INFORMATION TO USERS

INFORMATION TO USERS
INFORMATION TO USERS
This manuscript has been reproduced from the microfilm master. UMI
films the text directly from the original or copy submitted. Thus, some
thesis and dissertation copies are in typewriter face, while others may
be from any type of computer printer.
The quality of this reproduction is dependent upon the quality of the
copy submitted. Broken or indistinct print, colored or poor quality
illustrations and photographs, print bleedthrough, substandard margins,
and improper alignment can adversely affect reproduction.
In the unlikely event that the author did not send UMI a complete
manuscript and there are missing pages, these will be noted. Also, if
unauthorized copyright material had to be removed, a note will indicate
the deletion.
Oversize materials (e.g., maps, drawings, charts) are reproduced by
sectioning the original, beginning at the upper left-hand corner and
continuing from left to right in equal sections with small overlaps. Each
original is also photographed in one exposure and is included in
reduced form at the back of the book.
Photographs included in the original manuscript have been reproduced
xerographically in this copy. Higher quality 6" x 9" black and white
photographic prints are available for any photographs or illustrations
appearing in this copy for an additional charge. Contact UMI directly
to order.
University Microfilms International
A Bell & Howell Information Company
300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA
313/761-4700 800/521-0600
Order Number 1346732
Exergy analysis of a pilot milk processing system
Fang, Zigang, M.S.
The University of Arizona, 1991
UMI
300 N. Zeeb R&
Ann Aibor, MI 48106
1
EXERGY ANALYSIS OF A PILOT MILK PROCESSING SYSTEM
by
Zigang Fang
A Thesis Submitted to the Faculty of the
DEPARTMENT OF AGRICULTURAL & BIOSYSTEMS ENGINEERING
in Partial Fulfillment of the Requirements
For the Degree of
MASTER OF SCIENCE
In the Graduate College
THE UNIVERSITY OF ARIZONA
19 9 1
2
STATEMENT BY AUTHOR
This thesis has been submitted in partial fulfillment of requirements for an
advanced degree at The University of Arizona and is deposited in the University
Library to be made available to borrowers under rules of the Library.
Brief quotations from this thesis are allowable without special permission,
provided that accurate acknowledgment of source is made. Requests for
permission for extended quotation from or reproduction of this manuscript in whole
or in part may be granted by the head of the major department or the Dean of the
Graduate College when in his or her judgment the proposed use of the material is
in the interests of scholarship. In all other instances, however, permission must
be obtained from the author.
SIGNED:
APPROVAL BY THESIS DIRECTOR
This thesis has been approved on the date shown below:
Dennis L. Larson
Associate Professor
of
Agricultural & Biosystems
Engineering
Date
3
In honor of my lovable grandmother who died in 1975
ACKNOWLEDGEMENT
The author greatly appreciates the continuous encouragement, guidance and
patience extended by Dr. Dennis L. Larson during his study in the Department of
Agricultural and Biosystems Engineering, University of Arizona. This thesis would
not have been possible without his support.
Special thanks are conveyed to Dr. Gregory J. Fleischman whose academic
direction was a great help in completing the thesis research. Thanks also go to the
members of the committee, Dr. Kenneth A. Jordan and Dr. Heriberto Cabezas Jr.
5
TABLE OF CONTENTS
LIST OF FIGURES
7
LIST OF TABLES
8
ABSTRACT
9
NOMENCLATURE
10
Chapter 1 INTRODUCTION
13
Chapter 2 EXPERIMENTAL ANALYSIS
2.1
Basic Theory
2.2
System and Experimental Description
2.3
Derivation of Energy and Exergy Relationships
18
18
22
25
Chapter 3
3.1
3.1.1
3.1.2
3.1.3
3.1.4
3.1.5
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.3
3.3.1
3.3.2
35
35
35
36
38
39
39
40
41
44
46
47
48
48
55
OPERATIONAL OPTIMIZATION
Background
Optimization
Key Elements of an Optimization Study
Mathematical Formulation of Optimization Problems
Operational Optimization
GAMS/MINOS
Modeling of Processing Systems
State Variables
Balance Equations
Operational Relationships
Objective Function
Optimization Study of the Pilot Milk Processing System
System Modeling
Regenerator Modeling
Chapter 4 RESULTS AND DISCUSSION
4.1
Data Collection Under Mean Steady State
4.2
Irreversibility Distribution
4.3
Optimal Irreversibility Distribution
4.4
Influence of Overall Heat Transfer Coefficients
on System Exergy Performance
4.5
Comparison of the Energy and Exergy Analyses
4.6
Difference between Systematic and Component Optimization
4.7
Operational Approach
Chapter 5 CONCLUSIONS
57
57
60
62
.
66
66
69
70
72
6
TABLE OF CONTENTS -- Continued
APPENDIX A
Listing of the Program of MKSYSOPT.ASC
SELECTED BIBLIOGRAPHY
73
79
7
LIST OF FIGURES
Figure 1-1
Research approach
Figure 2-1
Energy flow diagram of the pilot milk processing system .... 22
Figure 2-2
Schematic of the heat exchanger
27
Figure 2-3
Schematic of energy streams of the homogenizer
29
Figure 2-4
Energy flow of feedwater heater
32
Figure 3-1
Configuration of component energy streams
42
Figure 3-2
Energy flowsheet of an example heat exchanger system .... 43
Figure 3-3
Energy flow diagram of the pilot milk processing system .... 48
Figure 3-4
Change of the inlet and outlet temperature difference
with pumping power for the homogenizer
52
Fluid milk temperatures at different locations
versus time following system startup
58
Irreversibility comparison among the seven
milk processing units
60
Comparison of the system irreversibility distribution
between the experimental operating state and the optimal
operating state
64
Variation of minimum overall system irreversibility with
regenerator overall heat transfer coefficient when operated
at the exergy-oriented optimal state
65
Comparison of First and Second Law efficiencies under
an operating pressure of 2000 psi
68
Comparison of systematic and regenerator irreversibility
changes with regenerated milk temperature
69
Figure 4-1
Figure 4-2
Figure 4-3
Figure 4-4
Figure 4-5
Figure 4-6
16
8
LIST OF TABLES
Table 4-1
Mean steady state operating data collected
at different operating pressures
59
Irreversibility distribution and First and Second Law
efficiencies of each processing unit
59
Table 4-3
Comparison of simulation parameters and experimental data .
63
Table 4-4
Summary of irreversibility analysis conclusions
for the pilot milk processing system
71
Table 4-2
9
NOMENCLATURE
A
-- area of plate heat exchanger, m2
c
-- specific heat of incompressible substances;
for water, c = 4.1868 kJ/kg °K
cp
-- specific heat at constant pressure, kJ/kg °K
cv
-- specific heat at constant volume, kJ/kg °K
CL
-- energy consumption rate of cooler, kW
CTD
-- cooler logarithmic mean temperature difference, °K
exj
-- flow exergy of the stream located at j, kJ/kg, exj = hj-hr-Tr(sj-sr)
Ex
-- exergy of control volume, kJ, Ex = M[(u-ur) + pr(v-vr)-Tr(v-vr)l
FLE
-- first law efficiency, %
FWH -- energy consumption rate of feedwater heater, kW
h(g
-- specific enthalpy difference in phase change from liquid to gas, kJ/kg
hj
-- specific enthalpy of the stream located at j, kJ/kg
hr
-- specific enthalpy at reference state (Tr,pr)
HTD
-- heater logarithmic mean temperature difference, °K
lQ
-- irreversibility of component Q (not less than zero), kW
m
-- number of component balance equations
mj
-- flow rate of the stream located at j, kg/s
M
-- mass of control volume, kg
n
-- number of component state variables
N
-- number of system state variables
10
Pi
-- pressure of the stream located at j, kPa
p,
-- reference pressure, pr= 1 atm
Q
-- heat flux into component, kW
r
-- number of component independent state variables
R
-- number of system independent state variables
RP
-- regeneration percentage, %
RTD
-- regenerator logarithmic mean temperature difference, °K
SJ
-- specific entropy of the stream located at j, kJ/kg °K
S,
-- specific entropy at reference state (Tr,pr)
SEC
-- system energy consumption rate, kW
SIRR
-- system overall irreversibility, kW
SLE
~ second law efficiency, %
T,
- temperature of the stream located at j, °K
Tr
-- reference temperature, Tr=25 °C
T,
-- temperature on the control surface where heat transfer occurs, °K
ui
- specific internal energy of the stream located at j, kJ/kg
ur
-- specific internal energy at reference state (Tr,pr)
U
-- internal energy of control system, kj
U
-- overall heat transfer coefficient, kW/m2oK
vi
- specific volume of the stream located at j, m3/kg
vr
-- specific volume at reference state (Tr,p,)
W
-- work done by component per unit of time, kW
z
-- objective function
11
r
-- time scale, seconds
p
- density of liquid; for water, p= 1000 kg/m3
Subscripts:
c
-- cooler
h
-- milk heater
m
-- milk
s
-- steam
Q
-- system processing units, Q = i,ii,...vii
i
-- regenerator
ii
-- homogenizer
iii
- milk heater
iv
-- holding tube
v
-- cooler
vi
-- feedwater heater
vii
-- water pump
12
ABSTRACT
Exergy analysis is applied in the thesis research to evaluate the energy
usage of a pilot scale milk processing system. Using water as made-up fluid milk,
the performance of separate components of the system was examined during
steady state operation using both exergy and energy principles. The irreversibility
distribution among these components was obtained to show the impact of energy
degradation in each component on the overall system thermal performance. The
difference between energy and exergy methods is discussed through comparisons
of First and Second Law efficiencies to demonstrate the importance of exergy
analysis. A mathematical programming model was constructed in terms of the
exergy concept and solved numerically in an attempt to find a set of optimal
operating state variables (temperatures and flowrates) under which irreversibility
of the entire system is theoretically minimized. Finally, suggestions for operational
management of the system and its components are presented which could increase
the efficiency of energy usage in the system, thus reducing energy costs.
Chapter 1
INTRODUCTION
Traditional energy analysis is based on the First Law of Thermodynamics,
which states that energy is non-destructible but says nothing about the possible
reduction of the energy potential to do work in a physical and/or chemical process.
Therefore, the method is restricted to evaluating only the efficiency of energy
transfer in the process. This can be observed in an adiabatic throttling process.
As a fluid passes through a valve, its potential to do work is significantly reduced
while total energy (in the form of enthalpy) remains constant.
The potential
reflects the quality of energy, and reduction in the potential results from energy
degradation. Exergy balance, derived from both the First and Second Laws of
Thermodynamics, provides a measure of energy quality which complements the
efficiency measure of energy usage.
What is the exergy? Engineers recognize that different forms of energy
possess different capabilities. One unit of electricity can be entirely converted to
work, but only a fraction of one unit of heat can be converted to work, the rest
being irretrievably lost.
This loss is mandated by the Second Law of
Thermodynamics. Exergy is defined as that part of energy with potential to do
work, and thus provides a means for measuring energy quality. The remaining
unusable part is called the irreversibility. This portion can be viewed as energy
quality degradation or as a real loss. Energy therefore consists of exergy and
irreversibility, i.e.,
ENERGY = EXERGY + IRREVERSIBILITY.
For example, the conversion factor of heat to electricity is used as a quality index
for evaluating a thermal power plant. A factor of 3.601 kJ(heat)/kJ(electricity)
indicates that roughly 3.6 kJ of heat is required to generate 1 kJ of work in the
form of electricity. Thus, the exergy of the heat used in this process is 1 kJ and
its irreversibility is 2.6 kJ.
A great potential for eliminating the causes of irreversibility exists in food
industries because of their high energy use.
In this country, food industries
including production agriculture, processing, transportation, wholesale and retail
trade, and final preparation are responsible for 12-20% of the nation's energy
consumption (Stout et al., 1982). Exergy analysis has the potential to enhance
current energy analysis methods in evaluating this consumption. Heat transfer for
the purpose of pasteurization, for example, is one of the basic physical processes
in fluid milk processing. It involves heating raw milk to destroy all pathogenic and
most other types of bacteria, then cooling the milk immediately to a temperature
low enough to retard the growth of the surviving bacteria. Vickers and Shannon
(1977) reported pasteurization accounts for about 22.6% of the fuel and electricity
consumption of the processing operations in a typical milk processing plant.
Irreversibility in pasteurization is caused in part by finite temperature differences
between the heating or cooling media and the milk. Exergy analysis provides a
means for quantifying the magnitude of this irreversibility.
In the past two decades, exergy analysis has provided an important
enhancement to traditional energy analysis.
Thousands of papers and books
relating to the study and utilization of exergy analysis have been published in this
15
period (Szargut et al., 1988, Bejan, 1986 and Liu et al., 1983). The U.S. National
Science Foundation established a new funding area entitled Thermal Systems in
1983, in which the exergy analysis of thermal systems was highlighted to meet
the research demands of the engineering community (Winer et al., 1986).
Application of exergy analysis to food processing systems began in the early
1980's. TrSgSrdh (1981) conducted energy and exergy analysis of some food
processing industries, and presented exergy calculations for production of sweet
whey powder, starch derivatives and baked soft cakes. Rotstein (1982) presented
a computer package which performed exergy analysis and showed several
examples of industrial utilization. Rotstein (1983) discussed the use of the exergy
balance as a diagnostic tool for energy optimization in food processes. Fan et al.
(1983) applied the principle of multi-objective optimal synthesis to the design of
a milk evaporation process. Exergy production and evaporator heat transfer area
were the objective parameters of the system optimization. Forciniti et al. (1985)
studied the exergy balance of an existing tomato paste plant and adopted the pinch
point procedure to modify the energy use of the plant. Results indicated that the
closer the process approaches to being reversible, the larger will be the utility
savings. Forciniti et al. (1987) also simulated the operations of an apple juice and
aroma concentrate manufacturing plant, optimizing the system operation based on
the minimization of system irreversibility. However, no reports have been found
of exergy analysis use to evaluate the energy usage of milk processing systems.
The research presented in this thesis utilized both exergy and energy
principles to analyze a pilot milk processing system. Using water as made-up milk,
16
mathemoticol programming b
objective function —
biotechnical & technical conditions
system optimal operation —
conclusions
energy & exergy balance analysis
system actual operation —
experimental analysis b
Figure 1-1. Research Approach.
experimental testing and mathematical programming were carried out to determine
energy and exergy operating performance and search for optimal performance of
the system. Comparisons between experimental and optimal operating conditions
were used to determine desirable modifications in operational management and
components of the system.
The flow chart given in Figure 1-1 shows the
relationship between the two procedures.
In the experimental analysis,
irreversibility and exergy efficiency expressions, as functions of the measured
process variables, were derived for components of the "milk" processing system.
The system then was operated at steady state conditions to measure actual
temperatures, flowrates and pressures. Irreversibility and exergy efficiency of the
system components were calculated using the derived expressions and the
experimental data.
Finally, optimal system performance was determined by
mathematical programming.
The mathematical programming model contained
constraints from the energy and exergy balance and other technical and
17
biotechnical requirements and an objective function to minimize overall system
irreversibility.
The experimental and analytical procedures are discussed in
Chapters 2 and 3, respectively. The results of the analyses are compared and
discussed in Chapter 4. Chapter 5 presents research conclusions.
18
Chapter 2
EXPERIMENTAL ANALYSIS
The three sections in this chapter report basic theory development, system
and experiment description, and energy and exergy relationship derivation. The
basic theory section presents the thermodynamic principles used in the study. The
system and experiment description gives a technical description of the pilot milk
processing system and the experimental procedures.
The energy and exergy
relationships are derived for each processing unit in the third section.
§2-1.
Basic Theory
Energy and exergy balance equations are used as the principle tools for
deriving irreversibility and exergy efficiency expressions of each system component
of the pilot milk processing plant.
The general expressions for a system, as
presented by Moran (1982), are:
(2-1)
energy balance
(2-2)
exergy balance
input
output
The energy balance equation states that the rate of energy increase or
decrease within the system equals the difference between the rates of energy
transfer in and out across the boundary of the system. The mechanisms of energy
transfer are shown on the right hand side of the equation from left to right as the
outgoing and incoming energy quantities (mh); that accompany the j th mass
stream, work W and heat Q. The exergy balance equation states that the rate of
the system exergy change equals the difference between the rates of exergy
19
transfer across the boundary of the system and the rate of exergy destruction
within the system. The mechanisms of exergy transfer are shown on the right
hand side of the equation from left to right as the incoming and outgoing exergy
flows (mex)j that accompany the j th mass stream, thermal exergy loss (1-Tr/T,)Q
and work W. Although heat and work both represent energy, heat (Q) must be
scaled by (1-Tr/Tt) in the exergy equation while work (W) appears in the same
manner in both exergy and energy balance equations. This indicates that heat and
work do not have equivalent capabilities of doing work. Note that the equations
follow the sign convention that heat flux Q is considered positive when the system
absorbs heat, and work W is positive when performed by the system.
At steady state, the left hand sides of the two equations, which are energy
and exergy accumulations respectively, are zero. Hence, the equations reduce to:
energy balance
Q = £ Imh), - £ imh)f + W
output
exergy balance
'
=
53 lme*h ~ 53
input
(2-3)
input
output
+
^ ~Q - W
(2-4)
' t
Equation (2-3) states energy remains constant at steady-state, i.e., the rate
of energy input equals the rate of energy output.
The Second Law of
Thermodynamics mandates that exergy inflows exceed outflows, or that exergy
is not conserved. A balance equation (2-4) may nevertheless be written with an
additional term, irreversibility, which accounts for the reduction of the potential to
do work. Described in words,
IRREVERSIBILITY = EXERGY INPUT - EXERGY OUTPUT > 0
Based on the exergy balance equation, the second law efficiency (SLE), or exergy
20
efficiency, is defined as
c, c - EXERGY OUTPUT
EXERGY INPUT
The terms exergy input and output, as seen later, can be expressed as functions
of enthalpy and entropy values, which in turn can be expressed as temperatures
Tj and pressures p,.
Thus, the equations for calculating the irreversibility and
exergy efficiency can be expressed as functions of the Tj( p{ and flow rate, rrij,
values.
Although the thermodynamic state of a substance can be described by many
properties, the values of these properties are not all independent, i.e., the number
of degrees of freedom is limited.
For a pure substance with single phase, the
number of independent thermodynamic properties is two. Temperature, T, and
pressure, p, are preferred couple of the independent properties because they are
measurable and intensive. Any third thermodynamic property, z, of the substance,
thus, can be determined from the temperature and presure through a function z =
z(T,p). In practice, change of state is more frequently considered than a given
state itself. Therefore, the following differential form (2-5) is more useful than the
function itself.
dz = OidT + *Ldp
dT
dp
(2.5)
In the energy and exergy balance equations above, properties of internal
energy u, enthalpy h, and entropy s are the principle terms although they cannot
be measured directly. Internal energy, enthalpy and entropy may be found by
21
establishing the relationships between them and any pair of the directly measurable
properties-temperature, T, specific volume, v, and pressure, p.
Conventional
forms of the relationships are u = u(T,v), h = h(T,p), and s = sO\v) or s = s(T,p).
Their differential forms can be found in many thermodynamic reference books (e.g.
Moran et al., 1988) as:
or
du = cjdT + m|£), - p]dv
(2-6)
dh = cpdT + lv - T[^)p)dp
(2-7)
ds = SldT +
(2-8)
ds = SzdT - & dp
I
of
( 2_ 9)
where cv and cp are the specific heats, respectively, at constant volume and
constant pressure and are defined by cv = (3u/3T)v and cp = Oh/3T)„.
For an incompressible substance, the total and partial derivatives of specific
volume v are zero.
Comparison of equations (2-8) and (2-9) yields cv=cp =
T(ds/dT) = c, i.e., the two specific heats of an incompressible substance are equal.
Thus, the property equations (2-6,7,8,9) are simplified to:
du = cdT
(2-10)
dh = cdT + vdp
(2-11)
ds = c(dT/T)
(2-12)
where equations (2-10 and 12) show, for an incompressible substance, changes
of internal energy, u, and specific entropy, s, depend only on the change of
temperature, T. If the specific heat, c, is assumed to be a constant, a reasonable
assumption when an average value of specific heat is used for the temperature
range under consideration, integration of equations (2-10,11,12) yields:
22
u2 - u, = c(T2 - T,)
(2-13)
h2 - h, = c(T2 - T,) + (p2 - p,)v
(2-14)
s2 - s, = c ln(T2/T,)
(2-15)
The fluid milk was replaced by water in this study. Water can be considered
an incompressible substance and processes were modeled using these equations.
§2-2.
System and Experimental Description
raw milk
coolont In
produci •
milk .—*
12
HT
6
4_
toot loss
2
_±_
regenerolor
cooler
homogenizer
13
electricity
4
heater
heat lost
"t
_10
f.w.heater
f
steam
coolont out
water pump
'•i
electricity
holding tube
Milk Path
: 1-2-3-4-5-6-7 k
'
Water Path : 9-10-11-9
heat loss
Figure 2-1. Energy flow diagram of the pilot milk processing system.
A pilot milk processing system located at the University of Arizona, serving
the purposes of teaching and research, was utilized for this evaluation. It is made
up of seven components shown in Figure 2-1. The raw milk flows successively
through the regenerator to warm it, the homogenizer to break up its fat globules,
the heater to reach pasteurizing temperature, the holding tube where it remains
until all bacteria are killed, the regenerator, again, to recover heat energy and precool the milk, and, finally, the cooler to lower the milk temperature to storage
levels. Water, the heating medium, is circulated by a pump through the milk heater
and the feedwater heater which bubbles steam through the water. The seven
processing units are described as follows:
Regenerator. Milk Heater and Cooler
A plate heat exchanger contains sections which serve as the regenerator,
milk heater, and cooler. They are assembled compactly together with intermediate
terminals which divide the plates into the three sections.
Among them, the
regenerator uses fifteen plates with the flow arrangement of (3 + 3 + 2)/(3 + 3 + 2),
the milk heater uses five plates with the flow arrangement of (1 +1 + 1 )/3, and the
cooler uses seven plates with the flow arrangement of (2+1 + 1)/ (2 + 2), where
each number gives the number of parallel passes which the liquid flows through
in one direction and the slash distinguishes one stream of the heat exchanger from
another.
The left hand side of the slash represents the milk stream being
processed and the right hand side represents either the pasteurized milk, hot water,
or chilling water streams, depending on the component. Made of stainless steel
AISI 316, each plate is about 33.15 cm wide, 99.45 cm long and 0.8 mm thick.
The surface of each plate is corrugated with an arc pattern. The space between
any two plates is about 3 mm.
Homoaenizer
The homogenizer is a high pressure, reciprocating pump with three pistons,
fitted with a two-stage homogenizing valve. The pump belongs to the type of
positive displacement pumps which shows a very steep characteristic head-versusdischarge curve.
In pilot system operation, the pumping discharge flow rate
always remained about 0.2 kg/s although the head varied considerably. The motor
24
used to drive the homogenizer pump is a 3-phase electrical induction motor.
Feed Water Heater
The feed water heater is an uncovered water tank with steam and feed
water inlets, and drainage and feed water outlets. The incoming steam directly
mixes with and heats the water stored in the tank.
Holding Tube
The holding tube is a section of stainless steel sanitary pipe which conveys
the pasteurized milk from the milk heater to the regenerator. It retains the milk for
longer than 15 seconds at a temperature higher than 71.67 °C (161 F),
Water Pump
The water pump used to circulate the feed water between the milk heater
and the feed water heater is a centrifugal pump which has a flat characteristic
head-versus-discharge curve. A 3-phase electrical sanitary pump motor is used to
drive the pump.
Other Operating Information
The available energy sources include 3-phase AC electricity, 125 psi steam,
and 5.56 °C (42 F) chilling water. Energy prices are 6.90 per kWh for electricity,
$9.06 per ton lb for steam, and $6.59 per million Btu for chilling water.
Experiments were performed under steady state conditions to test the
operating system's energy performance. The system was initially operated with
the homogenizer valve full open (0 psi pressure drop across the valve). Data was
taken after temperature fluctuations ceased.
The valve was then closed in a
stepwise manner, data being taken at each subsequent pressure drop level after
25
steady state operation was re-established.
Temperature data was obtained using copper-constantan thermocouples at
the inlet and outlet of each component. A solid state kWh pulse initiator was used
to measure homogenizer pump electric power consumption. Flow rates of milk and
hot water were measured by timing and weighing the streams, and pressure was
obtained by appropriately located analog gauges. A 21X Datalogger (Campbell
Scientific Inc.) was linked with the thermocouples and pulse initiator to monitor
and record temperature and power data sequentially every thirty seconds.
Water was substituted in the experiment for fluid raw milk because the
fluids are practically identical in their processing traits except for the foaming range
of the fluid milk. Two experimental difficulties were encountered in this study.
The cooling section of the plate heat exchanger was not operational, and flowrate
of steam to the feed water heater could not be measured. It was believed that the
performance of cooling section of the plate heat exchanger would be of
fundamental importance to the analysis.
Thus, cooling was simulated with a
coolant water temperature of 278 K, assumed to lower the product milk
temperature to 280 K (45°F), the temperature recommended by Harper (1976).
The flowrate of steam was estimated from the energy and exergy balances for the
feedwater heater.
§2-3. Derivation of Energy and Exergy Relationships
The energy and exergy balance equations (2-3 and 4) were written for each
of the seven system components to obtain the component energy, irreversibility
and exergy efficiency expressions. Variables in the expressions have subscript
26
numbers corresponding to the stream numbering system shown in Figure 2-1. The
regenerator, heater and cooler are considered integrally as parts of the plate heat
exchanger model. General assumptions were:
a. water is an adequate physical replacement for milk such that results obtained
with water can be applied to the fluid milk;
b. water is assumed incompressible so the density of water (p) is constant and the
internal energy depends only on temperature;
c. the specific heats (c) of each liquid stream are assumed constant within the
range of temperature changes considered in the experiment;
d. the irreversibility caused by pressure head losses is insignificant;
e. the streams' kinetic energy changes caused by velocity changes and potential
energy or elevation changes are insignificant;
f. all components operate at steady state conditions except the feedwater heater
which is at a pseudo-steady state;
g. ail processes are in equilibrium or quasi-equilibrium.
With these assumptions as prerequisites, the energy and exergy expressions
for the seven processing units are as follows:
1. Regenerator, milk heater and cooler
The three components are plate heat exchangers.
For a plate heat ex­
changer system undergoing a steady adiabatic process, as in Figure 2-2, there are
no heat losses (Q = 0) and work (W = 0) by the system. From equation (2-4),
therefore, the exergy relationships are defined as:
27
Figure 2-2 Schematic of the heat exchanger.
Irreversibility
/
exergy efficiency
SLE -
EXERGY INPUT - EXERGY OUTPUT
= m h [h' h -hi! ~ T r ( s i s i ! ) ] - h i -T r (s" -si)]
=
EXEROr OVTFVT
EXERGY INPUT
=
m-l"<
~K ~T-(S'
m>[hl-hH-T^-sS)]
where ' represents the inlet and " represents the outlet. Using equations (2-14
and 15), with incompressible water as the heat transfer medium flowing
through both sides of the heat exchanger at flowrates mh and me, respectively,
and with constant specific heat c, the exergy input and output terms become:
T'
n' -n"
EXERGY INPUT = m h [c(T' h -T'! -T)nl!L)+ Ph Ph ]
Th
P
28
EXERGY OUTPUT = m e [c(T' e ' -Tj-T^lL)+ p " ~ P ' C ]
T'c
P
When the pressure drops are comparatively small, which is the case for
plate heat exchangers, the pressure terms may be neglected.
Thus, the
irreversibility I and exergy efficiency SLE are reduced to functions of tempera­
tures and flowrates as follows:
/(Tj,m h ,m c ) =m h c(T' h -T'h -T^J±.)-m c c(T!! -T' c -TfrlL)
7/i
Tc
(2-16)
SLE<TM^<iT<-Tj-T^T<IT;»
m h lTl-Tl' -TfniTUTl' )i
.2-17,
Applying the two expressions to the regenerator:
Kregen.) = m m c{T 5 -T 0+ T,-T 2 -T)nL^.)
'1'e
(2-18)
SLE(regen.) = W W V 7 i >
75-7e-7rln(r5/7fl)
(2-19)
To the heater:
/{heater) = mjc(T 9 -T w -T,\nlL) - m m c(T A -T 3 -T f \nL.)
'10
SLE(heater) =
(2-20)
'3
m ^ T *- T a- T ^ T * IT ^
mJT 9 -T, 0 -T}MT 9 /T, 0 )]
(2-21)
To the cooler:
/(cooler) = m m c(T e -T 7 -TJinIl) - m c c(T, 3 -T, 2 -T^Ll)
'7
SLE(cooler) =
(2-22)
'12
mJT e -T 7 -T,\n{T 6 /T 7 )]
{2 23)
2. Homogenizer
Figure 2-3 shows the energy streams of the homogenizer.
The
29
15
A
Q 15
MILK
T3 P;
n\J2 p2
HOMOGENIZER
3
I
14
W 14
VV
Figure 2-3 Schematic of energy streams of the homogenizer.
homogenizer basically includes a high pressure pump with a special homoge­
nizing valve on the discharge side.
The pump acts to move the fluid milk
throughout entire processing system.
The fluid milk flows in at the
homogenizer inlet (stream 2), through the valve where fat globules are broken
up, and then out (stream 3).
Passing through the valve, the fluid milk
undergoes a throttling process, a typical irreversible process which gives rise
to large exergy dissipation, although energy is conserved. From equations (2-3
and 4), the energy and exergy balances with steady state operation can be
expressed as
Q15 = mm(h2-h3) +W14
'h
=
C\/Te)Q15 " mmTr(S2-S3)
Note that Q15 is heat lost to the environment and W14 is the pump work. Using
property equations (2-14,15) under the general assumptions (a-g), the two
balance equations are rewritten as
Q15 = mmc(T2 - T3) + mm(p2 - p3)/p + W14
(2-24)
lH
(2-25)
= (Tr/T„)Q15- mmcTrln(T2/T3)
Furthermore, since the exergy input is just the pumping work W14 and the
exergy output, from equation (2-4), is equal to W14-(1-T0/T,)Q15-IH, the exergy
efficiency is
SLE(homo) = 1 - <1 ~TJT.)Qis + /w
W,4
(2-26)
Fluid pressure increases from inlet to outlet of the homogenizer ( p2-p3
< 0) with a vacuum existing at the inlet (p2 < 1 atm). In the experiment, a
gauge was installed at the outlet to measure p3, but no gauge was installed at
the inlet due to technical difficulties. The value of p2 was assumed to be 10
psi (absolute pressure, 1 atm = 14.696 psi). The boundary of the homogenizer
system was drawn to include the homogenizer valve. Homogenizer operating
pressure differs from the pressure increase, p2-p3, in that the operating pressure
refers to the pressure change across the valve while the pressure increase
refers to the pressure change from inlet to outlet of the system. The work,
W14, consumed by pumping was measured at 30-second intervals by a pulse
initiator which had a pulse rate of 1 pulse-Watt"1- minute'1. Thus, if a total of
31
N pulses were counted in 30 seconds, W14 = 3*3600*N/30 (Watts), where
the factor '3' refers to the phase number of the homogenizer electric motor.
Surface temperature, T,, theoretically refers to the integral average temperature
of the homogenizer shell surface.
The surface temperature, however, was
difficult to obtain because of the geometrically irregular surface of the
homogenizer. In the experiment, a thermocouple attached to a surface spot on
a comparatively flat, large surface area was used to measure the representative
surface temperature.
3. Feedwater heater
Figure 2-4 shows the energy streams of the feedwater heater.
The
feedwater heater heats incoming water at atmospheric pressure by mixing it
with saturated high temperature steam. The mixing process is also a typical
thermodynamic irreversible process in which the high energy quality steam
condenses, doing no work and becoming low energy quality water.
The feedwater heater has operational characteristics which differ from
other components because it does not operate at steady state. Although the
water circulation rate, mw, remains constant, the condensing steam increases
the mass in the feedwater heater tank. However, a control system keeps the
outlet temperature, T11( constant so a pseudo-steady state is enforced.
Additional assumptions made for the sake of simplification are:
i)
the supplied steam is 100% vapor;
ii)
the steam can be modeled as an ideal gas, i.e., p/p = RT;
32
condensed
steam
heat
loss
A18
A
0,8
ms T1 i P i i
MILK
MoRO
10
ITVr
FEEDWATER HEATER
8
TsPs
T 1lR
1
11
steam
m,
Figure 2-4 Energy flow of the feed water heater.
iii) the mixing of steam and water is so complete that the steam is entirely
condensed and reaches state 11, the state of the outlet water;
iv) the feedwater heater tank stays open with a constant pressure of 1 atm;
v)
there is no water leakage.
Thus, using equations (2-3,14), the feedwater heater energy balance equation
can be written as
Qi b = m,[hf0 + c(T8-T11)] - mwc(Tn-T10)
(2-27)
Also, using equations (2-2,14,15), the irreversibility of the feedwater heater
can be expressed as
33
I
f
= mwcTrln(Tn/T10) - m.th^/TB + cT^nda/Tn)] + Q18Tr/T.
(2-28)
where the term with m, is exergy input Exinputf and the term with mw is exergy
output Exoutput. The exergy efficiency of the feedwater heater is
m.\h,£+cTW^L)\
SLEif.w.heater) =
1®
—U—
(2-29)
mjcTW^l)
'10
The steam flowrate m, could not be measured in the experiment because
a meter was not available. Instead, m, was estimated using the two balance
equations (2-27,28) and constraining both Q18 and lF to be greater than zero,
which is consistent with real physical processes. In addition, the component
surface temperature Ts was replaced by the value of Tn in the calculations due
to difficulties in measurement.
4. Holding tube
Heat is transferred between the "milk" in the holding tube and the
environment.
Using equations (2-3,14), the holding tube energy balance
equation is
Q17 = mmc(T4 - Ts)
(2-30)
From equations (2-4,14,15), the exergy balance equation is
lT = (Tr/T4)Q17 - mmcTrln(T4/T5)
(2-31)
where the surface temperature is assumed equal to T4. The exergy efficiency
of the holding tube is zero because no exergy output is produced, and all the
exergy input is degraded to either irreversibility or heat loss.
34
5. Water pump
Since the water passes through the water pump in a very short time and
almost no heat loss can occur, it was assumed that the water undergoes an
adiabatic process when flowing through the pump. From equations (2-3,14),
the energy balance equation becomes
W16 = mJcOVT,,) + (pg-p^/p]
(2-32)
From equations (2-4,14,15), the exergy balance equation is
lP = mwcTr InnyT,,)
(2-33)
Note that the process is also assumed to be isothermal, so W16 = (p9-pn)/p, and
lP = 0, i.e., the pumping process is reversible since it is assumed to be adiabatic
and isothermal.
The derivation procedures above show that irreversibility, I, and exergy
efficiency, SLE, can be expressed as functions of flowrate, mi( and specific
enthalpy and entropy values, hf and sif end these later quantities are related to
the respective temperatures, Tj( and pressures, Pj. Thus, measured values of
mf, T; and Pi were used to obtain the irreversibility and exergy efficiency.
35
Chapter 3
OPERATIONAL OPTIMIZATION
The energy and exergy performance of the pilot milk processing system can
be quantitatively examined or determined using the method presented in Chapter
2. An additional objective is improvement or enhancement of system performance.
From the viewpoint of exergy analysis, lower system irreversibility yields better
exergy performance. Based on this concept, an operational optimization model of
the milk processing system was constructed to determine optimal exergy
performance. This chapter presents an introduction to optimization methods and
use, describes the modelling of processing systems, and then describes
optimization of the milk processing operation.
§3-1. Background
§3-1-1. Optimization
The term optimization is defined to be a mathematical procedure or rationale
used to achieve an improved solution (Shoup et al., 1987). Although it is desirable
to have the very best or "optimum" solution to a problem, the optimum is usually
unachievable. Thus, optimization is termed as the process of movement toward
improvement rather than achievement of perfection.
A transportation problem is given here to visualize the optimization. In the
problem, J markets are supplied by I plants with a single commodity. The supply
at plant i, represented by a„ the demand at market j, represented by bj, and the
unit cost of shipping the commodity from plant i to market j, Cy, are given. The
economic question is: how much shipment should there be between each plant and
36
each market so as to minimize total transport cost? The algebraic representation
of this problem is:
Indices:
i = 1,2...I plants
j = 1,2... J markets
Given Data: af = supply of commodity at plant i (in cases)
bj = demand for commodity at market j (in cases)
C|j = cost per unit shipment between plant i and market j ($/case)
Decision Variables:
xu = amount of commodity to ship from plant i to market j (cases)
Constraints: supply limit at plant i
demand at market j
positive shipment
Objective Function:
Minimize
ZjXy < a„ for all i
IjXy > bj( for all j
> 0,
for all i, j
1^0^
The example shows an optimization problem can be described using decision
variables, constraints and objective functions.
§3-1-2. Key Elements of an Optimization Study
An optimization study contains four key elements: definition of system
boundary, objectives, independent decision variables, and uncontrollable variables.
The boundaries of the system under investigation must be clearly defined
before undertaking any optimization study. In many situations, it may be desirable
to determine the optimum performance of the entire system, which is generally
different from that for individual system components. In this study, the study
boundary will be defined to encompass the entire milk processing system rather
37
than a study of the seven components individually.
It is predictable that the
individual optima may not be maintained in the effort to optimize the entire system.
The objectives used in an optimization study relate to the measures of
effectiveness of the system under study. Several objectives may be desired to
optimize the system. The optimization objectives, when modelled, become socalled objective functions. Reducing the irreversibility or the energy consumption
of the entire milk processing system is the optimization objective of this study.
A third key element in an optimization study is choosing the independent
decision variables that are under management control. In other words, the chosen
independent decision variables should be variables that are directly measurable and
technically controllable. For example, temperatures rather than entropies should
be chosen if the two types of variables mathematically appear in a model because
the temperatures are directly measurable.
The temperatures of system input
streams, rather than of interconnected streams between system components, are
preferred because the former are easier to control.
Another key optimization element is consideration of certain system
parameters which may not be under management control, but may change,
affecting the behavior of the system under study. Failure to analyze the effects
of the parameters on the system optimum behavior would lead to policies that
could not be implemented in practice.
For example, the overall heat transfer
coefficients of heat exchangers of a system under study may affect the system
optimum behavior but are not controllable and cannot be used as decision
variables.
38
§3-1-3. Mathematical formulation of optimization problems
The general optimization problem can be stated as follows:
Minimize
Z = F(X)
Subject to
a(X) < 0, i = 1,2,...,1
(3-1)
h,(X) = 0, j = 1,2,...,m
Although optimization can mean either minimization or maximization, the following
discussion is in terms of minimization. This is done without lack of generalization
because any maximization problem [Max Z = F(X)] can be reformulated in terms of
minimization of negative Z [Min (-Z)].
For the optimization problem, Z = F(X) is the objective function where X
denotes the vectoral representation of n-dimensional decision variables.
In a
thermodynamic system problem, X could denote the pressure, temperature,
enthalpy, entropy, or any other decision variables under consideration. The g(X)
and h(X) functions are known generally as the constraints in the problem.
Constraints can be of two types: inequality (denoted here by g) and equality
(denoted here by h). The region defined by the inequality equations, gj(X)<0, is
called the feasible solution region. The solution of the equality equation, hj(X) = 0,
is called feasible if it falls in the feasible solution region.
If all the constraints and objective functions of problem (3-1) are linear, the
optimization problem is called a linear programming (LP) problem. If one or more
nonlinear relationships are involved, the optimization problem is a nonlinear
programming (NLP) problem.
Optima of problem (3-1) can be classified as local and global optima. A
39
local minimum is a point in the feasible region that is lower than all other points
within its immediate vicinity. A global minimum is the best of all local minima. For
nonlinear programming problems, unfortunately, there is not a simple method of
finding the global optimum, especially when the shape of multi-dimensional feasible
region is irregular.
§3-1-4. Operational optimization
Engineering optimization generally deals not only with the design of
industrial and service systems, but also with operational problems of these
systems. The operational optimization of a pilot milk processing system will be
implemented in this study in an attempt to improve the system energy (or exergy)
operational performance.
In operational optimization problems, the structural
parameters (design variables) of system components, such as pipe diameter d,
length L, and heat transfer area A, are assumed to be known because of the
existence of the system under study.
Therefore, the decision variables to be
optimized are the system state variables, including the thermodynamic properties
(such as temperatures and pressures) and mass flow rates.
§3-1-5.
GAMS/MINOS (Brooke et al., 1988)
The operational optimization problem of the milk processing system is a
nonlinear programming problem which was solved using the GAMS/MINOS
computer optimization program package.
GAMS stands for General Algebraic
Modeling System and is a high level computer language for formulating models
with concise algebraic statements that are easily implemented and modified, and
are portable from one computer environment to another.
MINOS stands for
40
Modular In-core Nonlinear Optimization System and is a FQRTRAN-based optimizer
designed to solve large-scale optimization problems. The objective function and
constraints may be linear or nonlinear or a mixture of both. However, the nonlinear
functions must be smooth. Stable algorithms are employed for convergence of
numerical solutions. The GAMS/MINOS is an adaptation of MINOS that accepts
GAMS formulated input to solve linear and nonlinear programming problems.
When both objective function and constraints are nonlinear, which was the case
in this study, GAMS/MINOS employs a projected Lagrangian algorithm (Murtagh
and Saunders, 1982) which is based on a method presented by Robinson (1972).
The algorithm involves a sequence of major iterations, each of which requires the
solution of a linearly constrained subproblem. Each subproblem contains linearized
versions of the nonlinear constraints, as well as the original linear constraints and
bounds.
§3-2.
Modelling of processing systems
Processing systems are defined here as systems which consume energy
while making products. For operational optimization, modelling of a processing
system involves building mathematical relationships of the system operational
objectives and constraints. Optimization modelling procedures include:
a)
define the boundary of the system being studied;
b)
draw an energy flow diagram to relate individual components of the system;
c)
choose state variables for the system;
d)
derive mass, energy, pressure drop and exergy balance equations for each
system component in terms of the state variables;
41
e)
define the operational relationships which describe the physical and/or
chemical processes of each system component;
f)
define the inequality constraints and upper and lower bounds which limit the
system operation;
g)
choose the most measurable and controllable variables as independent state
variables;
h)
define the objective to be optimized, and derive the objective function.
Critical elements of the modeling process include description of state
variables, definition of mass and energy balance and operational relationships, and
specification of objective functions.
§3-2-1
State variables
A processing system usually contains several processing components, each
having several energy streams as shown in Figure 3-1.
If an energy stream
involves a simple compressible substance, its physical state, as indicated in
Chapter 2, can be determined by three state variables — mass flowrate and two
independent thermodynamic properties, for instance, temperature and pressure.
The energy stream, therefore, is called a 3-parameter energy stream, or 3-p stream
for short. If the energy stream carrier is a simple incompressible substance with
a relatively large density and small pressure change, the needed state variables
degenerate to mass flowrate and temperature, and the energy stream is called a
2-parameter, or 2-p, energy stream. In certain energy transfer mechanisms which
do not involve mass flow, such as shaft work when pumping or heat transfer due
to a temperature difference, a 1-parameter stream is defined since work or heat is
42
1 -p stream
3-p stream
2-p stream
INLETS
OUTLETS
3-p stream
2-p stream
1 -p stream
Figure 3-1 Configuration of component energy streams.
the only variable needed to describe the state of the energy stream.
The number, n, of variables needed to define the operating state of a
component is:
n = Z,(f x lf)
(3-1)
where f = 1, 2, or 3 for a f-p energy stream, and lf is the number of inlets and
outlets corresponding to the f-p stream.
For a system with L, inlet and outlet junctions corresponding to the f-p
stream, the number, N, of the state variables for the entire system is:
N = I,(f x L,)
(3-2)
43
HE1
HE2
HE3
FLUID
Figure 3-2 Energy flowsheet of an example heat exchanger system.
Figure 3-2 is an example energy flow diagram for a heat exchanger system which
includes three heat exchangers and two fans or pumps. Fluid I flows through five
inlets and outlets, numbered 1-5, while exchanging heat with fluid II which flows
through the other five inlets and outlets, numbered 6-10. Pumps I and II use
shaft work W, and WM respectively. If fluids I and II are air, 3-p stream models can
be applied to the heat exchangers and 1-p models to the fans.
Thirty two state
variables are needed to describe the operating state of the system, as computed
by equation (3-2). If flow rates m„ temperatures T„ and pressures p, are chosen
as the state variables, the state variable vector X can be expressed as
X = {W„Wll,ml,Tl.p( | i= 1,2...10}
If the two fluids are water with relatively small pressure changes, the 2-p models
can be applied instead of the 3-p models. Then, the number of the state variables
will decrease to 22, and the vector X will degenerate to
44
X = {W^rrvTi | i=1,2...10}
§3-2-2
Balance equations
According to physical principles, the four types of balance equations, mass,
energy, pressure drop, and exergy, are required to describe processes in any
system undergoing heat transfer and/or energy consumption.
The balance
equations are input as constraints in optimization modelling. For the component
shown in Figure 3-1 affected by J, 1-p streams, J2 2-p streams, and J3 3-p
streams:
1. mass balance equations
Only 2-p and 3-p energy streams involve the mass flows.
Their mass
balances are formulated in equations (3-3 and 3-4) respectively
(3-3)
(3-4)
where lj2= number of inlets and outlets for the j2th 2-p energy stream;
lj3= number of inlets and outlets for the j3th 3-p energy stream.
2. energy balance equation
J, '/,
J'
jr
/•2,3 /,•! /-1
where
J," = the number of 1-p streams related to heat losses;
J,w = the number of 1-p streams related to shaft work;
J1 = J,q + J,w-
(3-5)
45
3. pressure balance equations
Pressure only influences 3-p energy streams.
For such streams, the
pressure balance equations can be written as follows:
Pj! - pL - *Ph = °' i*
=
1.2..-/,
(3-6)
where p'j3 stands for inlet pressure of the jth 3-p energy stream and p"j3 for its
outlet pressure; Apj3 can be related to the state variables at the stream inlets and
outlets using particular hydraulic relationships.
The set of equations includes 2J3 equations from mass and pressure balance
for 3-p energy streams, J2 equations from mass balance for 2-p energy streams,
and one energy balance equation for each component being studied. The number,
r, of independent state variables then equals the difference between the total
number of state variables, from equation (3-1), and the number of balance
equations, i.e.,
r = 3I3 + 2I2 + l,-(2J3 + J2 + 1)
(3-7)
To extend the discussion to a system made up of U components, the total
number, M, of balance equations is:
M = £(2J3°+J2°+1)
u=1
(3-8)
The independent state variables number, R, for the entire system is the difference
between the number of state variables, N, from equation (3-2) and M, i.e.,
/? = 3L 3 +2L 2 +L,
(3-9)
u-1
In the heat exchanger system shown in Figure 3-2, for example, there are 5
46
components including two fans or pumps (PI and Pll) and three heat exchangers
(HT1, HT2 and HT3). When the air is the flow medium, J,(PI) = J,(Pll) = 1 and
j3(PI) = j3(Pil) = 1 for the two fans and J3(HE1) = J3(HE2) = J3(HE3) = 2 for the three
heat exchangers, therefore the number of balance equations is M = 21. Since the
total number, N, of state variables is 32, the number, R, of independent state
variables is 11. In the case of water, the fluid streams degenerate to 2-p energy
streams and N = 22. Therefore, M is equal to 13 and R is equal to 9.
4. exergy balance equation
Irreversibility is an important term in evaluating the exergy performance of
a component. The value of irreversibility, as stated in Chapter 3, must be greater
than or equal to zero due to the Second Law of Thermodynamics. The general
form of the exergy balance equation is as follows:
:
: lrr>e x )l-l - 0
A
I
(3-10)
Although the irreversibility is useful in helping engineers improve the operational
performance of components, it is an auxiliary parameter rather than a state
variable. The exergy balance equations, therefore, only play the role of inequalty
constraints and do not decrease the degrees of freedom of state variables.
§3-2-3
Operational relationships
Additional physical relationships are required for fuller description of system
or component operation. Such relationships include heat transfer equations for
heat exchangers and discharge and head characteristics for pumps or fans. These
relationships and other technical conditions and bounds should also appear as
47
constraints in the optimization model.
A general form of the heat transfer equation is Q = UAATlm, where the
overall heat transfer coefficient, U, can change as a function of state variables,
type of fluid media, flow arrangement, and material and structure and type of the
heat exchanger being studied.
Technically, the logarithmic mean temperature
difference (LMTD), ATlm( for heat exchangers cannot increase or decrease
unlimitedly, so upper and lower bounds of LMTD need to be stated in the model.
In certain circumstances, component operational relationships are not as
explicit as with heat exchangers. Sometimes experimental results are needed to
determine the relationships. In this study, an experiment was conducted with the
homogenizer to determine the operational relationship between the incoming and
outgoing fluid milk temperature difference and power consumption. In the
experiment, the homogenizer operating pressure was adjusted by closing the
homogenizer valve gradually from its full open position while measuring the
corresponding temperatures and power consumption. These data were processed
using a least-square method. The results of the experiment are described in §3-3.
§3-2-4
Objective function
The objective function is a mathematical description of the optimization
objective. In this study, system irreversibility and energy inputs were minimized
separately to compare the specifications determined from energy and exergy
analysis methods.
48
§3-3
Optimization study of the pilot milk processing system
The operational optimization model constructed for the pilot milk processing
system is presented in this section. The regenerator component also is modelled
individually to investigate the difference between component and systematic
analyses.
§3-3-1
a)
System Modelling
Boundary
The boundary of the system is chosen to be the external surfaces of the
seven system components. Each component is treated as an integral unit even
though it may be composed of several parts, such as the homogenizer which
consists of a valve and a pump.
b)
Energy flow diagram
Figure 3-3 shows the energy flow diagram. The numbers in the diagram
identify energy streams used in the system modeling.
raw milk
heat loss
coolant in
•Ai
product
milk
f 12
cooler
6
Jl
regenerator
7
13
coolant out
1
15
homogenizer
7
electricity
4
heater
heot lost
18^
^10
it
f.w.heater
1
steam
water pump
T
,6 J
electricity
holding tube
Milk Path : 1-2-3-4-5-6 1
I
'
Water Path : 9-10-11-9 |
heot loss
Figure 3-3. Energy flow diagram of the pilot milk processing system.
49
c)
State Variables
For the sake of simplicity, the fluid milk was replaced by water in the
system modelling (as in the experiment described in Chapter 2). Both water and
fluid milk are incompressible, thus, the system operates with only the 1 -p and 2-p
streams. As shown in Figure 3-3, the 2-p streams flow through the inlets and
outlets 1 to 13 and the 1-p streams through 14 to 18. The number of state
variables of the system, thus, is found to be 31 using equation (3-2). The state
variable vector is
X = {mi(Ti(W14,Q15,W16(Q17,Q18 | i=1,2...13}
d)
Mass and energy balance
Assuming that the system includes only 1-p and 2-p streams and undergoes
an equilibrated, steady process, the mass and energy balance equations are:
1.
2.
Mass Balance
m, = m2 ... = m7
(3-11)
m9 = m10 ~ mn
(3-12)
m12 = m13
(3-13)
Energy Balance
regenerator:
ir^OVT^ + mgtTg-Te) = 0
(3-14)
homooenizer:
m2c(T2-T3) +W14-Q15 = 0
(3-15)
milk heater:
m3(T3-T4) + m9(T9-T10) = 0
(3-16)
holding tube:
m4c(T4-T5)-Q17 = 0
(3-17)
cooler:
m6(T6-T7) + m12(T12-T13) = 0
(3-18)
f.w. heater:
m^cnVT^-mefh^' + cnYT^l-i-Q^ = 0
(3-19)
50
water pump:
#
mutcOVT,,) +0.0517VJ-Wie = 0
(3-20)
From linear regression of hfg versus temperature, performed using the saturated
steam temperature data tabulated in Burghardt (1986), the resultant function is,
with a r-squared value of 0.997,
hf0 = 3438.98 - 3.14T„
(3-21)
V Strictly speaking, water through the pump should be treated as a 3-p stream
since the pressure difference between outlet and inlet of the pump, p9-pn, is quite
large. But assuming Pa-P,, = 7.5 psi, the specific enthalpy difference is
h9-h,, = (ua-u,,) + (p9-p,,)/1000 = c(T9-T,,) + 0.0517 kJ/kg
3.
Exergy Balance
regenerator:
l,=m^cTr\n T±\ +mscT,\n
homooenizer:
/ff = m2cTr\n
milk heater:
lffl-m3cTr\n
holding tube:
/ /V =/77 4cT,ln
cooler:
iv=m6cTr In
f.w. heater:
C = Qi8yL+"?ioC7>
Kii - m w C T r \r\
(3-22)
(3-23)
+Qi5-£
(3-24)
Tk
r7
+Q17"
(3-25)
+m12c7"fln
7",,
10
'11
water pump:
T6
'9
13
(3-26)
T, 2
T,
-m^}'-mecTr\n
(3-27)
Tu
(3-28)
7*11
According to the Second Law of Thermodynamics, all seven irreversibilities are
greater than or at least equal to zero, that is:
lQ > 0, fi
= i,ii...vii
(3-29)
51
e)
Operational relationships
1.
Plate Heat Exchangers
regenerator:
n^cdVT,) = (UA^CIVTj)
(3-30)
where
TS-T2
(3-31)
and
U = 0.6* kW/m2K, A = 4.95 m2
milk heater:
1.0
(7-9-74)-(710-r3)
m3c(r4-r3)=(f/>fl)/1-
In
where
and
cooler:
T9-T4 > 1.0
(3-33)
T"lO"T3 s 1.0
(3-34)
U = 1.0* kW/m2K, A = 1.65 m2
m 6 c(T fi -T 1 )=(UA) t
(7"6-7*13)-(7"7 7"12)
In
where
and
(3-32)
(7"9-r4)
(T 6 -T, 3 )
(T 7 -T, Z )
(3-35)
T7-T12 > 1.0
(3-36)
T9-T13 a 1.0
(3-37)
U = 1.2* kW/m2K, A = 2.31 m2
* Although plate heat exchangers are one of the most widely used types of heat
transfer equipment for liquid food, relatively little material has been published
giving a deeper insight to their thermal behavior.
Shah and Focke (1986)
summarized the features of certain typical plate heat exchangers and reported the
U values (overall heat transfer coefficients) for water-water media ranged from 3
to 7 kW/m2K. Kessler (1981) reported the U value of a plate heat exchanger with
water-water media ranged from 1 to 4 kW/m2K, depending on the arrangement of
the plate and the flow rate. The U values assumed here may be inappropriate
52
since the values change with flow rate. However, the milk flow rate was only
about 0.2 kg/s in the experiment, so the assumption of 0.6 kW/m2K for the
regenerator is deemed reasonable.
regression
experiment
o
c
<D
L.
<D
O
«
3
O
a
a
E
t-a
1000
2000
5000
4000
3000
6000
7000
Power (Watt)
Figure 3-4. Change of the inlet and outlet temperature difference with
pumping power for the homogenizer.
2.
Homogenizer
As indicated in §3-2-3, a specific experiment was conducted to observe the
operational relationship between inlet and outlet temperature difference of the
homogenizer, T3-T2, and its power consumption, W14. The results are graphed in
Figure 3-4. The linear regression curve in the figure was found to be
T3-T2 = 1.028W14-1.698
with r2 = 0.994
(3-38)
53
3.
Water Pump
The pump body temperature rises as pumping duty increases, which can
increase the outgoing water temperature. The pumping duty results from the
demands of pressure head and water circulation flow rate. The head demand per
unit water was assumed to be 0.0517 kJ/kg. Thus, the temperature rise is only
related to the water flow rate. The relationship is assumed to be:
T9-T„ = 0.5m,,
4.
(3-39)
Holding Tube
The high temperature, short time pasteurization (HTST) process requires that
the holding tube hold the milk at a temperature not less than 71.67 °C for at least
15 seconds.
The time required for milk flow through the holding tube is
mJ2Lp/4m4, where d = 51 mm and L = 3.5 m. Thus, m4 < 0.477 kg/s, a value
included in the upper bound vector of state variables.
f)
Inequality constraints
Process Temperature Restrictions
T, < T2
(3-40)
T, < T6
(3-41)
T2 ^ T5
(3-42)
T3 < T4
(3-43)
"1*3 — T,o
(3-44)
T4 * T9
(3-45)
T4 > T5
(3-46)
T5
(3-47)
T6
54
2.
Te 2: T7
(3-48)
T6 2: T, 3
(3-49)
T7 a T,2
(3-50)
Tb2:T9
(3-51)
T9 a T,0
(3-52)
T9 a T,,
(3-53)
T,o — T,,
(3-54)
^12 — Tl3
(3-55)
State Variable Upper and Lower Bounds
Equations 3-11, 12 and 13 indicate that the flow rates are not independent.
In fact, only four of them are independent, which can be m,, m8, m9, and m,2,
representing the milk, steam, hot water, and coolant respectively.
The state
variable vector X, therefore, can be reformatted as
X — {Tj,W14,Q15,W16,0,7,0,8,01,,m8,m9,m,2 | i=1,2...13}
Based on certain technical conditions and physical and/or biological requirements,
the upper and lower bounds, UB and LB, of the state variables are given below
using the reformatted X:
UB = {277.6, 423.16, 423.16, 423.16, 423.16, 423.16, 280.4, 423.16
423.16, 423.16, 423.16, 280.40, 423.16, 7.0, 3.0, 1.5, 1.0, 5.0
0.477, 0.05, 3.0, 3.0}
LB = {274.16, 275.16, 274.16, 344.83, 344.83, 275.16, 274.16, 373.16
346.0, 298.16, 345.0, 278.72, 278.72, 1.0, 0.01, 0.01, 0.01, 0.01
0.15, 0.0001, 0.01, 0.01}
55
Apparently
g)
LB as X s UB
(3-56)
Independent and Dependent Variables
The relationships have been described by 21 equations which are related to
the 31 state variables. Among the equations, 9 were derived from mass balance,
7 from energy balance, and 5 from operational relationships. Among the state
variables, m1# me, m9, m12, T,, T4, T7, T8, T12, and W14 were selected to be the 10
independent variables and the 21 remaining as the dependent variables. Using
vector symbols, the vector of independent variables is
XI
=
{ml,m8,m9<m12,T1,T4,T7,T8,T12,W14}
and the dependent variables can be determined from the 21 equations.
h)
Objective Functions
Attainment of two different objectives is desired for the operating system
to meet constraints 3-11 through 3-56. The first objective is exergy-oriented to
minimize the entire system irreversibility and heat exergy losses Z1:
«3-57a)
Min
O'i
[
hs J
'6
J
[
'10
J
The second is energy-oriented to minimize the total source energy usage Z2:
Min
Z2 =mBlhfg+c{Te-T,y)]+m,2c{Ti3-T,2)+Wi4+Wi6
(3-57b)
The constraints (3-11 to 56) combined with the objective functions (3-57a,b)
constitute the operational optimization model of the pilot milk processing system.
A program was written for the GAMS package to solve the model numerically.
The program code is listed in Appendix A. The numerical optima are reported in
Chapter 4.
56
§3-3-2
Regenerator Modelling
Combining equations (3-11, 14, and 30) with equation (3-22), the
irreversibility of the regenerating unit can be expressed as
UT,+!$(T,-T,n
/, = 7/77,0 In
(3-58)
On the right hand side of the equation, T, and T2 are variables and the remainder
are known parameters. The variation of Ij with T2 for a fixed T, of 277.6 °K is
discussed in Chapter 4 to illustrate the difference in recommendations obtained
from systematic and component analyses.
57
Chapter 4
RESULTS AND DISCUSSION
The seven sections in this chapter report and discuss the results obtained
from experimental evaluation and theoretical analysis, respectively. After reporting
experimental data, the experimental and optimized irreversibility distributions in the
milk processing system are discussed. Then, the influence of change of overall
heat transfer coefficients on the system exergy performance is analyzed.
To
evaluate the importance of exergy analysis and system evaluation, the First and
Second Law analyses and system and component optimization evaluation results
are compared respectively. Finally, the chapter ends with a summary of methods
for operating a milk processing system to reduce irreversibility.
§4-1
Data Collection Under Mean Steady State
Experimental data were collected on milk processing system operation using
the equipment in the U of A dairy laboratory. The data included temperatures,
pressures, flow rates, and electricity consumption. The data was collected under
steady state conditions because the energy and exergy balance relationships were
derived for steady state operation. Figure 4-1 shows the transient temperature
measurements obtained for different components during the experiment. The data
for the period between 16.0 and 16.6 military hours when temperature fluctua­
tions were minimum were used.
Even during the stable periods shown in this figure, temperatures still
fluctuated slightly.
Randomly picking a value to represent the steady state
temperature over the experiment period may not be appropriate.
Marin et al.
58
360
| tCATER MLK OUIUT |
PRODUCT MLK ]
-f
14
1
14.5
1
15
1
15.5
1
16
1
16.5
1
17
17.5
TIME (MILITARY HOURS)
Figure 4-1. Fluid milk temperatures at different locations versus time
following system startup.
(1987) described a Mean Steady State (MSS) procedure to statistically obtain a
best estimation of the steady process parameters, filtering out any persisting
unsteady elements.
A simple application of the procedure is to take a time
weighted average of the measured data for a steady period as the representative
value for the period. Temperatures collected in each stable period were processed
using this method to obtain the representative temperatures shown in Table 4-1.
Table 4-1. Mean steady state operating data at different operating pressures.
pressures
temperatures*
flow ratas
elec. power
operating steam 1
2
3
4
5
6
7
8
9
10
12
13
15
milk hotwater steam homo, pump
psi
psi deg.K deg.K deg.K deg.K deg.K deg.K deg.K deg.K deg.K deg.K deg.K deg.K deg.K kg/min kg/min gram/sec
watt
1500
2000
2500
3000
54
54
55
56
301.7 337.3 338.4 347.4 346.2
301.3 337.3 339.3 347.4 346.3
301.6 337.4 340.1 347.4 346.2
302.4337.4 340.9 347.4 346.2
312.2
312.2
312.2
312.2
280.4 422.9
280.4 422.9
280.4 423.5
280.4 424.0
348.2 346.7
348.2 346.9
348.2 346.9
348.3 347.0
278.2 300.0 322.4
278.2 300.0 322.8
278.2 300.0 323.0
278.2 300.0 323.3
11.79
12.16
12.02
11.88
69.81
72.49
67.00
59.06
3.51
3.11
2.99
3.00
3665
4423
5236
5976
* The temperature identification numbers are identical with labels for the inlets and outlets in Figure 3-3.
Table 4-2. Irreversibility distribution and First and Second Law efficiencies of each processing unit.
pressure(psi)
SLE,%
5.8
41.1
69.4
33.9
65.2
0.0
100.0
Irr.W
396$
1085
1780
655
408
1
0
2000
FLE,%
54.9
86.1
100.0
100.0
100.0
0.0
100.0
SLE,%
6.8
42.8
70.8
33.8
55.8
0.0
100.0
Irr.W
4691
1049
1561
650
373
1
0
2500
FLE,%
57.3
79.6
100.0
100.0
100.0
0.0
100.0
SLE,%
7.1
39.5
70.9
33.5
54.7
0.0
100.0
lrr,W
5338
1055
955
643
271
1
0
3000
FLE,%
61.2
70.7
100.0
100.0
100.0
I
SLE,%|
7.6
35.0
71.1
33.6
63.0
o
6
1500
FLE,%
46.6
82.9
100.0
100.0
100.0
0.0
100.0
o
o
homogenizer
f.w.heater
regenerator
cooler
heater
holding tube
water pump
Irr.W
3305
1225
1135
635
349
1
0
100.0 100.0
Ln
vo
60
§4-2. irreversibility Distribution
6000
62.1%
5000
4000
5
>
t
i
i
i
i
OPERATING PRESSURE = 3000 PSI.
i3000
01
Of
OPERATING PRESSURE = 1500 PSI.
cc.
a.
2000
21.3%
16.5%
1000
7.5% 9.2%
negligible 0.0% 0.0%
homogenizer
f.w.heoter
regenerator
cooler
heater
holding tube water pump
SYSTEM COMPONENTS
Figure 4-2. Irreversibility comparison among the seven milk processing units.
The pilot milk processing system is made up of seven processing units:
regenerator, homogenizer, milk heater, holding tube, cooler, feed water heater and
water pump. Of these, the regenerator, cooler, milk heater and holding tube are
integral components of the plate heat exchanger. The irreversibility distribution of
each unit was calculated for different homogenizer operating pressures using the
equations derived in Chapter 2, and the results are shown in Table 4-2. Figure 4-2
shows the overall system irreversibility distribution graphically for operation at
1500 psi and 3000 psi. The irreversibility for each processing unit is represented
61
by a bar; the number on top of the bar represents the ratio of the irreversibility
generated in the individual unit to the irreversibility of the overall system, i.e.,
= 1 op v ^rr> . The figure allows easy visualization of the ranking of exergy
'
Ik!rrk
dissipators in the system; the homogenizer is the biggest exergy dissipator
r
followed by the feedwater heater and regenerator.
The irreversibilities in the
holding tube and water pump are so small compared to those of other units that
they can be neglected.
A homogenizer consists of a high-pressure pump and a throttling valve. The
valve breaks up molten fat globules, thereby distributing the fat uniformly and
homogenizing the milk.
The process is highly irreversible because the large
pressure drop caused by viscous dissipation takes place immediately across the
valve as the fluid milk flows through the valve. The larger the valve's operating
pressure, the greater the irreversibility.
The feedwater heater mixes incoming water at local atmospheric pressure
with saturated steam. The mixing process is a typical irreversible thermodynamic
process in which the high energy quality steam partially condenses, doing no work,
and becoming low energy quality water. Certain factors strongly influence the
irreversibility of the heating unit. First, reducing the mixing ratio mlteam/mH20 can
lessen the irreversibility, which requires a better mixing of the two streams. Next,
higher vapor pressure can cause the irreversibility to increase. Finally, heat loss
to the environment is accompanied by exergy loss of the unit.
The source of irreversibility in the plate heat exchanger sections is the heat
transfer due to large temperature differences. In heat transfer, energy is conserved
62
but exergy is destroyed. One way to reduce the section irreversibility is to reduce
the temperature difference, but a larger heat transfer area (greater number of
plates) then is required to achieve the same degree of heat transfer, as seen from
the heat transfer equation Q = UAAT,m. Higher temperatures of the coolant could
be tolerated (irreversibility unchanged) if an equivalent change in heat transfer area
is made, a change which could reduce the operating costs of the cooling unit.
§4-3.
Optimal Irreversibility Distribution
The GAMS/MINOS optimization program package was used to determine the
operational parameters yielding optimum irreversibility distribution for the system
described in relationships (3-11 to 57), Chapter 3. The results, for an operating
pressure equal to 2000 psi, are tabulated and compared with the corresponding
experimental data in Table 4-3. It is noted that the system overall irreversibility
(SIRR) would have reached a minimum of 6.95 kW through exergy-oriented optimal
operation, while it stayed at a higher value of 7.90 kW during experimental
operation.
Differences in exergy-oriented optima and experimental data were
mainly caused by relatively higher irreversibilities of the cooler and feedwater
heater at the experimental operating state.
The exergy-oriented optimization
approach provides information which could be used to improve the system exergy
performance.
The bar graph in Figure 4-3 shows the difference between the irreversibility
distribution of the experimental milk processing system and the system adjusted
to optimize exergy performance. Compared with the experimental distribution, the
graph indicates that operating at the optimum operating state will reduce the
63
Table 4-3.
Comparison of simulation parameters and experimental data.
variables
enerav-oriented
T,\K
274.16
T,,K
329.42
T».K
332.17
T/.K
345
Te.K
345
T*,K
289.74
T,\K
280.4
419.91
T„\K
T0.K
360.21
T,„,K
334.17
T,,.K
360.16
T,,\K
277.75
T,*.K
286.74
4.33
W,,\kW
Q.ckW
2.02
W,*.kW
0.03
Q,-,.kW
0
Q,«.kW
0.5
0.21
m,,\ka/s
m«*.ka/s
0.1
m«\a/s
4.74
m,\ka/s
0.2
SEC.kW
23.40
SIRR.kW
8.14
RP.%
78.01
FWH.kW
11.22
CL.kW
7.82
RTD.K
15.58
HTD.K
6.51
CTD.K
2.82
2.26
LkW
3.95
h,kW
l=:=.kW
0.23
l,..kW
0.00
0.08
L.kW
UkW
1.59
l.^.kW
0.02
h,_,kJ/ka
2119
* represents independent state variables.
exerav-oriented
277.6
330.18
332.93
345
345
292.42
280.4
373.16
358.85
334.93
358.8
276.84
288.71
4.33
2.02
0.03
0
0.5
0.2
0.1
4.55
0.2
25.01
6.95
78.01
10.58
10.07
14.82
6.12
3.63
2.02
3.95
0.20
0.00
0.14
0.63
0.02
2266
experiment
301.3
337.3
339.3
347.4
346.3
312.2
280.4
422.9
348.2
346.9
348.2
278.2
300.0
4.42
1.99
0.062
0.95
1.08
0.29
1.21
3.11
0.2
38.75
7.90
80.18
7.55
26.71
9.89
3.02
5.86
1.78
3.97
0.41
0.00
0.66
1.08
0.00
2115
64
4.5
optimol stole
regeneratorhomogenizer
heater
cooler
f.w.heater water pumpholdlng tube
system components
Figure 4-3. Comparison of the system irreversibility distribution between the
experimental operating state and the optimal operating state.
65
!o
8
'(/)
(1)
> 7.5
<D
E
<1)
(0
>»
O
0)
m
>
° 5.5
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.1
overall heat transfer coeff., KW/rrT2 K
Figure 4-4. Variation of minimum overall system irreversibility with regenerator
overall heat transfer coefficient when operated at the exergy-oriented optimal
state.
66
irreversibility of the feedwater heater, cooler, and milk heater and the overall
system although the irreversibility of regenerator will increase slightly.
This
example illustrates the essence of systematic analysis: the sacrifice of certain
component interests may be required to obtain the system optimum.
§4-4. Influence of overall heat transfer coefficients on system exergy performance
An interesting phenomenon was found in solving the optimization problem
(3-11 to 57): the optimal system exergy performance was fairly sensitive to the
overall heat transfer coefficients of the plate heat exchangers. Figure 4-4 shows
the sensitivity at a glance.
Reducing the heat transfer coefficient of the
regenerator from 1.0 to 0.3 kW/m2 K causes the overall system irreversibility to
increase from 6 to 9 kW.
Increasing the overall heat transfer coefficients,
therefore, can apparently improve system exergy performance. In actual operation,
it is desirable to have the largest possible mass flow rates through the plate heat
exchangers to maintain high values of heat transfer coefficients. Fouling of the
heat transfer surface can dramatically reduce the coefficient. Thus, cleaning the
heat exchangers is very important to the maintenance of system exergy
performance.
A plate heat exchanger, fortunately, can easily be opened for
inspection, mechanical cleaning, gasket replacement, and extension or reduction
to the number of plates.
§4-5. Comparison of the energy and exergy analyses
As indicated before, energy and exergy analyses differ from each other in
that the exergy method considers both quantity and quality aspects of energy
while the energy method emphasizes only quantity. The difference is illustrated
67
by the energy-oriented and exergy-oriented optimal results listed in Table 4-3. The
results show that although the system may consume less energy (23.40 rather
than 25.01 kW) when operating at the energy-oriented optimal state, it has a
higher overall irreversibility (8.14 instead of 6.95 kW) and requires higher quality
steam (419.91 rather than 373.16 Kelvin). In other words, the use of high quality
energy must be swapped to save energy in the energy-oriented operating approach.
This becomes important when considering cost of energy. If energy quality is
reflected in cost, then exergy analysis shows that comparing Btu's may not be
enough to lower operational costs.
In addition to the irreversibilities, energy and exergy efficiencies were
derived for each system component in Chapter 2. The difference between energy
and exergy analyses can also be illustrated by comparing these two efficiencies.
First law efficiencies (FLE) are frequently used to gauge the energy performance
of devices and processes and reflect the efficiency of energy transfer. Second law
efficiencies (SLE) also are used to measure the exergy performance and reflect the
efficiency of energy usage. Both FLE and SLE is defined as a ratio of output to
input. The connotation of energy output and input, however, is entirely different
from that of exergy output and input, and therefore, the results are different. The
difference is demonstrated in Table 4-2 through examination of the two efficiencies
based on experimental data.
All of the SLEs are markedly less than the
corresponding FLEs. Figure 4-5 graphically compares the two efficiencies at an
operating pressure of 2000 psi.
It shows clearly that although energy analysis
yields a near 100% FLE in each plate heat exchanger section, exergy analysis
68
100.0%
100
90-
O
o
Li_
Li_
Ld
100.0%
86.1%
80-
0.8%
70 60-
$
<
50-
o
z
40-
o
UJ
(/)
30 -
5.8%
54.9%
3.8%
o
I
20
CO
DC
100.0%
10"
homogenizer
f.w.heater
regenerator
cooler
heater
SYSTEM COMPONENTS
FIRST LAW
:igure
I SECOND LAW
4-5 Comparison of First and Second Law efficiencies at an operating
pressure of 2000 psi.
indicates that each section has a lower efficiency of energy usage with the cooling
section retaining only 33.8% of the original work capacity of the energy. This is
due to irreversibility resulting from a heat transfer process with a finite temperature
difference which the SLE accounts for while the FLE does not. The homogenizer,
the only component acting not as a heat exchanger but as a throttling valve, has
an FLE of 54.9% and SLE equal to 6.8%. The difference is due to irreversibility
stemming from the throttling process along with fluid viscous dissipation which the
SLE accounts for but the FLE still does not.
69
§4-6.
Difference between systematic and component optimization
7.15
overall
regenerator
system
-7.1
in 2.15
-7.05
-6.95
328.5
329
329.5
330
330.5
331
331.5
regenerated milk temperature (T2),
332.5
6.9
333
K
Figure 4-6. Comparison of systematic and regenerator irreversibility changes with
preheated milk temperature (T2).
To obtain the optimal system irreversibility distribution, the operating
strategy may require sacrificing certain component interests. In fact, reducing the
irreversibility of certain components without any systematic consideration may
worsen the overall system exergy performance.
To demonstrate the need for
system evaluation, the exergy performance of the regenerating unit was examined
using equation (3-58) in Chapter 3. The change of the regenerator irreversibility
with temperature of the regenerated milk was plotted in Figure 4-6. Also plotted
was the loci of optimal overall system irreversibility at different temperature values
of the regenerated milk.
The figure shows that although the component
70
irreversibility descends as the temperature drops, the overall system irreversibility
first decreases to reach a minimum at T2 = 330.5 K and then increases as the
temperature decreases further.
In other words, the overall system exergy
performance gets worse although the regenerator irreversibility alone continues to
decrease at temperatures less than 330.5 K.
§4-7.
Operational approach
The irreversibilities existing in the pilot milk processing system must be
understood to obtain management or operational benefits from exergy analysis.
Table 4-4 summarizes information on location, magnitude, and mechanism of
irreversibility for the system at different experimental operating states. Based on
the thermodynamic rationale, certain operational recommendations are also
included in the table which could improve the component operating exergy
performance in the future operation. The table shows that, of all the processes,
homogenizing is the most irreversible (48% to 62% of overall system irreversibility)
due to large fluid viscous dissipation as the milk flows through the homogenizer
valve.
In operation, the lowest possible homogenizer operating pressure is
preferred to reduce the dissipation. Irreversibility of the feedwater heater ranges
from 15% to 21% of overall system irreversibility with different operating
pressures. The irreversibility is caused by mixing high temperature steam with low
temperature water, can be reduced by lowering mixing ratio mgteifn/mH20 and steam
pressure. Irreversibilities in sections of the plate heat exchanger are caused by
heat transfer through a finite temperature difference, and can be reduced by
lowering the logarithmic mean temperature difference (LMTD) of heat transfer.
71
Lowering the LMTD may also reduce operating cost but requires a larger heat
transfer area to maintain the same heat transfer load.
A tradeoff between the
operating cost and investment, therefore, is needed to obtain the more costeffective benefits.
Table 4-4.
Summary of irreversibility analysis conclusions for the pilot milk
processing system
Location
Magnitude
Mechanism
Operating parameter
Operation approach
homogenizer
48%-62%
fluid viscous
dissipation
operating pressure
O.P.— ALAP*
feedwater
heater
15%-21 %
mixing of streams
having different
temperatures
mixing ratio rm
steam pressure pa
heat loss Q
rm — ALAP
p, — ALAP
insulate if possible
plate heat
exchangers
20 % -35 %
heat transfer
through a finite
temperature
difference
logarithmic average
temperature
difference
heat transfer area A
AT — ALAP
. *•
increase plates (A)
but require cost
tradeoff
* ALAP — As low as possible.
72
Chapter 5
CONCLUSIONS
Exergy analysis provided a meaningful measure of
energy quality
degradation in the fluid milk processing processes, supplementing traditional
energy analysis in its measure of energy transfer.
Although energy efficiencies (FLE) predicted near maximum performance in
heat transfer for the cooler, heater and regenerator, exergy efficiencies
(SLE) show that these are not very efficient in terms of the energy usage,
the cooler having the lowest SLE value.
Increasing the overall heat transfer coefficients of the plate heat exchangers
can dramatically reduce the system overall irreversibility.
The exergy-oriented optimization approach can be effective in improving
system exergy operating performance.
Compared with the exergy-oriented method, the energy-oriented optimiza­
tion approach requires a higher temperature steam source serving for the
system operation although it can help reduce system energy consumption.
Reducing the irreversibility of individual components without regard of the
system irreversibility can worsen the overall system exergy performance.
APPENDIX A
Listing of the program of MKSYSOPT.ASC
(An ASCII file written for GAMS to solve the operational
optimization problem of the pilot milk processing system)
$OFFSYMXREF OFFSYMLIST OFFUELLIST OFFUELXREF
SCALARS
MMFR
LHLF
HOPL
HOPH
MIRR
C
R
TO
PO
HST
UREG
AREG
UHT
AHT
UCL
ACL
RTD
HTD
CTD
FWH
CL
SIRR
SEC
REGP
IRR1
IRR2
IRR3
IRR4
IRR5
IRR6
IRR7
minimum milk flowrate in kg per second /0.2/
lowest heat loss from feedwater heater in kw /0.5/
lowest homogenizer operating pressure in psi /2000/
highest homogenizer operating pressure in psi /2500/
tolerant maximum overall irreversibility in kw /8.5/
specific heat of water in kj per kg k /4.1868/
specific H20 vapor constant in kj per kg k /0.4615/
reference temperature in kelvin /298.16/
reference pressure in kn per sq. meter /101.325/
homogenizer surface temperature in kelvin /322.0/
regenerator heat transfer coefficiency /0.6/
regenerator heat transfer area in sq. meter /4.95/
heater heat transfer coeff in kw per k sqm /1.0/
heater heat transfer area in sq. meter /1.65/
cooler heat transfer coeff in kw per k sqm /1.2/
cooler heat transfer area in sq. meter /2.31/
regenerator logarithm mean temp diff in k
heater logarithm mean temperature difference in k
cooler logarithm mean temperature difference in k
feedwater heater heat supply in kw
cooling load borne by cooler in kw
system overall irreversibility in kw
system energy consumption in kw
regeneration percentage
regenerator irreversibility in kw
homogenizer irreversibility in kw
heater irreversibility in kw
holding tube irreversibility in kw
cooler irreversibility in kw
feedwater heater irreversibility in kw
water pump irreversibility in kw ;
SETS J variable sequence ordinal number /J 1 * J21 /
I constraints ordinal number
/II *116/
PARAMETER
A(I,J) linear constraints coefficiencies
/I1.J1 = -1, 11 .J2 = + 1
12. J1 = -1, I2.J6 = 1
I3.J2 = -1, I3.J5 = 1
I4.J3 = -1, 14.J4 = 1
=
-1, I5.J10 = 1
I5.J3
=
-1, 16.J9 = 1
I6.J4
I7.J4 = 1, 17.J5 =- 1
I8.J5 = 1, I8.J6 =- 1
I9.J6 = 1,19.J7
1
=
1,
11
O.J
13
=
'
-1
I10.J6
=
1, I11.J12 =: -1
I11.J7
I12.J8 = 1, I12.J9 = -1
=
1, I13.J10 = -1
I13.J9
=
1, I14.J11 = -1
I14.J9
115.J10 = -1, I15.J11 = 1
116.J12 = -1, I16.J13 = 1 /;
PARAMETER
LB(J) lower bound
/ J1 274.16, J2 275.16, J3 274.16, J4 345.0
J5 345,
J6 275.16, J7 275.16, J8 373.16
J9 346, J10 298.16, J11 345, J12 270.94
J13 274.16, J14 1.0, J15 0.0, J16 0.0
J17 0.0, J21 0.1 /;
LBCJ18') = LHLF ;
LBCJ19') = 1.01 *MMFR ;
LBCJ20') = 1.01 *MMFR ;
PARAMETER
UB(J) upper bound
/ J1 277.6, J2 423.16, J3 423.16, J4 423.16
J5 423.16, J6 423.16, J7 280.4, J8 423.16
J9 423.16, J10 423.16, J11 423.16, J12 280.4
J13 423.16, J14 7.0, J15 3.0, J16 1.5
J17 2.0, J18 5.0, J21 50.0/;
UBCJ19') = 3.0 ;
UBCJ20') = 3.0 ;
PARAMETER F(J) initial solution
/J1 277.60,
J2 350.00
J3 332.76, J4 350.00, J5 346.77
J6 292.37, J7 280.40, J8 373.16, J9 359.16, J10 334.76
J11 359.11,
J12 276.86,
J13 288.68,
J14 4.33, J15 2.02
J16 0.03, J17 0.19, J18 0.50,
J19 0.20,
J20 0.10
J21 4.62 /;
VARIABLES
UFG
HFG
EXL
*
SEC
X(J)
water vapor internal energy change in kj per kg
water vapor enthalpy change in kj per kg
system exergy losses in kw ;
system energy consumption in kw;
POSITIVE VARIABLES X, UFG, HFG ;
X.LO(J) = LB(J);
X.UP(J) = UB(J);
X.L(J) = F(J);
UFG.L = 1926.6;
HFG.L =2115.0;
EQUATIONS
*
*
*
*
OBJ 1 reduce total exergy losses
OBJ2 reduce total energy consumption
LINE(I) the i th linear constraint
DWFR discontinuous point of water flow rate
DCFR discontinuous point of chilling water flow rate
SWTD steam water temperature difference in deg k
WPTD waterpump inlet & outlet temp diff in deg k
HOMO homogenizer milk temperature change vs power
ENER relationship between UFG and temperature
ENTH relationship between HFG and temperature
RLTD regenerator logarithm mean temperature difference
RHT regenerator heat transfer
HSST heater small side temperature difference limitation
HLST
HHT
CSST
CLST
CHT
heater large side temperature difference limitation
heater heat transfer
cooler small side temperature difference limitation
cooler large side temperature difference limitation
cooler heat transfer
ENB1
ENB2
ENB3
ENB4
ENB5
ENB6
ENB7
regenerator energy balance equation
homogenizer energy balance equation
heater energy balance equation
holding tube energy balance equation
cooler energy balance equation
feedwater heater energy balance equation
water pump energy balance equation
IT)
(/)
X
o
o
h*
IT)
CO
1,
X
£
5
o
c
o
'•p
ro •*
c
3 C
o
CT
O
'•p
V 4=
to
Q}
^
cr c O
c
C ^
V .2 V
%
0)
V
« o
O ro _
c 3
5- ^ c
5 a-jjj
£.2
"5 «
C
c o
.2 '•=
4-1 (0
CO 3
3 cr c
cr a> O
® ®
0) O ID
o c 3
c «J
SS ro ®
00 JO
•° >
§ t § s !
> o» «
°>ro ® o5
tt) X 5 S5 $ |
©
m
5
x ®
w
m
>• ™
<u m
®
o>
a>
a
k. 0) ' .a
O N Q}
ro «= X £ *• JZ 3
L . ® a>
0) a> v. o> ® ro a.
c o ® .E a> ^ aS
® £ ro 2
o> £ 0) o 2 ® ro
® 2 .c x: 8 5 5
«- cm co
to <o r*
CD 00 CO CD CO 00 CD
X
X
X
X
XX X
HI III III III III III III
-
CM
™
c
0
p
0
c
3
UL
.>
'*->
O
<u
'S
O
*
x
+
£x
p +
£
F F X F F X
N P) U ^ (O U
? ? o ? ? o
X X ^X X
a (5 ?r oa £r
oI oI ^
° o o^
«
CO
rs
pv
a>
<o
+
X
sO
So
O -J
O =:
•J *
00
r
?
j
F
^X
XL
0 £?
? u
S?
S t 1X
o»
o r CD o
r +?
- * iv
X U) + Px
0 -i.
CM
p 1®° i£
p
XI
XS
CO - j T ?
CO -«t 5S lo r» X
o —' 00
v?
(5 ^ p
p * <_>
p
(JTT(Jr o r ?
s
O7
X c co'^ ~ +5
«
O
O
y
~T
XX 2 x x S «- =j I- Q o + ™ ><
r* o o r 5 5 r "
-> r* Oi 2 w
T» o
oo
? I t
3b
5
0
U
I
o
o
O
O
O
O
X L. « *
f s _j _j K— —I —I J— o
• OC *£>*
r oo
U JL. * * * r* r* * t. n
— LL • o r "
O
• ~ o o o £ , £ > u rr O
X ^ 2 y oo
oo
DC «- I- h•
r
U. -» * *
i o r r (J —
oo
• I- p5
5 ~oo
«- CM
—«/)
oi-®
*
•
5 ^ OC DC ? i c P
CM CM O X x il!i CM CM «O U. U. y U - I L J ^
II O
X ~ ~ H p o II
22 * 2 5 * X
UJ
+
+ x X
o X X X
+ 2 2 +
X- ^
II
C UJ
_i
+ +
+ +
+ + + co
X
UJ
CM
->
I
m
O
-j
00
0
ll
LLI
..
SS
o ~ (O O)
CM 2 00 00
^
. . X -5: CO
CO to
11
o
• II II
II
SlUUl
o • . . . W O S 11 11
II
II
II CC rr
— t £ (J ui
= 5 1 2 II 1 1
x 52
s?.x
P in 2
< A 11 * X X ^ ^
CO CO
S
~
CM
+ +
N^ro
I? p ^ p
^
CD
O
3 ?
CO x X * X
* £ £
o
0)
!d
3
CO
*
S F o c ^Ql O
j w - -
S
S.dloycol t i H
X LLJ £j
II
u
II
(0
4-1
c
CM
•p
'ro
k_
+-•
M
C
o
a
(U
O)
c
ro
sz
o
X
LLI
•M
ro
X
*
XI
in
s
i
ro
k_
03
c
•
oO
o> H
a) _i
*- IE
77
RHT..
*
*
MMFR*C*(X('J2')-X{'J1')) =E =
UREG*AREG*(X('J5')-X('J2')) ;
heater:
HSST..
X('J9')-X{'J4') =G= 2.0;
HLST..
X('J10')-X('J3') =G= 2.0 ;
HHT..
MMFR*C#(X('J4')-X('J3'))*(LOG(X('J9')-X('J4'))LOG(X('J10')-X('J3'))) =E= UHT#AHT*(X('J9')X('J4')-X('J10')+X('J3')) ;
cooler:
CSST..
X('J7')-X('J12') = G = 2.0;
CLST..
X('J6')-X('J13') =G= 2.0;
CHT..
MMFR#C*(X('J6')-X('J7'))#{LOG(X('J6')-X('J13'))LOG(X('J7')-X('J12'))) =E= UCL*ACL*(X('J6')X('J13')-X('J7') +XCJ12')) ;
•Energy Balance Equations
ENB1..
ENB2..
ENB3..
XCJ1') - XCJ2') + XCJ5') - XCJ6') =E= 0 ;
MMFR*C#(X('J2')-X('J3')) + X('J14')-X('J15') =E= 0;
MMFR*(X('J3') - X('J4'))
+ X('J20')#(X('J9') - XCJ10')) =E= 0 ;
ENB4.. MMFR*C*(X('J4')-X('J5')) - XCJ17') =E= 0 ;
ENB5.. . MMFR*(X('J6') - X('J7'))
+ X('J19')*(X('J12') - XCJ13')) =E= 0 ;
ENB6.. X('J20')#C*(X('J11')-X('J10')) + XCJ18') =E =
XCJ21 ')/1000*(HFG + C#(X('J8')-X('J11')));
ENB7.. XCJ16') =E= X('J20')*(C*(X('J9')-X('J11')) + 0.0517);
•Exergy Balance Equations
EXB1.. LOG(X('J2')) + LOG(X('J6'))-LOG(X('J1'))-LOG(X('J5')) =G= 0;
EXB2.. MMFR*C*TO*(LOG(X('J3'))-LOG(X('J2'))) + XCJ15')*T0/HST
= G= (1098.8+1.426#HOPL)/1000 ;
EXB3.. MMFR*C#TO*(LOG(X('J4'))-LOG(X('J3')))
+ X('J20')*C*T0#(LOG(X('J10'))-LOG(X('J9'))) =G= 0;
EXB4.. MMFR*C#TO#(LOG(X('J5'))-LOG(X('J4'))) + X('J17')*T0/X('J5') =G= 0;
EXB5.. MMFR*C#TO#(LOG(X('J7'))-LOG(X('J6')))
+ XCJ19')*C*TO*(LOG(X('J13'))-LOG(X('J12'))) =G= 0;
EXB6.. XCJ18')*T0/X('J11') + X('J20')*C,TO#(LOG(X('J11 '))-LOG(X('J10')))
-X('J21')/1000#C#TO*(LOG(X('J8'))-LOG(X('J11')))
-XCJ21 ')/1O00*T0/X('J8')#HFG =G= 0;
EXB7.. X('J20')*C*TO#(LOG(X('J9'))-LOG(X('J11'))) =G= 0;
MODEL MILKSYSTEM /ALL/ ;
OPTION LIMROW = 0,LIMCOL = 0,X:2:0:21,SEC:4,FWH:4,CL:4,SIRR:4 ;
78
*
SOLVE MILKSYSTEM USING DNLP MINIMIZING EXL ;
SOLVE MILKSYSTEM USING NLP MINIMIZING SEC ;
FWH = X.LCJ21 ')/1000*(HFG.L + C*(X.L('J8')-X.L('J11'))) ;
CL = X.LCJ19')*C*(X.L('J13')-X.L('J12')) ;
SEC = X.L('J14') + X.L('J16') + FWH + CL ;
IRR1 = MMFR*C*TO#(LOG(X.L('J2')) + LOG(X.L('J6'»
-L0G(X.L('J1 '))-LOG(X.L('J5'))) ;
IRR2 = MMFR*C*TO#(LOG(X.L('J3'))-LOG(X.L('J2'))) + X.LCJ15')*T0/HST ;
IRR3 = MMFR*C*TO*(LOG(X.L('J4'))-LOG(X.L('J3')))
+ X.L('J20')*C*T0*(LOG(X.L('J10'))-LOG(X.L('J9'))) ;
IRR4 = MMFR*C#TO*(LOG(X.L('J5'))-LOG(X.L('J4')))
+ X.LCJ17')*T0/X.L('J5') ;
IRR5 = MMFR*C*TO*(LOG(X.L('J7'))-LOG(X.L('J6')))
+ X.L('J19')*C*TO*(LOG(X.L('J13'))-LOG(X.L('J12'))) ;
IRR6 = X.LCJ18')*T0/X.L('J11')
+ X.L('J20')*C*TO*(LOG(X.L('J11 '))-LOG(X.L('J10')))
-X.LCJ21 ')/1000#C*TO*(LOG(X.L('J8'))-LOG(X.L('J11')))
-X.LCJ21 ')/1000*T0/X.L('J8')*HFG.L ;
IRR7 = X.L('J20')*C*TO*(LOG(X.L('J9'))-LOG(X.L('J11'))) ;
SIRR = IRR 1 + IRR2 + IRR3 + IRR4 + IRR5 + IRR6 + IRR7 ;
RTD = X.L('J5')-X.L('J2');
HTD = (X.L('J9')-X.L('J4')-X.L('J10') + X.L('J3'))/(LOG(
X.L('J9')-X.L('J4'))-LOG(X.L('J10')-X.L('J3'))) ;
CTD = (X.L('J6')-X.L('J13')-X.L('J7') +X.LCJ12'))/(LOG(
X.L('J6')-X.L('J13'))-LOG(X.L('J7')-X.L('J12'))) ;
REGP = 100*(X.L('J2')-X.L('J1 '))/(X.L('J5')-X.L('J1')) ;
DISPLAY X.L,MMFR,SEC,SIRR,EXL.L,REGP,FWH,CL,RTD,HTD,CTD ;
DISPLAY IRR1 ,IRR2,IRR3,IRR4,IRR5,IRR6,IRR7,HFG.L ;
79
SELECTED BIBLIOGRAPHY
Ahem,J.E., 1980. THE EXERGY METHOD OF ENERGY SYSTEMS ANALYSIS.
Wiley, New York, N.Y., chapter 4.
Bejan, A., 1982. ENTROPY GENERATION THROUGH HEAT AND FLUID FLOW.
Wiley, New York, N.Y., preface.
Bejan, A., 1986. SECOND LAW ANALYSIS: THE METHOD FOR MAXIMIZING
THERMODYNAMIC EFFICIENCY OF THERMAL SYSTEMS. In: W.O.Winer et al.
(report committee). Research Needs in Thermal Systems. The American Society of
Mechanical Engineers, New York, N.Y., pp.186-196.
Boehm, R.F., 1987. DESIGN ANALYSIS OF THERMAL SYSTEMS. Wiley, New
York, NY, chapter 8, pp.168.
Brooke, Anthony, David Kendrick and Alexander Meeraus, 1988. GAMS
A
USER'S GUIDE. The Scientific Press. Redwood City, CA.
Brown, H.L. and B.B. Hamel et al., 1985. ENERGY ANALYSIS OF 108
INDUSTRIAL PROCESSES. Fairmont Press Edition, pp.18.
M. David, 1986. ENGINEERING THERMODYNAMICS WITH
APPLICATIONS. Third Edition. Harper & Row, Publishers, Inc. New York, NY.
Burghardt,
APPLICATION OF THE
THERMOECONOMIC APPROACH TO THE ANALYSIS AND OPTIMIZATION OF A
VAPOR-COMPRESSION DESALTING SYSTEM. Trans. A.S.M.E., J. Eng. Power, 92,
El-Sayed,
Y.M.
and
Aplenc,
A. J.,
1970.
pp. 17-26.
El-Sayed, Y.M. and Evans, R.B., 1970. THERMOECONOMICS AND THE DESIGN
OF HEAT SYSTEM. Trans. A.S.M.E., J. Eng. Power, 92, 1970, pp.27-34.
Evans, R.B., 1980. THERMOECONOMIC ISOLATION AND ESSERGY ANALYSIS.
Energy: The International Journal, Vol.5, No. 8-9, pp.805-821.
R.B., Grellin, G.L. and Tribus, M. 1966. THERMOECONOMIC
CONSIDERATIONS OF SEA WATER DEMORALIZATION, in Principles of
Evans,
Desalination (K.S. Spiegler, editor), Academic Press, pp.21-76.
Evans, R.B., Hendrix, W.A. and Kadaba, P.V., 1983. ESSERGETIC FUNCTIONAL
ANALYSIS FOR PROCESS DESIGN AND SYNTHESIS. In: R.A. Gaggioli (Editor),
Efficiency and Costing: Second Law Analysis of Processes, ACS Symposium Series
235. American Chemical Society, Washington, DC, pp.239-261.
80
Evans, R.B. and Tribus, M., August 1962. A CONTRIBUTION TO THE THEORY OF
THERMOECONOMICS. UCLA, Dept. of Engr.: Report No. 62-63, Los Angeles, CA.
Evans, R.B. and Tribus, M., 1965. THERMO-ECONOMICS OF SALINE WATER
CONVERSION. I&EC Process Design and Development, 4, pp. 195-206.
Fan, L.T. and Shieh, J.H., 1983. MULTIOBJECTIVE OPTIMAL SYNTHESIS, in
Efficiency and Costing - Second Law Analysis of Processes. A.C.S. Symposium
Series 235, Washington, D.C., pp. 307-332.
Forciniti, D., Rotstein, E. and Urbicain, M.J., 1985. HEAT RECOVERY AND
EXERGY BALANCE IN A TOMATO PASTE PLANT. J. Food Sci., 50: 934-939.
Forciniti, D., Urbicain, M.J. and Rotstein, E., 1987. SIMULATION TOWARDS
OPTIMIZATION OF AN APPLE JUICE CONCENTRATE PLANT. Unpublished.
Prepared for presentation at 1987 AlChE Summer National Meeting; ComputerAided Food Process Development Session. August, 1987. Minneapolis, Minnesota.
Frangopoulos, C.A., 1984. THERMOECONOMIC FUNCTIONAL ANALYSIS: AN
INNOVATIVE APPROACH TO OPTIMAL DESIGN OF THERMAL SYSTEMS. In: A.
Bejan et al.(Editor), Second Law Aspects of Thermal Design. HTD-Vol.33, The
American Society of Mechanical Engineers, New York, NY, pp.77-85.
Frangopoulos, C.A., 1984. THERMOECONOMIC ISOLATION AND THE
OPTIMIZATION OF THERMAL SYSTEM COMPONENTS. In: A. Bejan et al. (Editor),
Second Law Aspects of Thermal Design. HTD-Vol.33, The American Society of
Mechanical Engineers, New York, NY, pp.87-94.
Gaggioli, R.A. 1961. THERMODYNAMICS AND THE NON-EQUILIBRIUM SYSTEM.
Ph.D. Thesis, University of Wisconsin-Madison.
Gouy, M. 1889. Sur I6nergie utilisable. Journal de Physique, 2e. serie. 8: 501.
Harper, W.J., 1976. PROCESSING-INDUCED CHANGES. In Dairy Technology and
Engineering, ed. W.J. Harper and C.W. Hall, 539-596. Westport: the AVI
Publishing Company, Inc.
Keenan, J.H. 1932. A STEAM CHART FOR SECOND LAW ANALYSIS. Trans, of
the ASME, 54, pp. 195-204.
Kessler, H.G. 1 981. FOOD ENGINEERING AND DAIRY TECHNOLOGY. In chapter
6. Publishing House Verlag A. Kessler, Germany.
81
Liu, Y.A. and Wepfer, W.J., 1983. THEORY AND APPLICATIONS OF SECOND
LAW ANALYSIS: A BIBLIOGRAPHY, chapter 18 in: Gaggioli, R.A. (Editor),
Thermodynamics: Second Law Analysis. ACS Symposium Series 122, American
Chemical Society, Washington, DC.
Marin, J.M. and J.A. Turggano, 1987. STATISTICAL EXERGY ANALYSIS IN THE
INDUSTRIAL SECTOR. In the Fourth International Symposium on Second Law
Analysis of Thermal Systems, ed. M.J. Moran and E. Sciubba, 109-114. The
American Society of Mechanical Engineering, New York, N.Y.
Maxwell, J.C. 1871. THEORY OF HEAT. 1 st ed. Longmans Green, London.
Moran, M.J. 1982. AVAILABILITY ANALYSIS: A GUIDE TO EFFICIENT ENERGY
USE. In chapter 2, 3. Prentice-Hall, Inc., Englewood Cliffs, N.J.
Moran, M.J. and Howard N. Shapiro 1988. FUNDAMENTALS OF ENGINEERING
THERMODYNAMICS. In chapter 3. John Wiley & Sons, Inc., New York.
Murtagh, B. A. and M. A. Saunders, 1982. A PROJECTED LAGRANGIAN
ALGORITHM AND ITS IMPLEMENTATION FOR SPARSE NONLINEAR
CONSTRAINTS. Mathematical Programming Study 16, Algorithms for Constrained
Minimization of Smooth Nonlinear Functions, 84-117.
Obert, E.F. and Gaggioli, R.A. 1963. THERMODYNAMICS. McGraw-Hill, New York.
Rant, Z. 1956. EXERGY, A NEW WORD FOR "TECHNICAL AVAILABLE WORK".
(in German), Forsch. Ing. Wes., vol.22, no.1, pp.36-37.
Reynolds, W.C., 1979. THERMODYNAMIC PROPERTIES IN Sl~graphs, tables and
computational equations for 40 substances. Department of Mechanical
Engineering, Stanford University, Stanford, CA.
Robinson, S. M., 1972. A QUADRATICALLY CONVERGENT ALGORITHM FOR
GENERAL NONLINEAR PROGRAMMING PROBLEMS. Mathematical Programming
3, 145-156.
Rotstein, E., 1982. EXERGY PROGRAM ASSESS ENERGY STATUS. Oil and Gas
J. 80(13): 100.
Rotstein, E., 1983. THE EXERGY BALANCE: A DIAGNOSTIC TOOL FOR ENERGY
OPTIMIZATION. J. Food Sci., 48: 945-950.
Rotstein, E., 1986.
EXERGY ANALYSIS: A DIAGNOSTIC AND HEAT
INTEGRATION TOOL, chapter 4 in: R.Paul Singh (Editor), Energy in Food
Processing. Elsevier, New York, NY, pp.19.
82
Stout, B.A., C. Myers, G. Schwab and Z. Helsel, 1982. ENERGY MANAGEMENT
IN US PRODUCTION AGRICULTURE. In: D.W. Robinson et al.(Editor), Energy
Management and Agriculture. Royal Dublin Society, Dublin, R.I., pp.67.
Szargut, J., D.R. Morris and F.R. Steward, 1988. EXERGY ANALYSIS OF
THERMAL, CHEMICAL. AND METALLURGICAL PROCESSES. Hemisphere
Publishing Corporation, New York, NY.
Shoup, Terry E. and Farrokh Mistree 1987. OPTIMIZATION METHODS WITH
APPLICATIONS FOR PERSONAL COMPUTERS. Prentice-Hall, Inc., Englewood
Cliffs. N.J.
TrSgSrdh, C., 1981.
ENERGY AND EXERGY ANALYSIS IN SOME FOOD
PROCESSING INDUSTRIES. Lebensm. Wiss. Technol., 14: 213-217.
Vickers, V.T. and Shannon, D.V., 1977. ENERGY USE IN THE DAIRY INDUSTRY.
Rep. 25, New Zealand Energy Research and Development Committee, Auckland,
54pp.
Von Spakovsky, M.R. and R.B. Evans, 1987. THE OPTIMAL DESIGN AND
PERFORMANCE OF THERMAL SYSTEMS AND THEIR COMPONENTS. In: M.J.
Moran and R.A. Gaggioli (editor), Analysis and Design of Advanced Energy
Systems: Fundamentals. AES-Vol. 3-1, American Society of Mechanical Engineers,
New York, N.Y., pp.1-18.
Winer, W.O. et al. (report committee), 1986. RESEARCH NEEDS IN THERMAL
SYSTEMS. The American Society of Mechanical Engineers, New York, N.Y.
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement