Ammonia Synthisis Loop

Ammonia Synthesis with Alternate Feedstock

Rob Deobald Jeff Hayes

Stefan Sigurdson

Department of Chemical Engineering University of Saskatchewan

2006-2007

Executive Summary

Saskferco produces ammonia, urea and nitric acid (to make UAN). One future

option considered by the company is producing ammonia from a mixture of hydrogen

and nitrogen gas received from a petroleum coke gasification facility. This feed stream

would contain fewer impurities than the existing process. Our design team was requested

to design an ammonia synthesis loop based on the existing process to accommodate this

change in the feedstock. The project would involve determining the increase in the

extent of conversion achieved across the reactor catalyst beds, as well as examining the

excess heat that would be released from having a more pure feedstock. The excess heat

from the reaction would be recovered by steam boilers. This steam would be used to

power steam turbines that would compress both the incoming feed stream as well as a

carbon dioxide gas stream to be used in Saskferco’s urea plant. Before the steam created

can be used by the turbines, it must pass through a natural gas-fired superheater so that is

superheated upon its arrival at the turbines. Also generated in the superheater will be a

lower-pressure steam stream for the urea plant in order to optimize the heat recovery

from the superheater. Over a seven-month period, XDGR Engineering Systems has

developed an ammonia synthesis process designed to meet the specifications described

above. The following report gives a detailed examination of the design process that was

followed and the conclusions that were reached in the synthesis of ammonia with an

alternate feedstock.

i

Table of Contents Nomenclature……………………………………………………………………………...1 1.0 Project Background……………………………………………………………………7 2.0 Project Definition……………………………………………………………………...8 3.0 Ammonia Conversion………………………………………………………………..10 4.0 Steam Superheater…………………………………………………………………...12

4.1 Overview……………………………………………………………………..12 4.2 Heat Requirements…………………………………………………………...14 4.3 Optimum Steam Passes and Number of Tubes………………………………15 4.4 Radiant Section…………………………………………………………........16 4.5 Shield Bank Section…………………………………………….....................19 4.6 Finned Bank Section…………………………………………………………20 4.7 Emission Stack……………………………………………………………….22 4.8 Construction Material………………………………………………………..24

5.0 Heat Exchangers……………………………………………………………………..26 5.1 Overview……………………………………………………………………..26

5.2 Gas/Gas Heat Exchanger…………………………………………………….26 5.3 Waste Heat Exchangers ……………………………………………………..27 5.4 Heat Exchange Summary…………………………………………………….28

6.0 Compressors and Turbines…………………………………………………………...29 6.1 Compressors………………………………………………………………….29

6.1.1 Synthesis Gas Compressor…………………………………………29 6.1.2 CO2 Compressor…………………………………………………...30

6.2 Steam Turbines………………………………………………………………31 6.3 Compressor and Turbine Summary………………………………………….32

7.0 Economics……………………………………………………………………………34 7.1 Overview……………………………………………………………………..34

7.2 Compressor Pricing………………………………..…………………………35 7.3 Steam Turbine Pricing……………………………………………………….35 7.4 Heat Exchange Equipment Pricing…………………………………………..36 7.5 Feasibility of Firing the Superheater with Hydrogen………………………..37 7.6 Ammonia Convertor Pricing………………………………………………....38 7.7 Stream Cost Analysis………………………………………………………...39 7.8 Economic Summary………………………………………………………….40

8.0 Conclusion…………………………………………………………………………...41

ii

References………………………………………………………………………………..44 Acknowledgements………………………………………………………………………45 Appendix A: Process Flow Diagram…………………………………………………….46 A.1 Process Flow Diagram and Stream Compositions…………………………..47 Appendix B: Ammonia Conversion……………………………………………………...50

B.1 Determining the Feed Requirement to Produce 1900 Tonnes of Ammonia/day…………………………………………………………………….51

B.2 Deriving Equations to Interpret Stream Composition Changes……………..53 B.3 Estimating the Equilibrium Conversion of the Ammonia Synthesis Reaction………………………………………………………………………….56

B.4 Reactor Composition Iterative Procedure for 8R1 and 8R2………………...60 B.5 Energy Balance Iteration Procedure for 8R1 and 8R2………………………70 Appendix C: Steam Superheater…………………………………………………………74 C.1 Calculating the Net Heating Value of the Natural Gas Stream……………...75 C.2 Heating Requirements of the Steam Streams………………………………..77 C.3 Calculations for the Radiant Section………………………………………...79 C.4 Determining the Optimum Number of Superheated Steam Passes………….81 C.5 Determining the Optimum Number of Urea Steam Passes………………….82 C.6 Calculations for the Shield Bank Section……………………………………83 C.7 Finned Bank Section Calculations (Vaporization of Urea Water Stream)…..87 C.8 Finned Bank Section Calculations (Heating of Liquid Urea Stream).………91 C.9 Calculating the Minimum Allowable Tube Wall Thickness………………...95 C.10 Calculating the Required Stack Dimensions……………………………….97 C.11 Determining the Required Number of Tubes in the Radiant Section…….100 C.12 Summary of Superheater Results…………………………………………102 Appendix D: Heat Exchangers………………………………………………………….109 D.1 Heat Exchanger Specifications…………………………………………….110 Appendix E: Compressors and Turbines……………………………………………….111 E.1 Compressor and Turbine Specifications……………………………………112 E.2 Synthesis Gas Compressor Pressure Safety Valve Design…………………113 E.3 CO2 Compressor Pressure Safety Valve Design…………………………...115 Appendix F: Economics………………………………………………………………...117

F.1 Determining the Bare Module Cost of the Required Equipment…………..119 F.2 The Feasibility of Firing the Super Heater using Hydrogen………………..125 F.3 Stream Cost Analysis……………………………………………………….126

iii

List of Tables

Table A.1.1: Ammonia synthesis loop streams………………………………………….47

Table A.1.2: Water and steam system streams…………………………………………..47

Table A.1.3: CO2 compressor streams…………………………………………………...48

Table A.1.4: Superheater fuel and flue gas streams……………………………………...48

Table B.3.1: Conversion of hydrogen as a function of temperature……………………..58

Table B.4.1: Stream 1 concentrations entering 8R1. ……………………………………64

Table B.4.2: Synthesis loop composition at zero conversion. …………………………..65

Table B.4.3: Stream 2 exiting 8R1. ……………………………………………………...66

Table B.4.4: Stream 3 exiting 8R2. ……………………………………………………...67

Table B.4.5: The recycle stream.………………………………………………………...68

Table B.4.6: Summary of final stream compositions and flow rates…………………….69

Table B.5.1: Example stream compositions for an equilibrium temperature of 750 K

for reactor 8R1 and an equilibrium temperature of 720K for reactor

8R1…………………………………………………………………………72

Table C.1.1: Calculating the average molecular weight…………………………………75

Table C.1.2: Calculating the average lower heating value………………………………75

Table C.1.3: Calculating the air requirement for combustion…………………………...75

Table D.1.1: Heat exchanger specifications……………………………………………110

Table D.1.2: Heat exchanger inlet and outlet specifications…………………………...110

Table E.1.1: Summary of compressor/turbine information…………………………….112

Table E.1.2: Stream compositions as H/N ratio varies…………………………………112

Table F.1.1: Summary of the cost of each piece of process equipment………………...118

Table F.1.2: Feed stream costs………………………………………………………….118

Table F.1.3: Product stream prices……………………………………………………..118

iv

List of Figures

Figure 3.1: Ammonia synthesis loop…………………………………………………….10

Figure 4.1: Steam superheater schematic………………………………………………...13

Figure 6.1: Synthesis gas compressor and turbine system……………………………….30

Figure 6.2: Carbon dioxide compressor and turbine system……………………………..31

Figure A.1.1: Process flow diagram……………………………………………………..49

Figure B.3.1: Ammonia synthesis equilibrium at various stream compositions………...59

Figure C.12.1: Heat available from the combustion of a 19,700 Btu/lb (LHV) refinery

gas.…..……………………..…………………………………………...104

Figure C.12.2: Distribution of radiant heat transfer rate around the tubes, dependent

upon coil arrangement and firing mode…………………………………105

Figure C.12.3: Determining the duty-split between radiant and convection sections

based on the bridgewall temperature...………………..………………..106

Figure C.12.4: Finding the dimensionless parameter J to determine the heat transfer

coefficients on the flue-gas side of serrated fins.…..…………………...107

Figure C.12.5: Determining the fin efficiency based on the convection film

coefficient as well as the fin design & thermal conductivity.………..…108

v

Nomenclature

A Area (m2)

AC Cross-sectional area of schedule 40 piping (m2)

AFB,LIQ Convective heat transfer surface, liquid heating phase (m2)

AFB,VAP Convective heat transfer surface, vaporization phase (m2)

AFREE Finned bank free area (m2)

Ai Inner surface area per tube length (ft2/ft)

Ao Outer surface area per tube length (ft2/ft)

AR Required radiant surface area (m2)

ARE Air requirement for 20% excess air (kg air/kg fuel)

ARm Air requirement (kg air/100kmol fuel)

ARw Air requirement (kg air/kg fuel)

ASB Shield bank surface area (m2)

ASS Surface area required for the superheated steam (m2)

At Finned tube surface area per unit tube length (ft2/ft)

AUS Surface area required for the urea steam (m2)

AVT Vertical tube radiant surface (m2)

BWT Bridgewall temperature (ºC)

c Catalyst cost ($/kg)

CBM Bare module cost ($)

CP Average fluid heat capacity (BTU/lb·°F)

CP1 Average heat capacity of synthesis stream in reactor 8R1 (kJ/kmol·K)

CP2 Average heat capacity of synthesis stream in reactor 8R2 (kJ/kmol·K)

CPur Purchased equipment cost ($)

D Required diameter of the stack (m)

DG Draft gain (inH2O)

DGC Convection section draft gain (inH2O)

DL Damper loss

do Outer diameter of each tube (in)

Do Orifice diameter (m)

DUA Draft under arch

1

ef Fin efficiency

ETL Effective vertical tube length (m)

F Correction factor specific to the type of tubes used

FAR Molecular flow rate of argon gas stream (kmol/day)

FBL Finned bank loss

FBM Base bare module factor

FBMa Actual bare module factor

FC Mass flow rate of fuel consumed (kg/h)

fc/c Factor for conductive/convective effects (0.85)

FG Flue gas mass flow rate (kg/h)

FGT Flue gas temperature exiting the convection section (ºC)

fh Fin height (in)

FH2 Molecular flow rate of hydrogen gas stream (kmol/day)

FIN Inlet molar flow rate (kmol/s)

Flwf Lost work due to friction (W/(kg/s))

FM Material factor

FNH3 Molecular flow rate of ammonia gas stream (kmol/day)

FP Pressure factor

FSS Superheated steam mass flow rate (kg/s)

FSS’’ Superheated steam mass velocity (kg/s⋅m2)

ft Fin thickness (in)

FUS’’ Urea steam mass velocity (kg/s⋅m2)

FUS Urea steam mass flow rate (kg/s)

fv Factor for local variation in heat flux (1.25)

g Acceleration due to gravity (9.81 m/s2)

G Fluid mass velocity (kg/s⋅m2)

h Height above datum (m)

H Required stack height (m)

%H Percent heat extraction from the superheater

HA,BWT Heat made available based on the bridgewall temperature (kJ/kg)

2

HA,FGT Heat available based on the flue gas temperature exiting the convection

section (kJ/kg)

HA,SB Heat made available based on the flue gas temperature leaving the shield

bank (kJ/kg).

hC Convection film heat transfer coefficient (W/m2·K)

hi In tube heat transfer coefficient (W/m2·K)

ho Total convection coefficient (W/m2·K)

(ho)eff Effective total convection heat transfer coefficient (W/m2·K)

ΔHR1 Available heat of reaction per mole of hydrogen reacted in reactor 8R1

(MJ/kmol)

ΔHR2 Available heat of reaction per mole of hydrogen reacted in reactor 8R2

(MJ/kmol)

hRG Gas radiation heat transfer coefficient (W/m2·K)

HT Total heat fired by the superheater (GJ/h)

hw Tube wall heat transfer coefficient (W/m2·K)

I.D. Inner diameter (m)

J Dimensionless parameter applied to determine the flue gas heat transfer

coefficient for serrated fins

k Average fluid thermal conductivity (BTU/ft·h·°F)

KM Tube wall thermal conductivity (BTU·in/ft2·h·°F)

L Horizontal tube length (ft)

LHV Lower heating value of the natural gas (kJ/100kmol)

LMTD Log-mean temperature difference (°C)

LS Section height (ft)

LVessel Length/Height of Vessel (m)

m& Mass flow rate (kg/s)

m~ Molar flow rate (kmol/s)

mAr Mass flow rate of argon (tonnes/day)

mH2 Mass flow rate of hydrogen (tonnes/day)

mNH3 Mass flow rate of ammonia (tonnes/day)

mTOTAL Total mass flow rate(tonnes/day)

3

MW Molecular weight (kg/kmol)

MWave Average molecular weight (kg/kmol)

nAr Molar flow rate of argon (kmol/day)

nH2 Molar flow rate of hydrogen (kmol/day)

nNH3 Molar flow rate of ammonia (kmol/day)

nSS Number of superheated steam passes

nTOTAL Total molar flow rate(kmol/day)

nUS Number of urea steam passes

N Number of tubes per row

Nf Number of fins per inch of tube

NHV Net heating value of the natural gas (kJ/kg)

NR Number of tube rows

NSE Net stack effect (inH2O/ft)

NSS Number of vertically aligned superheated steam tubes in the radiant

section

NT Number of tubes per row

NUS Number of vertically aligned urea steam tubes in the radiant section

P Pressure (Pa)

ΔP Change in pressure (Pa)

Patm Atmospheric pressure (psia)

PSS Superheated steam operating pressure (psia)

Q Volumetric flow rate (m3/s)

QC Heat transfer in the convective section (GJ/h)

QFB, LIQ Convection section heat absorption, liquid water heating phase (GJ/h)

QFB, VAP Convection section heat absorption, vaporization phase (GJ/h)

QMAX’’ Maximum local radiant heat flux (BTU/h·ft2)

QR Heat transfer in the radiant section (GJ/h)

QR’’ Average radiant heat flux (BTU/h·ft2)

QSB Heat absorption in the shield bank section (W)

QSS Heat absorbed by the superheated steam (GJ/h)

QT Total heat duty for the superheater (GJ/h)

4

QUS Heat absorbed by the urea steam (GJ/h)

r Ratio of maximum radiant heat flux to average radiant heat flux (1.93)

%R Predicted radiant heat losses

Re Flue gas Reynolds number

Rt Total heat transfer resistance (m2·K/W)

s Spacing between tube centers (in)

S Design stress, 90% of the yield strength for austenitic steel (psia)

SBL Shield bank loss

SD Required stack draft (inH2O)

SD’ Stack draft gain per foot of stack (inH2O/ft)

SEL Stack entrance loss

SFA Shield-bank free area (m2)

SFL Stack frictional loss per foot (inH2O/ft)

SOL Stack outlet loss

t Tube wall thickness (in)

T Temperature (K)

ΔT Temperature Change (K)

Ta Ambient temperature (°R)

TCD Tube-circle diameter in the radiant section (m)

TFG Total flue gas (kg flue gas/kg fuel)

TFG Temperature of flue gas (°C)

(TFG)AVE Average flue gas temperature (°F)

(TFG)IN Inlet flue gas temperature

(TFG)OUT Outlet flue gas temperature

Tga Flue gas temperature (°R)

TM Tube metal temperature (K)

tMARGIN Margin of tube wall allowance against corrosion and creep (cm)

tMIN Minimum allowable tube thickness (cm)

TRTW Radiant tube wall temperature (ºC)

(TSS)OUT Outlet superheated steam temperature (ºF)

TUS Temperature of urea steam (°C)

5

(TUS)IN Inlet urea water temperature (ºF)

(TUS)OUT Outlet urea steam temperature (ºF)

tw Tube wall thickness (in)

u Bulk fluid viscosity (lb/ft·h)

U Overall heat transfer coefficient (W/m2·K)

V Velocity (m/s)

V2 Exit velocity (m/s)

Vg Specific volume of the flue gas at the point in question (ft3/lb)

VH Velocity head (inH2O)

wS Shaft power (W)

X Hydrogen gas conversion across the ammonia reactor

X8R1 Extent of conversion of hydrogen across reactor 8R1

X8R2 Extent of conversion of hydrogen across reactor 8R2

(yAr)F Mole fraction of argon in the feed stream

(yH2)F Mole fraction of hydrogen in the feed stream

(yNH3)F Mole fraction of ammonia in the feed stream

(yAr)P Mole fraction of argon in the product stream

(yH2)P Mole fraction of hydrogen in the product stream

(yNH3)P Mole fraction of ammonia in the product stream

(yAr)R Mole fraction of argon in the recycle stream

(yH2)R Mole fraction of hydrogen in the recycle stream

(yNH3)R Mole fraction of ammonia in the recycle stream

εi Efficiency (%)

ρ Density (kg/m3)

ρ~ Molar density (kmol/m3)

ρB Catalyst bulk density (kg/m3)

ρSS Density of superheated steam (kg/m3)

ρUS Density of urea steam (kg/m3)

μ Calculated efficiency

%~ Mole Percent

6

1.0 Project Background

Saskferco is one of the largest producers of nitrogen fertilizers in North America.

Their facility is located in Belle Plaine, Saskatchewan and has been operating since 1992.

Originally they produced 1500 tonnes per day of anhydrous ammonia, 77% of which was

used to produce 2000 tonnes of granular urea. Their current anhydrous ammonia

synthesis process was upgraded in 1997 to increase the production of ammonia to 1900

tonnes per day, which increased production of granular urea to 2900 tonnes per day.

They have also added the production of a small nitric acid plant, for the production of

urea ammonium nitrate, in both 28% and 32% solutions.

The existing feed to their ammonia synthesis loop has a composition of

approximately 73.43 mol% hydrogen gas, 24.92 mol% nitrogen gas, 1.26 mol% methane,

and 0.39 mol% argon and helium. Hydrogen for this reaction is prepared through the

steam reforming of methane. The synthesis gas is compressed to a pressure of 190 bars,

and mixed with any unreacted gas that left the two ammonia convertors in the synthesis

loop. After compression, the synthesis gas is put through the reactors, and cooled off

with large waste heat steam boilers after each reactor. The gas then enters the separation

system, where the ammonia is separated from the hydrogen and nitrogen reactants. A

fraction of this recycle stream is purged, to keep impurities from building up in the

system, and then it is sent back to the compressors to be mixed with the fresh feed gas.

7

2.0 Project Definition

In the future, it may be possible for Saskferco to purchase synthesis gas for the

production of ammonia from a new petroleum coke gasification facility being built

nearby. One option for this new feed that is being considered is constructing a second

ammonia synthesis loop, producing an additional 1900 tonnes per day of ammonia. The

new feed for the process would consist of 74.25 mol% hydrogen gas, 24.75 mol%

nitrogen gas, and only 1 mol% argon. Because many of the inert components in the

original feed stream are recycled through the synthesis loop, the feed currently enters the

first ammonia convertor, 8R1, containing approximately 11 mol% methane, helium, and

argon. These impurities lower the partial pressure of hydrogen, which lowers the overall

conversion of the reactor. With the new feed stream, only approximately 3 mol% of inert

argon enters the first ammonia convertor, resulting in a higher partial pressure of the

reactants, which results in higher conversions and larger temperature rises across the

catalytic reactor beds. There are three challenges to redesigning a synthesis loop to use

the new feedstock. The first is analyzing the kinetics of the ammonia synthesis reaction

and determining the new conversions now that the impurities have been reduced. The

second is to design a steam superheater that will convert the waste heat recovered from

the ammonia reactors into high pressure steam. The final design challenge is to take the

high pressure steam and use it to power the compressors that bring the feed up to the

pressure required for the reaction.

Determining the behaviour of the ammonia synthesis reaction was accomplished

by finding an equation for the conversion of hydrogen as a function of equilibrium

temperature based on ammonia synthesis data from literature. Once we had this

equation, it was possible to calculate the composition of the streams leaving both reactors

8

2.0 Project Definition

8R1, and 8R2; however, to do so we must use two iteration loops. The first assumes the

outlet temperatures of the two reactors, and calculates the composition of the product

streams, and must be iterated until these compositions no longer change due to changes in

the recycle stream. The second iteration is an energy balance over the reactors, and must

be iterated until the outlet temperatures calculated are the same as those we assumed

when calculating the outlet compositions. To complete these calculations, some

assumptions had to be made about the separation system. A detailed design of the

ammonia separator units is beyond the scope of our project. We remove heat of reaction

from the system through waste heat boilers positioned after each of the reactors. This

heat boils water making high pressure (120 bar) saturated steam. To make this steam

useful, we must send it to a natural gas-fired superheater that brings the temperature up to

510oC. Excess energy generated by the superheater is also used to generate 23 bar

saturated steam at a rate of 25 tonnes/h for use in a Saskferco urea plant. Enough

superheated steam is generated by the superheater to power two compressors. The first

compressor takes an almost pure stream of carbon dioxide at 5 bar, and brings the

pressure up to 150 bar at a rate of 95 tonnes/h. The second compressor brings the

synthesis gas feed at 50 bar up to 190 bar, and mixes it with the recycle gas from the

reactors. A turbine is associated with each compressor, which takes the 120 bar

superheated steam, and exhausts it at a vacuum pressure of 30 kPa.

9

3.0 Ammonia Conversion

Feed enters the ammonia synthesis loop straight from the synthesis gas

compressor which is discussed in Section 6.1, where it has been mixed with the recycle

gas from the ammonia separator and been compressed to 190 bar. The gas then passes

through the gas/gas exchanger that heats up the synthesis gas feed with the hot gas

leaving the system and heading towards the separator. The feed then enters the first

ammonia convertor, 8R1. This reactor has two catalyst beds, and a small internal heat

exchanger with a heat exchange area of 239.6 m2. The first bed has an effective catalyst

volume of 21.55 m3 and the second having a volume of 29.70 m3. The second convertor,

8R2, has a single catalyst bed with a volume of 46.70 m3. Both reactors use an alumina-

supported iron catalyst promoted with alkali and various other metal oxides.

Figure 3.3: Ammonia synthesis loop The ammonia synthesis reaction, shown as equation B.1.1, is highly exothermic.

This leads to a significant temperature rise across both reactors. As is shown in

Appendix B, having specified the inlet temperature to 8R1 as 300oC, the conversion,

10

3.0 Ammonia Conversion

outlet temperature and outlet composition was able to be calculated. The conversion of

hydrogen was determined to be 32.8%, resulting in an exit temperature of 507.8oC. The

gas is cooled in the waste heat boiler, 8E1, directly following the first reactor. This

exchanger cools the synthesis gas down to 400oC by creating high pressure saturated

steam. It is discussed in detail in Section 5.0, and in Appendix E. Conversion across

8R2 was determined to be an additional 11.8%, resulting in an outlet synthesis gas

temperature of 473.0oC. Concentrations in each stream are summarized in Table B.4.6.

Data for modeling the ammonia synthesis reaction was found in the publication

Catalytic Ammonia Synthesis by J.R. Jennings1. In this publication, equilibrium data was

given for a feed stream identical to the new feed stream being implemented. This

equilibrium data was converted into the form of total hydrogen conversion at equilibrium

as a function of temperature. Because the reaction will not reach equilibrium before

leaving each reactor, an approach to equilibrium of 10°C was used to approximate the

actual hydrogen conversion achieved. The temperatures of the synthesis gas leaving each

reactor were approximated from data given for the current temperature rise across each

reactor. Because the same reactors will be used for the new feedstock, a reaction

enthalpy was found per hydrogen gas converted and was applied for the new synthesis

stream. These heats of reaction estimated in Appendix B.5 to be approximately

36.6 MJ/kmol of hydrogen converted under the conditions present in 8R1, and

38.2 MJ/kmol of hydrogen under the conditions present in 8R2.

11

4.0 Steam Superheater

4.1 Overview:

The purpose of the steam superheater is to heat the saturated steam leaving the

waste heat boilers at an approximate pressure of 120 bar. After heating the waste heat

boiler steam, the resulting superheated steam would be split between the synthesis gas

turbine and the CO2 turbine to run their corresponding compressors. The temperature of

saturated steam at 120 bar was determined from the Peng-Robinson thermodynamic

model in the HYSYS program to be 323.7°C. The temperature of the superheated steam

was recommended by our supervisor to be 510°C. In order for the superheated steam to

generate enough power for the two turbines at 510°C temperature and 120 bar pressure, it

was determined that the mass flow rate of the steam must be 90.65×103 kg/h. To heat

this amount of steam, a superheater was designed to run off of natural gas. The

combustion of this gas would heat the piping of the steam stream and would therefore

heat the steam within. In order to reach the desired superheated steam temperature, the

waste heat boiler steam would have to be heated in the radiant section of the superheater.

In this section, entirely radiant heat transfer is assumed between the steam and the radiant

walls of the superheater. The tubes in this section would be bare with no fins would

encircle the combustion flame in the radiant section in the form of a vertical radiant coil.

Once the flue gas from the radiant section combustion leaves the radiant section,

much of its heat will be unrecovered by the superheated steam. However, by this point,

the flue gas will not be hot enough to be used by the superheated steam. To take

advantage of this available flue gas heat, a second stream of steam could potentially be

heated. This stream was decided to be a stream 23 bar saturated steam to be used by

Saskferco’s urea plant. The water used to make this steam was specified to reach the

12


superheater as a liquid at a pressure of 23 bar and a temperature of 131.8°C. This water

would be heated into the form of saturated steam at 23 bar, giving it a temperature of

220.1°C. The water would be heated by convective heat transfer by the flue gas and

partially by radiant heat transfer from the radiant section. The water would flow in cross

flow with respect to the flue gas flowing up towards the emission stack. The tubes in the

finned bank section would be equipped with circular fins to improve the process of

convective heat transfer. The urea water stream would flow down the finned bank section

before reaching the shield bank section. In this section, the tubes are bare, and the heat

transfer in this section is assumed to be a combination of convective and radiant heat

transfer. The urea steam would then briefly enter the radiant section in order to optimize

the available heat within the section before being sent to the urea plant.

Figure 4.1: Steam superheater schematic

13


Once the desired heat has been removed, the flue gas exits the superheater to the

atmosphere through an emission stack. The stack should be tall enough to induce a

negative draft within the radiant section. This allows for safe observation of the natural

gas combustion through a peep door. The stack should also have a large enough diameter

so that the flue gas exits at a desired mass velocity. Shown on the previous page is a

diagram illustrating the approximate layout and design of the superheater. This type of

furnace is classified as being vertical-cylindrical with a cross flow convection section.

The superheater was designed based on the published recommendations of

Herbert Berman found in the Journal of Chemical Engineering2. The calculations

performed for the superheater design can be found in Appendix C. These calculations are

placed in Appendix C in the order by which they were performed. The most crucial

assumption that was used in the design of the superheater was assuming a negligible drop

in the steam pressures. Because many of the equations and correlations given in

Berman’s publication were performed in empirical units, the majority of the calculations

were performed in these units. All of the significant final results have been converted to

SI units and have been communicated as such within this section. A summary of the

important results determined from the superheater analysis can be found in section 12 of

Appendix C.

4.2 Heating Requirements:

The natural gas stream used to fuel the superheater was specified to have the

following molar composition: 92% methane, 5% ethane, and 3% propane. For this gas

stream, the net heating value was estimated to be 49.51 MJ/kg. The net heating value

14


was found based on the lower heating values of each of the components. This net heating

value also assumed complete combustion of the natural gas stream. To ensure enough air

would be made available for complete combustion, it was specified 20% excess air by

mass would be made available. This was found to result in 21.33 kg of flue gas per

kilogram of natural gas combusted.

Based on implementing the Peng-Robinson thermodynamic model in the HYSYS

program, the heating requirement to produce the urea steam was found to be 57.61 GJ/h.

As well, the heating requirement for the superheated steam was found to be 50.64 GJ/h.

This results in the total heating duty of the superheater to be 108.25 GJ/h. The flue gas

was specified to be leaving the convection section at a temperature of 215.1°C. Based on

heat available at this temperature from Figure C1 of Appendix C, the heating efficiency

of the superheater was found to be 87.85%. From this, it was determined that 2433 kg/h

of natural gas would be required to meet the heating demands of the furnace, and 51.9

tonnes/h of flue gas would be released into the atmosphere. The natural gas stream was

assumed to not contain particulates or impurities. Based on this assumption, the flue gas

would be comprised entirely of CO2, H2O, N2 and O2 gas. The molar composition of the

emitted flue gas was determined to be 72.8% N2, 15.7% H2O, 8.27% CO2 and 3.23% O2.

All sample calculations pertaining to the heating requirements of the superheater can be

found in sections 1 & 2 of Appendix C.

4.3 Optimum Steam Passes and Number of Tubes:

Before the steam streams could be passed through the superheater, the optimum

number of passes for each of the two steam streams had to be determined. As was found

15


in Berman’s publication2, the optimum mass velocity for superheated steam in a

superheated steam generator should be between 146.5 and 366.2 kg/s·m2. It was also

specified that the optimum linear velocity of the steam exiting the superheater should be

10 m/s. For the given exiting density of the steam, the optimum mass velocity of the

superheated steam sold to the turbines was found to be 365.8 kg/s·m2. Because schedule

40 piping was used for all of the piping within the superheater, the cross-sectional area

could be determined (8.21×10-3 m2). This provided enough information to determine that

the optimum number of superheated steam passes would be 8.38 for the superheater.

Rounding up, this gave 9 actual superheated steam passes within the furnace. Sample

calculations for this part of the analysis can be found in section 4 of Appendix C.

The optimum mass velocity for the generating saturated steam was found to be

between 488.2 and 732.4 kg/s·m2. Using a mass velocity of 500 kg/s·m2 for the exiting

23 bar saturated steam for the urea plant, and given the cross-sectional area for schedule

40 piping, the optimum number of urea steam passes was found to be 1.69. Because the

number of passes of saturated steam through the superheater has to be a whole number,

the mass velocity for the urea steam can’t fall within the optimum range for saturated

steam. It was decided that it was better to have two steam passes instead of one so that

some steam would still be sent to the urea plant in case one of the passes would fail.

Sample calculations for this part of the analysis can be found in section 5 of Appendix C.

4.4 Radiant Section:

As previously stated, entirely radiant heat transfer is assumed to occur in the

radiant section. As was recommended by Berman2, the temperature of the radiant tube

16


walls was designed to be 75ºF (41.7ºC) hotter than the exit temperature of the

superheated steam. This gave a radiant tube temperature of 552ºC. Based on this tube-

wall temperature, the bridgewall temperature was found from Figure C3 of Appendix C

to be 927ºC. By determining the ratio of the heat available at the bridgewall and radiant

tube temperatures, the ratio of the heat transfer in the radiant section to the total heat

transfer in the superheater should have the same value. From this analysis, the heat

transfer in the radiant section was determined to be 63.60 GJ/h. Because the total heat

transfer to the steam streams was previously determined to be 108.24 GJ/h, this means

the heat transferred in the radiant section would be 44.64 GJ/h. Because this value is less

than the total heat requirement for the saturated urea steam (57.61 GJ/h), this means that

the urea steam would have to pass through part of the radiant section in order to be

completely saturated steam once sent to the urea plant.

When determining the required surface area of tubing required for absorbing all of

the available heat in the radiant section, he first row of the shield bank section must be

acknowledged. This row is assumed to absorb its share of the radiant heat released from

the furnace walls due to its vicinity to the radiant section. The total surface area of the

bottom row of the shield bank section was found to be 28.0m2. Given an assumed radiant

heat flux of 0.125 GJ/h·m2 (average expected heat flux for a steam superheater)

throughout the entire radiant section, the required surface area to absorb the total radiant

heat transfer was found to be 509.1m2. This means that the total surface area of the

vertical tubes within the radiant section must be equal to 481.1 m2. Calculations

pertaining to this analysis can be found in section 3 of Appendix C.

17


Based on the surface area required in the radiant section, the number of vertical

tubes required for both the superheated steam and the urea steam would have to be

determined. Based on the heating requirement of each type of stream, the distribution of

the vertical tube surface area in the radiant section was found to be 405.4 m2 for the

superheated steam and 75.7 m2 for the saturated urea steam. The number of vertical

tubes for each steam stream must then be of the same ratio as the surface areas for each

steam stream. Additionally, the number of tubes for each steam stream must be divisible

by the number of passes for each stream. In other words, the number of superheated

steam vertical tubes must be divisional by 9 and the number of urea steam vertical tubes

must be divisible by 2. When 108 vertical tubes for the superheated steam were

specified, it was found that approximately 20 vertical tubes for the urea steam were

required. This gives a total of 128 vertically aligned bare tubes within the radiant section.

Based on the number of superheated steam tubes and the required surface area for the

superheated steam, it was determined that the required equivalent tube length for each

tube in the coil would be 10.45 m. When this equivalent tube length was applied to the

urea steam in the radiant section, it was found that the surface area for the urea steam

would be 75.1 m2. This means that the surface area exposed for the urea steam would be

0.6 m2 less than initially determined. This wasn’t considered a problem as this deficit in

urea steam surface area would be made up for within the convection section calculations.

Given a spacing of 8 inches between the vertical tubes, the approximate diameter of the

radiant tube circle was found to be 8.28 m. The ratio between the equivalent tube lengths

with respect to the tube circle diameter would then be 1.26. Design calculations outlined

within this paragraph can be found in section 11 of Appendix C.

18


4.5 Shield Bank Section:

In the shield bank of the convection section, it was assumed that heat would be

transferred to the urea steam both by convective heat transfer and by radiant heat transfer.

It was decided that the shield bank section would consist of 3 rows, each having 16 bare

tubes 4.88 meters in length. To determine the temperature of the flue gas exiting the

shield bank of the convection section, an iterative technique was used starting with an

initial guess for the outlet temperature. What was known was that the temperature of the

urea steam would be constant during this phase (220.1°C). The inlet temperature of the

flue gas was known because it would be the same as the bridgewall temperature

(926.7°C). The final value of the flue gas outlet temperature was found to be 765.6°C.

The log-mean temperature difference between the flue gas and the steam was found to be

622.6°C based on these temperatures. To find the heat transfer coefficient outside of the

tubes, empirical equations given by Berman2 were used to find the coefficients of both

convective heat transfer and radiant heat transfer. These results were then combined by

equation C.6.4 to determine the overall heat transfer coefficient outside of the shield bank

tubes. The total convection coefficient outside the tubes was found to be 17.93 W/m2·K.

Based on the average thermodynamic properties of the two-phase water within the shield

bank section, the convection coefficient within the tube was determined to be

963.2 W/m2·K. Based on the thermal conductivity of the tube wall itself, the tube

convection coefficient was found to be 2396 W/m2·K. To determine the overall heat

transfer coefficient (U), a summation of the thermal resistances was found, and the

reciprocal of the total thermal resistance was taken as U. Using this value, the log-mean

19


temperature difference, and the total surface area exposed in the section, the total amount

of heat absorbed in this section was determined to be 3.28 GJ/h.

Using equation C.6.11, a ratio of the heat absorbed before and after the shield

bank was equated to the ratio of the heat made available before and after the shield bank

to determine the heat made available based on the assumed outlet flue gas temperature.

The heat made available after the shield bank was determined to be 12,140 BTU/lb. This

value was then plotted on Figure C1 to determine the outlet flue gas temperature to see if

it was the same as was initially assumed. If this weren’t the case, the steps outline in this

paragraph would be repeated until the determined outlet flue gas temperatures converged

to be same value. Once this temperature converged, the shield bank calculations were

complete. The iterative process used can be found in section 6 of Appendix C.

4.6 Finned Bank Section:

The finned bank section was divided into two separate sets of calculations: one

for set the feed water is being heated, the other for when the feed water begins to be

vaporized. It was determined using the HYSYS simulation program that 26.21 GJ/h

would be absorbed to vaporize water within the finned bank section, and 7.81 GJ/h would

be needed to heat the water after it initially enter the furnace. It was decided that rows

consisting of 16 finned tubes each 4.88 meters in length would be used in the design.

The number of rows required would be determined from the calculation process. The

fins that would be used in our design would be circular fins. They would be spaced 3 per

inch (1.2 fins per cm), ¾ inches high (1.9 cm), and 0.05 inches thick (0.13 cm). The

amount of surface area that these tubes would possess per unit of tube length was found

20


to be 2.23 m2/m, and the total free area across each tube row was found to be 6.49 m2.

From this determined free area, the flue gas mass velocity through the finned bank must

then be 2.22 kg/m2·s.

For the vaporization phase of the finned bank, the corresponding Reynolds

number for the flue gas flowing past the tubes would be 7304. From Figure C4, this

corresponds to the dimensionless J parameter having a value of 0.01. The parameter J is

required when estimating the convection coefficient outside of the tubes. From this

parameter, and based on the thermodynamic properties at this stage in the convection

section, the outer convection coefficient was determined to be 10.46 W/m2·K. However,

this value is misleading as it assumes a fin efficiency of 100%. The efficiency of the fins

must be taken from Figure C5 of Appendix C. Once this value is known, the effective

outer convection coefficient can be found. This value was determined to be 8.97 W/m2·K

based on a fin efficiency of 83%. As for the shield bank, the in-film convection

coefficient and the tube wall heat transfer coefficient can be determined based on the

properties of the urea steam and the tube. These values were determined to be

1282 W/m2·K and 2396 W/m2·K. A summation of the thermal resistances can then be

found, and from this, the overall heat transfer coefficient can be found for the

vaporization phase of the finned bank section. This value was found to be 8.34 W/m2·K.

Based on the heating requirement of this part of the superheater, as well as the overall

heat transfer coefficient and the assumed log-mean temperature difference, the required

surface area was then found. For the vaporization phase of the finned bank, it was

determined that 947 m2 would be required. From the number and length of the tubes, it

was found that 3.48 rows of finned tubes would be needed in this part of the finned bank

21


section. To ensure complete vaporization of the urea steam, the number of tube rows was

rounded up to 4 rows. This analysis can be found in section 7 of Appendix C.

For the water heating phase of the finned bank section, the same technique was

used for finding the number of required finned tube rows. The only changes to be made

would be the thermodynamic properties of the flue gas and the water. As for all of the

superheater design calculations, the thermodynamic properties of the steam and flue gas

streams were found based on the Peng-Robinson thermodynamic model. The value of J

was determined to be 0.011. The fin efficiency was determined to be 88% for this phase

of the finned bank, giving an effective outer heat transfer coefficient of 9.66 W/m2·K.

The overall heat transfer coefficient was determined to be 8.93 W/m2·K, and the required

surface area for the water heating phase of the finned bank was found to be 733.3 m2.

The number of tube rows was then determined to be 2.69, which was rounded up to 3

rows to ensure the urea steam would be completely in the vapor phase. The analysis for

this portion of the finned bank section can be found in section 8 of Appendix C.

4.7 Emission Stack:

When designing the emission stack for the superheater, it must have a sufficient

diameter to provide a desired mass flux of flue gas into the atmosphere. The height of the

stack must be of sufficient length to induce a draft that provides a slightly negative

pressure in the radiant section. The negative radiant section pressure would allow for

safe observation of the tubing within the radiant section through the peep doors of the

furnace.

22


It was recommended from Berman2 that the stack be designed to accommodate a

flue gas mass flux of 0.8 lb/s·ft2, which is equivalent to 3.91 kg/s·m2. It was also

recommended that the stack be designed to accommodate for a 25% increase in the mass

flow rate of flue gas. Given the flue gas emission rate of 51,905 kg/h, the stack will

require a diameter of 2.42 meters.

For determining the required stack height, the pressure losses, or velocity head,

caused by the flue gas flowing across each section of the superheater must be determined.

These velocity head losses were determined based on equation C.10.1 of Appendix C.

The head losses were determined for the draft under arch and across the shield bank,

finned bank, stack entrance, stack exit, and the dampers. The total velocity head losses

were determined to be 0.3962 inH2O. Based on equation C.10.8 of Appendix C, the draft

gain across the convection section could be determined. The convection section gain was

determined to be 0.0946 inH2O. By subtracting the convection section draft gain from

the velocity head losses, the draft gain required by the emission stack can be determined.

This required stack draft was determined to be 0.3016 inH2O. Using equation C.10.8, the

stack draft gain can be found per unit length of stack height. This value was determined

to be 0.005485 inH2O/ft. Before this value can be used to determine the required height

of the stack, the frictional energy losses in the flue gas as it passes up the stack must be

taken into account. From equation C.10.13, these frictional losses were determined to be

0.0003066 inH2O/ft, making the required net stack draft gain equal to 0.005179 inH2O/ft.

This means that the height of the required stack must be 17.75 meters. Calculations

performed regarding for the stack design can be found in section 11 of Appendix C.

23


4.8 Construction Material:

The final calculations performed in the superheater design were determining if the

tube wall thickness would be suffice to withstand the effects of corrosion and creep

within the tube walls. Corrosion would be caused along the tube walls by the tube metal

losing electrons by reacting with the flowing water streams. Creep is a term used to

describe the tendency of a metal to move or deform permanently to relive the stress2.

Creep commonly occurs when a metal is put under high temperatures and pressures for

long periods of time.

To combat creep, the tubes would have to be constructed out of a material capable

of withstanding high operating temperatures. Because the operating temperature of the

radiant section is 927°C, the tube metal chosen must be capable of withstanding these

high operating temperatures. The tubing material chosen was type HK-40 austenitic

steel. Austenitic steels are classified as alloys consisting of various combinations of iron,

chromium, and nickel. Type HK-40 steel composition by mass is defined as 25%

chromium, 20% nickel, and 55% iron. The limiting design metal temperature of HK-40

austenitic steel is approximately 1000°C,2 73°C hotter than the maximum operating

temperature.

It was determined from equation C.9.1 of Appendix C that the maximum expected

heat flux in the radiant section would be 71.15 kW/m2. The in-film convection

coefficient at the outlet temperature and thermodynamic properties of the superheated

steam was found to be 391.0 W/m2·K. Under these conditions, and given the thermal

conductivity of austenitic steel, the tube metal temperature at the superheated steam exit

was determined to be 584.7°C. To allow for a margin of safety, the maximum operating

24


tube temperature was set at 650°C, which is well within the constraints of HK-40

austenitic steel. The large buffer between the maximum operating temperature and the

limiting design temperature for HK-40 steel ensures that issues of corrosion and creep

will not be an issue in the designed superheater.

To determine if the tube walls are thick enough to withstand the stress of

operating pressures, the minimum allowable tube thickness was determined for HK-40

austenitic steel. Based on the maximum operating pressure (120 bar), the outer diameter

of the tubes (11.4 cm), and the design stress (90% of the yield strength) for HK-40 steel

under the operating conditions, the minimal allowable tube wall thickness for the HK-40

tubes was determined to be 0.307 cm. Given that schedule 40 piping has a wall thickness

of 0.602 cm, this allows for a 0.295 cm margin against the effects of corrosion and creep.

Calculations regarding the tube wall material can be found in section 9 of Appendix C.

25

5.0 Heat Exchangers

5.1 Overview

There are three unique shell-and-tube heat exchangers implemented within the

specified design. These heat exchangers include a gas/gas heat exchanger, and two waste

heat boilers. The gas/gas heat exchanger serves two purposes. Its first purpose is to heat

the incoming synthesis feed entering the first ammonia convertor to reach a feasible

reaction temperature. Its second purpose is to cool the synthesized ammonia stream so

that the separation units can remove the product more easily. The waste heat exchangers

remove heat from the synthesis streams leaving each of the two ammonia convertors.

The steam recovered by the waste heat exchangers is then superheated for use by the

steam turbines.

5.2 Gas/Gas Heat Exchanger

The purpose of the gas/gas heat exchanger is two fold. It must heat the feed

entering the first ammonia convertor to a reasonable reaction temperature as well as

cooling the ammonia product stream so that it is more easily separated in the separation

units.

The result of the exchanger is the synthesis gas feed stream being heated from

31°C to 300°C by the ammonia product before it enters the first ammonia convertor,

while the ammonia product stream is cooled from 340°C to 56°C by the feed stream. In

order to achieve this large heat exchange between the gas streams, a large effective

surface area of 2420 m2 is required. The heat exchanger designed consists of one shell

pass of the feed stream and one tube pass of the product stream. Due to the high

temperatures of the gases the exchanger had to be constructed from special materials.

26

5.0 Heat Exchangers

The steels used in the gas/gas exchanger have high quantities of chromium and

molybdenum to help prevent creep and corrosion. The shell side is constructed from

SA387 Gr.11 Cl.2 stainless steel and also has 24 baffles to help with the heat exchange.

The tubes of the exchanger are constructed from a slightly different stainless steel,

SA213/T11.

5.3 Waste Heat Exchangers

Along with the gas/gas exchanger there are also two waste heat exchangers in the

process. The purpose of the waste heat exchangers is to remove the heat from the

product streams leaving the ammonia convertors. To achieve this boiler feed water is

used as the coolant and is heated to saturated steam while cooling the product stream

from the ammonia convertors. This steam is then superheated so that it can be used by

the steam turbines to power the compressors.

The boiler feed water enters both exchangers as water at 130°C and exits each

exchanger as saturated steam at 324°C and 120 bar pressure. This results in the synthesis

stream temperatures being lowered from 508°C to 400°C in the first boiler and from

473 °C to 340°C in the second boiler. The split between the boiler feed water required

for each exchanger was 41.03 tonnes/hr for the first boiler and 49.62 tonnes/hr for the

second boiler, resulting in 90.65 tonnes/hr being sent to the superheater where the steam

is superheated for use by the steam turbines. The flow rates of boiler feed water needed

were calculated using a HYSYS simulation. It was known how much steam was required

to power the two compressors therefore that was the flow rate of boiler feed water used.

The boiler feed water temperature and pressure was also specified. Using these

27

5.0 Heat Exchangers

specifications, the amount of heat transferred was calculated and the inlet and outlet

temperature of each stream was calculated.

Each of the two heat exchangers consists of one shell pass of feed water and two

tube passes of the ammonia product. The shell sides of both exchangers have four

baffles, to enhance heat exchange, and are constructed from carbon steel. The tube side

of each exchanger is constructed using TP 316 stainless steel. These exchangers have

exchange areas of 163 m2 and 220 m2 respectively.

5.4 Heat Exchanger Summary

Three different heat exchangers were designed to heat and cool different process

streams. A gas/gas heat exchanger was designed to cool the product stream to aid the

separation process while heating the feed stream to the first ammonia convertor to a

decent reaction temperature. The gas/gas exchanger has an area of 2420 m2 and has one

tube pass and one shell pass. Due to extreme temperatures special

chromium/molybdenum stainless steels had to be used. Two waste heat exchangers were

also designed to remove the heat from the product streams leaving the ammonia

convertors while providing saturated steam for the steam superheater. Each of these two

heat exchangers consist of one shell pass of and two tube passes and have exchange areas

of 163 m2 and 220 m2 respectively. A summary of the heat exchanger information can be

found in Appendix D, Tables D.1.1 and D.1.2.

28

6.0 Compressors and Turbines

6.1 Compressors

A compressor is a machine that increases the pressure of a gas by mechanically

decreasing its volume. Two compressors had to be designed and modeled for use as part

of the new ammonia synthesis loop. One compressor was designed to push the synthesis

gas through the synthesis loop so that the ammonia could be made. The other compressor

was designed to compresses carbon dioxide from 5 bar to 150 bar so that it can be used in

the urea plant to make urea.

6.1.1 Synthesis Gas Compressor

The synthesis gas compressor takes the feed for the new process and compresses

it from 50 bar to the required 190 bar where it then enters the process loop. A four staged

compressor was designed using the HYSYS program (see Figure 6.1). The first three

stages take the feed and compress it to 180 bars with a compression ratio of 1.5. In

between these three stages the streams are cooled to 25°C before they enter the next

stage. This requires in total of 294.6 tonnes per hour of 25°C cooling water that is heated

to 60°C. The feed to the fourth stage contains a mixture of the stage 3 outlet as well as a

recycle stream which contains the un-reacted hydrogen and nitrogen, along with some

argon and ammonia. This mixture is then compressed to the required 190 bar in the

fourth stage. The material chosen for the compressor is made out of carbon steel. It then

leaves the compressor and heads into the first ammonia convertor. It was determined that

this compressor uses 13,704 kW of the power that is generated by the feed steam turbine.

29


One issue of safety that had to be taken into consideration was the possibility of

over pressuring the existing synthesis loop. The maximum allowable pressure in the

synthesis loop is 210 bar. To ensure that over pressurization of the loop by the synthesis

gas compressor could not take place a PSV was designed. The PSV constructed was a

simple orifice plate with a diameter of 0.044 m (~2 in, see Appendix E, E.1.1 to E.1.4).

Figure 6.1: Synthesis gas compressor and turbine system

6.1.2 CO2 Compressor

The second compressor takes carbon dioxide and compresses it from 5 bar to 150

bar so that it can be used by the urea plant to make urea. This compressor also has four

stages and uses 6,855 kW of power which is generated by the carbon dioxide turbine.

This compressor is also made of carbon steel. Condensation of the carbon dioxide had to

be taken into consideration when deciding the flow rates of the water used in the

intercoolers. If the carbon dioxide condensed in the compressor there would be major

problems. In between the first two stages the stream is cooled to 30°C before it enters the

second stage. The next two stages are only cooled to 41°C and 45°C. This is to ensure

that the carbon dioxide does not condense in the third or fourth stage of the compressor

under the specified pressure. The cooling system requires a total of 160 tonnes per hour

30


of 25°C cooling water that is heated by the compressed gases to 60°C. This compressor

and cooling system was also designed using the HYSYS simulation (see Figure 6.2).

Like the synthesis gas compressor the CO2 compressor will have to have a PSV

to prevent the over pressurization of the existing CO2 loop. The maximum allowable

pressure in the synthesis loop is 173 bar. The PSV constructed for this compressor was a

similar simple orifice plate with a diameter of 0.019 m (~3/4 in, see Appendix E, E.2.1 to

E.2.4).

Figure 6.4: Carbon dioxide compressor and turbine system

6.2 Steam Turbines

With each of the two compressors requiring different amounts of power to

compress different gases, two separate steam turbines had to be designed to supply the

different amounts of power required by each of the compressors. Steam turbines were

used because superheated steam was available from the superheater and steam turbines

are able to provide tremendous power using relative small space. The power from a

steam turbine is generated using steam, which in this case is provided by the designed

superheater, to turn a rotor that in turn produces the power needed for the compressors to

compress their specific gases.

31


The CO2 turbine uses 34% or 30.2 tonnes/h of the 510°C steam generated by the

superheater and puts out the required 6,855 kW needed to operate the CO2 compressor.

The synthesis gas turbine uses the remaining 66% or 60.4 tonnes/h of the 510°C steam to

produce the required 13,704 kW to power the synthesis gas compressor. Both of the

above turbines exhaust to vacuum (30 kPa absolute) to generate the needed power.

One safety issue that had to be considered with regards to the turbines is the

possibility of liquid water in them. This would be possible if the water level in the waste

heat boilers is too high. This would cause more water to enter into the superheater and it

is possible that the superheater would not be able to completely vaporise all of it.

Therefore liquid water could possibly enter into the turbine. This would cause major

damage to the two turbines and cause the shutdown of the whole plant. To prevent the

possibility of this occurring, a trip was designed that will shut the compressors off and

close off the boiler feed water valves closed to protect the turbines. This would still

cause the whole plant to shut down without damaging the turbines.

6.3 Compressors and Turbines Summary

Two compressors were designed to compress two different gases. One

compressor was designed to compress the synthesis gas stream from 50 bar to 190 bar

before it enters. The second compressor was designed to compress CO2 from 5 bar to

150 bar for use in the urea plant. Both of these compressors were designed using the

HYSYS simulation. These compressors each have four stages, are centrifugal and are

made from carbon steel. Each compressor has a PSV to prevent over pressurization of

the individual loops. Two steam turbines were also designed to supply the power

32


required by the compressors. These two turbines use the steam generated by the

superheater to produce the required 6,885 kW for the CO2 compressor as well as the

13,704 kW for the synthesis gas compressor. Trips were installed in the waste heat

boilers to prevent the possibility of liquid water from entering the turbine. A summary of

the compressor and turbine information can be found in Appendix E, Table E.1.1.

33

7.0 Economics

7.1 Overview

With the complexity and large scope of the project and the design chosen there

were many things that were considered with regards to the economics. One of the major

things included was the cost of the necessary equipment needed to make and power the

process. This included such things as ammonia convertors, heater exchangers, a

superheater and a couple of compressors and steam turbines. Another thing that was

looked at was the amount of money the plant would make. This is important because no

matter how good a design is it more than likely will not be implemented if the process

loses money. Besides the cost of the equipment needed for the process and the money

making prospect of this venture other things were also considered. These things included

such things as the feasibility of firing the superheater with the feed stream instead of

natural gas and coming up with a reasonable price for the ammonia product.

The first thing that was tackled was the costing of the equipment. Note that the

following costs do not include installation or maintenance costs. There were ten separate

pieces of equipment that needed to be priced. These ten pieces of equipment included

two compressors, two turbines, two waste heat exchangers, a gas/gas heat exchanger, two

ammonia convertors and lastly a steam superheater. Each unit was priced with the

methods specified in Ulrich3 (see Appendix F for detailed calculations). A summary of

the bare module costs for each piece of equipment can be found in Table F.1.1 while the

stream cost/price analysis is found in Tables F.1.2 and F.1.3.

34

7.0 Economics

7.2 Compressor Pricing

The two compressors were priced first. The three main factors in determining the

price of the compressors were the power required, their efficiencies and the material of

construction. The efficiency of each compressor was assumed to be 75% and the

material of construction chosen for the compressors was carbon steel. Next the power

needed by the compressor was determined using the HYSYS modeling program. These

power requirements were found to be 6,855 kW for the CO2 compressor and 13,704 kW

for the synthesis gas compressor. With these powers and efficiencies known the purchase

price was looked up in the proper Figure. Once the purchase cost was known it was

multiplied by the material factor and the bare module cost of the compressors was

determined. It was found that the bare module cost of the CO2 compressor was

$17,250,000 while the bare module cost of the synthesis gas compressor was determined

to be $6,612,500.

7.3 Steam Turbine Pricing

With the cost of the compressors now determined the next step was pricing the

two steam turbines that power them. Unlike the compressors there are only two main

factors in determining the cost of a steam turbine, power supplied and material of

construction. The material of construction once again was chosen to be carbon steel and

the power supplied by each individual turbine is the same as that used by its compressor.

Using Figure 5.21 from Ulrich3, it was found that the purchase cost of the turbine that

powers the CO2 compressor was $270,000 while the turbine that powers the synthesis

compressor had a purchase cost of $300,000. Once again the purchase cost and the

35

7.0 Economics

material factor were multiplied together to give the bare module cost. The bare module

cost for the synthesis gas compressor was found to be $1,610,000 while the bare module

cost of the CO2 was determined to be slightly lower at $1,086,750.

7.4 Heat Exchange Equipment Pricing

Next the cost of the three heat exchangers and the superheater were calculated.

The most important factors when determining the cost of heat exchangers are the

exchanger surface area, the material of construction and the pressure under which they

operate. The first heat exchangers cost to be calculated was the gas/gas heat exchanger.

This unit operates under 190 bar of pressure and has a heat exchanger area of 2420 m2.

This unit is made of carbon steel and titanium due to the high temperature of the gases

and also their high pressures. Knowing the area for heat exchanger the purchase cost was

determined using Figure 5.39 in Ulrich3. Once this was known the bare module factor

was found using Figure 5.38. This was then multiplied together with the purchase cost

and the bare module cost was determined. The bare module cost for the gas/gas heat

exchanger was found to be $5,635,000.

With the large and expensive gas/gas heat exchanger out of the way the bare

module cost of the two waste heat boilers were determined. The method for obtaining the

costs for these two pieces of equipment is almost identical to the way in which the cost of

the gas/gas heat exchanger was found. In this case the areas are 220 m2 and 162 m2

respectively. Using the same material as the previous exchanger the bare module costs

for these exchangers were calculated to be $483,000 for the first waste heat exchanger

and $442,750 for the second waste heat exchanger.

36

7.0 Economics

The last heat transfer related piece of equipment for which a cost had to be

determined was the superheater. The most important factor when determining the cost of

a superheater is its heating duty. This factor along with the materials of construction and

the exiting steam pressure were used to calculate the cost of the superheater. The

pressure of the exiting steam is 120 bar and the material of construction chosen was

austenitic steel due to the high temperatures used in the superheater. Using the heating

duty of the superheater the purchase cost of the superheater was found. This was then

multiplied by the pressure factor and the bare module factor, which is directly related to

the material of construction, to obtain a bare module cost for the superheater. It was

found that the bare module cost of the superheater is $ 4,992,000.

7.5 Feasibility of Firing the Superheater with Hydrogen

Another economic issue with regards to the superheater that was taken into

account was the possibility of using the hydrogen gas from the feed stream to fire the

superheater instead of natural gas. It was thought that it would be quite feasible to fire

the superheater with the feed stream given the rising cost of natural gas and the fact that

hydrogen gas has a decent heating value. So with the given price of the feed stream

given as $6.50/GJ and knowing that it takes 32 GJ to produce one tonne of ammonia the

energy cost of hydrogen gas was determined. The analysis found that the energy cost of

hydrogen was $10.22/GJ. This is higher than the current price of natural gas that is

currently at around $8.50/GJ. This made it unfeasible to used hydrogen gas from the feed

stream to fire the superheater at this point in time. It is possible, however, that if the

37

7.0 Economics

price of natural gas could rise above the threshold price $10.22/GJ in the future, using the

feed to fire the superheater might be feasible.

7.6 Ammonia Convertor Pricing

The last two pieces of equipment to have their bare module costs calculated were

the two ammonia convertors. Both of these reactors contain catalyst that aid in the

efficiency of the reactor but also add to the complexity of their calculations. With that in

mind the cost of the catalyst had to be determined as it contributed to the cost of the

reactor. Using Figure 5.47 in Ulrich, the cost and bulk density of the catalyst were

determined to be $8.00/kg and 800 kg/m3 respectively. With this known the bare module

factor was determined using a trusted relationship. Now, knowing the inner diameters of

each of the two different convertors the purchase price of the catalyst part of the reactor

was found using Figure 5.47. With both the bare module factor and the purchase price of

the catalyst known the bare module cost of the catalyst part of the reactor was

determined. The bare module cost of both ammonia convertors was found to be

$341,333. Now the cost of the actual reaction vessel itself could be calculated. Knowing

the operating pressure (190 bar) and the material of both convertors to be carbon steel the

bare module factor was found using Figure 5.46. With the height and inner diameter of

each reactor known to be almost the same the purchase cost for the vessel was calculated.

The vessel purchase cost and the bare module factor were then used to determine the bare

module cost of the vessel. Once this was found the bare module cost for the vessel and

the bare module cost were summed together to give the total bare module cost for the

38

7.0 Economics

reactor. The total bare module cost for each reactor was found to be $1,312,533 for the

first reactor and $1,058,613 for the second reactor.

7.7 Stream Cost Analysis

Knowing the expense of all the necessary equipment needed to produce the

ammonia was only part of the financial analysis. The money made by production of the

ammonia still needed to be calculated. To do this, a method of stream cost/price analysis

was used as not enough information was known to do a complete financial study. There

are eight major streams used in the process of producing ammonia. The cost streams

include the synthesis gas feed, boiler feed water, cooling water and fuel gas for the

superheater. The streams that are worth money are the CO2 produced for the urea plant,

the low pressure steam used by the urea plant, the turbine condensate and the ammonia

product made. With the mass flow rates of each of the different streams already

calculated a price per unit mass was just needed to determine the cost or price of the

specific streams. Most of the prices for these streams were set by Saskferco while a

reasonable ammonia price had to be calculated. The method used was based on the

model conventionally used in industry. The price of ammonia depends heavily upon the

natural gas price. Knowing the energy to produce a tonne of ammonia (32 GJ/tonne) and

the price of natural gas (~$8.00/GJ) a minimum price was calculated. To this a margin of

$75/tonne and a combined utility and chemical cost of $10/tonne were added. This gave

the final price of ammonia, at this current cost for natural gas, to be $341/tonne.

Multiplying the cost per unit mass by the mass flow rate gave a cost/price per unit time

for each of the different streams (see Appendix F, F.3.1 to F.3.10). Overall, it was found

39

7.0 Economics

that the revenue from this process is $11,700/hr. This does not include the utility,

maintenance or operating costs that would be incurred by this process.

7.8 Economic Summary

With the bare module cost of each piece of equipment in the process calculated as

well as the revenue that would be made from this process it was found that the economics

of this project are quite good. The total bare module cost of all the equipment was found

to be $41,231,946 while the stream analysis yielded a revenue of $11,700/hr. It was also

determined that at this moment firing the superheater using the hydrogen gas from the

feed stream was not viable but could possibly be explored again in the future.

40

8.0 Conclusions

From our analysis of an ammonia synthesis loop for an alternate feedstock,

several significant conclusions were reached regarding its design. It is the feeling of this

design team that the conclusions reached from our analysis were found with a high level

of accuracy and credibility. It was found through the process of designing the ammonia

synthesis loop that:

• The synthesis gas stream would enter the first ammonia convertor at a molar

flow rate of 8.047 kmol/s with an ammonia mole fraction of 0.0270. The synthesis gas

would exit the convertor at a molar flow rate of 7.066 kmol/s with an ammonia mole

fraction of 0.1696. The extent of hydrogen gas conversion to ammonia would increase

from 5.33% to 29.39%. The temperature of the synthesis gas across the catalyst bed

would rise from 300.0°C to 507.8°C.

• The synthesis gas stream would enter the second ammonia convertor at a molar

flow rate of 7.066 kmol/s with an ammonia mole fraction of 0.1696. The stream would

exit the second convertor at a molar flow rate of 6.755 kmol/s with an ammonia mole

fraction of 0.2234. The extent of hydrogen gas conversion would increase from 29.39%

to 37.02%. The temperature of the synthesis gas across the catalyst bed would rise from

400.0°C to 473.0°C.

• After specifying complete recycle of hydrogen and nitrogen gas, the final

product stream from the separation units would have a molar flow rate of 1.318 kmol/s,

consisting of 98.02 mol% ammonia and 1.98 mol% argon.

• The first waste heat boiler lowers the temperature of the synthesis gas stream

leaving the first ammonia convertor from 507.8°C to 400.0°C in one shell pass. In two

41

8.0 Conclusions

tube passes, boiler feed water is at 130.0°C is converted to saturated steam at 323.7°C

and 120 bar at a rate of 41.03 tonnes/h.

• The second waste heat boiler lowers the temperature of the synthesis gas stream

leaving the first ammonia convertor from 473.0°C to 340.1°C in one shell pass. In two

tube passes, boiler feed water is at 130.0°C is converted to saturated steam at 323.7°C

and 120 bar at a rate of 49.63 tonnes/h.

• The gas/gas heat exchanger heats the synthesis feed stream from 31.2°C to

300.0°C in one shell pass at a rate of 8.047 kmol/s. In one tube pass, the product stream

exiting the second ammonia convertor is cooled from 340.1°C to 55.6°C at a rate of

6.755 kmol/s.

• The steam superheater produces two steam products. Saturated steam at 120 bar

pressure from the waste heat boilers is superheated from 323.7°C to 510°C in the radiant

section at a rate of 90.65 tonnes/h. Boiler feed water at 131.8°C and 23 bar is heated in

the finned bank section, the shield bank section, and the radiant section to saturated steam

at 220.1°C at a rate of 25.00 tonnes/h. The heater is fuelled by natural gas at a rate of

2433 kg/h, resulting in a flue gas emission rate of 51.9 tonnes/h.

• Using 60.42 tonnes/h of the produced superheated steam, the synthesis gas

turbine with 70% adiabatic efficiency is powered to produce 13704 kW for the synthesis

gas compressor.

• Using 30.23 tonnes/h of the produced superheated steam, the CO2 turbine with

70% adiabatic efficiency is powered to produce 13704 kW for the CO2 compressor.

• The synthesis feed stream is compressed by a four stage synthesis gas

compressor having a 75% adiabatic efficiency. The recycled hydrogen and nitrogen gas

42

8.0 Conclusions

is reintroduced to the feed stream between the third and fourth compression stage. The

feed enters at a pressure of 50 bar, a temperature of 25.0°C, and a mass flow rate of 82.95

tonnes/h. The effluent gas exits at a pressure of 50 bar, a temperature of 31.2°C, and a

mass flow rate 265.8 tonnes/h. The synthesis is cooled in the compressor by 3

intercoolers by a combined water flow rate of 295 tonnes/h at 25°C and at atmospheric

pressure.

• The synthesis feed stream is compressed by a four stage synthesis gas

compressor having an adiabatic efficiency of 75%. The recycled hydrogen and nitrogen

gas is reintroduced to the feed stream between the third and fourth compression stage.

The feed enters at a pressure of 50 bar, a temperature of 25.0°C, and a mass flow rate of

82.95 tonnes/h. The effluent gas exits at a pressure of 50 bar, a temperature of 31.2°C,

and a mass flow rate 265.8 tonnes/h. The synthesis stream is cooled between the

compressor stages by 3 intercoolers at a combined cooling water flow rate of 295

tonnes/h at 25°C and atmospheric pressure.

• The CO2 stream for the urea plant is compressed by a four stage CO2

compressor having an adiabatic efficiency of 75%. The CO2 feed stream enters the

compressor at a temperature of 30.0°C, a pressure of 5 bar, and a mass flow rate of 95.03

tonnes/h. The CO2 stream exits at a pressure of 150 bar and a temperature of 126.6°C.

The CO2 stream is cooled between the compressor stages by 3 intercoolers at a combined

cooling water flow rate of 485 tonnes/h at 25°C and atmospheric pressure.

It is of the opinion of this design team that this project has produced results satisfying

enough to warrant the implementation of the design by Saskferco. This design team is

confident in the reliability and feasibility of the conclusions reached from this project.

43

Works Cited

1. Jennings J.R. Catalytic Ammonia Synthesis: Fundamentals and Practice. New

York: Plenum Press, 1991. 2. Berman H.L. ‘Fired Heaters: Part I-IV’, Journal of Chemical Engineering.

Volume 85, June-September 1978. 3. Ulrich G.D., Vasudevan P.T. Chemical Engineering Process Design and

Economics: a Practical Guide. 2nd Edition, Boca Raton, FL: CRC Press, 2004.

44

Acknowledgments

• Bob Edmondson, Saskferco Technical Director

• Gordon Hill, ChE 422 Advisor

• Hui Wang, ChE 422 Advisor

• Richard Evitts, Professor, University of Saskatchewan

• Mehdi Nemati, Professor, University of Saskatchewan

45

Appendix A: Process Flow Diagram

46

Appendix A Process Flow Diagram

A.1 Process Flow Diagram and Stream Compositions

Table A.1.1: Ammonia synthesis loop streams Flow Rate Temperature Pressure Composition

kmol / s oC bar yH2 yN2 yNH3 yAr

Synthesis Gas Feed 101 2.6096 25.0 5.0 0.7425 0.2475 0.0000 0.0100 Compressor Stage 1 Discharge 102 2.6096 77.8 76.6 0.7425 0.2475 0.0000 0.0100 Compressor Stage 2 Suction 103 2.6096 25.0 76.6 0.7425 0.2475 0.0000 0.0100 Compressor Stage 2 Discharge 104 2.6096 77.9 117.4 0.7425 0.2475 0.0000 0.0100 Compressor Stage 3 Suction 105 2.6096 25.0 117.4 0.7425 0.2475 0.0000 0.0100 Compressor Stage 3 Discharge 106 2.6096 78.0 180.0 0.7425 0.2475 0.0000 0.0100 To Stage 4 Mixer 107 2.6096 25.0 180.0 0.7425 0.2475 0.0000 0.0100 Compressor Stage 4 Suction 108 8.0468 25.0 180.0 0.7195 0.2398 0.0270 0.0136 Compressor Stage 4 Discharge 109 8.0468 31.2 190.0 0.7195 0.2398 0.0270 0.0136 Inlet to 8R1 110 8.0468 300.0 189.0 0.7195 0.2398 0.0270 0.0136 Outlet from 8R1 111 7.0660 507.8 184.8 0.6112 0.2037 0.1696 0.0155 Inlet to 8R2 112 7.0660 400.0 183.9 0.6112 0.2037 0.1696 0.0155 Outlet from 8R2 113 6.7551 473.0 183.4 0.5703 0.1901 0.2234 0.0162 To Gas/Gas Exchanger 114 6.7551 340.1 183.1 0.5703 0.1901 0.2234 0.0162 To Separation 115 6.7551 55.6 182.0 0.5703 0.1901 0.2234 0.0162 Recycle To Stage 4 Mixer 116 5.4372 25.0 180.0 0.7085 0.2362 0.0400 0.0154 Ammonia Product 117 1.3178 4.3 5.0 0.0000 0.0000 0.9802 0.0198

Table A.1.2: Water and steam system streams Flow Rate Temperature Pressure

kmol / s oC bar Total Boiler Feed Water 201 1.7833 130.0 129.0 BFW to Synthesis Loop 202 1.3978 130.0 129.0 BFW to Fired Heater 203 0.3856 130.0 129.0 BFW to 8E1 204 0.6325 130.0 129.0 BFW to 8E2 205 0.7653 130.0 129.0 Saturated Steam from 8E1 206 0.6325 323.7 120.0 Saturated Steam from 8E2 207 0.7653 323.7 120.0 Saturated Steam to Superheater 208 1.3978 323.7 120.0 Low Pressure Saturated Steam 209 0.3856 220.1 23.0 High Pressure Steam to Turbines 210 1.3978 510.0 120.0 Steam to CO2 Turbine 211 0.4660 510.0 120.0 Steam to Synthesis Gas Turbine 212 0.9318 510.0 120.0 CO2 Turbine Condensate 213 0.4660 69.2 0.3 Synthesis Gas Turbine Condensate 214 0.9318 69.2 0.3

47


Table A.1.3: CO2 compressor streams Flow Rate Temperature Pressure Composition

kmol / s oC bar CO2 H2O N2 O2 Stage 1 Feed 301 0.6111 30.0 5.0 0.9500 0.0040 0.0400 0.0060Stage 1 Discharge 302 0.6111 110.8 11.7 0.9500 0.0040 0.0400 0.0060Stage 2 Suction 303 0.6111 30.0 11.7 0.9500 0.0040 0.0400 0.0060Stage 2 Discharge 304 0.6111 111.7 27.4 0.9500 0.0040 0.0400 0.0060Stage 3 Suction 305 0.6111 41.0 27.4 0.9500 0.0040 0.0400 0.0060Stage 3 Discharge 306 0.6111 126.0 64.1 0.9500 0.0040 0.0400 0.0060Stage 4 Suction 307 0.6111 45.0 64.1 0.9500 0.0040 0.0400 0.0060Stage 4 Discharge 308 0.6111 126.6 150.0 0.9500 0.0040 0.0400 0.0060

Table A.1.4: Superheater fuel and flue gas streams

Flow Rate Temperature Pressure Composition kmol / s oC bar CH4 C2H6 C3H8 CO2 O2 N2 H20 Natural Gas 401 1.7981 9.0 21.0 0.0000 0.0000 0.0000 0.0000 0.2323 0.7647 0.0030Combustion Air 402 0.0659 5.0 21.0 0.9200 0.0500 0.0300 0.0000 0.0000 0.0000 0.0000Premixed Fuel 403 1.8639 8.7 21.0 0.0326 0.0017 0.0011 0.0000 0.2241 0.7376 0.0029Flue Gas 404 1.9050 202.1 1.0 0.0000 0.0000 0.0000 0.0826 0.0323 0.7282 0.1569

48



49

49

Appendix B: Ammonia Conversion

50

Appendix B Ammonia Conversion

B.1 Determining the Feed Requirement to Produce 1900 Tonnes of Ammonia/day

322 23 NHNH ⇒+ (B.1.1)

n ≡ molar flow rate (kmol/day). m ≡ mass flow rate (tonnes/day). MW ≡ molecular weight (kg/kmol). y ≡ mole fraction in the feed stream.

( )( )( )

daykmol

NH

kmolkg

tonnekg

daytonnes

NH

NH

NHNH

n

n

MWmn

565,1110304.17

10001900

3

3

3

33

=

=

=

(B.1.2)

( )day

kmolH

daykmol

H

NHH

n

nnn

348,167

565,111

2

23

2

323

2

=

×=

×=

(B.1.3)

( )day

kmolN

daykmol

N

NHN

n

nnn

783,55

565,111

2

21

2

321

2

=

×=

×=

(B.1.4)

( ) ( ) ( )day

tonnesH

kmolkg

kgtonne

daykmol

H

HHH

m

m

MWnm

4.337

01588.2348,167

2

10001

2

222

=

××=

×=

(B.1.5)

( ) ( ) ( )day

tonnesN

kmolkg

kgtonne

daykmol

N

NNN

m

m

MWnm

7.1562

0134.28783,55

2

10001

2

222

=

××=

×=

(B.1.6)

51


( )

daykmol

Ar

daykmol

Ar

HH

ArAr

n

n

nyyn

2254

348,167)7425.0()0100.0(

22

=

=

=

(B.1.7)

( ) ( ) ( )day

tonnesAr

kgtonne

kmolkg

daykmol

Ar

ArArAr

m

m

MWnm

0.90

948.392254 10001

=

××=

×=

(B.1.8)

( )day

kmolTOTAL

daykmol

TOTAL

NHArTOTAL

n

nnnnn

385,225

55783167348225422

=

++=

++=

(B.1.9)

( )day

tonnesTOTAL

daytonnes

TOTAL

NHArTOTAL

m

mmmmm

1.1990

7.15624.3370.9022

=

++=

++=

(B.1.10)

52


B.2 Deriving Equations to Interpret Stream Composition Changes Subscript 1 ≡ variable from the stream entering the ammonia reactor. Subscript 2 ≡ variable from the stream exiting the ammonia reactor. F ≡ molecular flow rate of a particular gas stream (kmol/day). X ≡ extent of conversion of hydrogen gas across the ammonia reactor. Equation 1: Overall mole balance

( ) ( )[ ]( ) XFFF

XFXFFF

H

HH

1232

12

1231

1221

12

−=

+−=

( ) XyFF

H 1232

1

2 1−= (B.2.1)

Equation 2: Ammonia mole balance ( ) ( ) ( )

( ) ( ) ( )2

131232

23

131232

23

FFXF

y

FXFF

NHHNH

NHHNH

+=

+= (B.2.2)

Substitute equation 1 into equation 2 to get equation 3:

( ) ( ) ( )( )

( ) ( ) ( )( )

( ) ( ) ( )( ) Xy

yXyy

XFyFFyXFy

y

XFFFXF

y

H

NHHNH

H

NHHNH

H

NHHNH

1232

131232

23

11232

1

11311232

23

1232

1

131232

23

1−+

=

−+

=

−+

=

( ) ( ) ( )( ) Xy

Xyyy

H

HNHNH

12

121323 23

23−

+= (B.2.3)

Rearranging equation 3 gives equation 4:

( ) ( )[ ]( ) ( )[ ]2312

1323

123

NHH

NHNH

yyyy

X+−

= (B.2.4)

53


Equation 5: Hydrogen mole balance ( ) ( ) ( )( ) ( ) [ ]

( ) ( ) [ ]2

1222

1222

121222

11

FXF

y

XFFXFFF

HH

HH

HHH

−=

−=

−=

(B.2.5)


( ) ( ) [ ]( )

( ) ( ) [ ]( )

( ) ( ) [ ]( ) Xy

Xyy

XyFFXyF

y

XFFXF

y

H

HH

H

HH

H

HH

1232

1222

12132

1

12122

1232

1

1222

11

1

1

−−

=

−−

=

−−

=

( ) ( ) [ ]( ) Xy

Xyy

H

HH

12

1222 23

13−

−= (B.2.6)

Equation 7: Nitrogen mole balance ( ) ( ) ( )( ) ( ) ( ) ( )[

( ) ( ) ( )]

( )[ ]2

1231

12122

1231

12122

1231

1222

FXyyF

y

XyyFFXFFF

HNN

HNN

HNN

−=

−=

−=

(B.2.7)


( ) ( ) ( ) ( )[ ]( )

( ) ( ) ( ) ( )[ ]( )

( ) ( ) ( )( ) Xy

Xyyy

XyFFXyyF

y

XFFXyyF

y

H

HNN

H

HNN

H

HNN

1232

1231

1222

12132

1

1231

12122

1232

1

1231

12122

1−−

=

−−

=

−−

=

( ) ( ) ( )( ) Xy

Xyyy

H

HNN

12

121222 23

3−

−= (B.2.8)

All of the above equations (B.2.1 through B.2.8) are dependent on hydrogen gas being the limiting reagent of the ammonia synthesis reaction.

54


Equation 9: Argon mole balance ( ) ( )( ) ( )

( ) ( )12

12

1122

12

ArAr

ArAr

ArAr

yFF

y

yFyFFF

=

=

=

(B.2.9)


( ) ( )( ) Xyy

yH

ArAr

1232

12 1−= (B.2.10)

55


B.3 Estimating the Equilibrium Conversion of the Ammonia Synthesis Reaction

Data for the mol percent of ammonia at equilibrium for several synthesis gases

feed compositions was found in Catalytic Ammonia Synthesis by J.R. Jennings1.

Interpolation between the data at 175 bar and 200 bar was used to arrive at a set of data

for 190 bar. This data was then converted to mole fraction, and using equation B.2.4, we

were able to calculate the conversion of hydrogen as a function of the equilibrium

temperature, shown in Table B.3.1. Similar data was collected for the original Saskferco

stream compositions. This data is presented in Figure B.3.1 for comparison.

We were given that a 10 degree approach to equilibrium is a reasonable

approximation for calculating the extent of the reaction. This means the conversion value

should be calculated as if the stream were 10 degrees hotter than it actually is.

Using the trend line option in MS Excel, an 5th order polynomial equation for the

conversion as a function of temperature was fitted, with an R2 value of 1.00.

12.053710) (T1063269.910) (T103.3009310) (T105.15002-

10) (T104.27614 10) (T 10-1.28433X

2-

24-37-

4-105-132

++×−

+×++×

+×++×=H

(B.3.1)

56


Example:

855.81%~205.80%~

15.503

200

175

=

=

=

=

=

barP

barP

KT

175200

175190175200190 )%~%~(%~

PPPP

barPbarPbarP −−

−= === (B.3.2)

159.81175200175190)205.80855.81(%~ 190 =

−−

−== barbarbarbar

barP

81159.0100

%~)( 190

2)3== = barP

NHy

( ) ( )[ ]( ) ( )[ ] 0.89984

)81159.01(7425.081159.05.1

123

2312

13232

=+

=+−

=NHH

NHNHH yy

yyX

57


Table B.3.1: Conversion of hydrogen as a function of temperature Initial Mole %: H2 - 74.25%, N2 - 24.75%, CH4 - 0%, Ar - 1.00%

Mole percent of NH3 at equilibrium

Mole fraction of NH3 at equilibrium (yNH3)2

T (K) P=175 bar P=200bar P=190bar P=175 bar P=200bar P=190bar Conversion of H2 (XH2)

423.15 92.595 93.244 92.984 0.92595 0.93244 0.92984 0.96710 433.15 91.538 92.288 91.988 0.91538 0.92288 0.91988 0.96174 443.15 90.347 91.207 90.863 0.90347 0.91207 0.90863 0.95562 453.15 89.018 89.995 89.604 0.89018 0.89995 0.89604 0.94868 463.15 87.546 88.647 88.207 0.87546 0.88647 0.88207 0.94087 473.15 85.929 87.161 86.668 0.85929 0.87161 0.86668 0.93213 483.15 84.165 85.533 84.986 0.84165 0.85533 0.84986 0.92241 493.15 82.256 83.764 83.161 0.82256 0.83764 0.83161 0.91166 503.15 80.205 81.855 81.195 0.80205 0.81855 0.81195 0.89984 513.15 78.017 79.810 79.093 0.78017 0.79810 0.79093 0.88691 523.15 75.700 77.634 76.860 0.75700 0.77634 0.76860 0.87284 533.15 73.262 75.335 74.506 0.73262 0.75335 0.74506 0.85760 543.15 70.715 72.921 72.039 0.70715 0.72921 0.72039 0.84119 553.15 68.071 70.404 69.471 0.68071 0.70404 0.69471 0.82359 563.15 65.347 67.797 66.817 0.65347 0.67797 0.66817 0.80483 573.15 62.559 65.115 64.093 0.62559 0.65115 0.64093 0.78494 583.15 59.724 62.373 61.313 0.59724 0.62373 0.61313 0.76395 593.15 56.860 59.588 58.497 0.56860 0.59588 0.58497 0.74191 603.15 53.985 56.777 55.660 0.53985 0.56777 0.55660 0.71891 613.15 51.118 53.957 52.821 0.51118 0.53957 0.52821 0.69503 623.15 48.276 51.147 49.999 0.48276 0.51147 0.49999 0.67038 633.15 45.478 48.363 47.209 0.45478 0.48363 0.47209 0.64508 643.15 42.737 45.620 44.467 0.42737 0.45620 0.44467 0.61925 653.15 40.070 42.934 41.788 0.40070 0.42934 0.41788 0.59305 663.15 37.487 40.318 39.186 0.37487 0.40318 0.39186 0.56661 673.15 35.000 37.784 36.670 0.35000 0.37784 0.36670 0.54009 683.15 32.618 35.341 34.252 0.32618 0.35341 0.34252 0.51365 693.15 30.346 32.998 31.937 0.30346 0.32998 0.31937 0.48743 703.15 28.190 30.762 29.733 0.28190 0.30762 0.29733 0.46158 713.15 26.153 28.635 27.642 0.26153 0.28635 0.27642 0.43622 723.15 24.235 26.623 25.668 0.24235 0.26623 0.25668 0.41150 733.15 22.436 24.725 23.809 0.22436 0.24725 0.23809 0.38750 743.15 20.754 22.941 22.066 0.20754 0.22941 0.22066 0.36431 753.15 19.187 21.269 20.436 0.19187 0.21269 0.20436 0.34202 763.15 17.730 19.708 18.917 0.17730 0.19708 0.18917 0.32068 773.15 16.379 18.254 17.504 0.16379 0.18254 0.17504 0.30034 783.15 15.129 16.902 16.193 0.15129 0.16902 0.16193 0.28101 793.15 13.975 15.648 14.979 0.13975 0.15648 0.14979 0.26272 803.15 12.911 14.487 13.857 0.12911 0.14487 0.13857 0.24546 813.15 11.930 13.413 12.820 0.11930 0.13413 0.12820 0.22921 823.15 11.028 12.422 11.864 0.11028 0.12422 0.11864 0.21396

58


Figure B.3.1: Ammonia synthesis equilibrium at various stream compositions

59


B.4 Reactor Composition Iterative Procedure for 8R1 and 8R2

This iterative procedure calculates the compositions of the several streams, given

the inlet and outlet temperatures of both reactors.

• Stream 1: the stream entering the 8R1. A combination of the feed stream and the

recycle stream.

• Stream 2: the stream exiting 8R1.

• Stream 3: has concentration identical to stream 2

• Stream 4: the stream exiting 8R2.

• Recycle: the stream being returned to the process after the ammonia product has been

separated out.

The composition of the feed was given as yF,H2=0.7425, yF,N2=0.2475, and

yF,Ar=0.0100, and in section B.1 it was calculated that a rate of 225,385 kmol/day or

2.6096 kmol/s of feed was required to produce 1900 tonnes of ammonia per day. The

temperatures for each stream are given as follows: T1=573.15 K, T2=780.90 K,

T3=673.15 K, and T4=746.15 K.

Using the fifth order polynomial equation that was developed in Appendix B.3 we

can calculate the percent of hydrogen as ammonia for a 10oC stream 2 equilibrium

approach.

2939.090.780T2== KX

This value is the extent of the conversion of hydrogen gas to ammonia. This is

equal to the conversion of hydrogen, if we take state 1 to be the concentrations when any

ammonia in the system is converted back to hydrogen and nitrogen (ie. y1,NH3 = 0).

60


Using equations B.2.3, B.2.4, B.2.6, B.2.8 and B.2.10 developed earlier, and the

conversion calculated above, we can calculate the resulting concentrations exiting both

reactors.

To calculate the concentrations for the recycle stream, we first needed to develop

a rough model for our separators. An in depth separator design was beyond the scope of

our project.

We were given that the ammonia in the recycle stream, yR,NH3=0.0400, and that

100% of the hydrogen and nitrogen are recycled. We assumed the amount of argon

recycled in the original Saskferco design would be proportional to the amount recycled in

our system. Based on this, 76.2% of the argon is recycled. The rest leaves dissolved in

the ammonia product stream.

( ) 04.03

=RNHy (B.4.1)

RNH

ArNHR y

yyyFF

)(1)(762.0)()(

3

22 4444 −

++= (B.4.2)

( ) ( )R

ArRAr F

Fyy 44762.0= (B.4.3)

( ) ( )R

H

RH FFy

y 442

2= (B.4.3)

( ) ( )R

N

RN FFy

y 442

2= (B.4.4)

61


The final step in the first iteration is to calculate the product stream.

RP FFF −= 4 (B.4.5)

( ) ( ) ( )P

RNHRNH

PNH FyFyF

y 33

3

44 += (B.4.6)

( ) ( ) ( )P

RArRArPAr F

yFyFy

+= 44 (B.4.7)

Since 100% of the hydrogen and nitrogen are recycled, yH2,P and yN2,P equal 0.00.

Now, to recalculate the concentrations in stream 1:

nRF

n FFF −=+ 11 (B.4.8)

( ) ( ) ( )1

1

1

122

2 ++ += n

nR

n

RHFFHnH F

FyFyy (B.4.9)

( ) ( ) ( )1

1

1

122

2 ++ += n

nR

n

RNFFNnN F

FyFyy (B.4.10)

( ) ( ) ( )1

1

1

133

3 ++ += n

nR

n

RNHFFNHnNH F

FyFyy (B.4.11)

( ) ( ) ( )1

1

11 ++ += n

nR

nRArFFArn

Ar FFyFy

y (B.4.12)

Using equation B.2.4, and the equations listed below we can calculate the

concentrations of a fictional stream where all the ammonia has been broken down to

hydrogen and nitrogen.

62


( )( ) ( )

( ) 1

1

1

1

1

11*

3

32

2 123

+

++

+

+

+= n

NH

nNH

n

Hn

H y

yyy (B.4.13)

( )( ) ( )

( ) 1

1

1

1

1

11*

3

32

2 121

+

++

+

+

+= n

NH

nNH

n

Nn

N y

yyy (B.4.14)

( ) ( )( ) 1

1

1

11*

31 +

++

+= n

NH

n

Arn

Ar yy

y (B.4.15)

( )( ) ( ) 1

1

1

1

111*

32321 ++

++

−=

nNH

n

H

nn

yZ

FF (B.4.16)

Now we can go back and calculate the concentrations in the streams exiting both

reactors using equations B.2.3, B.2.4, B.2.6, B.2.8 and B.2.10, as we did above, and keep

iterating until the concentrations in the final streams no longer change. Please see Tables

B.4.1 through B.4.6 for an example of these calculations.

63


Table B.4.1: Stream 1 concentrations entering 8R1

n ( )12HX ( )

12Hy ( )12Ny ( )

13NHy ( )1Ary 1F (kmol/s)

0 0.0000 0.7425 0.2475 0.0000 0.0100 2.6096 1 0.0316 0.7301 0.2434 0.0159 0.0106 4.3253 2 0.0416 0.7259 0.2420 0.0210 0.0111 5.4988 3 0.0463 0.7238 0.2413 0.0234 0.0115 6.3015 4 0.0489 0.7225 0.2408 0.0248 0.0119 6.8508 5 0.0504 0.7217 0.2406 0.0256 0.0122 7.2269 6 0.0514 0.7211 0.2404 0.0261 0.0125 7.4844 7 0.0520 0.7207 0.2402 0.0264 0.0127 7.6608 8 0.0525 0.7204 0.2401 0.0266 0.0129 7.7817 9 0.0527 0.7202 0.2401 0.0267 0.0130 7.8646

10 0.0529 0.7200 0.2400 0.0268 0.0131 7.9215 11 0.0531 0.7199 0.2400 0.0269 0.0132 7.9606 12 0.0531 0.7198 0.2399 0.0269 0.0133 7.9874 13 0.0532 0.7197 0.2399 0.0270 0.0134 8.0058 14 0.0532 0.7197 0.2399 0.0270 0.0134 8.0185 15 0.0533 0.7196 0.2399 0.0270 0.0135 8.0273 16 0.0533 0.7196 0.2399 0.0270 0.0135 8.0333 17 0.0533 0.7196 0.2399 0.0270 0.0135 8.0374 18 0.0533 0.7196 0.2399 0.0270 0.0136 8.0403 19 0.0533 0.7196 0.2399 0.0270 0.0136 8.0423 20 0.0533 0.7195 0.2398 0.0270 0.0136 8.0437 21 0.0533 0.7195 0.2398 0.0270 0.0136 8.0446 22 0.0533 0.7195 0.2398 0.0270 0.0136 8.0453 23 0.0533 0.7195 0.2398 0.0270 0.0136 8.0457 24 0.0533 0.7195 0.2398 0.0270 0.0136 8.0461 25 0.0533 0.7195 0.2398 0.0270 0.0136 8.0463 26 0.0533 0.7195 0.2398 0.0270 0.0136 8.0464 27 0.0533 0.7195 0.2398 0.0270 0.0136 8.0466 28 0.0533 0.7195 0.2398 0.0270 0.0136 8.0466 29 0.0533 0.7195 0.2398 0.0270 0.0136 8.0467 30 0.0533 0.7195 0.2398 0.0270 0.0136 8.0467 31 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468 32 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468 33 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468 34 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468 35 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468 36 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468 37 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468 38 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468 39 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468 40 0.0533 0.7195 0.2398 0.0270 0.0136 8.0468

64


Table B.4.2: Synthesis loop composition at zero conversion

n ( )*2Hy ( )*

2Ny ( )*Ary *F (kmol/s)

0 0.7425 0.2475 0.0100 2.6096 1 0.7422 0.2474 0.0105 4.3939 2 0.7418 0.2473 0.0109 5.6143 3 0.7415 0.2472 0.0113 6.4492 4 0.7413 0.2471 0.0116 7.0205 5 0.7411 0.2470 0.0119 7.4116 6 0.7409 0.2470 0.0121 7.6794 7 0.7407 0.2469 0.0124 7.8629 8 0.7406 0.2469 0.0125 7.9886 9 0.7405 0.2468 0.0127 8.0748

10 0.7404 0.2468 0.0128 8.1340 11 0.7403 0.2468 0.0129 8.1746 12 0.7403 0.2468 0.0130 8.2025 13 0.7402 0.2467 0.0130 8.2217 14 0.7402 0.2467 0.0131 8.2349 15 0.7402 0.2467 0.0131 8.2440 16 0.7401 0.2467 0.0132 8.2502 17 0.7401 0.2467 0.0132 8.2545 18 0.7401 0.2467 0.0132 8.2575 19 0.7401 0.2467 0.0132 8.2596 20 0.7401 0.2467 0.0132 8.2610 21 0.7401 0.2467 0.0132 8.2620 22 0.7401 0.2467 0.0132 8.2627 23 0.7401 0.2467 0.0132 8.2632 24 0.7401 0.2467 0.0133 8.2635 25 0.7401 0.2467 0.0133 8.2638 26 0.7401 0.2467 0.0133 8.2639 27 0.7401 0.2467 0.0133 8.2640 28 0.7401 0.2467 0.0133 8.2641 29 0.7401 0.2467 0.0133 8.2642 30 0.7401 0.2467 0.0133 8.2642 31 0.7401 0.2467 0.0133 8.2642 32 0.7401 0.2467 0.0133 8.2643 33 0.7401 0.2467 0.0133 8.2643 34 0.7401 0.2467 0.0133 8.2643 35 0.7400 0.2467 0.0133 8.2643 36 0.7400 0.2467 0.0133 8.2643 37 0.7400 0.2467 0.0133 8.2643 38 0.7400 0.2467 0.0133 8.2643 39 0.7400 0.2467 0.0133 8.2643 40 0.7400 0.2467 0.0133 8.2643

65


Table B.4.3: Stream 2 exiting 8R1

( )22Hy ( )

22Ny ( )23NHy ( )2Ary( )

22HX 2F n (kmol/s)

0 0.2939 0.6135 0.2045 0.1702 0.0117 2.2300 1 0.2939 0.6132 0.2044 0.1702 0.0122 3.7550 2 0.2939 0.6129 0.2043 0.1701 0.0127 4.7983 3 0.2939 0.6126 0.2042 0.1700 0.0132 5.5122 4 0.2939 0.6124 0.2041 0.1699 0.0136 6.0008 5 0.2939 0.6122 0.2041 0.1699 0.0139 6.3354 6 0.2939 0.6120 0.2040 0.1698 0.0142 6.5646 7 0.2939 0.6118 0.2039 0.1698 0.0145 6.7217 8 0.2939 0.6117 0.2039 0.1697 0.0147 6.8294 9 0.2939 0.6116 0.2039 0.1697 0.0148 6.9033

10 0.2939 0.6115 0.2038 0.1697 0.0150 6.9540 11 0.2939 0.6114 0.2038 0.1697 0.0151 6.9888 12 0.2939 0.6114 0.2038 0.1696 0.0152 7.0128 13 0.2939 0.6113 0.2038 0.1696 0.0153 7.0293 14 0.2939 0.6113 0.2038 0.1696 0.0153 7.0406 15 0.2939 0.6113 0.2038 0.1696 0.0154 7.0484 16 0.2939 0.6112 0.2037 0.1696 0.0154 7.0538 17 0.2939 0.6112 0.2037 0.1696 0.0154 7.0575 18 0.2939 0.6112 0.2037 0.1696 0.0154 7.0601 19 0.2939 0.6112 0.2037 0.1696 0.0155 7.0619 20 0.2939 0.6112 0.2037 0.1696 0.0155 7.0631 21 0.2939 0.6112 0.2037 0.1696 0.0155 7.0640 22 0.2939 0.6112 0.2037 0.1696 0.0155 7.0646 23 0.2939 0.6112 0.2037 0.1696 0.0155 7.0650 24 0.2939 0.6112 0.2037 0.1696 0.0155 7.0653 25 0.2939 0.6112 0.2037 0.1696 0.0155 7.0655 26 0.2939 0.6112 0.2037 0.1696 0.0155 7.0657 27 0.2939 0.6112 0.2037 0.1696 0.0155 7.0658 28 0.2939 0.6112 0.2037 0.1696 0.0155 7.0658 29 0.2939 0.6112 0.2037 0.1696 0.0155 7.0659 30 0.2939 0.6112 0.2037 0.1696 0.0155 7.0659 31 0.2939 0.6112 0.2037 0.1696 0.0155 7.0659 32 0.2939 0.6112 0.2037 0.1696 0.0155 7.0660 33 0.2939 0.6112 0.2037 0.1696 0.0155 7.0660 34 0.2939 0.6112 0.2037 0.1696 0.0155 7.0660 35 0.2939 0.6112 0.2037 0.1696 0.0155 7.0660 36 0.2939 0.6112 0.2037 0.1696 0.0155 7.0660 37 0.2939 0.6112 0.2037 0.1696 0.0155 7.0660 38 0.2939 0.6112 0.2037 0.1696 0.0155 7.0660 39 0.2939 0.6112 0.2037 0.1696 0.0155 7.0660 40 0.2939 0.6112 0.2037 0.1696 0.0155 7.0660

66


Table B.4.4: Stream 3 exiting 8R2

n ( )32HX ( )

32Hy ( )32Ny ( )

33NHy ( )3Ary 3F (kmol/s)

0 0.3702 0.5726 0.1909 0.2243 0.0122 2.1314 1 0.3702 0.5722 0.1907 0.2242 0.0128 3.5892 2 0.3702 0.5719 0.1906 0.2241 0.0133 4.5866 3 0.3702 0.5717 0.1906 0.2240 0.0138 5.2690 4 0.3702 0.5714 0.1905 0.2239 0.0142 5.7362 5 0.3702 0.5712 0.1904 0.2238 0.0146 6.0562 6 0.3702 0.5711 0.1904 0.2237 0.0149 6.2754 7 0.3702 0.5709 0.1903 0.2237 0.0151 6.4256 8 0.3702 0.5708 0.1903 0.2236 0.0153 6.5286 9 0.3702 0.5707 0.1902 0.2236 0.0155 6.5993

10 0.3702 0.5706 0.1902 0.2236 0.0157 6.6478 11 0.3702 0.5705 0.1902 0.2235 0.0158 6.6812 12 0.3702 0.5705 0.1902 0.2235 0.0159 6.7041 13 0.3702 0.5704 0.1901 0.2235 0.0160 6.7199 14 0.3702 0.5704 0.1901 0.2235 0.0160 6.7307 15 0.3702 0.5704 0.1901 0.2235 0.0161 6.7382 16 0.3702 0.5703 0.1901 0.2235 0.0161 6.7434 17 0.3702 0.5703 0.1901 0.2234 0.0161 6.7470 18 0.3702 0.5703 0.1901 0.2234 0.0162 6.7494 19 0.3702 0.5703 0.1901 0.2234 0.0162 6.7511 20 0.3702 0.5703 0.1901 0.2234 0.0162 6.7523 21 0.3702 0.5703 0.1901 0.2234 0.0162 6.7532 22 0.3702 0.5703 0.1901 0.2234 0.0162 6.7537 23 0.3702 0.5703 0.1901 0.2234 0.0162 6.7541 24 0.3702 0.5703 0.1901 0.2234 0.0162 6.7544 25 0.3702 0.5703 0.1901 0.2234 0.0162 6.7546 26 0.3702 0.5703 0.1901 0.2234 0.0162 6.7547 27 0.3702 0.5703 0.1901 0.2234 0.0162 6.7548 28 0.3702 0.5703 0.1901 0.2234 0.0162 6.7549 29 0.3702 0.5703 0.1901 0.2234 0.0162 6.7550 30 0.3702 0.5703 0.1901 0.2234 0.0162 6.7550 31 0.3702 0.5703 0.1901 0.2234 0.0162 6.7550 32 0.3702 0.5703 0.1901 0.2234 0.0162 6.7550 33 0.3702 0.5703 0.1901 0.2234 0.0162 6.7550 34 0.3702 0.5703 0.1901 0.2234 0.0162 6.7551 35 0.3702 0.5703 0.1901 0.2234 0.0162 6.7551 36 0.3702 0.5703 0.1901 0.2234 0.0162 6.7551 37 0.3702 0.5703 0.1901 0.2234 0.0162 6.7551 38 0.3702 0.5703 0.1901 0.2234 0.0162 6.7551 39 0.3702 0.5703 0.1901 0.2234 0.0162 6.7551 40 0.3702 0.5703 0.1901 0.2234 0.0162 6.7551

67


Table B.4.5: The recycle stream

n ( )RHX

2 ( )

RHy2

( )RNy

2 ( )

RNHy3

( )RAry RF (kmol/s)

0 0.0778 0.7113 0.2371 0.0400 0.0116 1.7157 1 0.0778 0.7109 0.2370 0.0400 0.0121 2.8892 2 0.0779 0.7105 0.2368 0.0400 0.0126 3.6919 3 0.0779 0.7102 0.2367 0.0400 0.0131 4.2413 4 0.0779 0.7099 0.2366 0.0400 0.0134 4.6173 5 0.0780 0.7097 0.2366 0.0400 0.0138 4.8748 6 0.0780 0.7094 0.2365 0.0400 0.0141 5.0512 7 0.0780 0.7093 0.2364 0.0400 0.0143 5.1721 8 0.0780 0.7091 0.2364 0.0400 0.0145 5.2550 9 0.0780 0.7090 0.2363 0.0400 0.0147 5.3119

10 0.0780 0.7089 0.2363 0.0400 0.0148 5.3510 11 0.0780 0.7088 0.2363 0.0400 0.0149 5.3778 12 0.0781 0.7087 0.2362 0.0400 0.0150 5.3962 13 0.0781 0.7087 0.2362 0.0400 0.0151 5.4089 14 0.0781 0.7086 0.2362 0.0400 0.0152 5.4177 15 0.0781 0.7086 0.2362 0.0400 0.0152 5.4237 16 0.0781 0.7086 0.2362 0.0400 0.0152 5.4278 17 0.0781 0.7085 0.2362 0.0400 0.0153 5.4307 18 0.0781 0.7085 0.2362 0.0400 0.0153 5.4327 19 0.0781 0.7085 0.2362 0.0400 0.0153 5.4341 20 0.0781 0.7085 0.2362 0.0400 0.0153 5.4350 21 0.0781 0.7085 0.2362 0.0400 0.0153 5.4357 22 0.0781 0.7085 0.2362 0.0400 0.0153 5.4361 23 0.0781 0.7085 0.2362 0.0400 0.0153 5.4365 24 0.0781 0.7085 0.2362 0.0400 0.0154 5.4367 25 0.0781 0.7085 0.2362 0.0400 0.0154 5.4369 26 0.0781 0.7085 0.2362 0.0400 0.0154 5.4370 27 0.0781 0.7085 0.2362 0.0400 0.0154 5.4370 28 0.0781 0.7085 0.2362 0.0400 0.0154 5.4371 29 0.0781 0.7085 0.2362 0.0400 0.0154 5.4371 30 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 31 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 32 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 33 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 34 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 35 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 36 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 37 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 38 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 39 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372 40 0.0781 0.7085 0.2362 0.0400 0.0154 5.4372

68


Table B.4.6: Summary of final stream compositions and flow rates

Feed Stream:

( )12Hy ( )

12Ny ( )13NHy ( )1Ary 1F (kmol/s)

0.7425 0.2475 0.0000 0.0100 2.6096 Product Stream:

( )PHy

2 ( )

PNy2

( )PNHy

3 ( )PAry PF (kmol/s) Ammonia Flow rate

(kmol/day) Ammonia Flow rate

(tonnes/day) 0.0000 0.0000 0.9802 0.0198 1.3178 111607 1900

Recycle Stream:

( )RHy

2 ( )

RNy2

( )RNHy

3 ( )RAry RF (kmol/s)

0.7085 0.2362 0.0400 0.0154 5.4372 Stream Exiting 8R2:

( )32Hy ( )


0.5703 0.1901 0.2234 0.0162 6.7551 Stream Exiting 8R1:

( )22Hy ( )


0.6112 0.2037 0.1696 0.0155 7.0660 Stream Entering 8R1:

( )12Hy ( )


0.7195 0.2398 0.0270 0.0136 8.0468

69


B.5 Energy Balance Iteration Procedure for 8R1 and 8R2

This iterative procedure calculates the temperature of the gas leaving the reactors

8R1 and 8R2. Inlet values for the reactors 8R1 and 8R2 were selected to be 300oC and

400oC respectively. (573.15 K and 673.15 K)

Guess a value for the outlet temperatures for 8R1 and 8R2. These will be the

temperature at which equilibrium will be reached. Using the iterative procedure for

calculating reactor compositions in Appendix B.4, find the outlet composition of the

reactors.

Using equation B.2.4 developed in Appendix B.2, the conversion across each

reactor can be calculated:

322

33

,2,1,1

,1,28R1 5.1X

NHHH

NHNH

yyyyy

+

−= ` (B.5.1)

322

33

,4,2,2

,2,48R2 5.1X

NHHH

NHNH

yyyyy

+

−= (B.5.2)

These reactors are well insulated, so at steady state almost all of the heat

generated goes to heating the synthesis gas in the system, and very little is lost to the

atmosphere. This means we can calculate the outlet temperature of the gas if we know

the heat capacity of our synthesis gas, and the heat of reaction.

18,

18,18,112

22

RP

RHRH

CHXy

TTΔ

+= (B.5.3)

28,

28,28,234

22

RP

RHRH

CHXy

TTΔ

+= (B.5.4)

70


Use the new values for T2 and T4 as the guessed values, and iterate. Alternately,

you can use a program like solver from MS Excel to minimize the differences between

the guessed and calculated temperature values.

The heat capacity was estimated using the HYSIS simulation program. The

average of the heat capacity at the inlet and outlet temperature was used and new values

were used in the calculations after each iteration until the values stopped changing.

Heat of reaction was estimated for both reactors based on the information about the

original Saskferco process that we were provided:

In Reactor 8R1:

CP1 ≡ average heat capacity of synthesis stream in reactor 8R1 (kJ/kmol·K). ΔHR1 ≡ available heat of reaction per mole of hydrogen reacted in reactor 8R1(MJ/kmol). X1 ≡ extent of conversion of hydrogen across reactor 8R1. ΔT = TOUT – TIN ≡ temperature change of the synthesis stream across the reactor bed (K). FIN ≡ inlet molar flow rate (kmol/s).

( )( )

( ) ( )

( )( )

( )( )( )( )

26.36

6116.02576.0573740

1

259.3650.32

1

2

11

1

21

1

21

211

HkmolMJ

R

KkmolkJ

R

INH

PINOUTR

P

INHRINOUT

INOUTPIN

INHINR

INHRPIN

H

KKH

yXCTT

H

CyXH

TT

TTCF

yXFHT

FXHTCF

⋅

⋅+

=Δ

−=Δ

−=Δ

Δ=−

−=Δ

=Δ

Δ=Δ

(B.5.5)

71


In Reactor 8R2:

CP2 ≡ average heat capacity of synthesis stream in reactor 8R2 (kJ/kmol·K). ΔHR2 ≡ available heat of reaction per mole of hydrogen reacted in reactor 8R2(MJ/kmol). X2 ≡ extent of conversion of hydrogen across reactor 8R2.

( )( )

( ) ( )

( )( )

( )( )( )( )

22.38

5073.008115.0673716

2

215.3793.35

2

22

22

2

222

2

222

2222

HkmolMJ

R

KkmolkJ

R

INH

PINOUTR

P

INHRINOUT

INOUTPIN

INHINR

INHRPIN

H

KKH

yXCTT

H

CyXH

TT

TTCF

yFXHT

FXHTCF

⋅

⋅+

=Δ

−=Δ

−=Δ

Δ=−

−=Δ

=Δ

Δ=Δ

(B.5.6)

Example:

Guess T2 and T4 equal to 750 K and 720 K respectively. From the procedure in

Appendix B.4 we get the following information about the streams:

Table B.5.1: Example stream compositions for an equilibrium temperature of 750 K for reactor 8R1 and an equilibrium temperature of 720K for reactor 8R1 Stream Entering First Convertor: y1,H2 y1,N2 y1,NH3 y1,Ar

0.7194 0.2398 0.0242 0.0166 Stream Exiting First Convertor: y2,H2 y2,N2 y2,NH3 y2,Ar

0.5733 0.1911 0.2159 0.0197 Stream Exiting Second Convertor: y4,H2 y4,N2 y4,NH3 y4,Ar

0.5295 0.1765 0.2733 0.0206

72


3288.)2168(.7195.7195.

0274.2168.5.15.1X322

33

,2,1,1

,1,28R1 =

+−

=+

−=

NHHH

NHNH

yyyyy

1179.)2733(.5733.5733.

2159.2733.5.15.1X322

33

,4,2,2

,2,48R2 =

+−

=+

−=

NHHH

NHNH

yyyyy

KkmolKkJ

kmolkJC

HXyTT

RP

RHRH 9.841/21.32

)/36600)(3288)(.7194(.15.57318,

18,18,112

22 =+=Δ

+=

KkmolKkJ

kmolkJC

HXyTT

RP

RHRH 9.747/54.34

)/38200)(1179)(.5733(.15.67328,

28,28,234

22 =+=Δ

+=

KKKTT 9.917509.841*22 =−=−

KKKTT 9.277209.747*44 =−=−

Iterate again until T2 – T2* and T4 – T4

* converge on 0. The final temperature

values are T2 = 780.9 K and T4 = 746.1 K.

73

Appendix C: Steam Superheater

74

Appendix C Steam Superheater

C.1 Calculating the Net Heating Value of Natural Gas Stream Table C.1.1: Calculating the average molecular weight

Component Molecular Weight Mole % kg/100kmol of fuel CH4 16.042 92.0 1475.864 C2H6 30.068 5.0 150.340 C3H8 44.094 3.0 132.282

Total 1758.486 Table C.1.2: Calculating the average lower heating value

Component Lower Heating Value (kJ/kg) kJ/100kmol of fuel CH4 49,994 73.784×106

C2H6 47,489 7.139×106

C3H8 46,371 6.134×106

Total 87.057×106

Table C.1.3: Calculating the air requirement for combustion

Component kg air / kg fuel kg air / 100kmol of fuel CH4 17.195 25,377 C2H6 15.899 2,390 C3H8 15.246 2,017

Total 29,785 MWAVE ≡ average molecular weight (kg/kmol).

( )( ) ( )( ) ( )( )( )( ) ( )( ) ( )( )[ ]

kmolkg

kmolkg

AVE

kmolkg

AVE

HCHCHCHCCHCHAVE

MW

MW

yMWyMWyMWMW

100

8383626244

5.1758585.17

030.0094.44050.0068.30920.0042.16

==

++=

++=

(C.1.1)

NHV ≡ net heating value of the natural gas (kJ/kg). LHV ≡ lower heating value of the natural gas (kJ/100kmol).

( )( )

kgMJ

kmolkg

kmolkJ

AVE

NHV

NHV

MWLHVNHV

51.495.175810057.87

100

1006

=

×=

=

(C.1.2)

75


ARw ≡ air requirement (kg air/kg fuel). ARm ≡ air requirement (kg air/100kmol fuel).

( )( )

fuelkgairkg

w

fuelkmolfuelkg

fuelkmolairkg

w

AVE

mw

AR

AR

MWAR

AR

⋅⋅

⋅⋅

⋅⋅

=

=

=

94.16

5.1758

785,29

100

100 (C.1.3)

ARE ≡ air requirement for 20% excess air (kg air/kg fuel).

( )( )( )

fuelkgairkg

E

fuelkgairkg

E

wE

AR

AR

ARAR

⋅⋅

⋅⋅

=

=

=

33.20

94.1620.1

20.1

(C.1.4)

TFG ≡ total flue gas (kg flue gas/kg fuel).

( )( )

fuelkggasfluekg

fuelkggasfluekg

fuelkggasfluekg

E

TFG

TFG

ARTFG

⋅⋅⋅

⋅⋅⋅

⋅⋅⋅

=

+=

+=

33.21

33.201

1

(C.1.5)

76


C.2 Heating Requirements of the Steam Streams QUS ≡ heat absorbed by the urea steam (GJ/h). QUS = 57.61 GJ/h QSS ≡ heat absorbed by the superheated steam (GJ/h). QSS = 50.64 GJ/h QR” ≡ average heat flux in the radiant section (kJ/h·m2). QR” = 11,000 BTU/h·ft2 = 0.1249 GJ/h·m2

FGT ≡ flue gas temperature exiting the convection section (ºC). (TUS)IN ≡ inlet urea water temperature (ºF).

( )( )

CFFGTFFFGT

FTFGT INUS

oo

oo

o

1.2152.4191502.269

150

==

+=

+=

(C.2.1)

HA,FGT ≡ heat available based on the flue gas temperature exiting the convection section

(kJ/kg). HA,FGT = 17,700 BTU/lb = 41,168 kJ/kg %H ≡ percent heat extraction from the superheater.

( )( )

%85.89%

%100819,45168,41

%

%100%,

,

=

×=

×=

H

H

HH

H

kgkJ

kgkJ

MAXA

FGTA

(C.2.2)

μ ≡ calculated efficiency. %R ≡ predicted radiant heat losses.

%85.87%00.2%85.89

%%

=−=

−=

μμμ RH

(C.2.3)

77


QT ≡ total heat duty for the superheater (GJ/h).

( )h

GJT

hGJ

T

SSUST

QQ

QQQ

25.10864.5061.57

=

+=

+=

(C.2.4)

HT ≡ total heat fired by the superheater (GJ/h).

( )( )

hGJ

T

hGJ

T

TT

H

H

QH

5.1208785.025.108

=

=

=μ

(C.2.5)

FC ≡ mass flow rate of fuel consumed (kg/h).

( )( )

hkg

C

kgkJ

hkJ

C

TC

F

F

NHVHF

2433

510,49105.120 6

=

×=

=

(C.2.6)

FG ≡ mass flow rate of flue gas (kg/h).

( ) ( )hkg

G

fuelkggasfluekg

hfuelkg

G

CG

F

F

TFGFF

900,51

33.212433

=

×=

×=

⋅⋅⋅⋅ (C.2.7)

78


C.3 Calculations for the Radiant Section TRTW ≡ radiant tube wall temperature (ºC). (TSS)OUT ≡ outlet superheated steam temperature (ºF).

( )( )

CFT

FFT

FTT

RTW

RTW

OUTSSRTW

oo

oo

o

5521025

75950

75

==

+=

+=

(C.3.1)

BWT ≡ bridgewall temperature (ºC). BWT = 1700ºF = 927ºC (from Figure C3) HA,BWT ≡ heat made available based on the bridgewall temperature (kJ/kg). HA,BWT = 10,400 BTU/lb = 24,189 kJ/kg (from Figure C1) QR ≡ heat transfer in the radiant section (GJ/h).

( )( ) ( )

hGJ

R

hGJ

R

kgkJ

kgkJ

T

R

FGTA

BWTA

Q

Q

QQ

HH

60.63

24.108168,41189,24,

,

=

=

=

(B.3.2)

QC ≡ heat transfer in the convective section (GJ/h).

( )h

GJC

hGJ

C

RTC

QQ

QQQ

64.4460.6324.108

=

−=

−=

(C.3.3)

SFA ≡ shield-bank free area (m2). N ≡ number of tubes per row. L ≡ horizontal tube length (ft). s ≡ spacing between tube centers (in). do ≡ outer diameter of each tube (in).

( )( )( )( )(

22121

94.667.74

5.40.81616

mftSFA

ininftSFA

dsLNSFA

inft

o

==

−=

−⋅⋅=

) (C.3.4)

79


G ≡ flue gas mass velocity (kg/s⋅m2).

( )( )( )

208.2

360094.6905,512

mskg

hs

hkg

G

G

mG

SFAF

G

⋅=

=

=

(C.3.5)

ASB ≡ surface area of first shield bank row (m2).

( )( ) ( )(22

121

02.286.301

5.41616

mftA

inftA

dNLA

SB

inft

SB

oSB

==

=

=

π )π

(C.3.6)

AR ≡ required radiant surface area (m2).

( )( )

2

''

1.509

1249.060.63

2

mA

A

QQ

A

R

mhGJh

GJ

R

R

RR

=

=

=

⋅

(C.3.7)

AVT ≡ vertical tube radiant surface (m2).

(2

2

1.481

02.281.509

mA

mA

AAA

VT

VT

SBRVT

=

−=

−=

) (C.3.8)

80


C.4 Determining the Optimum Number of Superheated Steam Passes FSS’’ ≡ superheated steam mass velocity (kg/s⋅m2). Optimum Mass Velocity: 22 2.366''5.146

mskg

SSmskg F

⋅⋅≤≤

ρSS ≡ density of superheated steam (kg/m3). ( )( ) 3

3

58.36

70.75

mkg

OUTSS

mkg

INSS

=

=

ρ

ρ (C.4.1)

Optimum linear velocity: ( ) s

mOUTSSV 10=

( ) ( )( )( )

2

3

8.365''

1058.36''

''

mskg

SS

sm

mkg

SS

OUTSSOUTSSSS

F

F

VF

⋅=

=

= ρ

(C.4.2)

AC ≡ cross-sectional area of schedule 40 piping (m2). t ≡ tube wall thickness (in).

( ) ( )(23

1045.6

2

2

10211.8

237.025.4

2

24

2

2

2

mA

ininA

td

A

C

cmm

incm

C

oC

−×=

⎟⎠⎞

⎜⎝⎛ −=

⎟⎠⎞

⎜⎝⎛ −=

π

π

) (C.4.3)

nSS ≡ number of superheated steam passes. FSS ≡ superheated steam mass flow rate (kg/s).

( )( )( )

passesn

mn

AFF

n

SS

mskg

skg

SS

CSS

SSSS

938.8

008211.08.3651746.25

''

22

≈=

=

×=

⋅

(C.4.4)

81


C.5 Determining the Optimum Number of Urea Steam Passes FUS’’ ≡ urea steam mass velocity (kg/s⋅m2). Optimum Mass Velocity: 22 4.732''2.488

mskg

USmskg F

⋅⋅≤≤

ρUS ≡ density of urea steam (kg/m3). ( )( ) 3

3

20.11

4.921

mkg

OUTUS

mkg

INUS

=

=

ρ

ρ (C.5.1)

nUS ≡ number of urea steam passes. FUS ≡ urea steam mass flow rate (kg/s). Let FUS’’ = 500 kg/s⋅m2

( )( )( )

passesn

mn

AFF

n

US

mskg

skg

US

CUS

USUS

269.1

008211.0500944.6

''

22

≈=

=

×=

⋅

(C.5.2)

82


C.6 Calculations for the Shield Bank Section TUS ≡ temperature of urea steam (°C). (TUS)IN = (TUS)OUT = 220.1°C (in the process of being vaporized) TFG ≡ temperature of flue gas (°C). (TFG)IN = 926.7°C (TFG)OUT = 765.6°C LMTD ≡ log-mean temperature difference (°C).

( ) ( )[ ] ( ) ( )[ ]( ) ( )[ ]( ) ( )[ ]

[ ] [ ][ ][ ]

[ ] [ ][ ][ ]

CLMTD

CC

CC

CCCC

CCCCLMTD

TTTT

TTTTLMTD

INUSOUTFG

OUTUSINFG

INUSOUTFGOUTUSINFG

o

o

oo

oo

oo

oooo

6.622

5.5456.706

ln

5.5456.706

1.2206.7651.2207.926

ln

1.2206.7651.2207.926

ln

=

−=

−−

−−−=

−

−−−−

=

(C.6.1)

hC ≡ convection film heat transfer coefficient (W/m2·K). (TFG)AVE ≡ average flue gas temperature (°F). G ≡ water mass velocity (lb/ft2·s). do ≡ outer tube diameter (in).

( )

( ) ( )( )

KmW

FhftBTU

C

sftlb

C

o

AVEFGC

hin

Fh

dTG

h

⋅⋅⋅==

⋅⋅=

⋅⋅=

22

2

36.10913.55.4

15504257.014.2

14.2

4.0

28.06.0

4.0

28.06.0

o

o

(C.6.2)

hRG ≡ gas radiation heat transfer coefficient (W/m2·K).

( )[ ]( )[ ]

KmW

FhftBTU

RG

FhftBTU

RG

FhftBTU

AVEFGRG

h

Fh

Th

⋅⋅⋅

⋅⋅

⋅⋅

==

−=

−=

22

2

2

936.53875.3

5.015500025.0

5.00025.0

o

o

o

o (C.6.3)

83


ho ≡ total convection coefficient (W/m2·K).

( )( )( )( )

KmW

o

KmW

o

RGCo

h

hhhh

⋅

⋅

=

+=

+=

2

2

93.17

936.536.101.11.1

(C.6.4)

hi ≡ in tube heat transfer coefficient (W/m2·K). G ≡ water mass velocity (lb/ft2·h). do ≡ outer tube diameter (ft). k ≡ average fluid thermal conductivity (BTU/ft·h·°F). cP ≡ average fluid heat capacity (BTU/lb·°F). u ≡ bulk fluid viscosity (lb/ft·h).

( )

( )( )( )

( )( )( )

( )( )( )

KmW

FhftBTU

i

FhftBTU

hftlb

FlbBTU

hftlb

hftlb

FhftBTU

i

Po

oi

h

ft

fth

kuc

uGd

dkh

⋅⋅⋅

⋅⋅

⋅⋅

⋅

⋅⋅⋅

==

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎥⎦⎤

⎢⎣⎡

⎥⎦⎤

⎢⎣⎡⎟⎟⎠

⎞⎜⎜⎝

⎛=

22

2

2.9636.549

15263.013281.077725.0

13281.0

311720375.0

375.0

15263.0027.0

027.0

333.08.0

333.08.0

o

o

oo

(C.6.5) hw ≡ tube wall heat transfer coefficient (W/m2·K). KM ≡ tube wall thermal conductivity (BTU·in/ft2·h·°F). tw ≡ tube wall thickness (in).

( )( )

KmW

FhftBTU

w

FhftinBTU

w

w

Mw

hin

h

tKh

⋅⋅⋅

⋅⋅⋅

==

=

=

22

2

23961367237.0

324

o

o

(C.6.6)

84


Rt ≡ total heat transfer resistance (m2·K/W). Ao ≡ outer surface area per tube length (ft2/ft). Ai ≡ inner surface area per tube length (ft2/ft).

( )( )( )

( )( )( ) ( )

( )W

Kmt

WKm

t

KmW

ftft

KmW

ftft

ftft

KmW

ftft

t

oiw

o

ii

ot

R

R

R

hAhA

AhA

R

2

2

2

2

2

2

2

2

2

0573992.0

0557724.00004665.00011603.0

93.171

054.12396

178.1

054.12.963

178.1

1

=

++=

++=

++=

(C.6.7)

U ≡ overall heat transfer coefficient (W/m2·K).

( )Km

WW

Km

t

U

U

RU

2

2

42.170573992.0

1

1

=

=

=

(C.6.8)

ASB ≡ shield bank surface area (m2). NR ≡ number of tube rows. NT ≡ number of tube per row. L ≡ horizontal tube length (ft).

( ) ( ) ( ) ( ) (C.6.9) 22 05.847.904

178.1161632

mftA

ftA

ALNNA

SB

ftft

SB

oTRSB

==

⋅⋅⋅=

⋅⋅⋅=

QSB ≡ heat absorption in the shield bank section (W).

( ) ( ) ( )h

GJSB

KmW

SB

SBSB

kWQ

mKQ

ALMTDUQ

282.36.911

05.846.62242.17 22

==

⋅⋅=

⋅⋅=

(C.6.10)

85


Verifying the flue gas temperature leaving the shield bank section: HA,SB ≡ heat made available based on the flue gas temperature leaving the shield bank

(kJ/kg).

( )( )

lbBTU

kgkJ

SBA

hGJ

hGJ

SBA

kgkJ

SBR

R

SBA

BWTA

H

H

QQQ

HH

139,12437,25

282.360.63)60.63(189,24

,

,

,

,

==

+=

+=

(C.6.11)

From chart, @ HA,SB =12,139 BTU/lb, (TFG)OUT ≈ 765.6°C (as initially assumed)*. *Note that this procedure was repeated via successive substitution on Microsoft Excel until the outlet flue gas temperature for the shield bank converged.

86


C.7 Finned Bank Section Calculations (Vaporization of Urea Water Stream) QFB, VAP ≡ convection section heat absorption, vaporization phase (GJ/h). QFB, LIQ ≡ convection section heat absorption, liquid water heating phase (GJ/h). QFB, LIQ = 7.400×106 BTU/h = 7.81 GJ/h. (From HYSYS)

( )

hGJ

hBTU

VAPFB

hBTU

VAPFB

LIQFBSBUSRUSVAPFB

Q

Q

QQQQQ

21.261084.24

10400.7078.10285.126.546

,

6,

,.,,

=×=

×−−−=

−−−=

(C.7.1)

(TUS)IN ≡ inlet urea steam temperature = 428.2°F = 220.1°C (TUS)OUT ≡ outlet urea steam temperature = 428.2°F = 220.1°C (TFG)IN ≡ inlet flue gas temperature = 1410°F = 765.6°C (TFG)OUT ≡ outlet flue gas temperature = 650.8°F = 34.8°C

( ) ( )[ ] ( ) ( )[ ]( ) ( )[ ]( ) ( )[ ]

( ) ( )[ ] ( ) ([ ]( ) ( )[ ]( ) ( )[ ]

)

KFLMTDFFFF

FFFFLMTD

TTTT

TTTTLMTD

INUSOUTFG

OUTUSINFG

INUSOUTFGOUTUSINFG

2.2846.5112.4288.6502.4281410ln

2.4288.6502.4281410

ln

==

−−

−−−=

−−

−−−=

o

oo

oo

oooo

(C.7.2)

AFREE ≡ finned bank free area (m2). ft ≡ fin thickness (in). fh ≡ fin height (in). Nf ≡ number of fins per inch of tube. s ≡ spacing between tube centers (in). Nt ≡ number of tubes per row.

( ) ( )

( ) ( ) ( )( )

( ) ( ) ( )( )

22 49.687.69

12375.005.02

125.40.81616

122

12

mftA

inininftA

NffdsLNA

FREE

ftin

ftinFREE

ftin

fht

ftin

otFREE

==

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅⋅⋅−

−⋅⋅=

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅⋅⋅−

−⋅⋅=

(C.7.3)

87


G ≡ flue gas mass velocity (kg/m2·s). FG ≡ flue gas mass flow rate (lb/h).

( )( )

smkg

sftlb

hftlb

hlb

FREE

G

G

ftG

AF

G

222 22.2455.085.1637

87.69114431

2

===

=

=

(C.7.4)

u ≡ flue gas bulk viscosity (lb/ft·h). Re ≡ flue gas Reynolds number.

( ) ( )( )3.7304Re

0841.0

85.1637Re

Re

2125.4

=

⋅=

⋅=

⋅hftlb

hftlb

o

ftu

gd

(C.7.5)

At this number, dimensionless parameter J = 0.01 (from Figure C4) k ≡ flue gas thermal conductivity (BTU/ft·h·°F). cP ≡ flue gas heat capacity (BTU/lb·°F). ho ≡ total convection heat transfer coefficient (W/m2·K).

( ) ( ) ( )( ) ( )

( )Km

WFhft

BTUo

FhftBTU

FlbBTU

hftlb

hftlb

FlbBTU

o

P

Po

h

h

kCu

GCJh

22

2

46.1097.5

03397.02968.00841.0

85.16372968.001.0

32

32

==

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ⋅

⋅⋅=

⎟⎠⎞

⎜⎝⎛ ⋅

⋅⋅=

⋅⋅

⋅⋅

⋅⋅

⋅

o

o

o

o

(C.7.6)

ef ≡ fin efficiency. From Figure C5, ef = 0.83 .

88


(ho)eff ≡ effective total convection heat transfer coefficient (W/m2·K). At ≡ finned tube surface area per unit tube length (ft2/ft).

( )

( ) ( )( )

KmW

FhftBTU

effo

ftft

ftft

ftft

ftft

FhftBTU

effo

t

ootfoeffo

h

h

AAAAe

hh

22

2

222

2

97.812.5

33.7

178.1)]178.133.7(83.0[97.5

)]([

==

⎥⎥⎦

⎤

⎢⎢⎣

⎡ +−⋅⋅=

⎥⎦

⎤⎢⎣

⎡ +−⋅⋅=

⋅⋅

⋅⋅

o

o (C.7.7)

hi ≡ in-tube film heat transfer coefficient, average water properties used (W/m2·K).

( )

( )( )

( )( ) ( )

KmW

FhftBTU

i

FhftBTU

hftlb

FlbBTU

hftlb

hftlb

FhftBTU

i

Po

oi

h

ft

fth

kuC

uGD

Dkh

22

2

2.12827.731

3037.02423.0075.1

2423.0

85.1637375.0

375.0

3037.0027.0

027.0

333.08.0

333.08.0

==

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

⎥⎦⎤

⎢⎣⎡ ⋅

⎥⎦⎤

⎢⎣⎡ ⋅⎟⎟⎠

⎞⎜⎜⎝

⎛=

⋅⋅

⋅⋅

⋅⋅

⋅

⋅⋅

o

o

oo

(C.7.8) Rt ≡ total heat transfer thermal resistance (m2K/W).

( )

( )( ) ( )( ) ( )BTU

Fhftt

FhftBTU

ftft

FhftBTU

ftft

ftft

FhftBTU

ftft

t

effoiw

t

ii

tt

R

R

hAhA

AhA

R

o

ooo

⋅⋅

⋅⋅⋅⋅⋅⋅

=

++=

++=

2

2

2

2

2

2

2

2

210.0

12.51

054.11367

33.7

054.166.731

33.7

1

(C.7.9)

U ≡ total heat transfer coefficient (W/m2·K).

KmW

FhftBTU

BTUFhft

t

U

U

RU

⋅⋅⋅

⋅⋅

==

=

=

22

2

34.876.4210.0

1

1

o

o (C.7.10)

89


AFB,VAP ≡ convective heat transfer surface, vaporization phase (m2).

( )( )22

,

6

,

,,

94710193

6.51176.41084.24

2

mftA

FA

LMTDUQ

A

VAPFB

FhftBTU

hBTU

VAPFB

VAPFBVAPFB

==

×=

⋅=

⋅⋅o

o

(C.7.11)

NR ≡ number of required rows.

( ) ( )

( ) ( ) ( ) ( )22

,

,

2

,

6.108911728

33.716164

448.3

33.7161610193

2

2

mftA

ftALNNA

N

ftftN

ALNA

N

VAPFB

ftft

tTRVAPFB

R

ftftR

tT

VAPCBR

==

⋅⋅⋅=⋅⋅⋅=

≈=

⋅⋅=

⋅⋅=

(C.7.12)

90


C.8 Finned Bank Section Calculations (Heating of Liquid Urea Stream) QFB, LIQ = 7.400×106 BTU/h = 7.81 GJ/h. (From HYSYS) (TUS)IN ≡ inlet urea steam temperature = 269.2°F = 131.8°C (TUS)OUT ≡ outlet urea steam temperature = 428.2°F = 220.1°C (TFG)IN ≡ inlet flue gas temperature = 650.8°F = 343.8°C (TFG)OUT ≡ outlet flue gas temperature = 419.2°F = 215.1°C

( ) ( )[ ] ( ) ( )[ ]( ) ( )[ ]( ) ( )[ ]

( ) ( )[ ] ( ) ( )[ ]( ) ( )[ ]( ) ( )[ ]

KFLMTDFFFF

FFFFLMTD

TTTT

TTTTLMTD

INUSOUTFG

OUTUSINFG

INUSOUTFGOUTUSINFG

2.1029.1832.2692.4192.4288.650ln

2.2692.4192.4288.650

ln

==

−−

−−−=

−−

−−−=

o

oo

oo

oooo

(C.8.1)

AFREE ≡ finned bank free area (m2). ft ≡ fin thickness (in). fh ≡ fin height (in). Nf ≡ number of fins per inch of tube. s ≡ spacing between tube centers (in). Nt ≡ number of tubes per row.

( ) ( )

( ) ( ) ( )( )

( ) ( ) ( )( )

22 49.687.69

12375.005.02

125.40.81616

122

12

mftA

inininftA

NffdsLNA

FREE

ftin

ftinFREE

ftin

fht

ftin

otFREE

==

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅⋅⋅−

−⋅⋅=

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅⋅⋅−

−⋅⋅=

(C.8.2)

G ≡ flue gas mass velocity (kg/m2·s). FG ≡ flue gas mass flow rate (lb/h).

( )( )

smkg

sftlb

hftlb

hlb

FREE

G

Gft

G

AF

G

222 22.2455.085.163787.69

1144312

===

=

=

(C.8.3)

91


u ≡ flue gas bulk viscosity (lb/ft·h). Re ≡ flue gas Reynolds number.

( ) ( )( )

5.9649Re

06365.0

85.1637Re

Re

2125.4

=

⋅=

⋅=

⋅hftlb

hftlb

o

ftu

gd

(C.8.4)

At this number, dimensionless parameter J = 0.011 (from Figure C4) k ≡ flue gas thermal conductivity (BTU/ft·h·°F). cP ≡ flue gas heat capacity (BTU/lb·°F). ho ≡ total convection heat transfer coefficient (W/m2·K).

( ) ( ) ( )( ) ( )

( )Km

WFhft

BTUo

FhftBTU

FlbBTU

hftlb

hftlb

FlbBTU

o

P

Po

h

h

kCu

GcJh

22

2

74.1013.6

02389.02793.006365.0

85.16372793.0011.0

32

32

==

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ⋅

⋅⋅=

⎟⎠⎞

⎜⎝⎛ ⋅

⋅⋅=

⋅⋅

⋅⋅

⋅⋅

⋅

o

o

o

o

(C.8.5)

ef ≡ fin efficiency. From Figure C5, ef = 0.88 . (ho)eff ≡ effective total convection heat transfer coefficient (W/m2·K). At ≡ finned tube surface area per unit tube length (ft2/ft).

( )

( ) ( )( )

KmW

FhftBTU

effo

ftft

ftft

ftft

ftft

FhftBTU

effo

t

ootfoeffo

h

h

AAAAe

hh

22

2

222

2

66.951.5

33.7

178.1)]178.133.7(88.0[13.6

)]([

==

⎥⎥⎦

⎤

⎢⎢⎣

⎡ +−⋅⋅=

⎥⎦

⎤⎢⎣

⎡ +−⋅⋅=

⋅⋅

⋅⋅

o

o (C.8.6)

92


hi ≡ in-tube film heat transfer coefficient, average water properties used (W/m2·K).

( )

( )( )

( )( ) ( )

KmW

FhftBTU

i

FhftBTU

hftlb

FlbBTU

hftlb

hftlb

FhftBTU

i

Po

oi

h

ft

fth

kuc

uGD

Dkh

22

2

2.12665.722

3920.03699.0123.1

3699.0

85.1637375.0

375.0

3920.0027.0

027.0

333.08.0

333.08.0

==

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

⎥⎦⎤

⎢⎣⎡ ⋅

⎥⎦⎤

⎢⎣⎡ ⋅⎟⎟⎠

⎞⎜⎜⎝

⎛=

⋅⋅

⋅⋅

⋅⋅

⋅

⋅⋅

o

o

oo

(C.8.7) Rt ≡ total heat transfer thermal resistance (m2K/W).

( )

( )( ) ( )( ) ( )BTU

Fhftt

FhftBTU

ftft

FhftBTU

ftft

ftft

FhftBTU

ftft

t

effoiw

t

ii

tt

R

R

hAhA

AhA

R

o

ooo

⋅⋅

⋅⋅⋅⋅⋅⋅

=

++=

++=

2

2

2

2

2

2

2

2

196.0

51.51

054.11367

33.7

054.15.722

33.7

1

(C.8.8)

U ≡ total heat transfer coefficient (W/m2·K).

KmW

FhftBTU

BTUFhft

t

U

U

RU

⋅⋅⋅

⋅⋅

==

=

=

22

2

93.810.5196.0

1

1

o

o (C.8.9)

AFB,LIQ ≡ convective heat transfer surface, liquid heating phase (m2).

( )( )22

,

6

,

,,

3.7337893

9.18310.510400.7

2

mftA

FA

LMTDUQ

A

LIQFB

FhftBTU

hBTU

LIQFB

LIQFBLIQFB

==

×=

⋅=

⋅⋅o

o

(C.8.10)

93


NR ≡ number of required rows.

( ) ( )

( ) ( ) ( ) ( )22

,

,

2

,

2.8178796

33.716163

369.2

33.716167893

2

2

mftA

ftALNNA

N

ftftN

ALNA

N

LIQFB

ftft

tTRLIQFB

R

ftftR

tT

LIQFBR

==

⋅⋅⋅=⋅⋅⋅=

≈=

⋅⋅=

⋅⋅=

(C.8.11)

94


C.9 Calculating the Minimum Allowable Tube Wall Thickness QR’’ ≡ average radiant heat flux (BTU/h·ft2). r ≡ ratio of maximum radiant heat flux to average radiant heat flux = 1.93 (obtained from Figure C2) fv ≡ factor for local variation in heat flux = 1.25 (assumed) fc/c ≡ factor for conductive/convective effects = 0.85 (assumed) QMAX’’ ≡ maximum local radiant heat flux (BTU/h·ft2).

( )22

2

7115422557''

85.025.193.111000''

''''

mW

fthBTU

MAX

fthBTU

MAX

ccvRMAX

Q

Q

ffrQQ

==

⋅⋅⋅=

⋅⋅⋅=

⋅

⋅ (C.9.1)

FSS ≡ superheated steam mass flow rate = 199847 lb/h = 90650 kg/h FSS’’ ≡ superheated steam mass velocity per tube = 251177 lb/ft2·h = 1.226×106 kg/m2·h (TSS)OUT ≡ final superheated steam temperature = 950°F = 510°C hi ≡ in-tube film heat transfer coefficient, water properties used @ (TSS)OUT (W/m2·K).

( )

( )( )

( )( ) ( )

KmW

FhftBTU

i

FhftBTU

hftlb

FlbBTU

hftlb

hftlb

FhftBTU

i

Po

oi

h

ft

fth

kuC

uGD

Dkh

22

2

0.3911.223

04692.007301.03998.0

07301.0

251177375.0

375.0

04692.0027.0

027.0

333.08.0

333.08.0

==

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ⋅

⎟⎟⎠

⎞⎜⎜⎝

⎛=

⎥⎦⎤

⎢⎣⎡ ⋅

⎥⎦⎤

⎢⎣⎡ ⋅⎟⎟⎠

⎞⎜⎜⎝

⎛=

⋅⋅

⋅⋅

⋅⋅

⋅

⋅⋅

o

o

oo

(C.9.2) TM ≡ tube metal temperature (K). KM ≡ tube metal thermal conductivity (BTU/h·ft·°F).

( ) ( )

( ) ( ) ( )( ) ( )

( ) ( ) ( )( ) ( )

CFT

inin

inin

in

inFT

tdKtdQ

dhdQ

TT

M

FfthBTU

fthBTU

FhftBTU

fthBTU

M

mom

moMAX

ii

oMAXOUTSSM

oo

o

oo

7.5844.1084

237.05.4264

237.05.422557

026.41.223

5.422557950

''''

2

2

2

==

+⋅

⋅⋅+

⋅

⋅+=

+⋅⋅⋅

+⋅⋅

+=

⋅⋅

⋅

⋅⋅

⋅ (C.9.3)

95


To allow for a safety margin, the maximum design tube temperature is set at 1200°F ≈ 650°C. PSS ≡ superheated steam operating pressure = 120 bar = 1740 psia tMIN ≡ minimum allowable tube thickness (cm). S ≡ design stress, 90% of the yield strength for austenitic steel (psia).

( ) ( )( ) ( )

cmintpsiapsia

inpsiat

PSdP

t

MIN

MIN

SS

oSSMIN

307.0121.01740315002

5.417402

==+⋅

=

+⋅

=

(C.9.4)

tMARGIN ≡ margin of tube wall allowance against corrosion and creep (cm).

(cmt

cmtttt

MARGIN

MARGIN

MINMMARGIN

295.0307.0602.0

=−=

−=) (C.9.5)

96


C.10 Calculating the Required Stack Dimensions

( ) gVGfNVH ⋅⋅⋅⋅= 20030.0 (C.10.1) VH ≡ velocity head (inH2O). N ≡ number of tubes per row. F ≡ correction factor specific to the type of tubes used. G ≡ flue gas mass velocity at the point in question (lb/s⋅ft2). Vg ≡ specific volume of the flue gas at the point in question (ft3/lb). Finding the total velocity for a 25% increase in the flue gas mass velocity: DUA ≡ draft under arch.

OinHVH DUA 250.0= SBL ≡ shield bank loss.

( )( )( )( )( ) (

OinHVH

VH

VGfNVH

SBL

lbft

ftslb

SBL

gSBL

2

2

2

02688.0

74.5242571.025.10030.02.03

0030.03

2

=

×=

⋅⋅⋅⋅=

⋅) (C.10.2)

FBL ≡ finned bank loss.

( )( )( )( )( ) (

OinHVH

VH

VGfNVH

FBL

lbft

ftslb

FBL

gFBL

2

2

2

2444.0

98.354550.025.10030.00.17

0030.03

2

=

×=

⋅⋅⋅⋅=

⋅) (C.10.3)

SEL ≡ stack entrance loss.

( )( )( )( ) (

OinHVH

VH

VGfVH

SEL

lbft

ftslb

SEL

gSEL

2

2

2

02208.0

00.238.00030.05.0

0030.03

2

=

=

⋅⋅⋅=

⋅) (C.10.4)

DL ≡ damper loss.

( )( )( )( ) (

OinHVH

VH

VGfVH

DL

lbft

ftslb

DL

gDL

2

2

2

06625.0

00.238.00030.05.1

0030.03

2

=

=

⋅⋅⋅=

⋅) (C.10.5)

97


SOL ≡ stack outlet loss.

( )( )( )( ) (

OinHVH

VH

VGfVH

SOL

lbft

ftslb

SOL

gSOL

2

2

2

03660.0

07.198.00030.00.1

0030.03

2

=

=

⋅⋅⋅=

⋅) (C.10.6)

( )OinHVH

OinHVHVHVHVHVHVHVHVH SOLDLSELFBLSBLDUA

2

2

3962.003660.006625.002208.02444.002688.0050.0

=+++++=

+++++= (C.10.7)

(stack designed to accommodate a mass velocity of 0.8 lb/s⋅ft2 = 3.9 kg/s⋅m2)

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅⋅⋅=

gaaatmS TT

PLDG 1152.0 (C.10.8)

DG ≡ draft gain (inH2O). LS ≡ section height (ft). Patm ≡ atmospheric pressure (psia). Ta ≡ ambient temperature (°R). Tga ≡ flue gas temperature (°R). DGC ≡ convection section draft gain (inH2O).

( )

( ) ( ) ( ) ( ) ( )OinHDG

RRpsiaftDG

TTPLDG

C

C

gaaatmSC

209462.027.1519

167.509169.145.952.0

1152.0

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅⋅⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅⋅⋅=

oo (C.10.9)

SD ≡ required stack draft (inH2O).

(OinHSD

OinHSDDGVHSD C

2

2

3016.009462.03962.0

=−=

−=) (C.10.10)

98


SD’ ≡ stack draft gain per foot of stack (inH2O/ft).

( )

( ) ( ) ( ) ( ) ( )ft

OinH

gaaatmS

SD

RRpsiaftSD

TTPLSD

2005485.0'

27..8031

67.509169.140.152.0'

1152.0'

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅⋅⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅⋅⋅=

oo (C.10.11)

D ≡ required diameter of the stack (m).

( )( )( )( )

ftmDD

DF

G

sh

hkg

mskg

G

95.742.2

905,5125.1905982.3

25.1

24

36001

24

2

==

⋅=

⋅=

⋅ π

π

(C.10.12)

SFL ≡ stack frictional loss per foot (inH2O/ft).

( )( ) ( )( )( )

ftOinH

ftslb

ga

SFL

ft

RSFL

DTG

SFL

2

2

0003066.0

95.7211000

67.8038.0

2110002

2

=

⋅=

⋅=

⋅o

(C.10.13)

NSE ≡ net stack effect (inH2O/ft).

( )

ftOinH

ftOinH

NSE

NSE

SFLSDNSE

2

2

005179.0

0003066.0005485.0

'

=

−=

−=

(C.10.14)

H ≡ required stack height (m).

( )( )

mftH

OinHH

NSESDH

ftOinH

75.1724.58

005179.03016.0

2

2

==

=

=

(C.10.15)

99


C.11 Determining the Required Number of Tubes in the Radiant Section ASS ≡ surface area required for the superheated steam (m2).

( )( )

24.405

1249.064.50

''

2

mA

A

QQ

A

ss

mhGJh

GJ

ss

R

SSss

=

=

=

⋅

(C.11.1)

AUS ≡ surface area required for the urea steam (m2).

(2

2

7.75

4.4051.481

mA

mA

AAA

US

US

SSVTUS

=

−=

−=

) (C.11.2)

NSS ≡ number of vertically aligned superheated steam tubes in the radiant section. NUS ≡ number of vertically aligned urea steam tubes in the radiant section. For each vertical tube to be the same length:

( )( )

1868.0

4.4057.75

2

2

=

==

=

SS

US

SS

US

SS

US

US

US

SS

SS

NN

mm

AA

NN

NA

NA

(C.11.3)

NSS must be a multiple of 9 (nine steam passes), NUS must be a multiple of 2 (two steam passes). For NSS equal to 108:

2017.201868.0)108(

1868.0

≈=×=×=

US

US

SSUS

NN

NN (C.11.4)

NTOTAL = NSS + NUS = 128 vertical tubes (C.11.5)

100


ETL ≡ effective vertical tube length (m).

( )( )

mftETLft

ftETL

dNA

ETLoSS

SS

45.1030.34108

64.4363

125.4

2

==

⋅⋅=

⋅⋅=

π

π

(C.11.6)

( )( )( )( )( )( )( )(

2212

5.4

07.7508.808

2030.34

mftA

ftftAdNETLA

US

US

oUSUS

==

=

=

π )π

(C.11.7)

TCD ≡ tube-circle diameter in the radiant section (m).

( )

mftTCD

ftTCD

sNTCD TOTAL

28.816.27

128 128

==

⋅=

⋅=

π

π

(C.11.8)

26.128.845.10

==mm

TCDETL (C.11.9)

101


C.12 Summary of Superheater Results Heating requirements:

• Superheated steam absorption: 50.64 GJ/h

• Saturated urea steam absorption: 57.61 GJ/h

• Natural gas consumption: 2433 kg/h

Flue gas properties:

• Flue gas emission rate: 51.9 tonnes/h

• Radiant section operating temperature: 927ºC

• Exiting flue gas temperature: 132ºC

• Heat extraction efficiency: 87.9%

Radiant section:

• 128 vertically-aligned bare tubes.

• 20 tubes for the saturated urea steam (2 passes, 10 tubes for each pass)

• 108 tubes for the superheated steam (9 passes, 12 tubes for each pass)

• Effective tube length: 10.45 meters

• Tube circle diameter: 8.28 meters (20.3 cm tube-center spacing)

• Ratio of effective tube height to tube circle diameter: 1.26

Shield bank section:

• 3 rows, 16 bare tubes per row (20.3 cm tube-center spacing)


• Saturated steam for the urea plant (2 passes)

102


Finned bank section:

• 7 rows, 16 finned tubes per row (20.3 cm tube-center spacing)

• 3 circular fins per inch of tube length (1.2 fins/cm)

• Circular fins: ¾ inches high × 0.05 inches thick (1.91 cm high × 0.13 cm thick)

• Surface area: 2.23 m2 per meter of tube length


• Saturated steam for the urea plant (2 passes)

Emission Stack:

• Stack diameter: 2.42 meters

• Stack height: 17.75 meters

Tubing:

• Schedule 40 piping

• Outer diameter: 4.5 inches (11.4 cm)

• Inner diameter: 4.03 inches (10.2 cm)

• Tube wall thickness: 0.237 inches (0.602 cm)

• Construction material: type HK-40 austenitic steel.

• Type HK-40 mass composition: 25% chromium, 20% nickel, 55% iron.

• Minimum allowable tube wall thickness: 0.307 cm

• Tube wall thickness margin against corrosion and creep: 0.295 cm

103


Figure C.12.1: Heat available from the combustion of a 19,700 Btu/lb (LHV) refinery gas

104


Figure C.12.2: Distribution of radiant heat transfer rate around the tubes, dependent upon coil arrangement and firing mode

105


Figure C.12.3: Determining the duty-split between radiant and convection sections based on the bridgewall temperature

106


Figure C.12.4: Finding the dimensionless parameter J to determine the heat transfer coefficients on the flue-gas side of serrated fins

107


Figure C.12.5: Determining the fin efficiency based on the convection film coefficient as well as the fin design & thermal conductivity

108

Appendix D: Heat Exchangers

109

Appendix D Heat Exchangers

D.1 Heat Exchanger Specifications Table D.1.1: Heat exchanger specifications

Duty Surface

Area Overall Heat

Transfer Coefficient Shell Tube

Unit (kW) (m2) (kW/K) Passes PassesWaste Heat Exchanger 1 27765 162 124 1 2 Waste Heat Exchanger 2 36835 220 207 1 2 Gas/Gas Heat Exchanger 65855 2420 2083 1 1

Table D.1.2: Heat exchanger inlet and outlet specifications

Shell Shell Tube Tube

Unit Inlet Outlet Inlet Outlet

Waste Heat Exchanger 1

boiler feed water 130°C

129 bar

boiler feed water 323.7°C 120 bar

synthesis gas 507.8°C 184.8 bar

synthesis gas 400°C

183.9 bar

Waste Heat Exchanger 2

boiler feed water 130°C

129 bar

boiler feed water 323.7°C 120 bar



Gas/Gas Heat Exchanger

synthesis gas 31.22°C 190 bar

synthesis gas 300°C

189.9 bar

ammonia product 340.1°C 183.1 bar

ammonia product

55.64°C 1 182 bar

110

Appendix E: Compressors and Turbines

111

Appendix E Compressors and Turbines

E.1 Compressor and Turbine Specifications Table E.1.1: Summary of compressor/turbine information

Unit Power Required Steam Flow Rate Cooling Water

Flow Rate PSV Size

Or Generated (kW) (tonnes/hr) (tonnes/hr) (m) Synthesis Gas Compressor 13 704 N/A 295 0.044 CO2 Compressor 6 855 N/A 160 0.019 Synthesis Gas Turbine 13 704 60.4 N/A N/A

CO2 Turbine 6 855 30.2 N/A N/A

Table E.1.2: Stream compositions as H/N ratio varies

H/N ratio [H2] [N2] [Ar] MW

2.5 0.7061 0.2825 0.0114 5.1239

3 0.7425 0.2475 0.0100 4.6145

3.5 0.7709 0.2202 0.0089 4.2173

112


E.2 Synthesis Gas Compressor Pressure Safety Valve Design

Case: The discharge of the compressor is blocked in. This will result in no flow through

the compressor.

We must determine the largest orifice diameter required for our PSV to vent the

system. The maximum allowable pressure inside the compressor is 21x106 Pa. Using the

mechanical energy balance equation:

lwfs F

mWvghP

−=⎟⎟⎠

⎞⎜⎜⎝

⎛++Δ

&2

2

ρ

Let us define our control volume as the PSV. Entering this volume is the fluid at

21x106 Pa, and leaving the control volume the fluid is venting to an atmospheric pressure

of 101 Pa.

In this situation, we can make three assumptions:

• No work is being preformed by the system.

• The change in height across the PSV is negligible.

• The friction loss across the PSV will also be negligible.

• The fluid will start from rest, because there will be no flow when the compressor

outlet is blocked in.

These assumptions reduce the MEB equation to:

02

22 =⎟⎟⎠

⎞⎜⎜⎝

⎛−

Δ vPρ

The target composition for the synthesis gas stream is a ‘hydrogen to nitrogen’

(H/N) ratio of 3. However, it is conceivable that this ratio might vary in a worst case

113


scenario. As we can see in Table E2, the as the H/N ratio gets smaller, the density and

molecular weight of the synthesis gas stream gets larger. This smaller H/N ratio will

result in a lower velocity, which will increase the size of the PSV required.

As the synthesis gas is being compressed to 21x106 Pa, its temperature will

increase to approximately 77oC. As a result, the density of the stream, with a H/N ratio

of 2.5 will be 65.43 kg/m3, or 6.681 kmol/m3.

Solving the MEB for the resulting velocity:

smmkg

PaPaPv /799/43.65

)1011021(22 3

6

2 =−×

=Δ

=ρ

(E.1.1)

The combined flow entering the fourth stage of the synthesis gas compressor is

8.05 kmol/s. Converting this to a volumetric flow rate:

smmkmolskmolmQ /205.1

/681.6/05.8

~~

33 ===

ρ (E.1.2)

The required diameter for the PSV orifice is then:

233

2

2 1051.1/799

/205.14

msm

smvQDA −×====

π (E.1.3)

.72.10438.0)1051.1(44 23 inmmAD ==×== −

ππ (E.1.4)

Rounding this value up to 2” allows for some extra capacity, and will be a more

readily available size.

114


E.3 CO2 Compressor Pressure Safety Valve Design

Case: The discharge of the compressor is blocked in, resulting in no flow through the

compressor.

We must determine the largest orifice diameter required for our PSV to vent the

system. The maximum allowable pressure in the CO2 compressor was assumed to be

17.25x106 Pa. This is 15% greater than the outlet pressure of 15x106 Pa that the

compressor will operate at. Following a similar development as in Appendix E.1, we

arrive at the following equation.

ρPv Δ

= 22

Compressed to this pressure, the CO2 would be 141oC, with a density of

274.1 kg/m3, and a molar density of 6.346 kmol/m3.

smmkg

PaPaPv /354/1.274

)1011025.17(22 3

6

2 =−×

=Δ

=ρ

(E.2.1)

The combined flow entering the fourth stage of the CO2 compressor is

0.611 kmol/s. Converting this to a volumetric flow rate:

smmkmolskmolmQ /0963.0

/346.6/611.0

~~

33 ===

ρ (E.2.2)

The required diameter for the PSV orifice is then:

233

2

2 10272.0/354

/0963.04

msm

smvQDA −×====

π (E.2.3)

.733.00186.0)10272.0(44 23 inmmAD ==×== −

ππ (E.2.4)

115


Rounding this orifice diameter up to 3/4” allows for some extra capacity. This

will also be a more readily available orifice size.

116

Appendix F: Economics

117

Appendix F Economics

Table F.1.1: Summary of the cost of each piece of process equipment Price

($CDN) Process Unit Synthesis Gas Compressor $17,250,000Synthesis Gas Turbine $1,610,000CO2 Compressor $6,612,500CO2 Turbine $1,086,750Gas/Gas Heat Exchanger $5,635,000Waste Heat Exchanger 1 $483,000Waste Heat Exchanger 2 $442,750Superheater $5,740,800Ammonia Convertor 1 $1,312,533Ammonia Convertor 2 $1,058,613Total Equipment Cost $41,231,946 Table F.1.2: Feed stream costs

Stream Mass Flow Rate Cost Cost (tonne/hr) ($/tonne) ($/hr) Synthesis Gas 79.2 208 16474 Boiler Feed Water 115.9 0.95 110 Cooling Water 455.5 0.50 228 Fuel Gas 2.433 400 973 Combustion Air 49.46 N/A N/A Low Pressure CO2 95.03 N/A N/A

Total Stream Cost $17,785

Table F.1.3: Product stream prices

Stream Mass Flow Rate Price Price (tonne/hr) ($/tonne) ($/hr) Ammonia Product 79.2 341 27007 Low Pressure CO2 95.03 20.00 1901

Steam (23 bar) 25 20.00 500 Turbine Condensate 90.83 0.85 77 Flue Gas 51.89 N/A N/A Used Cooling Water 455.5 N/A N/A

Total Stream Cost $29,485

118


F.1 Determining the Bare Module Cost of the Required Equipment

NOTE: Equations and data used were found from Ulrich and Vasudevan, 20043.

Compressors and Turbines:

CO2 (Centrifugal) Compressor:

si wpowerfluid ×= ε

(F.1.1) kW685575.0 ×=

kW5141=

From Figure 5.30 of Ulrich3, Cpur = $2,300,000

BMPurBM FCC ×=

(F.1.2) 5.2000,300,2$ ×=

000,750,5$=

Synthesis Gas (Centrifugal) Compressor:

si wpowerfluid ×= ε

(F.1.3) kW1370475.0 ×=

kW278,10=

From Figure 5.30 of Ulrich3, Cpur = $6,000,000

BMPurBM FCC ×=

(F.1.4) 5.2000,000,6$ ×=

000,000,15$=

119


CO2 Turbine:

ws = 6 855 kW FBM = 3.5 for steam turbine

From Figure 5.21 of Ulrich3, Cpur = $270,000

BMPurBM FCC ×=

(F.1.5) 5.3000,270$ ×=

000,945$=

Synthesis Gas Turbine:

ws = 13 704 kW FBM = 3.5 (Steam Turbine)

From Figure 5.21 of Ulrich3, Cpur = $300,000

BMPurBM FCC ×=

(F.1.6) 5.3000,400$ ×=

000,400,1$=

Heat Exchangers:

Gas/Gas Heat Exchanger:

From Figure 5.38 of Ulrich3,

7=aBMF

A = 2420 m2

From Figure 5.36 of Ulrich3, 000,700$=PurC

aBMPurBM FCC ×=

(F.1.7) 7000,700$ ×=

000,900,4$=

120


Waste Heat Exchanger 1:


7=aBMF

A = 220 m2


000,60$=PurC

aBMPurBM FCC ×=

(F.1.8) 7000,60$ ×=

000,420$=

Waste Heat Exchanger 2:


7=aBMF

A = 162 m2


000,55$=PurC

aBMPurBM FCC ×=

(F.1.9) 7000,55$ ×=

000,385$=

121


Superheater:

pBMPurBM FFCC ××=

(F.1.10) 65.13.9000,300,1$ ××=

000,992,4$=

Reactors:

Ammonia Convertor 1:


kgc /00.8$= 3/800 mkgB =ρ

3/6400$ mc B =ρ

3

3

/3750$/6400$mmFBM = (F.1.11)

7067.1=

000,200$=PurC

Catalyst Cost:

BMPurBM FCC ×=1

(F.1.12) 7067.1000,200$ ×=

333,341$=

Vessel Cost:

I.D. = 2.477m

LVessel = 10.94 m

122



94.7=PF (Operating Pressure = 190 bar)

00.1=MF (Carbon Steel)


16=aBMF


CPur = $50,000

aBMPurBM FCC ×=

2

(F.1.13) 16000,50$ ×=

000,800$=

Total Cost:

21 BMBMBM CCC +=

(F.1.14) 000,800$333,341$ +=

333,141,1$=

Ammonia Convertor 2:


kgc /00.8$= 3/800 mkgB =ρ

3/6400$ mc B =ρ

3

3

/3750$/6400$mmFBM = (F.1.15)

7067.1=

000,200$=PurC

123


Catalyst Cost:

BMPurBM FCC ×=1

(F.1.16) 7067.1000,200$ ×=

333,341$=

Vessel Cost:

I.D. = 2.794m

LVessel = 10.85 m


94.7=PF (Operating Pressure = 190 bar)

00.1=MF (Carbon Steel)


16=aBMF


CPur = $33,000

aBMPurBM FCC ×=

2

(F.1.17) 16000,33$ ×=

000,528$=

Total Cost:

21 BMBMBM CCC +=

(F.1.18) 000,528$533,392$ +=

533,920$=

124


F.2 The Feasibility of Firing the Superheater Using Hydrogen Synthesis Gas Cost: $6.50/GJ

Required Energy to produce Ammonia: 32 GJ/tonne NH3

3

3250.6$NHtonne

GJGJ

AmmoniaofCost ×= (F.2.1)

gassynlbNHtonne −==

094.0$208$

3

gassynlbmolgassynlb −=− 11325.01

gassynlbmolgassynlbmol

molH−×

−= 11375.07425.0 2 (F.2.2)

2084088.0 Hlbmol=

2

22

0158.2084088.0Hlbmol

HlbHlbmol ×=

21695046.01 Hlbgassynlb =−

Net Heating Value of Hydrogen Gas: 54 492 kJ/ lb H2

gassynlbHlb

HlbGJgassynofValueHeatingNet

−×=− 2

2

1695406.0054459.0 (F.2.3)

gassynlbGJ −= /009231.0

gassynlbGJ

gassynlbHfromCostEnergy

−×

−=

009231.0094.0$2 (F.2.4)

GJ/22.10$=

GJGasNaturalofCostEnergy /50.8$=

Based on this analysis, natural gas is the more economically viable option for

firing the superheater.

125


F.3 Stream Cost Analysis

Feed Stream Costs:

tflowfeedgassynofCost cos×=−

tonnehr

tonne 208$2.79×= (F.3.1)

hr/16500$=

tflowwaterfeedboilerofCost cos×=

3

3 95.0$9.115mhr

m×= (F.3.2)

hr/100$=

tflowwaterCoolingofCost cos×=

3

3 50.0$5.455mhr

m×= (F.3.3)

hr/200$=

tflowgasfuelofCost cos×=

tonnehr

tonne 400$433.2×= (F.3.4)

hr/1000$=

126


Product Stream Prices:

Calculation of Ammonia Price:

tutilityinmprofittenergypriceproductammonia cosargcos ++=

tonnetonneGJtonne

GJ 10$75$00.8$32++×= (F.3.5)

tonne

341$=

priceflowproductammoniaofice ×=Pr

tonnehr

tonne 341$2.79×= (F.3.6)

hr/000,27$=

priceflowCOcompressedofice ×=2Pr

tonnehr

tonne 20$53.90×= (F.3.7)

hr/900,1$=

priceflowsteambarofice ×=23Pr

tonnehr

tonne 20$25×= (F.3.8)

hr/500$=

priceflowcondensateturbineofice ×=Pr

3

3 85.0$83.90mhr

m×= (F.3.9)

hr/75$=

127


Overall Revenue:

∑ ∑−= tpricevenueOverall cosRe

( )hrhrhrhr /75$/500$/1900$/27000$ +++= (F.3.10)

( )hrhrhrhr /1000$/200$/100$/16500$ +++−

hr/700,11$=

128

Ammonia Synthisis Loop

Documents

Transcript of Ammonia Synthisis Loop