of the solids transportation model.
Under steady-state conditions, b, and bd are both equal to b. However, these
parameters are allowed to vary temporarily following a change in feed flow rate in
order to obtain the assumed constant volume ratio between the active zone and the
total volume of solids (Duchesne et al., 1996). The rate of water evaporation (R), is
proportional to the water vapour partial-pressure difference between the solid
boundary layer and the gas phase :
C. Duchesne, J. Thibault and C.Bazin
It was assumed that the partial pressure of water vapour at the gas-solids
interface is equal to the saturation partial pressure evaluated using the solids
temperature of the active zone, and it was computed from Wagner’s expression (Reid
et al., 1987). The latent heat of vaporisation of water was computed using a
polynomial regression analysis on steam table data (Smith and Van Ness, 1987), in
the range 0 to 100°C. The volumetric mass transfer coefficient is K& and it was
assumed constant along the length of the dryer.
The variation in enthalpy of the active zone depends on the inlet and outlet flow
rates of the cell, the rate of exchange between active and dead zones, the total heat
exchange between gas, solids and refractories, and the quantity of water that is
evaporated, as given by the following equation :
where Ua is the volumetric heat transfer coefficient which was assumed constant
along the length of the dryer. A few correlations were proposed to estimate the
volumetric heat transfer coefficient, whereas none were found for the volumetric
mass transfer coefficient. In the steady-state regime, most volumetric heat transfer
coefficients were reported on the basis of the rotary dryer volume (Friedman and
Marshall, 1949; McCormick, 1962; Myklestad, 1963). However, in this
investigation, the volumetric heat and mass transfer coefficients were defined on the
basis of the local volume of solids in the dryer. This implies that even though the
volumetric heat (Ua) and mass (Q) transfer coefficientsare kept constant, the rates
of heat and mass transfer are modulated by the axial variation of the solids volume
within the dryer. Since the volume of material normally decreases along the dryer
(Lebaset al., 1994; Duchesne et al., 1996), it is clear that the transfer rates should
decrease because of the smaller transfer area.
For the dead zone, the enthalpy variation is only due to the exchange of wet
solids with the active zone as expressed by the following equation :
Modelling and dynamic simulation of an industrial rotary dryer
It is assumed that the dead zone does not exchange heat and mass with the gas
phase ;I&i and H,,,i are the enthalpies of the wet solids evaluated as a function of the
moisture content and the temperature of the active and dead zones of mixer i. These
quantities are defined by Equation (7), with two species : the concentrate (mainly
zinc sulphide) and water.
Gas Model
The residence time of the gas phase in the rotary dryer is significantly smaller than
the residence time of the solid phase (Douglas et al., 1993). The average residence
time is 4 seconds for the gas compared to 20 minutes for the solids in the rotary
cylinder. The gas phase was therefore solved as a plug-flow system, that is as a
pseudo-steady-state system. The overall mass and water balances on the gas phase
are given by :
- gJ-1
. +Rw
mg.i M g . i
= mg,i-l Mg,i-l + R w
...( 16)
where the gas consists of a dry portion, that remains constant within the rotary dryer,
and the evaporated water from the solids. It was assumed that solids entrainment by
the gas is negligible.
As it flows through the dryer, the hot gas transfers heat to the solids and picks up
the evaporated water from the solids. Heat is also lost to the environment. The
overall heat balance can rherefore be expressed as follows :
C. Duchesne, J. Thibault and C. Bazin
where R is an adjustable thermal resistance used to calibrate the thermal losses
through the dryer shell. Since the heat and mass transfer are evaluated at the mean
gas properties (between the inlet and outlet of a ell), few iterations are needed to
converge to the mean temperature within an accuracy of 0.05"C.The gas specific
enthalpy in cell i (I&d is also defined by Equation (7) with the five species
mentioned previously. The mean heat transfer coefficient from the gas to the walls
(hb is calculated from Gnielinski's correlation using a hydraulic diameter (Incropera
and DeWitt, 1990). The total heat transfer coefficient (convection and radiation) was
evaluated from the same correlation used for the furnace external walls. The gas
temperature is computed by Newton's method to satisfy the gas heat balance
(Equation 18).
Both the mean global volumetricheat and mass transfer coefficients (Ua and K@)
were determined in order to fit as closely as possible the experimental data. They are
defined per unit volume of solids and assumed constant over the dryer length. The
volumetric heat transfer coefficient accounts for all heat transfer effects including
convection and radiation within the rotary dryer.
Results and Discussion
(a) Furnace Model
In this section, the furnace model is evaluated as to its ability to predict flow rate,
composition and temperature of the gas stream leaving the furnace and entering the
rotary dryer. In practice, the secondary air flow rate is not measured. Only the fuel
flow rate and the gas temperature, remrded via a thermocouple in the furnace
enclosure, are normally available on-line. The primary air flow rate is set to a fixed
ratio based on the oil mass flow rate according to stoichiometry. With these three
variables and with the furnace model described by Eguations (1) to (7), it is possible
to estimate the secondary air flow rate that would completely define the exit gas from
the furnace. Occasionally. the secondary air flow rate was measured manually,
periodically during Day 1 of the sampling campaign. In practice, the secondary air
Modelling and dynamic simulation of an industrial rotary dryer
flow rate is manipulated via a damper but its value is not measured on-line. Figures
4 to 6 show the variation of the fuel flow rate, the measured temperature and the
estimated secondary air flow rate respectively. Figure 6 also shows the measured
secondary air flow rate and the stoichiometric primary air flow rate. The estimated
secondary air flow rate is significantly lower than the measured flow rate, due to
measurement errors of the gas temperature which are discussed in the next section.
I= 0.00
Time ( s )
Figure 4. Variation of the furnace oil mass~owrate for Day 1.
lndusuial D a Q
Predicted Data
Corrected Oata
Time ( s )
Figure 5. Comparison between the measured and predicted furnace temperatures.
The h a m thermocouplehas no radiation shield to prevent its direct exposure to
the flame thermal radiation. Therefore, it was expected that the recorded temperature
would be higher than the actual gas temperature because the radiative heat exchange
between the flame and the thermocouple cannot be compensated by the convective
heat transfer between the thermocouple and the gas stream (Saeman and Mitchell,
C. Duchesne, J. Thibault and C. Bazin
1954; Kreith, 1965). To evaluate the measurement error due to radiation, it was
necessary to measure the secondary air flow rate in order to calculate the actual gas
temperature. With this flow rate (from Figure 6) and the furnace model, a more
realistic gas temperature was calculated (compared to Figure 5). in order to satisfy
the energy balance for the furnace. These results clearly show the significant bias in
the gas temperature which is due to the radiative heat exchange. Because the
secondary air flow rate is not currently measured, in order to use the model on the
actual process it is necessary to find a way to correct the recorded temperature fiom
the measured process variable. Hence estimate as accurately as possible the
temperature of the gas entering the rotary dryer.
.< O
Measured SA
Calculated SA
- ,. .... . - .. - - - - . . ... . . . - - ._......... .. PA
* .
Time ( s )
Figure 6. Plot of the ptimaty and secondary airflow rates and total gas flow rate.
The heat transfer phenomena taking place within the furnace chamber are very
complex. The presence of a luminous flame, the combustion products (H20 and C02)
participate in the absorption and re-emission of the thermal radiation, and the
evaluation of the various emissivities certainly contribute to the complexity of the
problem. To rigorously solve this problem would require considerable effort. In this
case, it is desired to simply estimate as accurately as possible the exit gas
temperature by correcting the thermocouple reading and adding some dynamics to
the f m c e model.
The thermocouple receives a net radiative heat flux from its surroundings and
looses heat to the gas stream by convection. A higher gas velocity reduces the
temperature error due to radiation. Saeman and Mitchell (1954) argued that with a
Modelling and dynamic simulation of an industrial rotary dryer
very high gas velocity, the temperature measurement error would be negligible. It is
therefore not surprising that in Figure 5 the difference between the measured and
estimated gas temperatures is smaller at higher gas flow rates. To estimate this
temperature difference, an energy balance was performed on the thermocouple where
only the convective heat transfer, and the net radiative heat flux between the flame
and the thermocouple are considered :
The adiabatic flame temperature was dculated and the flame emissivity was
calculated as the combined emissivities of H20 and C02,evaluated at the flame
temperature using the method proposed by Hottel and Sarofm (1967). The
was correlated as a function of the Reynolds
convective heat transfer coefficient (h~)
number. Since Equation (20) does not give an exhaustive representation of all the
heat transfer modes encountered in the furnace, and the values of the flame
temperature and emissivity are not well known, the convective heat transfer
coefficient accounts for all these modelling errors. The gas temperature estimated
with Equation (20) is presented in Figure 5, and on this basis, a correction of 154°C
was applied. In practice the secondary air flow rate is not measured, so that Equation
(20) would be used to converge simultaneouslyon the total gas flow rate and the gas
temperature with the knowledge of the erroneous thermocouple reading. The
corrected gas temperature, with Equation (ZO), compares very well to the furnace
temperature calculated using the measured secondary air mass flow rate, which is not
influenced by radiation. Most of the observed discrepancies may be attributed to the
changing behaviour of the flame temperature with the oil flow rate. It is interesting
to note that by performing the temperature correction to compensate for thermal
radiation, the energy imbalance on the dryer was reduced fkom 92.7% to 3.4% which
indirectly validates the procedure used for correcting the gas temperature.
The wall of the furnace provides a certain degree of thermal inertia that smooths
the gas temperature variation, due to a change in the oil flow rate or the secondary
air flow rate. These dynamics were simulated with Equation (3),and the wall
temperature is presented in Figure 5. Under steady-state conditions, the model
assumes that the wall temperature would be equal to the gas temperature although
C. Duchesne. J. Thibault and C. Bazin
the wall temperature would actually be higher because of the thermal radiation from
the flame.
(b) Dynamic Behaviour of Dryer
The calibration of the simulator was performed by adjusting the volumetric heat and
mass transfer coefficients (Ua and Kgi) and the heat losses, to produce a dynamic
response as close as possible to the industrial measurements when subjected to the
same inputs. The two main measured variables with which the two transfer
coefficients could be calibrated are the solids moisture content and the gas
temperature at the exit of the rotary dryer. Since it was felt that the discharge
moisture content is the most crucial for the operation of the dryer, it was decided to
calibrate the simulator with this variable, and to use the gas temperature as an
indirect validation of the simulator calibration. The values of the two transfer
coefficients were therefore determined in order to minimise the sum of squares of the
difference between the predicted and measured discharge moisture contents. The
values of Ua and Q were found to be respectively 10 kW/m3K and 1 kg/s m3kPa.
The thermal losses through the dryer shell were calibrated by adjusting the resistance
R in Equation (22) in order to obtain the estimated average temperature of 70°C on
the outside surface of the rotary dryer shell.
Figure 7 shows the variation of the concentrate feed flow rate and the measured
and predicted concentrate discharge flow rates for Day 1. A good agreement exists
between the predicted and measured values of the &scharge flow rates. These results
clearly show that the solids transportation model adequately represents the solids
flow behaviour within the rotary dryer. The discharge flow rate shows a Iarge
fluctuation that cannot be simulated with the measured concentrate feed flow rate.
This stochastic behaviour is characteristic of the transportation of wet solids where
sudden local accumulation of material within the rotary dryer can oc(w,followed by
the rapid tumbling of material towards the exit of the dryer. Overall, the discharge
flow rate is well predicted. The largest deviation is observed when the concentrate
feed flow rate was drastically reduced (at around 100 min) which may suggest that
for flow rates significantly different from calibrations, the solids transportation
model is not able to adequately represent the solids flow behaviour within the rotary
dryer. However, it is important to point out that the inlet concentrate feed rate in that
Modelling and dynamic simulation of an industrial rotan dryer
time span should have led to higher hscharge flow rate. Therefore, this large
deviation may also be due in part to the stochastic behaviour discussed above since
the lowest and highest discharge flow rates are observed during this t h e period.
Industrial Data
Predicted Data
Time ( s )
Figure 7. Plot of the solids massjlow rates - Day 1
The solids transportation model was further evaluated with the data set of Day 2
which has a much larger concentrate feed flow rate. Results of this simulation are
presented in Figure 8. The concentrate feed flow rate, in addition to being much
higher than for Day 1, shows significant fluctuations. Alternatively, the measured
discharge feed flow rate is much smoother than that for the previous case.
Considering that the solids transportation model was calibrated on a different rotary
dryer and that the concentrate feed flow rate varies significantly with time, the solids
transportation model provides satisfactory representation of the dynamics of the
solids behaviour within the rotary dryer. However, there are some difficulties when
C. Duchesne, J. Thibaulr and C. Bazin
the concentrate flow rate is significantly higher or lower than the flow rate for which
the solids transportation model was calibrated. In order to make the model more
robust over a wider range of flow rates, b e parameters of the solids transportation
model would have to be expressed as a function of the solids mass flow rate. This
could be achieved by performing additional tracer tests at different concentrate feed
flow rates.
y" 15
i Y 5
2 0
Industrial Data
Predicted Data
.-: : o
Time ( s )
Figure 8. Plot of the solids massfIow rates - Day 2.
The prediction of the discharge concentrate moisture content for Day 1 is
presented in Figure 9, with the measured values. The prediction is good for both the
dynamics and the level of the solids moisture content. This was expected since the
two transfer coefficients were fitted with these data points. The relatively high
variance of the data is mainly due to the sensor used to measure the moisture m t e n t
of the solids. The largest deviation is again observed when the feed flow rate was
Modelling and dynamic simulation of an industrial rotaq d n e r
drasticallyreduced. This time, it is difficult to evaluate the real value of the deviation
because the sensor was outside its calibration range. Indeed, during eleven minutes,
the recorded value was equal to the minimum value that the sensor could record.
Induslnal Data
Prbduted Data
Time ( s )
Figure 9. The measured and predicted product moisture contents.
When the feed flow rate dropped, the predicted moisture content almost
decreased to zero. However, in practice, it should level off at a higher moisture
Content. Indeed, when the concentrate reaches the critical moisture content, the
temperature of the solids rises and the drying rate falls off rapidly. In addition, the
drylng rate should approach zero at some equilibrium moisture content which is the
minimum value that can be achieved with a particular solid with the drying
conditions prevailing within the dryer (Foust et al., 1960). The falling drying rate is
normally obtained for moisture contents in the range of 2-3% (Mujumdar, 1987). To
include this phenomenon in the simulator, it would be necessary to perform some
dryrng experiments to determine the drylng curve at lower moisture contents.
However, this does not invalidate the simulator for normal operation. The variation
of the moisture Content is well represented by the model. A better prediction could
certainly be achieved if the inlet moisture content was measured continuously instead
of being set to a constant value of 16.5%.
The comparison between the predicted and measured outlet gas temperatures is
presented in Figure 10 for Day 1. This comparison can be used as an indirect
validation of the complete simulator since it was calibrated strictly on the
concentrate discharge moisture content and not on the outlet gas temperature. Apart
C. Duchesne, J. Thibault and C. Bazin
ffom the drastic change that occurred around 5000 sec, the simulator is able to
predict the gas outlet temperature with an average error of approximately6.5"C.This
is very good considering that the gas temperature is reduced from about 600°C to
8VC, that is the average temperature deviation is slightly less than 2% of the total
temperature drop of the gas. This deviation can have many sources, such as : (i) the
small residual energy imbalance of the industrial data ; (ii) measurement errors ; (iii)
larger heat losses ; (iv) the assumption of constant volumetric heat and mass transfer
coefficients ; and (v) air leakage from outside.
Time ( s )
Figure 10. Measured and predicted discharge gas temperatures.
Prduted Data
The plant operating personnel indicated that air infiltration at the discharge end
of the rotary dryer is probably the main cause of this difference. As shown in Figure
1, three fans are used to manage the gas flow : the primary and secondary air fans for
which the flow can be controlled, and the scrubber fan for which the flow is not
controlled. Depending on the gas flow rate through the dryer, the gage pressure at
the end of the dryer m a y be negative. Air infiltration through the discharge seals of
the rotary dryer can then occur, resulting in a decrease of the measured outlet gas
temperature. For a lower gas flow rate, the gage pressure would be lower and the
infiltratian of air would be more important. This is corroborated by the results of
Figure 10. A rough calculation, using the geometry of the seals and the solids output
port, has shown that air infiltration could realistically account for a major component
of the observed gas temperature discrepancies.
I 74
Modelling and dynamic simulation of an industrial rotan dryer
(c) Volumetric Heat and Mass Transfer Coefficients
The volumetric heat and mass transfer coefficients are both the product of two
distinct parameters : either the global heat transfer (U) or mass transfer(K&
coefficient and the solids interfacial area (a). Since the interfacial area is unknown,
only the product of the two parameters can be estimated. In this investigation,
constant values of Ua and K,+ along the dryer were assumed. However, it is most
liely that the two transfer coefficients and the solids interfacial area vary with the
operating conditions prevailing within the rotary dryer.
A direct relation between the volumetric interfacial area (a) and the volume of
solids should not be expected. Basic principles suggest that the interfacial area
should increase with a decrease in the moisture content because of the lower
compaction and the higher bed void associated with a lower moisture content. The
area should also increase with a decrease of the solids volume because a higher
proportion of solids would be directly exposed to the hot gas.
The heat and mass transfer coefficients (U and KJ should realistically increase
with an increase in the gas flow rate. However, increasing the gas flow rate leads to a
reduction of the residence time of the solids within the rotary dryer, resulting in a
reduction of the contact time between the gas and the solids, thereby opposing the
beneficial effect of higher transfer coefficients.
In view of the above considerations, it would be difficult to derive a universal
correlation for predicting the volumetric heat and mass transfer coefficients. The
assumption made in this investigation of constant volumetric heat and mass transfer
coefficients appears reasonable and practical.
(d) Static Application of the Simulator
Results presented in the previous sections demonstrated the ability of the simulator to
realistically represent the dynamic behaviour of an industrial rotary dryer. To assess
the simulator under steady-state conditions, a simulation was performed with a
concentrate feed flow rate of 6.87 kg/s, oil flow rate of 0.057 kg/s, primary and
secondary air flow rates of 0.754 and 2.79 kg/s. The resulting temperature of the gas
entering the rotary dryer was 686°C. The temperature and the moisture content
profiles of the gas and the solids as a function of the position along the dryer are
presented in Figure 11.
I 75
C. Duchesne, J. Thibault and C. Bazin
10 6
Axial Position ( m )
Figure 11. Axial profiles of the temperatures and moisture content.
Both gas and solids temperature profiles are consistent with those reported by
Friedman and Marshall (1949) which used dry material. Most of the heat is
transferred to the solids within the first 5 m of the dryer. According to Saeman and
Mitchell (1954), it is usually observed that 90% of the heat transferred in a murrent
flow rotary dryer OCCUTS within the first 10 % of the dryer length. Near equilibrium
conditions for heat and mass transfer are obtained at about 5 m from the entrance
and the outlet solids temperature is close to the gas wet-bulb temperature. Therefore,
the gas and solids moisture contents are almost constant in the last 10 m of the dryer.
The exhaust gas is only at one half of its water saturation, showing that the heat and
mass gradients between the gas and the solids, are limiting the heat and mass
transfer. Therefore, it would be interesting to reduce the sensitivity of the operating
conditions in order to reach the desired moisture content near to the discharge end,
rather than at one-third of the dryer length. This type of study may results in
considerable fuel economy.
(e) Sensitivity Analysis
The sensitivity of important simulated process variables, with respect to the input
variables and parametersof the model, are of utmost importance in the interpretation
of predictions and in the design of future sampling campaigns. Furthermore, a
sensitivity analysis can assist in the selection of manipulated variables for controlling
and optimising the process. The relative sensitivity of each variable and parameter
was evaluated using the following sensitivity index :
Modelling and dynamic simulation of an industrial rotan)d q e r
The sensitivity index was determined by changing one parameter at the time by
10%.and then by performing a complete simulation using operating conditions of
Day 1. The values Y and Yrefcorrespond to the output variable after the change and
its reference value respectively, whereas aef
is the nominal value of the modified
parameter and w is the new value used to generate a new value of the output variable
being considered. Three process variables and fourteen parameters were changed in
turn and their effect was observed on four dryer outputs, namely: the moisture
content and temperature of both the outlet gas and solids streams. The results are
presented in Table 3 and the sensitivity of the various parameters and variables can
be easily assessed.
The sensitivity analysis of the three input process variables (secondary air, fuel
and concentrate feed mass flow rates) shows that the secondary air flow rate is ten
times less sensitive than the other two input variables. The logical control strategy
calls for the manipulation of the oil mass flow rate since the concentrate feed flow
rate cannot be manipulated. In addition, the sensitivity analysis shows that in the
region of the nominal operating conditions, the secondary air flow rate should be as
small as possible. Therefore, the sensitivity analysis of the input variables suggests
adjusting the fuel flow rate in order to suppIy sufficient energy necessary to
evaporate the water, and to set the secondary air flow rate to give an entrance gas
temperature as high as possible while satisfymg mechanical and thermal constraints.
This strategy is consistent with the strategy used by the operators at Brunswick
Mining and Smelting.
The sensitivity of the volumetric heat transfer coefficient is much more
significant than the sensitivityof the volumetric mass transfer coefficient. This result
confirms that, under normal operating conditions, heat transfer controls the drying
process.Tbe three parameters that have the most influence on the concentrate
discharge moisture content are: the heat of combustion, the latent heat of
vaporisation, and the inlet solids moisture content. The latent heat of vaporisation is
known, and therefore for correct simulation, an accurate value of the fuel oil heat of
C.Duchesne, J. Thibaulr and C. Bazin
Table 3. Sensitiviv index (S)of the four main process outputs.
- 1.250
combustion should be available. As expected the feed moisture content greatly
influences the discharge moisture content. For a more accurate calibration of the
simulator, and if a feedforward control strategy is to be implemented, it would be
necessary to measure the inlet moisture content on-line. In the present investigation,
it was assumed constant and equal to 16.5%. The relatively high sensitivity index
suggests that the assumption of constant inlet solids moisture content may be
Modelling and dynamic simulation of an indusrrial rorary dryer
responsible for some of the observed deviations between experimental and simulation
A dynamic simulator for an industrial rotary dryer was presented. The mathematical
models included the production of combustion gas in a furnace, solids transportation
within the romy dryer, gas flow and heat and mass transfer phenomena. The
simulator was calibrated with a limited number of experimental data gathered over a
period of 8 hours.
The solids transportation model uses interactive mixers in series with, 25% of the
volume occupied by the dead zone. This model is able to adequately represent the
flow of solids through the rotary dryer under both steady and transient conditions,
provided that the mass flow does not deviate too far fiom normal operating
conditions. The volumetric heat and mass transfer coefficients were then determined
in order to minimise the prediction error on the discharge solids moisture content.
The outlet gas temperature was predicted satisfactorily and served as an indirect
validation of the complete simulator since the two transfer coefficients were not
adjusted to minimise the deviations of this variable.
A sensitivity analysis has provided the relative influence of the input process
variables and model parameters on the temperature and moisture content of the gas
and solids at the discharge of the dryer. Results suggest an appropriate discharge
solids moisture control strategy for the moisture content of the discharging solids.
The results also indicated the importance of measuring the feed solids moisture
content for better calibration of the simulator, and for possible implementation of a
feedforward control strategy.
Despite limited measurement of some process variables, it is believed that the
described simulator provides a good representation of the various phenomena taking
place within an industrial rotary dryer. This investigation developed and calibrated a
rotary dryer simulator based on dynamic industrial data. In future sampling
campaigns, it would be desirable to determine the influence of concentrate and gas
flow rates on the residence time distribution curve, because the solids transportation
model has a major impact on all phenomena taking place within an industrial rotary
I 79
C.Duchesne. J. Thibault and C.Bazin
The authors would like to thank a consortium of eight mining companies under the
umbrella of CAMIRO, NSERC, Centre de Recherches Minerales du MER and
CANMET for their support of the KBAC research program. Special thanks goes to
Brunswick Mining and Smelting for their co-operation during the sampling
Solids interfacial area
Cross sectional area
Specific heat capacity
Fuel specific combustion heat
Mean total heat transfer coefficient
Heat transfer coefficient to environment
Total enthalpy of a stream
Flow conductanceof wet solids
Volumetric mass transfer coefficient
Dryer length
Furnace length
Mass of material
Moisture content (wet basis)
Mass flow rate
Number of chemical species in a stream
Number of dryer slices
Water partial pressure in the flue gas
Saturation water vapor-pressure
Heat losses
Reynold's number
Thermal resistance used in Equation (27)
Water evaporation rate
Sensitivity index
Ambient air temperature
Volumetric heat transfer coefficient
Wet solids volume
Componentmass fraction
Modelling and dynamic simulation of an industrial rotary dryer
Greek letters
Volume of active zone to the total solids volume
Absorptivity of the thermocouple
Mass flow rate exchange ratio between active and dead zones
Corrected mass flow rate fraction entering a dead zone
mass flow rate fraction going out of a dead zone
Emissivity of the flame
Emissivity of the thermocouple
in Equation ( 5 )
Water latent heat of vaporisation
(kW I m2 K)
Coefficient in Quation (5)
Air density
kg I m3)
(W I m2 K")
Variable in Equation (21)
Variable in Equation (21)
Active zone
Interface block insulation - carbon steel
Carbon steel
Dead zone
External carbon steel wall
External furnace wall
Furnace losses
Furnace wall
Indicates properties associated with the itb cell
Internal carbon steel wall
Inside dryer shell
Indicates a species or acts like a counter in a summation
Refractory block insulation
Refractory wall
Secondary air
Shell losses
C. Duchesne, J. Thibault and C. Bazin
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Received :20 December 1996 ;Accepted afrer revision : 5 June 1997.
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