Final report 412

KING FAHD UNIVERSITY OF
PETROLEUM & MINERALS
Mechanical Engineering
Department
(152)
Senior Design Project
Design Project
ME 412/416
Balancing of water VS Electricity generation (Rankine-MSF)
Name: Alkathiri, Ali Ahmed ID# 201158730
Name: Julaidan, Mohammed ID# 201168370
Name: Alhujaili, Amjad ID# 201050560
Name: ID#
Name: ID#
Advisor Name:
MOHAMMED A. ANTAR
Coordinator Name:
26/04/2016

ii
EVALUATION SHEET
Editorial Structural
Criteria Evaluation Criteria Evaluation Criteria Evaluation Criteria Evaluation
Cover page*
Introduction
Overview
Final Design
Overall description
Conclusion &
Recommendation
Conclusion*
Title*
Problem
definition*
Detailed design description Recommendation*
Abstract* Objectives* Analysis & results*
Appendices
Decision matrix
Table of
contents*
Project
management*
Material selection Gantt chart*
List of figures
Background
Existing product Cost analysis
Final drawing
List of table Market research Drawings
List of vendors, contact
information and pricing
Heading Technical data*
Product
Realization
Manufacturing processes
Specification for
supplied materials
Language Patent search
Prototype verses planned
design
Detailed supporting
analysis
Figure/table
Design &
Development
Conceptual
design
Manufacturing processes
Captions
List of
constraints* Future manufacturing
recommendation
Final Report Score
List of standards*
Figure/table
citation Concept selection
Design
verification
Test description
References
Preliminary
analysis*
Detailed results
Proof of concept Specification verification list
Items in (red) with asterisks (*) are mandatory.

ME 412 | Balancing of water VS Electricity generation (Rankine-MSF)

1

Table of Contents
List of tables: ..................................................................................................................... 2
List of figures: .................................................................................................................... 2
Chapter 1: ......................................................................................................................... 3
Introduction: ..................................................................................................................... 3
1.1 Power Plant: .................................................................................................................... 3
Classification of power station: ................................................................................................... 3
1.1.1 By heat source: [1] .......................................................................................................... 3
1.1.2 By prime mover: ............................................................................................................. 3
1.1.3 By duty (scheduled): ....................................................................................................... 4
1.2 Desalination Plant: .......................................................................................................... 5
1.2.1 Types of distillation process: .......................................................................................... 5
1.2.2 How it works: .................................................................................................................. 6
1.2.3 Challenges: ..................................................................................................................... 7
1.3 Objective: ........................................................................................................................ 7
Chapter 2: ......................................................................................................................... 8
2.1 Power Plant: .................................................................................................................... 8
2.1.1 Boiler: ........................................................................................................................... 10
2.1.2 High Pressure Turbine: ................................................................................................. 10
2.1.3 Low Pressure Turbine: .................................................................................................. 11
2.1.4 Condenser: ................................................................................................................... 12
2.1.5 Open Feed Water Heater: ............................................................................................ 12
2.1.6 Closed Feed Water Heater 2: ....................................................................................... 13
2.1.7 Closed Feed Water Heater 1: ....................................................................................... 14
2.2 Desalination Plant: ........................................................................................................ 15
2.1.1 Mass balance modeling: ............................................................................................... 17
2.1.2 Temperature Drop Modeling: ...................................................................................... 18
2.1.3 The Temperature at each Stage: .................................................................................. 18
2.1.4 Heat transfer areas: ...................................................................................................... 18
2.1.5 Flashing Stage Dimensions Modeling: .......................................................................... 20
2.1.6 Performance Modeling: ................................................................................................ 20
Chapter 3: ....................................................................................................................... 21
Results and discussion: .................................................................................................... 21
3.1 Power plant ................................................................................................................... 21
3.1.1 The optimum pressure: ................................................................................................ 21
3.1.2 The effect of mass extraction from power plant to MSF plant .................................... 22
3.1.3 The effect of the condition of the extraction mass ...................................................... 24
3.1.4 Make up water for the power plant: ............................................................................ 25
3.1.5 Comparison between data: .......................................................................................... 26
3.2 MSF Plant ...................................................................................................................... 29
3.2.1 The effect of condition of the steam ............................................................................ 29
3.2.2 Extraction “b” from power plant to the MSF ............................................................... 32


2

Chapter 4: ....................................................................................................................... 33
Conclusion ....................................................................................................................... 33
References: ..................................................................................................................... 34
Appendix A: ..................................................................................................................... 35
Appendix B: ..................................................................................................................... 36

List of tables:
Table 1: Reheat pressure ...................................................................................................................... 21
Table 2: optimum pressure for P [12] ................................................................................................... 22
Table 3: Mass extraction and effect on efficiency ................................................................................ 23
Table4 : effect of the condition of the extraction ................................................................................. 24
Table 5: Efficiency with returning water from MSF .............................................................................. 25
Table 6: Efficiency with returning water 25 C ....................................................................................... 26
Table 7: pressure and its temperatures ................................................................................................ 29
Table 8: steam temperature and its effect on Q and number of stages ............................................... 29
Table 9: table show how much “b” we need to satisfy the MSF at different top brine temperature .... 32

List of figures:
Figure 1: Schematic of a 'once-through' multi-stage flash desalinates: ................................................. 6
Figure 2: Power plant in Saudi Arabia (Qurrayyah)[2] ........................................................................... 8
Figure 3: Power Plant schematic diagram .............................................................................................. 9
Figure 4 : Once through Multi-Stage Flash Distillation System ............................................................ 16
Figure 4: preheat/Boiler Vs eff .................................................................................................................... 21
Figure 5: Effincy Vs Extraction fraction ................................................................................................. 23
Figure 6: : T-S diagram shows how hfg increase as pressure decreases ................................................ 24
Figure 7: Efficiency Vs Pbrine ................................................................................................................... 24
Figure 9: the effect of make water in Efficiency ................................................................................... 27
Figure 10: The effect of make water in Work net ................................................................................. 28
Figure 11: number of stage Vs Top brine temperature ........................................................................ 30
Figure 12: Msteam Vs Top brine temperature ......................................................................................... 31
Figure 13: performance ratio Vs Top brine temperature ..................................................................... 31


3

Chapter 1:
Introduction:
Water desalination is one of the most important facilities in Saudi Arabia since
Saudi Arabia does not have a natural resource for water. So, we need to save any
amount of energy with increasing the efficiency of the factory. Our problem is how to
increase the efficiency and consume some power.
1.1 Power Plant:
Power plant is a facility that used to generate electrical power. Here in Saudi
Arabia we have Gazlan power plant that has power capacity of 2400 MW.
Classification of power station:
1.1.1 By heat source: [1]
o Fossil-fuel power stations may also use a steam turbine
generator or in the case of natural gas-fired plants may use a
combustion turbine. The steam drives a steam turbine and
generator that then produces electricity
o Nuclear power plants use a nuclear reactor's heat that is
transferred to steam which then operates a steam turbine and
generator. About 20 percent of electric generation in the USA
is produced by nuclear power plants.
o Geothermal power plants use steam extracted from hot
underground rocks.
o Biomass-fuelled power plants may be fuelled by waste from
sugar cane, municipal solid waste, landfill methane, or other
forms of biomass.
o Waste heat from industrial processes is occasionally
concentrated enough to use for power generation, usually in a
steam boiler and turbine.
o Solar thermal electric plants use sunlight to boil water and
produce steam which turns the generator.
1.1.2 By prime mover:
o Steam turbine plants use the dynamic pressure generated by
expanding steam to turn the blades of a turbine. Almost all
large non-hydro plants use this system. About 90 percent of all


4

electric power produced in the world is through use of steam
turbines.
o Gas turbine plants use the dynamic pressure from flowing gases
(air and combustion products) to directly operate the turbine.
Natural-gas fuelled (and oil fueled) combustion turbine plants
can start rapidly and so are used to supply "peak" energy during
periods of high demand, though at higher cost than base-loaded
plants. These may be comparatively small units, and sometimes
completely unmanned, being remotely operated. This type was
pioneered by the UK, Princetown being the world's first,
commissioned in 1959.
o Combined cycle plants have both a gas turbine fired by natural
gas, and a steam boiler and steam turbine which use the hot
exhaust gas from the gas turbine to produce electricity. This
greatly increases the overall efficiency of the plant, and many
new baseload power plants are combined cycle plants fired by
natural gas.
o Internal combustion reciprocating engines are used to provide
power for isolated communities and are frequently used for
small cogeneration plants. Hospitals, office buildings, industrial
plants, and other critical facilities also use them to provide
backup power in case of a power outage. These are usually
fuelled by diesel oil, heavy oil, natural gas, and landfill gas.
o Microturbines, Stirling engine and internal combustion
reciprocating engines are low-cost solutions for using
opportunity fuels, such as landfill gas, digester gas from water
treatment plants and waste gas from oil production.
1.1.3 By duty (scheduled):
o Base load power plants run nearly continually to provide that
component of system load that doesn't vary during a day or
week. Baseload plants can be highly optimized for low fuel
cost, but may not start or stop quickly during changes in system
load. Examples of base-load plants would include large modern


5

coal-fired and nuclear generating stations, or hydro plants with
a predictable supply of water.
o Peaking power plants meet the daily peak load, which may only
be for one or two hours each day. While their incremental
operating cost is always higher than base load plants, they are
required to ensure security of the system during load peaks.
Peaking plants include simple cycle gas turbines and sometimes
reciprocating internal combustion engines, which can be started
up rapidly when system peaks are predicted. Hydroelectric
plants may also be designed for peaking use.
o Load following power plants can economically follow the
variations in the daily and weekly load, at lower cost than
peaking plants and with more flexibility than baseload plants.
1.2 Desalination Plant:
Desalination is a process that removes minerals from saline water.
More generally, desalination may also refer to the removal of salts and
minerals, as in soil desalination, which also happens to be a major issue for
agricultural production.

1.2.1 Types of distillation process:
a. Multi-Stage flash distillation.
b. Multiple-effect distillation.
c. Vapor-Compression.


6

1.2.1 Multi-Stage flash distillation [1]:
Multi-stage flash distillation is a water distillation process that distills
seawater by flashing a portion of the water into steam in multiple stages of
what are essentially countercurrent heat exchangers.

1.2.2 How it works:
The plant has a series of spaces called stages, each containing a heat
exchanger and a condensate collector. The sequence has a cold end and a hot
end while intermediate stages have intermediate temperatures. The stages
have different pressures corresponding to the boiling points of water at the
stage temperatures. After the hot end there is a container called the brine
heater.

Figure 1: Schematic of a 'once-through' multi-stage flash desalinates:
A - Steam in
B - Seawater in
C - Potable water out
D - Waste out
E - Steam out
F - Heat exchange
G - Condensation collection
H - Brine heater


7

1. The cold water pumped from the sea through a heat exchanger and it warms it up.
(with each stage, the temperature of sea water increase).

2. Then, when it reaches the brine heater, it already had got nearly the maximum
temperature.

3. The water enters the brine heater and some heat is added.

4. After the heater, the water flows through valves back into the stages that have
ever lower pressure and temperature. The water now called brine.

5. The brine enters each stage at temperature higher than the boiling temperature.
As a result, small fraction of brine flashes to steam until its temperature reduce to
equilibrium. Then enters the next stage.

6. The steam cools and condense against the heat exchanger tube, and it heats up
the water coming from the sea.

7. At the final stage, the temperature in nearly same as the inlet temperature.

1.2.3 Challenges:
There is a maximum temperature of brine heater that the water can’t
be heated above 120, because this will result in corrode the heat exchanger
as well as scale formation, which is the salt from sea. It can be avoided by
adding Nano filters, so the water is out of Mg and Na.
Also, another challenge is about how to balance the heat used in brine
heater, that it gives the best performance with low energy lost.

1.3 Objective:
Our objective is to find a balance between the power plant and the desalination
plant so that we get the optimum performance for both systems.


8

Chapter 2:
Here in this chapter, we are going to specify the model for the power plant as
well as the desalination plant.
2.1 Power Plant:
We chose a power plant (See Fig.2)based on real data. The power
plant we chose have one boiler, two turbines, condenser, one open
feed water heater, two closed feed water heater, and three pumps.
We develop the general equation for the whole system. Next, we will
develop the general equation for each element. Our objective is to
find the optimum extraction pressure with the maximum efficiency in
the power plant (See Appendix A for the EES code).

Figure 2: Power plant in Saudi Arabia (Qurrayyah)[2]


9

Figure 3: Power Plant schematic diagram


10

2.1.1 Boiler:
in the boiler, we increase the water temperature up to 500 C
with pressure of 6000 KPa. Also, there is a reheat part that comes out
from the high pressure turbine. Here is the energy balance equation
representing the heat added to the water as well as the heat added to
Z-extraction (reheat):
!"# = &'() ℎ 11 − ℎ 10 + / ℎ 15 − ℎ 14 (1)
where:
§ h[11] represent the enthalpy for the whole steam coming out of
the boiler to the high pressure turbine.
§ h[10] represent the enthalpy for the whole water coming into of
the boiler.
§ h[15] represent the enthalpy for the Z- fraction of steam coming
out of the boiler to the low pressure turbine.
§ h[14] represent the enthalpy for the Z- fraction of steam coming
out of the high pressure turbine to the reheat.
§ mdot represent the mass flow rate for the whole system.
§ Z represent the fraction that is going to the reheat and the low
pressure turbine.

2.1.2 High Pressure Turbine:
In the high pressure turbine, we have three fractions being
extracted at different pressure and the first one is going to the closed
feed water heater 1, and the other one is going to the closed feed
water heater 2, and the third one is going to the reheat, and then to
the low pressure turbine. The high pressure turbine has isentropic
efficiency of 80% and here is the energy balance equation for the high
pressure turbine:
2345 = &'() 6 ℎ 11 − ℎ 12 + 8 ℎ 11 − ℎ 13 +
/ ℎ 11 − ℎ 14 (2)


11

here is the mass flow rate fraction balance:
1 = 6 + 8 + / (3)
where:
§ h[12] represents the enthalpy of X-fraction of steam from the
high pressure turbine at P[12] and T[12].
§ h[13] represents the enthalpy of Y-fraction of steam from the
§ h[14] represents the enthalpy of Z-fraction of steam from the

2.1.3 Low Pressure Turbine:
In the low pressure turbine, we have three fractions being
extracted at different pressure and the first one is going to the open
feed water heater, and the other one is going to the MSF-OT plant,
and the third one is going to the condenser. The low pressure turbine
has isentropic efficiency of 85% and here is the energy balance
equation for the low pressure turbine:
2:45 = &'() /×ℎ 15 − &×ℎ 16 − =×ℎ 17 − ?× ℎ@A"#B[18]
(4)
here is the mass flow rate fraction balance:
/ = & + = + ? (5)
where:
§ h[15] represents the enthalpy of Z-fraction of steam from the
reheat at P[15] and T[15] to the low pressure turbine.
§ h[16] represent the enthalpy of m-fraction of steam from the
low pressure turbine at P[16] and T[16] and going to the open
feed water heater.
§ h[17] represents the enthalpy of n-fraction of steam from the
low pressure turbine at Pcondenser and T[17] going to the
condenser.
§ hbrine[18] represents the enthalpy of b-fraction of steam from
the reheat at Pbrine[18] and Tbrine[18] and going to the MSF.


12

§ m represents the fraction of steam that is going to the open feed
water heater.
§ n represents the fraction of steam that is going to the condenser.
§ b represents the fraction of steam that is going to the MSF brine
heater.

2.1.4 Condenser:
In the condenser, the water enters the condenser at Pcondenser
and the water gets out with zero quality. Here is the energy balance
equation for the condenser:
!(F) = &'() = ℎ 17 − ℎ 1 (7)
where:
§ h[1] represents the enthalpy of n-fraction of water from the
condenser at Pcondenser and T[1] to pump 1.

2.1.5 Open Feed Water Heater:
In the open feed water heater, n-fraction after pump 1, m-
fraction from low pressure turbine, b-fraction from MSF. Here is the
energy balance equation for the open feed water heater:
ℎ 2 × = + ℎ 16 × & + ℎ 6 × 6 + 8 + ?×ℎ 20 = ℎ 3 (8)
here is the mass flow rate fraction balance equation:
? + 6 + 8 + & = 1 (9)
where:
§ h[2] represents the enthalpy of n-fraction of water from the
condenser at P[2] and T[2] and going to the open feed water
heater.
§ h[6] represents the enthalpy of (x&y)-fraction of steam from
trap 2 at P[6] and T[6] and going to the open feed water
heater.
§ h[20] represents the enthalpy of b-fraction of steam from MSF
at Pbrine and Tbrine[18] and going to the open feed water heater.


13

§ h[3] represents the enthalpy of whole mass fraction of steam
from open feed water heater and going to pump 2, which
increase the water pressure up to Pboiler.

2.1.6 Closed Feed Water Heater 2:
In the closed feed water heater 2, we have three lines entering
the heat exchanger: y-fraction coming from the high pressure turbine,
whole mass from pump 2 and x-fraction from trap 1. Also, we have
two lines going out from the heat exchanger: one is going to the
closed feed water heater 1 and the other going trap 2. Here is the
energy balance equation for the closed feed water heater with
effectiveness of 0.8 :
8×GH 13 × I 13 − IJK) 13 + 8×ℎLM 13 + ℎ 4 + ℎ 9 ×6 =
6 + 8 ×ℎ 5 + ℎ 7 (10)
where:
§ Cp[13] represents the specific heat of y-fraction of water from
the high pressure turbine at P[13] and T[13] and going to the
closed feed water heater 2.
§ hfg[13] represents the vaporization enthalpy of y-fraction of
steam from high pressure turbine at P[13] and T[13] and going
to the closed feed water heater 2.
§ h[4] represents the enthalpy of whole mass fraction of water
from pump 2 at P[4] and T[4] and going to the closed feed
water heater 2.
§ h[9] represents the enthalpy of x-fraction of water from trap 1
and going to the closed feed water heater 2.
from closed feed water 2 and going to the closed feed water
heater 1.


14

2.1.7 Closed Feed Water Heater 1:
In the closed feed water heater 1, we have two fractions going
to the heat exchanger: one from the closed feed water 2 and the
other from the high pressure turbine. Also, we have two fractions
going out from the heat exchanger: one is going to the boiler and the
other is going to trap 1. Here is the energy balance equation for the
closed feed water heater 1:
6×GH 12 × I 12 − IJK)[12] + 6×ℎLM[12] + ℎ 7 = ℎ 8 ×6 + ℎ 10
(11)
where:
§ Cp[12] represents the specific heat of x-fraction of water from
the high pressure turbine at P[12] and T[12] and going to the
closed feed water heater 1.
§ hfg[12] represents the vaporization enthalpy of x-fraction of
steam from high pressure turbine at P[12] and T[12] and going
to the closed feed water heater 1.
§ h[8] represents the enthalpy of x-fraction of steam from
closed feed water 1 and going to trap 1.
from closed feed water 1 and going to the boiler.


15

2.2 Desalination Plant:
We chose to work on a once through multi-stage flash distillation
system consists of two basic sections, a heat addition section and a heat
recovery section as can be seen in the Fig.4, in the next page. The heat
recovery section consists of a condenser, the distillate collection trays
and the flashing chamber. On the other hand, the heat addition section
consists mainly of a brine heater. (See Appendix B for the EES code)


16

Figure 4 : Once through Multi-Stage Flash Distillation System


17

To carry out the mathematical modeling of the MSF plant, the
following assumptions are made:
a) The temperature drops across each flashing stage as well as the
temperature rise in each condenser stage is equal.
b) The effect of boiling point rise and non-equilibrium losses on the
stage energy balance is considered negligible.

2.1.1 Mass balance modeling:
As seen in Figure 2 there is one input which is the seawater Mf and
two output which are distillated water Md and brine blow down Mb. So
the mass flow rate balance will be:
(12)
And if we added the salinity:
(13)
Node: the distillated water has a zero salinity.
The total distillate mass flow rate is obtained by:
(14)

Where: (15)

The steam mass flow rate:
(16)


18

2.1.2 Temperature Drop Modeling:
As we assumed that the temperature drop in every stage is constant,
so the equation will be:
(17)
Where:
To: Temperature of seawater leaving the brine heater, the top brine
temperature.
Tn: Temperature of brine leaving the last stage of the flashing chamber.
n: the number of flashing stages.

2.1.3 The Temperature at each Stage:
(18)
Where i represents the stage number.

2.1.4 Heat transfer areas:
The equation of the brine heat transfer area required Ab is:
(19)
Where Ub and Tlmtd,b are:

Also, the condenser heat transfer area in the first stage is:
(20)
Where Tlmtd,c and Uc are:


19

Where Tv,1 can be calculated as flow:

And the total heat transfer area can be calculated is flows:
(21)


20

2.1.5 Flashing Stage Dimensions Modeling:
The gate height at each stage, GH is:

(22)

And the brine pool height, H:
(23)

Also, the width of each chamber is calculated by:

(24)

2.1.6 Performance Modeling:
The performance of the desalination plants is expressed as the
performance ratio, PR, which defined as the amount of distillate produced
per unit of steam consumption. And is calculated by:
(25)


21

Chapter 3:
Results and discussion:
3.1 Power plant
3.1.1 The optimum pressure:
The optimum pressure in the power plant in boiler, reheat and extraction
line from turbines to feed water. All following pressure calculate at extraction
equal 0.

3.1.1.1 Boiler pressure
The pressure of the boiler is the maximum pressure in the power plant. The
pressure set it to be 12MPa and all following pressure will depends on this
pressure. We use 12 MPa. As we increase the pressure of the boiler, the
efficiency of the cycle will increase but this increase should have some
constrain.

3.1.1.2 Reheat pressure
The best condition of the reheat pressure is to be 20-25 % of the boiler
pressure, which is equal to 2400 KPa. We can see that from the following
graph and table.
Table 1: Reheat pressure

Wnet
(KW)
Efficiency
(%)
Pressure
(KPa)
71119236.197000
71739036.296500
72376936.386000
73034636.475500
73714536.555000
74419236.634500
75151436.74000
75914636.763500
76712236.83000
77547736.822500
77719536.822400
78422236.82000
Figure 5: preheat/Boiler Vs eff


22

3.1.1.3 Extraction pressure p [12]
The extraction pressure from the HPT to CFWH1. We can see P =
2500 KPa is the best condition. This pressure cannot be lower than the
pressure of reheat.

3.1.2 The effect of mass extraction from power plant to MSF plant
Here in this part, we want to see the effect of the amount of mass that
extract form the power plant to the MSF plant. As we can see from the figure
and the table, the effect of the extraction is not going to effect the power plant.
If we say that we need to extract 10 % of the mass flow rate of the power plant,
we will loss 0.43% from the efficiency and if we compare this loss to how much
are we going to produce water, that loss will be nothing. The value of extraction
represent how much do we take from the power plant to the MSF. The following
table shows extraction value starts from 0% to 34% of the mass flow rate of the
power plant. The following data are at 700 KPa and we will discuss latter why
we choose this pressure for the extraction.
Wnet
(KW)
Efficiency
(%)
Pressure
(KPa)
59678031.715000
63562733.044500
67334834.214000
71041835.253500
74734736.173000
78474936.972500
Table 2: optimum pressure for P [12]


23

Table 3: Mass extraction and effect on efficiency
Wnet
(KW)
Efficiency
(%)
Extraction
fraction
77719536.820
77629836.780.01
77540036.730.02
77450236.690.03
77360536.650.04
77270736.610.05
77181036.560.06
77091236.520.07
77001436.480.08
76911736.440.09
76821936.390.1
76373136.180.15
75924335.970.2
75475535.760.25
75026735.540.3
74667635.370.34
Figure 6: Effincy Vs Extraction fraction


24

3.1.3 The effect of the condition of the extraction mass
Here we are going to see, how the condition of the extraction can effect
on the power plant system. The following result is when we extract 10 % of
the mass flow rate of the power plant. As we can see, decreasing the pressure
will lead to decrease the value of hg . However, hfg will increase because as we
decrease the pressure hfg increase from the
T-S diagram. From here we can calculate the
amount of heat that will be delivered to the
MSF plant which equal to = m*hfg.. From
here, we can control the condition of the
pressure of extraction based on the needed
heat in the MSF plant.
Table4 : effect of the condition of the extraction
Q Desalination
(KJ)
Wnet
(KW)
Efficiency
(%)
hg
(KJ/Kg)
Pressure
(KPa)
15883476857736.4127841200
15997176847536.4127811100
16116976838536.427781000
16243976831036.42774900
16379676825336.42769800
16526176821936.392763700
16686376821636.392757600
16864376825536.42749500
17067476835536.42739400
17307976855136.412725300
17612476891936.432707200
18059876969836.462675100
Figure 8: Efficiency Vs Pbrine
Figure 7: : T-S diagram shows how hfg increase
as pressure decreases


25

3.1.4 Make up water for the power plant:
The losses in the mass flow rate from the power plant during the extraction
to the MSF plant should be compensating. Usually the makeup water that for the
power plant is water at 25 Co
. in this project we tried to see how we could use the
same water that used in the MSF plant. Water that come back again will have less
energy than that delivered to MSF because the energy used to heat up the see
water temperature.
1- Using the water from the MSF:
Steam that used in MSF plant will have hg at the extraction pressure. The
outlet of the brine heater will have hf at the extraction pressure. In this case, we
can use this water and pump it back to the open feed eater at the same pressure of
the OFWH. This water will be the makeup water for the power plant. We can see
from the table 5, how the efficiency will be if we return the water from MSF plant.
Table 5: Efficiency with returning water from MSF
Wnet
(KW)
Efficiency
(%)
b
77719536.820
77629836.780.01
77540036.730.02
77450236.690.03
77360536.650.04
77270736.610.05
77181036.560.06
77091236.520.07
77001436.480.08
76911736.440.09


26

2- Using water at 25Co
As we extract steam from power plant we should have make up water to
complete the cycle. In this case we will have makeup water in 25 C. we will pump
this water to same pressure of OFWH. The flowing data are at 700 KPa for the
make water and its efficiency.
Table 6: Efficiency with returning water 25 C
Wnet
(KW)
Efficiency
(%)
b
77719536.820
77557136.740.01
77394636.650.02
77232136.570.03
77069736.490.04
76907236.410.05
76744736.320.06
76582336.240.07
76419836.160.08
76257336.070.09
3.1.5 Comparison between data:
This table will show how much is the difference in efficiency and Wnet between make
up water from MSF or at 25 C
Defiance
(KW)
Wnet
(KW)
Wnet
(KW)
Defiance
(%)
Efficiency
(%)
Efficiency
(%)
b
0777195777195036.8236.820
7277755717762980.0436.7436.780.01
14547739467754000.0836.6536.730.02
21817723217745020.1236.5736.690.03
29087706977736050.1636.4936.650.04
36357690727727070.236.4136.610.05
43637674477718100.2436.3236.560.06
50897658237709120.2836.2436.520.07
58167641987700140.3236.1636.480.08
65447625737691170.3736.0736.440.09


27

Figure 9: the effect of make water in Efficiency
36
36.1
36.2
36.3
36.4
36.5
36.6
36.7
36.8
36.9
0 0.02 0.04 0.06 0.08 0.1
b Vs Efficiency
Back from MSF at 25 C


28

Figure 10: The effect of make water in Work net

760000
762000
764000
766000
768000
770000
772000
774000
776000
778000
0 0.02 0.04 0.06 0.08 0.1
b Vs Wnet
Back from MSF At 25 C


29

3.2 MSF Plant
In MSF plant, we are going to see how much steam do we need from the
power plant to produce 378.8 Kg/s of desalt water. Also, how can the temperature of
the steam can affect the performance ration of the MSF.
3.2.1 The effect of condition of the steam
As we see previously how the extraction condition can effect on the power plant.
It is also effect on MSF. As we increase the pressure of extraction, the temperature of
the steam will increase. Therefore, the temperature of top brine will increase also. We
can see how temperature will be difference with pressure in the following table.
Table 7: pressure and its temperatures
TsatPextraction
1881200
184.11100
179.91000
175.4900
170.4800
165700
158.9600
151.9500
143.6400
133.6300
120.2200
99.63100
Increasing the pressure of extraction will led to increase in performance ratio and
increasing in number of stages. In addition, it will led to decrease the amount of steam
that need in MSF plant. The following table shows how temperature will effect in the
energy needed (Q) and number of stages.
Table 8: steam temperature and its effect on Q and number of stages
MsteamQ (KJ)PR∆T (Co
)nTn (Co
)To (Co
)
95.70492118373.9582.752440106
90.839332000254.172.82540110
80.819291756904.6872.7586212940120
73.099191567515.1822.81253240130
66.996821416115.6542.7777783640140
62.067841292236.1032.754040150
58.026961188926.5282.7906984340160
54.692461101556.9262.7659574740170


30

Tn: Brine Temperature in last stage
To: Top brine temperature
n: Total number of stages
∆T: The temperature drop per stage
PR: performance ratio
Q: heat need in brine heater
In figure 11, we can see the relation between the top brine temperature, which is (Tsat – 10),
and the number of stages. As we increases number of stages the performance ratio will
increases.

Figure 11: number of stage Vs Top brine temperature
y = 0.3613x - 14.543
20
25
30
35
40
45
50
100 110 120 130 140 150 160 170


31

The following figure shows, what is the relation between the top brine temperature and mass
flow rate of the steam. As we increase temperature of the steam we will need less mass flow
rate so less amount of extraction from the power plant.

Figure 12: Msteam Vs Top brine temperature
We can see from the following graph how performance ratio will effect by increasing the top
brine temperature. Actually increasing the temperature led to increase number of stage which
is going to increase the performance ratio.

Figure 13: performance ratio Vs Top brine temperature

40
50
60
70
80
90
100
100 110 120 130 140 150 160 170
y = 0.0455x - 0.7828
1
2
3
4
5
6
7
8
100 110 120 130 140 150 160 170


32

3.2.2 Extraction “b” from power plant to the MSF
b = ms / mp
ms: mass of steam required in MSF
mp: mass flow rate of water in power plant, which is 800 Kg/s
The following table show how much “b” we need to satisfy the MSF at different top
brine temperature.
Table 9: table show how much “b” we need to satisfy the MSF at different top brine temperature
bmsteam
(Kg/s)
Q
(KJ)
To
(Co
)
0.11963195.7049211837106
0.11354990.83933200025110
0.10102480.81929175690120
0.09137473.09919156751130
0.08374666.99682141611140
0.07758562.06784129223150
0.07253458.02696118892160
0.06836654.69246110155170


33

Chapter 4:
Conclusion
To sum up, we focused on this project to find the optimum performance ratio by
combining the steam power plant with the MSF distillation plant. First, we worked on the
power plant and we found out the best reheat pressure to be 2400 kPa. Then, we looked on
the effect of the extraction, which is going to supply steam to the MSF plant, on the
efficiency of the power plant and we found out that if we take 8% of the mass in the power
plant the efficiency will decrease by 1% which is very small compared to what we will get in
the MSF. After that, we found that the best pressure of the extraction to be 700 kPa and we
looked on the effect of the makeup mass to the power plant. If the makeup was water at
temperature of 165 C or water at 25 C and we found that the efficiency will decrease by
0.36% if we put a makeup water at 25 C. Then, we looked at the MSF and see the effect of
the increasing the temperature of the supplied steam. As we increase the steam
temperature, the number of stages increase which will lead us to an increase in the
performance ratio. If we increase the steam temperature from 106 C to 170 C, the
performance ratio will increase by almost 100%. These changes caused big improvement on
the combination of the power plant and MSF which will save a lot of money.


34

References:
[1] Wikipedia
[2] acwapower.com
[3] Hisham T. El-Dessouky and Hisham M. Ettouney "Fundamentals of Salt
Water Desalination", Elsevier, 2002.
[4] MOHAMMED A. ANTAR and SYED M. ZUBAIR “Analysis and Assessment of
Performance of a MSF Evaporation Desalination Plant”,February 2010.


35

Appendix A:

File:powerplant6withoptimumpresuure.EES4/25/20169:30:38PMPage1
EESVer.9.901:#1696:DepartmentofMechanicalEngineeringKingFahdUniversityPetroleumandMinerals
Boiler
HPTLPT
Condenser
CFWH1CFWH2OPWH
P2
P1
Trap1Trap2
(11)
(10)
(12)(13)
(14)
(15)
(16)
(17)
(1)(2)
(3)(4)
(5)
(6)
(7)
(8)
(9)
Pboiler=
*
****
T11=
*
**
T12=
*
**
P12=
*
***
Preheat=
*
***
T14=
*
****
x=
*
*****
P13=
*
***
T13=
*
****
y=
*
*****
z=
*
*****
T15=
*
**P16=
*
**
T16=
*
****
b=
*
******
m=
*
******
n=
*
*****
Pcond=
*
**
T17=
*
***
P2=
*
**
P1=
*
**
T3=
*
****
T4=
*
****T7=
*
****
T5=
*
**
T6=
*
****
T8=
*
****
T10=
*
**
Pbrine,18=
*
**
b=
*
******
T2=
*
****
sys,new=
*
****
Preheat=
*
***

File:powerplant6 with optimum presuure.EES 4/25/2016 9:34:25 PM Page 1
EES Ver. 9.901: #1696: Department of Mechanical Engineering King Fahd University Petroleum and Minerals
Knowen information
Pboiler = 12000
P12 = 2600
P13 = 2500
Preheat = 2400
P16 = 900
Pcond = 7.5
T11 = 565
T15 = 550
HPT = 0.8
LPT = 0.85
b = 0.07254
Pbrine,18 = 700
rat =
Preheat
Pboiler
Qdesel = b · M · hbrinefg,18
M = 800
CFWH1 = CFWH2
CFWH2 = 0.4
massdes = M · b
Heat Transfer Coefficient of steam at Steam Temperature
hbrinefg,18 = Enthalpyvaporization SteamIAPWS , P = Pbrine,18
HPT
h11 = h Steam , T = T11 , P = Pboiler
s11 = s Steam , T = T11 , P = Pboiler
Isontropic turbine
s11 = s12
s11 = s13
s11 = s14
hiso,12 = h Steam , s = s12 , P = P12
hiso,13 = h Steam , s = s13 , P = P13

hiso,14 = h Steam , s = s14 , P = Preheat
HPT =
h11 – h12
h11 – hiso,12
HPT =
h11 – h13
h11 – hiso,13
HPT =
h11 – h14
h11 – hiso,14
T12 = T Steam , s = s12 , P = P12
T13 = T Steam , s = s13 , P = P13
T14 = T Steam , s = s14 , P = Preheat
1
Mass balance
1 = z + x + y
WHPT = M · x · h11 – h12 + y · h11 – h13 + z · h11 – h14
LPT
h15 = h Steam , T = T15 , P = Preheat
s15 = s Steam , T = T15 , P = Preheat
Isontropic turbine
s15 = s16
s15 = s17
hiso,16 = h Steam , s = s16 , P = P16
hiso,17 = h Steam , s = s17 , P = Pcond
LPT =
h15 – h16
h15 – hiso,16
LPT =
h15 – h17
h15 – hiso,17
T16 = T Steam , s = s16 , P = P16
T17 = T Steam , s = s17 , P = Pcond
2
Mass Balance
z = m + n + b
hbrine,18 = h Steam , x = 1 , P = Pbrine,18

WLPT = M · z · h15 – m · h16 – n · h17 – b · hbrine,18
Condencer
h1 = h water , P = Pcond , x = 0
To calculate the work in pump 1
v1 = v water , P = Pcond , x = 0
Qout = M · n · h17 – h1
Pump 1
P2 = P16
P1 = Pcond
Wp1 = M · n · v1 · P2 – P1
M · n · h2 – h1 = Wp1
OFWH
3
h2 · n + h16 · m + h6 · x + y + b · h20 = h3
Hrecovery = M · n · h2 + h16 · m + h6 · x + y + b · h20
hnew,3 =
Hrecovery
M
h21 = h water , T = 25 , P = 101
h3 = h water , P = P16 , x = 0
To calculate the work in pump 2
v3 = v water , P = P16 , x = 0
T3 = T water , P = P16 , h = hnew,3
T2 = T water , P = P16 , h = h2
T6 = T water , P = P16 , h = h6
Pump 2
P4 = Pboiler
P3 = P16
Wp2 = M · v3 · P4 – P3
M · h4 – hnew,3 = Wp2
T4 = T3
pump 3

P16 = P20
v19 = v water , P = Pbrine,18 , x = 0
WP3 = M · b · P20 – Pbrine,18 · v19
WP3 = M · b · h20 – h19
h19 = h water , P = Pbrine,18 , x = 0
CFWH 2
4
y · Cp13 · T13 – Tsat,13 + y · hfg,13 + h4 + h9 · x = x + y · h5 + h7
Tsat,13 = Tsat water , P = P13
Tavg,13 =
T13 + Tsat,13
2
Cp13 = Cp water , T = Tavg,13 , P = P13
hfg,13 = Enthalpyvaporization Steam , P = P13
T7 – T4
T13 – T4
= CFWH2
T5 = T water , P = P13 , x = 0
h7 = h water , T = T7 , P = P4
Trap 2
h5 = h6
h5 = h water , P = P13 , x = 0
CFWH 1
5
x · Cp12 · T12 – Tsat,12 + x · hfg,12 + h7 = h8 · x + h10
Tsat,12 = Tsat water , P = P12
Tavg,12 =
T12 + Tsat,12
2
Cp12 = Cp water , T = Tavg,12 , P = P12
hfg,12 = Enthalpyvaporization Steam , P = P12
h8 = h water , P = P12 , x = 0
T10 – T7
T12 – T7
= CFWH1

T8 = T water , P = P12 , x = 0
h10 = h water , T = T10 , P = P4
Trap 1
h8 = h9
Boiler
Qin = M · h11 – h10 + z · h15 – h14
The System effecince
Wtotal,pump = Wp1 + Wp2 + WP3
Wnet = WLPT + WHPT – Wp1 – Wp2 – WP3
sys,new =
Wnet
Qin
· 100
HC,2 = M · n · h2
HC,4 = M · h4
HC,5 = M · x + y · h5
HC,6 = M · x + y · h6
HC,7 = M · h7
HC,8 = M · x · h8
HC,9 = M · x · h9
HC,10 = M · h10
HC,11 = M · h11
HC,12 = M · x · h12
HC,13 = M · y · h13
HC,14 = M · z · h14
HC,15 = M · z · h15
HC,16 = M · m · h16
HC,17 = M · n · h17
HC,18 = M · b · hbrine,18
SOLUTION
Unit Settings: SI C kPa kJ mass deg
b = 0.07254 CFWH1 = 0.4
CFWH2 = 0.4 HPT = 0.8

LPT = 0.85 sys,new = 36.51sys,new = 36.51
Hrecovery = 594343 m = 0.07824
massdes = 58.03 M = 800
n = 0.4825 Pboiler = 12000
Pcond = 7.5 Preheat = 2400
Qdesel = 119881 Qin = 2.111E+06
Qout = 907519 rat = 0.2
WHPT = 309122 WLPT = 471878
Wnet = 770684 Wp1 = 347.3
Wp2 = 9956 WP3 = 12.86
Wtotal,pump = 10316 x = 0.1523
y = 0.2144 z = 0.6333
38 potential unit problems were detected.
Arrays Table: Main
Cpi hi hbrine,i HC,i hfg,i hiso,i hnew,i Pi Pbrine,i si
1 168.8 7.5
2 169.7 65487 900
3 742.9 742.9 900
4 755.4 604299 12000
5 962 282218
6 962 282218
7 995.3 796218
8 971.7 118388
9 971.7 118388
10 1163 930464
11 3519 2.815E+06 6.699
12 2.612 3145 383111 1831 3051 2600 6.699
13 2.605 3137 538036 1840 3041 2500 6.699
14 3128 1.585E+06 3031 6.699
15 3575 1.811E+06 7.483
16 3294 206156 3244 900 7.483
17 2520 972659 2334 7.483
18 2763 160361 700
19 697.4
20 697.6 900
21 104.8
Arrays Table: Main
Ti Tavg,i Tsat,i vi hbrinefg,i
1 0.001008
2 40.33
3 175.4 0.001121
4 175.4
5 224
6 175.4
7 230.7
8 226.1
9
10 266
11 565
12 319 272.6 226.1
13 313.7 268.8 224
14 308.2
15 550

Arrays Table: Main
Ti Tavg,i Tsat,i vi hbrinefg,i
16 389.9
17 40.3
18 2066
19 0.001108
20
21
There are a total of 114 equations in the Main program.
Block Rel. Res. Abs. Res. Units Calls Time(ms) Equations
0 0.000E+00 0.000E+00 OK 1 0 P_boiler=12000
0 0.000E+00 0.000E+00 OK 1 0 P[12]=2600
0 0.000E+00 0.000E+00 OK 1 0 P[13]=2500
0 0.000E+00 0.000E+00 OK 1 0 P_reheat=2400
0 0.000E+00 0.000E+00 OK 1 0 P[16]=900
0 0.000E+00 0.000E+00 OK 1 0 P_cond=7.5
0 0.000E+00 0.000E+00 OK 1 0 T[11]=565
0 0.000E+00 0.000E+00 OK 1 0 T[15]=550
0 0.000E+00 0.000E+00 OK 1 0 Eta_HPT=0.8
0 0.000E+00 0.000E+00 OK 1 0 Eta_LPT=0.85
0 0.000E+00 0.000E+00 OK 1 0 b=.07254
0 0.000E+00 0.000E+00 OK 1 0 P_brine[18]=700
0 0.000E+00 0.000E+00 OK 1 0 M_dot=800
0 0.000E+00 0.000E+00 OK 1 0 epsilon_CFWH2=0.4
0 0.000E+00 0.000E+00 OK 4 0 rat=P_reheat/P_boiler
0 0.000E+00 0.000E+00 OK 4 0 mass_des=M_dot*b
0 0.000E+00 0.000E+00 ? 4 0 h_brinefg[18]=Enthalpy_vaporization(Steam_IAPWS,P=P_brine[18])
0 0.000E+00 0.000E+00 ? 4 0 h[11]=Enthalpy(Steam,T=T[11],P=P_boiler)
0 0.000E+00 0.000E+00 ? 4 0 s[11]=Entropy(Steam,T=T[11],P=P_boiler)
0 0.000E+00 0.000E+00 OK 4 0 s[11]=s[12]
0 0.000E+00 0.000E+00 OK 4 0 s[11]=s[13]
0 0.000E+00 0.000E+00 OK 4 0 s[11]=s[14]
0 0.000E+00 0.000E+00 ? 4 0 h_iso[12]=Enthalpy(Steam,S=S[12],P=P[12])
0 0.000E+00 0.000E+00 ? 4 0 h_iso[13]=Enthalpy(Steam,S=S[13],P=P[13])
0 0.000E+00 0.000E+00 ? 4 0 h_iso[14]=Enthalpy(Steam,S=S[14],P=P_reheat)
0 1.355E-19 -5.073E-17 OK 4 0 Eta_HPT=(h[11]-h[12])/(h[11]-h_iso[12])
0 1.355E-19 5.182E-17 OK 4 0 Eta_HPT=(h[11]-h[13])/(h[11]-h_iso[13])
0 2.033E-19 -7.942E-17 OK 4 0 Eta_HPT=(h[11]-h[14])/(h[11]-h_iso[14])
0 0.000E+00 0.000E+00 ? 4 0 T[12]=Temperature(Steam,S=S[12],P=P[12])
0 0.000E+00 0.000E+00 ? 4 0 T[13]=Temperature(Steam,S=S[13],P=P[13])
0 0.000E+00 0.000E+00 ? 4 0 T[14]=Temperature(Steam,S=S[14],P=P_reheat)
0 0.000E+00 0.000E+00 ? 4 0 h[15]=Enthalpy(Steam,T=T[15],P=P_reheat)
0 0.000E+00 0.000E+00 ? 4 0 s[15]=Entropy(Steam,T=T[15],P=P_reheat)
0 0.000E+00 0.000E+00 OK 4 0 s[15]=s[16]
0 0.000E+00 0.000E+00 OK 4 0 s[15]=s[17]
0 0.000E+00 0.000E+00 ? 4 0 h_iso[16]=Enthalpy(Steam,S=s[16],P=P[16])
0 0.000E+00 0.000E+00 ? 4 0 h_iso[17]=Enthalpy(Steam,S=s[17],P=P_cond)
0 1.276E-19 3.587E-17 OK 4 0 Eta_LPT=(h[15]-h[16])/(h[15]-h_iso[16])
0 1.276E-19 1.346E-16 OK 4 0 Eta_LPT=(h[15]-h[17])/(h[15]-h_iso[17])
0 0.000E+00 0.000E+00 ? 4 0 T[16]=Temperature(Steam,S=s[16],P=P[16])
0 0.000E+00 0.000E+00 ? 4 0 T[17]=Temperature(Steam,S=s[17],P=P_cond)
0 0.000E+00 0.000E+00 ? 4 0 h_brine[18]=Enthalpy(Steam,x=1,P=P_brine[18])
0 0.000E+00 0.000E+00 ? 4 0 h[1]=Enthalpy(Water,P=P_cond,x=0)
0 0.000E+00 0.000E+00 ? 4 0 v[1]=Volume(Water,P=P_cond,x=0)
0 0.000E+00 0.000E+00 OK 4 0 P[2]=P[16]
0 0.000E+00 0.000E+00 OK 4 0 P[1]=P_cond
0 0.000E+00 0.000E+00 ? 4 0 h[21]=Enthalpy(Water,T=25,P=101)

0 0.000E+00 0.000E+00 ? 4 0 h[3]=Enthalpy(Water,P=P[16],x=0)
0 0.000E+00 0.000E+00 ? 4 0 v[3]=Volume(Water,P=P[16],x=0)
0 0.000E+00 0.000E+00 OK 4 0 P[4]=P_boiler
0 0.000E+00 0.000E+00 OK 4 0 P[3]=P[16]
0 0.000E+00 0.000E+00 OK 4 0 W_p2=m_dot*v[3]*(P[4]-P[3])
0 0.000E+00 0.000E+00 OK 4 0 P[16]=P[20]
0 0.000E+00 0.000E+00 ? 4 0 v[19]=Volume(Water,P=P_brine[18],x=0)
0 0.000E+00 0.000E+00 OK 4 0 W_P3=m_dot*b*(P[20]-P_brine[18])*v[19]
0 0.000E+00 0.000E+00 ? 4 0 h[19]=Enthalpy(Water,P=P_brine[18],x=0)
0 0.000E+00 0.000E+00 ? 4 0 T_sat[13]=T_sat(Water,P=P[13])
0 0.000E+00 0.000E+00 OK 4 0 T_avg[13]=((T[13]+T_sat[13])/2)
0 0.000E+00 0.000E+00 ? 4 0 Cp[13]=Cp(Water,T=T_avg[13],P=P[13])
0 0.000E+00 0.000E+00 ? 4 15 h_fg[13]=Enthalpy_vaporization(Steam,P=P[13])
0 0.000E+00 0.000E+00 ? 4 0 T[5]=Temperature(Water,P=P[13],x=0)
0 0.000E+00 0.000E+00 ? 4 0 T_sat[12]=T_sat(Water,P=P[12])
0 0.000E+00 0.000E+00 OK 4 0 T_avg[12]=((T[12]+T_sat[12])/2)
0 0.000E+00 0.000E+00 ? 4 0 Cp[12]=Cp(Water,T=T_avg[12],P=P[12])
0 0.000E+00 0.000E+00 ? 4 16 h_fg[12]=Enthalpy_vaporization(Steam,P=P[12])
0 0.000E+00 0.000E+00 ? 4 0 T[8]=Temperature(Water,P=P[12],x=0)
0 0.000E+00 0.000E+00 OK 4 0 h[8]=h[9]
0 0.000E+00 0.000E+00 OK 4 0 H_C[11]=m_dot*h[11]
0 0.000E+00 0.000E+00 OK 4 0 H_C[18]=m_dot*(b)*h_brine[18]
0 0.000E+00 0.000E+00 OK 4 0 Q_desel=b*M_dot*h_brinefg[18]
0 0.000E+00 0.000E+00 OK 4 0 epsilon_CFWH1=epsilon_CFWH2
0 1.087E-16 -1.398E-15 OK 4 0 W_P3=m_dot*b*(h[20]-h[19])
0 0.000E+00 0.000E+00 OK 4 0 h[5]=h[6]
0 0.000E+00 0.000E+00 ? 4 0 T[6]=Temperature(Water,P=P[16],h=h[6])
1 0.000E+00 0.000E+00 OK 48 0 1=(z+x+y)
1 0.000E+00 0.000E+00 OK 48 0 z=(m+n+b)
1 0.000E+00 0.000E+00 OK 40 0 W_p1=m_dot*(n*v[1]*(P[2]-P[1]))
1 1.919E-08 -6.663E-06 OK 48 0 m_dot*(n)*(h[2]-h[1])=W_p1
1 1.121E-11 -8.325E-09 OK 64 0 h[2]*(n)+h[16]*m+h[6]*(x+y)+b*h[20]=h[3]
1 1.121E-11 6.662E-06 OK 72 0 H_recovery=m_dot*(n*h[2]+h[16]*m+h[6]*(x+y)+b*h[20])
1 0.000E+00 0.000E+00 OK 40 0 h_new[3]=H_recovery/m_dot
1 2.002E-14 3.512E-12 ? 82 109 T[3]=Temperature(Water,P=P[16],h=h_new[3])
1 6.245E-19 -6.217E-15 OK 40 0 m_dot*(h[4]-h_new[3])=W_p2
1 0.000E+00 0.000E+00 OK 40 0 T[4]=T[3]
1 0.000E+00 0.000E+00 OK 56 0 y*Cp[13]*(T[13]-T_sat[13])+y*h_fg[13]+h[4]+h[9]*x=(x+y)*h[5]+h[7]
1 1.152E-18 4.608E-19 OK 40 0 (T[7]-T[4])/(T[13]-T[4])=epsilon_CFWH2
1 1.104E-16 -1.099E-13 ? 40 0 h[7]=Enthalpy(Water,T=T[7],P=P[4])
1 8.468E-20 1.110E-16 OK 48 0 x*Cp[12]*(T[12]-T_sat[12])+x*h_fg[12]+h[7]=h[8]*x+h[10]
1 1.897E-18 7.589E-19 OK 40 0 (T[10]-T[7])/(T[12]-T[7])=epsilon_CFWH1
1 2.148E-17 -2.498E-14 ? 40 0 h[10]=Enthalpy(Water,T=T[10],P=P[4])
2 3.174E-10 -9.812E-05 OK 3 0 W_HPT=m_dot*(x*(h[11]-h[12])+y*(h[11]-h[13])+z*(h[11]-h[14]))
3 3.174E-10 -1.498E-04 OK 3 0 W_LPT=m_dot*(z*h[15]-m*h[16]-n*h[17]-b*h_brine[18])
4 2.525E-09 2.291E-03 OK 3 0 Q_out=m_dot*(n*(h[17]-h[1]))
5 4.229E-14 1.705E-12 ? 3 16 T[2]=Temperature(Water,P=P[16],h=h[2])
6 2.525E-09 5.329E-03 OK 3 0 Q_in=m_dot*(h[11]-h[10]+z*(h[15]-h[14]))
7 3.786E-11 3.905E-07 OK 3 0 W_total_pump=W_p1+W_p2+W_p3
8 2.525E-09 1.946E-03 OK 3 0 W_net=W_LPT+W_HPT-W_p1-W_p2-W_p3
9 4.218E-14 1.540E-12 OK 3 0 Eta_sys_new=(W_net/q_in)*100
10 3.786E-11 2.479E-06 OK 3 0 H_C[2]=m_dot*n*h[2]
11 2.525E-09 1.526E-03 OK 3 0 H_C[4]=m_dot*h[4]
12 3.174E-10 -8.958E-05 OK 3 0 H_C[5]=m_dot*(x+y)*h[5]
13 3.174E-10 -8.958E-05 OK 3 0 H_C[6]=m_dot*(x+y)*h[6]
14 2.525E-09 2.010E-03 OK 3 0 H_C[7]=m_dot*h[7]
15 3.174E-10 -3.758E-05 OK 3 0 H_C[8]=m_dot*(x)*h[8]

16 3.174E-10 -3.758E-05 OK 3 0 H_C[9]=m_dot*(x)*h[9]
17 2.525E-09 2.349E-03 OK 3 0 H_C[10]=m_dot*h[10]
18 3.174E-10 -1.216E-04 OK 3 0 H_C[12]=m_dot*x*h[12]
19 2.525E-09 1.358E-03 OK 3 0 H_C[13]=m_dot*(y)*h[13]
20 2.525E-09 4.001E-03 OK 3 0 H_C[14]=m_dot*(z)*h[14]
21 2.525E-09 4.572E-03 OK 3 0 H_C[15]=m_dot*(z)*h[15]
22 3.174E-10 -6.544E-05 OK 3 0 H_C[16]=m_dot*(m)*h[16]
23 2.525E-09 2.456E-03 OK 3 0 H_C[17]=m_dot*(n)*h[17]
Parametric Table: overall viwe
b T10 sys,new Wnet T3 hnew,3 x y z n
Run 1 0 266 36.82 777195 175.4 742.9 0.1523 0.2144 0.6333 0.5428
Run 2 0.01 266 36.78 776298 175.4 742.9 0.1523 0.2144 0.6333 0.5345
Run 3 0.02 266 36.73 775400 175.4 742.9 0.1523 0.2144 0.6333 0.5262
Run 4 0.03 266 36.69 774502 175.4 742.9 0.1523 0.2144 0.6333 0.5179
Run 5 0.04 266 36.65 773605 175.4 742.9 0.1523 0.2144 0.6333 0.5095
Run 6 0.05 266 36.61 772707 175.4 742.9 0.1523 0.2144 0.6333 0.5012
Run 7 0.06 266 36.56 771810 175.4 742.9 0.1523 0.2144 0.6333 0.4929
Run 8 0.07 266 36.52 770912 175.4 742.9 0.1523 0.2144 0.6333 0.4846
Run 9 0.08 266 36.48 770014 175.4 742.9 0.1523 0.2144 0.6333 0.4763
Run 10 0.09 266 36.44 769117 175.4 742.9 0.1523 0.2144 0.6333 0.468
Run 11 0.1 266 36.39 768219 175.4 742.9 0.1523 0.2144 0.6333 0.4597
Run 12 0.11 266 36.35 767321 175.4 742.9 0.1523 0.2144 0.6333 0.4514
Run 13 0.12 266 36.31 766424 175.4 742.9 0.1523 0.2144 0.6333 0.4431
Run 14 0.13 266 36.27 765526 175.4 742.9 0.1523 0.2144 0.6333 0.4347
Run 15 0.14 266 36.22 764629 175.4 742.9 0.1523 0.2144 0.6333 0.4264
Run 16 0.15 266 36.18 763731 175.4 742.9 0.1523 0.2144 0.6333 0.4181
Run 17 0.16 266 36.14 762833 175.4 742.9 0.1523 0.2144 0.6333 0.4098
Run 18 0.17 266 36.1 761936 175.4 742.9 0.1523 0.2144 0.6333 0.4015
Run 19 0.18 266 36.05 761038 175.4 742.9 0.1523 0.2144 0.6333 0.3932
Run 20 0.19 266 36.01 760140 175.4 742.9 0.1523 0.2144 0.6333 0.3849
Run 21 0.2 266 35.97 759243 175.4 742.9 0.1523 0.2144 0.6333 0.3766
Run 22 0.21 266 35.93 758345 175.4 742.9 0.1523 0.2144 0.6333 0.3683
Run 23 0.22 266 35.88 757448 175.4 742.9 0.1523 0.2144 0.6333 0.36
Run 24 0.23 266 35.84 756550 175.4 742.9 0.1523 0.2144 0.6333 0.3516
Run 25 0.24 266 35.8 755652 175.4 742.9 0.1523 0.2144 0.6333 0.3433
Run 26 0.25 266 35.76 754755 175.4 742.9 0.1523 0.2144 0.6333 0.335
Run 27 0.26 266 35.71 753857 175.4 742.9 0.1523 0.2144 0.6333 0.3267
Run 28 0.27 266 35.67 752959 175.4 742.9 0.1523 0.2144 0.6333 0.3184
Run 29 0.28 266 35.63 752062 175.4 742.9 0.1523 0.2144 0.6333 0.3101
Run 30 0.29 266 35.59 751164 175.4 742.9 0.1523 0.2144 0.6333 0.3018
Run 31 0.3 266 35.54 750267 175.4 742.9 0.1523 0.2144 0.6333 0.2935
Run 32 0.31 266 35.5 749369 175.4 742.9 0.1523 0.2144 0.6333 0.2852
Run 33 0.32 266 35.46 748471 175.4 742.9 0.1523 0.2144 0.6333 0.2769
Run 34 0.33 266 35.42 747574 175.4 742.9 0.1523 0.2144 0.6333 0.2685
Run 35 0.34 266 35.37 746676 175.4 742.9 0.1523 0.2144 0.6333 0.2602
m
Run 1 0.0905
Run 2 0.08881
Run 3 0.08712
Run 4 0.08543
Run 5 0.08374
Run 6 0.08205

m
Run 7 0.08036
Run 8 0.07867
Run 9 0.07698
Run 10 0.07529
Run 11 0.0736
Run 12 0.07191
Run 13 0.07022
Run 14 0.06853
Run 15 0.06684
Run 16 0.06515
Run 17 0.06346
Run 18 0.06177
Run 19 0.06008
Run 20 0.05839
Run 21 0.0567
Run 22 0.05501
Run 23 0.05332
Run 24 0.05163
Run 25 0.04994
Run 26 0.04825
Run 27 0.04656
Run 28 0.04487
Run 29 0.04318
Run 30 0.04149
Run 31 0.0398
Run 32 0.03811
Run 33 0.03642
Run 34 0.03473
Run 35 0.03304
Parametric Table: O.P for P_12
P12 sys,new Wnet x z y m n
Run 1 5000 31.71 596780 0.4112 0.4441 0.1447 0.04252 0.4016
Run 2 4500 33.04 635627 0.3552 0.4801 0.1647 0.05165 0.4285
Run 3 4000 34.21 673348 0.301 0.5171 0.1819 0.06104 0.4561
Run 4 3500 35.25 710418 0.2479 0.5559 0.1962 0.07088 0.485
Run 5 3000 36.17 747347 0.195 0.5973 0.2076 0.08139 0.516
Run 6 2500 36.97 784749 0.1415 0.6428 0.2158 0.09291 0.5499
Parametric Table: O.P for P_13
P13 sys,new Wnet x z y m n
Run 1 2000 36.88 796997 0.2084 0.6563 0.1353 0.09147 0.4923
Run 2 1900 37.01 803773 0.2123 0.6664 0.1213 0.09493 0.4989
Run 3 1800 37.14 810485 0.2163 0.6766 0.1071 0.09839 0.5057
Run 4 1700 37.25 817126 0.2205 0.687 0.09246 0.1019 0.5126
Run 5 1600 37.35 823694 0.2249 0.6976 0.07744 0.1054 0.5198
Run 6 1500 37.44 830179 0.2295 0.7085 0.06195 0.1089 0.5271
Run 7 1400 37.51 836574 0.2343 0.7197 0.04595 0.1124 0.5348
Run 8 1300 37.57 842866 0.2394 0.7312 0.02936 0.116 0.5427

Parametric Table: O.P for P_reheat
Preheat rat sys,new Wnet x z y m n
Run 1 7000 0.5833 36.19 711192 0.1523 0.6333 0.2144 0.09917 0.5341
Run 2 6500 0.5417 36.29 717390 0.1523 0.6333 0.2144 0.09855 0.5347
Run 3 6000 0.5 36.38 723769 0.1523 0.6333 0.2144 0.09789 0.5354
Run 4 5500 0.4583 36.47 730346 0.1523 0.6333 0.2144 0.09717 0.5361
Run 5 5000 0.4167 36.55 737145 0.1523 0.6333 0.2144 0.09639 0.5369
Run 6 4500 0.375 36.63 744192 0.1523 0.6333 0.2144 0.09554 0.5377
Run 7 4000 0.3333 36.7 751514 0.1523 0.6333 0.2144 0.09459 0.5387
Run 8 3500 0.2917 36.76 759146 0.1523 0.6333 0.2144 0.09351 0.5398
Run 9 3000 0.25 36.8 767122 0.1523 0.6333 0.2144 0.09228 0.541
Run 10 2500 0.2083 36.82 775477 0.1523 0.6333 0.2144 0.09083 0.5425
Run 11 2400 0.2 36.82 777195 0.1523 0.6333 0.2144 0.0905 0.5428
Run 12 2000 0.1667 36.8 784222 0.1523 0.6333 0.2144 0.08905 0.5442
Parametric Table: P_brine
Pbrine,18 hbrine,18 b Wnet sys,new T3 Qdesel T10
Run 1 1200 2784 0.1 768577 36.41 175.4 158834 266
Run 2 1100 2781 0.1 768475 36.41 175.4 159971 266
Run 3 1000 2778 0.1 768385 36.4 175.4 161169 266
Run 4 900 2774 0.1 768310 36.4 175.4 162439 266
Run 5 800 2769 0.1 768253 36.4 175.4 163796 266
Run 6 700 2763 0.1 768219 36.39 175.4 165261 266
Run 7 600 2757 0.1 768216 36.39 175.4 166863 266
Run 8 500 2749 0.1 768255 36.4 175.4 168643 266
Run 9 400 2739 0.1 768355 36.4 175.4 170674 266
Run 10 300 2725 0.1 768551 36.41 175.4 173079 266
Run 11 200 2707 0.1 768919 36.43 175.4 176124 266
Run 12 100 2675 0.1 769698 36.46 175.4 180598 266
Parametric Table: 1234
b T10 sys,new Wnet T3 hnew,3 x y z n
Run 1 0 263.4 37.14 822747 179.9 762.9 0.2505 0.04243 0.7071 0.586
Run 2 0.01 263.4 37.13 822602 179.9 762.9 0.2505 0.04243 0.7071 0.5776
Run 3 0.02 263.4 37.12 822456 179.9 762.9 0.2505 0.04243 0.7071 0.5692
Run 4 0.03 263.4 37.12 822311 179.9 762.9 0.2505 0.04243 0.7071 0.5608
Run 5 0.04 263.4 37.11 822165 179.9 762.9 0.2505 0.04243 0.7071 0.5524
Run 6 0.05 263.4 37.1 822019 179.9 762.9 0.2505 0.04243 0.7071 0.5439
Run 7 0.06 263.4 37.1 821874 179.9 762.9 0.2505 0.04243 0.7071 0.5355
Run 8 0.07 263.4 37.09 821728 179.9 762.9 0.2505 0.04243 0.7071 0.5271
Run 9 0.08 263.4 37.08 821583 179.9 762.9 0.2505 0.04243 0.7071 0.5187
Run 10 0.09 263.4 37.08 821437 179.9 762.9 0.2505 0.04243 0.7071 0.5103
Run 11 0.1 263.4 37.07 821291 179.9 762.9 0.2505 0.04243 0.7071 0.5018
Run 12 0.11 263.4 37.06 821146 179.9 762.9 0.2505 0.04243 0.7071 0.4934
Run 13 0.12 263.4 37.06 821000 179.9 762.9 0.2505 0.04243 0.7071 0.485
Run 14 0.13 263.4 37.05 820854 179.9 762.9 0.2505 0.04243 0.7071 0.4766
Run 15 0.14 263.4 37.04 820709 179.9 762.9 0.2505 0.04243 0.7071 0.4682
Run 16 0.15 263.4 37.04 820563 179.9 762.9 0.2505 0.04243 0.7071 0.4598
Run 17 0.16 263.4 37.03 820418 179.9 762.9 0.2505 0.04243 0.7071 0.4513
Run 18 0.17 263.4 37.02 820272 179.9 762.9 0.2505 0.04243 0.7071 0.4429
Run 19 0.18 263.4 37.02 820126 179.9 762.9 0.2505 0.04243 0.7071 0.4345
Run 20 0.19 263.4 37.01 819981 179.9 762.9 0.2505 0.04243 0.7071 0.4261

Parametric Table: 1234
m
Run 1 0.1211
Run 2 0.1195
Run 3 0.1179
Run 4 0.1163
Run 5 0.1147
Run 6 0.1132
Run 7 0.1116
Run 8 0.11
Run 9 0.1084
Run 10 0.1068
Run 11 0.1053
Run 12 0.1037
Run 13 0.1021
Run 14 0.1005
Run 15 0.09893
Run 16 0.09735
Run 17 0.09576
Run 18 0.09418
Run 19 0.0926
Run 20 0.09102
0.1 0.2 0.3 0.4 0.5 0.6
36
36.5
37
Preheat/P,boiler
sys,new

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
35
35.5
36
36.5
37
37.5
38
b
sys,new
0 200 400 600 800 1000 1200
36.3
36.4
36.5
Pbrine[18]
sys,new


36

Appendix B:

File:C:UsersAli AlkathiriDesktopSDPFinalMSF_32 (1).EES 4/25/2016 9:26:31 PM Page 1
Inputs
Md = 378.8 Total Distillate Flow Rate
n = 42 Total Number of Stages
Tf = 25 [C] Feed Seawater Temperature
To = 160 [C] Top Brine Temperature
Tsteam = 170 [C] Steam Temperature
Tn = 40 [C] Brine Temperature In Last Stage
Xf = 42000 [ppm] Salinity of Feed Seawater
Cp = Cp water , T = Tf , x = 0 Heat Capacity of Liquid Streams
Cd = 0.5 Weir Friction Cofficient
Vvn = 6 [m/s] Vapor Velocity in the last Stage
Vb = 180 [Kg/ms] Brine Mass Flow Rate Per Stage Width
Temprutres Calcution
Tavg =
To + Tn
2
Avrege Temperature of Brine Seawater
hfg,av = Enthalpyvaporization SteamIAPWS , T = Tavg Heat Transfer Coefficient of Braine at Avrege Temperature
hfg,steam = Enthalpyvaporization SteamIAPWS , T = Tsteam Heat Transfer Coefficient of steam at Steam Temperature
T =
To – Tn
n
The Temperature Drop Per Stage
Ti = To – T Temperature at i Stage
Tii,DELTA,T = To – T · i for i = 1 to n
T1 = Tf + n · T Seawater Temperature leavs the first stage of the condenser
T2 = T1 – T Seawater Temperature leavs the second stage of the condenser
i = Tf + n – i – 1 · T for i = 1 to n xi=Ti
flow rate
for first stage
y = Cp ·
T
hfg,av
specific ratio of Sensible Heat
Md = Mf · 1 – 1 – y
n
Mb = Mf – Md Rejected Brine Mass Flow Rate
Xf · Mf = Xb · Mb X is Salt Concentration

Msteam = Mf · Cp ·
To – T1
hfg,steam
Steam Flow Rate
Heat transfer Area
Ab = Msteam ·
hfg,steam
Ub · Tlmtd,b
Area of Brine Preheater
Ub = 1.7194 + 3.2063 · 10
– 3
· Tsteam + 1.5971 · 10
– 5
· Tsteam
2
– 1.9918 · 10
– 7
· Tsteam
3
Tlmtd,b =
Tsteam – To – Tsteam – T1
ln
Tsteam – To
Tsteam – T1
Logarithmic Mean Temperature
Ac =
Mf · Cp · T1 – T2
Uc · Tlmtd,c
Area of Condenser
Uc = 1.7194 + 3.2063 · 10
– 3
· Tv,1 + 1.5971 · 10
– 5
· Tv,1
2
– 1.9918 · 10
– 7
· Tv,1
3
Tv,1 = Ti – BPE1 – NEA1 – T1 Vapor Temperature
BPE1 = X1 · B + X1 · C · 10
– 3
Boiling Point Elevation
X1 =
Mf · Xf
B1
B1 = Mf – D1
D1 = y · Mf Amount of Flashing Vapor Formed in First Stage
B = 6.71 + 6.34 · 10
– 2
· Ti + 9.74 · 10
– 5
· Ti
2
· 10
– 3
C = 22.238 + 9.59 · 10
– 3
· Ti + 9.42 · 10
– 5
· Ti
2
· 10
– 8
NEA1 = 0.9784
To
· 15.7378
H1
· 1.3777
Vb
· 10
– 6
Non-Equilibrium Allawnce
T1 = 0
Tlmtd,c =
Tv,1 – T1 – Tv,1 – T2
ln
Tv,1 – T1
Tv,1 – T2
A = n · Ac + Ab
Dii = Mf · 1 – 1 – y
i
for i = 1 to n Md in each stage + all stages before
Mb,i = Mf – Mf · 1 – 1 – y
i
for i = 1 to n R = Mb
Xi =
Mf · Xf
Bi
for i = 1 to n
Bi = Mf – Dii for i = 1 to n
stage Diamentions
GH1 =
Mf · 2 · bi · Pi
– 0.5
Cd · W
Gate Height
bi = 1002

Pi = 10490 Presure in each Stage
GH : gate height
dP : stage pressure drop
db : brine density
Cd : weir friction coeff.
W : stage width
H1 = 0.2 + GH1
W =
Mf
Vb
Width of the Stage
PR =
Md
Msteam
Performance
Q = Msteam · hfg,steam
Msteam = 800 · bex Bex : the extraxtion fraction of mass flow rate
SOLUTION
Unit Settings: SI C kPa kJ mass deg
A = 46290 [m2
] Ab = 4156 [m2
]
Ac = 1003 [m2
] B = 0.01908
BPE1 = 1.27 [C] B1 = 1885 [Kg/s]
bex = 0.07253 C = 2.607E-07
Cd = 0.5 Cp = 4.183 [Kj/Kg-C]
bi = 1002 Pi = 10490
T = 2.857 [C] T1 = 0 [C]
D1 = 10.04 [Kg/s] GH1 = 0.07852 [m]
H1 = 0.2785 [m] hfg,av = 2256 [Kj/Kg]
hfg,steam = 2049 [Kj/Kg] Mb = 1516 [Kg/s]
Md = 378.8 [Kg/s] Mf = 1895 [Kg/s]
Msteam = 58.03 [Kg/s] n = 42
NEA1 = 0.06547 [C] PR = 6.528
Q = 118885 T1 = 145 [C]
T2 = 142.1 [C] Tavg = 100 [C]
Tf = 25 [C] Ti = 157.1 [C]
Tlmtd,b = 16.37 [C] Tlmtd,c = 12.18 [C]
Tn = 40 [C] To = 160 [C]
Tsteam = 170 [C] Tv,1 = 155.8 [C]
Ub = 1.747 [Kw/m2
-C] Uc = 1.853 [Kw/m2
-C]
Vb = 180 [Kg/ms] Vvn = 6 [m/s]
W = 10.53 [m] X1 = 42224
Xb = 52496 [ppm] Xf = 42000 [ppm]
y = 0.005297
264 potential unit problems were detected.
Arrays Table: Main
i Dii Bi Xi Mb,i Tii,3
1 145 10.04 1885 42224 1885 157.1
2 142.1 20.02 1875 42449 1875 154.3
3 139.3 29.95 1865 42675 1865 151.4

Arrays Table: Main
i Dii Bi Xi Mb,i Tii,3
4 136.4 39.82 1855 42902 1855 148.6
5 133.6 49.65 1845 43130 1845 145.7
6 130.7 59.42 1835 43360 1835 142.9
7 127.9 69.14 1825 43591 1825 140
8 125 78.81 1816 43823 1816 137.1
9 122.1 88.43 1806 44056 1806 134.3
10 119.3 98 1797 44291 1797 131.4
11 116.4 107.5 1787 44527 1787 128.6
12 113.6 117 1778 44764 1778 125.7
13 110.7 126.4 1768 45002 1768 122.9
14 107.9 135.8 1759 45242 1759 120
15 105 145.1 1749 45483 1749 117.1
16 102.1 154.3 1740 45725 1740 114.3
17 99.29 163.6 1731 45969 1731 111.4
18 96.43 172.7 1722 46213 1722 108.6
19 93.57 181.9 1713 46460 1713 105.7
20 90.71 190.9 1704 46707 1704 102.9
21 87.86 200 1695 46956 1695 100
22 85 208.9 1686 47206 1686 97.14
23 82.14 217.9 1677 47457 1677 94.29
24 79.29 226.7 1668 47710 1668 91.43
25 76.43 235.6 1659 47964 1659 88.57
26 73.57 244.4 1650 48219 1650 85.71
27 70.71 253.1 1641 48476 1641 82.86
28 67.86 261.8 1633 48734 1633 80
29 65 270.4 1624 48994 1624 77.14
30 62.14 279 1616 49255 1616 74.29
31 59.29 287.6 1607 49517 1607 71.43
32 56.43 296.1 1598 49781 1598 68.57
33 53.57 304.6 1590 50046 1590 65.71
34 50.71 313 1582 50312 1582 62.86
35 47.86 321.4 1573 50580 1573 60
36 45 329.7 1565 50850 1565 57.14
37 42.14 338 1557 51120 1557 54.29
38 39.29 346.3 1548 51393 1548 51.43
39 36.43 354.5 1540 51666 1540 48.57
40 33.57 362.6 1532 51941 1532 45.71
41 30.71 370.7 1524 52218 1524 42.86
42 27.86 378.8 1516 52496 1516 40
There are a total of 299 equations in the Main program.
Block Rel. Res. Abs. Res. Units Calls Time(ms) Equations
0 0.000E+00 0.000E+00 OK 1 0 M_d=378.8
0 0.000E+00 0.000E+00 OK 1 0 n=42
0 0.000E+00 0.000E+00 OK 1 0 T_f=25[C]
0 0.000E+00 0.000E+00 OK 1 0 T_o=160[C]
0 0.000E+00 0.000E+00 OK 1 0 T_steam=170[C]
0 0.000E+00 0.000E+00 OK 1 0 T_n=40[C]
0 0.000E+00 0.000E+00 OK 1 0 X_f=42000[ppm]
0 0.000E+00 0.000E+00 OK 1 0 C_d=0.5
0 0.000E+00 0.000E+00 OK 1 0 V_vn=6[m/s]
0 0.000E+00 0.000E+00 OK 1 0 V_b=180[Kg/ms]
0 0.000E+00 0.000E+00 OK 1 0 DELTA_T1=0
0 0.000E+00 0.000E+00 OK 1 0 DELTA_bi=1002
0 0.000E+00 0.000E+00 OK 1 0 DELTA_Pi=10490
0 0.000E+00 0.000E+00 OK 4 0 C_p=Cp(Water,T=T_f,x=0)

0 0.000E+00 0.000E+00 OK 4 0 T_avg=(T_o+T_n)/2
0 0.000E+00 0.000E+00 OK 4 0 h_fg_av=Enthalpy_vaporization(Steam_IAPWS,T=T_avg)
0 0.000E+00 0.000E+00 OK 4 0 h_fg_steam=Enthalpy_vaporization(Steam_IAPWS,T=T_steam)
0 0.000E+00 0.000E+00 OK 4 0 DELTA_T=(T_o-T_n)/n
0 0.000E+00 0.000E+00 OK 4 0 T_i=T_o-DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 Ti[1,3]=T_o-DELTA_T*1
0 0.000E+00 0.000E+00 ? 4 0 Ti[2,3]=T_o-DELTA_T*2
0 0.000E+00 0.000E+00 ? 4 0 Ti[3,3]=T_o-DELTA_T*3
0 0.000E+00 0.000E+00 ? 4 0 Ti[4,3]=T_o-DELTA_T*4
0 0.000E+00 0.000E+00 ? 4 0 Ti[5,3]=T_o-DELTA_T*5
0 0.000E+00 0.000E+00 ? 4 0 Ti[6,3]=T_o-DELTA_T*6
0 0.000E+00 0.000E+00 ? 4 0 Ti[7,3]=T_o-DELTA_T*7
0 0.000E+00 0.000E+00 ? 4 0 Ti[8,3]=T_o-DELTA_T*8
0 0.000E+00 0.000E+00 ? 4 0 Ti[9,3]=T_o-DELTA_T*9
0 0.000E+00 0.000E+00 ? 4 0 Ti[10,3]=T_o-DELTA_T*10
0 0.000E+00 0.000E+00 ? 4 0 Ti[11,3]=T_o-DELTA_T*11
0 0.000E+00 0.000E+00 ? 4 0 Ti[12,3]=T_o-DELTA_T*12
0 0.000E+00 0.000E+00 ? 4 0 Ti[13,3]=T_o-DELTA_T*13
0 0.000E+00 0.000E+00 ? 4 0 Ti[14,3]=T_o-DELTA_T*14
0 0.000E+00 0.000E+00 ? 4 0 Ti[15,3]=T_o-DELTA_T*15
0 0.000E+00 0.000E+00 ? 4 0 Ti[16,3]=T_o-DELTA_T*16
0 0.000E+00 0.000E+00 ? 4 0 Ti[17,3]=T_o-DELTA_T*17
0 0.000E+00 0.000E+00 ? 4 0 Ti[18,3]=T_o-DELTA_T*18
0 0.000E+00 0.000E+00 ? 4 0 Ti[19,3]=T_o-DELTA_T*19
0 0.000E+00 0.000E+00 ? 4 0 Ti[20,3]=T_o-DELTA_T*20
0 0.000E+00 0.000E+00 ? 4 0 Ti[21,3]=T_o-DELTA_T*21
0 0.000E+00 0.000E+00 ? 4 0 Ti[22,3]=T_o-DELTA_T*22
0 0.000E+00 0.000E+00 ? 4 0 Ti[23,3]=T_o-DELTA_T*23
0 0.000E+00 0.000E+00 ? 4 0 Ti[24,3]=T_o-DELTA_T*24
0 0.000E+00 0.000E+00 ? 4 0 Ti[25,3]=T_o-DELTA_T*25
0 0.000E+00 0.000E+00 ? 4 0 Ti[26,3]=T_o-DELTA_T*26
0 0.000E+00 0.000E+00 ? 4 0 Ti[27,3]=T_o-DELTA_T*27
0 0.000E+00 0.000E+00 ? 4 0 Ti[28,3]=T_o-DELTA_T*28
0 0.000E+00 0.000E+00 ? 4 0 Ti[29,3]=T_o-DELTA_T*29
0 0.000E+00 0.000E+00 ? 4 0 Ti[30,3]=T_o-DELTA_T*30
0 0.000E+00 0.000E+00 ? 4 0 Ti[31,3]=T_o-DELTA_T*31
0 0.000E+00 0.000E+00 ? 4 0 Ti[32,3]=T_o-DELTA_T*32
0 0.000E+00 0.000E+00 ? 4 0 Ti[33,3]=T_o-DELTA_T*33
0 0.000E+00 0.000E+00 ? 4 0 Ti[34,3]=T_o-DELTA_T*34
0 0.000E+00 0.000E+00 ? 4 0 Ti[35,3]=T_o-DELTA_T*35
0 0.000E+00 0.000E+00 ? 4 0 Ti[36,3]=T_o-DELTA_T*36
0 0.000E+00 0.000E+00 ? 4 0 Ti[37,3]=T_o-DELTA_T*37
0 0.000E+00 0.000E+00 ? 4 0 Ti[38,3]=T_o-DELTA_T*38
0 0.000E+00 0.000E+00 ? 4 0 Ti[39,3]=T_o-DELTA_T*39
0 0.000E+00 0.000E+00 ? 4 0 Ti[40,3]=T_o-DELTA_T*40
0 0.000E+00 0.000E+00 ? 4 0 Ti[41,3]=T_o-DELTA_T*41
0 0.000E+00 0.000E+00 ? 4 0 Ti[42,3]=T_o-DELTA_T*42
0 0.000E+00 0.000E+00 OK 4 0 T_1=T_f+n*DELTA_T
0 0.000E+00 0.000E+00 OK 4 0 T_2=T_1-DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[1]=T_f+(n-(1-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[2]=T_f+(n-(2-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[3]=T_f+(n-(3-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[4]=T_f+(n-(4-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[5]=T_f+(n-(5-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[6]=T_f+(n-(6-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[7]=T_f+(n-(7-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[8]=T_f+(n-(8-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[9]=T_f+(n-(9-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[10]=T_f+(n-(10-1))*DELTA_T

0 0.000E+00 0.000E+00 ? 4 0 xi[11]=T_f+(n-(11-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[12]=T_f+(n-(12-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[13]=T_f+(n-(13-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[14]=T_f+(n-(14-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[15]=T_f+(n-(15-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[16]=T_f+(n-(16-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[17]=T_f+(n-(17-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[18]=T_f+(n-(18-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[19]=T_f+(n-(19-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[20]=T_f+(n-(20-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[21]=T_f+(n-(21-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[22]=T_f+(n-(22-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[23]=T_f+(n-(23-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[24]=T_f+(n-(24-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[25]=T_f+(n-(25-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[26]=T_f+(n-(26-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[27]=T_f+(n-(27-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[28]=T_f+(n-(28-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[29]=T_f+(n-(29-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[30]=T_f+(n-(30-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[31]=T_f+(n-(31-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[32]=T_f+(n-(32-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[33]=T_f+(n-(33-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[34]=T_f+(n-(34-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[35]=T_f+(n-(35-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[36]=T_f+(n-(36-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[37]=T_f+(n-(37-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[38]=T_f+(n-(38-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[39]=T_f+(n-(39-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[40]=T_f+(n-(40-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[41]=T_f+(n-(41-1))*DELTA_T
0 0.000E+00 0.000E+00 ? 4 0 xi[42]=T_f+(n-(42-1))*DELTA_T
0 0.000E+00 0.000E+00 OK 4 0 y=C_p*DELTA_T/h_fg_av
0 7.327E-20 2.776E-17 OK 4 0 M_d=M_f*(1-(1-y)^n)
0 0.000E+00 0.000E+00 OK 4 0 M_b=M_f-M_d
0 0.000E+00 0.000E+00 OK 4 0 X_f*M_f=X_b*M_b
0 0.000E+00 0.000E+00 OK 4 0 M_steam=M_f*C_p*(T_o-T_1)/h_fg_steam
0 0.000E+00 0.000E+00 ? 4 0 U_b=1.7194+(3.2063*10^(-3))*T_steam+1.5971*10^(-5)*T_steam^2-1.9918*10^(
0 0.000E+00 0.000E+00 OK 4 0 T_lmtd_b=((T_steam-T_o)-(T_steam-T_1))/ln((T_steam-T_o)/(T_steam-T_1))
0 0.000E+00 0.000E+00 OK 4 0 D_1=y*M_f
0 0.000E+00 0.000E+00 ? 4 0 B=(6.71+6.34*(10^(-2))*T_i+(9.74*10^(-5))*(T_i^2))*10^(-3)
0 0.000E+00 0.000E+00 ? 4 0 C=(22.238+9.59*10^(-3)*T_i+9.42*10^(-5)*T_i^2)*10^(-8)
0 0.000E+00 0.000E+00 ? 4 0 Di[1]=M_f*(1-(1-y)^(1))
0 0.000E+00 0.000E+00 ? 4 0 M_b[1]=M_f-M_f*(1-(1-y)^(1))
0 0.000E+00 0.000E+00 ? 4 0 B[1]=M_f-Di[1]
0 0.000E+00 0.000E+00 ? 4 0 Di[2]=M_f*(1-(1-y)^(2))
0 0.000E+00 0.000E+00 ? 4 0 M_b[2]=M_f-M_f*(1-(1-y)^(2))
0 0.000E+00 0.000E+00 ? 4 0 B[2]=M_f-Di[2]
0 0.000E+00 0.000E+00 ? 4 0 Di[3]=M_f*(1-(1-y)^(3))
0 0.000E+00 0.000E+00 ? 4 0 M_b[3]=M_f-M_f*(1-(1-y)^(3))
0 0.000E+00 0.000E+00 ? 4 0 B[3]=M_f-Di[3]
0 0.000E+00 0.000E+00 ? 4 0 Di[4]=M_f*(1-(1-y)^(4))
0 0.000E+00 0.000E+00 ? 4 0 M_b[4]=M_f-M_f*(1-(1-y)^(4))
0 0.000E+00 0.000E+00 ? 4 0 B[4]=M_f-Di[4]
0 0.000E+00 0.000E+00 ? 4 0 Di[5]=M_f*(1-(1-y)^(5))
0 0.000E+00 0.000E+00 ? 4 0 M_b[5]=M_f-M_f*(1-(1-y)^(5))
0 0.000E+00 0.000E+00 ? 4 0 B[5]=M_f-Di[5]
0 0.000E+00 0.000E+00 ? 4 0 Di[6]=M_f*(1-(1-y)^(6))
0 0.000E+00 0.000E+00 ? 4 0 M_b[6]=M_f-M_f*(1-(1-y)^(6))

0 0.000E+00 0.000E+00 ? 4 0 B[6]=M_f-Di[6]
0 0.000E+00 0.000E+00 ? 4 0 Di[7]=M_f*(1-(1-y)^(7))
0 0.000E+00 0.000E+00 ? 4 0 M_b[7]=M_f-M_f*(1-(1-y)^(7))
0 0.000E+00 0.000E+00 ? 4 0 B[7]=M_f-Di[7]
0 0.000E+00 0.000E+00 ? 4 0 Di[8]=M_f*(1-(1-y)^(8))
0 0.000E+00 0.000E+00 ? 4 0 M_b[8]=M_f-M_f*(1-(1-y)^(8))
0 0.000E+00 0.000E+00 ? 4 0 B[8]=M_f-Di[8]
0 0.000E+00 0.000E+00 ? 4 0 Di[9]=M_f*(1-(1-y)^(9))
0 0.000E+00 0.000E+00 ? 4 0 M_b[9]=M_f-M_f*(1-(1-y)^(9))
0 0.000E+00 0.000E+00 ? 4 0 B[9]=M_f-Di[9]
0 0.000E+00 0.000E+00 ? 4 0 Di[10]=M_f*(1-(1-y)^(10))
0 0.000E+00 0.000E+00 ? 4 0 M_b[10]=M_f-M_f*(1-(1-y)^(10))
0 0.000E+00 0.000E+00 ? 4 0 B[10]=M_f-Di[10]
0 0.000E+00 0.000E+00 ? 4 0 Di[11]=M_f*(1-(1-y)^(11))
0 0.000E+00 0.000E+00 ? 4 0 M_b[11]=M_f-M_f*(1-(1-y)^(11))
0 0.000E+00 0.000E+00 ? 4 0 B[11]=M_f-Di[11]
0 0.000E+00 0.000E+00 ? 4 0 Di[12]=M_f*(1-(1-y)^(12))
0 0.000E+00 0.000E+00 ? 4 0 M_b[12]=M_f-M_f*(1-(1-y)^(12))
0 0.000E+00 0.000E+00 ? 4 0 B[12]=M_f-Di[12]
0 0.000E+00 0.000E+00 ? 4 0 Di[13]=M_f*(1-(1-y)^(13))
0 0.000E+00 0.000E+00 ? 4 0 M_b[13]=M_f-M_f*(1-(1-y)^(13))
0 0.000E+00 0.000E+00 ? 4 0 B[13]=M_f-Di[13]
0 0.000E+00 0.000E+00 ? 4 0 Di[14]=M_f*(1-(1-y)^(14))
0 0.000E+00 0.000E+00 ? 4 0 M_b[14]=M_f-M_f*(1-(1-y)^(14))
0 0.000E+00 0.000E+00 ? 4 0 B[14]=M_f-Di[14]
0 0.000E+00 0.000E+00 ? 4 0 Di[15]=M_f*(1-(1-y)^(15))
0 0.000E+00 0.000E+00 ? 4 0 M_b[15]=M_f-M_f*(1-(1-y)^(15))
0 0.000E+00 0.000E+00 ? 4 0 B[15]=M_f-Di[15]
0 0.000E+00 0.000E+00 ? 4 0 Di[16]=M_f*(1-(1-y)^(16))
0 0.000E+00 0.000E+00 ? 4 0 M_b[16]=M_f-M_f*(1-(1-y)^(16))
0 0.000E+00 0.000E+00 ? 4 0 B[16]=M_f-Di[16]
0 0.000E+00 0.000E+00 ? 4 0 Di[17]=M_f*(1-(1-y)^(17))
0 0.000E+00 0.000E+00 ? 4 0 M_b[17]=M_f-M_f*(1-(1-y)^(17))
0 0.000E+00 0.000E+00 ? 4 0 B[17]=M_f-Di[17]
0 0.000E+00 0.000E+00 ? 4 0 Di[18]=M_f*(1-(1-y)^(18))
0 0.000E+00 0.000E+00 ? 4 0 M_b[18]=M_f-M_f*(1-(1-y)^(18))
0 0.000E+00 0.000E+00 ? 4 0 B[18]=M_f-Di[18]
0 0.000E+00 0.000E+00 ? 4 0 Di[19]=M_f*(1-(1-y)^(19))
0 0.000E+00 0.000E+00 ? 4 0 M_b[19]=M_f-M_f*(1-(1-y)^(19))
0 0.000E+00 0.000E+00 ? 4 0 B[19]=M_f-Di[19]
0 0.000E+00 0.000E+00 ? 4 0 Di[20]=M_f*(1-(1-y)^(20))
0 0.000E+00 0.000E+00 ? 4 0 M_b[20]=M_f-M_f*(1-(1-y)^(20))
0 0.000E+00 0.000E+00 ? 4 0 B[20]=M_f-Di[20]
0 0.000E+00 0.000E+00 ? 4 0 Di[21]=M_f*(1-(1-y)^(21))
0 0.000E+00 0.000E+00 ? 4 0 M_b[21]=M_f-M_f*(1-(1-y)^(21))
0 0.000E+00 0.000E+00 ? 4 0 B[21]=M_f-Di[21]
0 0.000E+00 0.000E+00 ? 4 0 Di[22]=M_f*(1-(1-y)^(22))
0 0.000E+00 0.000E+00 ? 4 0 M_b[22]=M_f-M_f*(1-(1-y)^(22))
0 0.000E+00 0.000E+00 ? 4 0 B[22]=M_f-Di[22]
0 0.000E+00 0.000E+00 ? 4 0 Di[23]=M_f*(1-(1-y)^(23))
0 0.000E+00 0.000E+00 ? 4 0 M_b[23]=M_f-M_f*(1-(1-y)^(23))
0 0.000E+00 0.000E+00 ? 4 0 B[23]=M_f-Di[23]
0 0.000E+00 0.000E+00 ? 4 0 Di[24]=M_f*(1-(1-y)^(24))
0 0.000E+00 0.000E+00 ? 4 0 M_b[24]=M_f-M_f*(1-(1-y)^(24))
0 0.000E+00 0.000E+00 ? 4 0 B[24]=M_f-Di[24]
0 0.000E+00 0.000E+00 ? 4 0 Di[25]=M_f*(1-(1-y)^(25))
0 0.000E+00 0.000E+00 ? 4 0 M_b[25]=M_f-M_f*(1-(1-y)^(25))
0 0.000E+00 0.000E+00 ? 4 0 B[25]=M_f-Di[25]
0 0.000E+00 0.000E+00 ? 4 0 Di[26]=M_f*(1-(1-y)^(26))

0 0.000E+00 0.000E+00 ? 4 0 M_b[26]=M_f-M_f*(1-(1-y)^(26))
0 0.000E+00 0.000E+00 ? 4 0 B[26]=M_f-Di[26]
0 0.000E+00 0.000E+00 ? 4 0 Di[27]=M_f*(1-(1-y)^(27))
0 0.000E+00 0.000E+00 ? 4 0 M_b[27]=M_f-M_f*(1-(1-y)^(27))
0 0.000E+00 0.000E+00 ? 4 0 B[27]=M_f-Di[27]
0 0.000E+00 0.000E+00 ? 4 0 Di[28]=M_f*(1-(1-y)^(28))
0 0.000E+00 0.000E+00 ? 4 0 M_b[28]=M_f-M_f*(1-(1-y)^(28))
0 0.000E+00 0.000E+00 ? 4 0 B[28]=M_f-Di[28]
0 0.000E+00 0.000E+00 ? 4 0 Di[29]=M_f*(1-(1-y)^(29))
0 0.000E+00 0.000E+00 ? 4 0 M_b[29]=M_f-M_f*(1-(1-y)^(29))
0 0.000E+00 0.000E+00 ? 4 0 B[29]=M_f-Di[29]
0 0.000E+00 0.000E+00 ? 4 0 Di[30]=M_f*(1-(1-y)^(30))
0 0.000E+00 0.000E+00 ? 4 0 M_b[30]=M_f-M_f*(1-(1-y)^(30))
0 0.000E+00 0.000E+00 ? 4 0 B[30]=M_f-Di[30]
0 0.000E+00 0.000E+00 ? 4 0 Di[31]=M_f*(1-(1-y)^(31))
0 0.000E+00 0.000E+00 ? 4 0 M_b[31]=M_f-M_f*(1-(1-y)^(31))
0 0.000E+00 0.000E+00 ? 4 0 B[31]=M_f-Di[31]
0 0.000E+00 0.000E+00 ? 4 0 Di[32]=M_f*(1-(1-y)^(32))
0 0.000E+00 0.000E+00 ? 4 0 M_b[32]=M_f-M_f*(1-(1-y)^(32))
0 0.000E+00 0.000E+00 ? 4 0 B[32]=M_f-Di[32]
0 0.000E+00 0.000E+00 ? 4 0 Di[33]=M_f*(1-(1-y)^(33))
0 0.000E+00 0.000E+00 ? 4 0 M_b[33]=M_f-M_f*(1-(1-y)^(33))
0 0.000E+00 0.000E+00 ? 4 0 B[33]=M_f-Di[33]
0 0.000E+00 0.000E+00 ? 4 0 Di[34]=M_f*(1-(1-y)^(34))
0 0.000E+00 0.000E+00 ? 4 0 M_b[34]=M_f-M_f*(1-(1-y)^(34))
0 0.000E+00 0.000E+00 ? 4 0 B[34]=M_f-Di[34]
0 0.000E+00 0.000E+00 ? 4 0 Di[35]=M_f*(1-(1-y)^(35))
0 0.000E+00 0.000E+00 ? 4 0 M_b[35]=M_f-M_f*(1-(1-y)^(35))
0 0.000E+00 0.000E+00 ? 4 0 B[35]=M_f-Di[35]
0 0.000E+00 0.000E+00 ? 4 0 Di[36]=M_f*(1-(1-y)^(36))
0 0.000E+00 0.000E+00 ? 4 0 M_b[36]=M_f-M_f*(1-(1-y)^(36))
0 0.000E+00 0.000E+00 ? 4 0 B[36]=M_f-Di[36]
0 0.000E+00 0.000E+00 ? 4 0 Di[37]=M_f*(1-(1-y)^(37))
0 0.000E+00 0.000E+00 ? 4 0 M_b[37]=M_f-M_f*(1-(1-y)^(37))
0 0.000E+00 0.000E+00 ? 4 0 B[37]=M_f-Di[37]
0 0.000E+00 0.000E+00 ? 4 0 Di[38]=M_f*(1-(1-y)^(38))
0 0.000E+00 0.000E+00 ? 4 0 M_b[38]=M_f-M_f*(1-(1-y)^(38))
0 0.000E+00 0.000E+00 ? 4 0 B[38]=M_f-Di[38]
0 0.000E+00 0.000E+00 ? 4 0 Di[39]=M_f*(1-(1-y)^(39))
0 0.000E+00 0.000E+00 ? 4 0 M_b[39]=M_f-M_f*(1-(1-y)^(39))
0 0.000E+00 0.000E+00 ? 4 0 B[39]=M_f-Di[39]
0 0.000E+00 0.000E+00 ? 4 0 Di[40]=M_f*(1-(1-y)^(40))
0 0.000E+00 0.000E+00 ? 4 0 M_b[40]=M_f-M_f*(1-(1-y)^(40))
0 0.000E+00 0.000E+00 ? 4 0 B[40]=M_f-Di[40]
0 0.000E+00 0.000E+00 ? 4 0 Di[41]=M_f*(1-(1-y)^(41))
0 0.000E+00 0.000E+00 ? 4 0 M_b[41]=M_f-M_f*(1-(1-y)^(41))
0 0.000E+00 0.000E+00 ? 4 0 B[41]=M_f-Di[41]
0 0.000E+00 0.000E+00 ? 4 0 Di[42]=M_f*(1-(1-y)^(42))
0 0.000E+00 0.000E+00 ? 4 0 M_b[42]=M_f-M_f*(1-(1-y)^(42))
0 0.000E+00 0.000E+00 ? 4 0 B[42]=M_f-Di[42]
0 0.000E+00 0.000E+00 ? 4 0 W=(M_f/V_b)
0 0.000E+00 0.000E+00 OK 4 0 PR=M_d/M_steam
0 0.000E+00 0.000E+00 ? 4 0 Q=M_steam*h_fg_steam
0 5.979E-20 3.469E-18 ? 4 0 m_steam=800*b_ex
0 0.000E+00 0.000E+00 OK 4 0 A_b=M_steam*h_fg_steam/(U_b*T_lmtd_b)
0 0.000E+00 0.000E+00 OK 4 0 B_1=M_f-D_1
0 0.000E+00 0.000E+00 ? 4 0 X[1]=(M_f*X_f)/B[1]
0 0.000E+00 0.000E+00 ? 4 0 X[2]=(M_f*X_f)/B[2]
0 0.000E+00 0.000E+00 ? 4 0 X[3]=(M_f*X_f)/B[3]

0 0.000E+00 0.000E+00 ? 4 0 X[4]=(M_f*X_f)/B[4]
0 0.000E+00 0.000E+00 ? 4 0 X[5]=(M_f*X_f)/B[5]
0 0.000E+00 0.000E+00 ? 4 0 X[6]=(M_f*X_f)/B[6]
0 0.000E+00 0.000E+00 ? 4 0 X[7]=(M_f*X_f)/B[7]
0 0.000E+00 0.000E+00 ? 4 0 X[8]=(M_f*X_f)/B[8]
0 0.000E+00 0.000E+00 ? 4 0 X[9]=(M_f*X_f)/B[9]
0 0.000E+00 0.000E+00 ? 4 0 X[10]=(M_f*X_f)/B[10]
0 0.000E+00 0.000E+00 ? 4 0 X[11]=(M_f*X_f)/B[11]
0 0.000E+00 0.000E+00 ? 4 0 X[12]=(M_f*X_f)/B[12]
0 0.000E+00 0.000E+00 ? 4 0 X[13]=(M_f*X_f)/B[13]
0 0.000E+00 0.000E+00 ? 4 0 X[14]=(M_f*X_f)/B[14]
0 0.000E+00 0.000E+00 ? 4 0 X[15]=(M_f*X_f)/B[15]
0 0.000E+00 0.000E+00 ? 4 0 X[16]=(M_f*X_f)/B[16]
0 0.000E+00 0.000E+00 ? 4 0 X[17]=(M_f*X_f)/B[17]
0 0.000E+00 0.000E+00 ? 4 0 X[18]=(M_f*X_f)/B[18]
0 0.000E+00 0.000E+00 ? 4 0 X[19]=(M_f*X_f)/B[19]
0 0.000E+00 0.000E+00 ? 4 0 X[20]=(M_f*X_f)/B[20]
0 0.000E+00 0.000E+00 ? 4 0 X[21]=(M_f*X_f)/B[21]
0 0.000E+00 0.000E+00 ? 4 0 X[22]=(M_f*X_f)/B[22]
0 0.000E+00 0.000E+00 ? 4 0 X[23]=(M_f*X_f)/B[23]
0 0.000E+00 0.000E+00 ? 4 0 X[24]=(M_f*X_f)/B[24]
0 0.000E+00 0.000E+00 ? 4 0 X[25]=(M_f*X_f)/B[25]
0 0.000E+00 0.000E+00 ? 4 0 X[26]=(M_f*X_f)/B[26]
0 0.000E+00 0.000E+00 ? 4 0 X[27]=(M_f*X_f)/B[27]
0 0.000E+00 0.000E+00 ? 4 0 X[28]=(M_f*X_f)/B[28]
0 0.000E+00 0.000E+00 ? 4 0 X[29]=(M_f*X_f)/B[29]
0 0.000E+00 0.000E+00 ? 4 0 X[30]=(M_f*X_f)/B[30]
0 0.000E+00 0.000E+00 ? 4 0 X[31]=(M_f*X_f)/B[31]
0 0.000E+00 0.000E+00 ? 4 0 X[32]=(M_f*X_f)/B[32]
0 0.000E+00 0.000E+00 ? 4 0 X[33]=(M_f*X_f)/B[33]
0 0.000E+00 0.000E+00 ? 4 0 X[34]=(M_f*X_f)/B[34]
0 0.000E+00 0.000E+00 ? 4 0 X[35]=(M_f*X_f)/B[35]
0 0.000E+00 0.000E+00 ? 4 0 X[36]=(M_f*X_f)/B[36]
0 0.000E+00 0.000E+00 ? 4 0 X[37]=(M_f*X_f)/B[37]
0 0.000E+00 0.000E+00 ? 4 0 X[38]=(M_f*X_f)/B[38]
0 0.000E+00 0.000E+00 ? 4 0 X[39]=(M_f*X_f)/B[39]
0 0.000E+00 0.000E+00 ? 4 0 X[40]=(M_f*X_f)/B[40]
0 0.000E+00 0.000E+00 ? 4 0 X[41]=(M_f*X_f)/B[41]
0 0.000E+00 0.000E+00 ? 4 0 X[42]=(M_f*X_f)/B[42]
0 0.000E+00 0.000E+00 ? 4 0 GH_1=(M_f*(2*DELTA_bi*DELTA_Pi)^(-0.5))/(C_d*W)
0 0.000E+00 0.000E+00 ? 4 0 H_1=0.2+GH_1
0 0.000E+00 0.000E+00 ? 4 0 X_1=(M_f*X_f)/B_1
0 0.000E+00 0.000E+00 ? 4 0 NEA_1=(0.9784^T_o)*(15.7378^H_1)*(1.3777^(V_b*10^(-6)))
0 0.000E+00 0.000E+00 ? 4 0 BPE_1=X_1*(B+X_1*C)*10^(-3)
0 0.000E+00 0.000E+00 OK 4 0 T_v_1=T_i-BPE_1-NEA_1-DELTA_T1
0 0.000E+00 0.000E+00 OK 4 0 T_lmtd_c=((T_v_1-T_1)-(T_v_1-T_2))/ln((T_v_1-T_1)/(T_v_1-T_2))
0 0.000E+00 0.000E+00 ? 4 0 U_c=1.7194+(3.2063*10^(-3))*T_v_1+(1.5971*10^(-5))*(T_v_1)^2-(1.9918*10^(-7
0 0.000E+00 0.000E+00 OK 4 0 A_c=(M_f*C_p*(T_1-T_2))/(U_c*T_lmtd_c)
0 0.000E+00 0.000E+00 OK 4 0 A=n*A_c+A_b


37

Our Contacts:
Name: Alkathiri, Ali Ahmed
Mobile: 0544662184
Email: Ali.alkthiri@hotmail.com

Name: AL-HUJAILI, AMJAD AYMAN
Mobile: 0545906048
Email: Amjadhuj@gmail.com

Name: JULAIDAN, MOHAMMED ABDULLAH
Mobile: 0548218777
Email: Mohammed.julaidan@gmail.com

Final report 412

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Final report 412