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Dryer Control
In order to control any process, we need a good understanding of the process itselfWhat is the drying process?Dryer classifications and typesProcess analysis Macro vs. Nano, Micro
Dryers – A common yet costly unit operation
Dryers used in chemical processing, food processing and pharmaBatch or continuousEnergy intensiveFrequently over dried at added costs, dusting, product lossDrying accounts for ~12% manuf. costs
What is the Drying Process …
Removal of small amount of liquid, usually water – Large amounts of water normally removed by press or centrifuges. Thermal methods employed. Heat and Mass transfer
Hot dry air Hum id air
W et Material
D ry Material
Solid drying process is very complexwith micro and nano mechanisms
Liquid movement due to capillary forcesDiffusion due to concentration gradientsLiquid vapor flow due to pressure differencesVapor diffusion due to vapor pressure differences,
concentration differencesOsmotic pressure created by colloidal bodies has
soluble and insoluble fractions Vapor Effusion – A relationship of vapor flow to pore
diameterThermodiffusionVaporization-condensation mechanism
Macro Drying Process
This program will not study these nano and micro relationships; we will develop our controls based on the macro mechanisms
What is the Drying Process …
Drying - water liquid vaporization; not as efficient as centrifuge, 1050 BTU/lb of water removed. Final moisture varies “dried” table salt contains 0.5 % water, dried coal 4%.Solids can have many different forms, flakes, granules, crystals, powders, etc. The liquid can be on the surface, within the surface in cellular structures, such as wood. Consider the method of handling, dusting, rough or gentle treatment.
Equilibrium MoistureThe solid’s moisture content is a function of the humidity of the drying air. The moisture cannot be lower than the equilibrium moisture content corresponding the humidity of the incoming air.
50% RH air equilibrium moisture
Wool 12.5 % Newspaper 5.5%
The Drying Process can be described in several ways…
Batch or Continuous; how the material is processed. A single charge – BatchContinuous input and output.
The Drying equipment can be described as “dryer types”
Dryer Types; the classification as to the method solids travel through the heated zone, the heat source and transfer method.
The Drying Process can be classified as:
Classifications
Adiabatic Dryers are the type where the solids are dried by direct contact with gases, usually forced air. With these dryers, moisture is on the surface of the solid.
Non-Adiabatic Dryers When a dryer does not use heated air or other gasses to provide the energy required the drying process is considered a non-adiabatic.
In the case of Adiabatic Dryers
The process can be considered to be two related processes:
Solids Drying
Air Humidification
We will view dryer control from the air humidification process
Adiabatic dryers, solids are exposed to the heated gasses in various methods:
Blown across the surface cross circulationBlown through a bed of solids, through-circulation; solids stationary; wood, corn etcDropped slowly through a slow moving gas stream, rotary dryerBlown through a bed of solids that fluidize the particles; solids moving; frequently called fluidized bed dryerSolids enter a high velocity hot gas stream and conveyed pneumatically to a collector Flash Dryer
What can the Psychometric Properties tell us about the drying process?
In many ( or most ) cases, the nano and macro drying mechanisms are not know. However, we do know air properties Lets make use of the air properties to control our dryer
Psychometric chart - displays phase conditions
of water vapour in air
29.225 inHg650 ft
F 45 50 55 60 65 70 75 80 85 90 95 100 105 110
0.005lbm/lbm
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
1
Btu/lbm 75
70
65
60
55
50
45
40
35
30
25
20
15
10
ft^3/lbm 13.2 13.8 14.4
Tw Wet Bulb Temperature Lines
Relative Humidity Lines
The Psychometric chart computer program
Akton Associates Inc.
PO Box 2076
Edmond, OK 73034
(405) 513-8537
http://www.aktonassoc.com/
Properties shown on psychometric chart…
The air temperature - dry bulb temperature of the stable air water vapour mixture; on the x axisThe dew point temperature - temperature where condensation begins to form as the water is condensed from the wet air; not shown on the chartThe wet bulb temperature is the temperature at which adiabatic heat is transferred during the drying of solid or humidification of air. For a dryer, moisture in the solid is transferred to the air. The air will gain moisture while the solid looses moisture, therefore or humidification of the air occurs. This process will occur at a constant wet bulb temperature. The dry bulb air temperature will decrease during this process and be lower exiting the dryer or chamber. This temperature is shown as a series of curved lines sloping downward.
Properties shown on psychometric chart…
Relative humidity is the ratio of the water vapour pressure at the dew point to the water vapour pressure at the dry bulb temperature. This ratio is usually expressed as a percent. This ratio is multiplied by 100 to obtain the percentage reading. These lines are the curved lines sloping upward.Vertical line on the right shows the absolute moisture; pounds of moisture per pound of dry air.
Relative Humidity
The relative humidity is calculated as a ratio of partial pressures:
is the water vapor pressure at the dew point temperature
is the water vapor pressure at the dry bulb temperature.
ow
w
p
pRH *100
wp
owp
Relative Humidity
The water vapor pressure can be calculated by an exponential equation:
p in psia and T in DegF
0.385
3.7071exp*10*04466.2 6
tp
Drying is in one of two zones or periods…
Constant rate and Falling rate zones
Constant Rate Zone a.k.a. first period of drying
Layer of saturated air on solid surface
This rate is determined by the capacity and properties of the inlet gas or vapor
Solid temperature is equal to the wet bulb temperature during this period
Free water drying
Falling Rate Zone a.k.a. second period of drying
inflection point at the “critical moisture”
begins when the surface or free water is removed
solid temperature increases form wet bulb temp to that approaching the inlet air, gas, temperature
Batch DryingIf air is passed over a moist solid, air temperature will be
reduced as the water is evaporated. Calculated through an enthalpy balance:
Ti = Inlet Dry Bulb Temperature
To = Outlet Dry Bulb Temperature
G = Air Mass Flow
C = Air Heat Capacity
Fw = Mass rate of water evaporation
Hv = Heat of vaporization
vwoi HFTTGC )(
Batch Drying
The outlet temperature value will be between the inlet and the wet bulb temperature. The rate of evaporation dFw is equal to:
Ti Inlet Dry Bulb Temperature
Tw Wet Bulb Temperaturea Mass transfer coefficientR Rate coefficientdA Surface Area
)( ww TTaRdAdF
a RdA
dF wG
T i
T o
T w
T
H v
)( ww TTaRdAdF vwHdFGCdT
a = M ass transfer coeffic ientR = R ate coeffic ientC = A ir S pecific H eat
E vapora tion M ode l; A ir tem pera ture decreases as the m o istu re is rem oved from the so lid
C onstant w et bu lbtem perature
W ater heat o fvaporization
hr
lbsR
Ffta
2
1
Batch Drying
As the air passes over the moist solid, the air temperature will fall by dT
Assuming R = kw, a line that passes through to origin, the above equations can be solved for the outlet moisture:
vwHdFGCdt
wo
wi
v TT
TT
akAH
GCw ln
wo
wic
v
TT
TTKw
CG
akAHln
Batch DryingThe final outlet To temperature to achieve a
desired final moisture is w* is:
Eliminating the wet bulb temperature form the above yields:
Where Toc is the outlet moisture at the critical moisture.
)(**
wiKw
wo TTeTT
cc Kw
Kw
iKw
Kw
oco ee
Tee
TT11
111
**
*
)( wiKw
woc TTeTT o
Batch Dryer, extra credit problem
Use algebraic substitution, show how to arrive at equation (7) from (6) and (6a) in your handout.
10 points credit
Constant rate – Falling rate
The fraction term can be defined as K*
cc Kw
Kw
iKw
Kw
oco ee
Tee
TT11
111
**
*
*** 1 KTKTT ioco
Batch Dryer
This method calculates the outlet temperature required to obtain specified moisture in a batch dryer. It uses inferential moisture calculation based on temperature difference.
A better approach can be taken if the dryer constant, K, is recalculated each time.
Mass Transfer Equations Rate of Evaporation
m evaporation Rate
hv heat transfer coefficient
T inlet gas temperature
Ti interface temperature or Wet Bulb Temperature
A Area
i heat of vaporization BTU/lb
i
iv ATThm
)(
Heat Transfer coefficient can be estimated as
G mass velocity lb/ft^2 hr, note different G!
De airflow channel diameter ft
4.0
6.0026.0
ey D
Gh
Mass Velocity
For packed beds, calculation requires knowledge of void fractions… Void Fractions
Dp/Dt
e for spheres
e for cylinders
0.00 0.34 0.340.10 0.38 0.350.20 0.42 0.390.30 0.46 0.450.40 0.50 0.530.50 0.55 0.60
Packing Factor
Leva, M., Grunmer, M.Chem Eng Progress 43:713 (1947)
Drying Rate Control
To control the drying rate, you control the temperature differences.
Ti = Inlet Dry Bulb Temperature
To = Outlet Dry Bulb Temperature
G = Air Mass Flow
C = Air Heat Capacity
Fw = Mass rate of water evaporation
Hv = Heat of vaporization
vwoi HFTTGC )(
Drying Rate Control
But the outlet temperature lags the inlet by some amountThis lag is due to the thermal time constant of the solid
Drying Rate Control
First order lag must be applied to the inlet temperature before the difference is calculated.
Continuous Dryer outlet moisture calculation…
The adiabatic drying process has two zones, falling rate and a constant rate. When the product becomes sufficiently dry that there are dry areas on the product surface. Further drying results in a falling rate of moisture removal.
Inferential measurement of product moisture is accomplished by the measurement of temperatures of the gas entering and exiting the dryer and performing a calculation using these temperatures. This technique uses mass and energy balances of the dryer to calculate the product moisture and is valid during the falling rate zone only.
H eater
W et Feed
D ry P roductO ut
A ir Fan
T in
T out
N atura l G as
w
Air O utto dust co llector
Rotary D ryer Counter Current F low
Product MoistureC alculation
The relationship between outlet moisture
and the temperatures are:
wp = k*ln( (Ti - Tw) / (To - Tw) )where:
wp = Outlet Moisture
Ti = Inlet Dry Bulb Temperature
Tw = Wet Bulb Temperature
To = Outlet Dry Bulb Temperature
k = Dryer Constant
Combustion air wet bulb temperature
For water and air systems, the wet bulb temperature is the same at the inlet as it is in the outlet.
Natural gas combustion wet bulb temperature degF is related by an empirical relationship that is:
Tw = 164 - ( 16900/Ti )
Combustion air wet bulb temperature
Combustion air wet bulb temperature
Colder air cannot contain as much absolute moisture as warmer airColder air requires more gas to heat, and therefore adds more moisture to the combustion productRelationship good for temperatures above 300 DegF
Inferential moisture control
PID control of this equation:
wp = k*ln( (Ti - Tw) / (To - Tw) )difficult due to inverse response
The problem in controlling this equation is that the dynamics of the equation result in reverse action, i.e. if the moisture set point is lowered, the instantaneous action would be to increase the inlet temperature, which causes the calculated moisture to increase before the outlet temperature is increased to such an extent as to lower the moisture to its new stable set point. This is because of the dead time and time constant between the inlet and outlet temperatures. Using conventional PID control on this relationship results in unstable control.
Inferential moisture controlIf the inlet temperature signal was transformed through a dead time and time constant control function blocks in the control algorithm, then applied to the inferential calculation, the resultant response would be closer to the actual moisture. This is because the present time observation of outlet temperature is the result of a past inlet temperature.
lagtimede lay
lag
f
in le t_ Tw Tc
dryer_tc
ti_w e ll
tw
con tro l_td
lagtou t_p rocess1 time
de lay
ou tlet_ Tw Tc
tou t_p ro cess2
drye r_ td
to ut_ we ll
lagti_c trl1
con tro l_tc
ftw _ctrl
ti_c trl
d rye r s im u lation
tise t
to u t
In fe ren tia l Dryer Contro ls
x(1)
x(2) x (3 )
x (4 )
w_ calc k * logti_ well tw
tout_ well tw
w_ctrl k *log
ti_ ctrl tw_ ctrl
tout_ well tw_ ctrl
un com pe nsa ted fa llin g ra te co m pe n sa ted fallin g rate m ois ture