DK4102_C005

5Spreadsheet-Aided Dryer Design
Z.B.Maroulis,G.D.Saravacos,and Arun S.Mujumdar CONTENTS
5.1Introduction (121)
5.2Principles and Techniques of Spreadsheet-Aided Process Design (121)
5.3Design of a Conveyor Belt Dryer (126)
5.3.1Process Description (126)
5.3.2Process Model (126)
5.4Excel Implementation of a Belt Dryer Design (127)
Nomenclature (129)
References (134)
5.1INTRODUCTION
Spreadsheet software has become an indispensable tool for engineers,because of the availability of per-sonal computers,ease of use,and adaptability to many types of problems.Spreadsheet software has achieved great popularity because of its availability for microcomputers at reasonable cost,the ease of learning and using the software,and itsflexible appli-cations to many problems.
Furthermore,general-purpose spreadsheet soft-ware can be used effectively in process design(Maroulis and Saravacos,2003).For example,Microsoft Excel with Visual Basic for Applications is an effective tool for process design.Spreadsheets offer suffi-cient process model‘‘hospitality.’’They are con-nected easily and online with charts and graphic objects,resulting in powerful and easy-to-use graph-ical interfaces.Excel also supports mathematical and statistical tools.For instance,Solver is an excellent tool for solving sets of equations and performing optimization.Databases are effectively and easily ac-cessed.In addition,Visual Basic for Applications offers a powerful object-oriented programming lan-guage,capable of constructing commercial graphics interfaces.
It is the objective of this chapter to present step-by-step procedures in order to allow application of various dryer models into the Excel environment. This chapter refers to two main topics.The principles for solution of a process design problem are presented first and then the principles for Excel implementation are described.
The reader needs to become familiar with the following topics regarding Excel software,using the related literature:
.Modeling and spreadsheets
.Analyzing the Solver
.Sensitivity analysis using Excel tables
.Controls and dialog boxes to input data
.Graphics to get the results
.Databases
.Visual Basic as a programming language
5.2PRINCIPLES AND TECHNIQUES OF
SPREADSHEET-AIDED PROCESS DESIGN Computer-aided design is based on computer simu-lators,whereas computer simulators are based on process modeling.The basic terms,such as modeling, simulat i on, and de s ign, are defi n ed in Table 5.1. Mo d-eling is the procedure of translating the physical laws of a process to mathematical equations to analyze or design the process.Simulation is the appropriate soft-ware,which predicts the real performance of a pro-cess.It is based on mathematical modeling plus the appropriate graphics interface in a computer environ-ment.Design is a procedure of sizing and rating a process in order to achieve specific goals,such as economic production,product quality,and protection of the environment.
Modeling and simulation are useful tools in process design. Table 5.2 summ a rizes a step- b y-step procedu r e for pr o cess modeli n g, wher e as Table 5.3
summ a rizes a step- b y-step procedure for process sim u-lation. These steps are further ana l yzed.
The equations constituting a model describe the physical laws, which apply to the process. They are derived from material and energy balances, thermo-dy n a m ic e q ui l i b r i um r e la t ions h i p s , t r a n spor t phe n om -ena, geometry, equipment characteristics, etc. Generally some assumptions are also built into the model.
A degrees -of-fre e dom an a lysis is shown in Table
5.4 and in Figure 5.1. Suppos e that M variab l es are incorporated into the mathematical model of N equa-tions; generally,M is greater than or equal to N, and the difference M–N corresponds to the degrees of freedom of the process . The degrees of freedom is ch a racteris -tic of the process . In pro c ess design, some varia b les have given values , due to the de s ign specifica t ions , and the remaind e r corres p onds to design variab l es.
The number of design varia b les is charact e ristic of the problem . Several different pro b lems c o uld be de -fined for every process (see, for example ,Table 5.5) . The values for the design varia b les are decided by the design engineer . The remai n der NÂN set of eq u ations is solved by using mathe m ati c al techni q ues. In chem-ical an d food engineer i ng the resul t ing syst e m is sparse , that is every varia b le ap p ears in a few eq -uations . In that case the system can be solved sequenti a lly (down trian g le matrix) or by using a few trial varia b les.
The ab o ve ap p roach is suit a ble for impl e ment a-tion in a spreads h eet en v ironmen t. The resul t ing simulat o r has generally the outline present e d in Figure 5.2. Four diff e rent units are dist i nguished , with each one developed in a different sheet (Maroul i s and Saravacos , 2002).
The ‘‘Proc e ss Mod e l Worksheet ’’ is the he a rt of the syst e m calcul a tions.It co n tains the proce s s model. When no interactio n s are ne e ded, the mod e l solution uses only works h eet functi o ns. In that case, when any change in inpu t variab l es (free va r iables) occu r s, the solution is obtaine d automa t ically on this works h eet.
Since the use of the simulator requ i res the solution of diff e rent pro b lems, several different problem s are formu l ated in the ‘‘Problem Solution Visual Basic Modu l e.’’ Their solution is based on the sim p lest problem of the pro c ess model worksh e et above, and uses the Solver or the Goal Seek utilities of Excel via a Visual Basic program,to obtain a solution for the alternative problems.
All technical and required data are retrieved from the‘‘Database worksheet,’’which contains all the required information in the form of‘‘data lists.’’These data are extended and modified via appropriate dialog boxes.
‘‘Graphics interface worksheet’’is a user-friendly way for human–machine communication.It usually consists of three parts:(a)Problem specifications:The specifications and the required data for the problem
TABLE 5.1
Basic Defini t ions
Modeling: is the procedure to translate the physical laws of a process to mathematical equations
Simulation : is the appropriate software which guesses the real performance of a process
Design: is a procedure to size and rate a process in order to obtain a specific goal
Sizing:given the process specifications calculate the equipment size and characteristics
Rating:given the process specifications and the equipment size and characteristics calculate the operating conditions
TABLE 5.2
Process Modeling
1.Process model formulation
2. Degrees-of-freedom analysis
3. Alternative problem formulations
4.Problem-solution algorithm
5.Cost estimation and project evaluation analysis
6.Process optimization TABLE 5.3
Process Simulation Procedu r e in a Sp r eadshee t Enviro n ment
1. Model development in a spreadsheet
2. Implementation of alternative problem solutions or optimization
procedures
3.Development of graphics interface
TABLE 5.4
Degrees- o f-Fre e dom Analysis
Total number of variables M
Total number of equations N
Degrees of freedom F ¼M–N Process characteristic Degrees of freedom F
Problem specifications K
Design variables D¼F–K Problem characteristic
to be so l ved are entere d by the use r or estimat e d from the databas e s. Data are inser t ed via dialog box e s or buttons for changing some impor t ant magn i tudes. (b)Problem- t ype selection: The type of pro b lem to be solved is selec t ed via buttons . (c) Resul t s present a -tion: The resul t s are obtaine d automa t ica l ly, an d are present e d in the form of table s or ch a rts. Since these charts are updated automa t ica l ly, the user has at his disposa l all the infor m ation ne e ded for sizi n g, rati n g,sensitiv i ty an a lysis, or compari s on of alte r native solution s .
The foll o wing steps co m prise an Excel impl e men-tation proced u re:
1. Workboo k preparation
2. Process mo d eling in a sp r eadsheet
3. Using ‘‘Solver’ ’ for process optimizat i on
4. Using graphs and table s for present a tion of the results
5. Introduc i ng dialog box e s and control s to mo d -ify data
6. Toward a n integ r ated graphic s inter f ace Step 1: Workbook Preparation
Create a new workbook an d name it to de s cribe the process , e.g., ‘‘BeltDr y er.xls.’’ Insert an d na m e blank sheets are present e d in Tabl e 5.6.
Step 2: Process Modeling in a Spreadsheet
Into the spreads h e e t ‘‘Proc e ss’’ consider seven separ-ate ranges, as it is present e d in Table 5.7.
Eac h range consis t s of three columns and severa l rows, one row for every varia b le in the range. In each range the first column contai n s the variable names,the second the varia b le values or variab l e form u las,and the thir d the units use d . Name all cells in second columns accordi n g to the names in the first c o lumn.(You can use the ‘‘Ctrl þS hift þF 3’’ option .)
TABLE 5.5
Some Typical Problem s
Direct
Given the characteristics of input streams
the equipment characteristics the operating conditions
Calculate the characteristics of the output streams Design
Given the characteristics of input streams
the characteristics of output streams
Calculate the equipment characteristics
the operating conditions Rating
Given the characteristics of input streams
the characteristics of output streams the equipment characteristics
Calculate the operating conditions
Identification
Given the characteristics of input streams
the characteristics of output streams the operating conditions
Calculate the equipment characteristics
FIGURE 5.1Degrees-of-freedom analysis.
FIGURE 5.2Simulator architecture on a spreadsheet environment.
The ranges ‘‘Technical Data,’’‘‘Design Vari-ables,’’‘‘Process Specifications,’’and ‘‘Economic Data’’contain only data.The ranges ‘‘Process
Model,’’‘‘Process Constraints,’’and ‘‘Economic Model’’contain formulas.
Having inserted data and formulas,the process model implementation has been completed.The resulting spreadsheet ‘‘Process’’looks like that pre-sented in Figure 5.3.The cell ranges can be colored with different colors.The drawn arrows show the information flow in the spreadsheet.
The spreadsheet process model is now ready for use.Any changes in process data,economic data,process specifications,design variables are taken into account and the results are updated immediately.Any optimization technique,graphical or tabu-lated reports,any scenario analysis,or sensitivity an-alysis,any sophisticated graphics interface can be based on the ‘‘Process’’spreadsheet.Some examples follow.
Step 3:Using ‘‘Solver’’for Process Optimization
Create a Visual Basic subroutine with the name ‘‘optimum’’in the ‘‘Optimize’’module.The approp-riate code is shown in Table 5.8.
TABLE 5.6
Sheets in ‘‘BeltDryer.xls’’Workbook
Sheet Name Purpose
Spreadsheets Process Process model Flow sheet Process flow sheet
Report Summary report of results Control
Graphics interface
Visual Basic Modules Optimize Process optimization subroutines
Controls
Subroutines for dialog boxes and controls Dialog box sheets Spec Process specifications Tech Technical data Cost
Economical data
TABLE 5.7
Cell Content in ‘‘Process’’Spreadsheet
Range Name Content Technical data Data Design variables
Data Process specifications Data Economic data Data Process model
Formulas Process constraints Formulas Economic model
Formulas
FIGURE 5.3Model implementation in the ‘‘Process’’spreadsheet.
TABLE 5.8
Visual Basic Subroutine for Process Optimization
Sub optimum()
1Sheets(‘‘Process’’).Activate 2SolverReset
3SolverOk SetCell:¼Range(‘‘objective’’),MaxMinVal:¼1,ByChange:¼Range(‘‘variables’’)
4SolverAdd CellRef:¼Range(‘‘constraints’’),Relation:¼3,FormulaText:¼0#
5SolverSolve UserFinish:¼True 6Beep End Sub
Statement1activates the‘‘Process’’spreadsheet. Statement2resets the Solver.Statement3selects the cell with the name‘‘objective’’to be the ob-jective function[SetCell:¼Range(‘‘objective’’)],re-quires the minimization of the objective function [MaxMinVal:¼2],and selects the range‘‘variables’’to be the decision variables[ByChange:¼Range (‘‘variables’’)].Statement4suggests that all cells in the range‘‘constraints’’[CellRef:¼Range(‘‘constraints’’)] must be greater than[Relation:¼3]zero[Formula-Text:¼0#].Statement5activates the solver tofind the optimum.
The above-mentioned cell names must be defined. Thus,in the sheet‘‘Process’’name:
.The cells that contain the values of the design
variables as‘‘variables’’
.The cells that contain the process constraints as
‘‘constraints’’
.The cell that contains the profit as‘‘objective’’In the sheet‘‘Process’’insert a new button,name it ‘‘optimizer’’and assign it to the subroutine‘‘opti-mum.’’
Press the button‘‘optimizer’’and the optimum is reached in a few seconds.
Step4:Using Excel Tables and Charts for Presenta-tion of the Results
The process design results can be further analyzed using the tools‘‘Tables’’and‘‘Charts’’supported by Excel.
For example,a processflow sheet can easily be constructed in Excel as follows:in the sheet‘‘Flow sheet’’draw aflow sheet by using the drawing tool-bar.Any information concerning process conditions can be inserted in cells near the desired point of the flow sheet.For each piece of information there need to be three cells,one for the variable name,one for the variable value,and one for the variable units. That is,to insert a streamflow rate,select a cell near the icon of the stream arrow and insert the symbolic name of the streamflow rate,i.e.,‘‘F¼,’’in a neigh-boring cell insert the formula‘‘¼F’’to get the value from the‘‘Process’’sheet,and in another cell, nearby,insert the units,i.e.,‘‘kg/s.’’You can add any information you like.Any changes in data are up-dated immediately.
In order to plot the effect of the design variable (X)on a technical(Y)and an economic(Z)variable the following steps can be used:construct a one-di-mensional Excel table in which the‘‘Column Input Cell’’is the cell with the name‘‘X.’’The second and third output columns refer to the cells‘‘Y’’and‘‘Z,’’respectively.Next construct a‘‘XY(Scatter)’’chart in which thefirst column of the table corresponds to x-values and the second to y-values.Similarly,con-struct a second‘‘XY(Scatter)’’chart in which thefirst column of the table corresponds to x-values and the third to y-values.
Any other tabulated results or desired reports can be easily obtained as follows:select a spreadsheet to incorporate the required information.Insert text or graphics as you like.Get the information from the ‘‘Process’’sheet,as described previously in theflow sheet construction procedure.
Step5:Introducing Dialog Boxes and Controls to Modify Data
A dialog box can be used to modify the values of process specifications,which are included in the range‘‘Process Specifications’’in the spreadsheet ‘‘Process.’’
In the Dialog Module‘‘db_spec’’insert for every variable one‘‘Label’’(from the toolbar‘‘forms’’)for its description,one‘‘Edit Box’’(from the toolbar ‘‘forms’’)for its value,and one‘‘Label’’for its units. Name all the Edit Boxes with the name of the corre-sponding variable.
In the Visual Basic Module‘‘vb_controls’’type a subroutine to use the dialog box in the sheet ‘‘d_spec,’’as described in Table5.9.
In the spreadsheet‘‘Process’’insert a button, name it‘‘specifications,’’and assign it to the subrou-tine‘‘DialogSpecifications.’’
Press the button‘‘specifications’’and a dialog box appears in order to modify data for process specifications.
A scroll bar can be used for each design variable in order to modify the values of the design variables, which are included in the range‘‘Design Variables’’in the spreadsheet‘‘Process.’’
TABLE5.9
A Subroutine to Activate the Dialog Box
Sub DialogSpecifications()
dbName¼‘‘d_spec’’
DialogSheets(dbName).EditBoxes(‘‘W’’).Text¼Range(‘‘W’’).Value DialogSheets(dbName).EditBoxes(‘‘Xo’’).Text¼Range(‘‘Xo’’).Value DialogSheets(dbName).EditBoxes(‘‘Yo’’).Text¼Range(‘‘Yo’’).Value If DialogSheets(dbName).Show Then
Range(‘‘W’’).Value¼DialogSheets(dbName).EditBoxes(‘‘W’’).Text Range(‘‘Xo’’).Value¼DialogSheets(dbName).EditBoxes(‘‘Xo’’).Text Range(‘‘Yo’’).Value¼DialogSheets(dbName).EditBoxes(‘‘Yo’’).Text End If
Beep
End Sub
A scrol l bar, in order to ha n dle the va r iable X, can be inserted as follows :
.Insert the scrol l bar icon from the too l bar
‘‘forms ’’
.Insert the mini m um allowabl e value in a cell
named ‘‘X.m i n’’
.Insert the maxi m um allowabl e value in a cell
named ‘‘X.m a x’’
.Insert the coded value in a cell na m ed ‘‘X.C V’’The co d ed value ranges between 0 and 100 and is defined as follows :
X.CV ¼ (XÀX.min) /(X.max ÀX min)*1 00
.Insert a scroll ba r from the toolbar ‘‘forms’’ and
assign the ‘‘Cel l Link ’’ (in the ‘‘Form a t Object’’
menu) to the coded value ‘‘X.CV ’’
.Repla c e the con t ent of the cell named ‘‘X’’ wi t h
the foll o wing form u la:
¼ X.min þX.CV *(X.ma xÀX.m i n)/100
It must be noted that the range ‘‘va r iables’’ which is hand l ed by the solver during optim i zation must be redefined to refer to coded values , instead of the ac-tual values . This modificat i on g u arante e s the prop e r perfor m ance of the optimizat i on and of scrol l bars.
Step 6: Toward an Integrated Graphics Interface
Any desired graphics interface can be developed in the spreadsheet ‘‘Control.’’ It can be constructed as follows:
.Draw a proc e ss flow sheet in sheet ‘‘Contr o ls,’’
as de s cribed in Step 5
.Insert buttons to appear and disappea r the cru-
cial graphs
.Insert buttons to activate the desired dialog boxes .Insert scrol l bars to modif y the desir e d pro c ess
variab l es
.Insert buttons to solve different pro b lems, e.g. ,
process optimizat i on.
The user has now at his dispo s al a process sim u la-tor. He can en t er da t a via scroll ba r s or dialog box e s and observe the resul t s via buttons , which acti v ate the desired grap h s or report s.
The graphic s interface could be furt h er impr o ved to loo k professional using appropri a te program m ing code in Visual Bas i c.
5.3 DESIGN OF A CONVEYOR BELT DRYER In this section a design app r oach is descri b ed for a conveyo r belt dr y er (Maroul i s an d Sa r avacos , 2003).5.3.1 P R OCESS D ESCRIPTION
A typic a l flow sheet of a con v eyor belt dryer is pre-sented in Figure 5.4. The wet feed at flow rate F (kg/ s db), tempe r atur e T0 (8 C) , and humidi t y X0 (kg/kg db) is dist r ibuted on the belt as it en t ers the dryer. The dried produ c t exits the dry e r at the same flow rate on dry basis F (kg/ s db) , tempe r ature T (8 C), and mois -ture content X (kg/ k g db). The belt is moving a t a velocity u (m/s) and req u ires an elect r ical power E b (kW). The dr y ing air enters the dryer at a flow rate F f (kg/s db),temperature T(8C),and humidity Y(kg/kg db).The drying air temperature is controlled in the heater,and the drying air humidity is controlled through theflow rate of the fresh air F a(kg/s db). An electrical power E f(kW)is expended by the fan and a thermal power Q(kW)is expended by the heater.The air conditions for design can be consid-ered constant due to the high air recirculation.
5.3.2P ROCESS M ODEL
A mathematical model of the process presented in Figure 5.4 is summ a rize d in Tabl e 5.10.
Equation T10.1calculates the vapor pressure at drying temperature,whereas Equation T10.2is the psychrometric equation.Equation T10.1and Equa-tion T10.2are used to calculate the water activity at drying conditions(i.e.,temperature T and air humid-ity Y).Equation T10.3calculates the equilibrium material moisture content at drying conditions, whereas Equation T10.4estimates the drying time constant at drying conditions.Both Equation T10.3 and Equation T10.4are used in Equation T10.5, which calculates the required drying time.
Equation T10.6and Equation T10.7constitute the moisture balance at the dryer.Equation T10.6 refers to solid,and Equation T10.7to air.The ther-mal energy requirements for drying are
summarized FIGURE5.4Schematic representation of a belt dryer.
in Equat i on T10 .8 through Equation T10.11. Equa-tion T10 .8 refers to wat e r evap o ration, Equation T10.9 to solid s he a ting, Equat i on T10.10 to rejec t ed air heating , an d Equat i on T10.11 refer s to the total energy requir e d by the heater .
Equat i on T10 .12 is used for sizing the heater . Equation T10 .13 throu g h Equation T10 .17 are used for sizi n g the belt.
Equat i on T10 .13 correl a tes the reside n ce time with the mass hold u p, an d Equat i on T10.14 the mass hol d up with the vo l ume hold u p. These eq u a-tions are valid for all dryer types. Equation T10 .15 is the geomet r ical dist r ibution of the volume holdu p on the belt. Equation T10 .16 calcul a tes the required belt area, and Equat i on T10.17 the requir e d be l t veloci t y to obt a in the desired resi d ence time.
Equat i on T10 .18 through Equat i on T10.20 are used for sizing the fan. Equat i on T10 .18 calcul a tes the pressure loss of air through the load e d belt. Equa-tion T10.19 co r relates the airflow with the air vel-ocity. Equation T10.20 esti m ates the requir e d electrica l power to ope r ate the fan.
Equat i on T10.21 estimat e s the required electrica l power to mo v e the belt. Equat i on T10 .22 calcul a tes the req u ired total elect r ical power .
Fin a lly, Equat i on T10.23 and Equation T10 .24 define two crucial dr y er perfor m ance indice s. Equa-tion T10 .23 defines the dryer thermal perfor m ance, whereas Equation T10 .24 calcul a tes the evap o rating capacity per unit belt area.
Thi r ty-seven variables pr e sented in Tabl e 5.11 are involv e d in the model of 24 equatio n s present e d in Table 5.10. The corres p onding techn i cal data are summ a rized in Tabl e 5.12. The process specifica t ions of a typical design prob l em are present e d in Table 5.13, wher e as a degrees -of-fre e dom an a lysis is sho w n in Table 5.14, whi c h results in four de s ign varia b les. Table 5.15 suggest s a selec t ion of de s ign v a riables and the corresp o nding solut i on algorithm is pr e sented in Table 5.16. The total an n ualiz e d cost (T A C) pr e-sented in Table 5.17 is used as object i ve function in process optim i zation. The requir e d cost data are summ a rized in Table 5.18.
5.4 EXCEL IMPLEMENTATION OF A BELT
DRYER DESIGN
In this sectio n the dryer design mo d el pr e sented in Sectio n 5.3 is implement e d in an Exc e l en v ironme n t accordi n g to the princi p les and techni q ues present e d in Se c tion 5.2.
Steps 1–3 of Section 5.2 are applied and the dryer model is created on the spreadsheet ‘‘process’’ as shown in Figure 5.5. The ranges ‘‘Technical Data,’’ ‘‘Process Specifications,’’ ‘‘Design Variables,’’ and ‘‘Cost Data’’contain data according to Table 5.12, Table 5.13, Table 5.15, and Table 5.18, respectively. The range ‘‘Model Solution’’ contains the solution of the model in Table 5.10 according to the solution presented in Table 5.16, and the range ‘‘Cost Analysis’’ represents the analysis presented in Table 5.17. Finally, the button ‘‘optimize’’performs an optimization, i.e., it finds the (optimal) values of the design variables (Y, T, V, D), which min-imize the objective function (TAC). Figure 5.5 consti-tutes a simple but accurate belt dryer design simulator. Different problems (different material, financial envir-onment, process specifications) can be solved instant-aneously.
Step 4 of Section 5.2 is app l ied, as an exampl e, (a) to construct a dynamic process flow sheet (Figure 5.6);
TABLE 5.10
Belt Dryer Model
Psychrometric equations
P s¼exp[a1Àa2/(a3þT)](T10.1) Y¼ma w P s/(PÀa w P s)(T10.2)
Drying kinetics
X e¼b1exp[b2/(273þT)][a w/(1Àa w)]b3(T10.3) t c¼c0d c1V c2T c3Y c4(T10.4) t¼Àt c ln[(XÀX e)/(X0ÀX e)](T10.5) Material balance
W¼F(X0ÀX)(T10.6) W¼F a(YÀY0)(T10.7) Thermal energy requirements
Q we¼F(X0ÀX)[D H0À(C PLÀC PV)T](T10.8) Q sh¼F[C PSþX0C PL](TÀT0)(T10.9) Q ah¼F a[C PAþY0C PV](TÀT0)(T10.10) Q¼Q weþQ shþQ ah(T10.11) Air heater
Q¼A s U s(T sÀT)(T10.12)
Belt dryer
M¼tF(1þX0)(T10.13) M¼(1À«)r s H(T10.14) H¼Z0DL(T10.15) A b¼LD(T10.16) u b¼L/t(T10.17)
Fan
D P¼f1Z0V2(T10.18) F i¼r a VDL(T10.19)
E f¼D P
F f/r a(T10.20)
Belt driver
E b¼e1L(1þX0)F(T10.21)
Electrical energy requirements
E¼E bþE f(T10.22)
Performance indices
n¼Q we/Q(T10.23) r¼W/A b(T10.24)
(b) to investiga t e the effe c t of one design variab l e on an eco n omic varia b le (Figur e 5.7); (c) to analyze the effect of two design varia b les on a techni c al varia b le (Figur e 5.8); (d) to summ a rize the resul t s of the de s ign on a syno p tic report (Figur e 5.9). Any other analys i s
TABLE 5.11
Process Variables
Drying air F a ton/h Fresh airflow rate F f ton/h Recycle airflow rate T 8C
Drying air temperature Y kg/kg db Drying air humidity V m/s Drying air velocity P bar Drying pressure
T 08C
Ambient temperature Y 0kg/kg db Ambient humidity
P s bar Vapor pressure at drying conditions a w —Water activity at drying conditions Material F ton/h Material flow rate
X 0kg/kg db Initial moisture content X kg/kg db Final moisture content
X e kg/kg db Equilibrium moisture content at drying conditions d m Particle size
t c h Drying time constant at drying conditions t h Drying time
Dryer W ton/h Drying rate L m Dryer length D m Dryer width
M ton Dryer mass holdup H m 3Dryer volume holdup A b m 2Belt area
A s m 2Air heater transfer area u b m/s Belt velocity Z 0m Loading depth
D P
bar
Pressure loss of air flowing through belt Thermal load Q we kW Water vaporization Q sh kW Solid heating Q ah kW Air heating
Q kW Total thermal load T s
8C Steam temperature Electrical load E b kW Belt driver E f kW Fan
E
kW Total power requirement Performance n —
Thermal efficiency
r
kg/h m 2
Specific rate of evaporation
TABLE 5.12Technical Data
Density (kg/m 3)r w Water r a Air
r s
Dry material Specific heat (kJ/kg K)C PL Water
C PV Water vapor C PA Air
C PS
Dry material
Latent heat (kJ/kg)D H 0Steam condensation at 08C
Other U s Heat transfer coefficient at air heater (kW/m 2K)
«
Void (empty)fraction of loading Empirical constants a 1,a 2,a 3Antoine equation for vapor pressure of water
b 1,b 2,b 3
Oswin equation for material isotherms c 0,c 1,c 2,c 3,c 4Drying kinetics equation e 1Belt driver power equation f 1
Pressure loss equation
TABLE 5.13
Process Specifications
F ton/h db Feed flow rate
X 0kg/kg db Initial material moisture content X kg/kg db Final material moisture content d m Material characteristic size T 08C
Ambient temperature Y 0kg/kg db Ambient humidity Z 0m Loading depth P bar Ambient pressure
T s
8C
Heating steam temperature
TABLE 5.14
Degrees-of-Freedom Analysis
Process variables 37Degrees of freedom 13Process equations 24Specifications 9Degrees of freedom
13
Design variables
4
TABLE 5.15
Design Variables
Y kg/kg db Drying air humidity T 8C Drying air temperature V m/s Drying air velocity D
m
Belt width。