Handbook of Industrial Drying

5

Spreadsheet-Aided Dryer Design Z.B. Maroulis, G.D. Saravacos, and Arun S. Mujumdar

CONTENTS 5.1 5.2 5.3

Introduction ........................................................................................................................................... Principles and Techniques of Spreadsheet-Aided Process Design.......................................................... Design of a Conveyor Belt Dryer .......................................................................................................... 5.3.1 Process Description .................................................................................................................... 5.3.2 Process Model............................................................................................................................. 5.4 Excel Implementation of a Belt Dryer Design ....................................................................................... Nomenclature ................................................................................................................................................. References ......................................................................................................................................................

5.1 INTRODUCTION Spreadsheet software has become an indispensable tool for engineers, because of the availability of personal 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 its flexible applications to many problems. Furthermore, general-purpose spreadsheet software 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 sufficient process model ‘‘hospitality.’’ They are connected easily and online with charts and graphic objects, resulting in powerful and easy-to-use graphical 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 accessed. In addition, Visual Basic for Applications offers a powerful object-oriented programming language, capable of constructing commercial graphics interfaces. It is the objective of this chapter to present stepby-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.

ß 2006 by Taylor & Francis Group, LLC.

121 121 126 126 126 127 129 134

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

5.2 PRINCIPLES AND TECHNIQUES OF SPREADSHEET-AIDED PROCESS DESIGN Computer-aided design is based on computer simulators, whereas computer simulators are based on process modeling. The basic terms, such as modeling, simulation, and design, are defined in Table 5.1. Modeling is the procedure of translating the physical laws of a process to mathematical equations to analyze or design the process. Simulation is the appropriate software, which predicts the real performance of a process. It is based on mathematical modeling plus the appropriate graphics interface in a computer environment. 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 summarizes a step-by-step procedure for process modeling, whereas Table 5.3

TABLE 5.1 Basic Definitions 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 5.3 Process Simulation Procedure in a Spreadsheet Environment 1. Model development in a spreadsheet 2. Implementation of alternative problem solutions or optimization procedures 3. Development of graphics interface

summarizes a step-by-step procedure for process simulation. These steps are further analyzed. The equations constituting a model describe the physical laws, which apply to the process. They are derived from material and energy balances, thermodynamic equilibrium relationships, transport phenomena, geometry, equipment characteristics, etc. Generally some assumptions are also built into the model. A degrees-of-freedom analysis is shown in Table 5.4 and in Figure 5.1. Suppose that M variables are incorporated into the mathematical model of N equations; 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 characteristic of the process. In process design, some variables have given values, due to the design specifications, and the remainder corresponds to design variables. The number of design variables is characteristic of the problem. Several different problems could be defined for every process (see, for example, Table 5.5). The values for the design variables are decided by the design engineer. The remainder NN set of equations is solved by using mathematical techniques. In chemical and food engineering the resulting system is sparse, that is every variable appears in a few equations. In that case the system can be solved

sequentially (down triangle matrix) or by using a few trial variables. The above approach is suitable for implementation in a spreadsheet environment. The resulting simulator has generally the outline presented in Figure 5.2. Four different units are distinguished, with each one developed in a different sheet (Maroulis and Saravacos, 2002). The ‘‘Process Model Worksheet’’ is the heart of the system calculations. It contains the process model. When no interactions are needed, the model solution uses only worksheet functions. In that case, when any change in input variables (free variables) occurs, the solution is obtained automatically on this worksheet. Since the use of the simulator requires the solution of different problems, several different problems are formulated in the ‘‘Problem Solution Visual Basic Module.’’ Their solution is based on the simplest problem of the process model worksheet 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 5.2 Process Modeling

TABLE 5.4 Degrees-of-Freedom Analysis

1. 2. 3. 4. 5. 6.

Total number of variables Total number of equations Degrees of freedom Degrees of freedom Problem specifications Design variables

Process model formulation Degrees-of-freedom analysis Alternative problem formulations Problem-solution algorithm Cost estimation and project evaluation analysis Process optimization


M N F ¼ M–N F K D ¼ F–K

Process characteristic

Problem characteristic

Total number of variables (M )

Total number of equations (N )

Degrees of freedom (F ) (Process characteristic)

Problem specifications (K ) (Problem characteristic)

Design variables (D )

FIGURE 5.1 Degrees-of-freedom analysis.

to be solved are entered by the user or estimated from the databases. Data are inserted via dialog boxes or buttons for changing some important magnitudes. (b) Problem-type selection: The type of problem to be solved is selected via buttons. (c) Results presentation: The results are obtained automatically, and are presented in the form of tables or charts. Since these charts are updated automatically, the user has at his disposal all the information needed for sizing, rating, sensitivity analysis, or comparison of alternative solutions. The following steps comprise an Excel implementation procedure:

TABLE 5.5 Some Typical Problems Direct Given

Calculate Design Given Calculate Rating Given

Calculate Identification Given

Calculate

the characteristics of input streams the equipment characteristics the operating conditions the characteristics of the output streams the characteristics of input streams the characteristics of output streams the equipment characteristics the operating conditions

1. 2. 3. 4.

Workbook preparation Process modeling in a spreadsheet Using ‘‘Solver’’ for process optimization Using graphs and tables for presentation of the results 5. Introducing dialog boxes and controls to modify data 6. Toward an integrated graphics interface Step 1: Workbook Preparation Create a new workbook and name it to describe the process, e.g., ‘‘BeltDryer.xls.’’ Insert and name blank sheets are presented in Table 5.6. Step 2: Process Modeling in a Spreadsheet Into the spreadsheet ‘‘Process’’ consider seven separate ranges, as it is presented in Table 5.7. Each range consists of three columns and several rows, one row for every variable in the range. In each range the first column contains the variable names, the second the variable values or variable formulas, and the third the units used. Name all cells in second columns according to the names in the first column. (You can use the ‘‘CtrlþShiftþF3’’ option.)

Graphics interface worksheet

Problem solution Visual Basic module

Database worksheet

Process model worksheet

the characteristics of input streams the characteristics of output streams the equipment characteristics the operating conditions the characteristics of input streams the characteristics of output streams the operating conditions the equipment characteristics


FIGURE 5.2 Simulator architecture on a spreadsheet environment.

TABLE 5.6 Sheets in ‘‘BeltDryer.xls’’ Workbook Sheet Name Spreadsheets Process Flow sheet Report Control Visual Basic Modules Optimize Controls Dialog box sheets Spec Tech Cost

Purpose

Process model Process flow sheet Summary report of results Graphics interface Process optimization subroutines Subroutines for dialog boxes and controls Process specifications Technical data Economical data

The ranges ‘‘Technical Data,’’ ‘‘Design Variables,’’ ‘‘Process Specifications,’’ and ‘‘Economic Data’’ contain only data. The ranges ‘‘Process

Content

Technical data Design variables Process specifications Economic data Process model Process constraints Economic model

Data Data Data Data Formulas Formulas Formulas

Economic data

Step 3: Using ‘‘Solver’’ for Process Optimization Create a Visual Basic subroutine with the name ‘‘optimum’’ in the ‘‘Optimize’’ module. The appropriate code is shown in Table 5.8.

TABLE 5.8 Visual Basic Subroutine for Process Optimization

TABLE 5.7 Cell Content in ‘‘Process’’ Spreadsheet Range Name

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 presented 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 tabulated reports, any scenario analysis, or sensitivity analysis, any sophisticated graphics interface can be based on the ‘‘Process’’ spreadsheet. Some examples follow.

Sub optimum( ) 1 Sheets(‘‘Process’’).Activate 2 SolverReset 3 SolverOk SetCell: ¼ Range(‘‘objective’’), MaxMinVal: ¼ 1, ByChange: ¼ Range(‘‘variables’’) 4 SolverAdd CellRef: ¼ Range(‘‘constraints’’), Relation: ¼ 3, FormulaText: ¼ 0# 5 SolverSolve UserFinish: ¼ True 6 Beep End Sub

Economic model

Excel solver

Process model

Excel table

Technical data

Process specifications Design variable

Data

Process constraints

Equations

FIGURE 5.3 Model implementation in the ‘‘Process’’ spreadsheet.


Excel graph

Excel tools

Statement 1 activates the ‘‘Process’’ spreadsheet. Statement 2 resets the Solver. Statement 3 selects the cell with the name ‘‘objective’’ to be the objective function [SetCell: ¼ Range(‘‘objective’’)], requires the minimization of the objective function [MaxMinVal: ¼ 2], and selects the range ‘‘variables’’ to be the decision variables [ByChange: ¼ Range (‘‘variables’’)]. Statement 4 suggests that all cells in the range ‘‘constraints’’ [CellRef: ¼ Range(‘‘constraints’’)] must be greater than [Relation: ¼ 3] zero [FormulaText: ¼ 0#]. Statement 5 activates the solver to find 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 ‘‘optimum.’’ Press the button ‘‘optimizer’’ and the optimum is reached in a few seconds. Step 4: Using Excel Tables and Charts for Presentation of the Results The process design results can be further analyzed using the tools ‘‘Tables’’ and ‘‘Charts’’ supported by Excel. For example, a process flow sheet can easily be constructed in Excel as follows: in the sheet ‘‘Flow sheet’’ draw a flow sheet by using the drawing toolbar. 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 stream flow rate, select a cell near the icon of the stream arrow and insert the symbolic name of the stream flow rate, i.e., ‘‘F ¼ ,’’ in a neighboring cell insert the formula ‘‘ ¼ F’’ 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 updated 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-dimensional 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 the first column of the table corresponds to x-values and the second to y-values. Similarly, construct a second ‘‘XY(Scatter)’’ chart in which the first 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 the flow sheet construction procedure. Step 5: 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 corresponding variable. In the Visual Basic Module ‘‘vb_controls’’ type a subroutine to use the dialog box in the sheet ‘‘d_spec,’’ as described in Table 5.9. In the spreadsheet ‘‘Process’’ insert a button, name it ‘‘specifications,’’ and assign it to the subroutine ‘‘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.’’

TABLE 5.9 A Subroutine to Activate the Dialog Box Sub DialogSpecifications( ) dbName ¼ ‘‘d_spec’’ DialogSheets(dbName).EditBoxes(‘‘W’’).Text ¼ Range(‘‘W’’).Value DialogSheets(dbName).EditBoxes(‘‘Xo’’).Text ¼ Range(‘‘Xo’’).Value DialogSheets(dbName).EditBoxes(‘‘Yo’’).Text ¼ Range(‘‘Yo’’).Value If DialogSheets(dbName).Show Then Range(‘‘W’’).Value ¼ DialogSheets(dbName).EditBoxes(‘‘W’’).Text Range(‘‘Xo’’).Value ¼ DialogSheets(dbName).EditBoxes(‘‘Xo’’).Text Range(‘‘Yo’’).Value ¼ DialogSheets(dbName).EditBoxes(‘‘Yo’’).Text End If Beep End Sub

A scroll bar, in order to handle the variable X, can be inserted as follows: .

.

.

.

Insert the scroll bar icon from the toolbar ‘‘forms’’ Insert the minimum allowable value in a cell named ‘‘X.min’’ Insert the maximum allowable value in a cell named ‘‘X.max’’ Insert the coded value in a cell named ‘‘X.CV’’

The coded value ranges between 0 and 100 and is defined as follows: X.CV ¼ (XX.min)/(X.maxXmin)*100 .

.

Insert a scroll bar from the toolbar ‘‘forms’’ and assign the ‘‘Cell Link’’ (in the ‘‘Format Object’’ menu) to the coded value ‘‘X.CV’’ Replace the content of the cell named ‘‘X’’ with the following formula:

¼ X.minþX.CV*(X.maxX.min)/100 It must be noted that the range ‘‘variables’’ which is handled by the solver during optimization must be redefined to refer to coded values, instead of the actual values. This modification guarantees the proper performance of the optimization and of scroll 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 process flow sheet in sheet ‘‘Controls,’’ as described in Step 5 Insert buttons to appear and disappear the crucial graphs Insert buttons to activate the desired dialog boxes Insert scroll bars to modify the desired process variables Insert buttons to solve different problems, e.g., process optimization.

5.3.1 PROCESS DESCRIPTION A typical flow sheet of a conveyor belt dryer is presented in Figure 5.4. The wet feed at flow rate F (kg/s db), temperature T0 (8C), and humidity X0 (kg/kg db) is distributed on the belt as it enters the dryer. The dried product exits the dryer at the same flow rate on dry basis F (kg/s db), temperature T (8C), and moisture content X (kg/kg db). The belt is moving at a velocity u (m/s) and requires an electrical power Eb (kW). The drying air enters the dryer at a flow rate Ff (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 the flow rate of the fresh air Fa (kg/s db). An electrical power Ef (kW) is expended by the fan and a thermal power Q (kW) is expended by the heater. The air conditions for design can be considered constant due to the high air recirculation.

5.3.2 PROCESS MODEL A mathematical model of the process presented in Figure 5.4 is summarized in Table 5.10. Equation T10.1 calculates the vapor pressure at drying temperature, whereas Equation T10.2 is the psychrometric equation. Equation T10.1 and Equation T10.2 are used to calculate the water activity at drying conditions (i.e., temperature T and air humidity Y). Equation T10.3 calculates the equilibrium material moisture content at drying conditions, whereas Equation T10.4 estimates the drying time constant at drying conditions. Both Equation T10.3 and Equation T10.4 are used in Equation T10.5, which calculates the required drying time. Equation T10.6 and Equation T10.7 constitute the moisture balance at the dryer. Equation T10.6 refers to solid, and Equation T10.7 to air. The thermal energy requirements for drying are summarized

The user has now at his disposal a process simulator. He can enter data via scroll bars or dialog boxes and observe the results via buttons, which activate the desired graphs or reports. The graphics interface could be further improved to look professional using appropriate programming code in Visual Basic.

5.3 DESIGN OF A CONVEYOR BELT DRYER In this section a design approach is described for a conveyor belt dryer (Maroulis and Saravacos, 2003).


FIGURE 5.4 Schematic representation of a belt dryer.

TABLE 5.10 Belt Dryer Model Psychrometric equations Ps ¼ exp [a1a2/(a3 þ T)] Y ¼ mawPs/(PawPs)

(T10.1) (T10.2)

Drying kinetics Xe ¼ b1 exp[b2/(273þT)] [aw/(1aw)]b3 tc ¼ c0dc1Vc2Tc3Yc4 t ¼ tc ln[(XXe)/(X0Xe)]

(T10.3) (T10.4) (T10.5)

Material balance W ¼ F (X0X) W ¼ Fa(Y Y0)

(T10.6) (T10.7)

Thermal energy requirements Qwe ¼ F(X0 X) [DH0 (CPL CPV)T] Qsh ¼ F [CPS þ X0CPL] (T T0) Qah ¼ Fa [CPA þY0CPV] (T T0) Q ¼ Qwe þ Qsh þ Qah

(T10.8) (T10.9) (T10.10) (T10.11)

Air heater Q ¼ AsUs(TsT)

(T10.12)

Belt dryer M ¼ tF (1þX0) M ¼ (1«)rsH H ¼ Z0DL Ab ¼ LD ub ¼ L/t

(T10.13) (T10.14) (T10.15) (T10.16) (T10.17)

Fan DP ¼ f1Z0V2 Fi ¼ raVDL Ef ¼ DPFf/ra

(T10.18) (T10.19) (T10.20)

Belt driver Eb ¼ e1L(1þX0)F

(T10.21)

Electrical energy requirements E ¼ Eb þ Ef

(T10.22)

Performance indices n ¼ Qwe/Q r ¼ W/Ab

(T10.23) (T10.24)

in Equation T10.8 through Equation T10.11. Equation T10.8 refers to water evaporation, Equation T10.9 to solids heating, Equation T10.10 to rejected air heating, and Equation T10.11 refers to the total energy required by the heater. Equation T10.12 is used for sizing the heater. Equation T10.13 through Equation T10.17 are used for sizing the belt. Equation T10.13 correlates the residence time with the mass holdup, and Equation T10.14 the mass holdup with the volume holdup. These equations are valid for all dryer types. Equation T10.15 is the geometrical distribution of the volume holdup on the belt. Equation T10.16 calculates the required belt area, and Equation T10.17 the required belt velocity to obtain the desired residence time.


Equation T10.18 through Equation T10.20 are used for sizing the fan. Equation T10.18 calculates the pressure loss of air through the loaded belt. Equation T10.19 correlates the airflow with the air velocity. Equation T10.20 estimates the required electrical power to operate the fan. Equation T10.21 estimates the required electrical power to move the belt. Equation T10.22 calculates the required total electrical power. Finally, Equation T10.23 and Equation T10.24 define two crucial dryer performance indices. Equation T10.23 defines the dryer thermal performance, whereas Equation T10.24 calculates the evaporating capacity per unit belt area. Thirty-seven variables presented in Table 5.11 are involved in the model of 24 equations presented in Table 5.10. The corresponding technical data are summarized in Table 5.12. The process specifications of a typical design problem are presented in Table 5.13, whereas a degrees-of-freedom analysis is shown in Table 5.14, which results in four design variables. Table 5.15 suggests a selection of design variables and the corresponding solution algorithm is presented in Table 5.16. The total annualized cost (TAC) presented in Table 5.17 is used as objective function in process optimization. The required cost data are summarized in Table 5.18.

5.4 EXCEL IMPLEMENTATION OF A BELT DRYER DESIGN In this section the dryer design model presented in Section 5.3 is implemented in an Excel environment according to the principles and techniques presented in Section 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 minimize the objective function (TAC). Figure 5.5 constitutes a simple but accurate belt dryer design simulator. Different problems (different material, financial environment, process specifications) can be solved instantaneously. Step 4 of Section 5.2 is applied, as an example, (a) to construct a dynamic process flow sheet (Figure 5.6);

TABLE 5.11 Process Variables

TABLE 5.12 Technical Data

Drying air Fa Ff T Y V P T0 Y0 Ps aw

ton/h ton/h 8C kg/kg db m/s bar 8C kg/kg db bar —

Fresh airflow rate Recycle airflow rate Drying air temperature Drying air humidity Drying air velocity Drying pressure Ambient temperature Ambient humidity Vapor pressure at drying conditions Water activity at drying conditions

Density (kg/m3) rw ra rs

Water Air Dry material

Specific heat (kJ/kg K) CPL CPV CPA CPS

Water Water vapor Air Dry material

Material F X0 X Xe

ton/h kg/kg db kg/kg db kg/kg db

d tc

m h

t

h

Material flow rate Initial moisture content Final moisture content Equilibrium moisture content at drying conditions Particle size Drying time constant at drying conditions Drying time

Dryer W L D M H Ab As ub Z0 DP

ton/h m m ton m3 m2 m2 m/s m bar

Drying rate Dryer length Dryer width Dryer mass holdup Dryer volume holdup Belt area Air heater transfer area Belt velocity Loading depth Pressure loss of air flowing through belt

Thermal load Qwe Qsh Qah Q Ts

kW kW kW kW 8C

Water vaporization Solid heating Air heating Total thermal load Steam temperature

Electrical load Eb Ef E

kW kW kW

Belt driver Fan Total power requirement

Performance n r

— kg/h m2

Thermal efficiency Specific rate of evaporation

Latent heat (kJ/kg) DH0 Other Us

Steam condensation at 08C Heat transfer coefficient at air heater (kW/m2 K) Void (empty) fraction of loading

« Empirical constants a1, a2, a3

Antoine equation for vapor pressure of water Oswin equation for material isotherms Drying kinetics equation Belt driver power equation Pressure loss equation

b1, b2, b3 c0, c1, c2, c3, c4 e1 f1

TABLE 5.13 Process Specifications F X0 X d T0 Y0 Z0 P Ts

ton/h db kg/kg db kg/kg db m 8C kg/kg db m bar 8C

Feed flow rate Initial material moisture content Final material moisture content Material characteristic size Ambient temperature Ambient humidity Loading depth Ambient pressure Heating steam temperature

TABLE 5.14 Degrees-of-Freedom Analysis Process variables Process equations Degrees of freedom

37 24 13

Degrees of freedom Specifications Design variables

13 9 4

TABLE 5.15 Design Variables (b) to investigate the effect of one design variable on an economic variable (Figure 5.7); (c) to analyze the effect of two design variables on a technical variable (Figure 5.8); (d) to summarize the results of the design on a synoptic report (Figure 5.9). Any other analysis


Y T V D

kg/kg db 8C m/s m

Drying air humidity Drying air temperature Drying air velocity Belt width

TABLE 5.16 Model Solution Algorithm Equation T10.1 T10.2 T10.3 T10.4 T10.5 T10.6 T10.7 T10.8 T10.9 T10.10 T10.11 T10.12 T10.13 T10.14 T10.15 T10.16 T10.17 T10.18 T10.19 T10.20 T10.21 T10.22 T10.23 T10.24

! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

TABLE 5.18 Cost Data Ps aw Xe tc t W Fa Qwe Qsh Qah Q As M H L Ab ub DP Ff Ef Eb E n r

TABLE 5.17 Cost Analysis


$/kW h $/kW h

Cost of electricity Cost of heating steam

Equipment unit cost Cbel Cexc Cfan

$/m2 $/m2 $/kW

Belt dryer Heat exchanger Fan

Equipment size scaling factor nbel nexc nfan

— — —

Belt dryer Heat exchanger Fan

Other ty ir lf

h/yr — yr

Annual operating time Interest rate Lifetime

NOMENCLATURE

can be performed in a similar way according to the scope of the designer. Step 5 of Section 5.2 is also applied exemplarily to insert a ‘‘scroll bar’’ for each of the design variables and a ‘‘dialog box’’ to modify the process specifications. The results are shown in Figure 5.10. The resulting graphics interface of Figure 5.10 could be further improved by introducing more tools, tables, and graphs. It can also become more professional using appropriate programming in Visual Basic.

Equipment cost Ceq ¼ Cbel Anbel þ Cexc Ans exc þ Cfan Efnfan Annual operating cost Cop ¼ (Cs Q þ Ce E)ty Total annual cost (objective function) TAC ¼ eCeq þ Cop where the Capital Recovery Factor is calculated from the equation ir (1 þ ir )lf e¼ (1 þ ir )lf 1

Utility cost Ce Cs

(T17.1) (T17.2) (T17.3)

(T17.4)

ai Ab As aw bi ci Cbel Ce Cexc Cfan CPA CPL CPS CPV CPW Cs D d db E e e1 Eb Ef Er F f1 Fa Ff H ir L

Antoine equation constants belt area, m2 air heater transfer area, m2 water activity Oswin equation constants drying kinetics equation constants belt dryer unit cost, $/m2 cost of electricity, $/kW h heat exchanger unit cost, $/m2 fan unit cost, $/kW specific heat of air, kJ/kg K specific heat of water, kJ/kg K specific heat of dry material, kJ/kg K specific heat of water vapor, kJ/kg K specific heat of liquid water, kJ/kg K cost of heating steam, $/kW h dryer width, m particle size, m dry basis total power requirement, kW capital recovery factor belt driver power equation constant belt driver power, kW fan power, kW rotating driver power, kW material flow rate, ton/h db pressure loss equation power fresh airflow rate, ton/h recycle airflow rate, ton/h dryer volume holdup, m3 interest rate dryer length, m

Technical data 1.00 tn/m3 po 1.00 kg/m3 ps 1.75 tn/m3 4.20 kJ/kg C Cpl pw

1.90 kJ/kg C 1.00 kJ/kg C Cps 2.00 kJ/kg C ΔHo 2.50 MJ/kg 0.622– m Us 0.10 kW/m2 K e 0.40– 1.19E+01– a1 a2 3.99E+03– a3 2.34E+02–

Design variables y 0.100 kg/kg db T 90.0⬚C v 1.50 m/s D 2.0 m

Cpv

Cpo

b1 b2 b3 c0 c1 c2 c3 c4 e1 f1

7.35E+04– 1.75E+03– 4.00E+01– 0.50– 1.40– −0.25– −1.65– 0.12– 2.00– 2.00–

Optimize

Process specification F Xo X db To Yo Zo p Ts

0.10 tn/h 10 kg/kg db 0.1 kg/kg db 0.010 m 25.0⬚C 0.010 kg/kg db 0.20 m 1.0 bar 160⬚C

Cost data 0.10 $/kW h Ce 0.05 $/kW h Cs Cbel 25.00 k$ 2.00 k$ Cexc Cfan 1.00 k$ 0.95– Nbel 0.65– Nexc 0.75– Nfan ty 4000 h/y 0.08– tr lf 5.0 y

Model solution ps 0.70 bar ow 0.20 Xe 0.05 kg/kg db tc 0.54 h 2.87 h t W 0.99 tn/h 11 tn/h Fa Qwe 0.63 MW Qsh 0.08 MW Qah 0.20 MW 0.91 MW Q 130 m2 As M 3.16 tn H 5.06 m3 L 12.6 m Ab 25 m2 o 4.4 m/h Dp 0.9 bar Ff 137 tn/h Ef 34.1 kW Eb 27.8 kW E 62.0 kW 0.69– n 2 39.1 kg/hm r Cost analysis 599 k$ Ceq 207 k$/y Cop TAC 357 k$/y

FIGURE 5.5 Dryer model implementation in the ‘‘Process’’ spreadsheet.

FIGURE 5.6 Process flow sheet implemented in the spreadsheet ‘‘Flow sheet.’’


FIGURE 5.7 Analyze the effect of one design variable on some economic variables, using the ‘‘One-Dimensional Table’’ and ‘‘Chart’’ tools, supported by Excel.

lifetime, yr air–water molecular weight ratio dryer mass holdup, ton thermal efficiency belt dryer scaling factor heat exchanger number of flights fan scaling factor pressure, bar vapor pressure at temperature T, bar

Q Qah Qsh Qwe r t T tc T0 Ts

total thermal load, kW air-heating thermal load, kW solid-heating thermal load, kW water vaporization thermal load, kW specific rate of evaporation, kg/h m2 drying time, h drying air temperature, 8C drying time constant, h ambient temperature, 8C steam temperature, 8C

Belt are (m2)

lf m M n nbel nexc nf nfan P Ps

Drying are humidity (kg/kg db)

FIGURE 5.8 Analyze the effect of two design variables on a technical variable, using the ‘‘Two-Dimensional Table’’ and ‘‘Chart’’ tools, supported by Excel.


Belt Dryer Design Report Belt Dryer Design Report

page 3/5

page1/5 Cost Data

Problem Folmulation

Design Variables Drying Air Humidity Drying Air Temperature Drying Air Velocity Belt Width

F Xo X d To Yo Zo P Ts

= = = = = = = = =

Y T V D

= = = =

Belt Dryer Design Report

0.1 ton/h 10 kg/kg db 0.1 kg/kg db 0.01 m 25⬚C 0.01 kg/kg db 0.2 m 1 bar 160⬚C 0.1 kg/kg db 90⬚C 1.5 m/s 2m

page 2/5

Technical Data Density Water Air Dry Material Specific Heat Water Water Vapor Air Dry Material Latent Heat Steam Condensation Other Heat Transfer Coefficient Void Fraction of Loading Antoine Equation for Vapor Pressure of Water Oswin Equation for Material Isotherms Drying Kinetics Equations

Belt Driver Power Equation Pressure Loss Equation

rw = 1.00 ton/m3 ra = 1.00 kg/m3 rs = 1.75 ton/m3

Cpw Cpv Cpa Cps

= = = =

4.20 kJ/kgK 1.90 kJ/kgK 1.00 kJ/kgK 2.00 kJ/kgK

ΔHo = 2.50 MJ/kg Us = 0.10 kW/m2K ε = 0.40–

a1 a2 a3 b1 b2 b3 c0 c1 c2 c3 c4 e1 f1

= 1.19E+01 = 3.99E+03 = 2.34E+02 = 7.35E−04 = 1.75E+03 = 4.00E−01 = 5.00E−01 = 1.40E+00 = −2.50E−01 = −1.65E+00 = 1.20E−01 = 2.00E+00 = 2.00E+00

FIGURE 5.9 A summary report of the process design results.


Ce = 0.10 $/kWh Cs = 0.05 $/kWh

Equipment Unit Cost Belt Dryer Heat Exchanger Fan

Cbel = 25.0 k$/m2 Cexh = 2.00 k$/m2 Cfan = 1.00 k$/kW

xxxxxxx

Material Process Specification Feed Flow Rate Initial Material Moisture Content Final Material Moisture Content Material Characteristic Size Ambient Temperature Ambient Humidity Loading Depth Ambient Pressure Heating SteamTemperature

Utility Cost Electricity Heating Steam

Equipment Size Scaling Factor Belt Dryer Heat Exchanger Fan Other Annual Operating Time Interest Rate Lifetime

nbel = 0.95– nexh = 0.65– nfan = 0.75– ty = 4000 h/y ir = 0.08– lf = 5.00 y

Belt Dryer Design Report Results Drying Air Fresh Air Flowrate Recycle Air Flowrate Drying Air Temperature Drying Air Humidity Drying Air Velocity Drying Pressure Ambient Temperature Ambient Humidity Water Activity at Drying Conditions Material Material Flow Rate Initial Moisture Content Target Moisture Content Equiliblium Moisture Content Particle Size Drying Time Constant Drying Time Dryer Drying Rate Dryer Length Dryer Width Dryer Mass Holdup Dryer Volume Holdup Belt Area Air Heater Transfer Area Belt Velocity Loading Depth

page 4/5

Fa Ff T y V P To Yo aw

= 11 = 137 = 90 = 0.1 = 1.5 = 1 = 25 = 0.01 = 0.20–

F = Xo = X = Xe = d = tc = 0 t =

0.1 10 0.10 0.05 0.01 0.54 2.87

ton/h kg/kg db kg/kg db kg/kg db m h h

W L D M H Ab As u Zo

0.99 12.6 2 3.16 5.06 25.3 130 4.40 0.20

ton/h m m ton m3 m2 m2 m/s m

= = = = = = = = =

Thermal Load Water Vaporization Solid Heating Air Heating Total Thermal Load

Qwe = Qsh = Qah = Q =

Electrical Load Belt Drive Fan Total Power Requirement

Eb = Ef = E =

Performance Thermal Efficiency Specific Rate of Evaporation

ton/h ton/h ⬚C kg/kg db m/s bar ⬚C kg/kg db

0.63 MW 0.08 MW 0.20 MW 0.91 MW

27.8 kW 34.1 kW 62.0 kW

n = 0.69− r = 39.1 kg/hm2

Belt Dryer Design Report

page 5/5

Cost Analysis Results Equipment Cost Belt Dryer Heat Exchanger Fan Total Operating Cost Electricity Heating Steam Total Annualized Equipment Operating Total

FIGURE 5.9 (continued)

FIGURE 5.10 Toward an integrated graphics interface.


538 47 14 Ceq = 599 k$ 25 182 Cop = 207 k$ 150 207 TAC = 357 k$/y

ty ub Us V W X Xe X0 Y Y0 Z0 DH0 DP «

annual operating time, h/yr belt velocity, m/s heat transfer coefficient at air heater, kW/m2 K drying air velocity, m/s evaporating capacity, ton/h final moisture content, kg/kg db equilibrium moisture content, kg/kg db initial moisture content, kg/kg db drying air humidity, kg/kg db ambient air humidity, kg/kg db loading depth, m latent heat of water evaporation at 08C, kJ/kg pressure loss of air, bar void (empty) fraction of loading


ra rm rs rw

air density, kg/m3 construction material density, kg/m3 dry material density, kg/m3 water density, kg/m3

REFERENCES Maroulis ZB, Saravacos GD, 2002. Modeling, simulation and design of drying processes. Keynote Lecture at the 13th International Drying Symposium, IDS 2002, Beijing, China. Maroulis ZB, Saravacos GD, 2003. Food Process Design, Marcel Dekker, New York.