2002 DRT Rotary
2002 DRT Rotary
2002 DRT Rotary
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ABSTRACT
*E-mail: maroulis@chemeng.ntua.gr
771
INTRODUCTION
PROBLEM DEFINITION
The flow sheet of a typical rotary dryer is shown in Figure 1. Fuel with
flow rate Z (kg/h) is burned with atmospheric air with flow rate FA0 (kg/h),
temperature To ( C) and humidity Yo (kg/kg db). The flue gases flow rate
FAC (kg/h db), temperature TAC ( C) and humidity YAC (kg/kg db) are fed in
the rotary dryer and exit with flow rate FAC (kg/h db), temperature TA ( C)
and humidity YA (kg/kg db). Wet solids are fed to the dryer with flow rate Fs
(kg/h db) and moisture Xo (kg/kg db). The dried solids exit from the dryer
with flow rate Fs (kg/h db) and moisture Xs (kg/kg db).
The dryer size and characteristics as well as the operating conditions
can be calculated for given process specifications, minimizing the total
drying cost. Thus, the design problem of a rotary dryer for olive cake can be
defined as follows:
1. Process Specification
– Solids flow rate Fs (kg/h db)
– Input material moisture content Xo (kg/kg db)
– Output material moisture content Xs (kg/kg db)
2. The Characteristics of the Rotary Dryer are as Follows:
. Size:
– D: dryer diameter (m)
. Geometric characteristics:
– the length to diameter dimensionless ratio (L/D)
– the total hold-up to volume dimensionless ratio (H/V)
– the number of blades to diameter dimensionless ratio
(nf/D)
3. Drying Conditions
– Inlet temperature TAC ( C)
– Velocity u (m/s) at temperature TA
– The cylinder slope s (%)
PROCESS MODEL
I. Burner
Based on Eq. (1) the total balance and the moisture balance over the
burner are given by the following equations that describe the combustion
process:
FAC ð1 þ YAC Þ ¼ FA0 ð1 þ Yo Þ þ Z ð2Þ
II. Dryer
The following equations describe the mass and the energy balances of
the dryer:
where CPA (kJ/kg K) is the specific heat of air—vapour mixture and HV is
the latent heat of vaporization of water at reference temperature (kJ/kg) and
TA is taken as mean air—vapour temperature at the dryer output.
2. Drying Kinetics
3. Residence Time
4. Geometrical Constraints
5. Cost Estimation
The process unit cost of wet product ($/kg wb) has to be minimized:
Cp ¼ CT =t
op Fs ð1 þ XS Þ ð19Þ
where top is operation hours per year, Cp is the cost of the product due to
the process of drying, the total annual cost CT of the plant can be expressed
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©2002 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc.
where e is the capital recovery factor, eCeq is the yearly capital cost ($/y) and
Cop is the operating cost ($/y).
The capital recovery factor is given by the following equation:
ið1 þ iÞN
e¼ ð21Þ
ð1 þ iÞN 1
where aD, aZ are unit costs and nD, nZ are scaling factors of dryer and burner
respectively.
The operating cost concerns electrical energy and fuel cost:
where Ce and Cz are the electricity and the fuel cost respectively. The elec-
trical power hp for cylinder rotation is given as follows (Kelly, 1995):
hp ¼ qNDðM þ WÞ ð24Þ
where dx (m) is the dryer wall thickness and M is the metal density (kg/m3).
A degrees of freedom analysis suggests that five design variables are
available for the design problem described in the previous paragraphs. It
can be proved that an effective solution algorithm could be based on the
following selection of design variables: TAC, u, L/D, H/V, nf/D, where TAC
and u express the operating conditions and L/D, H/V, nf/D the dryer
shape.
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©2002 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc.
Figure 2. Drying constant versus temperature for various air velocities and
humidities.
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©2002 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc.
CASE STUDY
Process specifications
Solids flowrate Fs 5000 kg/h
Input material moisture content Xo 1.00 kg/kg db
Output material moisture content X 0.10 kg/kg db
Fresh air characteristics
Temperature To 25 C
Humidity Yo 0.01 kg/kg db
Thermophysical properties
Water to air molar fraction m 0.622 –
Air specific heat CPA 1.18 kJ/kg C
Water specific heat CPV 1.98 kJ/kg C
Heat of combustion Hf 15 MJ/kg
Latent heat of vaporization of water Ho 2500 kJ/kg
Porosity " 0.48 –
Empirical constants
Empirical constant in Eq. (14) k 0.003 –
Empirical constant in Eq. (24) q 1 –
Economic data
Dryer unit cost aD 8 k$/m2
Dryer scaling factor nD 0.62 –
Burner unit cost aZ 200 $/kg
Burner scaling factor nZ 0.4 –
Life time N 10 yr
Interest rate i 8 %
Operating time top 2000 h/y
Electricity cost Ce 0.07 $/kWh
Fuel cost Cz 0.05 $/kg
and each time all other variables are calculated. It must be noted that as air
drying temperature increases the fuel consumption increases and thus the
operating cost increases, while the size of equipment and consequently the
cost of equipment decreases. For a given air velocity the total unit cost (CT)
reaches a minimum at a specific air temperature (Figure 5).
In Figure 6 the total unit cost is presented as function of air tempera-
ture for different air velocities. Effect of air temperature on fuel and elec-
tricity cost is presented in Figure 7. As temperature increases it is evident
that the electrical cost decreases, while the fuel cost increases and is the most
important part of operating cost.
The model was adapted to an industrial rotary dryer 2.5 m in diameter
and 22 m long which has 24 blades. The drying conditions are 650 C input
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©2002 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc.
Design variables
Input air temperature TAC 700 C
Mean air–vapour velocity u 2.4 m/s
Total holdup to volume fraction H/V 15 %
Length to diameter fraction L/D 20 –
Number of blades to diameter fraction nf /D 10 1/m
Drying air characteristics
Mean air temperature TA 298 C
Humidity outlet Y 0.37 Kg w/kg db
Operating characteristics
Residence time t 0.3 h
Total holdup H 8.4 m3
Rotating velocity N 8.6 rpm
Dryer characteristics
Diameter D 1.5 m
Length L 30.6 m
Blade number nf 15 –
Utilities
Fresh air flowrate FA0 15 048 kg/h
Fuel rate Z 1066 kg/h
Economics
Electricity cost Ce 6286 $/y
Fuel cost Cz 106 606 $/y
Operating cost Cop 112 891 $/y
Cost of equipment Ceq 55 619 $/y
Total cost CT 168 510 $/y
Unit cost Cp 0.00843 $/kg wb
drying air temperature, 2.4 m/s mean air-vapour velocity, while the fuel rate
is 1500 kg/h. It must be noted that the operating conditions obtained from
process design calculations are close to the real ones.
CONCLUSIONS
A design procedure for a concurrent olive cake rotary dryer has been
developed. A simple mathematical model for the rotary dryer was used,
while material thermophysical properties have been calculated experimen-
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©2002 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc.
Figure 6. Total unit cost as function of air temperature, at various air velocities.
MARCEL DEKKER, INC. • 270 MADISON AVENUE • NEW YORK, NY 10016
©2002 Marcel Dekker, Inc. All rights reserved. This material may not be used or reproduced in any form without the express written permission of Marcel Dekker, Inc.
tally. A sensitivity analysis of the process unit cost has been achieved by
varying drying conditions (air temperature and velocity). It is noted that air
temperature affects significantly products cost, while the effect of air velocity
is less significant.
NOMENCLATURE
REFERENCES
Van’t Land, C.M. Selection of Industrial Dryers. Chem. Eng. 1984, 91,
53.
Van’t Land, C.M. Industrial Drying Equipment. Marcel-Dekker:
New York, 1991.