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C Letter of Transmittal C Squared
Consulting LLP
Benjamin Davis
Project Manager
C Squared Consulting LLP
41 Cooper Square
New York, NY 10003
May 7, 2012
Dear Mr. Davis,
As per your request, attached is the complete report on the design and economics of the
hydrogen fueling station to be constructed at 2040 Frederick Douglass Boulevard, New York,
NY 10026. This report represents the culmination of the work for this project assigned on
Tuesday, March 6, 2012 up until the requested due date of Monday, May 7, 2012.
In order for the City of New York to break even at the end of the plant lifetime, which occurs in
year 23, 99.9999 mole % hydrogen provided at 25 °C and 700 atm must be sold to the general
public at the price of $6.72/kg. 16.7 kg of hydrogen are produced per hour, which is the exact
amount required to fuel 100 cars per day.
If you have any questions or concerns, please do not hesitate to contact us via email at C Squared
Consulting LLP.
Sincerely,
Design Team # 4
C Squared Consulting LLP
41 Cooper Square
New York, NY 10003
2
C C Squared
Consulting LLP
Design and Economic
Analysis of a Hydrogen Fueling Station
The Cooper Union for the Advancement of Science and Art
Department of Chemical Engineering ChE161.2 Process Evaluation and Design II
Mr. Benjamin Davis, Project Manager
Mr. Charles Okorafor, Project Manager
Design Team # 4
May 7, 2012
2
Table of Contents
List of Tables .................................................................................................................................. 3
List of Figures ................................................................................................................................. 4
Project Executive Summary ............................................................................................................ 5
Project Scope .................................................................................................................................. 6
Introduction ................................................................................................................................. 6
Motivation and Markets .......................................................................................................... 6
Products................................................................................................................................... 6
Process .................................................................................................................................... 6
Previous Work ............................................................................................................................ 8
Technical Discussion .................................................................................................................. 9
Reactors and Furnace ............................................................................................................ 11
Pressure Swing Adsorption Units ......................................................................................... 14
Flash Tanks ........................................................................................................................... 16
Heat Exchangers and Utilities ............................................................................................... 17
Compressors .......................................................................................................................... 19
Pump ..................................................................................................................................... 20
Economic Summary .............................................................................................................. 22
Organizational Structure ........................................................................................................... 27
Health and Safety Plan .............................................................................................................. 28
Environmental Targets .............................................................................................................. 29
Conclusions ................................................................................................................................... 31
Performance Enhancement Strategies ....................................................................................... 33
References ..................................................................................................................................... 34
Appendix A – Reactor/Furnace Details ........................................................................................ 35
Reactor Modeling...................................................................................................................... 35
Fuel Requirements .................................................................................................................... 39
Furnace Costing ........................................................................................................................ 39
Appendix B - Adsorption Tower Sample Calculations ................................................................ 40
Adsorption Tower Sizing .......................................................................................................... 40
Adsorption Tower Costing ........................................................................................................ 43
Appendix C – Flash Tank Sample Calculations ........................................................................... 45
Flash Tank Sizing ..................................................................................................................... 45
Appendix D - Heat Exchanger Sample Calculations .................................................................... 46
Heat Exchanger Sizing .............................................................................................................. 46
Heat Exchanger Costing ........................................................................................................... 48
Cooling Water Utility Costing .................................................................................................. 49
Appendix E – Compressor Sample Calculations .......................................................................... 50
Compressor Sizing…………………………………………………………………………….51
Compressor Costing .................................................................................................................. 52
Appendix G - Fixed Operating Costs............................................................................................ 53
Appendix H – MATLAB Code for Reactor Design ..................................................................... 56
Appendix I – Detailed Spreadsheets ............................................................................................. 70
3
List of Tables
Table 1. Reactor Capital Costs. ..................................................................................................... 13
Table 2. PSA Specifications. ........................................................................................................ 15
Table 3. Flash Tank Specifications. .............................................................................................. 16
Table 4. Heat Exchanger Specifications. ...................................................................................... 17
Table 5. Compressor Specifications. ............................................................................................ 19
Table 6. Pump Specifications ....................................................................................................... 20
Table 7. Storage Vessel Specifications ......................................................................................... 21
Table 8. Capital Cost Breakdown. ................................................................................................ 22
Table 9. Variable Operating Cost Breakdown. ............................................................................. 22
Table 10. Fixed Operating Cost Breakdown. ................................................................................ 22
Table 11. Economic Analysis Summary. ...................................................................................... 24
Table 12. Summary of Costs. ........................................................................................................ 31
Table 13. Summary of Estimated Values. .................................................................................... 31
Table 14. Summary of DCFROR Analysis................................................................................... 31
Table 15. Summary of Sensitivity Analysis. ................................................................................ 32
Table 16. Activated Carbon Specifications. ................................................................................. 40
4
List of Figures
Figure 1. A block flow diagram of the methane steam reforming process. .................................... 9
Figure 2. Process flow diagram of the hydrogen fueling station. ................................................ 10
Figure 3. Simplified version of the three reactor system in PRO/II. ............................................ 11
Figure 4. The layout of the top burning furnace. .......................................................................... 12
Figure 5. PSA Concept Diagram. ................................................................................................. 14
Figure 6. Heat Integration Analysis for Heat Exchangers 1 through 4. ........................................ 18
Figure 7. Cash Flow Diagram for 20 year break-even point. ....................................................... 24
Figure 8. Cash Flow Diagram for 10% DCFROR. ....................................................................... 25
Figure 9. Cash Flow Diagram for 8 year break-even point. ........................................................ 25
Figure 10. Sensitivity Analysis, where various parameters were increased by 10%. ................... 26
Figure 11. Overhead view of hydrogen fueling station. ............................................................... 27
Figure 12. NAAQS set by the EPA as of October 2011 [1]. ........................................................ 29
Figure 13. MSR models. ............................................................................................................... 36
Figure 14. HTWGS Profiles. ........................................................................................................ 37
Figure 15. LTWGS Profiles. ......................................................................................................... 38
Figure 16. Breakthrough curve. .................................................................................................... 42
Figure 17. Mollier Diagram .......................................................................................................... 50
Figure 18. Compressor Costing Curve ......................................................................................... 52
5
Project Executive Summary
As there has been a push to decrease the impact of cars and industrial plants on the environment,
hydrogen is steadily being viewed as a potential useful and environmentally friendly energy
source. Hydrogen burns cleanly in the presence of oxygen with water being the only byproduct.
Hydrogen is used extensively in the petrochemical industry and ammonia production as well as
in other industries. The proposed plant and fueling station is located at 2040 Frederick Douglas
Boulevard in New York City at the northwest corner of Central Park. It will take two years to
construct and will be in operation for 20 years. The hydrogen product will be used to fuel
hydrogen fuel cell vehicles. Each car has a capacity of 4 kg of 99.9999 mole % pure hydrogen,
supplied at 700 atm and 25 °C. In one day, the plant can supply 100 fuel cell cars with hydrogen
while only emitting trace amounts of carbon compounds.
The selling price of hydrogen for this plant is $6.72/kg. This selling price is found by allowing
the plant to break even at the end of its life, thereby making no net income. For the plant the total
capital cost is $3,000,000. This includes the cost of reactors, storage tanks, separation vessels,
heat exchangers, compressors, and pumps. The total yearly utility cost for the plant is
$450,000/yr. This includes the electricity, cooling water, reactor catalyst, adsorbents, and raw
materials. The total yearly fixed cost is $450,000/yr. There are 5 workers on site at all times with
one supervisor. Also, there is a laboratory for quality control to ensure that the product meets all
standards that are mandated.
If the City of New York wishes to make a profit on this venture, then the selling price of
hydrogen would need to be increased. If hydrogen is sold for $9.00/kg then a there will be a 10%
return on investment and the plant will break even in the 11th
year. If the city wants to make back
its investment sooner, then the hydrogen can be sold for $11.23/kg. This would lead to a rate of
return of 16% and a break-even point in the 8th
year. The target selling price for the hydrogen
was $4.00/kg because a kilogram of hydrogen contains about as much energy as a gallon of
gasoline and it is desired that the hydrogen be sold competitively with gasoline. Although the
price of hydrogen is above the target value, the long term environmental impact is minimal.
A sensitivity analysis on the plant reveals that the three major factors in the selling price of
hydrogen are the price of natural gas, the capital investment of the plant, and the fixed cost. This
means that if the price of natural gas unexpectedly increases, a major piece of equipment needs
to be purchased, or a worker needs to be added, then increases in cost would lead to the highest
increase in hydrogen selling price.
For future consideration for this project, use computer simulation software to rigorously model
the major pieces of equipment is recommended. This would include the furnace, a unit operation
responsible for providing the energy necessary for certain processes to take place, and the
pressure swing adsorption units, which are unit operations that are responsible for the bulk of the
separation in the plant. This would hopefully lead to more efficient designs and lower the cost of
the equipment. Furthermore, it is recommended to research better methods of natural gas storage,
as it is a major part of the capital investment.
6
Project Scope
Introduction
Motivation and Markets
Due to the rapid exhaustion of light crude oil reserves used to make liquid fuels, there is a
growing demand for alternative sources of energy as fuels [1]. Hydrogen (H2) production is one
such area which holds some promise as an alternative source of energy. Currently, natural gas
and coal are the cheapest sources of H2. However, since carbon dioxide (CO2) is produced in H2
production, CO2 storage and capture is essential to reduce emissions. Another obstacle in
adopting H2 as an alternative energy source is storing H2 in fuel cell vehicles (FCVs). The aim is
to store 4 kg of H2 (sufficient for a drive of about 400 km) while minimizing cost, volume,
weight, and refueling time. However, H2 storage requires energy-intensive compression at a high
pressure (350-700 atm), which necessitates about 12% of the H2 lower heating value (LHV) [2].
Though commercial options are available, they do not currently meet the requirements for cost,
drive-range, and efficiency. Currently, of the hydrogen produced annually in the United States
(11 million tons per year as of 2006), half is consumed in ammonia production (for fertilizing
applications). The other half is used to convert heavy petroleum fractions into lighter ones
(hydrocracking). The remainder is used in specialized applications such as in hydrogen fueling
stations. As of 2007, about 140 H2 fueling stations were operational worldwide, fueling about
400 FCVs and 100 buses [2]. In terms of hydrogen production, a big obstacle in reducing the
environmental footprint is capturing and storing CO2 in order to reduce emissions. Another
obstacle is the production and distribution of hydrogen. Even if the hydrogen can be produced
efficiently, the storage and distribution costs make it impractical to do at the industrial level.
Thus the goal of this project is to design a hydrogen production plant/fueling station that
provides 4 kg of H2 to about 100 cars a day at a competitive price.
Products
The products of this hydrogen refueling station are H2 and CO2. Specifically, the hydrogen
product is aimed to be 99.9999% pure by mole at 700 atm and 25 , with enough hydrogen to
fuel 100 vehicles a day with a tank size of 4 kg. In order to minimize the environmental
footprint of the hydrogen fueling station, the total emissions of carbon (CO, CO2, etc.) is aimed
to be below 10-6
kg per kg hydrogen produced. The desired selling point of hydrogen is
approximately $4/kg. Since it is assumed that the utilities are reliable in the city of New York
only 2 hours worth of storage for the natural gas and water will be required in case of any supply
issues.
Process
Over 90% of the hydrogen produced in the United States is produced by a process known as
methane steam reforming. The main chemical reaction of this process is shown below.
7
The main ingredients for hydrogen production are methane (CH4) and water (H2O). This
reaction is highly endothermic, which requires tremendous amount of energy in order to proceed.
This requires the use of a furnace and a methane steam reformer, which is essentially a catalyst-
filled packed bed reactor. It is the most widely used and most developed chemical engineering
process in the production of hydrogen. Alternative methods, such as electrolysis (passing
electric current through ionic solution) and thermolysis (water decomposition at temperatures of
2500 ), exist, but are mainly used as “proof of principle” methods rather than industrial
processes and research is currently being done into more efficient methods of producing
hydrogen.
8
Previous Work
In order to safely and efficiently utilize methane steam reforming technology for industrial
applications, a thorough understanding of the fundamental mechanisms and kinetic studies in the
relevant reforming reactions is required. The mechanism and the kinetics of the reforming
reactions have been studied and modeled extensively by Xu and Ferrmont [3]. The kinetic rate
expressions developed by Xu and Fermont were used to model the temperature and
concentration flux profiles in the design of the methane steam reformer in the hydrogen fueling
station.
Posada and Manousiouthakis have performed heat and power integration studies for
conventional methane steam reforming hydrogen production plants [4]. The model developed by
Posada et al. for the conventional process of methane steam reforming based hydrogen
production includes not only the essential unit operations such as heat exchangers and
compressors required in the process but also their associated parameters. Thus, this model
served as a starting point for the design of the hydrogen fueling station. In addition, the
information from the results of the pinch analysis served as good background knowledge in
performing the pinch analysis and subsequent heat integration for this particular hydrogen
fueling station.
For pressure swing adsorption (PSA) systems associated with hydrogen production, many PSA
systems involve multiple-bed adsorbers. It is a versatile technology for gas separation and
purification. Since hydrogen product purity is required for safe and efficient operation of fuel
cell vehicles, widespread industrial application of PSA for hydrogen production has called for an
efficient simulation and optimization of PSA design. Jiang et al. have developed a set of partial
differential equations and an algorithm for modeling an efficient multiple-bed adsorption system
[5].
Various sources such as Turton et al. and Peters and Timmerhaus have included many heuristics
and guidelines for designing, sizing, and costing for various unit operations [6, 7]. CAPCOST
was also used to cost various unit operations [8]
9
Technical Discussion
Figure 1. A block flow diagram of the methane steam reforming process.
There are four essential steps to methane steam reforming – a pretreatment process, the steam
reformer, shift reactors, and a gas purification process. In the pretreatment process the reagents
need to be brought to the ideal operating conditions for the reforming reaction. Namely, the
natural gas is treated or sent through a separation system (such as a pressure swing adsorption
unit) to yield methane, which is then heated and fed to the methane steam reformer (MSR).
Water is heated to produce steam which is also fed to the MSR. As both the methane and the
water are fed to the MSR, hydrogen is produced at high temperatures (around 850 K) and
moderate pressures (15 atm). Due to the endothermic nature of the reactions, the MSR is
contained within a furnace. The process stream then proceeds through the high-temperature
water gas shift reactor, and then through the low-temperature water-gas shift reactor, where a
secondary exothermic reaction occurs, in which extra hydrogen is produced through the
conversion of carbon monoxide, as the process stream is cooled to a lower temperature. Water is
then removed from the process stream, which then goes through a separation system that
separates carbon dioxide from hydrogen. The hydrogen product stream is then compressed by a
series of compressor to the appropriate conditions (700 atm and 25 ).
A detailed process flow diagram of the simulation performed in PRO/II, a chemical engineering
modeling software program, is shown in Figure 2.
10
Figure 2. Process flow diagram of the hydrogen fueling station.
11
Reactors and Furnace
Figure 3. Simplified version of the three reactor system in PRO/II.
The design utilizes methane steam reforming for the production of hydrogen gas. This process
includes three different reactors: the methane steam reformer (MSR), high temperature water gas
shift reactor (HTWGS), and low temperature water gas shift reactor (LTWGS). The raw material
for methane steam reforming is methane gas and steam which are fed at high temperature
(850 °F) and moderate pressure (15 atm). The methane is obtained from natural gas, which is
purified by means of pressure swing adsorption (PSA). The methane is then compressed and
preheated by flue gas that comes from the furnace. Steam for use as feed is generated by heating
water using the flue gas and hot process streams in the reactor section. In order to produce 16.7
kg/hr of hydrogen through the reactor system, 42 kg/hr of methane and 145 kg/hr of steam is
feed into the MSR. Approximately three times more water than methane is fed to the reactors so
that coking does not occur.
The MSR contains Ni/MgAl2O3 (nickel-alumina) spinel catalyst which catalyzes three reversible
reactions for the production of hydrogen. These reactions are [2, 3]
( ) ( ) ( )
The overall reaction within the MSR is endothermic and heat needs to be provided to the reactor.
Therefore, the MSR is housed in a furnace where heat is generated by burning methane gas with
oxygen that has been purified to 93 mol% by pressure swing adsorption of air. The MSR consists
of 8 U-shaped tubes that are 6 meters in length. Each tube has an inner diameter of 0.1 m and is
0.006 m thick. The MSR tubes are made out of Haynes556 Alloy. MATLAB was used to model
the reactions as they proceed through the length of the tube. In modeling the reactor, variables
such as tube length, diameter, inlet temperature, and inlet pressure were varied in order to obtain
optimal conditions for the reactions. The residence time within the reactor is 40 seconds. Details
of the reactor modeling are shown in Appendix A.
The furnace which contains the steam reforming tubes is a top burning furnace. This means that
the oxygen combusts with the methane at the top of the furnace and the flames fire downward.
The steam and methane raw products enter at the top of the furnace. As the reaction proceeds,
energy is taken from the flue gas and that gas settles to the bottom of the furnace. It operates at
less than atmospheric pressure so that no flue gas can escape. Also, there is a negative induced
draft at the bottom of the furnace so that the flue gas can be transferred from the furnace and
used as a heating utility. There are 4 burners within the furnace and four tubes surround each
12
burner so that heat is transferred evenly to each tube. The furnace stands 4 m high and is 1.4 m
wide by 1.4 meters long and is made out of firebrick. The radiant surface area within the furnace
is 36.2 m2 and the convective surface area is 7.9 m
2. The convective area corresponds to the flue
gas heating the two raw material streams. The fuel requirement for the furnace is 11 kg/hr of
methane and the corresponding oxygen flow is 46 kg/hr. These values were obtained by using
the lower heating value of methane to determine how much fuel was required to meet the needed
heat duty in the furnace. Details of these calculations can be seen in Appendix A. The furnace
also burns the waste from the nature gas and hydrogen PSA units. This provides extra heating
due to the ethane and propane in the natural gas PSA unit waste and the methane in the hydrogen
PSA unit waste.
Figure 4. The layout of the top burning furnace.
The MSR product leaves the furnace at 1064 K and 13.5 atm and is cooled by a heat exchanger
to 750 K. The design for heat exchangers is displayed in Appendix D. The process stream then
enters a HTWGS reactor. This reactor and the LTWGS reactor are used so that the carbon
monoxide that was generated in the MSR can be converted into more hydrogen. This is possible
because the catalyst in each reactor allows only the second reaction (r2) to occur. Since this
reaction is exothermic there is a temperature rise in each of the shift reactors. The HTWGS
reactor contains Fe3O4-Cr2O3 (magnetite chromia) catalyst [9]. The LTWGS reactor has an inner
diameter of 0.03 m, and is 0.006 m thick and 0.1 m long. The temperature rise across the reactor
13
is 35 K and the residence time is 0.1 s. The reactor is made of stainless steel 316. Detailed
calculations are shown in Appendix A.
The product that leaves the HTWGS is at 785 K and 13 atm and is cooled by a heat exchanger to
400 K. The stream then enters the LTWGS reactor, which is used to convert remaining carbon
monoxide to hydrogen by allowing only r2 to occur. The LTWGS reactor contains Cu-ZnO
(copper-zinc oxide) catalyst for use in temperatures below 560K [10]. The reactor has an inner
diameter of 0.1 m, a tube thickness of 0.006 m, and is 1 m long. The temperature rise across the
reactor is 11 K and the pressure drop is 1 atm. The residence time is 0.5 seconds. The reactor is
made of Stainless Steel 316. Exiting the LTWGS reactor is a stream at 411 K and 12 atm which
is composed of 16.8 kg/hr of hydrogen, 8.6 kg/hr of methane, 91.5 kg/hr of carbon dioxide, 0.07
kg/hr of carbon monoxide, and 70.1 kg/hr of water.
Each reactor was cost based on the material of construction. Table 1 shows the final cost for
each reactor.
Reactor Material Material Cost ($/kg) Final Cost ($)
MSR Haynes 556 60.00 164,000
HTWGS Stainless Steel 316 17.11 30
LTWGS Stainless Steel 316 17.11 1,000
Table 1. Reactor Capital Costs.
The catalyst for each reactor was assumed to cost $10/kg and to last for four years. The total cost
of catalyst is $220/yr. The furnace was cost using CAPCOST for a reforming furnace based on
the heat load within the furnace [8]. The cost of the furnace is $77,400. Details of this calculation
can be seen in Appendix A.
14
Pressure Swing Adsorption Units
Pressure swing adsorption (PSA) units are used in order to separate one component from a multi-
component stream. In this design, PSA units are implemented to obtain pure methane from
natural gas, 93 mole% pure oxygen from air, and 99.9999 mole% pure hydrogen from a mixed
process stream. Adsorption involves the use of an adsorbent, or solid agent, to which the solute
will adsorb while the solvent stream passes through, resulting in a pure component stream. Each
PSA unit involves two beds, a purge stream, and a product stream, as displayed in Figure 5.
Figure 5. PSA Concept Diagram.
The separation of methane from natural gas involves a natural gas stream, which is assumed to
contain few impurities [11]. The major component of natural gas is methane, which is the solvent,
and although natural gas contains multiple other components, the solute is assumed to be ethane
for ease of modeling. For the separation of oxygen from air oxygen is the solvent, while nitrogen
is assumed to be the solute and other components are assumed to be negligible. The separation of
hydrogen involves a multi-component process stream containing carbon dioxide, methane,
carbon monoxide, water, and nitrogen. In order to simplify the modeling the solute is assumed to
be carbon dioxide, while hydrogen is the solvent.
In order to model the three adsorption processes it was assumed that all of the solute would be
adsorbed by the solid agent, while all of the solvent would be pass through. The adsorbent used
for the separation of methane from natural gas is activated carbon [11]. The solid agent used for
the separation of oxygen from air is molecular sieve zeolite [12]. As for the separation of
hydrogen from the process stream, three adsorption units are used in series that employ three
different solid agents: activated carbon, molecular-sieve zeolite, and activated alumina [13].
15
The PSA units were modeled according to the Klinkenberg method, which is outlined in detail in
Appendix B. From the Klinkenberg method, the sizes of each of the adsorption units were
determined. For each adsorption unit, two adsorption beds will be needed so that the adsorption
process can alternate between them every 5 minutes, with one being cleaned as the other
performs the adsorption. A clean purge stream is required in order to cleanse one of the beds, and
the necessary amount for a purge stream is 25% of the pure stream (e.g. 25% of the pure methane
stream goes to purging a bed containing adsorbent and adsorbed natural gas). Since two beds are
required, two beds must be cost for each adsorption unit.
Detailed cost calculations were performed for the adsorption units using CAPCOST, which are
outlined in Appendix B [8]. In order to cost the adsorbents associated with each of the PSA units,
it was taken into account that the adsorbents are changed twice yearly. Detailed calculations
involving the adsorbent costs are outlined in Appendix B. A summary of each of the PSA units
is displayed in the table below.
PSA Unit Adsorbent Temperature
(K)
Pressure
(atm)
Length
(m)
Diameter
(m) Cost ($)
Adsorbent
Cost ($/yr)
Methane
Separation
Activated
Carbon 397 3.8 4.2 1.38 319,000 25,000
Oxygen
Separation
Molecular-
Sieve Zeolite 436 3.8 4.5 1.49 290,000 56,000
Hydrogen
Separation
(1)
Activated
Carbon 177 40 1.4 0.46 113,000 5,600
Hydrogen
Separation
(2)
Molecular-
Sieve Zeolite 177 40 1.4 0.46 113,000 5,000
Hydrogen
Separation
(3)
Activated
Alumina 177 40 1.4 0.46 113,000 2,800
Table 2. PSA Specifications.
16
Flash Tanks
Flash tanks are used throughout the system in order to separate a liquid phase from a vapor phase.
The first implementation of a flash tank occurs after the reactor section, where liquid water is
separated from the process stream. Further along in the process, flash tanks are utilized in the
refrigeration cycles, which are discussed in detail in the following section. The final flash tank in
the process separates liquid carbon dioxide, which is then converted into dry ice, from the vapor
process stream containing primarily hydrogen, along with some impurities. These impurities are
removed via pressure swing adsorption, as discussed in the preceding section.
The flash tanks were sized according to the procedure detailed in Appendix C. They were cost
according in the same way as the adsorption towers, since flash tanks are vertical process vessels
as well. A summary of the flash tanks in the system is displayed in the table below.
Flash Tank Temperature
(K)
Pressure
(atm) Diameter (m) Length (m) Cost ($)
Water Separation 298 11 0.158 0.474 18,000
Carbon Dioxide Separation 435 3.8 0.183 0.550 20,000
Propylene (1) 240 1.8 0.313 0.940 24,000
Propylene (2) 252 2.9 0.203 0.608 19,000
Propylene (3) 265 4.5 0.187 0.562 18,000
Propylene (4) 308 14.6 0.216 0.648 19,000
Ethylene (1) 172 1.2 0.172 0.516 35,000
Ethylene (2) 204 5.2 0.238 0.714 32,000
Ethylene (3) 224 10.7 0.293 0.878 26,000
Ethylene (4) 233 14.6 0.311 0.933 27,000
Table 3. Flash Tank Specifications.
17
Heat Exchangers and Utilities
Heat exchangers are specialized equipment that facilitates efficient transfer of heat from one
medium to another. There are a total of 15 heat exchangers in the plant: 4 utility-process, 6
refrigeration-process, 4 process-process, and 1 refrigeration-refrigeration. The overall heat
transfer coefficient, U, has been specifically calculated for all heat exchangers in the hydrogen
plant. This was accomplished by using correlations presented by Peters et al [7]. The capital
costs were calculated using CAPCOST [8]. The utility costs for the heat exchangers as well as
the rest of the sample calculations are included in the Appendix D.
Heat
Exchanger
U
(W/m^2*K)
A
(m^2)
DTLM
(K)
Heat Load
(kW)
Capital cost
($)
Utility Cost
($/yr)
HEX1 219 0.15 280.7 9.2 11,800 -
HEX2 234 7.72 79 142 34,500 -
HEX3 530 0.61 276.9 89.8 18,600 -
HEX4 1342 0.19 187.3 47.2 12,800 -
HEX5 1438 2.75 21.5 85.1 27,700 8,580
HEX6 1508 1.62 10.5 25.6 34,800 15,000
HEX7 427 1.12 35.8 17.1 31,600 -
HEX8 319 0.59 7.5 1.4 26,300 -
HEX9 341 0.64 8.1 1.8 27,000 -
HEX10 551 4.85 10 26.7 44,900 -
HEX11 326 0.82 8.5 2.3 29,100 -
HEX12 333 3.16 9.5 10 40,900 -
HEX13 280 2.01 15.2 8.5 36,700 -
HEX14 447 0.75 9.7 6.4 17,400 1,490
HEX15 371 1.32 9.7 5.7 35,600 700
Table 4. Heat exchanger Specifications.
Table 4 above shows the calculated overall heat transfer coefficients, , for all heat exchanger
units in the hydrogen plant. As mentioned previously, since there are only 4 utility-process heat
exchangers, the table contains only 4 heat exchangers that have associated utility costs. The only
utility in the heat exchanger network is water. All heat exchangers operate in counter-current
flow. Due to the fact that the surface areas required by the heat exchangers are so small (i.e. less
than 10 m2), double-pipe heat exchangers made of stainless steel. There is a drastic difference
between the overall heat transfer coefficients assumed from Turton’s heuristics and the ones
calculated as shown in the sample calculations [6]. The primary reason for the discrepancy
between the assumed and the calculated values was due to difference in scale of various
parameters for heat transfer. The heuristics by Turton et al. are used as a “rule of thumb” for
industrial scale unit operations [6]. However, the heat exchangers being utilized for this
hydrogen plant have total surface areas around 0.02 m2, which means that the area available for
heat transfer is very limited. Therefore, the difference in the scale of production means there is
less heat to transfer, and thus, less material required to transfer the heat.
In order to effectively utilize all available energy in the plant heat integration with pinch analysis
was performed. Essentially, it is a method to optimize heat recovery systems in order to
minimize energy consumption from outside utilities. This was done using an online pinch
analysis tool [14]. The pinch analysis showed that no extra heat exchangers were required in the
18
system. This was due to the fact the flue gas that comes out of the furnace still contains
tremendous amounts of energy, which could still be used to heat other streams such as water to
produce steam. Therefore, in order to take advantage of the tremendous amount of heat given off
by the flue gas, the size of the heat exchangers (specifically heat exchangers 1 through 4) were
increased to utilize greater heat transfer. This design decision has added a net total of about
$9,700 in capital costs for the heat exchangers, but saves about $400,000 in utility costs. A
figure of the four heat exchangers is shown below.
Figure 6. Heat Integration Analysis for Heat Exchangers 1 through 4.
19
Compressors
Compressors are pieces of equipment that can convert electricity to kinetic energy in order to
increase the pressure of a gas. There are a total of 12 compressors in the fueling station – 6 in
the refrigeration cycles, and 6 in other processes. Based on the parameters specified in PRO/II,
the simulation generates the break horse power for each compressor in the system. Hand
calculations were performed in order to verify the results of PRO/II, which involves determining
the enthalpy from a Mollier diagram and substitution of that value into a relation for break horse
power. A simple conversion from break horse power to motor kilowatt-hour is performed. The
kilowatt-hour determined for each compressor was then used to cost each compressor using
relations given in Peters et al [7]. Detailed sample calculations are shown in the Appendix E.
The specifications for each compressor are shown below.
Compressor BHP kWh Head (ft) Capital
Cost ($)
Electricity
Cost ($/yr)
Inlet
Pressure
(atm)
Outlet
Pressure
(atm)
Temperature
Rise (K)
1 0.32 0.27 2500 3,520 158 1.5 2.93 17.3
2 0.38 0.32 2400 3,520 187 2.93 4.53 12.9
3 8.57 7.1 18000 3,960 4,230 4.53 14.97 43.8
4 4.01 3.3 29000 3,710 1,980 1.18 5.23 37.1
5 3.98 3.3 15000 3,710 1,960 5.23 10.7 19.9
6 2.36 1.9 7600 3,630 1,160 10.7 14.97 10.7
7 22.6 19 120000 4,700 11,200 11 40 118.72
8 5.5 4.6 97000 3,790 2,710 1 3.8 98.6
9 13.4 11 61000 4,210 6,590 1 3.8 137.3
10 5 4 1100000 42,000 2,466 40 370 213.9
11 5 4 490000 42,000 2,466 370 700 82.4
12 14.7 12 310000 4,280 7,250 1 15 244.16
Table 5. Compressor Specifications.
The above table shows some compressors have large amounts of head. Specifically,
compressors 10, 11, and 12 have heads that significantly surpass those of industrial sized
compressors. Thus, in order to mitigate this design issue, specialized hydrogen compressors
from HydroPac, Inc. was utilized in the design. A technical sales engineer of HydroPac, Inc., has
provided a quote of $42,000 for the compressor model C12-05-10500LX-H2/SS, which can
handle the loads as specified.
The only associated utility for the compressors is electricity, which is used to power the
compressors. The electricity is provided by a Consolidated Edison, also known as ConEd, and
priced at $0.07 per kilowatt-hour. The material of construction for all compressors is stainless
steel and driven by centrifugal motors.
20
Pump
There is only one pump in the entire station. This pump is responsible for transporting the water
that is separated from the process stream back to the furnace. The water that is transported back
is used to cool the high temperature process stream coming out of the reactors. This process
produces the steam which can be fed to the furnace and minimize water utility costs. Based on
the PRO/II simulation, the horsepower for the pump is estimated to be 0.1 HP. The reason for
the small size of the pump is due to the fact that a very small quantity (approx. 40 gallons/hr) of
water is being transported back to the furnace. The electricity cost can be computed by simple
unit conversions as shown in detail in the Appendix F. The specifications for the pump are
summarized below.
Material of Construction API-610 Cast steel casing (vertical motor)
Size 0.1 HP
Capital Cost 4000
Electricity Cost $49 / yr
Driver Type Centrifugal
Available NPSH 32.2 ft
Required NPSH 10 ft
Table 6. Pump Specifications
The net positive suction head (NPSH) is the difference between the actual pressure of a liquid in
a pipe and the liquid’s vapor pressure. This is an important parameter for pumps in design, as
the pressure of the liquid drops below the liquid vapor pressure, the liquid will start to boil,
causing cavitation to occur. Cavitation is when bubbles are formed and immediately implode
causing damaging the pump. Therefore, an indication of a well performing pump is one that has
a significantly higher available NPSH to the required NPSH. The required NPSH is provided by
a pump chart, while the available NPSH can be determined from a calculation shown in the
Appendix F.
21
Storage
Since it is assumed that the utilities in the city of New York are reliable in terms of uninterrupted
supply, only 2 hours of water and natural gas are stored in case of an emergency. The water and
natural gas will be stored in storage vessels. The hourly flow rate of the water and natural gas
specified in PRO/II were doubled to determine the quantity required for storage. The storage
vessels were sized based on an optimal height to diameter ratio of 3. CAPCOST was used to
cost the vessels [8]. Detailed calculations are shown in Appendix A.
Hydrogen storage can be accomplished by using metal hydrides. Depending on the solid metal
used, the hydrogen will adsorb and form ionic bonds to the metal (e.g. magnesium). This
circumvents the issue with exceedingly large sizes and costs associated with storing hydrogen at
high pressures (e.g. 700 atm). Metal hydride storage is not only cheaper but also is significantly
smaller than using high pressure storage vessels. The metal used for storage is magnesium, due
to its relatively cheap cost ($2.90/kg) and ease of use. The magnesium hydride (MgH2) cost was
calculated based on how much magnesium was required for the amount of hydrogen produced in
266 hours, which is the difference in the plant capacity (8500 hours) and the total amount of
hours per year including leap years (8766). 266 hours essentially represent the hours in which
the plant will not be running, storage for those hours are required. The cost for the metal hydride
is about $150,000. The vessel for the metal hydride storage was calculated in a similar manner
to that of flash tanks. Detailed calculations are shown in Appendix A. The specifications for all
storage in the station are summarized in the table below.
Storage Diameter (m) Height (m) Volume (m^3) Pressure (atm) Cost ($)
Natural Gas 1.1 3.3 3.5 40 170,000
Water 1.3 3.9 5.5 1 130,000
MgH2 2.6 7.8 40 1 541,000
Table 7. Storage Vessel Specifications
22
Economic Summary
The capital costs associated with the plant are due to the furnace, heat exchangers, flash tanks,
the pump, compressors, PSA units, storage units, and the refrigeration cycles. A summary of the
capital costs is displayed in below.
Furnace $80,000
Heat Exchangers $200,000
Flash Tanks $40,000
Pump and Compressors $100,000
PSA Units $900,000
Storage $1,000,000
Refrigeration Cycles $800,000
Total Capital Cost $3,120,000
Table 8. Capital Cost Breakdown.
The variable operating costs associated with the plant are due to the natural gas feed, water feed,
electricity (for the pump and compressors), reactor catalysts, and PSA unit adsorbents. A
summary of the variable operating costs is displayed in below.
Natural Gas $300,000/yr
Water $30,000/yr
Electricity $40,000/yr
Reactor Catalysts $200/yr
PSA Unit Adsorbents $100,000/yr
Total Variable Operating Cost $470,200/yr
Table 9. Variable Operating Cost Breakdown.
The fixed operating costs associated with the plant are due to labor, supervision, quality control,
and plant overhead. These costs are determined in Appendix G. A summary of the fixed
operating costs is displayed in below. The total annualized cost based on the capital cost and the
fixed and variable operating costs (over a 20 year plant lifetime) is $1 million.
Labor $200,000/yr
Supervision $60,000/yr
Quality Control $50,000/yr
Plant Overhead Cost $100,000/yr
Total Fixed Operating Cost $410,000/yr
Table 10. Fixed Operating Cost Breakdown.
An estimate for the working capital was determined to be $170,000 and the
decommissioning/shutdown cost for the plant was determined to be $104,000. The methods for
determining both of these costs are outlined in Appendix G.
A discounted cash flow rate of return (DCFROR) analysis was performed using the plant
economics summarized above along with sales revenue, tax information, and depreciation effects.
23
This analysis is used to determine the lowest possible selling price of hydrogen that leads to a
break-even point, or payback period, at the end of the plant life. In addition to this, the selling
prices of hydrogen that yield a 10% rate of return as well as an 8 year break-even point were
determined from a DCFROR analysis.
1,200,000 kg of dry ice are produced per year. At $0.02/kg, the yearly revenue from dry ice sales
is $24,000/yr. In order to break even after 20 years of operation a selling price for hydrogen
needs to be determined at which the 150,000 kg of hydrogen produced per year can be sold.
The first two years of the plant life involve the construction period, between which the capital
cost is spent evenly. The working capital is invested in the second year and incurred in the final
year of plant operation. During normal operation, which begins in the third year and proceeds for
20 years, the aforementioned amounts of dry ice (which is sold at the above price) and hydrogen
are produced. Yearly production costs, which are composed of the fixed and variable operating
costs, begin in the third year and proceed for 20 years. An inflation rate of 3% and straight-line
depreciation of the total capital cost are assumed, for which the calculations are outlined in
Appendix G. The yearly depreciation allowance is $156,000/yr.
An overall tax rate of 35% is assumed (federal and state). Taxation begins in the year after the
first year of production, which is year 4. The taxable profit of a given year is the cash flow
before tax of the previous year less the depreciation allowance for the aforementioned given year.
The cash flow before tax for a given year is the overall sales revenue, from both the dry ice and
hydrogen production, less the production and investment costs. The taxable profit is then taxed at
35%, which is paid to the government. The cash flow after tax for a given year is the cash flow
before tax less the tax paid to the government. The cumulative cash flow of a given year is then
determined by adding that year’s cash flow after tax to the previous year’s cumulative cash flow.
These equations are outlined in Appendix G.
The lowest possible selling price of hydrogen can be determined through trial and error in
Microsoft Excel. A spreadsheet is set up according to the manner outlined above, and the selling
price of hydrogen is manipulated until the cumulative cash flow for year 23 was $0, indicating
that no net income was made. The hydrogen selling price that yielded this result is $6.72/kg,
which is higher than the goal price of $4/kg. The plot generated from the DCFROR analysis is
displayed in Figure 7. The rate of return for this selling price of hydrogen is 0%.
As mentioned previously, the selling price of hydrogen that yields a 10% rate of return as well as
that which yields an 8 year break-even point were determined from a DCFROR analysis. In order
to obtain a 10% rate of return, the selling price of hydrogen is $9.00/kg. The break-even point, or
payback period, for this 10% rate of return, is year 11 and the final cumulative cash flow, or net
income, is $5.7 million. The plot associated with this DCFROR analysis is displayed in Figure 8.
In order to break even in year 8, the selling price of hydrogen is $11.23/kg. The rate of return in
this case is 16% and the net income is $11.3 million. The plot associated with this DCFROR
analysis is displayed in Figure 9. The results of the DCFROR analyses are displayed in below.
24
Hydrogen Selling Price Break-Even Point DCFROR Net Income
$6.72/kg 23rd
year 0% $0
$9.00/kg 11th
year 10% $5,700,000
$11.23/kg 8th
year 16% $11,300,000
Table 11. Economic Analysis Summary.
Figure 7. Cash Flow Diagram for 20 year break-even point.
-3,500,000
-3,000,000
-2,500,000
-2,000,000
-1,500,000
-1,000,000
-500,000
0
500,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Ca
sh F
low
($
)
Time (yr)
Cash Flow Diagram - Hydrogen Break-Even Price
Cumulative and
Discounted Cash
Flow
25
Figure 8. Cash Flow Diagram for 10% DCFROR.
Figure 9. Cash Flow Diagram for 8 year break-even point.
-6,000,000
-4,000,000
-2,000,000
0
2,000,000
4,000,000
6,000,000
8,000,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25Ca
sh F
low
($
)
Time (yr)
Cash Flow Diagram - 10% DCFROR
Cumulative
Cash Flow
Discounted
Cash Flow
-6,000,000
-4,000,000
-2,000,000
0
2,000,000
4,000,000
6,000,000
8,000,000
10,000,000
12,000,000
14,000,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Ca
sh F
low
($
)
Time (years)
Cash Flow Diagram - 8 yr BEP
Cumulative
Cash Flow
Discounted
Cash Flow
26
A sensitivity analysis of the process shows that changing capital cost, the price of natural gas, or
the fixed cost of the plant would affect the selling price of hydrogen the most. The analysis
considers the following parameters: capital cost, natural gas cost, electricity cost, carbon dioxide
selling price, water price, fixed capital and working capital. The analysis takes into account a
10% increase in each of these factors and the resulting cost of hydrogen is determined. The
factors that change the price of hydrogen the most are the factors to which the plant design is
most sensitive. Increasing the capital cost of the plant by 10% led to an increase in the selling
price of hydrogen by $0.13. This increase in capital could be due to higher than expected
maintenance costs or the replacement of a major piece of equipment. Increasing the price of
natural gas by 10% increased the selling price of hydrogen by $0.20. This increase could be due
to an unexpected increase in demand or a decrease in the supply of natural gas. Increasing the
fixed cost of the plant by 10% increased the selling price of hydrogen by $0.31. This increase
could be due to adding another worker or increasing the size of the laboratory. The results of the
sensitivity analysis are summarized in Figure 10.
Figure 10. Sensitivity Analysis, where various parameters were increased by 10%.
6.55
6.6
6.65
6.7
6.75
6.8
6.85
6.9
6.95
7
7.05
7.1
Base Price +10%
Capital
Cost
+10%
Natural
Gas Price
+10%
Electricity
Price
+10%
Dry ice
selling
price
+10%
Water
Price
+10%
Fixed Cost
+10%
Working
Capital
Hy
dro
gen
Pri
ce (
$/k
g)
Sensitivity Analysis
27
Organizational Structure
The fueling station is located on 2040 Frederick Douglass Blvd, New York, NY 10026. A
satellite image of the site, with labeled dimensions, is shown below.
Figure 11. Overhead view of hydrogen fueling station.
The site is sized at approximately 1,700 m2, which is more than spacious enough for the
proposed design based on the estimated sizes of all the required equipment (including storage).
The refueling station will be staffed with five capable chemical engineers, who will be
responsible for the proper maintenance and operation of the fueling station. Their
responsibilities include assisting customers with fueling their cars, as well as maintaining safe
operating conditions in the plant. In addition, one supervisor will be required in order to make
sure the plant is operated in the most efficient and safe manner. This staff accounts for the fixed
operating labor costs of the hydrogen plant during its 20 year lifetime. Based on the statistics
from the U.S. Department of Labor Bureau of Labor Statistics, the average annual income for
chemical engineering technicians is approximately $45,000 [15]. With five workers, the total
labor cost is about $225,000 per year. Ray et al. estimates the supervision cost to be about 25%
greater than the labor cost of a single worker, which is about $57,000 [16]. In terms of
administrative structure, two technicians will be assigned to monitor the control systems in the
hydrogen plant. Another two technicians will be assigned to assist the customers fuel their cars
with hydrogen. The last technician will be on call in case of any emergencies, while the
supervisor will oversee the general operations of the station.
The plant overhead includes general operating costs such as security, canteen, medical,
administration, etc. This item is often estimated to be about 50% of the fixed labor cost based on
Ray et al. [16]. Thus, the plant overhead is estimated to be approximately $110,000 per year.
28
Health and Safety Plan
Three of the biggest safety concerns on site include but are not limited to:
Hydrogen explosions
Chemical fires
Chemical leaks
Hydrogen combusts readily with oxygen at atmospheric conditions [17]. This is possible if
malfunctions occur in the reactors, which will expose the hydrogen to oxygen that is burning in
the furnace, and possibly to the oxygen in air. Although the risk is low, in the case of such of
event, the control system will activate all feed shut off valves (i.e. natural gas, air, and water) and
manually turn on the sprinklers to mitigate any damage caused by fire. The plant will also be
equipped with hydrogen and oxygen sensors to ensure that no hydrogen is accumulating in
places such as the roof of plant. A set point for the sensors will be put in place so that if the
hydrogen or oxygen levels are not within the set point or threshold levels, the feed valves will
automatically shut down. The technicians in the control room will communicate the issue to the
other technicians, who will be responsible for inspecting for any damages or potential safety
risks.
As mentioned previously, combustion with hydrogen cannot occur without oxygen [17]. This
means that combustion cannot occur in hydrogen vessels or any contained location with only
hydrogen. Therefore, the only possibility of any fires or explosions is if there is a leak or any
equipment malfunction that allows hydrogen to be exposed to oxygen. However, in the case of
any fire, there will be sensors and sprinkler systems in place with a control system that will
automatically shut off the feed valves.
In the case of leaks in the system, hydrogen cannot cause asphyxiation, which is a condition of
deficient oxygen supply due to the inability to breathe normally. This is because hydrogen is
about 14 times lighter than air and rises at a speed of 20 m/s, which is 6 times faster than natural
gas [17]. This means that in the case of any leaks, it will rise and disperse very quickly. Any gas,
with the exception of hydrogen, can cause asphyxiation in high enough concentrations.
Hydrogen is non-toxic and non-poisonous and does not contaminate ground water. Therefore,
due to the significantly low throughput of hydrogen product (only about 16 kg of H2 per day),
hydrogen gas from small leaks are not likely to cause any bodily harm to the workers or to the
people inhabiting the surrounding area. The highest risk, however, is hydrogen combustion,
which as mentioned previously, will be monitored through sensors and a safety control system.
If there is accumulation at the roof of the plant for instance, nitrogen that is separated from the
pressure swing adsorption system can be pumped to prevent accumulation.
29
Environmental Targets
Carbon emissions (CO, CO2) from the plant are about 10-6
kg per kg of hydrogen produced.
There are no wastes produced from this plant. As shown in the process flow diagram of this
station, “waste” streams can be recycled to actually further fuel the combustion reaction in the
furnace, minimizing utility costs for natural gas. Therefore, no on-site waste treatment is
required. The carbon dioxide product will be captured and stored as dry ice, which will be sold
to vendors. This means no gas will be emitted as part of the operation of the fueling station. The
United States Environmental Protection Agency has recently passed regulations regarding carbon
emissions for coal-based power plants. This regulation requires that coal-based power plants
must produce no more than 1000 lbs of CO2 per megawatt-hour of electricity produced [18].
However, New York State legislation does not currently cover emissions specifically for
hydrogen production plants. Facilities that do produce carbon emissions are required by the
Clean Air Act and under New York State rules and regulations (i.e. 6 NYCRR Part 201) to
register under the New York State Department of Environmental Conservation’s (DEC) Division
of Air Resources (DAR) [19]. The Environmental Protection Agency (EPA) manages the
emission standards. Thus, DAR will inspect and provide the permit that allows this station to
operate in the city. The inspection must pass the standards set by the EPA, however.
The Clean Air Act, amended in 1990, requires the EPA to set National Ambient Air Quality
Standards (NAAQS) for pollutants considered harmful to the public [20]. The figure below
shows the specific standards set by the EPA, which shows carbon monoxide emissions must be
below 9 ppm in an 8-hour period (primary standard) or below 35 ppm in a 1-hour period
(secondary standard). Since one of the objectives of this plant is to minimize its environmental
footprint, the fueling station will produce less than 1 ppm of carbon products, which is consists
of carbon monoxide and carbon dioxide, which already meets the NAAQS set by the EPA.
Figure 12. NAAQS set by the EPA as of October 2011 [1].
30
The state of California has more stringent emission standards, and other states may choose to
either follow its standards or those of set by the EPA. Since New York State does not have
legislation specifically addressing the emissions for hydrogen production plants, it is reasonable
to assume that it possible that it may follow the standards set by California Air Resources Board
(CARB).
CARB approved a mandatory regulation on December 6, 2007, which established a statewide
reporting system for greenhouse gas (GHG) emissions [21]. CARB has specifically laid out
regulations regarding emissions of greenhouse gases (carbon dioxide, methane, nitrous oxide,
etc.) from hydrogen plants. Hydrogen plants that produce more than 25,000 metric tons of CO2
per year are subject to regulations laid out by the mandate. The mandate is complicated and
multi-faceted, so the details will not be covered here, but essentially, hydrogen plants that
produce more than 25,000 metric tons of CO2 per year will be required to report fuel and
feedstock consumption, production, emission from stationary combustion, process emission, etc.
These plants are subject to further regulations that require reductions in their emissions. Plants
that can reduce their emissions to less than 20,000 metric tons are exempt from the mandate.
Since this plant produces approximately 400 kg of hydrogen per year with carbon emissions of
less than 1 ppm, this plant will produce less than 0.001 kg of emissions per year, which is
significantly less than the 20,000 metric tons of CO2.
In summary, the New York State DAR will perform annual inspections to validate a state permit
as certification the station meets all carbon emissions set by CARB and the EPA.
31
Conclusions
A summary of the capital cost as well as the fixed and variable operating costs, annualized
capital cost, and total annualized cost is displayed in Table 13 below.
Capital Cost $3,000,000
Annualized Capital Cost $150,000/yr
Fixed Cost $500,000/yr
Variable Cost $400,000/yr
Total Annualized Cost (TAC) $1,050,000/yr
Table 12. Summary of Costs.
A DCFROR analysis was performed based on the above costs as well as the assumptions
outlined in the economic summary section. These assumptions include a 20-year plant lifetime,
an inflation rate of 3%, an overall tax rate of 35%, and straight-line depreciation. Aside from
these assumptions, an estimate for the working capital was also implemented in the DCFROR
analysis. A summary of the yearly depreciation allowance and the working capital and
decommissioning/shutdown cost estimates is displayed in Table 14.
Depreciation Allowance $156,000/yr
Working Capital $170,000
Decommissioning/Shutdown Cost $104,000
Table 13. Summary of Estimated Values.
A DCFROR analysis was performed in order to determine the lowest possible selling price of
hydrogen that would result in a net income of $0, or a break-even point at the end of the plant
lifetime, which occurs in year 23. The results of this DCFROR analysis as well as the other two
analyses performed are discussed in detail in the economic summary section and summarized in
Table 15. The other two analyses were performed in order to determine the selling price of
hydrogen that corresponds to a 10% rate of return and a break-even point of year 8.
Hydrogen Selling Price Break-Even Point DCFROR Net Income
$6.72/kg 23rd
year 0% $0
$9.00/kg 11th
year 10% $5,700,000
$11.23/kg 8th
year 16% $11,300,000
Table 14. Summary of DCFROR Analysis.
From a sensitivity analysis, the primary economic risks were determined to be the capital cost,
the price of natural gas, and the fixed operating costs of the plant. The sensitivity analysis, which
is detailed in the economic summary section, involves increasing the price of various factors by
10% and determining the selling price of hydrogen associated with each change. It was
performed only on the data associated with the minimum cost of hydrogen, as that is the main
focus of this project. Aside from the capital cost, natural gas price, and fixed operating cost, the
other parameters investigated in this analysis were the electricity price, the dry ice selling price,
32
the water price, and the working capital. The summary of the effects of the major proponents
determined from the sensitivity analysis are summarized in Table 16.
Hydrogen Selling Price Difference from Base Price
Base Price $6.72/kg -
Capital Cost $6.85/kg $0.13/kg
Natural Gas Price $6.93/kg $0.21/kg
Electricity Price $6.76/kg $0.04/kg
Dry Ice Selling Price $6.73/kg $0.01/kg
Water Price $6.75/kg $0.03/kg
Fixed Operating Cost $7.03/kg $0.31/kg
Working Capital $6.73/kg $0.01/kg
Table 15. Summary of Sensitivity Analysis.
In conclusion, it is strongly recommended that this venture be pursued by the City of New York,
as hydrogen can be provided to the populace at a cost of $6.72/kg. Although this is higher than
that of a gallon of gasoline, which provides approximately the same energy as a kilogram of
hydrogen, it is not much higher and it is believed that people will purchase the product
consistently. Furthermore, if the city wishes to make a profit on this endeavor the hydrogen price
can be increased to $9.00/kg (for a 10% rate of return) and $11.23/kg (for a year 8 break-even
point). The convenience of a location bordering Central Park will serve to engage citizens to
spread the word about the benefits of hydrogen power and hydrogen fuel cell vehicles. The
benefits of utilizing hydrogen fuel will decrease dependence on foreign oil, as well as the
associated pollution due to both foreign and domestic oil. In closing, this project is an essential
step towards a conversion to a hydrogen economy, a greener city, and an overall eco-friendly
environment is desired, and there is no better place to start the trend than New York City.
33
Performance Enhancement Strategies
Despite rigorous calculations and strategies concerning the major components in the design of
the hydrogen fueling station, there are aspects of the design that can definitely be improved or
optimized.
The first aspect that can be optimized is the design of the furnace. As mentioned previously, the
design of the furnace is based on conventional, industrial-scale furnaces used in hydrogen
production. In order to ensure that the furnace is providing the heat transfer necessary for the
reforming reactions in the MSR, it is recommended to model and simulate the transport
phenomena (specifically the heat and mass transfer) associated with the furnace. The goal of
having a completely characterized furnace performance is the potential to save costs in burning
fuel required for the MSR. The sensitivity analysis has shown that the price of natural gas is the
second greatest source for the change in the final hydrogen selling price. This means that
reduction in natural gas utility can significantly impact the final hydrogen selling price. In
addition, the scale difference between the industrial-sized furnace and the furnace required for
this fueling station may have completely different transport phenomena. For these reasons, it is
highly recommended to model an efficient small-scale furnace.
The second aspect that is recommended for further study is the pressure swing adsorption system.
The design of the pressure swing adsorption system was based on the Klinkenberg model, which
is an approximate model for the behavior of pressure swing adsorbers [12]. Similar to the
recommendation for the furnace design, it is recommended to model the PSA’s more rigorously.
The reasons are similar to that of the furnace recommendation. Firstly, the difference in scale of
industrial PSA’s to that of the PSA’s required for this station can significantly affect the behavior
of the unit operation. Secondly, a more rigorous model can allow potential design strategies that
can reduce cost in utilities, such as reducing the amount adsorbent required for a particular PSA
cycle. Results from the sensitivity analysis shows that capital cost is the third greatest source for
the change in hydrogen price. PSA’s represent approximately a third of the total capital cost
(PSA capital costs approx. $1 million). Therefore, a good strategy to reducing the final selling
price of hydrogen is to reduce the capital costs for the PSA’s. For these reasons, a rigorous
model for the PSA system is the next logical step in terms of reducing the final hydrogen selling
price.
The third and final aspect that is recommended for further study is the storage system in the
station. Again, the sensitivity analysis shows that the capital cost is the third greatest source for
the change in the final hydrogen selling price. Storage also represents approximately a third of
the total capital cost for the fueling station (storage costs approx. $1 million). The majority of
the storage costs are attributed to the metal hydride storage system. As mentioned previously,
the storage vessel costs about $550,000 and the magnesium cost about $150,000. The high cost
is due to the fact that the storage system needs to be able to store 266 hours worth of hydrogen
produced. Therefore, it is recommended to research ways to optimize or reduce the cost of the
hydrogen storage system, specifically, the cost of the storage vessel for the metal hydride.
34
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10. Rase H. Chemical Reactor Design for Process Plants; 1977 Wiley (Case Study 105)
11. Judd, R. W., et al. “The Use of Adsorbed Natural Gas Technology for Large Scale Storage.”
BG Technology, Gas Research and Technology Centre. 1992.
12. Seader, J. D., et al. Separation Process Principles: Chemical and Biochemical Operations.
Hoboken, NJ: Wiley, 3rd Edition, 2011.
13. Baksh et al. Pressure Swing Adsorption Process for the Production of Hydrogen. Patent
6,503,299 B2. 7 Jan. 2003.
14. Online Pinch Analysis Tool
<http://www.uic-che.org/pinch/about_program.php> Accessed April 2012.
15. United States Department of Labor, Bereau of Labor Statistics. – “May 2010 National
Occupational Employment and Wage Estimates, United States.”
< http://www.bls.gov/oes/current/oes_nat.htm> Accessed March 2012.
16. Ray et al. Chemical Engineering Design Project: A Case Study Approach, Second Edition.
Gordon and Breach Science Publishers, Amsterdam. 1998.
17. “Safety, Codes, and Standards,” Fuel Cell Technologies Program, U.S. Department of
Energy.
18. Broder, John. “E.P.A. Expected to Regulate Carbon Dioxide,” N.Y. Times. February 12,
2009.
19. New York State Department of Environmental Conservation, Department of Air Resources,
< http://www.dec.ny.gov/chemical/8569.html> Accessed May 2012
20. United States Environmental Protection Agency, “NAAQS Criterion”
< http://www.epa.gov/air/criteria.html> Accessed May 2012.
21. California Air Resources Board, “Mandate for Greenhouse Gas Emissions.”
< http://www.associatesenvironmental.com/Greenhouse_Gas_CARB_web.pdf> Accessed
May 2012.
22. Nauman, E. Chemical Reactor Design, Optimization, and Scaleup. Hoboken; John Wiley and
Sons Inc. 2008.
23. “CEPCI”. Chemical Engineering. September 2011.
35
Appendix A – Reactor/Furnace Details
Reactor Modeling
The three reactions occurring in the MSR are extensively studied in the paper by Xu and
Fermont [3]. The reaction rates and equilibrium equations are given for the catalyst used. Using
these equations assuming that the reactor can be modeled as a PFR, ODE’s can be written to
solve for the flux profile of each species occurring in the reaction.
(1)
where is the flux of species i, is the rate of formation or disappearance of species i given by
Xu and Fermont, and z is the distance along the length of the reactor. Also, ODE’s for pressure
drop and an energy balance are included to calculate the pressure and temperature along the
length of the reactor. The pressure drop is modeled by the Ergun equation [22].
( ( )
)
(2)
Where is the pressure, is the density of the fluid, is the velocity of the fluid, is the
diameter of the catalyst, is the void fraction of the catalyst, and is the particle Reynolds.
( )
(3)
Where T is the temperature in the reactor, is the heat of reaction, R is the reaction rate, is
the specific heat, is the overall heat transfer coefficient, r is the radius of the tube, and is
the temperature on the outside surface of the reactor. Euler’s method of solving ODE’s was used
to solve all of the differential equations. The Matlab code used to solve the equations is shown in
Appendix H.
The flux, temperature, and pressure profiles for two water gas shift reactors were solved for
using the same method as above. The data for the reaction rates of the HTWGS reactor can be
found in an article by Keiski and the data for the LTWGS reactor can be found in a paper by
Rase [9, 10].
36
Figure 13. MSR models.
37
Figure 14. HTWGS Profiles.
38
Figure 15. LTWGS Profiles.
39
Fuel Requirements
The heat duty of the furnace was obtained from PRO/II. The value given was the sum of the
heats of formation of the products and the heat needed to increase the temperature of the outlet
products to 1064 K. The heat duty for the furnace for the heat provided to the reaction is 153 kJ/s.
The fuel for the furnace is methane which has a LHV of 50,520 kJ/kg. Therefore, the required
amount of fuel for the reactor is 11 kg/hr. The amount of oxygen that is needed for this
combustion is calculated using the combustion reaction
Or
Using the mass form of the combustion reaction, the desired amount of oxygen is calculated to
be 44 kg/hr.
Furnace Costing
The furnace was cost using CAPCOST. The heat duty in the furnace was the deciding factor for
the cost. The heat duty of just the MSR was 153 kJ/s. However, the waste gas from the natural
gas PSA was also being burned in the furnace. This contributed more fuel and heat in the furnace
due to the presence of ethane and butane. The total heat duty from all the combustion materials is
219 kJ/s.
( ( ( ( )) )
(4)
where Q is the heat duty in kJ/s and CEPCI is 1.48 for the price adjustment of equipment over
time. The final cost of the furnace comes out to be $77,400.
40
Appendix B - Adsorption Tower Sample Calculations
Adsorption Tower Sizing
In order to determine the size of the adsorption tower necessary to perform the adsorption,
certain properties of all of the solid agents were obtained. The properties of activated carbon,
obtained from Seader et al., are displayed below [12].
Pore Diameter dp 1.75 x 10-9
m
Particle Porosity εp 0.5
Particle Density ρp 700 kg/m3
Specific Surface Area Sg 800,000 m2/g
Tortuosity τ 2
Table 16. Activated Carbon Specifications.
All numbers mentioned in the following pages are associated with the modeling of the separation
of methane from natural gas using activated carbon as a solid agent.
The density of the natural gas stream entering the adsorption column, ρb, is 0.6967 kg/m3.
Equation 5 was then used in order to determine the bed porosity, εb, to be 0.999.
(5)
From here, the Knudsen diffusivity, DKn, was determined to be 3.08 x 10-11
m2/s by Equation 6.
√
(6)
T is the temperature, 397 K, and MA is the molecular weight of the solute (assumed to be purely
methane), 30.07 g/mol. The diffusivity of ethane in methane, DAB, was determined to be 6.86 x
10-6
m/s by Equation 7.
[(∑ )
(∑ )
] √( ) ( )
(7)
P is the pressure, 3.8 atm, MB is the molecular weight of the solute, methane, which is 16.04
g/mol, and the other terms represent the summation of atomic and structural diffusion volumes,
which are 45.66 cm3/mol and 25.14 cm
3/mol for ethane and methane, respectively. The effective
diffusivity, Deff, was determined to be 1.62 x 1010
m2/s by Equation 8.
41
[
] (8)
The Sherwood number, Sh, is 2 under the given conditions, so the mass transfer coefficient for
the solute, ethanol, kc,solute, was determined to be 1.85 x 1019
m/s from Equation 9.
(9)
The overall mass transfer coefficient, Kov, was determined to be 1.32 x 1019
m/s from Equation
10.
(10)
Originally, a bed diameter, dbed, of 1 m was chosen. Upon performing the remainder of the
analysis and modifying the diameter in order to obtain a length to diameter ratio of 3, the bed
diameter was determined to be 1.38 m. From this the bed area and superficial linear velocity, v,
of the entering stream were determined to be 1.50 m2 and 0.0138 m/s. A breakthrough time, t, of
5 minutes was specified, and the equilibrium constant, K, was assumed to be negligible due to
fast kinetics. With all of the above variables determined, the ratio of the concentration of the
solute in the bed to the concentration of the solute in the feed was plotted against the right hand
side of Equation 11, for which the remaining variable is bed length, z.
[ (√ √
√
√ )] (11)
√ and √ are dimensionless time and dimensionless axial distance, respectively, given by
Equations 12 and 13.
( )[
] (12)
[
] (13)
From the plot displayed in the figure below the bed length was determined to be the
breakthrough distance of 4.1 m, at which point the solute, ethanol, is fully adsorbed at a
breakthrough time of 5 minutes. This bed length was determined by repeating the analysis for
varying diameters until a length to diameter ratio of 3 was obtained.
42
Figure 16. Breakthrough curve.
0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5 6 7 8
C_bed/
C_feed
length of adsorber (m)
Separation of Methane from Natural Gas
43
Adsorption Tower Costing
CAPCOST was used in order to determine the costs of the adsorption towers, which fall under
the category of vertical process vessels [8]. All adsorption towers were decided to be constructed
of carbon steel, which can be used at temperatures as low as 172 K. Equation 14 displays the
purchased cost of the equipment, at ambient pressure and using carbon steel construction, , in
dollars, which is also the starting point of the costing for other units (i.e. heat exchangers,
compressors/expanders):
( )
(14)
A is the capacity or size parameter of the equipment, which is volume in cubic meters for vertical
process vessels, and K1, K2, and K3 are given constants for each type of unit. For a vertical
process vessel, K1, K2, and K3 are 3.4974, 0.4485, and 0.1074, respectively. Substituting these
values and solving for yields Equation 15:
( )
(15)
The pressure factor, FP,vessel for vertical process vessels is given by CAPCOST and affects the
cost [8]. The expression for it is given in Equation 16.
( ) [ ( )]
(16)
P is the pressure of the process vessel in bar gauge (barg), and D is the diameter of the process
vessel.Once and FP,vessel are known, the final cost of the vessel, CBM is determined taking into
account bare module factors. Given by CAPCOST, the equation for this cost is displayed in
Equation 17 [8].
( ) (17)
B1 and B2 are given constants for each type of unit, and for vertical process vessels they are 2.25
and 1.82, respectively. FM is the material factor, which is equal to 1 for vertical process vessels
made of carbon steel construction. Substituting these values and the expressions for and FP
yields Equation 18, which gives the final cost of a vertical process vessel, CBM, in dollars, in
terms of the volume, pressure, and diameter.
44
[ ( )
]
[ (
( ) [ ( )]
)]
(18)
For the PSA unit used to separate methane from natural gas, the diameter of one of the towers is
1.38 m, the volume is 5.796 m3, and the pressure is 2.837 barg. Substituting these values in the
above equation yields a capital cost of $97,820 for a single adsorption tower. Accounting for a
second tower and adjusting for the CEPCI yields a total capital cost of $289,550 for this
adsorption unit [23].
The adsorbent associated with a given adsorption tower is supplied to fill up the adsorption tower
to capacity. Therefore, the mass of adsorbent, m, is determined from the volume of an adsorption
tower, V, and the density of the adsorbent, ρp, according to Equation 19.
(19)
For the PSA unit used to separate methane from natural gas the volume of a tower is 5.796 m3
and the density of activated carbon is 700 kg/m3. Therefore, the mass of activated carbon needed
to fill a tower is 4,060 kg. Each PSA unit requires two towers, and each tower is refilled with
adsorbent twice a year. Therefore, based on the price per kg at which adsorbent can be
purchased; the yearly cost associated with PSA unit is given by Equation 20.
( ) (20)
Therefore, for the PSA unit used to separate methane from natural gas, since activated carbon is
available at $1550/metric ton, or $1.55/kg, the yearly cost of adsorbent is $25,200/yr.
45
Appendix C – Flash Tank Sample Calculations
Flash Tank Sizing
Turton et al. was used as a guideline for sizing the flash tank and the reflux drums associated
with the distillation towers [6]. The holdup time, τ, for each of these process vessels was stated to
be 5 minutes and the optimum length to diameter ratio, L/D, was stated to be 3. As well, the
heuristics state that the process vessels are half-full of liquid. The relation between volumetric
flow rate of liquid entering the flash tank, , liquid volume, VL, vessel volume, V, holdup time
and vessel length and diameter is given in Equation 21:
(
) (
) (
)(
)
(21)
The above equation can be rearranged to isolate the diameter, D, resulting in Equation 22:
√
(22)
Once the diameter of the process vessel was determined, the length was obtained by multiplying
the diameter by 3. For the flash tank which separates water from the process stream after the
reactor section, the liquid volumetric flow rate of water in the process stream entering the flash
tank is 0.0696 m3/hr. Substituting this, as well as the 5 minute (0.083 hr) holdup time, into
Equation 22 yields a tank diameter of 0.158 m. Multiplying by 3 yields a tank length of 0.474 m.
46
Appendix D - Heat Exchanger Sample Calculations
Heat Exchanger Sizing
The correlation for the inner convective heat transfer coefficient, , is presented by Sieder and
Tate as
( )
(
)
(
)
(23)
where is the thermal conductivity (W/m K), is the inner diameter in of the double-piped
heat exchanger, is the gas mass velocity (kg m/s), is the viscosity (Pa s), is the specific
heat of the stream (J/kg K), and is the viscosity of the stream at the tube wall (Pa s). This
correlation works for turbulent flow above the transition regime (i.e. Reynolds number > 10000),
which is appropriate since all flow in all streams were determined to be turbulent.
The correlation for the outer convective heat transfer coefficient, , is presented by Churchill
and Bernstein as
[ ( ) ] [ (
)
]
(24)
where is the outer diameter (m), is the Reynolds number, and is the Prandtl number.
If the outer wall area, , is used as the reference area for heat transfer, the overall heat transfer
coefficient, , is given as
(25)
where is the inner wall area (m2) is, is the thickness of the tube (m), is the thermal
conductivity of the wall (W/m K), and and are related to the fouling resistances in the
inner and outer tube.
If the inner wall area, , is used as the reference area for heat transfer, the overall heat transfer
coefficient, , is given as
(26)
where is the inner wall area (m2) is, is the thickness of the tube (m), is the thermal
conductivity of the wall (W/m K), and and are related to the fouling resistances in the
inner and outer tube.
47
The overall heat transfer coefficients are related by
(27)
where is the mean overall mass transfer coefficient, is the mean wall area.
Thus, for heat exchanger unit ‘HEX15,’ Equation 23 gives the inner convective heat transfer
coefficient
( ) ( ) ( )
Equation 24 gives the outer convective heat transfer coefficient.
( )
[ ( ) ] [ (
)
]
Equation 26 is used to determine the heat transfer coefficient using the inner wall area as
reference.
( ) ( )
( ) ( )
( )
Then, using Equation 27, to find the average overall heat transfer coefficient,
( )
This process completed for both the process and utility streams for all heat exchangers, which
were then averaged.
48
Heat Exchanger Costing
CAPCOST was used in order to cost the heat exchangers. All heat exchangers are designed to be
double pipe heat exchangers with stainless steel construction used for both the shell and tube.
Stainless steel construction is used because it does not corrode and it is the best material for
preventing hydrogen diffusion. The capacity or size parameter of the heat exchangers, A, is the
heat transfer area in square meters. In costing heat exchangers, the exact same process is carried
out as in costing vertical process vessels. The values of K1, K2, and K3 for double pipe heat
exchangers are 3.3444, 0.2745 and -0.0472, respectively. The pressure factor, FP, for double pipe
heat exchangers is 1 as they do not have pressure ratings. The material factor, FM, for stainless
steel double pipe heat exchangers, is 2.75. The values of B1 and B2 are 1.74 and 1.55,
respectively. Combining all of these values in the same way as they were for vertical process
vessels yields the bare module cost of a double pipe heat exchanger, displayed in equation 4, in
terms of the heat transfer area.
[ ( )
] [ ( )] (28)
Therefore, the cost for the heat exchanger in which methane is heated by the furnace flue gas
prior to entering the methane steam reformer is:
[ ( )
] [ ( )]
[ ( ) ( ( )) ] [ ( )]
Adjusting for the CEPCI yields a capital cost of $6,260.30 for this heat exchanger.
49
Cooling Water Utility Costing
The cost of the cooling water used to operate the heat exchangers were determined in two ways,
depending on whether cooling water was or was not used. If cooling water was used, then it was
assumed that the cooling water experienced a temperature change of 27 °F, which was obtained
from Turton et al.[6]. This value was used as the change in temperature, ΔT, along with the
specific heat capacity of water, cp, which is 4.18 J/g*K, and the required heat duty, q, in W in
order to determine the mass flow rate, , in lb/h.
(29)
Solving for the mass flow rate is displayed as
(30)
This mass flow was then converted to a volumetric flow by dividing by the density of water. In
order to find the volumetric flow per year the hourly volumetric flow was multiplied by the
operating time (8500 hours). Once the yearly volumetric flow was determined in gallons per year,
it was then multiplied by the cost of cooling water at $3.17 per 748 gallons to find the yearly cost
of cooling water for a given heat exchanger.
For the heat exchanger which cools the process stream immediately upon exiting the low
temperature water gas-shift reactor, cooling water at 60 °F (12.56 °C = 288.71 K) is supplied as
the coolant. From Pro/II, the heat duty for this heat exchanger is 85,060 W. Cooling water enters
the heat exchanger at 288.706 K and exits at 370 K. Therefore, the necessary mass flow rate of
cooling water is:
(
) ( )
250.4 g/s of cooling water is equivalent to 238.2 gal/hr, which costs $8,581 per year.
50
Appendix E – Compressor Sample Calculations
For one of the compressors in the ethylene refrigeration cycle, compressor C1, the change in
enthalpy of the ethylene stream is read off of the Mollier Diagram, as seen in Figure 17.
Figure 17. Mollier Diagram
51
The conversion for 1 Btu is 778 ft*lbf. For this compressor, the change is 13 Btu/lb. This is
initially from 1.5 atm and 235 K to 2.93 atm to 252 K.
(31)
The break horse power is defined to be
(32)
where is the mass flow rate of the cracked gas stream and is the adiabatic efficiency
(defined as 0.77).
For this specific stream the mass flow is 117.9 kg/hr, or 259.6 lb/hr. Another conversion is
needed to get the units to horse power. 1 ft*lbf/hr is equal to 5.015*10-7
HP.
(
)
( )
The motor kWh is defined to be
( ) (33)
The motor efficiency is assumed to be 90%.
52
Compressor Costing
The cost of each compressor was determined from the chart in Figure 1. For costs below
$10,000, the cost was determined based on the linear extrapolation of the cost curve for a
centrifugal-motor compressor.
For the compressor that compresses the natural gas feed stream from 298 K and 1 atm to 396.625
K and 3.8 atm, Pro/II determined the break horsepower requirement to be 4.23 hp. Accounting
for the efficiency, the break horsepower is increased to 5.49 hp. From Figure 18 the compressor
cost of $7,000 applies. Accounting for CEPCI, the capital cost of the compressor is $10,360.
Figure 18. Compressor Costing Curve [6].
53
Appendix G - Fixed Operating Costs
The values of the fixed operating costs were determined by first determining the labor cost
associated with the plant. The average yearly salary for a chemical plant technician in the United
States is $46,000 [16]. It was assumed that the plant has 5 workers. Therefore, the total labor
cost was determined as follows:
( )
From the labor cost value, the yearly supervision cost was determined based on the heuristic that
the supervision cost is 25% of the labor cost.
From the labor cost value, the yearly quality control cost was determined based on the heuristic
that the quality control cost is 20% of the labor cost.
From the labor cost value, the yearly plant overhead cost was determined based on the heuristic
that the plant overhead cost is 50% of the labor cost.
The working capital estimate is determined by subtracting the current assets from the current
liabilities. The current assets encompass yearly hydrogen and dry ice sales revenue as well as the
water and natural gas that are contained in the storage tanks. Current liabilities include yearly
fixed and variable operating costs.
The decommissioning/shutdown cost was determined from the heuristic that it is approximately
5% of the construction cost. The construction cost is approximately 2/3 of the capital cost. This
comes from the reasoning that the total capital cost is based on the cost of the equipment and the
installation of the equipment, with the latter comprising 2/3 of the capital cost. The
decommissioning/shutdown cost is determined as follows.
( )
( )
54
An inflation rate of 3% means that the sales revenue and production cost of each year following
the third year are 3% greater than they were in the previous year. The equation governing this
relationship applies for the sales revenue and production costs of years 4 through 22.
Straight-line depreciation means that the overall capital cost becomes a tax allowance in the form
of depreciation. Assuming that the plant has no residual value after 20 years, the entire capital
cost is used in determining the yearly depreciation allowance. Straight-line depreciation assumes
that the depreciation allowance is the same value year after year, for all the years for which tax is
payable. This time frame occurs from the year after the first year of production, which is year 4,
and the year after the last year of production, which is year 23. This timeline encompasses the
useful life of the plant. The value for the yearly deprecation is given below.
For the lowest possible selling price of hydrogen the total sales revenue of year 3 was $1,000,000.
The production cost for year 3 is $900,000 and there is no investment cost for year 3. Therefore,
the cash flow before tax for year 3 was determined as follows. (Note: the numbers in the
following sample calculations have been rounded, which is why they may differ from some
values within the body of the report).
From this value, the taxable profit of year 4 was determined as follows.
From this value, the tax payable of year 4 was then determined.
( )
From this value, the cash flow after tax for year 4 was determined.
( )
55
From this value, the cumulative cash flow after tax for year 4 was determined.
56
Appendix H – MATLAB Code for Reactor Design
clc clear all format long
%Inlet Conditions %index 1 = initial conditions P(1) = 15*1.01325; %bar, 1 atm = 1.01325 bar T(1) = 850; %K Twall = 1500; %K r_length = 6; %reactor length in m diameter = .1; %reactor diameter in m
e = 0.528; %void fraction R = 8.314*10^(-3); %kJ/mol K Rg = 8.314*10^(-5); % bar m^3/mol K dp = 2*10^(-4); % 0.2 mm particle diameter
mw(1) = 16.04; %MW of methane in kg/kmol mw(2) = 28.01; %MW of CO in kg/kmol mw(3) = 44.01; %MW of CO2 in kg/kmol mw(4) = 18.0153; %MW of H2O in kg/kmol mw(5) = 2.015894; %MW of H2 in kg/kmol
%viscocity coefficients %row 1: CH4, 2: CO, 3: CO2, 4: H2O, 5: H2 %column 1: A, 2: B, 3: C, 4: D, 5: E vc = [[5.2546E-07 0.59006 105.67 0 0] [1.1127E-06 0.5338 94.7 0 0] [0.000002148 0.46 290 0 0] [1.7096E-08 1.1146 0 0 0] [1.797E-07 0.685 -0.59 140 0]];
%heat capacity coefficients %row 1: CH4, 2: CO, 3: CO2, 4: H2O, 5: H2 %column 1: A, 2: B, 3: C, 4: D, 5: E cpc = [[33298 79933 2086.9 41602 991.96] [29108 8773 3085.1 8455.3 1538.2] [29370 34540 1428 26400 588] [33363 26790 2610.5 8896 1169] [27617 9560 2466 3760 567.6]];
%Thermal Conductivities %row 1: CH4, 2: CO, 3: CO2, 4: H2O, 5: H2 %column 1: A, 2: B, 3: C, 4: D tc = [[8.3983E-06 1.4268 -49.654 0] [0.00059882 0.6863 57.13 501.92] [3.69 -0.3838 964 1860000] [6.2041E-06 1.3973 0 0] [0.002653 0.7452 12 0]];
%heat of reactions in J/kmol
57
hr = [206.1 -41.15 164.9]*10^6;
%Inlet Feed Composition in terms of flux (in kmol/hr m^2) %1 = CH4 %2 = CO %3 = CO2 %4 = H2O %5 = H2 tube = 16; %water/methane = 3.12 F(1, 1) = 2.5/(pi*(diameter/2)^2)/tube; %kmol/hr m^2 F(1, 2) = 0; %kmol/hr m^2 F(1, 3) = 0; %kmol/hr m^2 F(1, 4) = F(1,1)*3.12; %kmol/hr m^2 %NOTE: INITIAL FLOW RATE OF HYDROGEN MUST BE ASSUMED IN ORDER FOR KINETICS %TO WORK F(1, 5) = 0.5/(pi*(diameter/2)^2)/tube; %kmol/hr m^2 %F(1, 5) = 0.01/(pi*(diameter/2)^2)/tube;
%Mole Fraction and partial pressures for i = 1:5 x(1, i) = F(1, i)/sum(F(1,:)); p(1, i) = x(1, i)*P(1); end
%density of catalyst in kg/m^3, or (210 kg/m^3) %dw = 2000; dw = 210; %kg catalyst in reactor w = (dw)*(((diameter/2)^2)*pi*(1-e)*r_length);
a = 10000; %number of iterations dl = r_length/a; %step size loop = 0:dl:r_length; %length of reactor
%Initial enthalpy (Water, Methane, and Hydrogen) in J/Kmol H(1) = ((cpc(4, 1) + cpc(4, 2)*((cpc(4, 3)/T(1))/sinh(cpc(4, 3)/T(1)))^2 ... + cpc(4, 4)*((cpc(4, 5)/T(1))/cosh(cpc(4, 5)/T(1)))^2)*x(1, 4)... + (cpc(1, 1) + cpc(1, 2)*((cpc(1, 3)/T(1))/sinh(cpc(1, 3)/T(1)))^2 ... + cpc(1, 4)*((cpc(1, 5)/T(1))/cosh(cpc(1, 5)/T(1)))^2)*x(1, 1)... + (cpc(5, 1) + cpc(5, 2)*((cpc(5, 3)/T(1))/sinh(cpc(5, 3)/T(1)))^2 ... + cpc(5, 4)*((cpc(5, 5)/T(1))/cosh(cpc(5, 5)/T(1)))^2)*x(1, 5))*T(1);
%Euler's Method, start loop for i = 1:length(loop)-1 %rate constants %1 = CH4 %2 = CO %3 = CO2 %4 = H2O %5 = H2 %6 = k1 %7 = k2
58
%8 = k3 k(i, 1) = (6.65*10^(-4))*exp(38.280/(R*T(i))); %bar^-1 k(i, 2) = (8.23*10^(-5))*exp(70.650/(R*T(i))); %bar^-1 k(i, 3) = 0; k(i, 4) = (1.77*10^5)*exp(-88.680/(R*T(i))); % dimensionless k(i, 5) = (6.12*10^(-9))*exp(82.900/(R*T(i))); %bar^-1 k(i, 6) = (4.225*10^15)*exp(-240.100/(R*T(i))); %kmol bar^0.5/ (kgcat hr) k(i, 7) = (1.955*10^6)*exp(-67.130/(R*T(i))); %kmol/(kgcat hr bar) k(i, 8) = (1.02*10^15)*exp(-243.900/(R*T(i))); %kmol bar^0.5/ (kgcat hr) %equilibrium constants K(i, 1) = exp(-26830/T(i)+30.114);%bar^2 K(i, 2) = exp(4400/T(i)-4.036);%dimensionless K(i, 3) = K(i, 1)*K(i, 2);%bar^2
%denominator of rate equations Den(i) = 1 + k(i, 1)*p(i, 1) + k(i, 2)*p(i, 2) + k(i, 5)*p(i, 5) + k(i,
4)*(p(i, 4)/p(i, 5));
%reaction rates in kmol/(hr m^3) r(i, 1) = dw*(k(i, 6)/Den(i)^2)*(p(i, 1)*p(i, 4)/p(i, 5)^2.5 - (p(i,
5)^0.5)*p(i, 2)/K(i, 1)); r(i, 2) = dw*(k(i, 7)/Den(i)^2)*(p(i, 2)*p(i, 4)/p(i, 5) - p(i, 3)/K(i,
2)); r(i, 3) = dw*(k(i, 8)/Den(i)^2)*((p(i, 1)*p(i, 4)^2)/(p(i, 5)^3.5) - (p(i,
3)*p(i, 5)^0.5)/K(i, 3));
%stepwise component flux determination in kmol/hr m^2 F(i+1, 1) = F(i, 1) + dl*((-r(i, 1) - r(i, 3))); F(i+1, 2) = F(i, 2) + dl*((r(i, 1) - r(i, 2))); F(i+1, 3) = F(i, 3) + dl*((r(i, 2) + r(i, 3))); F(i+1, 4) = F(i, 4) + dl*((- r(i, 1) - r(i, 2) - 2*r(i, 3))); F(i+1, 5) = F(i, 5) + dl*((3*r(i, 1) + r(i, 2) + 4*r(i, 3)));
for j = 1:5 x(i+1, j) = F(i+1, j)/(sum(F(i+1, :))); end
%Pressure Drop Determination c(i) = (P(i))/(Rg*T(i))/1000; %concentration kmol/m^3 (1 kmol = 1000 mol) amw(i) = (mw(1)*x(i, 1) + mw(2)*x(i, 2) + mw(3)*x(i, 3) + mw(4)*x(i, 4) +
mw(5)*x(i, 5)); %average molecular weight in kg/kmol rho(i) = c(i)*amw(i); %density in kg/m^3 us(i) = sum(F(i, :))/(c(i)*3600); %superficial gas velocity in m/s %viscosity in Pa s, or kg/(m s) mu(i) = ((vc(1, 1)*T(i)^vc(1, 2))/(1 + vc(1, 3)/T(i) + vc(1,
4)/T(i)^2))*x(i, 1)... + ((vc(2, 1)*T(i)^vc(2, 2))/(1 + vc(2, 3)/T(i) + vc(2,
4)/T(i)^2))*x(i, 2)... + ((vc(3, 1)*T(i)^vc(3, 2))/(1 + vc(3, 3)/T(i) + vc(3,
4)/T(i)^2))*x(i, 3)... + ((vc(4, 1)*T(i)^vc(4, 2))/(1 + vc(4, 3)/T(i) + vc(4,
4)/T(i)^2))*x(i, 4)... + ((vc(5, 1)*T(i)^vc(5, 2))/(1 + vc(5, 3)/T(i) + vc(5,
4)/T(i)^2))*x(i, 5); muwall(i) = ((vc(1, 1)*Twall^vc(1, 2))/(1 + vc(1, 3)/Twall + vc(1,
4)/Twall^2))*x(i, 1)...
59
+ ((vc(2, 1)*Twall^vc(2, 2))/(1 + vc(2, 3)/Twall + vc(2,
4)/Twall^2))*x(i, 2)... + ((vc(3, 1)*Twall^vc(3, 2))/(1 + vc(3, 3)/Twall + vc(3,
4)/Twall^2))*x(i, 3)... + ((vc(4, 1)*Twall^vc(4, 2))/(1 + vc(4, 3)/Twall + vc(4,
4)/Twall^2))*x(i, 4)... + ((vc(5, 1)*Twall^vc(5, 2))/(1 + vc(5, 3)/Twall + vc(5,
4)/Twall^2))*x(i, 5);
rep(i) = rho(i)*dp*us(i)/mu(i); %particle reynolds re(i) = rho(i)*diameter*us(i)/mu(i); %reynolds %Ergun Equation Pressure Drop in Pa pdrop(i) = -(dl)*(rho(i)*(us(i)^2)/dp)*((1-e)/e^3)*(150*(1-e)/rep(i) +
1.75); %100000 Pa = 1 bar P(i+1) = P(i) + pdrop(i)/100000;
%Save partial pressures for next iteration for reaction rates for j = 1:5 p(i+1, j) = x(i+1, j)*P(i+1); end
%Temperature Change Determination %1 = CH4 %2 = CO %3 = CO2 %4 = H2O %5 = H2 %Integrated Heat Capacities, or H, in J/kmol intcp(i, 1) = cpc(1, 1)*T(i) + cpc(1, 2)*cpc(1, 3)*coth(cpc(1,
3)/T(i)) ... - cpc(1, 4)*cpc(1, 5)*tanh(cpc(1, 5)/T(i)) ... - (cpc(1, 1)*298 + cpc(1, 2)*cpc(1, 3)*coth(cpc(1, 3)/298) ... - cpc(1, 4)*cpc(1, 5)*tanh(cpc(1, 5)/298)); intcp(i, 2) = cpc(2, 1)*T(i) + cpc(2, 2)*cpc(2, 3)*coth(cpc(2,
3)/T(i)) ... - cpc(2, 4)*cpc(2, 5)*tanh(cpc(2, 5)/T(i)) ... - (cpc(2, 1)*298 + cpc(2, 2)*cpc(2, 3)*coth(cpc(2, 3)/298) ... - cpc(2, 4)*cpc(2, 5)*tanh(cpc(2, 5)/298)); intcp(i, 3) = cpc(3, 1)*T(i) + cpc(3, 2)*cpc(3, 3)*coth(cpc(3,
3)/T(i)) ... - cpc(3, 4)*cpc(3, 5)*tanh(cpc(3, 5)/T(i)) ... - (cpc(3, 1)*298 + cpc(3, 2)*cpc(3, 3)*coth(cpc(3, 3)/298) ... - cpc(3, 4)*cpc(3, 5)*tanh(cpc(3, 5)/298)); intcp(i, 4) = cpc(4, 1)*T(i) + cpc(4, 2)*cpc(4, 3)*coth(cpc(4,
3)/T(i)) ... - cpc(4, 4)*cpc(4, 5)*tanh(cpc(4, 5)/T(i)) ... - (cpc(4, 1)*298 + cpc(4, 2)*cpc(4, 3)*coth(cpc(4, 3)/298) ... - cpc(4, 4)*cpc(4, 5)*tanh(cpc(4, 5)/298)); intcp(i, 5) = cpc(5, 1)*T(i) + cpc(5, 2)*cpc(5, 3)*coth(cpc(5,
3)/T(i)) ... - cpc(5, 4)*cpc(5, 5)*tanh(cpc(5, 5)/T(i)) ... - (cpc(5, 1)*298 + cpc(5, 2)*cpc(5, 3)*coth(cpc(5, 3)/298) ... - cpc(5, 4)*cpc(5, 5)*tanh(cpc(5, 5)/298));
%Heat of Reactions with Temperature Variation in J/kmol
60
%row = reaction number hrxn(i, 1) = hr(1) + (intcp(i, 2) + 3*intcp(i, 5) - intcp(i, 1) -
intcp(i, 4)); hrxn(i, 2) = hr(2) + (intcp(i, 3) + intcp(i, 5) - intcp(i, 2) - intcp(i,
4)); hrxn(i, 3) = hr(3) + (intcp(i, 3) + 4*intcp(i, 5) - intcp(i, 1) -
2*intcp(i, 4));
%sum of the heat of reactions in J/(hr m^3) dhrxnsum(i) = -(r(i, 1)*hrxn(1) + r(i, 2)*hrxn(2) + r(i, 3)*hrxn(3));
%average thermal conductivity in W/(m K) kc(i) = (tc(1, 1)*(T(i))^(tc(1, 2))/(1 + tc(1, 3)/T(i) + tc(1,
4)/T(i)^2))*x(i, 1)... + (tc(2, 1)*(T(i))^(tc(2, 2))/(1 + tc(2, 3)/T(i) + tc(2,
4)/T(i)^2))*x(i, 2)... + (tc(3, 1)*(T(i))^(tc(3, 2))/(1 + tc(3, 3)/T(i) + tc(3,
4)/T(i)^2))*x(i, 3)... + (tc(4, 1)*(T(i))^(tc(4, 2))/(1 + tc(4, 3)/T(i) + tc(4,
4)/T(i)^2))*x(i, 4)... + (tc(5, 1)*(T(i))^(tc(5, 2))/(1 + tc(5, 3)/T(i) + tc(5,
4)/T(i)^2))*x(i, 5);
%average heat capacity avcp(i) = (cpc(1, 1) + cpc(1, 2)*((cpc(1, 3)/T(1))/sinh(cpc(1,
3)/T(1)))^2 ... + cpc(1, 4)*((cpc(1, 5)/T(1))/cosh(cpc(1, 5)/T(1)))^2)*x(i, 1)... +(cpc(2, 2)*((cpc(2, 3)/T(1))/sinh(cpc(2, 3)/T(1)))^2 ... + cpc(2, 4)*((cpc(2, 5)/T(1))/cosh(cpc(2, 5)/T(1)))^2)*x(i, 2)... +(cpc(3, 2)*((cpc(3, 3)/T(1))/sinh(cpc(3, 3)/T(1)))^2 ... + cpc(3, 4)*((cpc(3, 5)/T(1))/cosh(cpc(3, 5)/T(1)))^2)*x(i, 3)... +(cpc(4, 2)*((cpc(4, 3)/T(1))/sinh(cpc(4, 3)/T(1)))^2 ... + cpc(4, 4)*((cpc(4, 5)/T(1))/cosh(cpc(4, 5)/T(1)))^2)*x(i, 4)... +(cpc(5, 2)*((cpc(5, 3)/T(1))/sinh(cpc(5, 3)/T(1)))^2 ... + cpc(5, 4)*((cpc(5, 5)/T(1))/cosh(cpc(5, 5)/T(1)))^2)*x(i, 5);
%average prandtl avgpr = avcp(i)*mu(i)/kc(i)/amw(i); %sieder-tate correlation for nusselt (solved for h) h =
0.027*((re(i))^0.8)*(avgpr^(1/3))*((mu(i)/muwall(i))^0.14)*kc(i)/diameter;
%energy balance in J/kmol dh(i) = dl*(dhrxnsum(i)/(c(i)*us(i)*3600)) + pdrop(i)/(c(i)) +
dl*(4*h*(Twall-T(i)))/(c(i)*us(i)*diameter); %J/kmol %dh(i) = dl*(dhrxnsum(i)/(c(i)*us(i)*3600)) + pdrop(i)/(c(i)); %Enthalpy Change in J/kmol H(i+1) = H(i) + dh(i);
%Temperature Change func = @(T) ((cpc(1, 1) + cpc(1, 2)*((cpc(1, 3)/T)/sinh(cpc(1,
3)/T))^2 ... + cpc(1, 4)*((cpc(1, 5)/T)/cosh(cpc(1, 5)/T))^2)*x(i, 1) ... + (cpc(2, 1) + cpc(2, 2)*((cpc(2, 3)/T)/sinh(cpc(2, 3)/T))^2 ... + cpc(2, 4)*((cpc(2, 5)/T)/cosh(cpc(2, 5)/T))^2)*x(i, 2) ... + (cpc(3, 1) + cpc(3, 2)*((cpc(3, 3)/T)/sinh(cpc(3, 3)/T))^2 ...
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+ cpc(3, 4)*((cpc(3, 5)/T)/cosh(cpc(3, 5)/T))^2)*x(i, 3) ... + (cpc(4, 1) + cpc(4, 2)*((cpc(4, 3)/T)/sinh(cpc(4, 3)/T))^2 ... + cpc(4, 4)*((cpc(4, 5)/T)/cosh(cpc(4, 5)/T))^2)*x(i, 4)... + (cpc(5, 1) + cpc(5, 2)*((cpc(5, 3)/T)/sinh(cpc(5, 3)/T))^2 ... + cpc(5, 4)*((cpc(5, 5)/T)/cosh(cpc(5, 5)/T))^2)*x(i, 5))*T - H(i+1); T(i+1) = fzero(func, T(i));
end
%Plotting all relevant data subplot(2, 2, 1); hold on plot(loop, F(:,1), 'r'); plot(loop, F(:,2), 'b'); plot(loop, F(:,3), 'g'); plot(loop, F(:,4), 'k'); plot(loop, F(:,5), 'c'); legend('CH4', 'CO', 'CO2', 'H2O', 'H2'); xlabel('Reactor Length (m)'); ylabel('Molar Flux (kmol/hr m^2)'); title('Molar Flow Profiles in MSR'); hold off subplot(2, 2, 2); hold on gloop = loop(1:a); plot(gloop, r(:,1), 'r'); plot(gloop, r(:,2), 'b'); plot(gloop, r(:,3), 'g'); legend('r1', 'r2', 'r3'); xlabel('Reactor Length (m)'); ylabel('Reaction Rate (kmol/(kgcat*hr))'); title('Reaction Rate Profile in MSR'); hold off subplot(2, 2, 3); hold on plot(loop, P(:)); xlabel('Reactor Length (m)'); ylabel('Pressure (bar)'); title('Reaction Rate Profile in MSR'); hold off subplot(2, 2, 4); hold on plot(loop, T(:)); xlabel('Reactor Length (m)'); ylabel('Temperature (K)'); title('Temperature Profile'); hold off
%Methane Conversion 1-F(10000, 1)/F(1, 1) %Hydrogen Molar Flow Rate (kg/hr) F(10000, 5)*(pi*(diameter/2)^2)*2*tube
HTWGSR Code clc clear all
62
format long
T(1)=750; %Temperature in Kelvin P(1)=12.5; %Pressure in bar epsilon=.75; dp=0.0095;
inmassmethane=.3608; %kg/hr inmasswater=72.4; %kg/hh inmassco=43.4575; inmassco2=24.0014; inmassh2=13.78; inmolesmethane=inmassmethane/16; %kmole/hr inmoleswater=inmasswater/18; %kmole/hr inmolesco=inmassco/28; inmolesco2=inmassco2/44; inmolesh2=inmassh2/2;
diameter=.1; %meters
Hrxn2f=-41150; %J/s Hrxn2r=41150;
intcpch4ref=33298*298+(79933*2086.9)*coth(2086.9/298)-
(41602*991.96)*tanh(6991.96/298); %J/kmol K intcph2oref=33363*298+(26790*2610.5)*coth(2610.5/298)-
(8896*1169)*tanh(1169/298); intcph2ref=27617*298+(9560*2466)*coth(2466/298)-(3760*567.6)*tanh(567.6/298); intcpcoref=29108*298+(8773*3085.1)*coth(3085.1/298)-
(8455.3*1538.2)*tanh(1538.2/298); intcpco2ref=29370*298+(34540*1428)*coth(1428/298)-(26400*588)*tanh(588/298);
molesch4(1)=inmolesmethane; molesh2o(1)=inmoleswater; molesco(1)=inmolesco; molesco2(1)=inmolesco2; molesh2(1)=inmolesh2; Cco(1)=(P(1)/(T(1)*.08314))*(molesco/(molesco+molesch4+molesh2o+molesco2+mole
sh2)); %mol/L Ch2(1)=(P(1)/(T(1)*.08314))*(molesh2/(molesco+molesch4+molesh2o+molesco2+mole
sh2)); Cch4(1)=(P(1)/(T(1)*.08314))*(molesch4/(molesco+molesch4+molesh2o+molesco2+mo
lesh2)); Ch2o(1)=(P(1)/(T(1)*.08314))*(molesh2o/(molesco+molesch4+molesh2o+molesco2+mo
lesh2)); Cco2(1)=(P(1)/(T(1)*.08314))*(molesco2/(molesco+molesch4+molesh2o+molesco2+mo
lesh2)); fluxch4=inmolesmethane/(((diameter/2)^2)*pi); fluxh2o(1)=inmoleswater/(((diameter/2)^2)*pi); fluxco(1)=molesco/(((diameter/2)^2)*pi); fluxco2(1)=molesco2/(((diameter/2)^2)*pi); fluxh2(1)=molesh2/(((diameter/2)^2)*pi); molefractionch4=(fluxch4/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2)); molefractionh2=(fluxh2/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2)); molefractionh2o=(fluxh2o/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2)); molefractionco=(fluxco/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2));
63
molefractionco2=(fluxco2/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2));
H(1)=((((33298+79933*(((2086.9/T(1))/sinh(2086.9/T(1)))^2)+41602*(((991.96/T(
1))/cosh(991.96/T(1)))^2))/1000)*(fluxch4/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxc
o(1)+fluxco2(1))))...
+(((33363+26790*(((2610.5/T(1))/sinh(2610.5/T(1)))^2)+8896*(((1169/T(1))/cosh
(1169/T(1)))^2))/1000)*(fluxh2o(1)/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxco(1)+fl
uxco2(1))))...
+(((27617+9560*(((2466/T(1))/sinh(2466/T(1)))^2)+3760*(((567.6/T(1))/cosh(567
.6/T(1)))^2))/1000)*(fluxh2(1)/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxco(1)+fluxco
2(1))))...
+(((29108+8773*(((3085.1/T(1))/sinh(3085.1/T(1)))^2)+8455.3*(((1538.2/T(1))/c
osh(1538.2/T(1)))^2))/1000)*(fluxco(1)/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxco(1
)+fluxco2(1))))...
+(((29370+34540*(((1428/T(1))/sinh(1428/T(1)))^2)+26400*(((588/T(1))/cosh(588
/T(1)))^2))/1000)*(fluxco2(1)/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxco(1)+fluxco2
(1)))))*T(1);
h=0.00001; %length step in meters l=0:h:.023; %length of reactor in meters
for i=1:length(l)-1 Cpch4(i)=33298+79933*(((2086.9/T(i))/sinh(2086.9/T(i)))^2)+41602*(((991.96/T(
i))/cosh(991.96/T(i)))^2); %J/kmol K Cph2o(i)=33363+26790*(((2610.5/T(i))/sinh(2610.5/T(i)))^2)+8896*(((1169/T(i))
/cosh(1169/T(i)))^2); Cph2(i)=27617+9560*(((2466/T(i))/sinh(2466/T(i)))^2)+3760*(((567.6/T(i))/cosh
(567.6/T(i)))^2); Cpco(i)=29108+8773*(((3085.1/T(i))/sinh(3085.1/T(i)))^2)+8455.3*(((1538.2/T(i
))/cosh(1538.2/T(i)))^2); Cpco2(i)=29370+34540*(((1428/T(i))/sinh(1428/T(i)))^2)+26400*(((588/T(i))/cos
h(588/T(i)))^2);
intcpch4(i)=33298*T(i)+(79933*2086.9)*coth(2086.9/T(i))-
(41602*991.96)*tanh(6991.96/T(i)); %J/kmol K intcph2o(i)=33363*T(i)+(26790*2610.5)*coth(2610.5/T(i))-
(8896*1169)*tanh(1169/T(i)); intcph2(i)=27617*T(i)+(9560*2466)*coth(2466/298)-
(3760*567.6)*tanh(567.6/298); intcpco(i)=29108*T(i)+(8773*3085.1)*coth(3085.1/T(i))-
(8455.3*1538.2)*tanh(1538.2/T(i)); intcpco2(i)=29370*T(i)+(34540*1428)*coth(1428/T(i))-
(26400*588)*tanh(588/T(i));
K2=exp((4400/T(i))-4.036);
beta=(1/K2)*(Cco2(i)*Ch2(i)/(Cco(i)*Ch2o(i)));
k11=h*(exp(26.1)*exp(-95/((8.31451*10^-
3)*T(i)))*(Cco(i)^1.1)*(Ch2o(i)^.53)*(1-beta))*(3/(((diameter/2)^2)*pi*10));
64
fluxh2(i+1)=fluxh2(i)+k11;
k22=h*(-(exp(26.1)*exp(-95/((8.31451*10^-
3)*T(i)))*(Cco(i)^1.1)*(Ch2o(i)^.53)*(1-beta))*(3/(((diameter/2)^2)*pi*10))); fluxh2o(i+1)=fluxh2o(i)+k22;
k33=h*(-(exp(26.1)*exp(-95/((8.31451*10^-
3)*T(i)))*(Cco(i)^1.1)*(Ch2o(i)^.53)*(1-beta))*(3/(((diameter/2)^2)*pi*10))); fluxco(i+1)=fluxco(i)+k33;
k44=h*(exp(26.1)*exp(-95/((8.31451*10^-
3)*T(i)))*(Cco(i)^1.1)*(Ch2o(i)^.53)*(1-beta))*(3/(((diameter/2)^2)*pi*10)); fluxco2(i+1)=fluxco2(i)+k44;
much4=((5.25*10^-7)*T(i)^.59006)/(1+((105.67)/T(i))); muh2=((1.797*10^-7)*T(i)^.685)/(1+((-.59)/T(i))+(140/T(i)^2)); muh2o=((1.71*10^-8)*T(i)^1.1146); muco2=((2.15*10^-6)*T(i)^.46)/(1+((290)/T(i))); muco=((1.11*10^-6)*T(i)^.5338)/(1+((94.7)/T(i))); muavg=much4*molefractionch4+muh2*molefractionh2+muh2o*molefractionh2o+muco2*m
olefractionco2+muco*molefractionco;
concentration=(P(i)./(T(i).*(8.314.*10.^-5)))./1000; %kmol/m^3 vel=(fluxch4+fluxh2(i)+fluxh2o(i)+fluxco(i)+fluxco2(i))./(concentration.*3600
); rhoavg=(fluxch4.*16+fluxh2o(i).*18+fluxh2(i).*2+fluxco(i).*28+fluxco2(i).*44)
./(vel.*3600);
Rep=vel*dp*rhoavg/muavg; k66=(h.*((rhoavg.*vel.^2)./dp).*((1-epsilon)./epsilon^3).*(150.*(1-
epsilon)./(Rep)+1.75))./100000; P(i+1)=P(i)-k66;
realHrxn2f=Hrxn2f+(((intcpco2(i)-intcpco2ref)+(intcph2(i)-intcph2ref)-
(intcpco(i)-intcpcoref)-(intcph2o(i)-intcph2oref))/1000); %J/mol realHrxn2r=Hrxn2r+((-(intcpco(i)-intcpcoref)-(intcph2(i)-
intcph2ref)+(intcpch4(i)-intcpch4ref)+(intcph2o(i)-intcph2oref))/1000);
RXN2f=exp(26.1)*exp(-95/((8.31451*10^-
3)*T(i)))*(Cco(i)^1.1)*(Ch2o(i)^.53)*3; %kmol/hr m^3 RXN2r=exp(26.1)*exp(-95/((8.31451*10^-
3)*T(i)))*(Cco(i)^1.1)*(Ch2o(i)^.53)*beta*3;
delHrxnSUM=realHrxn2f*(RXN2f*1000)+realHrxn2r*(RXN2r*1000); %J/hr
k77=-
h*(delHrxnSUM/(concentration*vel*1000000/3.6))+k66/(concentration*1000); %J/
mol H(i+1)=H(i)+k77;
molefractionco=(fluxco(i+1)/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+fluxh2o(i+1
)+fluxch4)); molefractionco2=(fluxco2(i+1)/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+fluxh2o(i
+1)+fluxch4));
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molefractionh2o=(fluxh2o(i+1)/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+fluxh2o(i
+1)+fluxch4)); molefractionch4=(fluxch4/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+fluxh2o(i+1)+f
luxch4)); molefractionh2=(fluxh2(i+1)/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+fluxh2o(i+1
)+fluxch4));
func=@(T)
((((33298+79933*(((2086.9/T)/sinh(2086.9/T))^2)+41602*(((991.96/T)/cosh(991.9
6/T))^2))/1000)*molefractionch4)...
+(((33363+26790*(((2610.5/T)/sinh(2610.5/T))^2)+8896*(((1169/T)/cosh(1169/T))
^2))/1000)*molefractionh2o)...
+(((27617+9560*(((2466/T)/sinh(2466/T))^2)+3760*(((567.6/T)/cosh(567.6/T))^2)
)/1000)*molefractionh2)...
+(((29108+8773*(((3085.1/T)/sinh(3085.1/T))^2)+8455.3*(((1538.2/T)/cosh(1538.
2/T))^2))/1000)*molefractionco)...
+(((29370+34540*(((1428/T)/sinh(1428/T))^2)+26400*(((588/T)/cosh(588/T))^2))/
1000)*molefractionco2))*T-H(i+1); T(i+1)=fzero(func,T(i));
Cco(i+1)=(P(i+1)/(T(i)*.08314))*molefractionco; Cco2(i+1)=(P(i+1)/(T(i)*.08314))*molefractionco2; Ch2o(i+1)=(P(i+1)/(T(i)*.08314))*molefractionh2o; Cch4(i+1)=(P(i+1)/(T(i)*.08314))*molefractionch4; Ch2(i+1)=(P(i+1)/(T(i)*.08314))*molefractionh2;
i=i+1; end
subplot(2,1,1) plot(l,fluxh2,'b',l,fluxh2o,'k',l,fluxco,'c',l,fluxco2,'r',l,fluxch4,'g') title('HTWGS Flux Profile') legend('fluxh2','fluxh2o','fluxco','fluxco2','fluxch4') xlabel('Distance (m)') ylabel('Flux (kmol/hr*m^2)') subplot(2,1,2) plot(l,T) title('HTWGS Teperature Profile') ylabel('Temperature (K)') xlabel('Distance (m)')
LTWGS Code clc clear all format long
T(1)=400; %Temperature in Kelvin P(1)=11.7; %Pressure in bar epsilon=.75; dp=0.0042;
66
inmassmethane=.3608; %kg/hr inmasswater=58.5966; %kg/hr inmassco=21.996; inmassco2=57.7216; inmassh2=15.3249; inmolesmethane=inmassmethane/16; %kmole/hr inmoleswater=inmasswater/18; %kmole/hr inmolesco=inmassco/28; inmolesco2=inmassco2/44; inmolesh2=inmassh2/2;
diameter=.1; %meters
Hrxn2f=-41150; %J/s Hrxn2r=41150;
intcpch4ref=33298*298+(79933*2086.9)*coth(2086.9/298)-
(41602*991.96)*tanh(6991.96/298); %J/kmol K intcph2oref=33363*298+(26790*2610.5)*coth(2610.5/298)-
(8896*1169)*tanh(1169/298); intcph2ref=27617*298+(9560*2466)*coth(2466/298)-(3760*567.6)*tanh(567.6/298); intcpcoref=29108*298+(8773*3085.1)*coth(3085.1/298)-
(8455.3*1538.2)*tanh(1538.2/298); intcpco2ref=29370*298+(34540*1428)*coth(1428/298)-(26400*588)*tanh(588/298);
molesch4(1)=inmolesmethane; molesh2o(1)=inmoleswater; molesco(1)=inmolesco; molesco2(1)=inmolesco2; molesh2(1)=inmolesh2; fluxch4=inmolesmethane/(((diameter/2)^2)*pi); fluxh2o(1)=inmoleswater/(((diameter/2)^2)*pi); fluxco(1)=molesco/(((diameter/2)^2)*pi); fluxco2(1)=molesco2/(((diameter/2)^2)*pi); fluxh2(1)=molesh2/(((diameter/2)^2)*pi); molefractionch4(1)=(fluxch4/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2)); molefractionh2(1)=(fluxh2/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2)); molefractionh2o(1)=(fluxh2o/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2)); molefractionco(1)=(fluxco/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2)); molefractionco2(1)=(fluxco2/(fluxch4+fluxh2o+fluxh2+fluxco+fluxco2));
H(1)=((((33298+79933*(((2086.9/T(1))/sinh(2086.9/T(1)))^2)+41602*(((991.96/T(
1))/cosh(991.96/T(1)))^2))/1000)*(fluxch4/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxc
o(1)+fluxco2(1))))...
+(((33363+26790*(((2610.5/T(1))/sinh(2610.5/T(1)))^2)+8896*(((1169/T(1))/cosh
(1169/T(1)))^2))/1000)*(fluxh2o(1)/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxco(1)+fl
uxco2(1))))...
+(((27617+9560*(((2466/T(1))/sinh(2466/T(1)))^2)+3760*(((567.6/T(1))/cosh(567
.6/T(1)))^2))/1000)*(fluxh2(1)/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxco(1)+fluxco
2(1))))...
+(((29108+8773*(((3085.1/T(1))/sinh(3085.1/T(1)))^2)+8455.3*(((1538.2/T(1))/c
67
osh(1538.2/T(1)))^2))/1000)*(fluxco(1)/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxco(1
)+fluxco2(1))))...
+(((29370+34540*(((1428/T(1))/sinh(1428/T(1)))^2)+26400*(((588/T(1))/cosh(588
/T(1)))^2))/1000)*(fluxco2(1)/(fluxch4+fluxh2o(1)+fluxh2(1)+fluxco(1)+fluxco2
(1)))))*T(1);
h=0.0001; %length step in meters l=0:h:1; %length of reactor in meters
for i=1:length(l)-1 Cpch4(i)=33298+79933*(((2086.9/T(i))/sinh(2086.9/T(i)))^2)+41602*(((991.96/T(
i))/cosh(991.96/T(i)))^2); %J/kmol K Cph2o(i)=33363+26790*(((2610.5/T(i))/sinh(2610.5/T(i)))^2)+8896*(((1169/T(i))
/cosh(1169/T(i)))^2); Cph2(i)=27617+9560*(((2466/T(i))/sinh(2466/T(i)))^2)+3760*(((567.6/T(i))/cosh
(567.6/T(i)))^2); Cpco(i)=29108+8773*(((3085.1/T(i))/sinh(3085.1/T(i)))^2)+8455.3*(((1538.2/T(i
))/cosh(1538.2/T(i)))^2); Cpco2(i)=29370+34540*(((1428/T(i))/sinh(1428/T(i)))^2)+26400*(((588/T(i))/cos
h(588/T(i)))^2);
intcpch4(i)=33298*T(i)+(79933*2086.9)*coth(2086.9/T(i))-
(41602*991.96)*tanh(6991.96/T(i)); %J/kmol K intcph2o(i)=33363*T(i)+(26790*2610.5)*coth(2610.5/T(i))-
(8896*1169)*tanh(1169/T(i)); intcph2(i)=27617*T(i)+(9560*2466)*coth(2466/298)-
(3760*567.6)*tanh(567.6/298); intcpco(i)=29108*T(i)+(8773*3085.1)*coth(3085.1/T(i))-
(8455.3*1538.2)*tanh(1538.2/T(i)); intcpco2(i)=29370*T(i)+(34540*1428)*coth(1428/T(i))-
(26400*588)*tanh(588/T(i));
Keq=exp(-4.72+(8640/(1.8*T(i))));
si=0.86+.14*P(i);
k11=h*360*(si*exp(12.88-
(3340/(1.8*T(i))))*(molefractionco(i)*molefractionh2o(i)-
((molefractionco2(i)*molefractionh2(i))/Keq))*(1/(379*90)))*(5/(((diameter/2)
^2)*pi)); fluxh2(i+1)=fluxh2(i)+k11;
k22=h*360*(-(si*exp(12.88-
(3340/(1.8*T(i))))*(molefractionco(i)*molefractionh2o(i)-
((molefractionco2(i)*molefractionh2(i))/Keq))*(1/(379*90))))*(5/(((diameter/2
)^2)*pi)); fluxh2o(i+1)=fluxh2o(i)+k22;
k33=h*360*(-(si*exp(12.88-
(3340/(1.8*T(i))))*(molefractionco(i)*molefractionh2o(i)-
((molefractionco2(i)*molefractionh2(i))/Keq))*(1/(379*90))))*(5/(((diameter/2
)^2)*pi)); fluxco(i+1)=fluxco(i)+k33;
68
k44=h*360*(si*exp(12.88-
(3340/(1.8*T(i))))*(molefractionco(i)*molefractionh2o(i)-
((molefractionco2(i)*molefractionh2(i))/Keq))*(1/(379*90)))*(5/(((diameter/2)
^2)*pi)); fluxco2(i+1)=fluxco2(i)+k44;
much4=((5.25*10^-7)*T(i)^.59006)/(1+((105.67)/T(i))); muh2=((1.797*10^-7)*T(i)^.685)/(1+((-.59)/T(i))+(140/T(i)^2)); muh2o=((1.71*10^-8)*T(i)^1.1146); muco2=((2.15*10^-6)*T(i)^.46)/(1+((290)/T(i))); muco=((1.11*10^-6)*T(i)^.5338)/(1+((94.7)/T(i))); muavg=much4*molefractionch4(i)+muh2*molefractionh2(i)+muh2o*molefractionh2o(i
)+muco2*molefractionco2(i)+muco*molefractionco(i);
concentration=(P(i)./(T(i).*(8.314.*10.^-5)))./1000; %kmol/m^3 vel=(fluxch4+fluxh2(i)+fluxh2o(i)+fluxco(i)+fluxco2(i))./(concentration.*3600
); rhoavg=(fluxch4.*16+fluxh2o(i).*18+fluxh2(i).*2+fluxco(i).*28+fluxco2(i).*44)
./(vel.*3600);
Rep=vel*dp*rhoavg/muavg; k66=(h.*((rhoavg.*vel.^2)./dp).*((1-epsilon)./epsilon^3).*(150.*(1-
epsilon)./(Rep)+1.75))./100000; P(i+1)=P(i)-k66;
realHrxn2f=Hrxn2f+(((intcpco2(i)-intcpco2ref)+(intcph2(i)-intcph2ref)-
(intcpco(i)-intcpcoref)-(intcph2o(i)-intcph2oref))/1000); %J/mol realHrxn2r=Hrxn2r+((-(intcpco(i)-intcpcoref)-(intcph2(i)-
intcph2ref)+(intcpch4(i)-intcpch4ref)+(intcph2o(i)-intcph2oref))/1000);
RXN2f=(si*exp(12.88-
(3340/(1.8*T(i))))*(molefractionco(i)*molefractionh2o(i))*(1/(379*90)))*15*36
0; %kmol/hr m^3 RXN2r=(si*exp(12.88-
(3340/(1.8*T(i))))*((molefractionco2(i)*molefractionh2(i))/Keq)*(1/(379*90)))
*15*360;
delHrxnSUM=realHrxn2f*(RXN2f*1000)+realHrxn2r*(RXN2r*1000); %J/hr
k77=-
h*(delHrxnSUM/(concentration*vel*1000000/3.6))+k66/(concentration*1000); %J/
mol H(i+1)=H(i)+k77;
molefractionco(i+1)=(fluxco(i+1)/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+fluxh2
o(i+1)+fluxch4)); molefractionco2(i+1)=(fluxco2(i+1)/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+flux
h2o(i+1)+fluxch4)); molefractionh2o(i+1)=(fluxh2o(i+1)/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+flux
h2o(i+1)+fluxch4)); molefractionch4(i+1)=(fluxch4/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+fluxh2o(i
+1)+fluxch4)); molefractionh2(i+1)=(fluxh2(i+1)/(fluxco(i+1)+fluxco2(i+1)+fluxh2(i+1)+fluxh2
o(i+1)+fluxch4));
69
func=@(T)
((((33298+79933*(((2086.9/T)/sinh(2086.9/T))^2)+41602*(((991.96/T)/cosh(991.9
6/T))^2))/1000)*molefractionch4(i))...
+(((33363+26790*(((2610.5/T)/sinh(2610.5/T))^2)+8896*(((1169/T)/cosh(1169/T))
^2))/1000)*molefractionh2o(i))...
+(((27617+9560*(((2466/T)/sinh(2466/T))^2)+3760*(((567.6/T)/cosh(567.6/T))^2)
)/1000)*molefractionh2(i))...
+(((29108+8773*(((3085.1/T)/sinh(3085.1/T))^2)+8455.3*(((1538.2/T)/cosh(1538.
2/T))^2))/1000)*molefractionco(i))...
+(((29370+34540*(((1428/T)/sinh(1428/T))^2)+26400*(((588/T)/cosh(588/T))^2))/
1000)*molefractionco2(i)))*T-H(i+1); T(i+1)=fzero(func,T(i));
i=i+1; end
subplot(2,1,1) plot(l,fluxh2,'b',l,fluxh2o,'k',l,fluxco,'c',l,fluxco2,'r',l,fluxch4,'g') title('LTWGS Flux Profile') legend('fluxh2','fluxh2o','fluxco','fluxco2','fluxch4') xlabel('Distance (m)') ylabel('Flux (kmol/hr*m^2)') subplot(2,1,2) plot(l,T) title('LTWGS Teperature Profile') ylabel('Temperature (K)') xlabel('Distance (m)')
70
Appendix I – Detailed Spreadsheets
See Attached:
- Heat Exchanger Stream Data (p. 71)
- DCFROR Analysis Spreadsheets (p. 72 – 74)
71
Stream T (K) P (atm)
Flow rate
(kg/hr) Composition
volumetric
flow (m^3/s)
diameter
(ft)
diameter
(m)
Cross Sectional
Area (m^2)
velocity
(m/s)
viscosity
(Pa s)
density
(kg/m^3)
specific heat
(J/kg*K)
thermal
conductivity
(W/m^2 K)
Reynolds
Number
Prandtl
Number
HEX14 Process S85 (in) 390.852 370 16.7003 Hydrogen 2.37E-04 0.0833 0.0254 0.000506707 4.67E-01 1.07E-05 19.606772 14842.685 0.21987 2.17E+04 7.24E-01
Process S87 (out) 298 370 16.7003 Hydrogen 1.88E-04 0.0833 0.0254 0.000506707 3.70E-01 8.90E-06 24.733939 14839.258 0.17798 26124.1 7.42E-01
Utility S91 (in) 288.9 1 159.63 Water 4.44E-05 0.0833 0.0254 0.000506707 8.76E-02 0.00111 998.991 4188.313 0.59754 2002.627 7.78E+00
Utility S92 (out) 323.395 1 159.63 Water 4.49E-05 0.0833 0.0254 0.000506707 8.86E-02 5.42E-04 987.942 4179.582 0.64095 4101.845 3.53E+00
HEX15 Process S86 (in) 380.389 700 16.7003 Hydrogen 1.41E-04 0.0833 0.0254 0.000506707 2.79E-01 1.05E-05 24.733939 14937.844 0.2153 16632.03 7.30E-01
Process S88 (out) 298 700 16.7003 Hydrogen 1.18E-04 0.0833 0.0254 0.000506707 2.33E-01 8.90E-06 39.233322 14914.306 0.17798 26108.85 7.46E-01
Utility S93 (in) 288.9 1 73.69 Water 2.05E-05 0.0833 0.0254 0.000506707 4.04E-02 0.00111 998.991 4188.313 0.59754 924.3937 7.78E+00
Utility S94 (out) 355.47 1 73.69 Water 2.11E-05 0.0833 0.0254 0.000506707 4.16E-02 3.41E-04 970.299 4197.579 0.66879 3011.676 2.14E+00
HEX13 Process S46 (in) 208.15 40 173.9499 Carbon Dioxide 1.18E-03 0.0833 0.0254 0.000506707 2.32E+00 8.45E-06 19.030348 3896 0.0907 132910.1 3.63E-01
Process S71 (out) 177 40 174.9499 Carbon Dioxide 9.19E-04 0.0833 0.0254 0.000506707 1.81E+00 6.69E-06 10.932477 7543 0.09949 75263.5 5.07E-01
Utility S67 (in) 172.4 1.18 122.8511 Ethylene 2.27E-03 0.0833 0.0254 0.000506707 4.49E+00 5.82E-06 2.420045 1253 0.00891 47368.76 8.19E-01
Utility S68 (out) 172.4 1.18 123.8511 Ethylene 9.58E-03 0.0833 0.0254 0.000506707 1.89E+01 5.82E-06 2.420045 1253 0.00891 199557.1 8.19E-01
HEX12 Process S45 (in) 227.59 40 172.9499 Carbon Dioxide 1.49E-03 0.0833 0.0254 0.000506707 2.94E+00 9.98E-06 31.098057 2423 0.07204 232434.8 3.36E-01
Process S46 (out) 208.15 40 173.9499 Carbon Dioxide 1.18E-03 0.0833 0.0254 0.000506707 2.32E+00 8.45E-06 19.030348 3896 0.0907 132910.1 3.63E-01
Utility S60 (in) 205.3 5.57 117.9101 Ethylene 3.75E-04 0.0833 0.0254 0.000506707 7.41E-01 7.02E-06 10.335272 1409 0.01143 27704.51 8.65E-01
Utility S61 (out) 205.3 5.57 118.9101 Ethylene 2.62E-03 0.0833 0.0254 0.000506707 5.17E+00 7.02E-06 10.335272 1409 0.01143 193481.3 8.65E-01
HEX11 Process S20 (in) 242.59 40 173.9499 Carbon Dioxide 1.62E-03 0.0833 0.0254 0.000506707 3.20E+00 1.06E-05 29.666408 2348 0.07462 227035.6 3.35E-01
Process S45 (out) 227.59 40 172.9499 Carbon Dioxide 1.49E-03 0.0833 0.0254 0.000506707 2.94E+00 9.98E-06 31.098057 2423 0.07204 232434.8 3.36E-01
Utility S52 (in) 224.51 11.04 140.2688 Ethylene 1.49E-04 0.0833 0.0254 0.000506707 2.93E-01 7.70E-06 20.258519 1604 0.01312 19595.12 9.42E-01
Utility S54 (out) 224.51 11.04 140.2688 Ethylene 4.40E-04 0.0833 0.0254 0.000506707 8.69E-01 7.70E-06 20.258519 1604 0.01312 58073.28 9.42E-01
HEX10 Process S47 (in) 234.26 14.97 280.5376 Propylene 2.69E-03 0.0833 0.0254 0.000506707 5.31E+00 8.04E-06 27.733493 1764 0.01402 465458.4 1.01E+00
Process S48 (out) 234.26 14.97 280.5376 Propylene 2.35E-04 0.0833 0.0254 0.000506707 4.65E-01 7.22E-05 330.976 3225 0.11836 54109.92 1.97E+00
Utility S40 (in) 252.51 2.93 117.9066 Propylene 5.68E-05 0.0833 0.0254 0.000506707 1.12E-01 1.34E-04 576.338 2316 0.11935 12248.35 2.60E+00
Utility S40 (out) 252.51 2.93 117.9066 Propylene 5.68E-05 0.0833 0.0254 0.000506707 1.12E-01 1.34E-04 576.338 2316 0.11935 12248.35 2.60E+00
HEX1 Process S102 (in) 640.79 15 42 Methane 9.54E-03 0.0833 0.0254 0.000506707 1.88E+01 2.93E-05 4.221 2195 0.06938 68860.03 9.28E-01
Process S103 (out) 850 15 42 Methane 1.03E-02 0.0833 0.0254 0.000506707 2.03E+01 3.18E-05 3.905 2224 0.07751 63424.34 9.13E-01
Utility S98 (in) 1200 11 60.0337 Flue Gas 2.61E-03 0.0833 0.0254 0.000506707 5.15E+00 4.51E-05 3.17 1709 0.10264 9199.538 7.51E-01
Utility S101 (out) 862.26 11 60.0337 Flue Gas 1.72E-03 0.0833 0.0254 0.000506707 3.40E+00 3.19E-05 4.804 1535 0.06281 13023.24 7.79E-01
HEX2 Process S95 (in) 788.63 15 145.009 Water 2.56E-03 0.0833 0.0254 0.000506707 5.05E+00 2.04E-05 4.556 3435 0.09217 28659.59 7.60E-01
Process S97 (out) 850 15 145.009 Water 3.40E-03 0.0833 0.0254 0.000506707 6.71E+00 2.50E-05 3.342 4120 0.13524 22767.76 7.62E-01
Utility S96 (in) 1200 11 29.8 Flue Gas 5.26E-03 0.0833 0.0254 0.000506707 1.04E+01 4.51E-05 3.17 1709 0.1026 18524.75 7.52E-01
Utility S99 (out) 794.11 11 29.8 Flue Gas 3.78E-03 0.0833 0.0254 0.000506707 7.45E+00 3.43E-05 4.419 1567 0.06971 24409.14 7.71E-01
HEX3 Process S2 (in) 1064.09 13.5 187.012 MSR Product 2.67E-02 0.0833 0.0254 0.000506707 5.26E+01 3.55E-05 1.947 3001 0.21951 73260.55 4.86E-01
Process S3 (out) 750 13.5 187.012 HTWGS Feed 1.88E-02 0.0833 0.0254 0.000506707 3.71E+01 2.64E-05 2.765 2785 0.15996 98612.03 4.60E-01
Utility S72 (in) 472.07 15 145.09 Water 4.07E-03 0.0833 0.0254 0.000506707 8.03E+00 1.62E-05 7.69 2974 0.03317 97025.78 1.45E+00
Utility S95 (out) 788.62 15 145.09 Water 9.59E-03 0.0833 0.0254 0.000506707 1.89E+01 2.93E-05 4.221 2195 0.06938 69220.85 9.28E-01
HEX4 Process S4 (in) 805 12.5 187.012 HTWGS Product 7.55E-03 0.0833 0.0254 0.000506707 1.49E+01 1.28E-05 6.397 2249 0.0887 189365.9 3.24E-01
Process S5 (out) 390 12.5 187.012 LTWGS Feed 8.54E-03 0.0833 0.0254 0.000506707 1.69E+01 1.50E-05 4.433 2877 0.1139 126346.2 3.79E-01
Utility S13 (in) 298.19 15 145.01 Water 4.04E-02 0.0833 0.0254 0.000506707 7.97E+01 8.89E-04 997 4178 0.6106 2268471 6.09E+00
Utility S72 (out) 472.07 15 145.01 Water 4.07E-03 0.0833 0.0254 0.000506707 8.03E+00 1.62E-05 7.69 2974 0.03317 97025.78 1.45E+00
HEX5 Process S10 (in) 411.53 11 276.842 LTWGS Product 1.50E-02 0.0833 0.0254 0.000506707 2.96E+01 1.58E-05 5.05 2337 0.0877 240158.2 4.21E-01
Process S7 (out) 298 11 276.842 Process Stream 7.55E-03 0.0833 0.0254 0.000506707 1.49E+01 1.28E-05 6.397 2249 0.08871 189395.5 3.24E-01
Utility S89 (in) 288 1 901.14 Water 2.51E-01 0.0833 0.0254 0.000506707 4.94E+02 1.14E-03 999 4189 0.596 11003853 8.01E+00
Utility S90 (out) 369.15 1 901.14 Water 2.60E-01 0.0833 0.0254 0.000506707 5.14E+02 2.91E-04 961 4212 0.6769 43106998 1.81E+00
HEX6 Process S26 (in) 308.86 14.97 420.8064 Propylene 2.52E-03 0.0833 0.0254 0.000506707 4.98E+00 8.92E-06 32 1917 0.01866 453890.3 9.16E-01
Process S27 (out) 308.86 14.97 420.8064 Propylene 2.40E-04 0.0833 0.0254 0.000506707 4.74E-01 8.73E-05 485 3053 0.09596 66829.07 2.78E+00
Utility water (in) 288.7 1 1576.07654 Water 8.35E-02 0.0833 0.0254 0.000506707 1.65E+02 1.14E-03 999 4189 0.596 3667951 8.01E+00
Utility water (out) 302.7 1 1576.07654 Water 8.68E-02 0.0833 0.0254 0.000506707 1.71E+02 3.62E-04 984 4221 0.6324 11827219 2.42E+00
HEX7 Process S73 (in) 416.72 40 173.9499 Carbon Dioxide 2.94E-03 0.0833 0.0254 0.000506707 5.79E+00 1.70E-05 16.5 2407 0.11788 142527.2 3.48E-01
Process S15 (out) 270.37 40 173.9499 Carbon Dioxide 1.84E-03 0.0833 0.0254 0.000506707 3.63E+00 1.17E-05 26.2 2340 0.0818 206654.9 3.35E-01
Utility S23 (in) 267.4 4.88 210.4032 Propylene 1.60E-03 0.0833 0.0254 0.000506707 3.17E+00 7.70E-06 10.36 1511 0.01441 108222.9 8.07E-01
Utility S29 (out) 275.3 4.88 210.4032 Propylene 5.86E-03 0.0833 0.0254 0.000506707 1.16E+01 7.93E-06 9.974 1534 0.01519 369259.6 8.01E-01
HEX8 Process S15 (in) 270.37 40 173.9499 Carbon Dioxide 1.84E-03 0.0833 0.0254 0.000506707 3.63E+00 1.17E-05 26.2 2340 0.0818 206654.9 3.35E-01
Process S19 (out) 258.15 40 173.9499 Carbon Dioxide 1.75E-03 0.0833 0.0254 0.000506707 3.45E+00 1.13E-05 27.6 2340 0.0787 214722.3 3.34E-01
Utility S34 (in) 255.32 3.27 70.243 Propylene 1.57E-04 0.0833 0.0254 0.000506707 3.10E-01 7.30E-06 7.085 1434 0.0132 7638.236 7.93E-01
Utility S36 (out) 255.32 3.27 70.243 Propylene 6.38E-04 0.0833 0.0254 0.000506707 1.26E+00 7.30E-06 7.085 1434 0.0132 31039.45 7.93E-01
HEX9 Process S19 (in) 258.15 40 173.9499 Carbon Dioxide 1.75E-03 0.0833 0.0254 0.000506707 3.45E+00 1.13E-05 27.6 2340 0.0787 214722.3 3.34E-01
Process S20 (out) 242.59 40 173.9499 Carbon Dioxide 1.62E-03 0.0833 0.0254 0.000506707 3.20E+00 1.06E-05 29.66 2348 0.01182 227003.6 2.11E+00
Utility S41 (in) 239.92 1.84 117.9066 Propylene 5.17E-04 0.0833 0.0254 0.000506707 1.02E+00 6.87E-06 4.138 1349 0.0746 15597.84 1.24E-01
Utility S42 (out) 239.92 1.84 117.9066 Propylene 1.51E-03 0.0833 0.0254 0.000506707 2.98E+00 6.87E-06 4.138 1349 0.01182 45591.84 7.84E-01
72
Hydrogen
Price: 6.72 $/kg
Yearly Cash Flow for 20 yr BEP
Investment Tax Allowances
(Depreciation) DCFROR Analysis - 20 yr BEP
Rate of Return = 0%
End of Year Plant Working
Capital Total
Hydrogen
Production
(kg)
Production
Cost
Sales
Revenue
Cash Flow
Before Tax Plant Total
Taxable Profit
in Previous
Year
Tax
Payable
Cash Flow
After Tax
Cumulative
Cash Flow
End of
Year
Discounted
Cash Flow
Discounted
Cumulative
Cash Flow
1 1,508,542 0 1,508,542 0 0 0 (1,508,542) 0 0 0 0 (1,508,542) (1,508,542)
1 (1,508,542) (1,508,542)
2 1,508,542 168,805 1,677,347 0 0 0 (1,677,347) 0 0 0 0 (1,677,347) (3,185,889)
2 (1,677,347) (3,185,889)
3 0 0 0 146392.2 891,335 1,007,001 115,666 0 0 0 0 115,666 (3,070,223)
3 115,666 (3,070,223)
4 0 0 0 146392.2 918,075 1,037,211 119,136 150,854 150,854 (35,189) (12,316) 131,452 (2,938,771)
4 131,452 (2,938,771)
5 0 0 0 146392.2 945,618 1,068,327 122,710 150,854 150,854 (31,719) (11,102) 133,811 (2,804,960)
5 133,811 (2,804,960)
6 0 0 0 146392.2 973,986 1,100,377 126,391 150,854 150,854 (28,145) (9,851) 136,242 (2,668,719)
6 136,242 (2,668,719)
7 0 0 0 146392.2 1,003,206 1,133,389 130,183 150,854 150,854 (24,463) (8,562) 138,745 (2,529,974)
7 138,745 (2,529,974)
8 0 0 0 146392.2 1,033,302 1,167,390 134,088 150,854 150,854 (20,672) (7,235) 141,323 (2,388,651)
8 141,323 (2,388,651)
9 0 0 0 146392.2 1,064,301 1,202,412 138,111 150,854 150,854 (16,766) (5,868) 143,979 (2,244,672)
9 143,979 (2,244,672)
10 0 0 0 146392.2 1,096,230 1,238,484 142,254 150,854 150,854 (12,743) (4,460) 146,714 (2,097,957)
10 146,714 (2,097,957)
11 0 0 0 146392.2 1,129,117 1,275,639 146,522 150,854 150,854 (8,600) (3,010) 149,532 (1,948,426)
11 149,532 (1,948,426)
12 0 0 0 146392.2 1,162,991 1,313,908 150,917 150,854 150,854 (4,332) (1,516) 152,434 (1,795,992)
12 152,434 (1,795,992)
13 0 0 0 146392.2 1,197,880 1,353,325 155,445 150,854 150,854 63 22 155,423 (1,640,569)
13 155,423 (1,640,569)
14 0 0 0 146392.2 1,233,817 1,393,925 160,108 150,854 150,854 4,591 1,607 158,502 (1,482,068)
14 158,502 (1,482,068)
15 0 0 0 146392.2 1,270,831 1,435,743 164,912 150,854 150,854 9,254 3,239 161,673 (1,320,395)
15 161,673 (1,320,395)
16 0 0 0 146392.2 1,308,956 1,478,815 169,859 150,854 150,854 14,057 4,920 164,939 (1,155,456)
16 164,939 (1,155,456)
17 0 0 0 146392.2 1,348,225 1,523,179 174,955 150,854 150,854 19,005 6,652 168,303 (987,153)
17 168,303 (987,153)
18 0 0 0 146392.2 1,388,671 1,568,875 180,203 150,854 150,854 24,100 8,435 171,768 (815,385)
18 171,768 (815,385)
19 0 0 0 146392.2 1,430,332 1,615,941 185,609 150,854 150,854 29,349 10,272 175,337 (640,048)
19 175,337 (640,048)
20 0 0 0 146392.2 1,473,242 1,664,419 191,178 150,854 150,854 34,755 12,164 179,013 (461,035)
20 179,013 (461,035)
21 0 0 0 146392.2 1,517,439 1,714,352 196,913 150,854 150,854 40,323 14,113 182,800 (278,235)
21 182,800 (278,235)
22 0 (168,805) (168,805) 146392.2 1,562,962 1,765,782 371,625 150,854 150,854 46,059 16,121 355,505 77,270
22 355,505 77,270
23 0 0 0 0 0 0 0 150,854 150,854 220,771 77,270 (77,270) 0
23 (77,270) 0
-3,500,000
-3,000,000
-2,500,000
-2,000,000
-1,500,000
-1,000,000
-500,000
0
500,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Cas
h F
low
($
)
Time (yr)
Cash Flow Diagram - 20 yr BEP
Cumulative andDiscounted CashFlow
73
Hydrogen
Price: 9.00 $/kg
Yearly Cash Flow for 10% DCFROR
Investment
Tax Allowances
(Depreciation) DCFROR Analysis - 10% DCFROR
Rate of Return = 0.1 = 10%
End of
Year Plant
Working
Capital Total
Hydrogen
Production
(kg)
Production
Cost
Sales
Revenue
Cash Flow
Before Tax Plant Total
Taxable
Profit
Tax
Payable
Cash Flow
After Tax
Cumulative
Cash Flow
End
of
Year
Discounted
Cash Flow
Discounted
Cumulative
Cash Flow
1 1,508,542 0 1,508,542 0 0 0 (1,508,542) 0 0 0 0 (1,508,542) (1,508,542)
1 (1,371,402) (1,371,402)
2 1,508,542 503,599 2,012,141 0 0 0 (2,012,141) 0 0 0 0 (2,012,141) (3,520,683)
2 (1,662,926) (3,034,328)
3 0 0 0 146392.2 891,335 1,342,102 450,766 0 0 0 0 450,766 (3,069,916)
3 338,667 (2,695,660)
4 0 0 0 146392.2 918,075 1,382,365 464,289 150,854 150,854 299,912 104,969 359,320 (2,710,596)
4 245,420 (2,450,240)
5 0 0 0 146392.2 945,618 1,423,836 478,218 150,854 150,854 313,435 109,702 368,516 (2,342,081)
5 228,819 (2,221,421)
6 0 0 0 146392.2 973,986 1,466,551 492,564 150,854 150,854 327,364 114,577 377,987 (1,964,093)
6 213,364 (2,008,057)
7 0 0 0 146392.2 1,003,206 1,510,547 507,341 150,854 150,854 341,710 119,599 387,743 (1,576,351)
7 198,973 (1,809,084)
8 0 0 0 146392.2 1,033,302 1,555,864 522,562 150,854 150,854 356,487 124,771 397,791 (1,178,559)
8 185,572 (1,623,511)
9 0 0 0 146392.2 1,064,301 1,602,540 538,239 150,854 150,854 371,707 130,098 408,141 (770,419)
9 173,092 (1,450,419)
10 0 0 0 146392.2 1,096,230 1,650,616 554,386 150,854 150,854 387,384 135,585 418,801 (351,617)
10 161,466 (1,288,953)
11 0 0 0 146392.2 1,129,117 1,700,134 571,017 150,854 150,854 403,531 141,236 429,781 78,164
11 150,636 (1,138,318)
12 0 0 0 146392.2 1,162,991 1,751,138 588,148 150,854 150,854 420,163 147,057 441,091 519,255
12 140,545 (997,773)
13 0 0 0 146392.2 1,197,880 1,803,672 605,792 150,854 150,854 437,294 153,053 452,739 971,994
13 131,142 (866,630)
14 0 0 0 146392.2 1,233,817 1,857,783 623,966 150,854 150,854 454,938 159,228 464,738 1,436,732
14 122,380 (744,250)
15 0 0 0 146392.2 1,270,831 1,913,516 642,685 150,854 150,854 473,112 165,589 477,096 1,913,827
15 114,213 (630,037)
16 0 0 0 146392.2 1,308,956 1,970,922 661,965 150,854 150,854 491,831 172,141 489,825 2,403,652
16 106,600 (523,437)
17 0 0 0 146392.2 1,348,225 2,030,049 681,824 150,854 150,854 511,111 178,889 502,935 2,906,588
17 99,503 (423,934)
18 0 0 0 146392.2 1,388,671 2,090,951 702,279 150,854 150,854 530,970 185,840 516,440 3,423,027
18 92,886 (331,048)
19 0 0 0 146392.2 1,430,332 2,153,679 723,348 150,854 150,854 551,425 192,999 530,349 3,953,376
19 86,716 (244,332)
20 0 0 0 146392.2 1,473,242 2,218,290 745,048 150,854 150,854 572,493 200,373 544,675 4,498,051
20 80,963 (163,369)
21 0 0 0 146392.2 1,517,439 2,284,838 767,399 150,854 150,854 594,194 207,968 559,432 5,057,483
21 75,596 (87,773)
22 0 (503,599) (503,599) 146392.2 1,562,962 2,353,383 1,294,020 150,854 150,854 616,545 215,791 1,078,229 6,135,712
22 132,456 44,683
23 0 0 0 0 0 0 0 150,854 150,854 1,143,166 400,108 (400,108) 5,735,604
23 (44,683) 0
-6,000,000
-4,000,000
-2,000,000
0
2,000,000
4,000,000
6,000,000
8,000,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Cas
h F
low
($
)
Time (yr)
Cash Flow Diagram - 10%DCFROR
Cumulative Cash Flow
Discounted Cash Flow
74
Hydrogen
Price: 11.23 $/kg
Yearly Cash Flow for 8 yr BEP
Investment Tax Allowances
(Depreciation) DCFROR Analysis - 8 yr BEP
Rate of Return = 16%
End of
Year Plant
Working
Capital Total
Hydrogen
Production
(kg)
Production
Cost
Sales
Revenue
Cash Flow
Before Tax Plant Total
Taxable Profit
in Previous
Year
Tax
Payable
Cash Flow
After Tax
Cumulative
Cash Flow
End of
Year
Discounted
Cash Flow
Discounted
Cumulative
Cash Flow
1 1,508,542 0 1,508,542 0 0 0 (1,508,542) 0 0 0 0 (1,508,542) (1,508,542)
1 (1,300,539) (1,300,539)
2 1,508,542 830,063 2,338,605 0 0 0 (2,338,605) 0 0 0 0 (2,338,605) (3,847,147)
2 (1,738,157) (3,038,696)
3 0 0 0 146392.2 891,335 1,668,556 777,221 0 0 0 0 777,221 (3,069,926)
3 498,015 (2,540,681)
4 0 0 0 146392.2 918,075 1,718,613 800,537 150,854 150,854 626,366 219,228 581,309 (2,488,617)
4 321,123 (2,219,558)
5 0 0 0 146392.2 945,618 1,770,171 824,553 150,854 150,854 649,683 227,389 597,164 (1,891,453)
5 284,397 (1,935,162)
6 0 0 0 146392.2 973,986 1,823,276 849,290 150,854 150,854 673,699 235,795 613,495 (1,277,958)
6 251,888 (1,683,273)
7 0 0 0 146392.2 1,003,206 1,877,974 874,769 150,854 150,854 698,436 244,452 630,316 (647,642)
7 223,111 (1,460,162)
8 0 0 0 146392.2 1,033,302 1,934,314 901,012 150,854 150,854 723,914 253,370 647,642 0
8 197,635 (1,262,527)
9 0 0 0 146392.2 1,064,301 1,992,343 928,042 150,854 150,854 750,157 262,555 665,487 665,487
9 175,079 (1,087,448)
10 0 0 0 146392.2 1,096,230 2,052,113 955,883 150,854 150,854 777,188 272,016 683,867 1,349,354
10 155,108 (932,341)
11 0 0 0 146392.2 1,129,117 2,113,677 984,560 150,854 150,854 805,029 281,760 702,800 2,052,154
11 137,423 (794,918)
12 0 0 0 146392.2 1,162,991 2,177,087 1,014,097 150,854 150,854 833,706 291,797 722,300 2,774,453
12 121,762 (673,156)
13 0 0 0 146392.2 1,197,880 2,242,400 1,044,519 150,854 150,854 863,242 302,135 742,385 3,516,838
13 107,892 (565,264)
14 0 0 0 146392.2 1,233,817 2,309,672 1,075,855 150,854 150,854 893,665 312,783 763,072 4,279,910
14 95,607 (469,657)
15 0 0 0 146392.2 1,270,831 2,378,962 1,108,131 150,854 150,854 925,001 323,750 784,380 5,064,291
15 84,726 (384,931)
16 0 0 0 146392.2 1,308,956 2,450,331 1,141,375 150,854 150,854 957,276 335,047 806,328 5,870,618
16 75,088 (309,843)
17 0 0 0 146392.2 1,348,225 2,523,841 1,175,616 150,854 150,854 990,520 346,682 828,934 6,699,552
17 66,549 (243,293)
18 0 0 0 146392.2 1,388,671 2,599,556 1,210,884 150,854 150,854 1,024,762 358,667 852,218 7,551,770
18 58,985 (184,309)
19 0 0 0 146392.2 1,430,332 2,677,542 1,247,211 150,854 150,854 1,060,030 371,011 876,200 8,427,970
19 52,283 (132,026)
20 0 0 0 146392.2 1,473,242 2,757,869 1,284,627 150,854 150,854 1,096,357 383,725 900,902 9,328,872
20 46,345 (85,681)
21 0 0 0 146392.2 1,517,439 2,840,605 1,323,166 150,854 150,854 1,133,773 396,821 926,345 10,255,218
21 41,083 (44,598)
22 0 (830,063) (830,063) 146392.2 1,562,962 2,925,823 2,192,924 150,854 150,854 1,172,312 410,309 1,782,615 12,037,832
22 68,157 23,559
23 0 0 0 0 0 0 0 150,854 150,854 2,042,069 714,724 (714,724) 11,323,108
23 (23,559) 0
-6,000,000
-4,000,000
-2,000,000
0
2,000,000
4,000,000
6,000,000
8,000,000
10,000,000
12,000,000
14,000,000
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Cas
h F
low
($
)
Time (years)
Cash Flow Diagram - 8 yr BEP
Cumulative Cash Flow
Discounted Cash Flow
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