PhD Thesis OPTIMAL PERFORMANCE ANALYSIS OF A SOLAR THERMAL ENERGY STORAGE PLANT BASED ON LIQUID AMMONIA Submitted by Engr. Sadaf Siddiq (08F-UET/PhD-ME-47) Supervised by Prof. Dr. Shahab Khushnood Department of Mechanical Engineering Faculty of Mechanical and Aeronautical Engineering University of Engineering and Technology Taxila, Pakistan July 2013
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PhD Thesis
OPTIMAL PERFORMANCE ANALYSIS OF A SOLAR THERMAL ENERGY STORAGE PLANT BASED ON
LIQUID AMMONIA
Submitted by
Engr. Sadaf Siddiq (08F-UET/PhD-ME-47)
Supervised by
Prof. Dr. Shahab Khushnood
Department of Mechanical Engineering Faculty of Mechanical and Aeronautical Engineering
University of Engineering and Technology Taxila, Pakistan
July 2013
ii
OPTIMAL PERFORMANCE ANALYSIS OF A SOLAR THERMAL ENERGY STORAGE PLANT BASED ON
LIQUID AMMONIA
by
Engr. Sadaf Siddiq (08F-UET/PhD-ME-47)
A proposal submitted for research leading to the degree of Doctor of Philosophy
in MECHANICAL ENGINEERING
Approved by
External Examiners
________________________________
(Engr. Dr. M. Javed Hyder) Dean of Engineering,
Pakistan Institute of Engineering & Applied Sciences Nilore, Islamabad.
________________________________ (Engr. Dr. Ejaz M. Shahid)
Associate Professor, Department of Mechanical Engineering,
University of Engineering & Technology, Lahore.
Internal Examiner (Research Supervisor)
________________________________ (Engr. Dr. Shahab Khushnood)
Professor, Department of Mechanical Engineering,
University of Engineering & Technology, Taxila.
Department of Mechanical Engineering Faculty of Mechanical and Aeronautical Engineering
University of Engineering & Technology Taxila, Pakistan.
iii
DECLARATION
I declare that all material in this thesis is my own work and that which is not, has been
identified and appropriately referenced. No material in this work has been submitted or
approved for the award of a degree by this or any other university.
Signature: _____________________________
Author’s Name: ________________________
It is certified that the work in this thesis is carried out and completed under my supervision. Supervisor: Prof. Dr. Shahab Khushnood Department of Mechanical Engineering Faculty of Mechanical and Aeronautical Engineering University of Engineering and Technology Taxila, Pakistan.
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ABSTRACT
This work focuses on extending the use of a solar thermal energy plant from an intermittent
energy source to a base load power plant by incorporating an efficient thermal storage feature.
A reference 10 MWe solar thermal plant design is considered with liquid ammonia as a
working fluid for energy production, in a Rankine Cycle, as well as a thermal storage
medium. During periods of no solar insolence, the recovery system, based on an industrial
ammonia synthesis system, is used to drive the power conversion unit and enable continuous
operation.
A thermofluid model, based on the continuity, momentum and energy conservation equations,
is used to carry out a numerical simulation of the plant, to determine the process variables
and subsequently carry out an integrated plant energy recovery analysis. The objective of this
work is to maximize the efficiency of the plant by a detailed consideration of the most critical
process in the plant: the energy recovery unit. This is carried out by (i) estimating the
sensitivity of non-uniform catalyst concentration in a synthesis reactor, and (ii) obtaining an
optimal configuration from a variational Lagrangian cost functional and applying
Pontryagin’s Maximum Principle. The optimal configuration is used to recommend a re-
design of the synthesis reactor and to quantify the energy recovery benefits emanating from
such a recommendation. Industrial optimal configurations are achieved by carrying out the
analysis with the simulation code, Aspen Plus™, to design a heat removal system
surrounding the catalyst beds, and incorporating the effect of standard industrial processes
v
such as purge gas removal, quench gas recycling, and recycle ratio to achieve the optimal
temperature profile obtained for the synthesis reactor considered in this work.
This work quantifies the maximum energy recovery in a base-load solar thermal plant
utilizing the existing environment of chemical process industry. It is concluded that a one-
dimensional model, with mass and energy conservation equations using the Temkin-Pyzhev
activity and pressure-based kinetics rate expressions, predicted an optimal ammonia
conversion of 0.2137 with a thermal energy availability of 20 MWth. A comprehensive
process simulation using Aspen Plus™ predicts an optimal ammonia conversion of 0.2762
mole fraction at exit, with two inter-bed heat exchangers having optimal temperature drops of
205K and 95K respectively, and yielding a thermal availability of 45.6 MWth. The thermal
energy availability of a base-load solar thermal plant can be increased by 15% in the
ammonia conversion and over 25% in thermal energy availability for energy recovery.
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To my family . . .
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ACKNOWLEDGEMENTS
During the development of my PhD studies at University of Engineering & Technology
Taxila, several persons and institutions collaborated directly and indirectly with my research.
Without their support it would be impossible for me to finish my work. That is why I wish to
dedicate this section to recognize their support.
I want to start expressing a sincere acknowledgement to my advisor, Prof. Dr. Shahab
Khushnood because he gave me the opportunity to research under his kind guidance and
supervision. I received motivation; encouragement and support from him during all my
studies. I owe Special thanks to Dr. Zafar Ullah Koreshi for the his support, guidance, and
transmitted knowledge for the completion of my work. With him, I have learned writing
papers for conferences and journals and sharing my ideas with the scientific community. I
also want to thank the example, motivation, inspiration and support I received from Dr.
Tasneem M. Shah, Dr. Arshad H. Qureshi and Dr. M. Bilal Khan.
The Grant from University of Engineering & Technology Taxila provided the funding and
resources for the development of this research and validation of my work. At last, but the
most important I would like to thank my family, for their unconditional support, inspiration,
love and prayers.
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NOMENCLATURE
A Cross-sectional area (m2)
ANU Austrailian National University
pC Specific heat at constant pressure (kJ kmol-1 K-1)
rC Compression Ratio
CSP Concentrating Solar Power
E Activation energy (kJ kmol-1)
sfF → Force (external, fluid to solid)
0NF Initial nitrogen molar flow rate (kmol h-1)
Gt Giga-ton (109 ton)
Η Hamiltonian
Η Enthalpy per unit mass
J Functional
*, ii JJ Molar Fluxes
K Kinetic Energy
aK Equilibrium constant
KBR Kellogg Brown and Root™
L Length of synthesis reactor (m)
MTD Metric tonnes per day
Mtoe Million ton of oil equivalent
MWe Megawatt electric
MWth Megawatt thermal
OEM One Equation Model
P Pressure (MPa)
Ρ Linear Momentum
PMP Pontryagin’s Maximum Principle
PV PhotoVoltaic
Q Heat
ix
R Universal gas constant 8.3144 kJ kmol-1 K-1
AR Reaction rate (kmol NH3 h-1 m-3 catalyst)
RK-4 4th order Runge-Kutta
S Surface Area (m2)
T Temperature (K)
TEM Two Equation Model
TSP Thermal Storage Plant
TWh Terawatt-hours (1012 Watt-hrs)
U Internal Energy (kJ)
U Internal Energy per unit mass
W Watts
ia Activity for speciei
c Total Molar Concentration
ic Molar Concentration of Specie i
pd Particle Diameter
g Gravitational acceleration (9.81 ms-2)
*, ii jj Mass Fluxes
kWe kilowatt Electric
kWchem. kilowatt chemical
kWth kilowatt thermal
m Mass (kg)
0in Initial mole flow rate of speciei (kmol h-1)
ppm Parts per million
r Molar Production
t Time
u Control variable
v Velocity (m s-1)
w Work
x Distance along catalyst bed (m)
x
x′ Normalized Distance along catalyst bed (m)
iy Mole fraction for specie i
o
iy Initial Mole fraction for specie i
Nzz, Fractional conversion of Nitrogen
Greek
rH∆ Heat of reaction (kJ kmol-1 NH3)
ε Extent of reaction
Φ Potential Energy
iφ Fugacity coefficient for speciei
ω Mass Flow Rate (kghr-1)
τ Shear Stress
η Catalyst effectiveness factor
ψ The void space of the bed
λ Lagrange multiplier
)(xξ Catalyst spatial factor
)(x′θ Optimal Temperature
ρ Density (kg m-3)
σr Vector containing state variables
Subscripts
eqm Equilibrium
i Species in a multi component system, Ni ,....4,3,2,1=
opt Optimal
s Isentropic
tot Total amount of entity in a macroscopic system
0 Evaluated at a surface
2,1 Evaluated at cross sections 1 and 2
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Table of Contents
ABSTRACT ....................................................................................................................................................... IV
ACKNOWLEDGEMENTS ............................................................................................................................ VII
NOMENCLATURE ...................................................................................................................................... VIII
TABLE OF CONTENTS .................................................................................................................................. XI
TABLE LIST ................................................................................................................................................... XIII
FIGURE LIST ................................................................................................................................................ XIV
1.1 SOLAR ENERGY: POTENTIAL AS A RENEWABLE ENERGY SOURCE ............................................................ 2 1.2 SOLAR POWER PLANTS IN OPERATION ...................................................................................................... 5
1.3 THERMAL ENERGY STORAGE REQUIREMENT ............................................................................................ 9 1.4 THERMAL STORAGE MATERIALS .............................................................................................................. 9 1.5 USE OF L IQUID AMMONIA AS STORAGE MATERIAL ................................................................................ 11
1.5.1 Poperties of Liquid Ammonia ....................................................................................................... 12 1.5.2 Dissociation and Synthesis of Ammonia ....................................................................................... 12 1.5.3 Commercial uses of Ammonia ...................................................................................................... 13 1.5.4 Industrial proprietary processes for Ammonia Production .......................................................... 14
1.5.4.1 Haldor Topsoe Ammonia Synthesis Process ........................................................................................... 15 1.5.4.2 Kellog Brown & Roots (KBR) Advanced Ammonia Process (KAPP).................................................... 15 1.5.4.3 Krupp Uhde GmbH Ammonia Process ................................................................................................... 16 1.5.4.4 ICI-Leading Concept Ammonia (LCA) Process...................................................................................... 17 1.5.4.5 The Linde Ammonia Concept (LAC) Ammonia (LCA) Process ............................................................ 17
1.6 THERMODYNAMIC CYCLES FOR SOLAR THERMAL POWER PLANTS ........................................................ 18 1.7 LITERATURE REVIEW .............................................................................................................................. 19 1.8 THESIS MOTIVATION ............................................................................................................................... 22 1.9 OBJECTIVES ............................................................................................................................................ 23 1.10 SUMMARY OF FOLLOWING CHAPTERS ............................................................................................... 24
2 DESCRIPTION OF THE THERMAL STORAGE PLANT .............................................................. 25
2.1 PLANT FEATURES .................................................................................................................................... 25 2.1.1 Process Design ............................................................................................................................. 25 2.1.2 Opertational Parameters .............................................................................................................. 27
2.2 OVERALL PLANT LAYOUT AND DESCRIPTION ......................................................................................... 28 2.2.1 Ammonia Dissociation .................................................................................................................. 29 2.2.2 Ammonia Synthesis ....................................................................................................................... 30 2.2.3 Syn Gas and Ammonia Storage .................................................................................................... 31 2.2.4 Heat Exchangers and Transport Piping ....................................................................................... 31 2.2.5 Compressors and Pumps .............................................................................................................. 31
2.3 THERMAL STORAGE PLANT PROCESS FLOW DIAGRAM ........................................................................... 32
3 MODELLING & SIMULATION OF THERMAL STORAGE PLANT .......................................... 34
3.1 MATHEMATICAL MODELLING .............................................................................................................. 34 3.1.1 Review of Mathematical Models of TSP ....................................................................................... 34 3.1.2 Mathematical Models for TSP ...................................................................................................... 41
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3.1.2.1 TEM Model using Activity based Temkin-Pyzhev Form (TP-A): .......................................................... 43 3.1.2.2 TEM Model using Partial Pressure based Temkin-Pyzhev Form (TP-B): ............................................... 45
3.2 MODELING UNIT OPERATIONS ................................................................................................................ 48 3.2.1 Dissociation Reactor .................................................................................................................... 48 3.2.2 Synthesis Reactor-Aspen Plus Model............................................................................................ 51 3.2.3 Synthesis Reactor- HYSYS Model ................................................................................................. 53 3.2.4 Flash Tank .................................................................................................................................... 55 3.2.5 Purge Gas & Recycle .................................................................................................................... 56 3.2.6 Heat Exchangers and Waste Heat Recovery................................................................................. 57
4.3.1 Effect of Temperature on Dissociation ......................................................................................... 78 4.3.2 Effect of Flow Rate on Dissociation ............................................................................................. 79 4.3.3 Effect of Pressure on Synthesis ..................................................................................................... 80 4.3.4 Effect of Temperature on Synthesis .............................................................................................. 80 4.3.5 Effect of Flash Temperature on Liquid Ammonia Separation ...................................................... 82 4.3.6 Effect of Purge Fraction on Ammonia Liquification .................................................................... 83 4.3.7 Effect of Recycle Stream on Synthesis .......................................................................................... 84
5 AN OPTIMAL STORAGE PLANT ...................................................................................................... 85
5.1 PROCESS MODIFICATIONS ..................................................................................................................... 85 5.1.1 Optimal Analysis Problem Formulation- Process Modifications ................................................. 85 5.1.2 OEM using Activity based Temkin-Pehzev form (OEM-TPA) ...................................................... 86 5.1.3 OEM using Partial Pressure based Temkin-Pehzev form (OEM-TPB) ........................................ 89 5.1.4 Process Modifications Validation: ............................................................................................... 94
APPENDIX A. AMMONIA 3D PHASE DIAGRAMS ...................................................................... 121
APPENDIX B MATLAB™ PROGRAMS FOR AMMONIA SIMULATION ............................... 122
APPENDIX B1: MATLAB ™ PROGRAM FOR OUTPUT OF STEADY STATE SYNTHESIS REACTOR ....................... 123 APPENDIX B2: MATLAB ™ PROGRAM FOR FINDING EQUILIBRIUM CONCENTRATIONS ................................... 149 APPENDIX B3: MATLAB ™ PROGRAM FOR FINDING OUTPUT OF COUNTER-FLOW SYNTHESIS REACTOR ....... 153 APPENDIX B4: MATLAB ™ PROGRAM FOR FINDING OUTPUT OF STEADY STATE SYNTHESIS REACTOR WITH 3
CATALYST ZONES .......................................................................................................................................... 157
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Table List
Tables Page TABLE 1.1: World’s Largest (25MWe or above) PV Plants in Operation .............................. 6 TABLE 1.2: Solar Themal Plants in Operation ........................................................................ 7 TABLE 1.3: Haldor Topsoe Ammonia Converter Features ................................................... 15
TABLE 2.1: Overall Plant Design for a 10 MW(e) Baseload Plant ....................................... 26 TABLE 3.1: Equations of change of Multi-component Mixtures in terms of the Molecular
Fluxes .............................................................................................................................. 35 TABLE 3.2: Coefficients of the correction factor polynomial in terms of pressure .............. 38 TABLE 3.3: Input Data for Dissociation Reactor .................................................................. 49 TABLE 3.4: Input Data for Synthesis Reactor ....................................................................... 51 TABLE 3.5: Reaction Input for Temkin-Pyzhev Power-Law Expression in Aspen Plus™ .. 52 TABLE 3.6: Flash Tank Output .............................................................................................. 56 TABLE 3.7: Molar Flow Rates of Components in and out of Splitter ................................... 56 TABLE 3.8: Percentage errors in 1-D Models compared with HYSYS™ and Aspen Plus™61 TABLE 4.1: Optimal solution for the exit conditions ............................................................ 67
xiv
Figure List
Figures Page
Figure 1.1 Volume Reduction with Phase Change Materials ................................................. 10 Figure 1.2 Materials for medium and high heat storage ......................................................... 10 Figure 1.3 Energy densities for different energy carriers ....................................................... 12 Figure 2.1: Thermal Storage Plant Schematic ........................................................................ 29 Figure 2.2: Array of 400 m2 Paraboloidal Solar Collectors [3] .............................................. 30 Figure 2.3: TSP Process Flow Diagram .................................................................................. 32 Figure 3.1 : Conversion of Nitrogen along a single-bed catalyst ........................................... 39 Figure 3.2 : Syngas temperature in converter ......................................................................... 39 Figure 3.3 : Molar flow rate in converter ................................................................................ 40 Figure 3.4 : Syngas compression requirement ........................................................................ 40 Figure 3.5 : 3-Bed Homogeneous Reactor with TP-A Kinetics ............................................. 45 Figure 3.6 : 3-Bed Homogeneous Reactor with TP-B Kinetics .............................................. 47
Figure 4.5 : GA Search Algorithm .......................................................................................... 67 Figure 4.6 : Four-Bed Synthesis Reactor ................................................................................ 68 Figure 4.7 : Effect of Quench gas on conversion efficiency ................................................... 69 Figure 4.8 : GA Algorithm for obtaining optimal temperature distribution ........................... 70
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Figure 4.9 : Optimal and Normal Ammonia Production Rates .............................................. 71 Figure 4.10 : Optimal and Normal Nitrogen Conversion and Reaction rates ......................... 71 Figure 4.11 : Effect of Temperature on Dissociation ............................................................. 79 Figure 4.12 : Effect of Flow Rate on Dissociation ................................................................. 79 Figure 4.13 : Effect of Pressure on Synthesis ......................................................................... 80 Figure 4.14 : Effect of Temperature on Synthesis .................................................................. 81 Figure 4.15 :Temperature & Pressure Parametric Sensitivity for Synthesis .......................... 81 Figure 4.16 :Effect of Flash Temperature on Ammonia Flow Rate ....................................... 82
Figure 4.17 :Effect of Flash Temperature on Ammonia Mole Fraction ................................. 83 Figure 4.18 :Effect of Purge Fraction on Ammonia Liquification ......................................... 83 Figure 5.1 : Homogeneous reactor with 1-D Model (TEM-TPA) showing gas temperatureT ,
equilibrium temperatureeqmT , and optimal temepratureoptT ............................................ 87
Figure 5.2 : Temperature in homogeneous reactor compared with one-equation optimal temperatureoptT and equilibrium temperatureeqmT . ......................................................... 91
Figure 5.3 : Homogeneous reactor: (a) ammonia mole fraction, (b) temperature profile, and (c) hydrogen/nitrogen/ammonia mole fractions. .................................................................. 92
Figure 5.4 : Homogeneous reactor with OEM-TPA, showing gas temperatureT , equilibrium temperatureeqmT , and optimal temperatureoptT . .............................................................. 93
Figure 5.5 : The Proposed Energy Recovery Plant with Process Modifications ................... 93
Figure 5.6 : PFR reactor beds with cooling between beds 1 and 2 ......................................... 94 Figure 5.7 : PFR reactor beds with cooling between beds ...................................................... 95 Figure 5.8 : Effect of temperature drop in the inter-bed heat exchanger, after the first bed, on
the ammonia mole fraction at reactor outlet. .................................................................. 95 Figure 5.9 : Effect of temperature drop in the inter-bed heat exchangers, after the first and
second beds, on the ammonia mole fraction at reactor outlet. ........................................ 96 Figure 5.10 : Homogeneous reactor: Nitrogen conversion in catalyst bed. ............................ 98
Figure 5.11 : Effect of varying spatial composition in reactor beds on the mole fraction of ammonia in the reactor compared with the reference (homogeneous) design with spatial concentration [1.00, 1.00, 1.00] ...................................................................................... 99
Figure 5.12 : Effect of varying spatial composition in reactor beds (1.50, 1.25, 1.00); a) nitrogen conversion, b) actual, optimal and equilibrium temperatures, c) hydrogen, nitrogen and ammonia mole fractions. .......................................................................... 100
Figure 5.13 : Bed1: Temperature Profile with different Catalyst Distribution ..................... 101 Figure 5.14 : Bed2: Temperature Profile with different Catalyst Distribution ..................... 102 Figure A.1 Ammonia 3D Phase Diagram ............................................................................. 121
Engr. Sadaf Siddiq (08F-UET/PhD-ME-47)
1
1 INTRODUCTION In the coming centuries of the decline of the world’s fossil energy stocks, an electricity
production mix will establish which will be inevitably dominated increasingly by alternate &
renewable energies.
The alternate energy sources are available in form of solar energy, wind energy,
hydroelectric, geothermal, wave and tidal power etc. The current global energy consumption
is 15TWe per year while the solar energy potential is estimated to be 86000 TWe per year
[46].
Solar energy can be utilized either as a direct photovoltaic (PV) source, where the light is
converted directly into electrical energy or as concentrated solar power where a fluid is
heated by concentrating the solar thermal energy to produce electricity in a thermal power
plant. Solar thermal energy is concentrated using different techniques, such as, Parabolic
Trough, dish System and power tower etc.
The success of solar thermal systems for electricity production hinges very crucially on the
selection, mechanical design and optimal operation of an energy storage system which can
enable the continuous operation of a power plant. The energy storage systems being
investigated include solid graphite, encapsulated Phase Change Materials (PCMs) in a
graphite matrix, and liquid ammonia [72].
This work focuses on extending the use of a solar thermal energy plant from an intermittent
energy source to a base load power plant by incorporating an efficient thermal storage feature.
A reference 10 MWe solar thermal plant design is considered with liquid ammonia as a
working fluid for energy production in a Rankine Cycle as well as a thermal storage medium.
Engr. Sadaf Siddiq (08F-UET/PhD-ME-47)
2
During periods of no solar insolence, the recovery system, based on an industrial ammonia
synthesis system, is used to drive the power conversion unit and enable continuous operation.
The objective of this work is to increase the efficiency of ammonia synthesis process for
maximum heat recovery and hence to improve the performance of Solar Thermal Storage
plant.
1.1 Solar Energy: Potential as a Renewable Energy Source Solar energy currently accounts for an installed capacity of about 23 GWe, compared with
geothermal (installed capacity 10.7 GW), and wind (160 GW) [8]. This is insignificant in the
global scenario where in 2010, the total primary energy consumption was 12002.4 Mtoe [8]
consisting of oil (33.8%), coal (29.6%), natural gas (23.8%), hydroelectric (6.5%) and
nuclear (5.6%). Even though renewable sources such as solar, geothermal and wind are not
presently significant, they offer the promise of providing clean and sustainable energy by
mitigating the effect of the carbon release from fossil fuels, in the form of greenhouse gases
[8], [14]. Such reductions are necessary for the environment and are binding on states
signatory to the Kyoto Protocol [117]. Emission of greenhouse gases (carbon dioxide,
methane, nitrous oxide, hydrofluorocarbons, perfluorocarbons and sulphur hexafluoride) as
well as toxic and pollutant gases, also have a harmful effect on people.
The Kyoto Protocol of 1997 [117] came into force on 16th February 2005 and establishes
quantified limitations on greenhouse gases, to promote sustainable development and calls for
member states to develop new forms of renewable energy and innovative environmentally
sound technologies.
Engr. Sadaf Siddiq (08F-UET/PhD-ME-47)
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According to a study by the World Energy Outlook [14] a Reference Scenario studies the
period 2006-2030 and estimates an increase in world primary energy demand of 45% from an
annual of 11730 Mtoe to over 17010 Mtoe at 1.6% increase per year. While oil remains the
dominant fuel, its share decreases from 34% to 30% over this period. In the same period, gas
rises at 1.8% per year to 22% while coal, at an annual increase of 2% rises from 26% to 29%.
Thus the fossil fuels contribute to 81% of the total primary energy demand by 2030.
Notwithstanding the impact of a nuclear renaissance, the contribution of nuclear power to
primary energy drops from 6% to 5%; this is an electricity generation share from 15% to 10%
by 2030.
In this period, renewable energy sources take second place after coal for electricity
generation. The contribution of hydropower drops from 16% to 14% while non-hydro
renewables, growing at an average annual rate of 7.2% increase from less than 1% to 4%.
The absolute magnitude of the non-hydro renewables increases from 66 Mtoe in 2006 to 350
Mtoe by 2030.
The power outlook has coal contribution to electricity generation increasing from 41% in
2006 to 44% in 2030, while the share of renewable grows from 18% to 23% in the same
period. The world’s final electricity consumption grows from 15665 TWh to 28141 TWh at
an average annual growth of 2.5%. This corresponds, in the Reference Scenario, to an
electricity generation of 18921 TWh in 2006 to 33265 TWh in 2030.
The factors accelerating the share of renewables are climate change, to attain the CO2 ppm
goal, the higher cost of oil and gas and energy security. Among the renewables, hydropower
Engr. Sadaf Siddiq (08F-UET/PhD-ME-47)
4
will continue to be the dominant while others will include wind, solar, biomass and
geothermal energy.
The sun, as the primary source of energy for the solar system, supplies over 30,000 TWyr/yr
which, compared with the global energy requirement of the order of 20 TWyr/yr over the
next generation, may be considered to be a virtually inexhaustible source [46]. Solar energy
is useable as thermal energy, bioenergy from photosynthesis, and as a source for photovoltaic
conversion. Solar energy is truly renewable and sustainable as it is non-depletable, carbon
emission free, scalable, readily accessible, robust and flexible. The issues which will ensure
its place in the future energy scenario is its economic competitiveness in comparison with
existing technologies. A key technological issue that lies at the core of economic
competitiveness of solar energy -- thermal energy storage, is the focus of this thesis.
For electricity generation, the solar energy options available are photovoltaic (PV)
technology and concentrated solar power (CSP) technology. PV technology is based on the
direct conversion of photon energy from the Sun to electricity. Since the energy from the sun
is spread over a large range of wavelengths, a PV collector is designed to utilize as much of
the available spectrum as possible. The primary limitation is the detection window of the
sensor material forming the collector. The efficiency of a PV collector has remained low
(about 20%) and thus its application has been generally limited to mini-power requirements
such as off-grid homes [168][175]. However, larger PV plants have been built and the total
PV technology had a global installed capacity of 6 GWe in 2006, growing by 2009 to
15GWe and by the end of 2009 to 23 GWe, but had the disadvantage of having the highest
generating cost (US$ 5500-9000 per kWh in 2007) compared to all renewable technologies.
Engr. Sadaf Siddiq (08F-UET/PhD-ME-47)
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The Reference Scenario estimates the cost to reduce to US$ 2600 per kWh by 2030. CSP
technology uses optics to focus sunlight to a small receiver where the energy can be utilized
to convert water to superheated steam for electricity generation in a turbine. The total
installed capacity of CSP was 354 MWe in 2006. This technology is expected to be
comparable in cost (US$ 2-3 per kW: 2007) with gas-fired, but generally more expensive
than coal-fired generation, wind and nuclear.
1.2 Solar Power Plants in Operation 1.2.1 PV Plants Though PV technology is considered to be of use for small off-grid locations, large plants
have been built and are currently in operation [46]. The PV power generation technology saw
a 70% increase in 2008 alone, to 13GWe. Two notable areas of growth witnessed in 2008
were the Building Integrated PV Plants (BIPV) in Europe, and the utility-scaled PV plants (>
200 kWe), By the end of 2008, over 1800 such plants were in operation worldwide. Several
of these plants can be considered to be large, with the 200 MWe Huanghe Hydropower
Golmud Solar Park plant, completed in China in 2011, to be the largest PV plant in the world.
Plants of this magnitude are currently under development in Europe, China, India, Japan, the
United States of America and other countries. Table 1.1 presents World’s largest PV plants in
operation while 38 more plants with a cumulative nominal power of about 13000 MWe are
planned or under construction and are expected to complete by 2019.
Engr. Sadaf Siddiq (08F-UET/PhD-ME-47)
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TABLE 1.1: World’s Largest (25MWe or above) PV Plants in Operation S.No. Name Country Nominal
Power(MWe) 1 Huanghe Hydropower Golmud Solar Park China 200 2 Perovo Solar Park Ukraine 100 3 Sarnia Photovoltaic Power Plan Canada 97 4 Montalto di Castro Photovoltaic Power
Station Italy 84.2
5 Solarpark Senftenberg Germany 82 6 Finsterwalde Solar Park Germany 80.7 7 Okhotnykovo Solar Park Ukraine 80 8 Lopburi Solar Farm Thailand 73 9 Lieberose Photovoltaic Park Germany 71.8 10 San Bellino Photovoltaic Power Plant Italy 70 11 Le Gabardan Solar Park France 67.2 12 Olmedilla Photovoltaic Park Spain 60 13 Sault Ste Marie Solar Park Canada 60 14 Strasskirchen Solar Park Germany 54 15 Tutow Solar Park Germany 52 16 Waldpolenz Solar Park Germany 50 17 Longyuan Golmud Solar Park China 50 18 Hongsibao Solar Park China 48 19 Serenissima Solar Park Italy 48 20 Copper Mountain Solar Facility USA 47.6
21 Puertollano Photovoltaic Park Spain 46 22 Moura photovoltaic power station Portugal 45 23 Kothen Solar Park Germany 45 24 Avenal Solar Facility USA 42.7 25 Cellino San Marco Solar Park Italy 40 26 Bitta Solar Park India 39.5 27 Fürstenwalde Solar Park Germany 38.3 28 Ralsko Solar Park Ra 1 Czech Republic 38 29 Reckahn Solar Park Germany 36.2 30 Alfonsine Solar Park Italy 35.1 31 Vepřek Solar Park Czech Republic 35 32 San Luis Valley Solar Ranch USA 34.4 33 Sant'Alberto Solar Park Spain 34 34 Planta Solar La Magascona & La Magasquila Italy 33 35 Ernsthof Solar Park Germany 32 36 Arnedo Solar Plant Spain 31.8 37 Parc Solaire Curbans USA 30.2
Engr. Sadaf Siddiq (08F-UET/PhD-ME-47)
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38 Long Island Solar Farm USA 30 39 Planta Solar Dulcinea Spain 30 40 Cottbus Drewitz Solar Park Germany 30 41 Agua Caliente Solar Project USA 30 42 Gunthawad Solar Farm India 30 43 Cimarron Solar Farm USA 30 44 Merida/Don Alvaro Solar Park Spain 29.9 45 Planta Solar Ose de la Vega Spain 27.5 46 Webberville Solar Park USA 26.4 47 Ševětín Solar Park Czech Republic 26 48 Solarpark Heideblick Germany 25.7 49 Solarpark Eiche Germany 25
1.2.2 Solar Thermal Plants The CSP technology showed a small generation increase by 0.06GWe to 0.5GWe by the end
of 2008. The world’s largest solar site is in California, owned by NextEra Energy Resources
[45] The power produced is 354 MWe, which is purchased by Southern California Edison
and provides to more than 230,000 homes at peak power during the day. It is thus as large as
a nuclear reactor such as CHASNUPP, and would be sufficient for a city of the size of
Islamabad. The site is spread over 1500 acres, and has more than 900,000 mirrors.
Other large CSP plants in the range of 30-150 MWe are also located in the United States and
Spain [21],[47]. Several other countries including Abu Dhabi, Algeria, Egypt, Israel,
Portugal and Morocco have projects underway [45]. One of the plants, a 20MWe CSP is
integrated with a 450MWe natural-gas combined-cycle plant in Morocco. Table 1.2 lists
solar thermal power plants in operation in different parts of the world with total capacity
amounting to 1702.65 MWe. The total capacity of under construction (to be completed by
2014) solar thermal plants is 2106.9 MWe.
TABLE 1.2: Solar Themal Plants in Operation
Serial #
Name Country Capacity (MWe)
Technology
1 Solar Energy Generating Systems
USA 354 parabolic trough
2 Solnova Solar Power Station Spain 150 parabolic trough 3 Andasol solar power station Spain 150 parabolic trough
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4 Extresol Solar Power Station Spain 100 parabolic trough 5 Palma del Rio Solar Power
Station Spain 100 parabolic trough
6 Manchasol Power Station Spain 100 parabolic trough 7 Valle Solar Power Station Spain 100 parabolic trough 8 Martin Next Generation Solar
Energy Center USA 75 ISCC
9 Nevada Solar One USA 64 parabolic trough 10 Ibersol Ciudad Real Spain 50 parabolic trough 11 Alvarado I Spain 50 parabolic trough 12 La Florida Spain 50 parabolic trough 13 Majadas de Tiétar Spain 50 parabolic trough 14 La Dehesa Spain 50 parabolic trough 15 Helioenergy 1 Spain 50 parabolic trough 16 Lebrija-1 Spain 50 parabolic trough 17 Solacor 1 Spain 50 parabolic trough 18 Puerto Errado 1+2 Spain 31.4 fresnel reflector 19 Hassi R'mel integrated solar
combined cycle power station Algeria 25 ISCC
20 PS20 solar power tower Spain 20 solar power tower
24 Gemasolar Spain 17 solar power tower 25 PS10 solar power tower Spain 11 solar power tower 26 Kimberlina Solar Thermal
Energy Plant USA 5 fresnel reflector
27 Sierra SunTower USA 5 solar power tower 28 Archimede solar power plant Italy 5 parabolic trough 29 Thai Solar Energy (TSE) 1 Thailand 5 parabolic trough 30 Liddell Power Station Solar
Steam Generator Australia 2 fresnel reflector
31 Keahole Solar Power USA 2 parabolic trough 32 Maricopa Solar USA 1.5 dish stirling 33 Jülich Solar Tower Germany 1.5 solar power tower 34 Saguaro Solar Power Station USA 1 parabolic trough 35 Shiraz solar power plant Iran 0.25 parabolic trough Overall Capacity 1702.65
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1.3 Thermal Energy Storage Requirement The major drawback of CSPs at the moment is the lack of thermal storage due to which
operation is only possible when daylight is available. Only two plants have storage viz the
Andasol-1 [48] plant in Spain which has more than seven hours of full-load thermal storage
capability, and a 280 MWe plant planned in Arizona which will also have a six-hour storage
capacity.
1.4 Thermal Storage Materials The thermal energy storage technologies can be classified [72] by the mechanism of heat viz
(i) sensible, (ii) latent, (iii) sorptive, and (iv) chemical. In the sensible heat storage systems,
there is the possibility of liquid (water tank, aquifier, thermal oil) and solid systems (building
mass, concrete, and ground etc.) [5]. In the latent heat storage systems, both organic
(parrafins) and inorganic (hydrate salts) compounds can be used. In the sorptive, both
absorption and adsorption systems can be used. Finally, in the chemical storage, energy can
be stored in chemical bonds which can be broken endothermically and recovered in a
synthesis exothermically.
When single-phase heat transfer fluids such as thermal oil or pressurized water are used, a
sensible heat storage system using concrete has been developed and experimentally tested
[51] in the temperature range 300-400 oC and found to be an attractive options for CSPs.
Storage materials and technology will also depend on the temperatures in the plant [66]. For
domestic hot water and space heating, the temperatures will be less than 100 oC; for process
heat, 100-250 oC; for electricity generation 250-1000 oC, while for hydrogen production they
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will be in excess of 1000 oC. The storage capacity of some pha
below [66]. It can be seen that the highest storage capacity is for salts.
Figure 1.1 Volume Reduction with Phase Change Materials
Figure 1.2 Materials for medium and high heat storage
ME-47)
10
C. The storage capacity of some phase change materials is shown
. It can be seen that the highest storage capacity is for salts.
Volume Reduction with Phase Change Materials
Materials for medium and high heat storage
se change materials is shown
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Salts freeze 350-500 oC and boil at ~1000 oC. They have a high volumetric heat capacity and
may be used, even in graphite blocks. Liquid fluoride salts are also widely available, as they
are used in aluminium metal extraction Hall electrolysis process in which aluminium oxide
is dissolved in cryolite which is a sodium-aluminium fluoride salt. Fluoride salts are
compatible with graphite upto 1400 oC [176].
1.5 Use of Liquid Ammonia as Storage Material Liquid ammonia is a candidate for large solar-thermal systems due to the storage of thermal
energy in its chemical bonds during, for example, solar insolation and recovery from
subsequent exothermic synthesis. To compare different storage opportunities, the energy
storage density is a value which is useful to determine the required size of storage for a
required amount of energy. With the kind of energy carrier, the amount of stored energy
varies strongly. A comparison between different energy carriers is presented in Figure 1.3
[79]. It is clear that thermo-chemical energy carriers offer the suitable most energy densities
i.e. of the order of 10 MJ/kg.
Ammonia is an abundantly produced chemical, globally and in Pakistan. It has an important
use as a fertilizer to boost agricultural production. Thus it is used in a synthesis process of
natural gas with carbon dioxide resulting in the formation of urea fertilizer, or carbamide
(NH2)2CO. In Pakistan, there are eight large urea fertilizer plants based on the reforming and
synthesis of natural gas mainly from the Sui and Marri gas fields. At an international price of
US$ 300/tonne, this represents an annual sales value of US$1,500 million. This amounts to
an average production of about 1600 tonnes per day (TPD) per plant [25].
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Figure 1.3 Energy densities for different energy carriers 1.5.1 Poperties of Liquid Ammonia Ammonia (NH3) stays in the liquid form at temperatures higher than its melting point
73.77− oC and has a density of 681.9 kg/m3 at its boiling point -33.34 oC ; it must thus be
kept at very low temperature or stored at very high pressure [165]. Liquid ammonia was first
produced on an industrial scale in Germany, during the First World War, by the Haber -
Bosch process [110].
1.5.2 Dissociation and Synthesis of Ammonia The dissociation of ammonia
223 32 HNNH +⇔ (∆H = 66.9 kJ/mol)
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is an endothermic reaction that can be carried out by thermo-catalytic decomposition using
catalysts: ruthenium, indium, nickel, Fe-Al-L, Fe-Cr. Typical temperatures are in the range of
850 – 1000 oC. Approximately 1.4 kW power per cubic meter of hydrogen is typically used.
Conversely, the synthesis of ammonia from nitrogen and hydrogen reactant gases
322 23 NHHN ⇔+ (∆H = -92.22 kJ/mol)
is an exothermic reaction for which the pressure required is in the range 130 – 250 bar, and
the temperature required is in the range 250 – 600 oC. High temperature gives higher reaction
rate, but as reaction is exothermic, higher temperature according to Le Chatelier’s principle
causes the reaction to move in the reverse direction hence a reduction in product. Similarly,
higher Temperature reduces the equilibrium constant and hence the amount of product
decreases; this is the Van’t Hoff equation
R
S
RT
HK
oo ∆+∆−=ln
An increase in pressure, however, causes a forward reaction and is thus favorable. Synthesis
is achieved by using catalysts such as osmium, ruthenium, and iron-based catalysts [110].
1.5.3 Commercial uses of Ammonia Ammonia is one of the most widely produced chemicals, amounting to over 15 million tones
in 2009. Its major uses are as fertilizer and for production of nitrogen containing compounds
such as nitric acid. It is used as a refrigerant and in textile processing. A very important
emerging use of ammonia is Hydrogen production, by its decomposition, to be used in
Hydrogen Fuel cells.
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1.5.4 Industrial proprietary processes for Ammonia Production
Global fertilizer industry produces about 170 million tones of fertilizer nutrients every year
[42] for boosting agricultural output. Fertilizers are based on nitrogen, phosphorus or
potassium. Nitrogen accounts for 78% of the earth’s atmosphere. Since plants can not breathe
nitrogen, it must be converted to a suitable form such as ammonia. The Haber-Bosch process,
first demonstrated by Fritz Haber in 1909 and scaled up to an industrial process by Carl
Bosch in 1913. Both Haber and Bosch were awarded Nobel Prizes for their inventions, and
ammonia was used in Germany in the First World War for the manufacture of explosives. A
greater use of the Haber-Bosch process was in the manufacture of fertilizers such as urea and
ammonium nitrate. About 70% of the ammonia produced is from natural gas as feedstock
and the rest is mainly from coal. The Haber-Bosch process, involving the steam reforming of
methane to produce hydrogen is used with nitrogen taken from the air, to produce ammonia.
The typical size of urea plants is 1000 MeT per day with a capital cost of US$ 150 million.
The total production of ammonia was 130 million tones in 2000, produced in 80 countries
and 85% of which was used for nitrogen fertilizer production. The largest chemical industry
in the world is in the U.S. [19], with ammonia being the most important intermediate
chemical compound produced in 41 plants. The energy intensity for ammonia manufacture in
the U.S. is 39.3 GJ/tonne (including feedstocks HHV). The theoretical minimum for
ammonia production by steam reforming is 21.6 GJ/tonne which represents the ideal goal.
The technology is now mature, with the market dominated by five licensers-Haldor Topsøe,
M.W. Kellogg, Uhde, ICI, and Brown & Root, of which Haldor Topsøe has a 50 per cent
world market share as supplier of the technology [42].
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1.5.4.1 Haldor Topsoe Ammonia Synthesis Process
The conventional sequence of process steps are optimized by the introduction of improved
catalysts (KM high strength, versatile, stable and poison-resistant catalyst, mainly magnetite
Fe3O4 with promoters mainly oxides of calcium, aluminum and potassium, operating
temperatures 340-550 oC [21]), new equipment design (such as improved synthesis
converters), and process optimization studies. The carbon monoxide concentrations have
been minimized at the exit of the shift converters, and a low-energy carbon dioxide removal
process (such as selexol) has been used. New syn converters S-250 and S-300 are improved
versions of the previous single bed S-50 and two-bed S-200 radial flow converters. Topsoe
recommends S-300, developed in 1999, for all new plants [[21], [24].
TABLE 1.3: Haldor Topsoe Ammonia Converter Features
Type Basic Design Comments S-50 One catalyst bed Simplest and cheapest S-200 Two catalyst beds and one interbed
heat exchanger Commissioned in 1979; 130 units installed
S-250 Combination of the S-200 followed by the S-50
S-300 Three catalyst beds with two interbed heat exchangers
Higher conversion for same catalyst volume of S-250; installed first in 1991.
1.5.4.2 Kellog Brown & Roots (KBR) Advanced Ammonia Process (KAPP)
KAAP uses a traditional high-pressure heat exchange based steam reforming process
integrated with a low-pressure advanced ammonia synthesis process. The steam reforming of
hydrocarbon based on Kellogg Brown and Root Reforming Exchange System (KRES) is
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carried out which reduces energy consumption and capital cost besides reduced emissions
and enhanced reliability.
After reforming, carbon monoxide is removed from the shift converter, and carbon dioxide is
removed from the process gas using hot potassium carbonate solution, methyl diethanol
amine (MDEA) etc.
KAAP uses a high activity graphite supported ruthenium catalyst, typically three stages, after
one stage of traditional iron catalyst. This is claimed to increase the activity 10 to 20 times
enabling very high conversion at a lower pressure of 90 bar [10].
KBR is a large player in the ammonia and urea industry. It has been involved in the licensing,
design, engineering and/or construction of more than 200 ammonia plants and 62 urea
projects in the range of 600 to 3500 MTPD worldwide, representing approximately half of
current global ammonia production [23].
1.5.4.3 Krupp Uhde GmbH Ammonia Process
The Krupp Uhde Gmbh process uses the traditional reforming process followed by a
medium-pressure ammonia synthesis loop[86].
The primary reforming is carried out at a pressure of 40 bar and temperature range of 800-
850 oC. Enhanced reliability is attained by using a top-fired steam reformer with high alloy
steel tubes. Process air is added in the secondary reformer through nozzles installed in the
wall of vessel thus providing proper mixing of the air and reformer gas. This also provides
high energy efficiency in high pressure steam generation and superheating. As in other
processes, carbon monoxide is converted to carbon dioxide in HT and LT shift converters,
and the MDEA or Benfield system is used for carbon dioxide removal.
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The ammonia synthesis loop uses two radial flow ammonia converters with three catalyst
beds, containing iron catalyst, and waste heat boiler located downstream of each reactor. The
converters have small grain iron catalyst.
Since 1994, Uhde has built 15 new ammonia and 13 new urea plants with annual production
capacities of more than 8 million tonnes of ammonia and 10 million tonnes of urea with
individual capacities ranging from 600 to 3,300 mtpd of ammonia and from 1,050 to 3,500
mtpd of urea [36]. Uhde has also been awarded a contract to build a 3300 MTPD “Uhde
Dual-Pressure Process” ammonia plant for Saudi Arabian Fertilizer Company (SAFCO) in
Al Jubail, Saudi Arabia [78].
1.5.4.4 ICI-Leading Concept Ammonia (LCA) Process
In this process, ammonia synthesis takes place at low pressure of below 100 kg/cm2g
(approximately 100 bar) using ICI’s highly active cobalt promoted catalyst. This process has
an energy consumption of approximately 7.2 Gcal/ MeT (30.1 GJ/MeT) ammonia for a 450
MeT per day plant [19].
1.5.4.5 The Linde Ammonia Concept (LAC) Ammonia (LCA) Process
The LAC process consists essentially of a modern hydrogen plant and a standard nitrogen
unit with a third-party license from Casale for a high efficiency ammonia synthesis loop [34].
Ammonia Casale [16] is one of the oldest companies in the business of synthetic ammonia
production, having been founded in Switzerland in 1921. To date it has been active in the
design of over 150 ammonia synthesis reactors and in the constructionof several new plants.
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The CO shift conversion is carried out in a single stage in the tube cooled isothermal shift
converter and gas is sent to pressure swing absorption (PSA) unit wherein the process gas is
purified to 99.99 mole % hydrogen . A low temperature air separation in cold box is used to
produce pure nitrogen. BASF’s MDEA process is also eliminated in this process used for
CO2 removal.
The ammonia synthesis loop is based on Casale axial-radial three-bed converter with internal
heat exchanger giving a high conversion. The energy consumption for ammonia production
is about 29.3 GJ/ MeT [16].
Thus far, four plants based on the relatively new Linde Ammonia Concept have been
constructed with capacities of between 230 to 1,350 MTPD of ammonia.
1.6 Thermodynamic Cycles for Solar Thermal Power Plants
The two commonly used thermodynamic cycles for solar plants are the Brayton and Rankine
Cycles depending on the temperatures of the working fluid. Power towers employing PCM
salts are able to achieve very high temperatures, typically in excess of 1000 oC which transfer
heat to inert gases such as helium, and at a lower temperature, water is converted to
superheated steam. Such plants draw heavily from the experience and resources available
with high temperature gas reactors in the nuclear industry. While the thermodynamic
efficiency of such systems is high, special materials and high safety features are required for
this technology [140].
Solar power plants based on the concentrating parabolic systems, ordinarily use water as a
working fluid and are thus based on the Rankine Cycle [130].
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1.7 Literature Review The literature survey covered a wide range of areas, this section reviews the potential of solar
energy as a renewable source for a sustainable and clean energy future, Solar thermal power
and its components, thermodynamic aspects of candidate solar plants, thermal storage
materials, energy inputs and outputs from various thermal storage materials, energy recovery
industrial process and energy efficiency analyses for plant performance and design
parameters for realized Solar thermal power plants. This design data from realized Solar
thermal power plants has been used as a starting point for component and overall simulation,
as well as optimization formulations for carrying out sensitivity analyses leading to an
optimal pant design. Modeling and Simulation techniques for component and integrated plant
design are discussed in section 3.1.1 while review of optimization techniques is presented in
section 4.1.
Concentrating solar power is a method of increasing solar power density. CSP has been
theorized and contemplated by inventors for thousands of years. The first documented use of
concentrated power comes from the great Greek scientist Archimedes (287-212 B.C.) in 212
B.C. [175]. The modern solar concentration is believed to begin by the experiments of
Athanasius Kircher (1601-1680) in seventeenth century [175]. Solar concentrators then
began being used as furnaces in chemical and metallurgical experiments [161]. In eighteenth
and nineteenth centuries CSP applications were restricted to low pressure steam generation
and solar pumps etc.
CSP systems can provide energy storage fully integrated within the electricity-generating
plant [2][4][5]. Solar thermal radiation can be concentrated using parabolic mirrors in the
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form of dishes, power towers, troughs and linear Fresnel etc. in commercial CSP systems.
The efficiency of these mechanisms can be evaluated on the basis of geometric concentration
ratio. The geometric concentration ratio for parabolic troughs and linear Fresnel systems can
be up to 100 and in excess of 1000 for power towers and dishes. This thermal energy can be
used to produce steam for immediate electricity generation, or alternatively it can be stored
prior to electricity generation using sensible heat storage in solids [27][49][66], molten salts
[88], phase change materials [9][39][145][153], or thermochemical storage cycles [15].
Thermochemical energy storage for CSP is less mature than molten salt and other thermal
storage methods, but it has the potential to achieve higher storage densities and hence smaller
storage size. Reactions involving ammonia, hydroxides, carbonates, hydrides, and sulfates
are the important candidates for thermochemical energy storage [15][67]. At first,
thermochemical storage loops based on methane reforming received considerable attention
[58][115][138][141]. Methane reforming is still under research for solar enhancement of
natural gas [30] and hydrogen production [31]. A lot of research is being conducted on solar
fuel production by making use of thermochemical processes [17][38].
The concept of ammonia-based energy storage for concentrating solar power systems was
first proposed by Carden in 1974 at the Australian National University [174][177] followed
by the researchers at Colorado State University in early 1980’s [163].
Researchers at ANU [132][167] and Colorado State University [163] have concluded after
theoretical analysis and experimental results [109] that dish concentrators are the most
suitable solar receiver designs for ammonia dissociation because they provide a
circumferentially homogenous solar flux profile [136] which can facilitate thermochemical
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reactor design inferring that only simple control systems are necessary, thus the mobile
receiver can be maintained at a light weight, and solar transients are easy to handle
[132][137]. Feasilbility of parabolic trough systems have also been investigated for use with
CSP employing ammonia based energy storage systems [97].
Prototype solar ammonia receiver/reactors, Mark I and Mark II were tested in 1994 and 1998
respectively both employing a 200-mm long cavity type reactor mounted on a 20-m2 faceted
paraboloidal dish. Haldor-Topsøe DNK-2R iron-cobalt catalyst was used in the annular
catalyst beds [108]. These reactors were rated for 1.0– 2.2-kWchem conversion. Recent work
is being conducted on paraboloibal dishes of area 400-m2, 489-m2 and newly constructed
500-m2 for a base load plant size of upto 10 MWe [11].
For solar collector/receiver design improvements, investigations into convection losses from
cavity receivers have been undertaken [12][81] as these improvements can amount to solar-
to-chemical efficiency gains of up to 7% absolute [106].
The kinetic mechanisms for the synthesis and decomposition of ammonia have been
described by various authors for ironbased catalysts [120][186][189][195] and for ruthenium-
based catalysts [111][121][126].
Comprehensive studies for solar energy heat [104],[106]] recovery have been carried out on
an experimental 1-kWchem. synthesis reactor by Kreetz and Lovegrove [106] in a laboratory-
scale high-pressure closed-loop system with a feed-gas mass flow rate of 0.3 g s-1 at
pressures ranging from 9.3 to 19 MPa. With external pre-heating of the feed gas, average
external wall temperature varying between 250-480°C and peak internal reactor temperatures
varying between 253-534°C, the maximum reaction was reported by Kreetz and Lovegrove
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[106] to have been achieved at approximately 450°C. In their ‘optimal’ system, a net heat
recovery rate of 391 W was reported. The study by Kreetz and Lovegrove [106] was extended
to a 10 kW system with an ammonia synthesis tubular reactor at a pressure of 20 MPa and a
flow rate of 0.9 g s-1 [79]. The larger system, with a controlled linear temperature profile in
the reactor wall, and the gas inlet temperature kept to 50 °C lower than the wall temperature
at the inlet, resulted in a maximum thermal output achieved at an average wall temperature of
475°C produced with an inlet temperature of 500 °C and a slope of -50 °C m-1. Such studies
have attempted to achieve optimal heat recovery by varying the inlet temperature arbitrarily
instead of attaining the optimal temperature suggested by theoretical models, such as
variational methods.
1.8 Thesis Motivation
Thermal Storage plants using ammonia as storage medium can take advantage of the well-
understood and extensively deployed ammonia dissociation and synthesis technologies. Their
efficiency, however, will depend on the optimization of the process parameters typical of the
system pressure and temperatures in the dissociation and synthesis reactors taken together
with those at the solar receiver.
A lot of research has been carried out on solar collector design and dissociation efficiencies
of more than 90% have been practically achieved using cavity type dissociation reactors in
conjunction with paraboloidal dish type solar receivers[105][106]. The motivation of plant
optimization is to maximize the efficiency of the plant by maximizing the heat recovery from
the most critical process in the plant: the synthesis reactor. This research is of great value to
industry as well because the same optimization techniques can be used for improving
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ammonia production rates at pressures lower than the industry standard pressures, hence
cutting the costs.
1.9 Objectives
The use of liquid ammonia, as a thermo-chemical energy storage medium, for endothermic
dissociation by solar energy during insolence and subsequent energy recovery by exothermic
synthesis is considered to be a strong candidate for the design of a base-load solar thermal
power plant.
The technology of ammonia production is well established as is the modeling and simulation
of ammonia synthesis. However, optimization of the process is an on-going challenge as
technological innovations enable better designs resulting in improved efficiency. As part of
this optimization challenge, this thesis considers the possible improvement in the recovery of
exothermic thermal energy by optimization of the ammonia synthesis process. While
ammonia production has remained almost the same for decades, the energy consumption has
reduced as technology improvements have been incorporated especially for the fertilizer
industry where over 90% of the energy utilization is for ammonia synthesis [76].
The objective of the study will be achieved by:
Parametric Sensitivity studies leading to an optimized design of a TSP
i. Numerical Simulation of Conservation Equations,
ii. Optimize physical dimensions of Synthesis Reactor,
iii. Optimal distribution of Catalyst (Optimal Control analysis),
iv. Overall Thermal Energy Recovery Analysis.
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1.10 Summary of Following Chapters The necessary background information is given in Chapter 1. Chapter 2 describes the thermal
storage plant features such as process design, operational parameters and process flow
diagram etc. Chapter 3 deals with the modeling and simulation of the components of thermal
storage plant while optimization of thermal storage plant has been done in chapter four both
by variational calculus and process engineering codes. The fifth chapter presents the optimal
TSP model, designed in the light of sensitivity and parmetric analyses in chapter four.
Conclusions and future recommendations are presented in Chapter 6.
25
2 DESCRIPTION OF THE THERMAL STORAGE
PLANT
2.1 Plant Features A thermal storage plant may be used as a baseload plant, when it operates on a continuous
basis just like a coal-fired, nuclear or hydroelectric power plant, or as a traditional PV
intermittent solar plant. The baseload operation is only possible if the plant has an integrated
thermal storage feature.
The major components of a baseload plant are the receiver system, a storage system, an
energy recovery system, a power conversion unit, and associated plant systems such as
compressors, pumps and heat exchangers.
The objective of the Thermal Storage Plant (TSP) considered here is to maximize the overall
efficiency of the plant, which is essentially the optimization of the ammonia synthesis
process.
2.1.1 Process Design
This section considers some basic aspects of the overall plant design with the objective of
getting orders of magnitude. Table 2.1 shows such overall conditions for a conceptual MS-
Excel calculation for a baseload plant of 10 MWe. It is assumed that a solar insolation of 1
kW/m2 is available for 8 hours in a day. With 400 parabolic dishes, each of area 400 m2 of
the type available to the ANU group [101][105], the thermal power intercepted by the plant is
26
4.608 TJ in a day. These assumptions are optimistic even for the high solar insolence of
about 20 MJ/m2 for Pakistan [150].
TABLE 2.1: Overall Plant Design for a 10 MW(e) Baseload Plant
BASIC DATA Dissociation Energy kJ/mol 66 Synthesis Energy kJ/mol 46.6 Power Density Watts / m^2 1000 Insolation Hours per Day Hr 8 Dish Area m^2 400 No. of Dishes 400 extent of dissociation reaction 0.9 Electrical Power Reqd (24hrs) MW(e) 10 Synthesis Conversion 0.2 Rankine Cycle Effciency 0.4 POWER INPUT
Thermal Power Available/day kW-hr/m^2 per day 8
Thermal Power Available/day MJ/m^2 per day 28.8
ThPower/day on one dish MJ per dish per day 11520
ThPower/day on all dishes MJ per day 4608000
Flow of NH3 per dish mol per dish during insolation 193939.39
Flow of NH3 per dish kg NH3 per dish during insolation 3296.97
Flow of NH3 MTD NH3 during insolation 1318.79
Flow rate of NH3 kg/s NH3 45.79 Flow rate of NH3 per dish kg/s NH3 0.1145 Electrical Energy Needed MJ(e) per day 288000 Thermal Energy Needed MJ(th) per day 720000 POWER OUTPUT Recoverd Synthesis Energy MJ per day 921600 Converted Synthesis Energy MJ per day 368640 Overall Efficiency % 8
27
Key design parameters are the thermal power intercepted by the plant during insolence (4.6
TJ), the thermal energy needed (2.1 TJ) for a baseload of 10 MW(e), the recovered synthesis
energy (0.922 TJ) and the final converted energy (0.368 TJ). In this scenario, three
efficiencies are assumed viz (i) the extent of dissociation (0.9) [47], (ii) the synthesis
conversion (0.2), and (iii) the Rankine efficiency (0.4) [[15],[79],[130].
The purpose of the present research is to estimate the best possible synthesis conversion, by
optimizing the catalyst distribution, to investigate the feasibility of such baseload operation.
2.1.2 Opertational Parameters
The operational parameters of TSP have to be chosen carefully as the use of a reversible
reaction to store energy is governed by the dependency of the thermodynamic equilibrium
composition on temperature and pressure. Conceptually, if a sample of ammonia were heated
slowly (quasi-statically), it would begin to decompose at temperatures of several hundred
degrees, around 700 K at 200 atmospheres (20MPa). Complete dissociation would only be
approached asymptotically at very high temperatures. The amount of energy absorbed at each
step would be proportional to the fraction of ammonia split. Reversing the process and
withdrawing heat would see ammonia resynthesize, with heat released progressively [196].
To implement this on an industrial scale, the limitations of reaction kinetics must also be
taken into account. Reaction rates are zero at equilibrium by definition; they increase by the
degree of departure from equilibrium (and in the direction needed to return the system to
equilibrium) and also increase rapidly with temperature in proportion to the well-known
28
Arrhenius factor. Thus, a real system absorbs heat at temperatures higher than the
equilibrium curves suggest and then releases it at lower temperatures.
The input temperature for the power cycle is an extremely important issue for all thermal-
based energy storage systems, not just thermochemical ones. Electric power generation via a
thermal cycle is limited by the second law of thermodynamics – lower temperature thermal
inputs reduce the efficiency of power generation. Thus, in designing and examining thermal
energy storage systems, it is necessary to consider both “thermal efficiencies” (energy
out/energy in) and “second law efficiencies” (potential for work out/potential for work in).
A TSP will have operational parameters, pressures, temperatures and flow rates, similar to
those in the ammonia units of urea fertilizer plants in the chemical process industry. These
require pressures in the range of 130-250 bar and temperatures in the range 250-600 oC for
flow rates typically of the order of 50 kg s-1 for a 1500 MTD ammonia plant. Such high
pressures require compression which is expensive in terms of equipment cost as well as
energy utilization
2.2 Overall Plant Layout and Description The schematic diagram of TSP is shown in figure 2.1[2]. In this closed loop system, a fixed
inventory of ammonia passes alternately between energy-storing (solar dissociation) and
energy-releasing (synthesis) reactors, both of which contain a catalyst bed. Coupled with a
Rankine power cycle, the energy-releasing reaction could be used to produce baseload power
29
for the grid. At 20 MPa and 300 K, the enthalpy of reaction is 66.8 kJ/mol, equivalent to 1.09
kWh/kg of ammonia, or 2.43 MJ/L, with the corresponding density of 0.6195 kg/L [165].
Figure 2.1: Thermal Storage Plant Schematic 2.2.1 Ammonia Dissociation Having the advantage of solar concentration of 3000 suns [105], a mirrored paraboloidal dish
focuses solar radiation onto a dissociation reactor (cavity type) through which anhydrous
ammonia is pumped. The reactor contains an annular catalyst bed which facilitates the
dissociation of ammonia at requisite temperature and pressure into gaseous nitrogen and
hydrogen termed “syngas”. The fact that the ammonia dissociation reaction has no possible
side reactions makes solar dissociation reactors easy to control and implement [2][160].
Typically, 400 such reactors mounted on paraboloidal dishes, of area 400 m2 each, are used
in an array patteren to feed the ammonia synthesis reactor.
30
Figure 2.2: Array of 400 m2 Paraboloidal Solar Collectors [3]
2.2.2 Ammonia Synthesis A reactor is used for energy recovery from the exothermic synthesis reaction in which syngas
is synthesized to produce ammonia in the presence of an annular catalyst bed. Since
ammonia synthesis is a developed technology for more than 100 years, synthesis reactors
used for TSP are based on standard and proprietary industrial technologies from companies
that include Haldor-Topsoe, Kellogg Brown & Root (KBR), AkzoNobel (formerly Imperial
Chemical Industries (ICI)), and Cassal [16],[21],[23],[24].
For the reference TSP in this work, KBR Advanced Ammonia Process (KAAP™) synthesis
convertor is chosen. In the KBR Advanced Ammonia Process (KAAP™)[23], the synthesis
converter uses a combination of catalysts to maximize the conversion and heat recovery, such
as one stage of traditional magnetite catalyst, followed by three stages of a proprietary
KAAP™ catalyst consisting of ruthenium on a stable, high-surface-area graphite carbon base
(KBR). This KAAP™ catalyst has an intrinsic activity ten to twenty times higher than
31
conventional magnetite catalyst and is used to lower the synthesis operating pressure to 90
bar which is one-half to two-thirds the operating pressure of a conventional magnetite
ammonia synthesis loop and hence cutting plant costs.
2.2.3 Syn Gas and Ammonia Storage The closed-loop TSP operates at a pressure (150 bar) above ambient temperature saturation
pressure of ammonia and the ammonia fraction in storage is present largely as a liquid which
causes automatic phase separation of ammonia. Thus, a common storage tank can be used to
store both syngas and liquid ammonia.
2.2.4 Heat Exchangers and Transport Piping
The heat exchangers shown in Fig. 2.1 serve to transfer heat from exiting reaction products to
the cold incoming reactants. In this way, the transport piping and energy storage volume are
all operated at close to ambient temperature, reducing thermal losses from the system, as well
as eliminating the need for costly specialized equipment.
2.2.5 Compressors and Pumps
Compressors are used for the pressure management of high pressure storage vessel and
synthesis loop. In the dissociation part of the system, a liquid ammonia feed pump is
incorporated with each paraboloidal dish. These pumps are used to control the actual process
conditions within the ammonia dissociation reactor. Mass flow control aims for 80% of the
ammonia feed being dissociated on average.
32
2.3 Thermal Storage Plant Process Flow Diagram Figure 2.3 presents a simplified process flow diagram of thermal storage plant. The input
stream (DIS-IN) to the solar driven dissociation reactor (DISRCTR), consisting of liquid
ammonia, is pumped from the high pressure storage tank (S-TANK).
The stream DIS-IN is pre-heated by passing it through the counter flow heat exchanger (CF-
HX) in order to increase its temperature. The output syngas stream (DIS-OUT), consisting of
nitrogen, hydrogen and small amounts of other gases, looses heat in heat exchanger (CF-HX)
and is fed into storage tank (S-TANK). The feed-stream (FEED1) from storage tank is
compressed to the pressure required for synthesis, 150 bar. Due to the unfavourable reaction
equilibrium, only part of the Syngas is converted to ammonia on a single pass through the
Synthesis Reactor (SYNRCTR). Since the unconverted Syngas is valuable, the majority of it
is recycled back to the SYNRCTR. A Mixer is used to combine the Recycle Stream (FEED2)
and fresh stream FEED1.
Figure 2.3: TSP Process Flow Diagram
33
This mixed stream (MIX-OUT), heated in SRIN-HX to a temperature of 370 oC and is fed
into the catalyst-containing synthesis reactor (SYNRCTR) where the synthesis reaction, in
the forward direction, converts nitrogen and hydrogen into ammonia and hence producing
energy.
The effluent stream passes through the recovery heat exchanger (SROUT-HX) into the
Knock-Out drum FLASH, where the liquid ammonia is sent back to the storage tank through
stream PRODNH3 and stream VAPOR is carried to the purging system. The VAPOR stream
from Flash tank (FLASHT) contain traces of undesirable gasses such as Argon, Carbon
Monoxide and Carbon Dioxide. Argon has high partial pressure while Carbon Monoxide and
Carbon Dioxide are poisons for the Catalyst. Some of the cycle gas must be purged from the
Synthesis Loop. Otherwise, the argon that enters the loop in the Syngas has no way to leave
and will build up in concentration. This will reduce the rate of the ammonia synthesis
reaction to an unacceptable level. To prevent this from happening, a small amount of the
cycle gas must be purged, the amount being determined by the amount of argon in the feed
and its acceptable level in the Synthesis Converter feed (generally about 10 mol %). A
splitter is used to divide the VAPOR stream into PURGE and RECYCLE streams.
Another re-cycle compressor (RCOMP) is required at this stage to restore the pressure to the
required level till the stream (FEED2) is mixed with the feed stream (FEED1) and enters as
stream MIXER-OUT.
34
3 MODELLING & SIMULATION OF THERMAL
STORAGE PLANT
3.1 Mathematical Modelling 3.1.1 Review of Mathematical Models of TSP
The synthesis of ammonia can be modeled using the laws of conservation of mass,
momentum and energy for non-isothermal multi-component systems undergoing chemical
reactions and mass transfer [85]. In the case of unsteady flow the governing equations are:
Mass:
0222021 ωρωωω +⟩⟨Σ=+Σ−Σ= Svmdt
dtot
3.1
Mass of Species i:
Nirmdt
dtotiiiitoti ,......3,2,1,021, =++Σ−Σ= ωωω
3.2
Momentum:
sftottot FFgmSpv
vSp
v
v
dt
d→−+++
⟩⟨
⟩⟨Σ−+⟩⟨
⟩⟨Σ=Ρ 022222
22
11111
21 )()( ωωωω
3.3
(Total) energy:
QQwHghv
vHgh
v
vUK
dt
dtottottot −++++
⟩⟨
⟩⟨Σ−++⟩⟨
⟩⟨Σ=+Φ+∧∧
02222
32
1111
31 )
21
()21
()( ωω
3.4
35
In terms of molar quantities, the continuity equation is expressed in terms of the molar
concentration c, and the mole fractions yi as
∑=
=−+⋅∇−=
∇⋅+∂∂ N
iiiii NiRyRJyvt
yc
1
** ,.....3,2,1)()(β
β 3.5
TABLE 3.1: Equations of change of Multi-component Mixtures in terms of the
Molecular Fluxes Total mass:
)( vDt
D ⋅∇−= ρρ
Species mass: (i=1,2,3,…..N) ii
i rjDt
D +⋅∇−= )(ωρ
Momentum: g
Dt
Dv ρτρρ +⋅∇−−∇= ][
Energy: )(])[()()()
21
( 2 gvvpvqvUDt
D ⋅−⋅⋅∇−⋅∇−⋅∇−=+∧
ρτρ
The above have been expressed by Dashti [64] as
( )
×−−×−−=∇−=
=∆−+
=
pp
NHrp
oN
NH
d
v
d
vv
dx
dP
RHdx
dTvC
AF
R
dx
dz
2
323
22 )1(
75.11
150
0)(
/2
3
2
3
ρψ
ψµψ
ψµ
ηρ
η
3.6
A simpler analysis ignores the pressure drop in flow reducing to the conservation equations
for mass and energy with reaction kinetics, used by Yuguo [152] and Dashti [64]
AF
R
dx
dzo
N
NH
/23
η=
3.7
0)(3
=∆−+ NHrp RHdx
dTvC ηρ
3.8
36
For the reaction kinetics, the Temkin-Pyzhev [64],[152] form for the synthesis reaction rate
as a function of the pressure, temperature, and activities is used
−=≡
5.1
5.12
2
3
3
2
232
H
NH
NH
HNaNHA a
a
a
aaKkRR
3.9
where the activities are defined as Pya iii φ= . The individual activities are:
and the reaction constant is given by the Arrhenius rate form [93] as
−=RT
EXk exp10849.8 14
where E=170.56 kJ/mol and respective activities (3
,, NHHN aaa ) and fugacity coefficients are
defined by equation 3.10.
The governing conservation, non-linear differential, equations are numerically solved using
the Runge-Kutta fourth order method in MATLAB™.
The three-bed KBR reactor data used is [10],[23] : Pressure=15 MPa, Inlet Temperature =
643 K, mass flow rate = 183600 kg h-1, mole fractions: 6567006.02
=Hy , 2363680.02
=Ny ,
0269300.03
=NHy , 0202874.0=Ary , 0597140.04
=CHy . Figure 3.5 shows the homogeneous
reactor with the TP-A model. The temperature increases from 643 K to 780 K with a
maximum ammonia mole fraction of 0.1162, corresponding to a molar flow increasing from
486 kmol h-1 to 1930 kmol h-1. It can be seen that the reaction is almost complete at 1.5 m
from inlet.
45
Figure 3.5 : 3-Bed Homogeneous Reactor with TP-A Kinetics
3.1.2.2 TEM Model using Partial Pressure based Temkin-Pyzhev Form (TP-B):
For the reaction kinetics, the Partial Pressure (Power Law) based Temkin-Pyzhev [142] (TP-
B) form is used for the synthesis reaction rate:
αα −
⋅−
⋅=
1
3
2
22
3
1
2
3
3
2
2
H
NH
NH
HNA p
pk
p
ppkR
3.23
for which the rate constants for synthesis and decomposition are
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5600
650
700
750
800
Distance (m)
Tem
pera
ture
(K)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.2
0.4
0.6
0.8
Distance (m)
Mol
e F
ract
ion
H2
N2
NH3
46
−=RT
kk o
20800exp11 and
−=RT
kk o
47400exp22 , 4
1 1078954.1 ×=ok kmol/m3-atm1.5
catalyst bed-hr, and 162 105714.2 ×=ok kmol-atm0.5/m3 catalyst bed-hr.
The parameter α in the kinetic expressions depends on the catalyst characteristics as well as
the range of operating variables [141] and although Temkin and Pyzhev [195] assigned the
value 0.5 in the power-law model for iron catalysts, Dyson and Simon [183] showed that both
values 0.5 and 0.75 satisfied experimental data. Another point that has been observed for this
expression is that the decomposition rate coefficient 2k , assumed constant, decreases with
pressure [194]. However different values of α can be used for the same catalyst. A limitation
of this expression, clearly, is that it is not valid for very low ammonia composition due to the
divergence of the first term. The value α=0.6 has been used in this work since Dashti et al
[64] have validated the results with industrial data, based on the Kellogg Brown and Root™
horizontal ammonia synthesis reactor.
The governing conservation, non-linear differential, equations are again numerically solved
using the Runge-Kutta fourth order method in MATLAB™. The three-bed KBR reactor data
is used to simulate the behavior of the reactor shown in figure 3.6.
47
Figure 3.6 : 3-Bed Homogeneous Reactor with TP-B Kinetics
With the TP-B model, Figure 3.6 shows a temperature increases from 643 K at inlet to 788 K
with a maximum ammonia mole fraction of 0.1221, and a mole flow increase from 486 kmol
h-1 to 2018 kmol h-1. The error of the power-law model, relative to the activity-based model,
is thus ~6% in ∆T and ~5% in the ammonia molar flow rate. A better model has been found
to be the activity based Temkin-Pyzhev model (TP-A) which does not have a singularity for
zero ammonia composition, which can be the case for a syngas inlet without recycle, and for
which 2k is constant.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5600
650
700
750
800
Distance (m)
Tem
pera
ture
(K)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.2
0.4
0.6
0.8
Distance (m)
Mol
e F
ract
ion
H2
N2
NH3
48
3.2 Modeling Unit Operations
The TSP model provides a useful description of the process. The simulations have been
developed using Aspen Plus™ and HYSYS™ modules of the AspenTech™ Process
Engineering Simulation Suit. These simulations make use of many of the capabilities of
AspenTech™ Process Engineering Simulation Suit including unit operation models, physical
property methods, models and data, and flowsheeting capabilities like convergence design
specs etc. The model provides rigorous mass and energy balance information for dissociation
process, ammonia production process, Flash tank and other components in storage plant [7].
This model can be used to support the conceptual process design. The TSP model is meant to
be used as a guide for process optimization for maximum energy recovery. It can also be
used as a starting point for more sophisticated models.
Both the Dissociation and Synthesis reactors are considered as fixed bed catalytic reactors.
In AspenTech™ Process Engineering Simulation Suit, the PFR is augmented by including
axial and radial dispersions, for both mass and heat transport [7] resulting in coupled partial
differential equations requiring advanced numerical techniques and more computational
effort.
3.2.1 Dissociation Reactor The dissociation reactor, considered as a fixed bed catalytic reactor, is modeled using a Plug
Flow Reactor (PFR) with a specified uniform external heat flux profile in Aspen Plus™ as
49
shown in figure 3.7. If the length of Plug Flow Reactor is less than its diameter, the axial
dispersion of mass and heat are not significant [7],[148].
Figure 3.7 : PFR Dissociation Reactor in Aspen Plus™
The dissociation is carried out in a temperature range of 520-580 oC and a pressure of 150
bar using Ni-Pt catalyst [128]. The data presented in table 3.3 is used as input to stream
DIS-IN.
TABLE 3.3: Input Data for Dissociation Reactor
Parameter Value Process Pressure P=15MPa (150 bar) Inlet Temperature T=793 K (520 oC) Mass Flow Rate m& =0.125 kgs-1 Reactor Length L=1m Reactor Diameter D=1.5m
The Temkin-Pyzhev reaction rate is specified in Aspen Plus™ through the stoichiometric
coefficients for ammonia (-1), nitrogen (0.5), and hydrogen (1.5) and with basis specified to
be partial pressures, for a liquid-vapor reaction phase. The reaction is specified as a Power-
law class for a kinetic expression of the form:
33exp NHoNH p
RT
Ekr
−=
50
where 3NHr is the reaction rate for decomposition of ammonia, ok is the frequency factor and
its value is 1.33x108 kmol m-3 s-1 Pa-1 while activation energy E equals 190000 kJ kmol-1 [6].
First, the governing equations are numerically solved to obtain the temperature and
concentration profiles shown in Figure 4.4.
Figure 4.4 : Temperature & Concentration Profiles along Converter Length
67
Figure 4.4 uses the same scale for Temperature and Concentration, it is not clear in reference
65 , whether these values of temperature and concentration have been normalized to show
them on the same scale or not.
The numerical solution is followed by an optimization exercise in which an objective
function ),,,(2 gfN TTNxf is defined along with the three governing equations, taken as
constraints. Thus, the problem has one variable (x; the reactor length) one degree of freedom
)1( =fN and, being underdetermined, can be solved for optimality. The GA search is carried
out as shown in Figure 4.5.
Figure 4.5 : GA Search Algorithm The optimal solution found for the exit conditions shown in Table 4.1.
TABLE 4.1: Optimal solution for the exit conditions
68
The optimization thus concludes that a reactor with initial guesses of Nitrogen concentration,
Mole fraction, feed gas and reacting gas temperatures, reactor length and cost result in an
optimal solution with values given in table 4.1.
Figure 4.6 : Four-Bed Synthesis Reactor
Sadeghi and Kavianiboroujeni [54] have used the Genetic Algorithm for a 1-D and 2-D
optimization of a Kellog-type ammonia plant, located at Khorasan (Iran). The axial reactor
(Figure 4.6) has four promoted-Fe catalytic fixed beds with a heat exchanger at the top.
Syngas flows vertically upwards in the spaces between the two walls of the reactor, where it
is pre-heated, then turns down through the beds and from the bottom fourth bed again turns
upwards, exiting from the top of the reactor. The independent parameters investigated are the
quench flow and quench temperature. Between the beds, the hot syngas is mixed with quench
streams (shown in three streams between the beds) to control the temperature.
69
Figure 4.7 : Effect of Quench gas on conversion efficiency The purpose of injecting the quench streams is, clearly, to increase the ammonia production
from the reactor; and since the forward synthesis chemical reaction is favoured by high
pressure and low temperature, the challenge is to reduce the temperature at every bed exit.
The ammonia and nitrogen conversion obtained by Sadeghi and Kavianiboroujeni [54] by a
numerical solution of the mass and energy balance equations is shown in the Figure 4.7. It
can be seen that most of the ammonia conversion takes place in the first bed even though it is
the shortest. The effect of the quench gas is to reduce the ammonia conversion after every
bed exit but this picks up as flow proceeds.
The paper uses GA for obtaining optimal temperature distribution, in this nonlinear
optimization problem, resulting from a given quench flow, and subsequently optimal quench
flow given quench temperature. In the optimization problem, the objective function is the
70
ammonia outlet flow-rate, while the constraints are (i) KT 800< , in the reactor for avoiding
hotspots, (ii) an ascending nitrogen conversion during optimal flow: xxx ZZ ∆+< || , and (iii)
for the syngas: outin TT < .
Figure 4.8 : GA Algorithm for obtaining optimal temperature distribution
The flow-chart, Figure 4.8, for this optimization is reproduced from the paper [54] and their
results, in Figure 4.9, give maximum ammonia conversion at a quench temperature of 650 K
and a maximum conversion flow-rate of 47%
71
Figure 4.9 : Optimal and Normal Ammonia Production Rates The important changes between normal and optimal operations for nitrogen conversion and
reaction rate are shown in Figure 4.10.
Figure 4.10 : Optimal and Normal Nitrogen Conversion and Reaction rates GA used for obtaining optimal temperature distribution has increased the ammonia
production of the Khorasan plant by 3.3% (8,470 tons per year).
When the reactor is isothermal, different catalysts can be loaded to enhance productivity and
when it is non-isothermal i.e. it has temperature gradients, then the catalyst may be non-
72
uniformly loaded or different catalysts may be used for different temperature regions, to
enhance productivity. Finding the optimal (spatial) distribution of catalyst is crucial to
optimizing the performance. Numerical search can be carried out by dividing the reactor in
zones and assuming uniform values of catalyst material in each zone; this will mostly result
in a sub-optimal solution.
4.2 Optimal Analysis using Variational Calculus
Variational methods have also been used to find optimal configurations for process variables
in a synthesis convertor. These methods originate from the works of Leibniz (1646-1716) and
Newton (1643-1727) credited for inventing and formalizing Calculus; followed by
“Variational Calculus” attributed to Leonhard Euler (1707-1783) through his published work
of 1733. Among the several contributors to variational calculus were Lagrange (1736-1813),
Legendre (1752-1833), Gauss (1777-1855), Cauchy (1789-1857), and Poisson (1781-1840).
The field of Optimal Control [180] is an area of optimization in which the “best possible”
strategy is chosen using the calculus of variations. While calculus can be used for
optimization of a function of variables, calculus of variations is used to obtain the extremum,
or stationary condition, of a functional (function of a function) by finding the function which
extremizes the functional. The first variational calculus optimal problem was the
Brachistochrone (shortest time) Problem solved by Bernoulli in 1696 [185]. The formulations
used are by Lev Semenovich Pontryagin (1908-1988), who developed the Maximum
Principle, and the terminology of “Bang-Bang control” to steer a system with maximum or
minimum control parameters, and of Bellman (1920-1984) who extended works of Hamilton
73
(1805-1865) and Jacobi (1804-1851) to the now well-known Hamilton-Jacobi-Bellman
(HJB) equations in Dynamic Programming.
Variational calculus [181],[182],[185] is used in areas that include optimal control, particle
transport, mechanics, optics and chemical plant design [158]. There is a vast range of
problems that determine complexity, such as whether the functional involves one or several
functions, derivatives of functions, and one or more than one independent variable. Another
class of variational calculus problems involves constrained problems with algebraic, integral
or differential equation constraints.
The optimality conditions for Pontryagin’s Maximum Priciple (PMP) can be derived from
the first principle of conservation of matter. Consider the reversible Ammonia synthesis
process
322 23 NHHN ⇔+
The mass balance equation for this reaction can be written in dimensionless form as:
],,,[3 aNHHN
N Kyyyfxd
dy =′
4.1
Where Hy ,3NHy and Ny represent the mole fractions of hydrogen, ammonia and nitrogen
respectively while x′ is the normalized distance along catalyst bed (m).
Mole fractions of hydrogen (Hy ) and ammonia (3NHy ) are related to nitrogen mole fraction
( Ny ) as:
)(233 N
oN
oNHNH yyyy −+=
4.2
74
)(3 NoN
oHH yyyy −−=
4.3
Where oNHy
3, o
Ny and oHy are initial mole fractions of ammonia, nitrogen and hydrogen
respectively.
In equation 4.2 and 4.3, the term NNoN zyy =− )( represents the converted moles of nitrogen
and fractional conversion of nitrogen can be presented as:
oN
NoN
N y
yyz
−=
4.4
So equations 4.2 and 4.3 in terms of fractional conversion of nitrogen are
NoN
oNHNH zyyy 2
33+=
4.5
NoN
oHH zyyy 3−=
4.6
Therefore mole fractions of hydrogen and ammonia can be removed from the reactor model
equation and making it only a function of Ny
))(),(())(,( xxyfKyfxd
dyNaN
N ′′≡−=′
θθ
4.7
Where ),( θNyf is the rate of reaction equation in terms of nitrogen mole fraction Ny and
temperature θ at any point along the length of reactor such that
at )1,0(;,0 ∈′== xyyt oNN
75
)(x′θ is the control variable for which the optimal variation along the length of the reactor is
sought, that maximizes the exit conversion.
Equation 4.4 can be written as:
)1( NoNN
oN
oNNN zyyyyzy −=⇒−=−
4.8
Differentiating Equation 4.8 w.r.t x′ yields
),(1 θN
NoN
NNoN
N yGxd
dy
yxd
dz
xd
dzy
xd
dy −=′
−=′
⇒
′−=
′ 4.9
The objective is to maximize the nitrogen conversion xd
dzN
′, so we can write
∫∫ ′−=′′
−=1
0
1
0
),(1
xdyGxdxd
dy
yM N
NoN
θ
4.10
Now if we consider that the optimal temperature profile that gives the maximum conversion
( M ) is )(x′θ and consider an infinitesimal variation in )(x′θ to make it δθθ + then )(xyN ′
will change to NN yy δ+ and M to MM δ+ . Thus,
∫ ′∂∂+
∂∂+−=+
1
0
]),([ xdG
yy
GyGMM N
NN δθ
θδθδ
4.11
and since, ∫ ′−=1
0
),( xdyGM N θ
thus,
∫ ′∂∂+
∂∂−=
1
0
] xdG
yy
GM N
N
δθθ
δδ
4.12
Comparing equation 4.7 and 4.9 yields
76
))(),(( xxyfxd
dzy
xd
dyN
NoN
N ′′=′
−=′
θ
4.13
Consider the change in f
δθθ
δδ∂∂+
∂∂= f
yy
ff N
N 4.14
δθθ
δδδ∂∂+
∂∂=
′=
′−⇒
fy
y
f
xd
dy
xd
dzy N
N
NNoN
δθθ
δδ∂∂+
∂∂=
′⇒
fy
y
f
xd
yd N
N
N
4.15
Multiplying equation 4.15 by the Lagrange Multiplier (sensitivity coefficient/ adjoint
variable), )(x′λ integrating from 0=′x to 1=′x and adding the result to equation 4.12 gives:
∫ ′
∂∂−
∂∂−
∂∂+
∂∂+
′=
1
0
xdG
yy
Gfy
y
f
xd
ydM N
NN
N
N δθθ
δδθθ
λδλδλδ
4.16
Rearranging equation 4.16 yields
∫∫ ′′
+′
∂∂−
∂∂−
∂∂+
∂∂=
1
0
1
0
xdyxd
dxd
Gy
y
Gfy
y
fM NN
NN
N
δλδθθ
δδθθ
λδλδ
4.17
The last term on the right hand side of equation 4.17 is integrated by parts to give:
∫∫ ′′
−−=′′
1
0
1
0
)0().0()1().1()( xdxd
dyyyxdy
xd
dNNNN
λδλδλδδλ
4.18
If we consider the feed concentration to have a fixed value, then, 0)0( =Nyδ and we impose
77
the boundary condition on the Lagrange multiplier as 0)1( =λ and define the Hamiltonian (
H ) of the system as,
GfH −= .λ
4.19
Then equation 4.16 can be written as,
∫∫ ′+′∂
′−
∂∂=
1
0
1
0
xdH
xdyxd
d
y
HM N
N
δθδθδλδ
4.20
For )(x′θ to be the optimal temperature profile, we must have, 0=Mδ .Thus the optimality
conditions are:
0=′
−∂∂
xd
d
y
H
N
λ and 0=∂
δθH
for all values of x′ 4.21
The adjoint equation is therefore:
Ny
H
xd
d
∂∂=
′λ
and 0)1( =λ 4.22
and the optimality condition according to Pontryagin’s maximum principle is:
0=∂δθH
4.23
Which gives the global maxima for the objective function [155],[180]
From the optimality condition (4.23), it can be shown that the problem reduces simply to that
of finding the temperature profile )(x′θ that maximizes the net rate of reaction at each point
along the length of the reactor. Since N
Ny
yfG ),(θ−= , the Hamiltonian can be written in
terms of ),( Nyf θ as follows:
78
xd
dzf
xd
dy
yff
yfGfH NN
oN
oN ′
+=′
−=−=−= .1
.1
.. λλλλ
Or
fxd
dzH N .λ+
′=
4.24
4.3 Parametric Sensitivity Analysis This section considers the optimal design of TSP by calculating the process variable
sensitivities for different components.
Sensitivity analysis is an optimization tool for determining how a process reacts to varying
key operating and design variables. It can be used to vary one or more flowsheet variables
and study the effect of that variation on other flowsheet variables. It is a valuable tool for
performing “what if” studies. Sensitivity analysis can be used to verify if the solution to a
design specification lies within the range of the manipulated variable [55].
4.3.1 Effect of Temperature on Dissociation
Objective: Minimize the molar composition of Ammonia in stream DIS-OUT
Manipulated Variable: Process Temperature
The results of Temperature Sensitivity of dissociation reaction at a pressure of 150 bar are
shown in figure 4.11. The favorable range of values for process temperature are from 450-
850 oC after which catalyst burns out and there is no conversion of ammonia.
79
Figure 4.11 : Effect of Temperature on Dissociation
4.3.2 Effect of Flow Rate on Dissociation
Objective: Minimize the molar composition of Ammonia in stream DIS-OUT
Manipulated Variable: Mass flow rate of ammonia in stream DIS-IN
Figure 4.12 : Effect of Flow Rate on Dissociation
The results of Flow rate Sensitivity of dissociation reaction at a pressure of 150 bar and
temperature of 520 oC are shown in figure 4.12. If the mass flow rate of ammonia in stream
80
DIS-IN increases 550 kg/hr, conversion process is not complete and mole fraction of
ammonia in stream DIS-OUT increases.
4.3.3 Effect of Pressure on Synthesis
Objective: Maximize the molar composition of Ammonia in stream SYN-OUT
Manipulated Variable: Process Pressure
Figure 4.13 : Effect of Pressure on Synthesis
The results of Pressure Sensitivity of Synthesis reaction at a temperature of 370 oC are
shown in figure 4.13. There exist nearly a direct proportionality in between increase in
pressure and mole fraction of ammonia at reactor exit from 100 bar to 500 bar. The limiting
case are the pressures below 100 bar, where ammonia production decreases.
4.3.4 Effect of Temperature on Synthesis
Objective: Maximize the molar composition of Ammonia in stream SYN-OUT.
Manipulated Variable: Process Temperature
81
Figure 4.14 : Effect of Temperature on Synthesis The results of Temperature Sensitivity of Synthesis reaction at a pressure of 150 bar are
shown in figure 4.14. As temperature increases, there is a decrease in ammonia production in
the reactor. It is clear from figure 4.14 that a temperature range of 280-400 oC is suitable for
a process pressure of 150 bar.
Figure 4.15 presents the results of parametric sensitivity for synthesis reactor. For higher
pressures, Ammonia production is possible at even lower process temperatures.
Figure 4.15 :Temperature & Pressure Parametric Sensitivity for Synthesis
82
4.3.5 Effect of Flash Temperature on Liquid Ammonia Separation For choosing flash temperature, there are two constraints, maximum liquification of
ammonia is desirable and the mole fraction of ammonia should be maximum in the stream
NH3PROD.
To achieve the desired results, two sensitivities are designed that yield exactly opposite
results to each other. Figure 4.16 depicts a decrease in molar flow of ammonia in stream
PRODNH3 with increase in temperature while an increase in flash temperature favors
increase in mole fraction of ammonia in product stream (figure 4.17).
Figure 4.16 :Effect of Flash Temperature on Ammonia Flow Rate Figure 4.16 depicts a decrease in molar flow of ammonia in stream PRODNH3 with increase
in temperature while an increase in flash temperature favors increase in mole fraction of
ammonia in product stream (figure 4.17).
83
Figure 4.17 :Effect of Flash Temperature on Ammonia Mole Fraction 4.3.6 Effect of Purge Fraction on Ammonia Liquification
The effect of purge fraction in Splitter on Ammonia liquification in stream PRODNH3 is
presented in figure 4.18 which predicts a direct proportionality between the two factors but
the maximum purge fraction is limited by the fact that Syngas is precious and higher purge
fractions will result in decrease in mass flow rate of the closed loop system.
Figure 4.18 :Effect of Purge Fraction on Ammonia Liquification
84
4.3.7 Effect of Recycle Stream on Synthesis
By using Recycle Stream, ammonia mole fraction in SYN-OUT stream increases from
0.1231 to 0.1355.
85
5 AN OPTIMAL STORAGE PLANT
5.1 Process Modifications This section is aimed at finding the optimal process parameters specially optimal temperature
profile for synthesis reactor using the principles of variational calculus described in section
4.2.
5.1.1 Optimal Analysis Problem Formulation- Process Modifications
The optimization problem for the activity based Two Equation Model (TEM-TPA) can be
formulated as: maximize ∫=−=ΕL
dxdx
dzzLz
0
)0()( subject to the constraints given by the
governing equations 3.20 and 3.21. The Hamiltonian is written as
2211 ffdx
dz λλ ++=Η
5.1
Where 21 λλ and are Lagrange multipliers and 21 fandf are constraint equations referring to
mass and energy conservation equations.
Equation 5.1 yields the Lagrange multipliers (Co-state equations) as:
zdx
d
∂Η∂−=1λ
5.2
and
Tdx
d
∂Η∂−=2λ
5.3
86
with the boundary conditions 0)()( 21 == LL λλ . For a stationary Hamiltonian 0/ =∂Η∂ u ,
where u is the control variable that represents the optimal temperature.
5.1.2 OEM using Activity based Temkin-Pehzev form (OEM-TPA)
Considering the case 02 →f , i.e. only the mass conservation equation, henceforth referred
to as the One-Equation Model (OEM-TPA), as considered by Mansson and Andresen [157],
an optimal condition can be found for the temperature T as the control variable. This reduces
to the case of a single Lagrange multiplier λλ ≡1 . The Hamiltonian is thus 1)1( fλ+=Η ,
and the optimality condition is
∂∂==
∂Η∂≡
∂Η∂
AF
R
TTu N
A
/20
0
ηξ
5.4
The optimal temperature distribution can be obtained by solving the equation
000
=∂∂+
∂∂
T
R
TR A
A ηη
5.5
Figure 5.1 shows the process gas temperature, the optimal temperature obtained from
equation 5.5, and the equilibrium temperature [1]. The gas temperatureT increases rapidly in
the reactor saturating to 780 K while the predicted optimal temperatureoptT starts at a high
value, decreases rapidly and saturates to 738 K. The equilibrium temperatureeqmT , following
the same trend as optT saturates to the higher value of 786 K. Best ammonia conversion is
thus achieved by realizing this optimal profile.
87
Figure 5.1 : Homogeneous reactor with 1-D Model (TEM-TPA) showing gas temperatureT , equilibrium temperature eqmT , and optimal temeprature optT
The equilibrium temperature,eqmT , is defined as the temperature at which the optimal
concentration would be at equilibrium. Thus, for the synthesis reaction 322 23 NHHN →+ ,
the optimal molar fractions oiX and system pressureP are used to obtain the equilibrium
constant at zero pressure0aK from which eqmT is found.
)()(
)(1
22
3
,3
,
2,
20NoHo
NHoa XX
X
PK = .
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5600
650
700
750
800
850
900
950
1000
Topt
Teqm
T
Distance (m)
Tem
pera
ture
(K)
88
For the equilibrium composition [96], we determine the extentε of the reaction, with the
optimal composition taken as the initial composition, from a numerical solution of the
equilibrium relationship
23
22
)()()3(
)2()2(3 PTK
nn
nnoptaoo
NoH
oT
oNH =
−−−+
εεεε
.
The optimal and equilibrium temperatures show a trend, especially at reactor inlet, which
represent a theoretical ‘goal’ to achieve optimality. It can be seen from Figure 5.1 that there
is a substantial difference between the inlet temperatures, actual and optimal, but this
decreases as the reaction proceeds. Ideally, the inlet gas should be heated to the optimal
temperature and a heat exchanger should gradually remove the heat of the (exothermic)
reaction so that the resulting temperature decreases, rather than increasing, as gas flows in the
reactor. The optimal profile of figure 5.1 is thus in line with the requirement of a high
temperature to favor a high reaction rate at inlet, but as the exothermic ammonia synthesis
reaction proceeds, heat is generated and, according to Le Chatelier’s principle, the reaction is
driven in the backward direction to favor reactants. Thus optimality requires a gradual
decrease in temperature, to increase the equilibrium constant given by the Van’t Hoff
equation, and subsequently increase product formation [93],[96]. The actual temperature, as
shown in figure 5.1 is in sharp contrast to the optimal temperature since the inlet temperature
is limited by process parameters and the limits of the catalyst supplied by the manufacturer.
This work evaluates the approach-to-optimal by the use of inter-bed heat exchangers which
succesively reduce inlet temperatures and permit saturation to the optimal profile, achieving
89
higher conversion, in line with the S-300 Haldor Topsøe™ [21] which is a feature of all new
ammonia plants.
5.1.3 OEM using Partial Pressure based Temkin-Pehzev form (OEM-TPB)
A simpler formulation [141] is here considered for the determination of the optimal heat
removal strategy with the objective of maximizing ammonia conversion. In this case, the
energy equation (3.21) can be written, with a control variable u~ , as
uxTxzfuRxHdx
dTvC Arp
~)](),([~)()( 2 −≡−∆= ηξρ
5.6
We thus seek heat removal max
~0 uu ≤≤ which can be found by expressing the Hamiltonian as
)( 2211 uffdx
dz −++=Η λλ
5.7
where )/(~pvCuu ρ≡ . The Costate equations are then
])1[( 22
11
1
z
f
z
f
zdx
d
∂∂+
∂∂+−=
∂Η∂−= λλλ
5.8
and
])1[( 22
11
2
T
f
T
f
Tdx
d
∂∂+
∂∂+−=
∂Η∂−= λλλ
5.9
With boundary conditions )(0)( 21 LL λλ == .
The Stationarity condition is defined as:
0)1(0 22
21
1 =−∂∂+
∂∂+==
∂∂ λλλ
u
f
u
f
u
H
5.10
90
20 λ−==∂∂
u
H
5.11
Substituting value 2λ of in equation 5.9 yields
0])1[( 22
11
2 =∂∂+
∂∂+−=
T
f
T
f
dx
d λλλ
5.12
This formulation yields the optimal temperature from a solution of
0
1
3
2
222
2
3
121
0 2
3
3
2
2=
−
=
∂∂
−αα
H
NH
NH
HN
A
P
Pk
RT
E
P
PPk
RT
E
T
R
5.13
Solving Eqn. 5.13 is thus analogous to maximizing the ammonia conversion in the reactor.
For equation 5.13, the optimal temperature is found in a compact form:
βln12
R
EETopt
−=
5.14
where22
3
3
2
110
220
NH
NH
PP
P
Ek
Ek≡β .
The effect of heat removal at the exit of the first bed is shown in figure 5.2. The drop in inter-
bed temperature, taken here as 106 K, is arbitrary and can be adjusted according to the power
requirement, but this will have an effect on the entrance temperature for the second bed, and
hence on the saturation length.
91
Figure 5.2 : Temperature in homogeneous reactor compared with one-equation optimal temperature optT and equilibrium temperature eqmT . The mole fractions of hydrogen, nitrogen and ammonia at bed exits are: 0.5894, 0.2153,
Figure 5.9 : Effect of temperature drop in the inter-bed heat exchangers, after the first and second beds, on the ammonia mole fraction at reactor outlet.
97
In order to obtain the maximum achievable ammonia conversion, and hence a maximum
available thermal energy availability, we consider a sensitivity analysis of two parameters viz
the inter-reactor temperature drops. These are shown in Fig. 5.8 and Fig. 5.9. Figure 5.8
shows an optimal temperature drop of 205oC, as mentioned above, for which the exit
ammonia mole fraction is 0.2230. Similarly, Fig.5.9 shows an optimal at a temperature drop
of 95oC, for which the final exit ammonia mole fraction is 0.2762, and a thermal energy
availability of 45.6 MWth.
5.2 Design Modifications
Best ammonia conversion is achieved by realizing the optimal temperature profile as
described in section 5.1. For a solar thermal power plant, this inlet temperature will be
constrained by the maximum temperature achievable at the dissociation side of the plant.
Thus, it is practically difficult to have an inlet gas temperature high enough as 870 K as
predicted by theory. We thus seek the industrially viable option so that the resulting
temperature difference, between actual and optimal, is minimized.
Two technology options that can make this possible include pre-heating the inlet gas and
progressively removing the heat of reaction from the reactor acordingly, and with the given
inlet tempeature and increasing profile, removing process gas heat from the ‘first catalyst bed’
at first saturation and achieving optimal temperature in the second bed, and repeating the
procedure in the third bed. The first option has been extensively investigated [65][77][100]
using a counter-flow arrangement in which heat at reactor exit is used for pre-heating the
98
feed gas. Another technological option [1] consisting of varying the catalyst concentration
taking advantage of the ‘importance’ of the beds, has been shown to enable optimal
configuration.
Figure 5.10 shows a steep 65% conversion in the first bed, a slower but increasing 35%
conversion in the second bed, followed by a slight 10% improvement in the third bed. All
beds are taken to be of height 1.5 m. A significant feature of figure 5.10 is the saturation of
the conversionz to a value 0.2534 at the reactor exit. Figure 5.3a shows the increase of
ammonia in the three beds at approximately linear rates with decreasing gradients in
successive beds. The homogeneous catalyst loading indicates that the third bed has a very
small contribution.
Figure 5.10 : Homogeneous reactor: Nitrogen conversion in catalyst bed.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.05
0.1
0.15
0.2
0.25
0.3
Distance (m)
Con
vers
ion
of N
2 (
Z)
99
5.2.1 The Proposed Design
Figure 5.11 shows the comparison of the reference (homogeneous) design with the proposed
process modifications. The three cases shown, between the reference (1,1,1) and the optimal,
are a 10% and a 20% increase in catalyst concentration in the first bed only, followed by a
simultaneous 50% increase in the first bed and a 25% increase in the second bed
(1.50,1.25,1.00). The first two cases are shown to marginally improve the conversion since
the design change is small, while the last case achieves the optimal conversion before the exit
from the first bed. It is seen that there is further scope for improvement in subsequent catalyst
beds.
Figure 5.11 : Effect of varying spatial composition in reactor beds on the mole fraction of ammonia in the reactor compared with the reference (homogeneous) design with spatial concentration [1.00, 1.00, 1.00]
In Figure 5.12, detailed results are illustrated for a 50% and 25% concentration increase in
the first and second beds respectively. The nitrogen conversion increases from 0.2534 to
0.2832 while the temperature profile moves closer to the OEM equilibrium for the first and
second beds.
Figure 5.12 : Effect of varying spatial composition in reactor beds (1.50, 1.25, 1.00); a) nitrogen conversion, b) actual, optimal and equilibrium temperatures, c) hydrogen, nitrogen and ammonia mole fractions. Saturation in the first bed appears in the last 0.30 m of the first bed. The engineering
implications are that, with fixed bed physical dimensions, this space could be utilized for
some other scheme such as pre-heating for the second bed inlet to bring inlet temperature
closer to the optimal. The highest temperature in the first bed increases to 780 K (from 775 K
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.1
0.2
0.3
Distance (m)
Con
vers
ion
of N
2 (
Z)
1 2 3 4600
700
800
900
1000
Topt
Teqm
Distance (m)
Tem
pera
ture
(K)
0 1 2 3 40
0.2
0.4
0.6
0.8
Distance (m)
Mol
e F
ract
ion H2
N2NH3
(a)
(b) (c)
101
in the homogeneous case) which brings it closer to the maximum permissible catalyst
temperature, and hence a reduction in the reactor safety margin. The ammonia mole fraction
at reactor exit has now increased to 0.1856; equivalent to 1186-MTD. Apart from an increase
in the ammonia production, the heat recovery potential from the first inter-bed heat
exchanger increases to 18.395 MW(th) and 14.277 MW(th) from the second inter-bed heat
exchanger. When the spatial concentration is also increased in the third bed so that the
concentrations are [1.50,1.25,1.25], the nitrogen conversion increases to 0.2901, and the
ammonia production increases to 0.1902 (1210-MTD); the heat recovery is 18.395 MW(th)
and 13.880 MW(th) (total: 32.275 MW(th)).
5.2.2 Design Modifications Validation: This section uses AspenPlusTM to estimate the effect of heterogeneous catalyst distribution
on the temperature profile in bed 1 and bed 2 of the KBR Synthesis reactor .
Figure 5.13 : Bed1: Temperature Profile with different Catalyst Distribution
102
Figure 5.13 presents the temperature profiles in the reactor bed1 with catalyst spatial factors
of 1 and 1.5. It is clear that in case of catalyst spatial facor of 1.5, the temperature value
saturates at reactor length of 0.7m, thereby approaching the optimal temperature profile faster
than in the uniform case; the equilibrium temperature can be achieved before the exit of the
first bed and hence a wider span is available for heat/energy extraction to be used by Solar
Thermal power plant.
Figure 5.14 : Bed2: Temperature Profile with different Catalyst Distribution
The same results can be observed in figure 5.14 for temperature profile of bed2, where a
catalyst spatial factor of 1.25 is used.
103
6 CONCLUSIONS AND FUTURE WORK
This work is aimed at maximizing the heat recovery and hence improving the overall
efficiency of a thermal storage plant, by estimating optimal geometric and process variables
for system components including ammonia dissociation reactor, heat exchangers, Flash tank,
purge gas removal, recycle streams and most importantly ammonia synthesis reactor.
Kellogg KBR industrial ammonia synthesis reactor has been used for computing the
ammonia production using mass and energy conservation equations with homogeneous as
well as non-uniform catalyst distributions. The momentum conservation equation has been
ignored since the pressure drop in this reactor has been shown [64] to be not more than 2% of
the system pressure. The optimal and equilibrium temperature profiles are then computed in
the reactor and compared with the temperature profile in the homogeneous reactor.
The optimal and equilibrium temperature profiles have been used as the desired profiles by
incorporating process, rather than design, changes in the heat recovery system. This led to a
study of a heterogeneous, or non-uniform, catalyst distribution in the beds.
The results indicated that optimal ammonia conversion requires a high inlet temperature to
favor a high reaction rate as opposed to the comparatively lower inlet temperatures which are
found in industrial reactors. The optimal design, based on the optimal temperature profile,
gives a 15% increase in ammonia yield, from 1082 MTD in the homogeneous configuration
104
to 1246 MTD in the optimal configuration. A non-uniform catalyst distribution can be used
to take advantage of the importance of the first bed, followed by successive beds, thereby
approaching the optimal temperature profile faster than in the uniform case; as a result of the
previous argument, the equilibrium temperature can be achieved before the exit of the first
bed; heterogeneous catalyst distribution, is a strategy which increases the concentration by 50%
in the first bed and 25% in the second bed, brings the temperature profile close to equilibrium
results with a 10% increase in ammonia conversion. A larger number of beds could be used,
in principle, to search for a catalyst distribution which would yield the optimal temperature
profile leading to a 15% increase in ammonia yield.
Finally it is concluded that a one-dimensional model, with mass and energy conservation
equations using the Temkin-Pyzhev activity and pressure-based kinetics rate expressions,
predicted an optimal ammonia conversion of 0.2137 with a thermal energy availability of 20
MWth. A comprehensive process simulation using Aspen Plus™ predicts an optimal
ammonia conversion of 0.2762 mole fraction at exit, with two inter-bed heat exchangers
having optimal temperature drops of 205K and 95K respectively, and yielding a thermal
availability of 45.6 MWth. The thermal energy availability of a base-load solar thermal plant
can be increased by 15% in the ammonia conversion and over 25% in thermal energy
availability for energy recovery.
105
Construction of experimental setup is recommended for validation of results presented in this
thesis and further research in this area. It is being considered at University of Engineering &
Technology Taxila through undergraduate students and development of initial funding
proposal is in progress.
Further work is suggested to quantify the performance increase in the considered system by
conducting an exergy analysis of the system components for better quantification of the
efficiency improvements as the major determinant of achievable performance for such a
system is the degree of thermodynamic irreversibility associated with the heat recovery
process.
The major irreversibilities occur within the exothermic reactor and the counterflow heat
exchanger between ingoing and outgoing reactants. In the suggested study, optimum reactor
control will yield exergetic efficiencies, which should translate to overall solar to electric
conversion efficiencies.
106
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[168] Frank Kreith and Jan F. Kreider, Principles of Solar Engineering, Hemisphere Publishing Corporation, New York, (1978). (document) 1.1
[169] Michaels, I. A., “An overview of the USA Program for the Development of Thermal Energy Storage for Solar Energy Applications”, Solar Energy, Vol. 27, pp. 159-167, 1978. (document) 1.2.2
[170] Morrison, D. J. and S. I. Abdel-Khalik, “Effects of Phase Change Energy Storage on the Performance of Air-Based and Liquid-Based Solar Heating Systems”, Solar Energy, Vol. 20, pp. 57-67, 1978. (document) 1.4
[171] P. Carden and O. Williams, “The efficiencies of thermochemical energy transfer”, Int. J. Energy Res., vol. 2, pp. 389–406, 1978. (document) 1.7
[172] Rajagopal, D., Krishnajwamy, et al., “A Simulation Study of Phase Change Energy Store”, Proceedings of the Int. Solar Energy Society Congress (1978), New Delhi, India. (document) 1.4
[173] L. D. Gaines, “Optimal Temperatures for Ammonia Synthesis Converters”, Ind. Eng. Chem. Process Des. Dev., Vol. 16, No.3, pp. 381-389, 1977. (document) 5.1.1
[174] P. Carden, “Energy Corradiation using the Reversible Ammonia Reaction”, Solar Energy Vol. 19, pp. 365–378, 1977. (document) 1.7
[175] Aden B Meinel and Marjorie P. Meilen, Applied Solar Energy, An Introduction, Addison-Wesley Publishing Company, Inc. Philippines, third edition, 1976. (document) 1.1, 1.7
[176] L. W. Brantley, “Thermal energy storage system”, IRE Transactions Elect Computers, Vol. 147-149, pp. 1-10, November 1976. (document) 1.4
[177] P. Carden, “A large scale solar plant based on the dissociation and synthesis of ammonia”, Dept. Eng. Phys., RSPhysS, Australian Nat. Univ., Canberra A.C.T. Australia, Tech. Rep. EC-TR-8, 1974. (document) 1.7
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[178] C. K. Lee, “Critical mass minimization of a cylindrical geometry reactor by two group diffusion equation”, J. Kor. Nuc. Soc. Vol. 5, No. 2, pp. 115-131, 1973. (document) 5.2
[179] A. Murase, H. L. Roberts, and A. O. Converse, "Optimal Thermal Design of an Autothermal Ammonia Synthesis Reactor", Industrial and Engineering Chemistry Process Design Development, Vol. 9, No. 4, pp. 503-513, 1970. (document) 5.1
[180] Kirk, D.E., Optimal Control Theory: An Introduction, Prentice Hall, Inc., Englewood Clifffs, New Jersey (1970). (document) 4.2, 4.4.2, 5.2
[181] M.M. Denn, Optimization by Variational Methods, McGraw-Hill Book Company, New York (1970). (document) 4.2
[182] Sagan Hans, Introduction to the Calculus of Variations, McGraw Hill Book Co., New York (1969). (document) 4.2
[183] D.C. Dyson and J.M. Simon, Industrial and Engineering Chemistry Fundamentals, Vol.7, ACS Publications, Washington D.C. (1968) (document) 3.1.2.2
[184] Crider J.E. and Foss A.S., “An Analytic Solution for the Dynamics of a Packed Adiabatic Chemical Reactor”, AIChE Journal, Vol. 14, No. 1, pp. 77-84, 1968. (document) 3.1.2
[185] Forray, M. J., Variational Calculus in Science and Engineering, McGraw-Hill Book Company, New York, (1968). (document) 4.2
[186] Nielsen, A., An Investigation on Promoted Iron Catalysts for the Synthesis of Ammonia, 3rd edition., Jul. Gjellerups Forlag, (1968). (document) 1.7
[187] D.C. Dyson, "Optimal Design of Reactors for single Exothermic Reversible Reactions", Ph.D. thesis, London University, 1965. (document) 4.1
[188] R.F. Baddour, P. L. T. Brian, B. A. Logeais, J. P. Eymery, "Steady-State Simulation of an Ammonia Synthesis Converter", Chemical Engineering Science, Vol. 20, pp. 281-292,1965. (document) 3.1.2
[189] A. Nielsen, J. Kjaer, and B. Hansen, “Rate equation and mechanism of ammonia synthesis at industrial conditions”, J. Catalysis, vol. 3, pp. 68–79, 1964. (document) 1.7
[190] Rutherford Aris, The Optimal Design of Chemical Reactors- A Study in Dynamic Programming, Academic Press Inc. Ltd. London (1961). (document) 4.1
[191] A. Ozaki and Hugh Taylor, “Kinetics and Mechanism of the Ammonia Synthesis”, Proceedings of the Royal Society, Vol. 258, pp. 47-62, 1960. (document) 3.1.2
[192] Aris R. and Amundson N. R., “An Analysis of Chemical Reactor Stability and Control”, Chem. Engg. Science, Vol. 07, No. 03, pp. 121-155, 1958. (document) 4.1
[193] D.Annable, "Application of the Temkin Kinetic Equation to Ammonia Synthesis in the Large-Scale Reactors", Chemical Engineering Science, July 1952. (document) 3.1.2.2
[194] Klaus Fuchs, “Pressure Dependence of the Equilibrium Constant of Ammonia”, Proceedings of the Royal Society, Vol. 179, pp. 433-438, 1942. (document) 3.1.2.2
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[195] M. Temkin and V. M. Pyzhev, “Kinetics of ammonia synthesis on promoted iron catalysts”, Acta Physicochimica, vol. 12, pp. 327–356, 1940. (document) 1.7, 3.1.2.2
[196] Edgar Philip Perman, “The Direct Synthesis of Ammonia”, Proceedings of the Royal Society, Vol. 76, pp. 167-174, 1905. (document) 2.1.2
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APPENDIX A. AMMONIA 3D PHASE DIAGRAMS
Figure A.1 Ammonia 3D Phase Diagram Critical Point*
APPENDIX B2: MATLAB ™ PROGRAM FOR FINDING EQUILIBRIUM CONCENTRATIONS This section lists the Program SSEqmProg Program SSEqmProg computes equilibrium mole fractio n, extent & Equilibrium Constant K
% Program Name: SSEqmProg % To find the eqm concn % % C:\MATLAB7\work\Ammonia\SSEqmProg.m % Author: Engr. Sadaf Siddiq ([email protected]) % % Jan 2011 % % open output file resl=fopen('out1.txt','w'); % INPUT and STREAM OUT PUT tic %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % step 1 specify an initial conc N2 mole = 1 H2= 3 NH3 = 0 % step 2 specify T, P % step 3 evaluate K(T) % step 4 calc eps (extent of reaction) % step 5 plot eps vs T for fixed P % STATIC DATA fprintf (resl,'\n physical data'); fprintf (resl,'\n universal data'); R_un = 8.314; % universal gas const J/(mol-K) fprintf (resl,'\n Universal Gas Const = %12.6f kJ/ (mol-K)\n',R_un); % chemical data from http://www-jmg.ch.cam.ac.uk/tools/magnus/PeriodicTable.html % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane MW1=2.0*1.0079759; MW2=2.0*14.0067231; MW4= 39.9476 613; MW3=(14.0067231+3.0*1.0079759); MW5 = (12.0110369+4 .0*1.0079759); MW = [ MW1;MW2;MW3;MW4;MW5 ]; %----------------- % STEP 1 initial composition n(2) = 1.0; % moles of nitrogen n(1) = 3*n(2); % moles of hydrogen n(3) = 0.0; % ammonia mole fraction nI = 0.0; % inerts mole fraction kappa= 0; % ratio of Ar/Methane n(4) = (kappa/(1+kappa))*nI; n(5) = nI - n(4); fprintf (resl,'\n ID Name Mol Wt (kg/kmol) Moles\n'); fprintf (resl,'\n 1 Hydrogen %8.4f %21.4f',MW(1), n(1)); fprintf (resl,'\n 2 Nitrogen %8.4f %21.4f',MW(2), n(2)); fprintf (resl,'\n 3 Ammonia %8.4f %21.4f',MW(4), n(3)); fprintf (resl,'\n 4 Argon %8.4f %21.4f',MW(3), n(4)); fprintf (resl,'\n 5 Methane %8.4f %21.4f',MW(5), n(5));
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fprintf (resl,'\n ----------------------------\n'); %------------------ NP = 6; NT = 20; % STEP 2 specify T, P Pressure = 0.0; % atm for j = 1:NP Pressure = Pressure+50 ; % atm ppp(j) = Pressure; % pressure of reaction fprintf (resl,'\n\n System pressure is %8.2 f atm',Pressure); temp = -50.0; % deg C for i = 1:NT temp = temp + 50.0; Temp = temp +273.15 % K %temp = 675-273.15; Temp=temp+273.15; % STEP 3 evaluate K(T,P) %[Ka] = EQNCN(Temp); % Dashti expression % Ka from Narayanan p.417 Eq. 9.58 lnKa = 79201/(R_un*Temp) - (48.8/R_un)*log(Temp) + (17.38e-3/R_un)*Temp + 14.169; Ka = (exp(1))^lnKa; % STEP 4 calc eps alpha = sqrt( 27.0 * Ka * Pressure^2 ); beta = alpha + 4.0; tt1 = 1.0 - alpha/beta; eps = 1.0e23; if (tt1>=0) tt2 = sqrt(tt1); eps1 = 1.0 + tt2; eps2 = 1.0 - tt2; end %fprintf (resl,'\n eps1 = %12.4f eps2 = %12.4e \n ',eps1,eps2); % now select the value less than 1 if (eps1 <= 1 ) eps = eps1; end if (eps2 <= 1 ) eps = eps2; end % what if both epsilons are +ve ? ttt(j,i) = temp; % deg C TTT(j,i) = Temp; % Kelvin eee(j,i) = eps; % extent of reaction kkk(j,i) = log10(Ka); % log10 of eqm const aaa(j,i) = 2*eps/(4 - 2*eps); end % end of temperature loop
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% write the results fprintf (resl,'\n No. temp (C) Temp (K) Ka eps'); for iP = 1: NT fprintf (resl,'\n %4.0f %9.2f %9.2f %12.4e %12.4f',iP,ttt(j ,iP),TTT(j,iP),kkk(j,iP),eee(j,iP)); end end % end of pressure loop % STEP 5 plot the results PlotExtent = 0; PlotNH3eqm = 1; PlotEqmConst = 0; if (PlotExtent == 1) for plotP = 1:NP for k = 1:NT X(k) = ttt(plotP,k); % temp deg C Y(k) = eee(plotP,k); % extent of reaction % Y(k) = kkk(plotP,k); % eqm const end plot(X,Y,'-k') hold on end xlabel (' Temp (^oC)','Fontsize',16) ylabel ('Extent (\epsilon ) ','Fontsize',16) grid off text(400,0.15,'50 ','Fontsize',12) text(560,0.35,'300','Fontsize',12) text(530,0.90,'\bf Pressure','Fontsize',12) text(450,0.85,'50,100,150,200,250,300 atm','Fontsiz e',12) end % end of plot of extent reaction if (PlotNH3eqm == 1) for plotP = 1:NP for k = 1:NT X(k) = ttt(plotP,k); % temp deg C Y(k) = aaa(plotP,k); % mol fraction of ammonia in eqm mixture % Y(k) = kkk(plotP,k); % eqm const end plot(X,Y,'-k') hold on end xlabel (' Temp (^oC)','Fontsize',16) ylabel ('NH_3 in Eqm. Mix. (mol. fr.) ','Fontsize', 16) grid on text(320,0.15,'50 ','Fontsize',12) text(480,0.35,'300','Fontsize',12) text(530,0.90,'\bf Pressure','Fontsize',12) text(450,0.85,'50,100,150,200,250,300 atm','Fontsiz e',12) end % end of plot of ammonia in eqm mixture if (PlotEqmConst == 1) for plotP = 1:NP for k = 1:NT X(k) = ttt(plotP,k); % temp deg C
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Y(k) = kkk(plotP,k); % eqm const end plot(X,Y,'-k') hold on end xlabel (' Temp (^oC)','Fontsize',16) ylabel ('Eqm. Const. (log_{10}K_a) ','Fontsize',16) grid on end % end of plot of Equilibrium Constant toc fclose(resl);
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APPENDIX B3: MATLAB ™ PROGRAM FOR FINDING OUTPUT OF COUNTER-FLOW SYNTHESIS REACTOR This section lists the Program RunSSoptim and its function SSoptim Program SSoptim computes output for counter flow sy nthesis reactor by solving three equations as described by B.V.Babu: c ounterflow feed/reacting Gas and temperature Data: inlet conditions Output: outlet conditions % Program Name: RunSSoptim % % C:\MATLAB7\work\Ammonia\RunSSoptim.m % Author: Engr. Sadaf Siddiq ([email protected]) % Last modified May 28 2011 % % % open output file resl=fopen('out1.txt','w'); % INPUT and STREAM OUT PUT tic options = odeset('RelTol',1e-6,'AbsTol',[1e-8 1e-8 1e-8]); [t,Y] = ode15s(@SSoptimKREETZ,[0 0.8],[663 663 0.02 51],options); % ammonia moles AmmMolesInit = 0.0029; NMolesInit = 0.0251; Amm = AmmMolesInit + 2*( NMolesInit - Y(:,3)); PlotTemp = 1; PlotComp = 0; PlotBoth = 0; % for plot showing temperatures only if (PlotTemp ==1) plot (t,Y(:,1),'-ok') hold on plot (t,Y(:,2),'-sk') grid on xlabel ('Distance (m)') ylabel ('Temperature (K)') h = legend('Feed Gas','Reacting Gas',1); % title 'Feed Gas Temperature and Reacting Gas Temperature' end
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% for plot showing molar compositions only if (PlotComp ==1) plot (t,Y(:,3),'-ok') hold on plot (t,Amm,'-sk') grid on xlabel ('Distance (m)') ylabel ('Molar Flow Rate (kmols/hr)') h = legend('N_2','NH_3',1); title 'Nitrogen and Ammonia Molar Flow Rates' end if (PlotBoth ==1) subplot(2,1,1) plot (t,Y(:,1),'-ok') hold on plot (t,Y(:,2),'-sk') grid on xlabel ('Distance (m)') ylabel ('Temperature (K)') h = legend('Feed Gas','Reacting Gas',1); % title 'Feed Gas Temperature and Reacting Gas Temperature' subplot (2,1,2) plot (t,Y(:,3),'-ok') hold on plot (t,Amm,'-sk') grid on xlabel ('Distance (m)') ylabel ('Molar Flow Rate (kmols/hr)') h = legend('N_2','NH_3',1); %title 'Nitrogen and Ammonia Molar Flow Rates ' end toc fclose(resl); function dy = SSoptim(t,y) dy = zeros(3,1); % a column vector % % last modified 28 May 2011 % % MATLAB commands to run this program % options = odeset('RelTol',1e-6,'AbsTol',[1e-8 1 e-8 1e-8]); % [t,Y] = ode15s(@SSoptim,[0 8],[700 700 701.2],o ptions); % plot(t,Y(:,1),'-',t,Y(:,2),'-.',t,Y(:,3),'.') Cpf=3.0 ; % kJ/(kg-K) cold feed gas Cpg=3.1 ; % kJ/(kg-K) hot reacting gas flowing do wnwards U=140.0; % heat transfer coefficient kW/(m^2-K)
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s1=2.*3.14159*7.9/1000; % surface area of cooling tubes per length of reactor W=1.08; % mass flow rate kg/s f=1.0; % catalyst effectiveness or concentratio n H=-100000.0;% kJ/(kmol N_2) R= 8.314472; % universal gas constant kJ/(kmol-K) Press=150; % system pressure atm s2=3.14159*7.9*7.9*1.0e-6; % cross-section area of catalyst zone % Moles kmol/h-m^2 at Feed % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane xFeed= [ 0.6567006; 0.2363680; 0.0202874; 0.026930; 0.059714]; % mole fractions TotalFeed = 0.1062; % kmols / hr H2F = xFeed(1) * TotalFeed; % kmol/h N2F = xFeed(2) * TotalFeed ; % kmol/h NH3F = xFeed(4) * TotalFeed; % kmol/h InertsF = (xFeed(3) + xFeed(5)) * TotalFeed; % kmol/h %fprintf (resl,'\n Total Feed = %12.4f moles/h-m^2 \n',TotalFeed); % dy(1) is dTf dy(2) is dTg dy(3 ) is dN % feed gas temp eqn dy(1)=((-U*s1)/(W*Cpf))*(y(2)-y(1)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % hot gas temp %Tf = TfLast; T=y(2); %this is the temp of the gas flowing downwa rds convertedN = N2F - y(3); H2Now = H2F - 3*convertedN ; N2Now = y(3); NH3Now= NH3F + 2*convertedN; InertsNow = InertsF; TotalMolesNow = TotalFeed - 2.0*convertedN ; % new mole fractions xH = H2Now/TotalMolesNow; xN = N2Now/TotalMolesNow; xA = NH3Now/TotalMolesNow; [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(Press,T,xH, xN,xA); [Ka] = EQNCN(T); [kArh]= RTCNT(T,R); [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3); dndx = -f* RNH3/2.0 ; dy(2) =(-U*s1)/(W*Cpg)*(y(2)-y(1))+ ( (-H*s2)/(W*Cp g) ) * ( -dndx ); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % moles of N2 % parameter T represents moles of N2 (normalized) %Tg=TgLast; Tg = y(2); [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(Press,T,xH, xN,xA);
APPENDIX B4: MATLAB ™ PROGRAM FOR FINDING OUTPUT OF STEADY STATE SYNTHESIS REACTOR WITH 3 CATALYST ZONES % Program Name: SSATSNonUnif % Steady State Ammonia Thermal Stora ge % % C:\MATLAB7\work\Ammonia\SSATS_NonUnif_New % % First Written: JULY 2010 % Last Update: 24 May 2011 % open output file resl=fopen('outSSATSnu.txt','w'); % INPUT and STRE AM OUTPUT tic %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % INPUT % System Pressure (atm) % Temp (K) % Total Mass Flow Rate (kg/hr) = % Mole fractions (H,N,Ar,Amm,Met) [x] = % Area = 20.0 ; % cross-section area of catalyst m^ 2 % Length of converter Lmax (m) % OUTPUT % graph of mol fractions of H, N, Amm vs length %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % program parameters NS = 10; % number of streams NC = 5; % number of components, H2,N2,NH3,Ar,CH4 fprintf (resl,'\n No. of Streams = %3.0f \n',NS) ; fprintf (resl,'\n No. of Components = %3.0f \n',NC) ; %%%%%%%%%%%%%%%%%%%%%%%%% DATA ********************** R_un = 8.314472; % universal gas const J/(mol-K) %R_un = 1545.349 ; % lbf.ft/lbmol.R %R_un = 1545.349; fprintf (resl,'\n Universal Gas Const = %12.6f kJ/ (mol-K)\n',R_un); % chemical data from http://www-jmg.ch.cam.ac.uk/tools/magnus/PeriodicTable.html % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane MW1=2.0*1.0079759; MW2=2.0*14.0067231; MW3= 39.9476 613; MW4=(14.0067231+3.0*1.0079759); MW5 = (12.0110369+4 .0*1.0079759); MW = [ MW1;MW2;MW3;MW4;MW5 ]; fprintf (resl,'\n ID Name Mol Wt (kg/kmol)\n') ; fprintf (resl,'\n 1 Hydrogen %8.4f ',MW(1)); fprintf (resl,'\n 2 Nitrogen %8.4f ',MW(2)); fprintf (resl,'\n 3 Argon %8.4f ',MW(3)); fprintf (resl,'\n 4 Ammonia %8.4f ',MW(4)); fprintf (resl,'\n 5 Methane %8.4f ',MW(5)); fprintf (resl,'\n ----------------------------\n'); % STREAM 1: SYN GAS ENTERING C-1 ****************** ************************ IS=1; fprintf (resl,'\n Stream No: %3.0f \n',IS); % STREAM INPUT
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P(1) = 100.0; % atm P_SIunits(1) = P(1)*1.0e5; %Pascals T(1) = 300.0; % Kelvin TotMassFlRate(IS) = 0.3*60*60/1000; % kg/hr this for comp; for stream 3, line 207 % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane x= [ 0.6567006; 0.2363680; 0.0202874; 0.026930; 0. 059714]; % mole fractions % x= [ 0.78; 0.20 ; 0.0 ; 0.02; 0.0] Area = 3.14159 * (1.58e-2)^2 ; % cross-section area of catalyst m^2 fprintf (resl,'\n Area = %12.4e m^2',Area); HghtReactor = 0.8; % meters VolCatalyst = Area * HghtReactor; fprintf (resl,'\n Vol of catalyst = %12.4e m^3 \n', VolCatalyst); %x= [ 0.7426; 0.2475; 0.0099; 0.0; 0.0]; % mole fra ctions %mfm = [ 750.0 ; 250.0 ; 10.0; 0.0; 0.0]; % kg-mo ls/hr % % stream computation............................... ........ MWT(IS) = 0.0; % average molecular weight of stream xT = 0.0; % total mol fr. this is should add up to 1.0 for i = 1:NC MWT(IS)=MWT(IS)+x(i)*MW(i); xT = xT +x(i); end RR(IS) = R_un/MWT(IS); % gas constant for this stre am (gas) %------------------------------- % mfrT = 0.0; % total mass flow rate/hr % for j=1:NC % mfr(j)=mfm(j)*MW(j); % kg/hr % mfrT = mfrT + mfr(j); % end % MolarFlRateMix(IS) = mfrT/MWT(IS); % moles per hr %-------------------------------- MolarFlRateMix(IS) = TotMassFlRate(IS)/MWT(IS); % i n kmols/hr mfrT=0.0; mfmT=0.0; for jk=1:NC mfr(jk) = x(jk)*MolarFlRateMix(IS); % units kmo l/hr mfrT = mfrT + mfr(jk); mfm(jk) = mfr(jk)*MW(jk); % units should be kg /hr mfmT = mfmT + mfm(jk); end % end of stream computation........................ .......
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% % STREAM OUTPUT fprintf (resl,'\n --------------------------------- --------------------\n'); fprintf (resl,'\n STREAM No: %3.0f \n',IS); fprintf (resl,'\n NC Mole Fr Molar flow rate Mass flow rate'); fprintf (resl,'\n kg-mols/hr kg/hr\n'); for i=1:NC fprintf (resl,'\n %2.0f %8.4f %8.4f %8.4f ',i,x(i),mfr(i),mfm(i)) end fprintf (resl,'\n \n Total %6.4f %8.4f %8.4f\n',xT,mfrT,mfmT); fprintf (resl,'\n Mol Wt of mixture MWt( %2.0f ) = %8.4f kg/kmol ',IS,MWT(IS)); fprintf (resl,'\n Gas Const of mixture RR ( %2.0f ) = %8.4f kJ/(kmol-K) ',IS,RR(IS)); fprintf (resl,'\n Molar Flow Rate of Stream %3.0f i s %8.2f kmoles / hr ',IS,MolarFlRateMix(IS)); fprintf (resl,'\n --------------------------------- --------------------\n'); % COMPRESSOR WORK FOR STREAM 1 % make the mixture Cp, Cv and gamma CpMix = 0.0; RMix = 0.0; % find the Cp values at this temp T1 and press P(1) [CpH2,CpN2,CpNH3,CpCH4,CpAr] = SPCHT(T(1),P(1)); % kJ/(kmol-K) Cp(1) = CpH2; Cp(2) = CpN2; Cp(3) = CpAr; Cp(4)=CpN H3; Cp(5)=CpCH4; jj=1; for j= NC+1:2*NC Cp(j) = Cp(jj)/MW(jj); jj=jj+1; end fprintf (resl,'\n --------------------------------- --------\n'); fprintf (resl,'\n Cp values from function SPCHT at T = %8.2f K and P = %6.2f atm\n',T(1),P(1)); fprintf (resl,'\n Component Cp kJ/(kmol-K) kJ/( kg-K)\n'); fprintf (resl,'\n 1 Hydrogen %12.4e %12.4e ',Cp(1 ),Cp(6)); fprintf (resl,'\n 1 Nitrogen %12.4e %12.4e ',Cp(2 ),Cp(7)); fprintf (resl,'\n 1 Argon %12.4e %12.4e ',Cp(3 ),Cp(8)); fprintf (resl,'\n 1 Ammonia %12.4e %12.4e ',Cp(4 ),Cp(9)); fprintf (resl,'\n 1 Methane %12.4e %12.4e ',Cp(5 ),Cp(10)); fprintf (resl,'\n --------------------------------- ---------\n'); for i = 1:NC % individual gas constants Rg(i) = R_un/MW(i); % kJ/(kmol-K) * kmol/kg = kJ/(k g-K) %RMix = RMix + Rg(i)*mfm(i)/mfmT; % based on mass fl rates RMix = RMix + R_un *mfr(i)/mfrT; % based on molar fl rates CpMix = CpMix + Cp(i)*mfr(i)/mfrT; % based on molar flow rates end CvMix = CpMix - RMix; % molar basis GammaMix = CpMix/CvMix; fprintf (resl,'\n Mixture properties (based on mola r ratios)\n'); fprintf (resl,'\n CpMix (kJ/(kmol-K) CvMix RMix GammaMix\n'); fprintf (resl,'\n %12.4e %12.4e %12.4e % 8.2f \n',CpMix,CvMix,RMix,GammaMix);
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% compressor work n=1; P(2) = 1.5 * P(1); % discharge pressure PressRatio = P(2)/P(1); [Ws]=COMPR(n,T(1),RMix,P(1),P(2),GammaMix); % gives Work in kJ/kmol of gas PowerComp = Ws * MolarFlRateMix(1); % kJ/hr PowerComp = (1./(60.*60.))*PowerComp; % kW fprintf (resl,'\n Compressor Power \n'); fprintf (resl,'\n Reciprocating Compressor\n') fprintf (resl,'\n No of stages = %2.0f ',n); fprintf (resl,'\n Suction Pressure = %12.4e atm \ n',P(1)); fprintf (resl,'\n Discharge Pressure = %12.4e atm \ n',P(2)); fprintf (resl,'\n Pressure Ratio = %6.2f \ n\n',PressRatio); fprintf (resl,'\n Compressor Work = %12.4e kJ/km ol \n',Ws); fprintf (resl,'\n Compressor Work = %12.4e kW \ n',PowerComp); % example from K.V.Narayanan p.134 % the R used in this is the universal Gas Const; th is prog uses RgasMix % (check again) %[Ws]=COMPR(1,300,8.314,1,10,1.3); %PowerComp = Ws * 1.114e-3; %fprintf (resl,'\n Compressor Work = %12.4e kW \n',PowerComp); %------------------------------ SYNTHESIS --------- ----------------- % STREAM 3 % give input data for stream % molar flow rate; mole fractions, pressure and te mperature % output will be mole fractions, temperature and pr essure % solve the equations using RK-4 method % STREAM 3: SYN GAS ENTERING R-1 ****************** ************************ IS=3; fprintf (resl,'\n Stream No: %3.0f \n',IS); % STREAM INPUT P(IS) =150.0 ; % atm P_SIunits(IS) = P(IS)*1.0e5; %Pascals %T(IS) = 371+273; % Kelvin Dashti paper inlet T %T(IS) = 291 + 273 - 10 ; % Kelvin with Manson Set 2 T(IS) = 390 +273; % Kreetz and Lovegrove 1999 InletTemp = T(IS); TotMassFlRate(IS) = 0.3*60*60/1000; % kg/hr Das hti p.20 % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane %x= [ 0.6567006; 0.2363680; 0.0202874; 0.026930; 0. 059714]; % mole fractions %x= [ 0.6567006; 0.2363680; 0.0202874; 0.026930; 0. 059714]; % mole fractions % mfm = [ 750.0 ; 250.0 ; 10.0; 0.0; 0.0]; % kg-m ols/hr % % stream computation............................... ........ MWT(IS) = 0.0; % average molecular weight of stream
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xT = 0.0; % total mol fr. this is should add up to 1.0 for i = 1:NC MWT(IS)=MWT(IS)+x(i)*MW(i); xT = xT +x(i); end RR(IS) = R_un/MWT(IS); % gas constant for this stre am (gas) TotMolarFlRate(IS) = TotMassFlRate(IS)/MWT(IS); % k moles per hr sumMol = 0.0; sumMas = 0.0; for j=1:NC MolFlRate(j) = x(j) * TotMolarFlRate(IS); % kmol/hr sumMol = sumMol + MolFlRate(j); MassFlRate(j)= MolFlRate(j) * MW(j); % kmol/hr * k g/kmol = kg/hr sumMas = sumMas + MassFlRate(j); end % end of stream computation........................ ....... % % STREAM OUTPUT fprintf (resl,'\n --------------------------------- --------------------\n'); fprintf (resl,'\n STREAM No: %3.0f \n\n',IS); fprintf (resl,'\n\n Pressure = %8.2f atm Temperat ure = %8.2f \n\n',P(IS),T(IS)); fprintf (resl,'\n NC Mole Fr Molar flow rate Mass flow rate'); fprintf (resl,'\n kmoles/hr kg/hr\n'); for i=1:NC fprintf (resl,'\n %2.0f %8.4f %8.4f %8.4f ',i,x(i),MolFlRate(i),MassFlRate(i)) end fprintf (resl,'\n \n Total %6.4f %12.4f %12.4f\n',xT,sumMol,sumMas); fprintf (resl,'\n Mol Wt of mixture MWt(%2.0f) = %8.2f kg/kmol \n',IS,MWT(IS)); fprintf (resl,'\n Gas Const of mixture RR (%2.0f) = %8.2f kJ/(kmol-K) ',IS,RR(IS)); fprintf (resl,'\n Molar Flow Rate of Stream %3.0f i s %8.4f kmoles / hr ',IS,TotMolarFlRate(IS)); fprintf (resl,'\n Mass Flow Rate of Stream %3.0f i s %8.4f kg /hr ',IS,TotMassFlRate(IS)); fprintf (resl,'\n --------------------------------- --------------------\n'); % SECTION BEGINS ================================= ==================== % do this section if you want to check manually the orders of magnitude % otherwise remove this section % activities: a_i = y_i * phi_i * P % y_i is the mole fraction which is available above , as x(i) % obtain phi_i from the function % function[phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P ,T,yH2,yN2,yNH3) [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P(IS),T(IS) ,x(1),x(2),x(4)); % now compute the equilibrium constant K % function[Ka] = EQNCN(T) [Ka] = EQNCN(T(IS)); % now find Arrhenius Rate Constant [kArh]= RTCNT(T(IS),R_un);
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% now find reaction rate [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3); [CpH2,CpN2,CpNH3,CpCH4,CpAr] = SPCHT(T(IS),P(IS)); Cp(1) = CpH2; Cp(2) = CpN2; Cp(3) = CpAr; Cp(4)=CpN H3; Cp(5)=CpCH4; jj=1; for j= NC+1:2*NC Cp(j) = Cp(jj)/MW(jj); % kJ/(kg-K) jj=jj+1; end CpMix = 0.0; for ii = 1:NC CpMix = CpMix + Cp(ii+5)*MassFlRate(ii)/TotMassFlRa te(IS); end [HtReact]= DeltaH(P(IS),T(IS)); % X is the height from the top of the catalyst (m) and StepX is the % increment in X fprintf (resl,'\n Test Section output begins ...\n' ); fprintf (resl,'\n Pressure = %6.2f atm Temp = % 6.2f',P(IS),T(IS)); X = 0.0; StepX=0.5; fprintf (resl,'\n X = %6.2f m StepX = %6.2f',X,St epX); Zold = 0; % no N2 has been converted as yet fprintf (resl,'\n Zold = %6.2f',Zold); Told = T(IS); % this is temp at the inlet of this v olume N20 = MolFlRate(2); % kmols/hr of N2 entering this volume element fprintf (resl,'\n N20 = %6.2f kmol/hr ',N20); fprintf (resl,'\n Mdot = %12.4e kg/hr',TotMassFlRat e(IS)); fprintf (resl,'\n Cp = %12.4e kJ/(kg-K) ',CpMix); fprintf (resl,'\n x(1) = %8.4f x(2)=%8.4f x(4 )=%8.4f ',x(1),x(2),x(4)); fprintf (resl,'\n RNH3 = %12.4e kmol/(hr-m^3) ',RNH 3); fprintf (resl,'\n HtReact = %12.4e kJ/kmol ',HtReac t); dZdX = Area*RNH3 /(2.0*N20); dTdX = abs(HtReact)*RNH3*Area/(TotMassFlRate(IS)*Cp Mix); fprintf (resl,'\n\n dZ/dx = %12.4e conversion p er meter',dZdX); fprintf (resl,'\n dT/dx = %12.4e K per meter \n',dTdX); % now use the above gradients to find new values fo r moles of H, N, Ammonia % the volume of this box is now Area * StepX DeltaVolume = Area * StepX; Znew = Zold + dZdX * StepX; Tnew = Told + dTdX * StepX; fprintf (resl,'\n New values Z = %6.2f T = %6. 2f K \n',Znew,Tnew); % now compute new moles and mole fractions % converted moles of N2 delta = Znew * MolFlRate(2); % new mole rates (kmols/hr) and mass flow rates (kg /hr)
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for ik =1:NC MolFlRateOld(ik) = MolFlRate(ik); MassFlRateOld(ik) = MassFlRate(ik); MolFlRateNew(ik) = 0.0; % need to compute this now MassFlRateNew(ik)= 0.0; % need to compute this now xold(ik) = x(ik); % old mole fractions xnew(ik) = 0.0; % new mole fractions end % new totals TotMolarFlRateOld(IS)=TotMolarFlRate(IS); TotMolarFlRateNew(IS)=0.0; TotMoleFrOld=0.0; TotMoleFrNew=0.0; TotMassFlRateOld(IS)=TotMassFlRate(IS); TotMassFlRateNew(IS)=0.0; MolFlRateNew(1) = MolFlRateOld(1) - 3.0* delta; % H 2 MolFlRateNew(2) = MolFlRateOld(2) - 1.0* delta; % N 2 MolFlRateNew(3) = MolFlRateOld(3); % A rgon MolFlRateNew(4) = MolFlRateOld(4) + 2.0* delta; % N H3 MolFlRateNew(5) = MolFlRateOld(5); % C H4 % for ik1 = 1:NC MassFlRateNew(ik1) = MW(ik1) * MolFlRateNew(ik1 ); end for ik2 = 1:NC TotMolarFlRateNew(IS) = TotMolarFlRateNew(IS) + MolFlRateNew(ik2); TotMassFlRateNew(IS) = TotMassFlRateNew(IS) + MassFlRateNew(ik2); end for ik11 = 1:NC xnew(ik11) = MolFlRateNew(ik11)/TotMolarFl RateNew(IS); end for ik12 = 1:NC TotMoleFrOld = TotMoleFrOld + xold(ik12); TotMoleFrNew = TotMoleFrNew + xnew(ik12); end % now write a summary of the change fprintf (resl,'\n\n SUMMARY AFTER CONVERSION in th is volume box Area*StepX \n'); fprintf (resl,'\n BEFORE CONVERSI ON AFTER CONVERSION\n'); fprintf (resl,'\n i MolFlRate mol fr MassFlRate MolFlRate mol fr MassFlRate'); fprintf (resl,'\n kmol/hr kg/hr kmol/hr kg/hr'); for ik3=1:NC
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fprintf (resl,'\n %3.0f %15.4e %8.4f %12.4e %20. 4e %8.4f %12.4e ',ik3,MolFlRateOld(ik3),xold(ik3),MassFlRateOld(ik3 ),MolFlRateNew(ik3),xnew(ik3),MassFlRateNew(ik3)); end fprintf (resl,'\n %21.4e %8.4f %12.4e %21.4e %9.4f %13.4e',TotMolarFlRateOld(IS),TotMoleFrOld,TotMassF lRateOld(IS),TotMolarFlRateNew(IS),TotMoleFrNew,TotMassFlRateNew(IS)); % how much energy is given off in this volume? % mass flow rate is the same before or after so can use either Power = TotMassFlRateOld(IS)*CpMix*(Tnew-Told); % ( kg/hr)*(kJ/kg-K)*(K) = kJ/hr Power = Power/(60*60); % kW fprintf (resl,'\n Power given off in synthesis of a mmonia in this vol element = %12.4e kW\n',Power); fprintf (resl,'\n Test Section ends.............\n\ n\n'); %SECTION ENDS ==================================== === Z=0.0; % N2 conversion percentage start with ) sin ce no N2 is converted at t=0 [Eta1]=ETA(P(IS),T(IS),Z);% fprintf (resl,'\n\n Pressure = %8.2f atm Temperat ure = %8.2f \n',P(IS),T(IS)); %fprintf (resl,'\n Temp phiH2 phiN2 p hiNH3 aH2 aN2 aNH3 Ka kArh RNH3\n '); %fprintf (resl,'\n %6.1f %10.2e %10.2e %10.2e %10.2 e %10.2e %10.2e %10.2e %10.2e %10.2e\n',T(IS),phiH2,phiN2,phiNH3,aH2,aN2,a NH3,Ka,kArh,RNH3); %-------------------------------------------------- -------- % begin RK 4th order for 2 1st-order coupled ODEs fprintf (resl,'\n\n R-K method \n\n'); %Area is defined above FoverA = MolFlRate(2)/Area; % molar flow rate for N itrogen at inlet Z = 0.0; T = T(IS); P = P(IS); ZZ(1)=0.0; % initial value of conversion percentage TT(1)=T; % initial value of temperature (K) Lmin =0.0; Lmax= HghtReactor; % height of the convtr in meters NZONES = 3; NPTZ=10; % 10 meshes in each zone NPTS = NPTZ*NZONES; % 30 meshes total h = (Lmax-Lmin)/NPTS;
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LL(1)=Lmin; for i = 2: NPTS+1 LL(i) = LL(i-1)+h; end LL L = LL(1); i = 1 ; % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane Hmoles(i) = MolFlRate(1); Nmoles(i) = MolFlRate(2); Rmoles(i) = MolFlRate(3); Amoles(i) = MolFlRate(4); Mmoles(i) = MolFlRate(5); TotalMoles(i) = Hmoles(i) + Nmoles(i) + Rmoles(i) + Amoles(i) + Mmoles(i); HmolesFr(i) = Hmoles(i)/TotalMoles(i); % for plotti ng, instead of mole fl rates NmolesFr(i) = Nmoles(i)/TotalMoles(i); AmolesFr(i) = Amoles(i)/TotalMoles(i); AmolesPC(i) = Amoles(i)/TotalMoles(i); % %%%%%%%%%%%%%%% patch added 18 May 2011 %%%%%%% for printout only Tsend = T; TotMassSend = TotMassFlRate(IS); [MWtMixture,CpMixKg,CpMixMo,TotMolarFlRateMix,Moles ,masses]=CpSummary(Tsend,P,x,MW,TotMassSend); CpKg(i) = CpMixKg; % kJ/(kg-K) CpMo(i) = CpMixMo; % kJ/(kmol-K) MWmix(i)= MWtMixture; % kg/kmol MdotCpKT(i) = ((TotMassFlRate(IS))/3600)*CpKg(i)*Ts end; % kg/s * kJ/(kg-K) * K = kW TMFMix(i)=TotMolarFlRateMix; hhh(i)=Moles(1); nnn(i)=Moles(2); rrr(i)=Moles(3); amm(i)=Moles(4); ch4(i)=Moles(5); massh(i)=masses(1); massn(i)=masses(2); massr(i)=ma sses(3); massa(i)=masses(4); massc(i)=masses(5); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end of patch 18 May 2011 %%%%%%%% %%%%%%%%%%%%%% patch added 15 May 2011 % now find, at this point as an initial condition, the equilibrium position Epsilon=0.0; i=1; [Epsilon] = EquilibriumC (P,T,Hmoles(i),Nmoles(i),A moles(i),TotalMoles(i)); HmolesEq(i) = Hmoles(i) - 3.0*Epsilon ; NmolesEq(i) = Nmoles(i) - Epsilon ; RmolesEq(i) = Rmoles(i) ; AmolesEq(i) = Amoles(i) + 2.0*Epsilon ; MmolesEq(i) = Mmoles(i) ; % TotalMolesEq(i) = HmolesEq(i) + NmolesEq(i) + Rmole sEq(i) + AmolesEq(i) + MmolesEq(i);
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AmolesPCEq(i) = AmolesEq(i)/TotalMolesEq(i); TTeps(1) = Epsilon; % now find equilibrium temp [Teqm] = EquilibriumT (x,P,T); TTeqm(i)=Teqm; % what if Teqm is not found? set it to max if (Teqm==0) TTeqm(i)=800.0; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% EachZoneHgt = Lmax/NZONES; LBDRY(1) = 0.0; for ibdry = 2:NZONES+1 LBDRY(ibdry)=LBDRY(ibdry-1)+EachZoneHgt; end LBDRY %%%%%%%%%%%%%%%%%%%%%%%%% CATALYST LOADING %%%%%%%%%%%%%%%%%% fprintf (resl,'\n No of catalyst zones = %2.0f \n', NZONES); frac = [1.5;1.25;1.0]; fprintf (resl,'\n Zone LBDRY Fraction of Catalys t'); for icat = 1:NZONES fprintf (resl,'\n %2.0f %6.2f %6.2f ',icat,LBD RY(icat+1),frac(icat)); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CatFrac = frac(1); % start with the fraction of zon e 1 fprintf (resl,'\n i x(1) x(2) x(3) x(4) x(5) Total Mole Fl Rate'); fprintf (resl,'\n %3.0f %8.4f %8.4f %8.4f %8.4f %8 .4f %15.4e',i,x(1),x(2),x(3),x(4),x(5),TotalMoles(i)); Toptimal(i) = 896.0; NPTS1=NPTS-1; PZ1 = 0; PZ2 =0; PZ3 = 0; % limits of i in zones % in zone 1 i goes from 1 to NPTZ+1 % 2 i NPTZ+1 to 2*NPTZ+1 % 3 i 2*NPTZ+1 to 3*NPTZ+1 iLIM1 = NPTZ+1; iLIM2 = 2*NPTZ+1; iLIM3 = 3*NPTZ+1 ; while (i <= NPTS) %-------------------------------- -- RK4 LOOP BEGINS i; % zone is defined by height from top L if (i<=iLIM1) thisZone = 1;
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LastZone = thisZone; PZ1 = PZ1 +1; % this counter runs from 1 to las t value of PZ1=NPTZ % fprintf (resl,'\n PZ1 = %3.0f ',PZ1); TMB(1,PZ1)=TT(i); LMB(1,PZ1)=LL(i); end if ((i>=iLIM1)&(i<=iLIM2)) thisZone = 2; if (LastZone==1) TT(i)=TT(3); LastZone = thisZone; end PZ2 = PZ2 +1; % this counter runs from 1 to las t value of PZ2 (20) % fprintf (resl,'\n PZ2 = %3.0f ',PZ2); TMB(2,PZ2)=TT(i); LMB(2,PZ2)=LL(i); end if ((i>=iLIM2)&(i<=iLIM3)) thisZone = 3; if (LastZone==2) % TT(i)=TT(2); LastZone = thisZone; end PZ3 = PZ3 +1; % this counter runs from 1 to las t value of PZ3 % fprintf (resl,'\n PZ3 = %3.0f ',PZ3); TMB(3,PZ3)=TT(i); LMB(3,PZ3)=LL(i); end CatFrac = frac(thisZone); %%%%%%%%%%%%%%%%%%%%%%%%%%% k1_z k1_T %%%%%%%%%%%%%%%%%%%% % first function % evaluate RHS of mass conservation equation FUNC1 [Eta1]=ETA(P,T,Z); [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T,x(1),x( 2),x(4)); [Ka] = EQNCN(T); [kArh]= RTCNT(T,R_un); [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3); FUNC1 = Eta1*CatFrac*RNH3/(2.0*FoverA); k1_z = FUNC1; % second function % evaluate RHS of energy conservation equation FUNC 2 [CpH2,CpN2,CpNH3,CpCH4,CpAr] = SPCHT(T,P);
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Cp(1) = CpH2; Cp(2) = CpN2; Cp(3) = CpAr; Cp(4)=CpN H3; Cp(5)=CpCH4; jj=1; for j= NC+1:2*NC Cp(j) = Cp(jj)/MW(jj); % kJ/(kg-K) jj=jj+1; end CpMix = 0.0; for ii = 1:NC CpMix = CpMix + Cp(ii+5)*MassFlRate(ii)/TotMassFlRa te(IS); end [HtReact]= DeltaH(P,T); FUNC2 = ( HtReact * Eta1 * CatFrac*RNH3 ) / ((TotMa ssFlRate(IS)/Area) * CpMix ); k1_T = -FUNC2; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % k2_z k2_P L = LL(i) + h/2. ; Z = ZZ(i) + k1_z * h/2.0; T = TT(i) + k1_T * h/2.0; % first function [Eta1]=ETA(P,T,Z); [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T,x(1),x( 2),x(4)); [Ka] = EQNCN(T); [kArh]= RTCNT(T,R_un); [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3); FUNC1 = Eta1*CatFrac*RNH3/(2.0*FoverA); k2_z = FUNC1; % second function [CpH2,CpN2,CpNH3,CpCH4,CpAr] = SPCHT(T,P); Cp(1) = CpH2; Cp(2) = CpN2; Cp(3) = CpAr; Cp(4)=CpN H3; Cp(5)=CpCH4; jj=1; for j= NC+1:2*NC Cp(j) = Cp(jj)/MW(jj); % kJ/(kg-K) jj=jj+1; end CpMix = 0.0; for ii = 1:NC CpMix = CpMix + Cp(ii+5)*MassFlRate(ii)/TotMassFlRa te(IS); end [HtReact]= DeltaH(P,T); FUNC2 = ( HtReact * Eta1 * CatFrac* RNH3 ) / ((TotM assFlRate(IS)/Area) * CpMix ); k2_T = -FUNC2; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % k3_z k3_P Z = ZZ(i) + k2_z * h/2.0; T = TT(i) + k2_T * h/2.0; % first function [Eta1]=ETA(P,T,Z); [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T,x(1),x( 2),x(4));
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[Ka] = EQNCN(T); [kArh]= RTCNT(T,R_un); [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3); FUNC1 = Eta1*CatFrac* RNH3/(2.0*FoverA); k3_z = FUNC1; % second function [CpH2,CpN2,CpNH3,CpCH4,CpAr] = SPCHT(T,P); Cp(1) = CpH2; Cp(2) = CpN2; Cp(3) = CpAr; Cp(4)=CpN H3; Cp(5)=CpCH4; jj=1; for j= NC+1:2*NC Cp(j) = Cp(jj)/MW(jj); % kJ/(kg-K) jj=jj+1; end CpMix = 0.0; for ii = 1:NC CpMix = CpMix + Cp(ii+5)*MassFlRate(ii)/TotMassFlRa te(IS); end [HtReact]= DeltaH(P,T); FUNC2 = ( HtReact * Eta1 * CatFrac* RNH3 ) / ((TotM assFlRate(IS)/Area) * CpMix ); k3_T = -FUNC2; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % k4_z k4_P L = LL(i) + h; Z = ZZ(i) + k3_z * h; T = TT(i) + k3_T * h; % first function [Eta1]=ETA(P,T,Z); [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T,x(1),x( 2),x(4)); [Ka] = EQNCN(T); [kArh]= RTCNT(T,R_un); [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3); FUNC1 = Eta1*RNH3/(2.0*FoverA); k4_z = FUNC1; % second function [CpH2,CpN2,CpNH3,CpCH4,CpAr] = SPCHT(T,P); Cp(1) = CpH2; Cp(2) = CpN2; Cp(3) = CpAr; Cp(4)=CpN H3; Cp(5)=CpCH4; jj=1; for j= NC+1:2*NC Cp(j) = Cp(jj)/MW(jj); % kJ/(kg-K) jj=jj+1; end CpMix = 0.0; for ii = 1:NC CpMix = CpMix + Cp(ii+5)*MassFlRate(ii)/TotMassFlRa te(IS); end [HtReact]= DeltaH(P,T);
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FUNC2 = ( HtReact * Eta1 * RNH3 ) / ((TotMassFlRate (IS)/Area) * CpMix ); k4_T = -FUNC2; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % get new values for Z, T i = i + 1; ZZ(i) = ZZ(i-1) + (h/6.)*(k1_z + 2.0*k2_z + 2.0*k3_ z + k4_z); TT(i) = TT(i-1) + (h/6.)*(k1_T + 2.0*k2_T + 2.0*k3_ T + k4_T); % if this is the last point, it will not go back, s o store the last point if (i==(NPTS+1)) TMB(3,PZ3+1)=TT(i); LMB(3,PZ3+1)=LL(i); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % update mole fractions % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane ConvertedMolesOfN = ZZ(i)*MolFlRate(2); Hmoles(i) = MolFlRate(1) - 3.0*( ConvertedMolesOfN ) ; Nmoles(i) = (1.0-ZZ(i)) *MolFlRate(2); Rmoles(i) = MolFlRate(3); Amoles(i) = MolFlRate(4) + 2.0*( ConvertedMolesOfN ) ; Mmoles(i) = MolFlRate(5); % TotalMoles(i) = Hmoles(i) + Nmoles(i) + Rmoles(i) + Amoles(i) + Mmoles(i); AmolesPC(i) = Amoles(i)/TotalMoles(i); Power(i-1) = TotMassFlRate(IS)*CpMix*(TT(i)-TT(i-1) ); % (kg/hr)*(kJ/kg.K)*K=kJ/hr Power(i-1) = Power(i-1)/(60*60); % kW % now to go back to the beginning of the loop, set new local parameters % P,T,Z. and also need P, T, x(1), x(2), x(4) for n ext iteration step x(1) = Hmoles(i)/TotalMoles(i); x(2) = Nmoles(i)/TotalMoles(i); x(3) = Rmoles(i)/TotalMoles(i); x(4) = Amoles(i)/TotalMoles(i); x(5) = Mmoles(i)/TotalMoles(i); %%%%%%%%%%%%%%% patch added 18 May 2011 %%%%%%% for printout only Tsend = TT(i); TotMassSend = TotMassFlRate(IS); [MWtMixture,CpMixKg,CpMixMo,TotMolarFlRateMix,Moles ,Masses]=CpSummary(Tsend,P,x,MW,TotMassSend); CpKg(i) = CpMixKg; % kJ/(kg-K) CpMo(i) = CpMixMo; % kJ/(kmol-K) MWmix(i)= MWtMixture; % kg/kmol MdotCpKT(i) = ((TotMassFlRate(IS))/3600)*CpKg(i)*Ts end; % kg/s * kJ/(kg-K) * K = kW TMFMix(i)=TotMolarFlRateMix; hhh(i)=Moles(1); nnn(i)=Moles(2); rrr(i)=Moles(3); amm(i)=Moles(4); ch4(i)=Moles(5); massh(i)=masses(1); massn(i)=masses(2); massr(i)=ma sses(3); massa(i)=masses(4); massc(i)=masses(5); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end of patch 18 May 2011 %%%%%%%%
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MolFlowRate(2) = Nmoles(i); % this is the N2 inlet for the next volume element %FoverA = MolFlRate(2)/Area; % molar flow rate for Nitrogen at inlet % Pressure remains same P=P; T=TT(i); Z=ZZ(i); fprintf (resl,'\n %3.0f %8.4f %8.4f %8.4f %8.4f %8. 4f %15.4e',i,x(1),x(2),x(3),x(4),x(5),TotalMoles(i)); % now go to find optimal temp at this point ------- -------------- 10 may 2011 [Topt] = OptimalT (x,P); Toptimal(i) = Topt; % what if Topt is not found? set it to max if (Topt==0) Toptimal(i)=850.0; end % now go back %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% patch added May 15 2011 % now find equilibrium temp [Teqm] = EquilibriumT (x,P,T); TTeqm(i)=Teqm; % what if Teqm is not found? set it to max if (Teqm==0) TTeqm(i)=800.0; end % now find, at this point as an initial condition, the equilibrium position %HmolesInit=Hmoles(i) %NmolesInit=Nmoles(i) %AmmMolesInit=Amoles(i) %TotMoles=TotalMoles(i) Epsilon=0.0; [Epsilon] = EquilibriumC (P,T,Hmoles(i),Nmoles(i),A moles(i),TotalMoles(i)); TTeps(i) = Epsilon; HmolesEq(i) = Hmoles(i) - 3.0*Epsilon ; NmolesEq(i) = Nmoles(i) - Epsilon ; RmolesEq(i) = Rmoles(i) ; AmolesEq(i) = Amoles(i) + 2.0*Epsilon ; MmolesEq(i) = Mmoles(i) ; % TotalMolesEq(i) = HmolesEq(i) + NmolesEq(i) + Rmole sEq(i) + AmolesEq(i) + MmolesEq(i); HmolesFr(i) = Hmoles(i)/TotalMoles(i); % for plotti ng, instead of mole fl rates NmolesFr(i) = Nmoles(i)/TotalMoles(i); AmolesFr(i) = Amoles(i)/TotalMoles(i); AmolesPCEq(i) = AmolesEq(i)/TotalMolesEq(i); % now to go back to the beginning of the loop, set new local parameters % P,T,Z. and also need P, T, x(1), x(2), x(4) for n ext iteration step
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%xEq(1) = HmolesEq(i)/TotalMolesEq(i); %xEq(2) = NmolesEq(i)/TotalMolesEq(i); %xEq(4) = AmolesEq(i)/TotalMolesEq(i); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end of patch added on May 13, 2011 %%%%%%%%%%%%% patch entered on 17 may 2011 % compute new mass fractions since Cp changes % stream computation............................... ........ %%%%%%%%%%%%% end of patch 17 may 2011 %%%%%%%%%%%%%%%%%% end % ------------------------------------- RK4 LOOP ENDS fprintf (resl,'\n\n i Toptimal Tequilibrium Epsilon'); for i2 = 1:NPTS+1 fprintf (resl,'\n %3.0f %8.2f %8.2f %12.4e',i2,Toptimal(i2),TTeqm(i2),TTeps(i2)); end fprintf (resl,'\n\n\n Summary of RK numerical solut ion \n \n \n'); fprintf (resl,'\n Moles Conversion % of N \n'); fprintf (resl,'\n i L H2 N2 Ar NH3 CH4 Total Z T Topt\n'); for i = 1: NPTS+1 fprintf (resl,'\n %3.0f %6.4f %8.4f %8.4f % 8.4f %8.4f %8.4f %10.4f %6.4f %6.2f %6.2f',i,LL(i),Hmoles(i),Nmoles(i),Rmoles(i),Amoles (i),Mmoles(i),TotalMoles(i),ZZ(i),TT(i),Toptimal(i)); end fprintf (resl,'\n\n\n Summary of Molar Quantities computed from CpSummary '); fprintf (resl,'\n i L H2 N2 Ar NH3 CH4 Total Z T CpKg CpMo MWtMix Power k W\n'); for i = 1: NPTS+1 fprintf (resl,'\n %2.0f %4.3f %8.4f %8.4f %8.4 f %8.4f %8.4f %10.4f %6.4f %6.2f %6.2f %6.2f %6.2f %6.2f',i,LL(i),hhh(i),nnn(i),rrr(i),amm(i),ch4(i),T MFMix(i),ZZ(i),TT(i),CpKg(i),CpMo(i),MWmix(i),MdotCpKT(i)); end % temps in each catalyst bed % straight line between x = LMB(1,20), y =TMB(1,20) % and x = LMB(2,1) , y =TMB(2,1) xSt12(1) = LMB(1,iLIM1); ySt12(1) = TMB(1,iLIM1); xSt12(2) = LMB(2,1) ; ySt12(2) = TMB(2,1); % straight line between x = LMB(2,20), y =TMB(2,20) % and x = LMB(3,1) , y =TMB(3,1) xSt23(1) = LMB(2,NPTZ+1); ySt23(1) = TMB(2,NPTZ+1); xSt23(2) = LMB(3,1) ; ySt23(2) = TMB(3,1);
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LMB; TMB; for ibed = 1: 3 fprintf (resl,'\n Bed no: %2.0f ',ibed); fprintf (resl,'\n j Length Temp '); for ip1 = 1:NPTZ+1 fprintf (resl,'\n %3.0f %9.3f %9.3f',ip1,LMB(ibed,ip1),TMB(ibed,ip1)); end end for ip1=1:NPTZ+1 LMB1(ip1) = LMB(1,ip1); LMB2(ip1) = LMB(2,ip1); LMB3(ip1) = LMB(3,ip1); TMB1(ip1) = TMB(1,ip1); TMB2(ip1) = TMB(2,ip1); TMB3(ip1) = TMB(3,ip1); end % Power available from exothermic reactions fprintf (resl,'\n\n\n\n i Power (kW)\n'); sumPower =0.0; for i = 1: NPTS1 fprintf (resl,'\n %3.0f %12.4e ',i,Power(i)); sumPower=sumPower+Power(i); end fprintf (resl,'\n total exothermic energy available is %12.4e kW ',sumPower); Power = TotMassFlRateOld(IS)*CpMix*(Tnew-Told); % ( kg/hr)*(kJ/kg-K)*(K) = kJ/hr Power = Power/(60*60); % kW fprintf (resl,'\n Power given off in synthesis of a mmonia in this vol element = %12.4e kW\n',Power); % Energy Available between 1st and 2nd bed TempBed1 = TMB(1,NPTZ+1); fprintf(resl,'\n Exit Temp from 1st Bed = %8.2f K\n ',TempBed1); fprintf(resl,'\n i Cp kJ/(kg-K) Mass Fl R ate(i) kg/hr'); CpMix1 = 0.0; for ii = 1:NC CpMix1 = CpMix1 + Cp(ii+5)*MassFlRate(ii)/TotMassFl Rate(IS); fprintf(resl,'\n %3.0f %8.2f %8.2f',ii,Cp(ii +5),MassFlRate(ii)); end fprintf(resl,'\n Total Mass Flow Rate = %12.2f kg/h r',TotMassFlRate(IS)); fprintf(resl,'\n Cp Mixture = %8.2f kJ/kg-K',CpMix1 ); HeatValue1 = (1./3600)*TotMassFlRate(IS)*CpMix1*Tem pBed1 ; fprintf (resl,'\n Power Value 1 = %12.4e kW',HeatV alue1); TempBed2 = TMB(2,1); fprintf(resl,'\n\n Exit Temp from 2nd Bed = %8.2f K \n',TempBed2); fprintf(resl,'\n i Cp kJ/(kg-K) Mass Fl R ate(i) kg/hr'); CpMix2 = 0.0; for ii = 1:NC CpMix2 = CpMix2 + Cp(ii+5)*MassFlRate(ii)/TotMassFl Rate(IS);
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fprintf(resl,'\n %3.0f %8.2f %8.2f',ii,Cp(ii +5),MassFlRate(ii)); end fprintf(resl,'\n Total Mass Flow Rate = %12.2f kg/h r',TotMassFlRate(IS)); fprintf(resl,'\n Cp Mixture = %8.2f kJ/kg-K',CpMix2 ); HeatValue2 = (1./3600)*TotMassFlRate(IS)*CpMix2*Tem pBed2 ; fprintf (resl,'\n Power Value 2 = %12.4e kW ',HeatV alue2); PowerExtracted = HeatValue1 - HeatValue2; fprintf (resl,'\n\n Power Extracted = %12.4e kW',Po werExtracted); InletTemp LL ZZ ThisPlot=4; if (ThisPlot==1) plot (LL,ZZ,'-k') grid on xlabel ('Distance (m)') ylabel ('Conversion of N_2 (Z)') xlim([0 HghtReactor]) % title 'Conversion of N_2 in the synthesis co nvertor' end if (ThisPlot==2) % plot (LL,TT,'-k') plot (LMB1,TMB1,'-k') hold on plot(xSt12,ySt12,'-k') hold on plot (LMB2,TMB2,'-k') hold on plot(xSt23,ySt23,'-k') hold on plot (LMB3,TMB3,'-k') hold on % now plot the optimal temp on this % plot (LL,Toptimal,'-k'); % hold on % plot (LL,TTeqm,'--k') grid on xlabel ('Distance (m)') ylabel ('Temperature (K)') title 'Temperature in synthesis convertor' end if (ThisPlot==3) %plot (LL,Hmoles,'-k') plot (LL,HmolesFr,'-k') hold on %plot (LL,Nmoles,'-.k')
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plot (LL,NmolesFr,'-k') hold on %plot (LL,Amoles,'--k') plot (LL,AmolesFr,'-k') xlabel ('Distance (m)') % ylabel ('Molar Flow Rate (kmols/hr)') ylabel ('Molar Fraction)') h = legend('H_2','N_2','NH_3',2); %title 'Molar flow rate of H_2, N_2 and NH_3 in convertor' title 'Molar fractions in convertor' end if (ThisPlot==4) subplot(2,2,1:2) % plot (LL,AmolesPC,'-k') % xlabel ('Distance (m)') % ylabel ('Ammonia Mole Fr') % grid on % title 'Mole % NH_3' plot (LL,ZZ,'-k') xlim([0 HghtReactor]) % ylim([0 0.301]) grid on xlabel ('Distance (m)') ylabel ('Conversion of N_2 (Z)') % title 'Conversion of N_2 in the synthesis c onvertor' subplot(2,2,3) % plot (LL,TT,'-k') plot (LMB1,TMB1,'-k') hold on plot(xSt12,ySt12,'-k') hold on plot (LMB2,TMB2,'-k') hold on plot(xSt23,ySt23,'-k') hold on plot (LMB3,TMB3,'-k') hold on % now plot the optimal temp on this plot (LL,Toptimal,'-k'); hold on plot (LL,TTeqm,'--k') grid on text (0.3,750,'T_{opt}'); text (0.5,850,'T_{eqm}'); xlim([0 HghtReactor]) %ylim([600 1000]) xlabel ('Distance (m)') ylabel ('Temperature (K)') % title 'Temperature' subplot(2,2,4) %plot (LL,Hmoles,'-k') plot (LL,HmolesFr,'-k') hold on
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%plot (LL,Nmoles,'-.k') plot (LL,NmolesFr,'-.k') hold on %plot (LL,Amoles,'--k') plot (LL,AmolesFr,'--k') grid on xlim([0 HghtReactor]) xlabel ('Distance (m)') % ylabel ('Molar Flow Rate (kmols/hr)') ylabel ('Molar Fraction') h = legend('H_2','N_2','NH_3',2); %title 'Molar flow rate of H_2, N_2 and NH_3 in convertor' %title 'Molar fractions in convertor' end if (ThisPlot==5) subplot(2,1,1) % plot (LL,TT,'-k') plot (LMB1,TMB1,'-k') hold on plot(xSt12,ySt12,'-k') hold on plot (LMB2,TMB2,'-k') hold on plot(xSt23,ySt23,'-k') hold on plot (LMB3,TMB3,'-k') hold on % now plot the optimal temp on this plot (LL,Toptimal,'-k'); hold on plot (LL,TTeqm,'--k') grid on text (0.15,810,'T_{opt}'); text (0.62,870,'T_{eqm}'); xlim([0 HghtReactor]) %ylim([600 1000]) xlabel ('Distance (m)') ylabel ('Temperature (K)') % title 'Temperature' subplot(2,1,2) %plot (LL,Hmoles,'-k') plot (LL,HmolesFr,'-k') hold on %plot (LL,Nmoles,'-.k') plot (LL,NmolesFr,'-.k') hold on %plot (LL,Amoles,'--k') plot (LL,AmolesFr,'--k') grid on xlim([0 HghtReactor]) xlabel ('Distance (m)') % ylabel ('Molar Flow Rate (kmols/hr)') ylabel ('Mole Fraction') h = legend('H_2','N_2','NH_3',2);
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%title 'Molar flow rate of H_2, N_2 and NH_3 in convertor' %title 'Molar fractions in convertor' end toc fclose(resl)
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APPENDIX B5: MATLAB ™ PROGRAM FOR FINDING OPTIMAL
TEMPERATURE This section lists the Program MansonOneEqn and its function OptimalT
% Program Name: MansonOneEqn % Steady State Ammonia Thermal Stora ge % % C:\MATLAB7\work\Ammonia\MansonOneEqn.m % % First Written: JULY 2010 % Last Update: Oct 19 2011 % open output file resl=fopen('outm.txt','w'); % INPUT and STREAM OUT PUT tic fprintf (resl,'\n MansonOneEqn.m \n'); fprintf (resl,'\n MansonOneEqn.m \n'); fprintf (resl,'\n MansonOneEqn.m \n'); fprintf (resl,'\n MansonOneEqn.m \n'); fprintf (resl,'\n MansonOneEqn.m \n'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % program parameters NC = 5; % number of components, H2,N2,NH3,Ar,CH4 fprintf (resl,'\n No. of Components = %3.0f \n',NC) ; R_un = 8.314472; % universal gas const J/(mol-K) fprintf (resl,'\n Universal Gas Const = %12.6f kJ/ (mol-K)\n',R_un); % chemical data from http://www-jmg.ch.cam.ac.uk/tools/magnus/PeriodicTable.html % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane MW1=2.0*1.0079759; MW2=2.0*14.0067231; MW3= 39.9476 613; MW4=(14.0067231+3.0*1.0079759); MW5 = (12.0110369+4 .0*1.0079759); MW = [ MW1;MW2;MW3;MW4;MW5 ]; fprintf (resl,'\n ID Name Mol Wt (kg/kmol)\n') ; fprintf (resl,'\n 1 Hydrogen %8.4f ',MW(1)); fprintf (resl,'\n 2 Nitrogen %8.4f ',MW(2)); fprintf (resl,'\n 3 Argon %8.4f ',MW(3)); fprintf (resl,'\n 4 Ammonia %8.4f ',MW(4)); fprintf (resl,'\n 5 Methane %8.4f ',MW(5)); fprintf (resl,'\n ----------------------------\n'); % STREAM INPUT P = 150.0; % atm P_SIunits = P*1.0e5; %Pascals TotMassFlRate = 183600; % kg/hr Dashti p.20 % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane x= [ 0.6567006; 0.2363680; 0.0202874; 0.026930; 0.0 59714]; % mole fractions % x= [ 0.75; 0.235 ; 0.0 ; 0.015; 0.0]; % mole frac tions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [Topt] = OptimalT (x,P); Toptimal(1) = Topt; % what if Topt is not found? set it to max if ((Topt==0)|(Topt>800))
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Toptimal(1)=780.0; end T=Toptimal(1); TT(1)=T; % for plotting Teqm=0; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% patch added May 13 2011 % now find equilibrium temp [Teqm] = EquilibriumT (x,P,T); TTeqm(1)=Teqm; % what if Teqm is not found? set it to max if (Teqm==0) TTeqm(1)=780.0; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end of patch added on May 13, 2011 Area = 20.0 ; % cross-section area of catalyst m^2 fprintf (resl,'\n Area = %6.2f m^2',Area); HghtReactor = 4.50; % meters VolCatalyst = Area * HghtReactor; fprintf (resl,'\n Vol of catalyst = %6.3f m^3 \n',V olCatalyst); % stream computation............................... ........ MWt = 0.0; % average molecular weight of stream xT = 0.0; % total mol fr. this is should add up to 1.0 for i = 1:NC MWt=MWt+x(i)*MW(i); xT = xT +x(i); end RR = R_un/MWt; % gas constant for this stream (gas) MolarFlRateMix = TotMassFlRate/MWt; % in kmols/hr TotMolarFlRate = TotMassFlRate/MWt; % kmoles per hr mfrT=0.0; mfmT=0.0; for jk=1:NC mfr(jk) = x(jk)*MolarFlRateMix; mfrT = mfrT + mfr(jk); mfm(jk) = mfr(jk)*MW(jk); mfmT = mfmT + mfm(jk); end % end of stream computation........................ ....... % % STREAM OUTPUT fprintf (resl,'\n --------------------------------- --------------------\n'); fprintf (resl,'\n NC Mole Fr Molar flow rate Mass flow rate'); fprintf (resl,'\n kg-mols/hr kg/hr\n'); for i=1:NC fprintf (resl,'\n %2.0f %8.4f %8.4f %8.4f ',i,x(i),mfr(i),mfm(i)) end fprintf (resl,'\n \n Total %6.4f %12.4f %12. 4f\n',xT,mfrT,mfmT); fprintf (resl,'\n Mol Wt of mixture MWt = %8.4f kg/kmol \n',MWt); fprintf (resl,'\n Gas Const of mixture RR = %8.4f kJ/(kmol-K) \n',RR); fprintf (resl,'\n Molar Flow Rate of Stream is %8.2 f kmoles / hr \n',MolarFlRateMix);
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fprintf (resl,'\n --------------------------------- --------------------\n'); % make the mixture Cp, Cv and gamma CpMix = 0.0; RMix = 0.0; % find the Cp values at this temp T1 and press P [CpH2,CpN2,CpNH3,CpCH4,CpAr] = SPCHT(T,P); % kJ/(km ol-K) Cp(1) = CpH2; Cp(2) = CpN2; Cp(3) = CpAr; Cp(4)=CpN H3; Cp(5)=CpCH4; jj=1; for j= NC+1:2*NC Cp(j) = Cp(jj)/MW(jj); % kJ/(kg-K) jj=jj+1; end fprintf (resl,'\n --------------------------------- --------\n'); fprintf (resl,'\n Cp values from function SPCHT at T = %8.2f K and P = %6.2f atm\n',T,P); fprintf (resl,'\n Component Cp kJ/(kmol-K) kJ/( kg-K)\n'); fprintf (resl,'\n 1 Hydrogen %12.4e %12.4e ',Cp(1 ),Cp(6)); fprintf (resl,'\n 2 Nitrogen %12.4e %12.4e ',Cp(2 ),Cp(7)); fprintf (resl,'\n 3 Argon %12.4e %12.4e ',Cp(3 ),Cp(8)); fprintf (resl,'\n 4 Ammonia %12.4e %12.4e ',Cp(4 ),Cp(9)); fprintf (resl,'\n 5 Methane %12.4e %12.4e ',Cp(5 ),Cp(10)); fprintf (resl,'\n --------------------------------- ---------\n'); for i = 1:NC % individual gas constants Rg(i) = R_un/MW(i); %RMix = RMix + Rg(i)*mfr(i)/mfrT; RMix = RMix + R_un*mfr(i)/mfrT; % kJ/(kmol-K) CpMix = CpMix + Cp(i)*mfr(i)/mfrT; % kJ/(kmol-K) end CvMix = CpMix - RMix; GammaMix = CpMix/CvMix; fprintf (resl,'\n Mixture properties (based on mass ratios)\n'); fprintf (resl,'\n CpMix CvMix RMix GammaMix\n'); fprintf (resl,'\n %12.4e %12.4e %12.4e % 8.2f \n',CpMix,CvMix,RMix,GammaMix); sumMol = 0.0; sumMas = 0.0; for j=1:NC MolFlRate(j) = x(j) * TotMolarFlRate; % kmol/hr sumMol = sumMol + MolFlRate(j); MassFlRate(j)= MolFlRate(j) * MW(j); % kmol/hr * k g/kmol = kg/hr sumMas = sumMas + MassFlRate(j); end % STREAM OUTPUT fprintf (resl,'\n --------------------------------- --------------------\n'); fprintf (resl,'\n\n Pressure = %8.2f atm Temperat ure = %8.2f \n\n',P,T); fprintf (resl,'\n NC Mole Fr Molar flow rate Mass flow rate'); fprintf (resl,'\n kmoles/hr kg/hr\n'); for i=1:NC fprintf (resl,'\n %2.0f %8.4f %8.2f %8.2f ',i,x(i),MolFlRate(i),MassFlRate(i)) end
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fprintf (resl,'\n \n Total %6.4f %12.4f %12.4f\n',xT,sumMol,sumMas); fprintf (resl,'\n Mol Wt of mixture MWt = %8.2f kg/kmol \n',MWt); fprintf (resl,'\n Gas Const of mixture RR = %8.2f kJ/(kmol-K) ',RR); fprintf (resl,'\n Molar Flow Rate of Stream is %8.2 f kmoles / hr ',TotMolarFlRate); fprintf (resl,'\n Mass Flow Rate of Stream is %8.2 f kg /hr ',TotMassFlRate); fprintf (resl,'\n --------------------------------- --------------------\n'); Z=0.0; % N2 conversion percentage start with ) sin ce no N2 is converted at t=0 [Eta1]=ETA(P,T,Z);% fprintf (resl,'\n\n Pressure = %8.2f atm Temperat ure = %8.2f \n',P,T); %-------------------------------------------------- -------- % begin RK 4th order for 1st-order coupled ODE fprintf (resl,'\n\n R-K method \n\n'); FoverA = MolFlRate(2)/Area; % molar flow rate for N itrogen at inlet Z = 0.0; ZZ(1)=0.0; % initial value of conversion percentage Toptimal(1)=T; TT(1)=T; % for plotting Lmin =0.0; Lmax= HghtReactor; % height of the convtr in meters NPTS = 20 ; % meshes total h = (Lmax-Lmin)/NPTS; LL(1)=Lmin; for i = 2: NPTS+1 LL(i) = LL(i-1)+h; end LL L = LL(1); i = 1 ; % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane Hmoles(i) = MolFlRate(1); Nmoles(i) = MolFlRate(2); Rmoles(i) = MolFlRate(3); Amoles(i) = MolFlRate(4); Mmoles(i) = MolFlRate(5); TotalMoles(i) = Hmoles(i) + Nmoles(i) + Rmoles(i) + Amoles(i) + Mmoles(i); HmolesFr(i) = Hmoles(i)/TotalMoles(i); % for plotti ng, instead of mole fl rates NmolesFr(i) = Nmoles(i)/TotalMoles(i); AmolesFr(i) = Amoles(i)/TotalMoles(i); AmolesPC(i) = Amoles(i)/TotalMoles(i); fprintf (resl,'\n i x(1) x(2) x(4) Total Mole Fl Rate'); fprintf (resl,'\n %3.0f %8.4f %8.4f %8.4f %15.4e',i,x(1),x(2),x(4),TotalMoles(i));
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%%%%%%%%%%%%%% patch added 15 May 2011 % now find, at this point as an initial condition, the equilibrium position Epsilon=0.0; i=1; [Epsilon] = EquilibriumC (P,T,Hmoles(i),Nmoles(i),A moles(i),TotalMoles(i)) HmolesEq(i) = Hmoles(i) - 3.0*Epsilon ; NmolesEq(i) = Nmoles(i) - Epsilon ; RmolesEq(i) = Rmoles(i) ; AmolesEq(i) = Amoles(i) + 2.0*Epsilon ; MmolesEq(i) = Mmoles(i) ; % TotalMolesEq(i) = HmolesEq(i) + NmolesEq(i) + Rmole sEq(i) + AmolesEq(i) + MmolesEq(i); AmolesPCEq(i) = AmolesEq(i)/TotalMolesEq(i); NmolesPCEq(i) = NmolesEq(i)/TotalMolesEq(i); TTeps(1) = Epsilon; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CatFrac = 1.0; NPTS1=NPTS-1; while (i <= NPTS) %-------------------------------- -- RK4 LOOP BEGINS i %%%%%%%%%%%%%%%%%%%%%%%%%%% k1_z %%%%%%%%%%%%%%%%%%%% % first function % evaluate RHS of mass conservation equation FUNC1 [Eta1]=ETA(P,T,Z); [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T,x(1),x( 2),x(4)); [Ka] = EQNCN(T); [kArh]= RTCNT(T,R_un); [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3); FUNC1 = Eta1*CatFrac*RNH3/(2.0*FoverA); k1_z = FUNC1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % k2_z k2_P L = LL(i) + h/2. ; Z = ZZ(i) + k1_z * h/2.0; % first function [Eta1]=ETA(P,T,Z); [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T,x(1),x( 2),x(4)); [Ka] = EQNCN(T); [kArh]= RTCNT(T,R_un); [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3); FUNC1 = Eta1*CatFrac*RNH3/(2.0*FoverA); k2_z = FUNC1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % k3_z k3_P Z = ZZ(i) + k2_z * h/2.0; % first function [Eta1]=ETA(P,T,Z); [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T,x(1),x( 2),x(4)); [Ka] = EQNCN(T); [kArh]= RTCNT(T,R_un); [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3);
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FUNC1 = Eta1*CatFrac* RNH3/(2.0*FoverA); k3_z = FUNC1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % k4_z L = LL(i) + h; Z = ZZ(i) + k3_z * h; % first function [Eta1]=ETA(P,T,Z); [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T,x(1),x( 2),x(4)); [Ka] = EQNCN(T); [kArh]= RTCNT(T,R_un); [RNH3]=RRATE(kArh,Ka,aH2,aN2,aNH3); FUNC1 = Eta1*RNH3/(2.0*FoverA); k4_z = FUNC1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % get new values for Z i = i + 1; ZZ(i) = ZZ(i-1) + (h/6.)*(k1_z + 2.0*k2_z + 2.0*k3_ z + k4_z); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % update mole fractions % component ID: 1 : H2 2: N2 3: Ar 4: Amm onia 5:Methane ConvertedMolesOfN = ZZ(i)*MolFlRate(2); Hmoles(i) = MolFlRate(1) - 3.0*( ConvertedMolesOfN ) ; Nmoles(i) = (1.0-ZZ(i)) *MolFlRate(2); Rmoles(i) = MolFlRate(3); Amoles(i) = MolFlRate(4) + 2.0*( ConvertedMolesOfN ) ; Mmoles(i) = MolFlRate(5); % TotalMoles(i) = Hmoles(i) + Nmoles(i) + Rmoles(i) + Amoles(i) + Mmoles(i); HmolesFr(i) = Hmoles(i)/TotalMoles(i); % for plotti ng, instead of mole fl rates NmolesFr(i) = Nmoles(i)/TotalMoles(i); AmolesFr(i) = Amoles(i)/TotalMoles(i); AmolesPC(i) = Amoles(i)/TotalMoles(i); NmolesPC(i) = Nmoles(i)/TotalMoles(i); % now to go back to the beginning of the loop, set new local parameters % P,T,Z. and also need P, T, x(1), x(2), x(4) for n ext iteration step x(1) = Hmoles(i)/TotalMoles(i); x(2) = Nmoles(i)/TotalMoles(i); x(4) = Amoles(i)/TotalMoles(i); MolFlowRate(2) = Nmoles(i); % this is the N2 inlet for the next volume element FoverA = MolFlRate(2)/Area; % molar flow rate for N itrogen at inlet Z=ZZ(i); fprintf (resl,'\n %3.0f %8.4f %8.4f %8.4f %15.4e',i,x(1),x(2),x(4),TotalMoles(i)); [Topt] = OptimalT (x,P); Toptimal(i) = Topt; % what if Topt is not found? set it to max if (Topt==0) Toptimal(i)=800.0; end
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% now go back T=Toptimal(i); TT(i)=T; % for plotting T %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% patch added May 13 2011 % now find equilibrium temp [Teqm] = EquilibriumT (x,P,T); TTeqm(i)=Teqm; % what if Teqm is not found? set it to max if (Teqm==0) TTeqm(i)=800.0; end % now find, at this point as an initial condition, the equilibrium position %HmolesInit=Hmoles(i) %NmolesInit=Nmoles(i) %AmmMolesInit=Amoles(i) %TotMoles=TotalMoles(i) Epsilon=0.0; [Epsilon] = EquilibriumC (P,T,Hmoles(i),Nmoles(i),A moles(i),TotalMoles(i)) TTeps(i) = Epsilon; HmolesEq(i) = Hmoles(i) - 3.0*Epsilon ; NmolesEq(i) = Nmoles(i) - Epsilon ; RmolesEq(i) = Rmoles(i) ; AmolesEq(i) = Amoles(i) + 2.0*Epsilon ; MmolesEq(i) = Mmoles(i) ; % TotalMolesEq(i) = HmolesEq(i) + NmolesEq(i) + Rmole sEq(i) + AmolesEq(i) + MmolesEq(i); AmolesPCEq(i) = AmolesEq(i)/TotalMolesEq(i); NmolesPCEq(i) = NmolesEq(i)/TotalMolesEq(i); % now to go back to the beginning of the loop, set new local parameters % P,T,Z. and also need P, T, x(1), x(2), x(4) for n ext iteration step %xEq(1) = HmolesEq(i)/TotalMolesEq(i); %xEq(2) = NmolesEq(i)/TotalMolesEq(i); %xEq(4) = AmolesEq(i)/TotalMolesEq(i); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% end of patch added on May 13, 2011 end % ------------------------------------- RK4 LOOP ENDS fprintf (resl,'\n\n i Toptimal Tequilibrium Epsilon'); for i2 = 1:NPTS+1 fprintf (resl,'\n %3.0f %8.2f %8.2f %12.4e',i2,Toptimal(i2),TTeqm(i2),TTeps(i2)); end Toptimal TTeqm fprintf (resl,'\n\n\n Summary of RK numerical solut ion'); fprintf (resl,'\n Moles Conversion % of N \n');
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fprintf (resl,'\n i L H2 N2 Ar NH3 CH4 Total Z T \n'); for i = 1: NPTS+1 fprintf (resl,'\n %3.0f %6.4f %8.2f %8.2f % 8.2f %8.2f %8.2f %10.2f %8.4f %8.2f',i,LL(i),Hmoles(i),Nmoles(i),Rmoles(i),Amoles (i),Mmoles(i),TotalMoles(i),ZZ(i),TT(i)); end %------------------- sept 4 2011 ------------------ ---- LLHom = [0;0.15;0.30;0.45;0.60;0.75;0.90;1.05;1.20;1.35;1.5 0;1.65;1.80;1.95;2.10;2.25;2.40;2.55;2.70;2.85;3.00;3.15;3.30;3.45;3.60;3.7 5;3.90;4.05;4.20;4.35;4.50]; NmolesHom = [0.2364;0.2349;0.2332;0.2312;0.2289;0.2262;0.2233;0 .2202;0.2174;0.2153;0.2142;0.2132;0.2121;0.2109;0.2097;0.2085;0.2073;0.2062 ;0.2051;0.2041;0.2032;0.2025;0.2020;0.2015;0.2012;0.2009;0.2008;0.2007;0.20 06;0.2005;0.2005]; fprintf (resl,'\n Comparison of Optimal, Equilibriu m from this program, and Normal from SSATS_NonUnif'); fprintf (resl,'\n i L Nopt Neq ' ); for izzz = 1:NPTS+1 fprintf (resl,'\n %3.0f %6.4f %8.4f %8.4f',izzz,LL(izzz),NmolesPC(izzz),NmolesPCEq(izzz )); end fprintf (resl,'\n i L Nhom'); for izzz = 1:31 fprintf (resl,'\n %3.0f %6.4f %8.4f ',izzz,LLHom(izzz),NmolesHom(izzz)); end %%%%%%%%%%----------------------------------------- ----- ThisPlot=5; if (ThisPlot==1) plot (LL,ZZ,'-k') xlabel ('Distance (m)') ylabel ('Conversion of N_2 (Z)') title 'Conversion of N_2 in the synthesis con vertor' end if (ThisPlot==2) plot (LL,TT,'-k') xlabel ('Distance (m)') ylabel ('Temperature (K)') title 'Temperature in synthesis convertor' end if (ThisPlot==3) plot (LL,Hmoles,'-k') hold on plot (LL,Nmoles,'-.k') hold on plot (LL,Amoles,'--k')
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xlabel ('Distance (m)') ylabel ('Molar Flow Rate (kmols/hr)') h = legend('H_2','N_2','NH_3',2); title 'Molar flow rate of H_2, N_2 and NH_3 i n convertor' end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if (ThisPlot==4) subplot(2,2,1:2) % plot (LL,AmolesPC,'-k') plot (LL,NmolesPC,'-k') xlabel ('Distance (m)') ylabel ('Mole Fraction N_2') % title 'Optimal Conversion of N_2 in the synt hesis convertor' hold on %plot (LL,AmolesPCEq,'--k') plot (LL,NmolesPCEq,'-k') % now get the results from SSATS_NonUnif (hom cas e) and paste the Nmoles % from a simple run, to compare with the optimal and eqm Nmoles obtained % in this prog hold on plot (LLHom,NmolesHom,'-k') xlim([0.25 4.5]) text (3.1,0.24,'{N_2}_{,hom}'); text (2.1,0.21,'{N_2}_{,opt}'); text (1.1,0.19,'{N_2}_{,eqm}'); % h = legend('opt','eqm',2); % xlabel ('Distance (m)') % ylabel ('Ammonia Mole Fr') grid on % title 'Mole % NH_3' subplot(2,2,3) % plot the optimal temp plot (LL,TT,'-k') hold on % plot the eqm temp plot (LL,TTeqm,'-k') %h = legend('opt','eqm',2); text (0.3,730,'T_{opt}'); text (1.5,800,'T_{eqm}'); grid on xlim([0.2 4.5]) xlabel ('Distance (m)') ylabel ('Temperature (K)') % title 'Temperature' subplot(2,2,4) % plot (LL,Hmoles,'-k') plot (LL,HmolesFr,'-k') hold on xlim([0.225 4.51]) %plot (LL,Nmoles,'-.k')
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plot (LL,NmolesFr,'-.k') hold on %plot (LL,Amoles,'--k') plot (LL,AmolesFr,'--k') xlabel ('Distance (m)') %ylabel ('Molar Flow Rate (kmols/hr)') ylabel ('Optimal Mole Fraction') h = legend('H_2','N_2','NH_3',2); grid on % title 'Mol fl rate of H_2, N_2 and NH_3' end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if (ThisPlot==5) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % these are the results for runs below %run C:\MATLAB7\work\Ammonia\SSATS_NonUnif_2Sept201 1 % cat distribution 1 1 1 Length = [0;0.1500;0.3000;0.4500;0.6000;0.7500;0.9000;1.0500 ;1.2000;1.3500;1.5000;1.6500;1.8000;1.9500;2.1000;2.2500;2.4000;2.5500;2.70 00;2.8500;3.0000;3.1500;3.3000;3.4500;3.6000;3.7500;3.9000;4.0500;4.2000;4. 3500;4.5000]; NmolesFr1 = [0.2364;0.2349;0.2332;0.2312;0.2289;0.2262;0.2233;0 .2202;0.2174;0.2153;0.2142;0.2132;0.2121;0.2109;0.2097;0.2085;0.2073;0.2062 ;0.2051;0.2041;0.2032;0.2026;0.2019;0.2013;0.2006;0.2000;0.1993;0.1986;0.19 79;0.1973;0.1966]; AmolesFr1 = [0.0269;0.0325;0.0392;0.0470;0.0560;0.0664;0.0780;0 .0900;0.1009;0.1089;0.1133;0.1172;0.1215;0.1261;0.1307;0.1354;0.1401;0.1446 ;0.1488;0.1526;0.1560;0.1585;0.1610;0.1635;0.1661;0.1687;0.1714;0.1740;0.17 66;0.1792;0.1817]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1.10 1.00 1.00 NmolesFr2 =[0.2364;0.2348;0.2329;0.2306;0.2279;0.2249;0.2215; 0.2183;0.2157;0.2143;0.2137;0.2128;0.2116;0.2105;0.2093;0.2081;0.2069;0.205 8;0.2047;0.2038;0.2030;0.2023;0.2017;0.2010;0.2003;0.1997;0.1990;0.1983;0.1 977;0.1970;0.1964]; AmolesFr2 =[0.0269;0.0331;0.0405;0.0494;0.0598;0.0717;0.0848; 0.0974;0.1073;0.1129;0.1152;0.1189;0.1233;0.1278;0.1325;0.1371;0.1417;0.146 1;0.1503;0.1539;0.1571;0.1596;0.1621;0.1647;0.1672;0.1698;0.1725;0.1751;0.1 777;0.1802;0.1827]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1.20 1.00 1.00 NmolesFr3 =[0.2364;0.2346;0.2325;0.2299;0.2269;0.2234;0.2198; 0.2166;0.2146;0.2138;0.2135;0.2126;0.2114;0.2102;0.2090;0.2078;0.2066;0.205 5;0.2045;0.2036;0.2028;0.2022;0.2015;0.2009;0.2002;0.1995;0.1989;0.1982;0.1 975;0.1969;0.1963]; AmolesFr3 =[0.0269;0.0337;0.0420;0.0519;0.0638;0.0773;0.0916; 0.1040;0.1118;0.1150;0.1
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159;0.1196;0.1241;0.1287;0.1334;0.1381;0.1427;0.147 1;0.1511;0.1546;0.1576;0.1601;0.1626;0.1652;0.1678;0.1704;0.1730;0.1756;0.1 782;0.1807;0.1832]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1.50 1.25 1.00 NmolesFr4 =[0.2364;0.2341;0.2313;0.2277;0.2234;0.2188;0.2153; 0.2138;0.2135;0.2134;0.2134;0.2122;0.2107;0.2091;0.2076;0.2061;0.2049;0.203 8;0.2030;0.2024;0.2021;0.2015;0.2008;0.2002;0.1995;0.1988;0.1982;0.1975;0.1 969;0.1962;0.1956]; AmolesFr4 =[0.0269;0.0356;0.0467;0.0606;0.0773;0.0952;0.1090; 0.1148;0.1160;0.1162;0.1162;0.1210;0.1271;0.1332;0.1392;0.1448;0.1497;0.153 8;0.1569;0.1591;0.1606;0.1628;0.1654;0.1679;0.1705;0.1732;0.1758;0.1783;0.1 808;0.1833;0.1856]; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % optimal ammonia concentration plot (LL,AmolesPC,'-k') hold on % equilibrium ammonia concentration %plot (LL,AmolesPCEq,'-k') %hold on plot (Length,AmolesFr1,'--k') hold on plot (Length,AmolesFr2,':k') hold on plot (Length,AmolesFr3,'-.k') hold on plot (Length,AmolesFr4,'+k') hold on xlabel ('Distance (m)') ylabel ('Mole Fraction NH_3') % title 'Optimal NH_3 in the synthesis convert or' % text (3.1,0.24,'{N_2}_{,hom}'); % text (2.1,0.21,'{N_2}_{,opt}'); % text (1.1,0.19,'{N_2}_{,eqm}'); h = legend('optimal','1.00 1.00 1.00','1.10 1.00 1. 00','1.20 1.00 1.00','1.50 1.25 1.00',2); % xlabel ('Distance (m)') % ylabel ('Ammonia Mole Fr') grid on % title 'Mole Fraction % NH_3' end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if (ThisPlot==6) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % these are the results for runs below %run C:\MATLAB7\work\Ammonia\SSATS_NonUnif_2Sept201 1 % cat distribution 1 1 1 Length = [0;0.1500;0.3000;0.4500;0.6000;0.7500;0.9000;1.0500 ;1.2000;1.3500;1.5000;1.
hold on plot (Length,NmolesFr3,'-.k') hold on plot (Length,NmolesFr4,'+k') hold on grid on xlabel ('Distance (m)') ylabel ('Mole Fraction N_2') % title 'Optimal N_2 in the synthesis converto r' % text (3.1,0.24,'{N_2}_{,hom}'); % text (2.1,0.21,'{N_2}_{,opt}'); % text (1.1,0.19,'{N_2}_{,eqm}'); h = legend('opt','1','2','3','4',2); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% toc fclose(resl); function [Topt] = OptimalT (x,P) % DATA % P, x(1), x(2), x(4) % gives Topt % scan between 500 and 1000 scanTlow = 500; scanTup=1000.0; scanDel = 2.0; Tchk = scanTlow-scanDel; scanT = (scanTup-scanTlow)/scanDel; % fprintf (resl,'\n Temp (K) diff=fLHS-fRHS'); for iTchk = 1:scanT Tchk = Tchk+scanDel; [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,Tchk,x(1) ,x(2),x(4)); [Ka] = EQNCN(Tchk); FatT = Ka^2*aN2*aH2^1.5/aNH3 - aNH3/aH2^1.5; fRHS = -( (20.523e3)/Tchk^2 ) * FatT; % now find deriv at this point T1=Tchk-1; T2=Tchk+1; [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T1,x(1),x (2),x(4)); [Ka] = EQNCN(T1); FatT1 = Ka^2*aN2*aH2^1.5/aNH3 - aNH3/aH2^1.5; [phiH2,phiN2,phiNH3,aH2,aN2,aNH3]=ACTVT(P,T2,x(1),x (2),x(4)); [Ka] = EQNCN(T2); FatT2 = Ka^2*aN2*aH2^1.5/aNH3 - aNH3/aH2^1.5; fLHS = 0.5*(FatT2-FatT1); diff=fLHS-fRHS; rootT(iTchk) = Tchk; rootY(iTchk) = diff; % fprintf(resl,'\n %3.0f %6.2f %12.4e',iTchk,rootT( iTchk),rootY(iTchk)); end Topt=0; for jTchk = 1:scanT-1 jT1=jTchk+1;
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if ((rootY(jTchk)>0)&(rootY(jT1)<0)) Topt = rootT(jTchk+1); end end for jTchk = 1:scanT-1 jT1=jTchk+1; if ((rootY(jTchk)<0)&(rootY(jT1)>0)) Topt = rootT(jTchk+1); end end