DESALINATION
Desalination 201 (2006) 224-240
www.elsevier.com/locate/desal
Exergy and thermoeconomic evaluation of
MSF process using a new visual package
A. S. Nafeya*, H. E. S. Fathb, A. A. Mabrouka
aFaculty
of Petroleum & Mining Engineering, Suez, Suez Canal University Egypt;
email: asnafey31@yahoo.com, abdul_naser70@yahoo.com,
bFaculty of Engineering, Alexandria University, Egypt; email: h_elbanna_f@yahoo.com
Received 7 January 2005; accepted 26 September 2005
Abstract
This paper presents a methodology of exergy and thermoeconomic analysis for performance of the Multi-Stage Flash
(MSF) process using the developed package. This methodology gets insight on details not available by the first law analysis.
The main target of these analyses is to improve the MSF process as well as to determine the unit product cost of the distilled water.
Using the developed VDS package, the energy analysis of the considered MSF plant in the rating mode (performance),
the gain ratio (GR) is calculated as 7.91. The exergy input, E⭈F, to the MSF plant is calculated as 10.7 MW which represents the exergy of the heating steam, exergy associated to the sea water feed, and electrical pumping power minus the
exergy of the brine heater condensate. Only 0.2 MW of an elevated exergy in the distilled stream is produced. The exergy
associated with blow down and rejection of cooling streams is 4.04 MW which nominated as an exergy loss. The remainder
part of E⭈ D = 6.46 MW is destroyed internally in the plant components as a result the exergetic efficiency of the considered MSF plant, ηII 1.87%. The unit product cost of the MSF desalination plant is calculated as 2.63 $/m3 by two different ways. The first one by calculating the capital and running costs which invested at the boundary of the MSF plant (input
streams); the second way is based on mathematical model (thermoeconomics) by which the outlet streams cost is calculated and charged their value to the desalted water. Thermoeconomic analysis shows that the overall cost of the desalination
plant will be obtained if the exergy destruction rate of the desuperheater, the distiller train is reduced. The monetary cost
of the streams indicated that any modifications in the first stages will cause more effect other than the last stages. Different partial load conditions for the real data of Eoun Mousa MSF plant are depicted and recorded by Data Control System
(DCS). These data are fed to the developed VDS software to investigate the performance of the MSF plant. The distillate
product varies from 104 (50%) m3/h to 208 (100%) m3/h as well as the top brine temperature varies from 86 to 110°C.
The heating steam consumption varies from 12 to 26 m3/h. Thermoeconomic analysis of MSF plant under different partial load conditions showed that the unit product cost increases to 21% when the load decreases to 50% of its design value.
Keywords:
Visual package, design and simulation MSF plant, Exergy, Thermoeconomics.
*Corresponding author
0011-9164/06/$– See front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.desal.2005.09.043
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A.S. Nafey et al. / Desalination 201 (2006) 224–240
1. Introduction
The conservative nature of the MSF desalination plant owner, their large number of operation
and maintenance (O&M) experience, as well as
the strategic characteristics of the product, makes
the MSF process favored over the other competitive thermal desalination methods [2]. Competing
desalination processes such as reverse osmosis
(RO) or vapor compression (VC) which get their
exergy from electricity are nowadays having
some market successes based on better economics and thermodynamic performance, but some
doubts arise from the lack of operating experience
and fouling problems [3]. On the other hand, more
development and innovations by better exergy
utilization are required in the MSF plants. Exergy
analysis is a method that uses the conservation of
mass and energy principles together with the second law of thermodynamics for the analysis, design and improvement of energy systems. Exergy
analysis of major recirculation multi-stage flash
desalting plants in Saudi Arabia is conducted via
a simple scheme [5]. The obtained results show
that the MSF desalting plants are highly irreversible with exergetic efficiency (the sum of all
rates of exergy outflows/the sum of all rates of
exergy inflows) ranging from 1.12–10.38%. Frederick [3] outlined an exergy analysis for the
MSF desalination plant (947 m3/h) of 1970s design, which showed that the second law efficiency
(exergy of distillate stream/the sum of exergy of inflows) of the MSF desalination is calculated as 4%.
Since exergy destruction measures the true
thermodynamic value of irreversibility effect on
the system, it is meaningful to use exergy as a
basis for assigning costs in thermal systems,
which is called thermoeconomics, Bejan et al. [6].
Thermoeconomics is an effective tool to reveal
opportunities for higher efficiency and lower cost
of a system of energy conversion devices [6,7].
Thermoeconomic analysis provides information
about the cost formation process and the flow of
costs in the system. Costing analysis of a com-
bined power (60 MW of electricity) and MSF
desalination plant (18,000 m3/day) was performed based on the exergy concept by Gaggioli
et al. [7]. In that work, the exergetic efficiency
(elevated exergy of distillate stream/ exergy of
inflows streams) of the MSF is calculated as 5%
in summer operation. The mathematical model
considers the money balance for each hardware
component (boiler, turbine, pump etc.) and several different set of auxiliary equations. However,
the model did not consider the distillation plant.
Here, in this regard, the interaction between
cost and efficiency still needs to be investigated
for MSF process. So, this paper presents energy,
exergy and thermoeconomic analysis for MSF
desalination process at different partial loads. The
main target of these analyses is to pinpoint the
locations of the improvement of MSF process as
well as to determine the unit product cost of the
desalinated water.
2. Overview on the VDS package
Using the developed Visual Design & Simulation (VDS) package, different types and configurations of thermal desalination plants can be
manipulated [8]. The object oriented programming
technique is used to build a friendly user-interface.
Different types of calculations such as energy,
exergy, and thermoeconomics can be performed
by the developed VDS package. Modifications in
existing plants can be evaluated. Desalination plant
components (units), such as heat exchangers, flash
chambers, evaporators, pumps, pipes, etc. are stored
as icons in a visual library. Using this visual library, different configurations can be constructed
by just clicking the mouse over the required units
(icons). Fig. 1 shows the brine circulation MSF-BR
plant. To construct such configuration, the designer needs to drag the required units from visual
library and drop it in the panel. Then these icons
(units) are visually arranged similar to the real
plant. A menu bar is created and located at the top
A.S. Nafey et al. / Desalination 201 (2006) 224–240
226
Fig. 1. Panel of process flowsheet of MSF-BR desalination plant.
of a panel which associated with drop-down submenus. The developed menu bar contains the following five submenus:
1. Calculations Mode menu: this menu is linked
with a drop-down sub-menu of (simulation, design, and optimization).
2. Connections menu: this menu is associated
with buttons that enable the user to connect all
units, and plant pipes.
3. Start Calculations menu: enables the user
to select the required type of calculations such
as energy, exergy, cost, and thermoeconomics
analysis.
4. Display Results menu: allows the user to
display the results in the same panel or another
window in both table and chart forms.
5. Print menu: to print the oriented form.
After all units and pipes are connected with
each others the scenario between the user and the
computer is stopped to start the numerical calcu-
lations phase which occurs at the behind of the
panel. The user can change the operating conditions of the desalination plant during run-time.
The desalination process configuration composes
of collective icons (units and pipes) which should
be seen mathematically as a large matrix that
assembled from sub matrices. Composing different configurations means that the location of the
icon (real unit) can change. Mathematically, this
means that the sub matrix elements position will
sequentially change. Therefore, the developed program has the following features:
1. It is a robust code modulates upon the unit
position and type changes.
2. It has a powerful graphic interface to build
up different configurations for different types easily.
3. It has a reliable code based on the sparse
matrices for technique. The details of the package
construction and verification are reported and
illustrated in [8].
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3. Exergy analysis
The specific exergy of a fluid stream with negligible kinetic and potential energies is given by
e = h – h0 – T0(s – s0). Since the saline water is a
mixture of pure water and salt, the properties of
salt must be taken into account along with pure
water properties. The molar specific enthalpy and
specific entropy of a solution can be expressed as
h = xw hw + xs hs and s = xw sw + xs ss – Ru (xw ln xw
+ xs ln xs). The enthalpy and the entropy values
for pure water and the salt in the above relations
are obtained from thermodynamic relations [11].
The reference state for water is T0 = sea water temperature, K, P0 =100 kPa and the state of salt at
0 is taken as reference state. So the exergy point of
certain saline stream is calculated as follows [4]:
e = eph + ech
(1a)
e ph = (Npure + Nsalt)[xw(hw – hw,0) + xs(hw – hs,0) –
T0 (xw(sw – sw,0) + xs(ss – ss,0))]
or
– (T – T ) + x C
–
e ph = Nm[xwC
p,w w
w,0
s p,s (Ts – Ts,0) –
T
p – p0
– ln —
T0(xw (C
– ———
—
—
—) +
p,f
T0 T0 * –ρf f
T
p – p0
xsCp,s ln — – ———
—
—
—)
T0 T0 * –ρf
⭈ = [N
⭈
⭈ ) and T = T = T
let N
+N
m
pure
salt
f
s
Then the above relation becomes:
–
–
⭈ [x C
e ph = N
m w p,w + xsCp,s (T – T0) –
T
–
–
T0[xw (Cp,w + xsCp,s (ln —) –
T0
p – p0
p – p0
(xw + xs )(———
—
— + ———
—
—
—)]]
T0 * –ρs T0 * –ρf
T
e ph = Cp,m (T – T0) – T0[Cp,m(ln —)
T0
p – po
– ———
—
—]
To * –ρm
(1b)
– +xC
–
where Cpm = N⭈ m(xwC
p,m
s p,s ) is mean specific
heat of saline water and
–ρ + –ρ
⭈ (—
w—
s is the density of saline
ρm = N
—
—
—
—
—
—
—)
m
ρf * –ρs
water, and (xw + xs ) = 1.
The chemical exergy is calculated with respect
the sea water composition as follows:
e ch = – N⭈ m RuT0 [(xw ln xw + xs ln xs)↓brine]
(1c)
Substituting Eqs. (1b) and (1c) into equation
(1a) the following equation is obtained
⭈ [e ph + e ch]
E⭈ b = M
b
(1)
By similarly the exergy of the distilled water
can be written as follows:
T
⭈ (C (T – T ) – T (C (ln —)
E⭈ d = M
–
d
p,d
0
0 p,d
T0
p – p0
—
—
—
—
—
—
—
—)) + Md (ΔG)P,T
T0 ρd
(2)
The first term on the right side of the above
equation is related to thermal and mechanical
exergy which calculated from equation 1 by substitute xs = 0 and xw = 1.
The second term is function of the minimum
power required for sea water separation. The minimum power of a material stream is Gibbs free
energy (ΔG)P,T of its composition change. The
minimum work forms a basis for comparison of
actual distillation processes, and the determination of the second-law efficiency. The pure water,
in terms of irreversibility, is expensively obtained
as the minimum work required is 0.936 kWh/m3
relative to Gulf sea water [3]. In another literature
[4], the minimum work input requirement for distillation process is accounted by 0.575 kWh/m3
based on driven relation. Another value is reported by El-Sayed [15], for sea water at 25°C and
45 g/l salt TDS and rejected brine as 65 g/l, of
1.345 kWh/m3.
A.S. Nafey et al. / Desalination 201 (2006) 224–240
228
The exergy rate of the heating steam is determined from the following equation:
⭈ (h – h – T (s – s )
E⭈ = M
(2)
v
v
0
0
0
The thermophysical properties are calculated
based on the relations illustrated in [11]. Based
on Eqs. 1, and 2, the exergy rate of all the process
streams are calculated. Exergy balance analysis
of each unit in the considered process is performed based on the following equation:E⭈ = E⭈ + E⭈ + E⭈
(3)
F
P
D
L
The rate of exergy product E⭈ P represents the
desired result produced by the unit. The rate of fuel
exergy (E⭈ P) represents the resources expended to
generate the product. The difference between the
fuel and product is mainly due to exergy destruction into the system (E⭈ D) and the exergy loss out
of the process (E⭈ L) Bejan et al. [6].
Because of the space limitation, only a flash
chamber unit is illustrated her to show how exergy
balance equations are applied. To understand the
exergy analysis of the flash chamber unit, it may
be divided into three subunits; splitter, mixer and
condenser which are operating in parallel as shown
in Fig. 2. Applying equation 4 the following equation are obtained:
(i) Splitter (brine pool) of the flash chamber:
E⭈ b,1 = E⭈ vapor + E⭈ b,2 + E⭈ D,spliter
(4)
(ii) Heat exchanger of the flash chamber:
E⭈
– E⭈
= E⭈
– E⭈
+ E⭈
cw,5
cw,6
vapor, in
condensate
D,exchanger
(5)
(iii) Mixer (distillate tray) of the flash chamber:
E⭈ + E⭈
= E⭈ + E⭈
(6)
d,3
condensate
d,4
D,mixer
By summing (4), (5), and (6), the exergy destruction in the flash chamber is obtained as:
E⭈ = E⭈ + E⭈ + E⭈ + E⭈ + E⭈
+ E⭈
(7)
D
b,1
b,2
d,3
d,4
cw,5
cw,6
The exergetic efficiency of the flash unit is:
Fig. 2. Schematic diagram of the flash chamber.
( E⭈ d,4 – E⭈ d,3) + ( E⭈ cw,5 – E⭈ cw,6 )
————
—————————
ηII = ——
E⭈ b,1 – E⭈ b,2
(8)
4. Thermoeconomic analysis
4.1. Mathematical modeling
The cost balance of the unit relates the rate of
the expenditures made to generate the product.
The general cost balance equation is written as
follows [6,7]:
C⭈ = C⭈ + Z⭈ CI+OM
(9)
P
F
The above equation shows that the cost rate
associated with the product stream equals the total
rate expenditures C⭈ F and the cost rates associated
with capital investment and operation and maintenance Z⭈ CI+OM.
On this basis, it can be deduced that the cost
balance equations for the flash chamber are:
(i) Splitter (pool brine): Since the inlet brine is
partly vaporized and the remaining brine leaves
the pool with higher salt concentration;
C⭈
= C⭈ – C⭈
+ Z⭈ (CI+OM)
(10)
flashed vapor
b,in
b,out
sp
(ii) Mixer (distillate tray): The condensate of the
flashed vapor is mixed with distilled water of previous stage, so
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A.S. Nafey et al. / Desalination 201 (2006) 224–240
(CI+OM)
C⭈ d,out = C⭈ d,in – C⭈ condensate + Z⭈ mix
(11)
(iii) Preheater/condenser: The incoming cooling
water temperature is increased at the expense of
the condensation of the flashed vapor.
C⭈
– C⭈
= C⭈
– C⭈
+ Z⭈ (CI+OM)
cw,out
cw,in
flashed vapor
condensate
hx
(12)
Summing up Eqs. (10), (11) and (12); the following equation is obtained for the overall cost
balance of flash chamber;
– C⭈ b,in + C⭈ b,out + C⭈ cw,out – C⭈ cw,in + C⭈ d,out –
C⭈ = Z⭈ (CI+OM)
(13)
d,in
As there are three outlet streams from each flash
chamber, two additional auxiliary equations are
required. The first auxiliary equation states the
equality of the average cost of the inlet and exit
brine.
C⭈ b,in C⭈ b,out
—
—
—–—
—
—
—=0
(14)
E⭈
E⭈
b,in
b,out
The second auxiliary equation states the equal
average cost of the flashed vapor and its condensate; i.e
C⭈ flashed vapor C⭈ condensate
—
—
——
——
—
—–—
—
———
—
—=0
(15)
E⭈
E⭈
flashed vapor
b,out
(i) Capital cost
Purchased equipment cost (PEC) = $7.7 × 106
Working capital investment (WCI) = $530 ×
103.
Intake system, [9] = 300$/(m3/day) × 5000 =
1.5 × 106 $
The total capital investment TCI = 9.73 × 106 $
Annual capital investment = TCI × CRF
Table 1
Operating conditions for Aoun Mousa MSF desalination
plant [12]
condensate
By substituting equations 10, 11 and 12 into
equation 15 thus;
C⭈ b,in – C⭈ b,out C⭈ d,out – C⭈ d,in
—
—
——
——
——
— – —⭈—
—
——
——
—— = 0
(16)
E⭈ – E⭈
E
– E⭈
b,in
the sum of the fixed capital cost depreciation rate
(FCCDR) per year and the annual operation and
maintenance (O&M) cost. The FCCDR is estimated
from the sum of individual capital items costs divided by the effective life period. The annual O&M
cost is the sum of individual annual costs necessary for operation of the desalination plant. The
annual operating and maintenance cost expenses
(OMC) include the operating Electricity, labor,
maintenance labor, maintenance materials, chemicals, and the cost of the consumed steam. A
recent tender of 5000 m3/day of MSF desalination
plant [12], is used to calculate the unit product
cost as shown in Tables 1, 2 and 3.
d,out
d,in
Following the same sequence, three equations
similar to Eqs. (13), (14) and (16) are generated
by VDS program according to the stages number.
4.2. Estimation of unit cost of the desalted water
The annualized cost expenses for production
of fresh water per year are simply based on both
Variables
Design data
Sea water feed, m3/h
TBT, °C
Make up, m3/h
Brine circulation flow, m3/h
Sea water temperature, °C
Heating steam, °C
Heating steam pressure, bar
Recycle splitter ratio, α1
Blow down splitter ratio, α2
Brine heater surface area, m2
Area of heat recovery section
Area of heat rejection section
1370
110
660
1847
27
205
7
0.724
0.482
780
17 × 488
3 × 357
A.S. Nafey et al. / Desalination 201 (2006) 224–240
230
Table 2
Chemical cost and dosing rate [13]
Chemical
Unit cost ($/kg)
Dosing rate (g/ton) of make up
Cost rate $/h
Sulfuric acid
Caustic soda
Anti-scalant
Chlorine
Total
0.504
0.701
1.9
0.48
—
24.2
14
4
4
—
24.2 × 660/1000 × 0.504 = 7.92
14 × 660/1000 × 0.701 = 6.47
4 × 660/1000 × 1.9 = 6.27
4 × 660/1000 × 0.482 = 1.2
21.93
Table 3
Capital cost of the MSF-BR desalination plant (5000
m3/day) [ 12]
Item
Cost, $
Capital cost
Lump sum price for designing,
furnishing, fabricating, testing, and
demisters, delivery including
evaporator trains with ejectors,
strainers, heat exchangers,
condensers, pumps and motors,
chemical feed systems, electrical
equipments and control systems,
chemicals for normal operation
and control room.
7.7 × 106
Salaries and wages during start up,
payroll taxes, insurance and plant
overhead, air travel.
103,112
Lump sum price for off-shore training
of owner’s personnel.
12,684
Lump sum price for job site training
of owner’s personnel.
19,054
Provisional sum
398,290
Total purchased order price
8.23 ×
Intake cost, $
1.5 × 106
Sub total, $
9.73 × 106
Grand total
11.68 × 106
Hourly depreciated cost, $/h
119
where the capital recovery factor (CRF) is given
by:
i × (1 + i)n 0.05 × (1 + 0.05)20
CRF = —
—
—
—
—
—
—
—
—
—
—
—
—
—
—=—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
— = 0.08
(1 + 0.05)20 – 1
(1 + i)n – 1
(18)
Interest rate, i = 5%
Amortization year, n = 20 years
The annual capital cost rate = 9.73 × 106 × 0.08
= 778,400 $/year.
Multiplying this figure by a cost index of 1.2 [17],
the annual capital cost in the time of evaluation is
calculated as:
106
The total annual of depreciation capital cost,
FCCDR = 934,080 $/year.
(ii) Annual operation and maintenance cost
(OMC)
Cost of extracted steam to MSF process =
347/26 = 13.36 $/m3, see appendix A. The cost
of extracted steam =13.4 ($/ton) × 26.5 (ton/h) ×
24 × 365 × 0.9 = 2,799,608 $/year
Specific cost of electricity = 33,423/
(320,000) = 0.1 $/kWh, see appendix A
Electricity cost = 0.1 ($/kWh × Power × 24 ×
365 × plant factor = 0.1 × 590 × 24 × 365 × 0.9 =
465,165 $/year
The reminder item of OMC per year of operation can be calculated as follows:
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A.S. Nafey et al. / Desalination 201 (2006) 224–240
The performance of a distillation plant depends
mainly on the overall heat transfer coefficient of
the evaporators and brine heater. The overall heat
transfer coefficient is affected by the fouling on
the tube surface. Therefore scale prevention is one
of the indispensable techniques in distillation processes. The distillation plant with high temperature additive treatment for feed make up sea water
is designed to have the maximum brine temperature of 110°C and recirculating brine circulation
of 63,000 ppm as shown in Table 1. The injection
Belgard EV is recommended to make up flow rate
for the reduction of bicarbonate ion in sea water
flow rate. The formation of alkaline scale of calcium carbonate and magnesium hydroxide over a
long period of operation can be prevented by the
use of acid cleaning. The chemical consumption and
dosing rate and their cost are given in Table 2.
The rate of chemical consumption and cost is
shown in Table 2.
Chemicals cost = 22 ($/h) × 24 × 365 × 0.9 =
173,448 $/year
The total annual operation and maintenance
cost = 3,438,221 $/year
The total annual cost = 934,080 +3,438,221 =
4,372,230 $/year
The unit product cost = 4,372,230/(5000 × 365
× 0.9) = 2.63 $/m3.
5. Thermoeconomic variables
Following the above analysis, the developed
VDS program is utilized to calculate the plant
streams cost flow rate. The cost flow rate of the
plant streams give an idea about the cost distribution, however, it does not help to take a decision.
So these results are processed in calculating the
thermoeconomics variables ηII cp, cF, CD, Z CI+OM,
r, f. For the sake of demonstration, the flash chamber is considered to define thermoeconomic variables as follows:
• Cost of the unit heating surface area, (Z⭈ CI+OM,
$/h)
The capital investment and operation and maintenance terms Z⭈ CI+OM is calculated for flash evaporator as follows:
The purchased cost of the pumps can be calculated from the following equation [14]:
PEC = 32000 × 0.000435 × M 0.65 ×
ηp
ΔP 0.55 × ———
—
1 – ηp
冢
冣
(20)
where M is the brine mass flow rate (kg/s), in kPa,
is the pump efficiency.
Based on this equation the purchased cost of
the feed pump, brine circulation pump, distillate,
and blow down pump are calculated as
Purchased equipment cost (PEC)
= $264,660
Working capital (WC) = 0.2 × 264,660 = $52,932
The total annual cost of the pumps = $317,592
The hourly cost = 317,292 × 0.13/(365 × 24 × 0.9)
= 5.2 $/h.
By excluding the cost of intake and the cost of
pumps, the cost of heating surface area is calculated as = 119 – (15 + 5.2) = 98.8 $/h. The cost per
unit surface area is calculated as follows:
98.8
Z⭈ CI+OM = ——
—— × heating surface area (m2)
10147
$/(hr.m2)
• Average cost per exergy unit of fuel (cF, $/GJ).
This variable represents the average cost at
which each exergy unit of fuel is supplied to the
flash chamber. This can be expressed as follows:
C⭈ f
C⭈ b,in – C⭈ b,out + C⭈ d,in
1000
cF = —⭈— = —
—
—
——
——
—
—
——
——
—— × —
——
—
— (21)
⭈
⭈
⭈
E
E –E
+E
3600
F
b,in
d,out
d,in
• Average unit cost of product, (cP). This represents the average cost at which each exergy unit
of the product of the flash chamber is generated.
C⭈
C⭈
– C⭈
+ C⭈
1000
P
cw,out
cw,out
d,out
A.S. Nafey et al. / Desalination 201 (2006) 224–240
cP = —⭈— = —
——
——
———
—
——
———
—— × —
——
— (21)
EP
E⭈cw,out – E⭈cw,out – E⭈d,out 3600
• Cost of exergy destruction (cD , $/h). The cost
associated with the exergy destruction in a process is a hidden cost. It can be revealed only as
follows:
C⭈ D = cF × E⭈ D
(23)
• Relative cost difference, r. This variable expresses the relative increase in average cost per
exergy unit between fuel and product of the component. This is expressed as:
cP – cF
r=—
—
—
—
—
—
—
—
—
—
cF
Exergy input
E⭈F
Unit product cost, $/m 3, C⭈w =
C⭈distilled + C⭈loss ($/h) C⭈disalted_water + C⭈L
——
——
—
——
—
——
—
——
—— = ——
——
—
—⭈—
—
——
—
——
Distilled flow rate
Md
Brine circulation ratio, BCR =
Brine recycle flow rate
——
——
—
——
——
—
—
——
———
—
——
——
Distilled output flow rate
6. Results and discussion
6.1. Design conditions
(24)
• Exergoeconomic factor. It expresses the contribution ratio of the non-exergy-related cost to the
total cost increase:
Z⭈ (CI+OM)
f=—
—
——
—
——
——
—
——
——
—
——
—
—
Z⭈ (CI+OM) + cF (ED + E⭈L)
232
(25)
Eoun Mousa desalination plant is a brine circulation MSF-BR process as shown in Fig. 1. To
perform the exergy and thermoeconomic analysis, the mass flow rate, temperature, pressure,
entropy, and cost of the process streams are
required. The VDS package is utilized to solve
mass, pressure, and energy equations iteratively
to obtain the mass, temperature and pressure
of the state points in the MSF system, then the
exergy flow rate of the streams is calculated. The
cost balance equation model is solved to obtain
the monetary cost flow rate of the streams.
The following parameters are calculated for
the overall plant performance analysis:
⭈
Distilled flow rate
M
d
Gain ratio, GR = ——
——
—
——
——
—
——
—–— = —
—
—
⭈
Steam flow rate
Ms
Exergy output
E⭈P
Exergetic efficiency, ηII = ——
——
—
——
——
—— = —
—
—
The recycle brine splitter ratio α1 and the blow
down brine splitter ratio α 2 are adjusted to set the
make up flow rate by 660 m3/h as well as to set
the brine circulation flow rate as 1847 m3/h. The
VDS package results of stream mass balance,
temperature, pressure, exergy, and monetary cost
are illustrated in the panel as shown in Fig. 3. This
panel also shows the main parameters such as
gain ratio (GR), exergetic efficiency, ηII , surface
area, and unit product cost. The energy analysis
of the considered MSF plant in the rating mode
(performance) shows that the gain ratio (GR) is
calculated as 7.91 as shown in Fig. 3.
The overall Exergy flow rate of the main variables is presented in Table 4. The exergy input, E⭈F,
of 10.7 MW represents the exergy of the heating
steam, exergy associated to the sea water feed,
and electrical pumping power minus the exergy
Table 4
Exergetic variables for MSF-BR process
Exergy flow rate
Calculated values
⭈
EF, MW
⭈
EL, MW
⭈
ED, MW
⭈
EP, MW
ηII
10.7
4.04
6.46
0.2
1.87
233
A.S. Nafey et al. / Desalination 201 (2006) 224–240
Fig. 3. Energy, exergy, cost results of the developed VDS package.
irreversibility’s, pressure drops in valves and tubes.
The exergetic efficiency of the MSF,
E⭈ P 0.2
—
——
——— = 0.0187.
ηII = —
E⭈ 10.7
F
Fig. 4. Exergy analysis of the overall MSF desalination
plant.
of the brine heater condensate, see Fig. 4. Only
0.2 MW of an elevated exergy in the distilled
stream is produced. The exergy associated with
blow down and rejected of cooling streams is 4.04
MW which nominated as an exergy loss. The
reminder part of E⭈D = 6.46 MW is destroyed internally in the plant components due to heat transfer
The exergetic efficiency and the exergy destruction of MSF flash chambers are presented in
Figs. 5a and 5b. These figures are in consistent to
show that low exergetic efficiency of the first and
last stages is mainly due to the exergy destruction
in these stages.
The exergetic efficiency and exergy destruction of the overall MSF plant units are given in
the first two columns in Table 5. The results show
that desuperheater, flash chambers, feed pump
and recirculation pump have lower exergetic efficiency (ηII ). This table shows that most exergy
destruction is occurred in the flash chambers.
Based on the items of Tables 3 and 6, the unit cost
of the product water for MSF-BR desalination
A.S. Nafey et al. / Desalination 201 (2006) 224–240
234
b
a
Fig. 5. a. Exergy destruction in flash chambers. b. Exergy efficiency of flash chambers.
Table 5
Thermoeconomic results of conventional MSF-BR
Unit
Desuperheated
brine heater 0
Distilate pump
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
Stage 6
Stage 7
Stage 8
Stage 9
Stage 10
Stage 11
Stage 12
Stage 13
Stage 14
Stage 15
Stage 16
Stage 17
Circu. pump
Brine mixer 1
Stage 18
Stage 19
Stage 20
FEED pump
B/D pump
Exergy
efficiency
0.77
0.72
0.70
0.82
0.87
0.87
0.88
0.88
0.88
0.89
0.89
0.88
0.88
0.87
0.87
0.85
0.83
0.81
0.78
0.73
0.82
1.00
0.80
0.80
0.80
0.78
0.67
Exergy
destruction
cf
cp
CD
Z
CD +Z
MW
$/GJ
$/GJ
$/h
$/h
$/h
1.55
1.08
0.01
0.37
0.24
0.21
0.19
0.17
0.16
0.15
0.13
0.12
0.12
0.11
0.11
0.11
0.11
0.11
0.11
0.11
0.08
0.02
0.17
0.17
0.17
0.03
0.01
14.90
18.13
31.66
57.77
64.79
68.36
71.97
75.65
79.45
83.41
87.62
92.16
97.13
102.67
108.97
116.26
124.87
135.26
148.08
164.32
32.79
33.53
68.93
68.93
68.93
22.10
27.78
19.44
25.97
44.93
71.95
75.67
79.39
83.19
87.12
91.26
95.72
100.61
106.09
112.37
119.71
128.52
139.33
152.98
170.79
194.55
229.47
39.94
33.64
84.03
84.03
84.03
43.06
47.60
83.05
70.52
1.53
77.93
54.98
52.99
49.85
47.48
45.36
43.50
42.25
41.40
41.13
41.52
42.67
44.70
47.79
52.15
58.15
66.38
8.92
2.72
41.64
41.64
41.64
2.20
1.47
0.00
10.26
0.64
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
6.42
7.62
0.00
4.69
4.69
4.69
2.53
0.68
83.05
80.77
2.17
84.35
61.40
58.81
56.27
53.90
51.78
50.01
48.66
47.82
47.55
47.94
49.09
51.12
54.20
58.57
64.57
72.72
16.54
2.72
46.34
46.34
46.34
4.72
2.15
r
f
0.23
0.43
0.30
0.20
0.14
0.14
0.13
0.13
0.13
0.13
0.13
0.13
0.14
0.14
0.15
0.17
0.18
0.21
0.24
0.28
0.18
0.00
0.18
0.18
0.18
0.49
0.42
0.00
0.13
0.29
0.08
0.10
0.11
0.11
0.12
0.12
0.13
0.13
0.13
0.13
0.13
0.13
0.13
0.12
0.11
0.10
0.09
0.46
0.00
0.10
0.10
0.10
0.53
0.32
235
A.S. Nafey et al. / Desalination 201 (2006) 224–240
Table 6
Hourly operation and maintenance cost
Items
Value
Chemical cost, $/h
Steam cost, $/h (40 $/barrel)
Electrical cost, $/h (40 $/barrel)
Sub total, $/h
22
354
55
431
Table 7
Summarized cost data for the computer package
The capital and O&M cost
flow rate per m2
Specified cost of the inlet steam
Electrical cost
Cost of seawater feed (intake)
0.0097 $/h m2
13.4 $/ton
0.1 $/kWh
15 $/h
plant of 208 m3/h, is calculated by another way as
follows:
The unit product cost = (capital cost ($/h) +
running cost ($/h))/capacity (m 3/h)
or
Running cost, C⭈F = C⭈steam + C⭈electrical + C⭈chemical
Capital cost, Z⭈
= 119 $/h
= 354 + 55 + 22 = 431 $/h
C⭈F + Z⭈ 431 + 119
Cost of disalted water = ——
——
—
— = ——
—
——
——
—
—
208
208
= 2.63 $/m 3
thermoeconomic results shows that the cost flow
rate of cooling water stream (feed + recycled) increases and reaches its maximum value at the inlet
to the brine heater. Inversely, the cost flow rate of
the brine stream decreases and reaches its minimum value at the exit of the last flash stage that is
due to the exergy loss of the flashed vapor. These
results also indicate that any modifications in the
first stages will cause more effect other than the
last stages.
By using thermoeconomic mathematical model,
the cost at the boundary of the MSF system is distributed on the internal streams. The over all stream
costs of the MSF desalination plant of 5000
m3/day are shown in Fig. 6. The unit cost of the
product is calculated based on the outlet streams.
The cost of both the cooling water reject and the
brine blow down streams are charged to the cost
of the distillate stream. The cost of the brine blow
down is obtained as 373 $/h as shown Fig. 6. The
cost of desalted stream is obtained by 175 $/h.
C⭈distilled_water
= 175 $/h
C⭈L = C⭈blowdown = 373 $/h
C⭈distilled + C⭈ L
Cost of disalted water = ——
——
—
——
——
—
—
208
175 + 373
= ——
——
——
—
— = 2.63 $/m 3
208
The cost of the exergy destruction, C⭈D, inside
the MSF is calculated as follows:
C⭈ F
1000
431
1000
However, this method does not show how to
minimize the unit cost. In other word, it gives no
information about the monetary cost in the plant
streams or how the expenditure cost is invested.
Fortunately the thermoeconomics can.
The summarized cost data of Table 7, are calculated by the VDS program and utilized to calculate the plant streams monetary cost flow rate. The
Fig. 6. Cost analysis of the overall MSF desalination
A.S. Nafey et al. / Desalination 201 (2006) 224–240
cF = —⭈— × —
——
—
— = ——— × —
——
—
— = 11.2 $/GJ
EF
3600
10.71 3600
C⭈D = cF × E⭈D = 11.2 × 6.46 × 3.6 = 262 $/h
Table 5 summarizes the thermoeconomic variables which are calculated for each component of
the MSF system under the considered design conditions. These variables include the exergetic efficiency, rate of exergy destruction, average costs
per unit fuel exergy cF, product exergy cp , cost
rate of exergy destruction C⭈D, investment and O
& M cost rate Z⭈ CI+OM, relative cost difference (r),
and exergoeconomic factor ( f). This table shows
that the distiller train generally has the highest
values of the sum Z⭈ + C⭈D in the conventional MSF
configuration especially the first stage, however
the desuperheater and brine heater come in the
next sequence. Therefore, these are the most important components to be considered for improvement from the thermoeconomics of point view.
The zero value of the exergoeconomic factor ( f)
for the desuperheater shows that the costs associated with the desuperheater are almost exclusively due to exergy destruction. The relatively
high values of ( f) in the brine heater, circulation
pump, feed pump, blow down pump, and distillate pump suggests a reduction in the investment
costs of these components. The desuperheater,
first, last stage, and brine recirculation pump have
the lowest exergetic efficiency value and the highest relative cost difference (r) value. Thus it might
be concluded that a decrease of the exergy destruction and capital cost in these components
could be costly effective for the entire MSF plant.
6.2. Partial load analysis
The MSF plant is adjusted to either partial load
operation or shut down mode by controlling the
rate of the heating steam source to count the distillate tank capacity limitation. Different partial
load conditions for the real data of Eoun Mousa
MSF plant are depicted and recorded by Data
236
Control System (DCS). These data are fed to the
VDS software to investigate the performance of
the MSF plant.
The distillate product varies from 104 (50%)
m3/h to 208 (100%) m3/h as well as the top brine
temperature varies from 86 to 110°C. The heating
steam consumption varies from 12 to 26 m3/h. The
calculated results of energy analysis are given in
Table 8, while the exergy analysis and thermoeconomic analysis are given in Tables 9 and 10
respectively.
Table 8 shows that the gain ratio increases
slightly with the decreasing the load and the brine
circulation ratio (BCR) increases rapidly. This is
mainly due to the decrease in the heating steam
temperature at which the latent heat of evaporation is increased. As a result the steam consumption will decrease. Table 8 shows also that the top
brine temperature (TBT) decrease with decreasing the load. This is due to the decrease of the
heating steam temperature. Table 8 showed also,
the salinity of the recycle stream (xrecycle) increases with the decrease of the load. This is mainly
due to the increase of the brine circulation ratio
(BCR).
Table 9 shows the exergy analysis at different
loads of MSF desalination plant based on the VDS
results of energy analysis. This table shows that
the exergy input to the MSF process decreases
with the decrease of the load. This is due to the
decrease in the steam consumption (slight increase of the gain ratio is obtained), as well as the
decrease in pumping power. The exergy associated with the distilled stream also decrease with
the decrease of the MSF capacity. This is mainly
due to the decrease in the product flow rate as well
as the distillate temperature (physical exergy).
The exergetic efficiency, ηII, decreases with the
decrease of the MSF capacity which indicates that
under these conditions, the exergy output is the
dominant.
The exergy associated to both the rejected cooling water and the blow down brine increases with
the decrease of the plant capacity. This is owing to
237
A.S. Nafey et al. / Desalination 201 (2006) 224–240
Table 8
Calculated results of partial load of MSF-BR desalination plant
Load
100%
90%
75 %
63%
50%
Mdistilled, m3/h
GR
Mfeed*, m3/h
Mmake up, m3/h
BCR
xfeed*, g/1
xrecycle, g/1
xreject, g/l
Tsteam*, °C
Tfeed*, °C
Tdesuperheater*, °C
TBT, °C
Tb,in*, °C
α1
α2
208
7.91
1370
660
8.86
45
63
70
205
27
113
109
101
0.482
0.72
185
8.2
1636
469.5
9.3
45
66
74
191
27
107
104
96
0.287
0.81
158
8.1
1620
405
10
45
67
74
165
27
100
98.8
90
0.25
0.83
132
8.22
1645
345
12.4
45
66
73
193
27
93
91
85
0.21
0.84
104.8
8.5
1670
265
12
45
68
74
172
27
87
85.8
80
0.16
0.86
*Specified parameter
Table 9
Exergy analysis at different partial load of MSF-BR plant
⭈
EF, MW
⭈
EL, MW
⭈
ED, MW
⭈
EP, MW
ηII, %
Table 10
Thermoeconomic analysis of MSF-BR at part load operation
100%
90%
75%
63%
50%
Variable
100% 90% 75% 63% 50%
10.7
4
6.46
0.2
1.87
10.9
4.72
5.95
0.19
1.75
10
4.65
5.34
0.16
1.58
9
4.69
4.23
0.12
1.33
8.3
4.74
3.44
0.1
1.21
Expenditure, $/h
Capital investment,
Z, $/h
Sub total, $/h
Distillate product, m3/h
Unit product cost, $/m3
431
387
327
275
119
550
208
2.63
119
506
185
2.74
119
446
158
2.82
119
394
132
2.98
the increase of the feed flow rate while decreasing
of the distillate product. The decrease in the exergy
destruction during the decrease of the capacity is
119
339
104
3.2
explained by the decrease of the irreversibility of
heat transfer.
Thermoeconomic analysis of partial loads for
MSF is shown in Table 10. This table shows that
A.S. Nafey et al. / Desalination 201 (2006) 224–240
the rate of the expenditure cost (C⭈F) decreases
with the decreasing of the load. This is due to the
decrease in steam consumption, chemicals cost
and electrical requirements. The capital invest⭈ is fixed with the load variation, as there
ment (Z)
is no change in MSF configuration. As a results,
the unit cost of the product increases with the
decrease of the load. The unit product cost increases by 21% when the load decreases to 50%
of its design value. This result indicated that the
operation at partial load is not recommended from
the cost point of view. It should be noted that the
unit product cost increases while the exergetic
efficiency (ηII) decreases. This result is in consistence with philosophy of the improvement which
ascertains that the operation at part load is not
preferable.
lated and charged their value to the desalted water.
Thermoeconomic analysis shows that the cost of
the overall the desalination plant will be obtained
if the exergy destruction rate of the desuperheater,
the distiller train is reduced. The monetary cost of
the streams indicated that any modifications in the
first stages will cause more effect other than the
last stages. Different partial load conditions for the
real data of Eoun Mousa MSF plant are depicted
and recorded by Data Control System (DCS).
These data are fed to the developed VDS software
to investigate the performance of the MSF plant.
The distillate product varies from 104 (50%) m3/h
to 208 (100%) m3/h as well as the top brine temperature varies from 86 to 110°C. The heating
steam consumption varies from 12 to 26 m3/h.
Thermoeconomic analysis of MSF plant under
different partial load conditions showed that the
unit product cost increases to 21% when the load
decreases to 50% of its design value.
7. Conclusion
Using the developed VDS package, the energy
analysis of the considered MSF plant in the rating
mode (performance), the gain ratio (GR) is calculated as 7.91. The exergy input, E⭈F, to the MSF
plant is calculated as 10.7 MW which represents
the exergy of the heating steam, exergy associated
to the sea water feed, and electrical pumping power
minus the exergy of the brine heater condensate.
Only 0.2 MW of an elevated exergy in the distilled stream is produced. The exergy associated
with blow down and rejected of cooling streams
is 4.04 MW which nominated as an exergy loss.
The reminder part of E⭈D = 6.46 MW is destroyed
internally in the plant components as a result the
exergetic efficiency of the considered MSF plant,
ηII 1.87%. The unit product cost of the MSF desalination plant is calculated as 2.63 $/m3 by two
different ways. The first one by calculating the capital and running costs which invested at the boundary of the MSF plant (input streams); the second
way is based on mathematical model (thermoeconomics) by which the outlet streams cost is calcu-
238
Nomenclature
C⭈ — cost flow rate, $/h
c
Cp
E⭈
e
f
h
P
⭈
M
⭈
Nm
s
T
Ru
r
x
⭈
W
⭈
Z
ρ
–ρ
— cost per unit exergy, $/GJ
— Molar specific heat, J/kmol.k
— Exergy flow rate, MW
— Specific exergy, kJ/kg
— Exergoeconomic factor
— Specific enthalpy, kJ/kg
— Pressure, kPa
— Mass flow rate, kg/s
— Molar flow rate of saline water
— Specific entropy, kJ/kg
— Temperature, K
— Universal gas constant, J/kmol.k
— Relative cost difference
— Mole fractions
— Power, MW
— Rate of the capital cost
— Density, kg/m3
— Molar density, kmol/m3
239
A.S. Nafey et al. / Desalination 201 (2006) 224–240
ηII — Exergetic efficiency (second law
efficacy)
Superscripts
CI — Capital investment
OM— Operation and Maintenance
Ph — physical
Ch — chemical
Subscripts
0 — Dead state
b — Brine water
cw — cooling water
D — Destruction
d — Distillate
F — Fuel
L — Loss
m — Mixer of pure and salt water
p — Product
s — salt water
v — Vapor
w — Pure water
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
References
[1] International Desalination Association (IDA) World
Wide Desalting Plants Inventory, report No. 16
(2000).
[2] A. Al-Shuaib, M. Al-Bahu, H. El-Dessouky and H.
Ettouney, Progress of the Desalination Industry in
Kuwait. IDA, 1999.
[3] B. Frederick, Combined Power and Process: An
Exergy Approach. Mechanical Engineering Publications Limited London, 1995.
[4] C. Yunus, The minimum work required for distillation
process. Exergy, 2 (2002) 15–23.
[5] F. A. Al-Sulaimman and B. Ismail, Exergy analysis
of major recirculating multi-stage flash desalting
plants in Saudi Arbia. Desalination, 103 (1995)
265–270.
[6] A. Bejan, G. Tsatsaronis and M. Moran, Thermal Design & Optimization. Wiley, 1996.
[7] R. A. Gaggioli, Y. M. Elsayed, A. M. El Nashar and
B. Kamaluddin, Second law efficiency and costing
[17]
analysis of a combined power and desalination plant.
Journal of Energy Resources Technology, 1988.
A. S. Nafey, H. S. Fath, A. A. Mabrouk and M. A.
Elzzeky, A new visual computer package for simulation of thermal desalination processes: development and verification. Eight International Water
Technology Conference, Alexandria, Egypt, 2004.
H. N.Ali and H. A. Arafa, Effect of desalination
plant performance on water cost in dual-purpose
plant for production of water and electricity. Fifth
International Water Technology Conference, Egypt,
2000.
S. H. Fath, Desalination Technology. El dar Elgameia,
Alexandia, 2000.
A. S. Nafey, Design and simulation of seawater thermal desalination plants. Leeds University Ph. D., 1988.
Babcock and Hitachi, Operation and Maintenance
Manual of Eoun Mousa Desalination Plant. Egypt,
1998.
H M. Ettouney, H. T. El-Dessouky, R. Faibish and
P. Gowin, Evaluating the economics of desalination.
CEP Magazine, 2002.
Y. M. El-Sayed, Designing desalination systems for
higher productivity. Desalination, 134 (2001) 129–158.
Y. El-Sayed, The future of solar desalination. Fifth
International Water Technology Conference, Alexandria, Egypt, 2000.
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Appendix (A)
Fig. A.1. Design conditions of DDP boiler.
A.S. Nafey et al. / Desalination 201 (2006) 224–240
Cost of heating steam and electricity
The cost of heating steam is the main item of
operating & maintenance cost of desalination
plant. Eoun Mousa MSF desalination plant uses
an extracted steam (7 bar and 205°C) of a power
plant turbine. The generated steam at a high pressure (170 bar and 540°C) form the steam generator is utilized to produce work before its use as
a heat source for the MSF process. The fuel used
to produce this steam should be charged to two
products (i.e. desalted water and power) according
certain rules, Darwish et al. [16]. In this work a rational basis based on the exergy (available energy)
method is utilized. The dual purpose plant (DPP)
boiler is supplied with fuel energy, Qf , in order
to raise the availability (exergy) of water steam
flowing through the boiler. The design conditions
of DDP boiler is 320 MW power and 5000 m3/day
desalted water as shown in Fig. A.1.
The specific enthalpy, entropy, and exergy flow
rate for all inlet and exit streams are calculated by
using VDS package.
The exergy of the boiler product is calculated as
follows:
E⭈
= (E⭈ – E⭈ ) + (E⭈ – E⭈ ) =
P,boiler
2
1
4
3
(446 – 780) + (414 – 312) = 470, MW
(A.1)
The exergy of the extracted steam is calculated as
follows:
E⭈
= 7 × [(2850 – 105) – 300 ×
ext,steam
(6.9 – 0.35)] = 5.6 MW
Based on the rational basis, the ratio of the fuel
charged to the MSF process is calculated as follows:
E⭈ ext,steam
5.63
——
—
— = ——
—
—=
Qf,MSF = Qf,boiler × ——
⭈
E
470
p,boiler
0.01198 × Qf,boiler
Where, Qf,MSF is the fuel charged to the boiler and
is calculated as follows:
240
M⭈ s × [(h2 – h1) + (h4 – h1)]
——
—
————
—
————
—
————
—
—
Qf,boiler = ——
ηb
302 × [(3394 – 1086) + (3560 – 2950)]
= ————
—
———————
—
————
—
————
—
————
—
—
0.92
= 958 MW
Assuming the cost of a typical processed oil barrel
is $40/barrel which produce 5.71 GJ of thermal
energy when burning.
Cost of fuel charged to the DDP boiler =
(40/5.71) × 0.958 = 6.71 $/s.
The cost of heating steam can be assumed to be
20% more than the consumed fuel to obtain that
energy due to the use of boilers and running costs,
[16]. So the cost of the fuel charged to the MSF
process = 0.01198 × 6.71 × 1.2 = 0.0958 $/s.
Cost of extracted steam to MSF process =
347/26=13.36 $/m3.
The cost of energy added in electrical (or mechanical) form is considered equal to 40% more
than the cost of fuel consumed in order to obtain
that energy by the use of a power plant consisting
of a boiler, turbine, generator, distribution lines,
etc. [16].
Cost of the fuel charged to the power =
(1 – 0.01198) × 6.71 × 1.4 = 9.28 $/s.
Cost of electricity = 9.28 × 3600 = 33,413 $/h
Specific cost of electricity = 33,423/(320,000) =
0.1 $/kWh