A PROJECT REPORT ON “Production of Sulphuric Acid from DCDA Process” SUBMITTED BY: AKSHAY AGARWAL (Roll No. 1104351003) ANURAG VERMA
(Roll No. 1104341009)
ISHA SHUKLA
(Roll No. 1104351015)
Report Submission Date:
Submitted in Partial fulfillment of the requirements for the awarding of degree of BACHELOR OF TECHNOLOGY IN CHEMICAL ENGINEERING Submitted To UTTAR PRADESH TECHNICAL UNIVERSITY, LUCKNOW UNDER THE EXPERT GUIDANCE OF: Er. PRADEEP YADAV DEPARTMENT OF CHEMICAL ENGINEERING BUNDELKHAND INSTITUTE OF ENGINEERING AND TECHNOLOGY JHANSI-284128 SESSION 2014-15 1
CERTIFICATE This is certified that Akshay Agarwal, Anurag Verma and Isha Shukla have carried out this project entitled “Production of Sulphuric Acid from DCDA Process” for the award of Bachelor of Technology from Uttar Pradesh Technical University, Lucknow under my supervision. The project embodies result of original work and studies carried out by student themselves and the contents of the project do not form the basis for the award of any other degree to the candidates or to anybody else.
Er. A.D. Hiwarikar
Er. Pradeep Yadav
Head of the department
Assistant Professor
BIET, Jhansi
BIET, Jhansi
Date:
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ACKNOWLEDGEMENT For the successful accomplishment of our project, we would like to thank The Almighty for His blessings. A special thanks to our project guide Er. Pradeep Yadav whose help, stimulating suggestions and encouragement, helped us to coordinate our project especially in writing this report. We rather find words short to express our gratitude to him. His involvement and personal interest has enabled us to accomplish this project work successfully. We are highly thankful to Er. A.D. Hiwarikar, Er. Sudeep Yadav, Er.Ravindra Kumar , Er. S.K.Srivastava, Er. Ajitesh Mehra and Er. Neeraj Singh, Department of Chemical Engineering, B.I.E.T. Jhansi for their full cooperation in providing necessary facilities, environment needed for the work. Finally we wish to express our modest and sincere regards to our parents and friends for their intensive support and encouragement for this project work.
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ABSTRACT The project includes the detailed designing of a four stage adiabatic catalytic bed reactor for a sulphuric acid plant of capacity 1000 TPD (tons per day). The feed is at 1 atm and 4100 C. There are two main processes for manufacturing of sulphuric acid namely the chamber process and the contact process. The pioneer sulphuric acid manufacturing plants, adopted the chamber process but at the beginning of the twentieth century with technological advancements, the contact process gained popularity as the conversion achieved was much higher than that achieved through chamber process. Chamber process produced sulphuric acid of concentration less than 80 %.The major disadvantage includes the limitations in throughput, quality and concentration of the acid produced. All known new plants uses the contact process although some older chamber process plants may still be in use. The contact process has been gradually modified to use double absorption (also called double catalyst), which increases yield and reduces stack emission of unconverted SO2. Conversions using single absorption contact process were typically about 97-98 percent. While in the current double absorption flow process, achievable conversions are as high as 99.7 percent. The project mainly comprise of the basic parts of the sulphuric acid manufacturing plant, the equipments and the catalyst used, flow of materials in and out of the equipments, their material and energy balances, heat duty of the heat exchangers, weight of the catalyst required and pollution control.
.
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TABLE OF CONTENTS 1. List of Tables…………………………………………………………………………………6 2. List of Figures……………………………………………………………………………...…7 3. Notations………………………………………………………………………………….…..8 4. Introduction…………………………….………………………………………………....…10 5. Literature Review…………………………………………………………………………....11 6. Uses and Applications……………………………………………………………………….12 7. Sulphuric Acid- World Market……………………………………………………………....13 8. Status of Existing Sulphuric Acid Plants In India………………………..………………….14 9. The Contact Process………………………………………………………………...…...…..16 10. Available Technologies for Pollution Control……………………………...…………….....20 11. Material Balance…………….………………………………………………..………….....23 12. Energy Balance……………………………………………………………..……….……....30 13. Weight of Catalyst…………………………………………………………..……………....42 14. Summary Sheet………………………………..……………………………………..…..….55 15. Conclusion…………………………………………………………………………………..57 16. References……………………………………………………………………………....…...58 17. Appendix………………………………………………………………….…...………….…59
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1. LIST OF TABLES
Table 1: Capacity wise number of sulphuric acid plants in India. Table 2: Combustion Chamber Material Balance. Table 3: Material Balance on First Three Catalytic Beds. Table 4: Material Balance on Fourth Catalytic Bed. Table 5: Heat Capacity equation constants for incoming gas mixture. Table 6: Heat Capacity equation constants for outgoing gas mixture. Table 7: Heat Capacity equation constants for incoming gas mixture. Table 8: Heat Capacity equation constants for outgoing gas mixture. Table 9: Heat Capacity equation constants for incoming gas mixture. Table 10: Heat Capacity equation constants for outgoing gas mixture. Table 11: Heat Capacity equation constants for incoming gas mixture. Table12: Heat Capacity equation constants for outgoing gas mixture. Table 13: Calculations of First Catalytic Bed. Table 14: Rate Calculations of First Catalytic Bed. Table 15: Calculations of Second Catalytic Bed. Table 16: Rate Calculations of Second Catalytic Bed. Table 17: Calculations of Third Catalytic Bed. Table 18: Rate Calculations of Third Catalytic Bed. Table 19: Calculations of Fourth Catalytic Bed. Table 20: Rate Calculations of Fourth Catalytic Bed. Table 21: Table for mole fractions expressed in terms of conversion. Table 22: Mole percent of gases entering the converter.
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2. LIST OF FIGURES Figure 1: Structure of H2SO4 molecule. Figure 2: Pie Chart showing Global Consumption of Sulphuric Acid. Figure 3: Sulfuric acid- structure of the world production capacity by region, 2012. Figure 4: Double Absorption Contact Process. Figure 5: Four Stage Catalytic Reactor for Contact Process. Figure 6: Activity of cesium based catalyst in comparison with conventional catalyst. Figure 7: Combustion Chamber Balance Figure 8: Material balance over first three catalytic beds. Figure 9: Primary absorption tower material balance. Figure 10: Fourth catalytic bed material balance. Figure 11: Final absorption tower material balance Figure 12: Enthalpy balance over first catalytic bed. Figure 14: Enthalpy balance over third catalytic bed. Figure 15: Enthalpy balance over fourth catalytic bed Figure 16: Plot of 1/-RA versus XA for first bed Figure 17: Plot of 1/-RA versus XA for second bed Figure 18: Plot of 1/-RA versus XA for third bed Figure 19: Plot of 1/-RA versus XA for fourth bed
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3. NOTATIONS ∑ HR
Sum of enthalpies of all materials entering the reaction process relative to the reference state for the standard heat of reaction at 298 K and 101.32 kPa.
∆Hº298
Standard heat of reaction at 298 K and 101.32 kPa.
q
Net energy or heat added to the system.
∑ HP
Sum of enthalpies of all leaving materials referred to the standard reference state at
298 K
ΔHºRT
Standard heat of reaction at temperature T (ºK)
[ ∑ (ni ΔHºf) ]products
Standard heat of formation of products.
[ ∑ (ni ΔHºf )]reactants
Standard heat of formation of reactants.
T
Temperature expressed in ºK
k1
Rate of forward reaction expressed in gmol/s-(gm cat)-atm3/2
k2
Rate of backward reaction expressed in gmol/s-(gm cat)-atm
NA
Number of moles at conversion XA.
NA0
Initial number of moles.
𝐺
Superficial mass velocity.
𝜌
Fluid density
𝑢𝑧
Superficial velocity in axial direction.
𝑟𝑣
Reaction rate expressed in pseudo homogeneous form (i.e. number of moles transformed per unit time per unit of total reactor volume)
∆𝐻
Enthalpy change for the reaction at the indicated conditions.
𝜌𝐵
Bulk density of the catalyst (total mass of catalyst / total volume of 8
reactor) 𝑟
𝑟𝑚 = 𝑝𝑣
Global reaction rate per unit mass of catalyst.
PA
Partial pressure of A
Po
Total pressure.
yA
Mole fraction of A
𝜈𝐴
Stoichiometric coefficient for reactant A (negative for reactants)
𝐵
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4. INTRODUCTION Sulfuric acid is a highly corrosive strong mineral acid with the molecular formula H2SO4 and structure shown in the figure below:
Figure 1: Structure of H2SO4 molecule.
It is a pungent-ethereal, colorless to slightly yellow viscous liquid which is soluble in water at concentrations. Sometimes, it is dyed dark brown during production to alert people to its hazards. The historical name of this acid is oil of vitriol. Sulphuric acid is an important chemical, which has large-scale industrial uses.
Its major user is the phosphate fertilizer
industry. Other important applications are in petroleum refining, steel pickling, rayon & staple fiber, alum, explosives, detergents, plastics and fibers etc. Sulphuric acid industry is very old and has been continuously adopting the technological developments. The progress made in sulphuric acid manufacture during recent decades has led to changes in the method and technology of its manufacture, resulting mainly in the reduction of emissions of sulphur compounds to air and reduction of harmful waste. [3] It started with Lead Chamber process followed by contact process with Single Conversion Single Absorption (SCSA) and now Double Conversion Double Absorption Process (DCDA). The Sulphuric Acid production through Contact Process is very mature. However, improvement in conversion and absorption stages are being introduced from time to time to increase conversion and absorption efficiencies, which also result in reduction in emissions. Most of the plants use elemental sulphur as raw material and in few cases Copper/ Zinc Smelters gases are being used to produce Sulphuric Acid. [3]
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5. LITERATURE REVIEW Although sulphuric acid is now one of the most widely used chemicals, it was probably little known before the 16th century. It was prepared by Johann Van Helmont (c.1600) by destructive distillation of green vitriol (ferrous sulfate) and by burning sulfur. [3] In the seventeenth century, the German-Dutch chemist Johann Glauber prepared sulfuric acid by burning sulfur together with saltpeter (potassium nitrate, KNO3), in the presence of steam. As saltpeter decomposes, it oxidizes the sulfur to SO3, which combines with water to produce sulfuric acid. In 1736, Joshua Ward, a London pharmacist, used this method to begin the first large-scale production of sulfuric acid.[3] In 1746 in Birmingham, John Roebuck adapted this method to produce sulfuric acid in leadlined chambers, which were stronger, less expensive, and could be made larger than the previously used glass containers. Sulfuric acid created by John Roebuck's process approached a 65% concentration. [3] After several refinements, this method, developed into the so-called the lead chamber process or "chamber process”. Later refinements to the lead chamber process by French chemist Joseph Louis Gay-Lussac and British chemist John Glover improved concentration to 78%. However, the manufacture of some dyes and other chemical processes require a more concentrated product. Throughout the 18th century, this could only be made by dry distilling minerals in a technique similar to the original alchemical processes. Pyrite (iron disulfide, FeS2) was heated in air to yield iron(II) sulfate, FeSO4, which was oxidized by further heating in air to form iron(III) sulfate, Fe2(SO4)3, which, when heated to 480 °C, decomposed to iron(III) oxide and sulfur trioxide, which could be passed through water to yield sulfuric acid in any concentration. However, the expense of this process prevented the large-scale use of concentrated sulfuric acid.[3] In 1831, British vinegar merchant Peregrine Phillips patented the contact process, which was a far more economical process for producing sulfur trioxide and concentrated sulfuric acid. It was little used until a need for concentrated acid arose, particularly for the manufacture of synthetic organic dyes. Today, nearly all of the world's sulfuric acid is produced using this method. In the current flow process, achievable conversions are as high as 99.7 percent.[3]
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6. USES AND APPLICATIONS Sulfuric acid is one of the most important compounds made by the chemical industry. It is used to make, literally, hundreds of compounds needed by almost every industry.
By far the largest amount of sulfuric acid is used to make phosphoric acid, used, in turn, to make the phosphate fertilizers. It is also used to make ammonium sulfate, which is a particularly important fertilizer in sulfur-deficient.
It is widely used in the manufacture of chemicals, e.g., in making hydrochloric acid, nitric acid, sulfate salts, synthetic detergents, dyes and pigments, explosives, and drugs.
It is used in petroleum refining to wash impurities out of gasoline and other refinery products, and in waste water treatment.
Also widely used in metal processing for example in the manufacture of copper and the manufacture of zinc and in cleaning the surface of steel sheet, known as ‘pickling.
It is also used to make caprolactam, which is converted into polyamide 6 and in the manufacture of titanium dioxide, used, for example, as a pigment.
It is used in the production of numerous goods including various cleaning agents, domestic acidic drain cleaners and electrolytes in lead-acid batteries.[2]
Global Sulphuric Acid Consumption By End Use Sector in 2013 Fertilizer Production 56% Other Applications 23% Manufacture of Chemicals 11% Agriultural Chemistry 10%
Figure 2: Pie Chart showing Global Consumption of Sulphuric Acid
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7. SULPHURIC ACID - WORLD MARKET The worldwide market for sulphuric acid witnessed stable growth between 2009-2012, supported by increasing demand from major end-use industries. In 2012, sulphuric acid production grew by more than 7 million tonnes and exceeded 230.7 million tonnes. Asia ranks as the leading sulfuric acid manufacturer, accounting for around 45% of the overall production. China, the US, India, Russia and Morocco are the top five sulfuric acid manufacturing countries.[6]
Figure 3: Sulfuric acid- structure of the world production capacity by region, 2012
APAC (Uganda) is the major sulphuric acid consumer. In 2012, its consumption volume surpassed the 106 million mark. The fertilizer industry is the product’s major end-use sector, consuming over55% of the overall sulfuric acid output. In 2011, the world foreign trade in sulphuric acid was valued at more than USD (US dollar) 1.87 billion. Europe is the leading sulphuric acid exporter, whilst Asia is a market leader in terms of imports. The worldwide sulphuric acid production is poised to increase in the forthcoming years to go beyond 257.6 million by end-2015. [6]
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8. STATUS OF EXISTING SULPHURIC ACID PLANTS IN INDIA In India, there are about 140 Sulphuric Acid Plants (130 Sulphur based & 10 Smelter Gas based) with Annual Installed Capacity of about 12 Million MT. [6] Table 1: Capacity wise number of sulphuric acid plants in India
Installed Capacity (MT/Day)
Number of Plants
%
upto 50
18
12.9
51-100
45
32.1
101-200
40
28.6
201-300
17
12.1
301-500
5
3.6
501-1000
9
6.4
1001- 2000
4
2.9
above 2000
2
1.4
140
100.0
Total
The current annual production of Sulphuric Acid is about 5.5 Million MT, against the installed capacity of 12 Million MT/Annum from Sulphur based as well as Smelter Gas based plants. The demand of Sulphuric Acid is fully met by the current production, as the installed capacity is more than double the demand. The environmental problems arising due to Sulphuric Acid manufacture include:
Off gases from absorption tower containing oxides of Sulphur (SOx) and acid mist.
Liquid effluent generated through waste heat boiler blow-down, spillage & leakage from equipment, washing of equipment, cooling tower bleeding etc.
Generation of Solid Waste viz. Sulphur muck & spent catalyst.
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Presently, Gaseous emission limits prescribed by CPCB for Sulphuric Acid Plants are as under: SO2
:
4.0 Kg/MT of Sulphuric Acid produced (Conc. 100%)
Acid Mist
:
50 mg/Nm3
However, due to advancement in process and pollution control technologies, it may be possible to further reduce & control the emissions of SOx and acid mist. In view of this, CPCB took up a project to revisit the emission standards. [6]
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9. THE CONTACT PROCESS Until 1990 there were no plants using the contact process, the more popular process being used was the chamber process. But, up to mid 1920’s there were considerable changes in the contact process technology, equipments and the catalyst being used. [2] The primary raw material for producing intermediate product of sulphur dioxide is elemental sulphur. This can either be made by burning sulphur in an excess of air or by heating sulphide ores like pyrite in an excess of air. In either case, an excess of air is used so that the sulphur dioxide produced is already mixed with oxygen for the next stage. [2] These traditional contact plants can be further subdivided into the double contact double absorption process (DCDA), which is the type of process now most commonly used in new plants with intermediate absorption and the older, without intermediate absorption also referred to as the single contact single absorption process (SCSA). In DCDA Plant, SO3 is removed from the gas stream after 3rd bed, which shifts the equilibrium and increases the rate of the forward SO2 to SO3 reaction resulting in higher overall conversion and reduces stack emission of unconverted SO2.Conversions using single absorption contact process were typically about 97-98 percent. While in the current double absorption flow process, achievable conversions are as high as 99.7 percent. [2] 6.1 Double Conversion Double Absorption (DCDA) Process The main steps involved in DCDA process are as below:
Melting solid Sulphur with steam coils, followed by filtration or settling of impurities to obtain clean sulphur containing less than 10 mg/l of ash.
Burning the molten Sulphur with air to produce gas-containing SO2.
Cooling the hot gas in Waste Heat Boiler System to produce superheated or saturated steam at conditions fixed, as per requirements.
Catalytic oxidation of SO2 to SO3 in three consecutive passes of converter containing V2O5 catalyst with intercooling of gas in between. The exothermic heat of reaction is utilized to produce steam in Waste Heat Boiler system and to reheat the gases going to pass IV from the intermediate absorber.[6]
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The process flow sheet is shown below:
Figure 4: Double Absorption Contact Process
6.2 Chemical Reactions In the manufacture of sulphuric acid from sulphur, the first step is the burning of sulphur in a furnace to form sulfur dioxide: [1] SO2 (g)
S (l) + O2 (g)
∆ H= -298.3 kJ
Following this step, the sulphur dioxide is converted to sulphur trioxide, using a catalyst, SO2 (g) + ½ O2 (g)
V 2O 5
SO3 (g)
∆ H= -98.3 kJ
The final step is reacting sulphur trioxide with water to form sulphuric acid. SO3 (g) + H2O (l)
H2SO4 (l)
∆H= -130.4 kJ
6.3 Catalyst A commercial sulphur dioxide- converting catalyst consists of 4-9 wt % vanadium pentaoxide, V2O5, as the active component, together with alkali metal sulphate promoters. At operating temperatures the active ingredient is a molten salt held in a porous silica pellet. Normally 17
potassium sulphate is used as a promoter but in recent years also caesium sulphate has been used. Caesium sulphate lowers the melting point, which means that the catalyst can be used at lower temperatures. The carrier material is silica in different forms. The lower temperature limit is 410430 °C for conventional catalysts and 380-390 °C for caesium doped catalysts. The upper temperature limit is 600-650 °C above which, catalytic activity can be lost permanently due to reduction of the internal surface. These catalysts are long lived up to twenty years and are not subject to poisoning except fluorine. [2] 6.4 Contact Process Equipments The main equipments being used in the process are 1) Combustion Chamber 2) Converters 3) Absorbers 4) Heat Exchangers 6.4.1 Converters - “heart” of the contact sulphuric acid plant The reactor is often the central unit around which a chemical plant is designed. Good reactor design is thus important for the performance of the plant. The chemical conversion of sulphur dioxide to sulphur trioxide is designed to maximize the conversion by taking into consideration that: 1) Equilibrium is an inverse function of temperature and a direct function of oxygen to sulphur dioxide ratio. 2) Rate of reaction is a direct function of temperature. 3) Gas composition and amount of catalyst affect the rate of conversion and kinetics of the reaction. 4) Removal of sulphur trioxide formed allows more sulphur dioxide to be converted. The commercialization of these basic conditions makes possible high overall conversion by using a multi pass converter wherein, at an entering temperature of 410°C to 440°C (the ignition temperature), the major part of conversion takes place (60 to 75 %) in the first catalytic bed with an exit temperature of 600°C or more, depending largely on the concentration of
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sulphur dioxide in the gas. The successive lowering of temperatures between stages ensures an overall high conversion. [2] The converter is usually provided with trays for supporting the catalyst and manholes for access to it. Converters have usually been made of cast iron and aluminum-coated steel, but stainless steel is now the preferred material of construction. Pressure drop through the converter must be minimized to reduce power consumption. All these must be optimized to secure the maximum yield and profit. [2] 6.5 Additional Data & Specification Total Pressure = 1 atm Feed composition (Mole Percent) SO2
10
O2
11
N2
79
Overall Conversion = 99.8 %. [1] The four stage catalytic reactor is shown below:
Figure 5: Four Stage Catalytic Reactor for Contact Process
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10. AVAILABLE TECHNOLOGIES FOR POLLUTION CONTROL In upcoming plants, following features are considered important:
Selection of 5-stage converter for maximum conversion efficiency.
Use of sulphur filter for minimizing ash content.
Use of Cesium based catalyst in last bed of Converter for maximum conversion efficiency.
Selection of high efficiency mist eliminators ensuring minimum acid mist exhaust.
Use of Waste heat recovery from acid system.
Use of suitable start-up scrubbing system.[6]
10.1Modified Converter Existing plants are generally based on 4 stage Converter except for very few plants based on 5 stage Converter that has come up recently. 5-stage converter helps in increasing the conversion efficiency. This minimizes the stack emissions level of SO2. With conventional catalyst the conversion efficiency can be increased from 99.7% to 99.8%. (1 kg SO2 instead of 2 Kg SO2 per MT of acid). [6] 10.2 Cesium Based Catalyst The addition of Cesium Catalyst (CS) to the conventional Alkali-Vanadium Catalyst has long been known to enhance the low temperature properties of the catalyst. Cesium based Catalyst offers high activity at low operating temperature. Emissions from existing plants can roughly be cut in half without increasing catalyst volume. The acid production capacity can be increased by using higher strength sulphur dioxide gas without increasing SO2 emissions and plant pressure drop. New acid plants may be designed with low SO2 emission by selecting different type of Catalysts for different stages. [6]
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Figure 6: Activity of cesium based catalyst in comparison with conventional catalyst.
10.3Mist Eliminators Mist is inevitably formed at various points in Sulphuric Acid Plants. If mist is unchecked, and carried through rest of the plant in the gas stream, it causes corrosion inside the plant and environmental menace outside it. Mist is distinct from acid spray, which is formed in the towers by purely physical process of aspiration into the gas stream of liquid droplets. Now a days, Mist eliminators that are designed to remove virtually any type of mist from any gas stream are available. Mist eliminators excel at collecting, the very difficult to remove sub micron size mist particles from gas stream. [6] 10.4
Waste Heat and Heat Recovery System
The waste heat system is completely integrated in DCDA plants. In economizers that cool the gases from third & fourth bed of converter, heat is utilized for preheating feed water for WHB System. Heat generated in Sulphur furnace, heats up this feed water and steam is generated at about 2500C temperatures. This steam is superheated to about 4000 C for cooling the 1st stage out converter gases. This superheated steam can be used for generating power and saturated steam for process heating. The Heat Recovery System is basically an absorber that operates at about 2000 C and uses a boiler to remove the absorption heat as low pressure steam (at upto 10 bar), instead of acid coolers (where heat is wasted). [6]
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10.5 Scrubbing System In DCDA Sulphuric Acid plants, emission levels of SO2 are higher during start-up or shut down when SO2 to SO3 conversion is not proper. Also in SCSA Plant, the emission levels of SO2 are normally high. While in first case, the start-up scrubbers are required to take care of extra SO2 load during unstabilized conditions, start-up & shutdown, in second case, a continuous scrubbing unit is required to take care of tail gases going out for the stack.[7]
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11. MATERIAL BALANCE 11.1 Assumptions 1. Complete burning of S in the burner. 2. 99.8% conversion of SO2 toSO3 in the reactor. 3. Overall absorption of SO3 in the process is 100% 4. 40% excess oxygen is provided. 5. Humidity of entering air is 65% at 300C 11.2 Calculations Capacity: 1000 TPD H2SO4 plant Basis: 1 hr of operation Purity: 98 % pure acid Reactions: S (l) + O2 (g)
SO2 (g) V2O 5
SO2 (g) + ½ O2 (g)
SO3 (g)
SO3 (g) + H2O (l)
H2SO4 (l)
1000 TPD H2SO4 = (1000 x 103)/ 24 = 41,666.67 kg/hr 98% pure acid produced = 41,666.67 x 0.98 = 40,833 kg/hr No. of moles of acid produced = 40,833.33 / 98 = 416.67 kmol/hr (Molecular weight of H2SO4=98) Overall absorption of acid = 100 % SO3 (g) + H2O (l)
H2SO4 (l)
Therefore, by stoichiometry, SO3 required =416.67 kmol/hr Overall conversion of SO2 to SO3 = 99.8 %
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V2O 5
SO2 (g) + ½ O2 (g)
SO3 (g)
Let SO2formed be X kmol/hr 0.998 X=416.67 SO2 required =X= 416.67/0.998 = 417.501 kmol/hr O2 required = 417.501 x 0.5 =208.75 kmol/hr 11.1.1 Combustion Chamber Balance
Figure 7: Combustion Chamber Balance
S (l) + O2 (g)
SO2 (g) (Assuming 100 % combustion)
S required = 417.501 kmol/hr =13,360.053 kg/hr O2 required = 417.501 x 1 = 417.501 kmol/hr Total O2 required = 417.501 + 208.75 = 626.25 kmol/hr O2 is taken in 40% excess O2 in the combustion chamber = 626.25 x 1.4 = 876.75 kmol/hr (Dry air contains 21% O2) Dry air in = 876.765/0.21 = 4175.07 kmol/hr (Molecular weight of air=29) Dry air in = 4175.07 x 29 = 121076.381 kg/hr 24
Table 2: Combustion Chamber Material Balance
Component
Inlet (kmol)
Inlet ( kg)
Outlet (kmol)
Outlet (kg)
S
417.501
13,360.032
-
-
O2
876.75
28,056.00
459.249
14,695.968
N2
3298.306
92,352.568
3298.306
92,352.568
SO2
-
-
417.501
26,720.064
Total
4592.557
133,768.6
4175.056
133,768.6
11.2.2 Overall Balance over First Three Catalytic Beds
Figure 8: Material balance over first three catalytic beds
SO2 (g) + ½ O2 (g)
SO3 (g) (Conversion =96.7 %)
SO2 in = 417.501 kmol O2 in = 459.249 kmol SO2 reacted = 417.501*0.967=403.723 kmol/hr O2reacted = 0.5*403.723 = 201.86 kmol/hr SO3formed = 403.723 kmol/hr SO2out = SO2 in – SO2reacted
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=417.501 – 403.723 =13.778 kmol/hr O2out = O2 in – O2reacted = 459.249 – 201.86
=257.389 kmol/hr Table 3: Material Balance on First Three Catalytic Beds
Component
Inlet (kmol)
Mole %
Inlet (kg)
Outlet (kmol)
Outlet (kg)
SO2
417.501
10
26,720.064
13.778
881.792
O2
459.249
11
14,695.968
257.389
8236.448
N2
3298.306
79
92,352.568
3298.306
92,353.568
SO3
-
-
-
403.723
32297.84
Total
4,175.056
100
133,768.6
3973.196
133769.648
After the third stage, 40 % of product goes to economizer and then to the Interpass Absorber. 11.2.3 Primary Absorber
Figure 9: Primary absorption tower material balance
26
(Assuming 100 % absorption) SO2 in = 0.4*13.778 = 5.5112 kmol/hr SO3 in = 0.4*403.723 = 161.489 kmol/hr O2 in = 0.4 * 257.389 = 102.955 kmol/hr N2 in = 0.4 * 3298.306 = 1319.3224 kmol/hr SO3 (g) + H2O (l)
H2SO4 (l)
H2SO4 formed = 161.489 kmol/hr (Sulphur dioxide, Oxygen and Nitrogen are recycled from inter pass absorber to the 4th stage of reactor). 11.2.4 Fourth Catalytic Bed
Figure 10: Fourth catalytic bed material balance
Conversion = 3.1 % (Overall = 99.8 %) Gases in to the fourth stage of reactor constitute 60 % of product from third stage and gases recycled from Interpass absorber. SO2 in = Total SO2out from the 3rd bed = 13.778 kmol/hr O2 in = Total O2out from the 3rd bed = 257.389 kmol/hr N2 in = 3298.306 kmol/hr 27
SO3 in = 60% of SO3out from the 3rd bed = 0.6 * 403.723 = 242.23 kmol/hr SO2 (g) + ½ O2 (g)
SO3 (g) (Overall Conversion =99.8 %)
SO2 reacted upto 4th bed = 99.8 % of SO2 entering the 1st bed = 0.998 * 417.501 = 416.67 kmol/hr SO2 out = Initial SO2 – Total SO2 reacted = 417.501 – 416.67 = 0.831 kmol/hr Therefore SO2 reacted in the 4th bed = SO2 in – SO2 out =13.778 – 0.831 = 12.947 kmol/hr O2 reacted = 12.947 * 0.5= 6.473 kmol/hr SO3 formed = 12.947 kmol/hr O2 out = O2 in – O2 reacted =257.389 – 6.473 = 250.916 kmol/hr Total SO3 outlet = SO3 inlet from the 3rd bed+ SO3 formed in the 4th bed = 242.23 + 12.947 = 255.177 kmol/hr Table 4: Material Balance on Fourth Catalytic Bed
Component
Inlet (kmol)
Inlet (kg)
Outlet (kmol)
Outlet (kg)
SO2
13.778
881.792
0.831
53.184
O2
257.389
8,236.448
250.916
8,029.312
N2
3298.306
92,353.568
3298.306
92,353.568
SO3
242.23
19378.4
255.177
20,414.16
Total
3,809.703
120,850.208
3,805.23
120,850.224
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11.2.5 Final Absorption Tower
Figure 11: Final absorption tower material balance
SO3 in = 255.173 kmol/hr SO2 in = 0.831 kmol/hr O2 in = 250.916 kmol/hr N2 in = 3298.306 kmol/hr H2SO4 formed = 255.173kmol/hr Total H2SO4 formed = 255.173 + 161.489=416.662kmol/hr
29
12. ENERGY BALANCE 12.1Theory 12.1.1 Law of Conservation of Energy Energy can neither be created nor be destroyed; it can only be changed from one form to another. In simpler words, all energy entering a process is equal to that leaving plus that left in the process. Energy can appear in many forms. Some of the forms are enthalpy, electrical energy, chemical energy (in terms of ∆H reaction), kinetic energy, potential energy, work, and heat inflow. In many cases in process engineering , which often takes place at constant pressure , electrical energy , kinetic energy, potential energy, and work either are not present or can be neglected. Then only the enthalpy of the materials (at constant pressure), the standard chemical reaction energy (∆Hº) at 25º C, and the heat added or removed must be taken into account in the energy balance .This is called heat balance. [5] 12.1.2 Heat Balance The energy or heat coming into a process in the inlet materials plus any net energy added to the process is equal to the energy leaving in the materials. Expressed mathematically, ∑ HR + (– ∆Hº298 ) + q = ∑ HP
(1)
where, ∑ HR is the sum of enthalpies of all materials entering the reaction process relative to the reference state for the standard heat of reaction at 298 K and 101.32 kPa. ∆Hº298 = standard heat of reaction at 298 K and 101.32 kPa. The reaction contributes heat to the process, so the negative of ∆Hº298 is taken to be positive input heat for an exothermic reaction. [5] q = net energy or heat added to the system. ∑ HP =sum of enthalpies of all leaving materials referred to the standard reference state at 298 K.
30
12.2 Equations for calculating net enthalpy change at catalyst bed[2] The temperature dependency of the heat capacity is given by the equation CPº = a+bT+cT2 +… ΔHºRT = T ∫298 ∑ (ni Cºpi) Reactants dT + ΔHº298 + 298 ∫T ∑ (ni Cºpi) Products dT
(2) (3)
where, ΔHºRT is the standard heat of reaction at temperature T (ºK) ΔHºRT = ΔHº298 + 298∫T ( ∑ (ni Cºpi) Products–∑ (ni Cºpi) Reactants)dT
(4)
Enthalpy change, with 298 K as the reference temperature, can be calculated from the formula, ∑H = ΔHºRT – ΔHº298 = ( ∑ ai ni )(T–298) + ((∑ bi ni)/2)(T2 – 2982) + …
(5)
Similarly, Enthalpy change between T1 K and T2 K, can be calculated from the formula ∑H = ( ∑ ai ni )(T1–T2) + ((∑ bi ni)/2)(T12 – T22) + …
(6)
Standard heat of reaction at 298 K (ΔHº298 ) from heat of formation is given by ΔHº298 = [ ∑ (ni ΔHºf) ]Products – [ ∑ (ni ΔHºf )]Reactants
(7)
where [ ∑ (ni ΔHºf) ]products = standard heat of formation of products and [ ∑ (ni ΔHºf )]reactants = standard heat of formation of reactants Net heat to be removed from the catalytic bed , q = ∑ HP –∑ HR + ∆Hº298 12.3 Data given 12.3.1 Inlet and Effluent Temperatures First stage: Inlet temperature = 410°C Effluent temperature = 602°C Second stage: Inlet temperature = 438°C Effluent temperature = 498°C Third stage: Inlet temperature = 432°C Effluent temperature = 444° C 31
(8)
Fourth stage: Inlet temperature = 427°C Effluent temperature = 435°C
12.3.2 Heat Capacities[1] N2= 29.5909 – 5.14 x 10-3T
(9)
O 2=26.0257 + 11.755 x 10-3T
(10)
SO 2 = 24.7706 + 62.9481 x 10-3 T
(11)
SO 3 = 22.0376 + 121.624 x 10-3 T
(12)
where , Heat capacity is expressed in kJ/kmol-ºK and T is temperature inº K. 12.4 Calculations ∆a = 22.036 – 24.771 – 0.5(26.026) = –15.748 ∆b*103 = 121.624 – 62.948 – 0.5(11.755) = 52.799 ∆c*106 = –91.867 – (– 44.258) – 0.5(–2.343) = – 46.438 ∆d*109 = 24.369 – 11.122 – 0.5(– 0.562) = 13.258 From equation (7) ΔHº298 = –395720 – (– 296810) = – 98910 kJ/kmol SO2 Substituting T=298 K in equation (6) – 98910 = ΔHo + (– 15.748*298) + (((52.799 * 10–3 ) /2)*2982) + (((–46.438 * 10–6 )/3)*2983) + (((13.258 * 10–9 )/4)*2984) ΔHo = –96178kJ/kmol SO2 reacted Substituting the value of ΔHo in equation (6), we get ∆HºRT = –96178 – 15.748 T+ (26.4*10-3) T2 – (15.48*10-6)T3+ (3.382*10-9)T4…
32
(13)
12.4.1 Calculation of Heat Duty Required In Each Bed First Catalytic Bed Table 5: Heat Capacity equation constants for incoming gas mixture
Component
ni (kmol/hr.)
ai
aini
bi
bini*103
SO2
417.501
24.7706
10341.75
62.9481
26280.89
O2
459.249
26.0257
11952.2767
11.7551
5398.518
N2
3298.306
29.5909
97599.843
-5.141
-16956.59
SO3
-
22.0376
-
121.624
-
Total
4175.056
-
119893.8697
-
14722.818
Enthalpy of incoming gas mixture at 683K over 298K can be calculated by substituting T=683 in equation (5), ∑HR = 119893.8697(683–298) + ((14722.818*10-3)/2) (6832–2982) =48939432.44 kJ/hr ∑HR = (48939432.44 /3600) = 13594.286 kW Table 6: Heat Capacity equation constants for outgoing gas mixture
Component
ni (kmol/hr.)
ai
aini
bi
bini*103
SO2
108.55
24.7706
2688.848
62.9481
6833.016
O2
304.77
26.0257
7931.852
11.7551
3582.6018
N2
3298.306
29.5909
97599.843
-5.141
-16956.59
SO3
308.95
22.0376
6808.516
121.624
37575.7348
Total
4020.576
-
115029.0566
-
31034.76286
Enthalpy of outgoing gas mixture at 875K over 298K can be calculated by substituting T=875 in equation (5), ∑Hp = 115029.0566(875–298) + ((31034.763*10-3)/2)(8752–2982) =76874549.2 kJ/hr ∑Hp = (76874549.2 /3600) = 21354.04144 kW 33
Total heat of reaction at 298 K, ΔHº298 = – 98910 kJ/kmol SO2 reacted = (417.501 – 108.55) (–98910/3600) = –8488.428 kW Net enthalpy change, q = ∑ HP –∑ HR + ∆Hº298 q = 21354.04144 –13594.286 – 8488.428 = –728.67 kW Thus, during the reaction, enthalpy equivalent to -728.67 kW is to be removed from the first catalytic bed in order to maintain the temperature of the outgoing gas mixture at 875K.
Figure 12: Enthalpy balance over first catalytic bed
Second Catalytic Bed Table 7: Heat Capacity equation constants for incoming gas mixture
Component
ni (kmol/hr.)
ai
aini
bi
bini*103
SO2
108.55
24.7706
2688.848
62.9481
6833.016
O2
304.77
26.0257
7931.852
11.7551
3582.6018
N2
3298.306
29.5909
97599.843
-5.141
-16956.59
SO3
308.95
22.0376
6808.516
121.624
37575.7348
Total
4020.576
-
115029.0566
-
31034.76286
34
Enthalpy of incoming gas mixture at 711K over 298K can be calculated by substituting T=711 in equation (5), ∑HR = 115029.056(711–298) + ((31034.763*10-3)/2) (7112–2982) =53973356.79 kJ/hr ∑HR = (53973356.79 /3600) = 14992.599 kW Table 8: Heat Capacity equation constants for outgoing gas mixture
Component
ni (kmol/hr.)
ai
aini
bini*103
bi
SO2
31.73
24.7706
785.97
62.9481
1997.343
O2
266.36
26.0257
6932.2054
11.7551
3131.088
N2
3298.306
29.5909
97599.843
-5.141
-16956.59
SO3
385.77
22.0376
8501.144
121.624
46918.89
Total
3982.166
-
113819.46
-
35090.7314
Enthalpy of outgoing gas mixture at 778K over 298K can be calculated by substituting T=778 in equation (5), ∑Hp = 1153819.46(778–298) + ((35090.7314*10-3)/2)(7782–2982) =60879790.44 kJ/hr ∑Hp = (60879790.44 /3600) = 16911.053 kW Total heat of reaction at 298 K, ΔHº298 = – 98910 kJ/kmol SO2 reacted = (108.55–31.73) (–98910/3600) = –2110.6295 kW Net enthalpy change, q = ∑ HP –∑ HR + ∆Hº298 q = 16911.053 – 14992.599 – 2110.6295 = –192.1755 kW Thus, during the reaction, enthalpy equivalent to –192.1755 kW is to be removed from the second catalytic bed in order to maintain the temperature of the outgoing gas mixture at 778 K.
35
Figure 13: Enthalpy balance over second catalytic bed
Third Catalytic Bed Table 9: Heat Capacity equation constants for incoming gas mixture
Component
ni (kmol/hr.)
ai
aini
bi
bini*103
SO2
31.73
24.7706
785.97
62.9481
1997.343
O2
266.36
26.0257
6932.2054
11.7551
3131.088
N2
3298.306
29.5909
97599.843
-5.141
-16956.59
SO3
385.77
22.0376
8501.144
121.624
46918.89
Total
3982.166
-
113819.46
-
35090.7314
Enthalpy of incoming gas mixture at 705K over 298K can be calculated by substituting T=705 in equation (5), ∑HR = 113819.46(705–298) + ((35090.7314*10-3)/2) (7052–2982) =53486906.95 kJ/hr ∑HR = (53486906.95 /3600) = 14857.474 kW
36
Table 10: Heat Capacity equation constants for outgoing gas mixture
Component
ni (kmol/hr.)
ai
aini
bi
bini*103
SO2
13.77
24.7706
341.091
62.9481
866.79
O2
257.38
26.0257
6698.494
11.7551
3025.5276
N2
3298.306
29.5909
97599.843
-5.141
-16956.59
SO3
403.77
22.0376
8898.1217
121.624
49103.257
Total
39732.226
-
113536.669
-
36038.989
Enthalpy of outgoing gas mixture at 717K over 298K can be calculated by substituting T=717 in equation (5), ∑Hp = 113536.669(717–298) + ((36038.989*10-3)/2) (7172–2982) =55235285.03 kJ/hr ∑Hp = (55235285.03 /3600) = 15343.1347 kW Total heat of reaction at 298 K, ΔHº298 = – 98910 kJ/kmol SO2 reacted = (31.73–13.77) (–98910/3600) = – 493.451 kW Net enthalpy change, q = ∑ HP –∑ HR + ∆Hº298 q = 15343.1347 – 14857.474 – 493.451= –7.7903 kW Thus, during the reaction, enthalpy equivalent to –7.7903 kW is to be removed from the third catalytic bed in order to maintain the temperature of the outgoing gas mixture at 717 K.
37
Figure 14: Enthalpy balance over third catalytic bed
Fourth Catalytic Bed Table 11: Heat Capacity equation constants for incoming gas mixture
Component
ni (kmol/hr.)
ai
aini
bi
bini*103
SO2
13.77
24.7706
341.091
62.9481
866.79
O2
257.38
26.0257
6698.494
11.7551
3025.5276
N2
3298.306
29.5909
97599.843
-5.141
-16956.59
SO3
242.238
22.0376
5338.344
121.624
29461.9545
Total
39732.226
-
109977.772
-
16397.686
.
Enthalpy of incoming gas mixture at 700K over 298K can be calculated by substituting T=700 in equation (5), ∑HR = 109977.772(700–298) + ((16397.686*10-3)/2) (7002–2982) =47500407.36 kJ/hr ∑HR = (47500407.36 /3600) = 13194.5576 kW
38
Table12: Heat Capacity equation constants for outgoing gas mixture.
Component
ni (kmol/hr.)
ai
aini
bini*103
bi
SO2
0.835
24.7706
20.6834
62.9481
52.5616
O2
250.9125
26.0257
6530.1734
11.7551
2949.5015
N2
3298.306
29.5909
97599.843
-5.141
-16956.59
SO3
255.173
22.0376
5623.4
121.624
31035.1609
Total
3805.2265
-
109774.0998
-
17080.634
Enthalpy of outgoing gas mixture at 708K over 298K can be calculated by substituting T=708 in equation (5), ∑Hp = 109775.0998(708–298) + ((17080.634*10-3)/2)(7082–2982) =48773723 kJ/hr ∑Hp = (48773723/3600) = 13548.256 kW Total heat of reaction at 298 K, ΔHº298 = – 98910 kJ/kmol SO2 reacted = (13.77–0.835) (–98910/3600) = –355.389 kW Net enthalpy change, q = ∑ HP –∑ HR + ∆Hº298 q = 13480.533 – 13194.5576 – 355.389= –1.69 kW Thus, during the reaction, enthalpy equivalent to –1.69 kW is to be removed from the fourth catalytic bed in order to maintain the temperature of the outgoing gas mixture at 708 K.
39
Figure 15: Enthalpy balance over fourth catalytic bed
12.4.2 Calculation of Heat Load for Heat Exchangers Heat load required between first and second catalytic bed: At the outlet of first catalytic bed: Σ aini = 115029.0566 Σ bini = 31034.76286* 10-3 First stage outlet temperature = 602°C = 875K Second stage inlet temperature = 438°C =711K Temperature change = 875 K to 711 K Heat load is calculated by substituting T1=875K and T2=711K in equation (6), ΔH1 = 115029.056(711–875) + ((31034.763*10-3)/2) (7112–8752) = –22900898.26 kJ/hr ∆H1 = (–22900898.26 /3600) = –6361.36 kW Heat load required between second and third catalytic bed: At the outlet of second catalytic bed: Σ aini = 113819.46 Σ bini = 35090.7314* 10-3 40
Second stage outlet temperature = 498°C = 771K Third stage inlet temperature = 432°C =705K Temperature change = 771 K to 705 K Heat load is calculated by substituting T1=711K and T2=705K in equation (6), ΔH2 = 113819.46(705–711) + ((35090.7314*10-3)/2) (7052–7112) = –831982.187 kJ/hr ∆H2 = (–831982.187/3600) = –231.106 kW Heat load required between third and fourth catalytic bed: At the outlet of third catalytic bed: Σ aini = 109977.772 Σ bini = 16397.686* 10-3 Third stage outlet temperature = 444° C = 717 K Fourth stage inlet temperature = 427°C =700 K Temperature change = 717 K to 700 K Heat load is calculated by substituting T1=700K and T2=717K in equation (6), ΔH3 = 109977.772(700–717) + ((16397.686*10-3)/2) (7002–7172) = –1996876.366 kJ/hr ∆H3 = (–1996876.366 /3600) = –544.68 kW
41
13. WEIGHT OF CATALYST 13.1 Theory and Data[1] The kinetic data are represented by a rate expression of the form −𝑟𝐴 =
𝑘1 𝑃𝑆𝑂2 𝑃𝑂2 − 𝑘2 𝑃𝑆𝑂3 𝑃𝑂0.5 2 0.5 𝑃𝑆𝑂 2
(14)
that may be regarded as a degenerate form of typical Hougen-Watson kinetics. The rate constants are given by ln 𝑘1 = 12.07 − 31000⁄𝑅𝑇
(15)
ln 𝑘2 = 22.75 − 53600⁄𝑅𝑇
(16)
where T is temperature expressed in ºK R is expressed in cal/gmolºK k1 is expressed in gmol/s-(gm cat)-atm3/2 k2 is expressed in gmol/s-(gm cat)-atm Derived equation for relationship between temperature and conversion: 𝑇=
𝑇𝑜 + 307.158(𝑋𝐴 − 𝑋𝐴𝑂 ) 1 + 0.0248(𝑋𝐴 − 𝑋𝐴𝑂 )
(17)
Where, T is reference temperature and XA is conversion at this temperature. T0 is initial temperature and XA0 is conversion at initial conditions. Relationship between number of moles and conversion:[4] 𝑁𝐴 = 𝑁𝐴𝑜
(1 − 𝑋𝐴 ) 𝑇𝑜 (1 +∈𝐴 𝑋𝐴 ) 𝑇
where NA is number of moles at conversion XA. NA0 is initial number of moles.
42
(18)
T0/T is temperature correction factor. Relationship between partial pressure and mole fraction: PA = yA Po
(19)
PA is partial pressure of A and Po is total pressure. yA is mole fraction of A. The partial pressures of the various species are numerically equal to their mole fractions since the total pressure is one atmosphere. Equation of Plug flow reactor for calculating weight of catalyst:[4] 𝑊 𝑑𝑋𝐴 =∫ 𝐹𝐴𝑜 −𝑟𝐴 where, W is weight of catalyst required. FA0 is molar flow rate of Sulphur dioxide entering in feed. 13.2 Calculations 13.2.1 First Catalytic Bed Sample Calculation: For T = 773 K, T0 = 683 K, XSO2 = 0 773 =
683 + 307.158 × 𝑋𝑆𝑂2 1 + 0.0248 × 𝑋𝑆𝑂2
𝑋𝑆𝑂2 = 0.3125 𝑁𝑆𝑂2 = 417.501
(1 − 0.3125) 683 (1 − 0.05 × 0.3125) 773
𝑁𝑆𝑂2 = 257.633 𝑘𝑚𝑜𝑙 𝑁𝑆𝑂2 𝑟𝑒𝑎𝑐𝑡𝑒𝑑 = 417.501 − 257.633 = 159.868 𝑘𝑚𝑜𝑙 𝑁𝑆𝑂3 = 159.868 𝑘𝑚𝑜𝑙 43
(20)
𝑁𝑂2 = 459.249 − (159.868⁄2) = 379.315 𝑘𝑚𝑜𝑙 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 = 257.633 + 159.868 + 379.315 + 3298.306 = 4095.122 𝑘𝑚𝑜𝑙 𝑃𝑆𝑂2 = 𝑦𝑆𝑂2 = 𝑃𝑂2 = 𝑦𝑂2 =
159.868 = 0.062 𝑎𝑡𝑚 4095.122
379.315 = 0.0926 𝑎𝑡𝑚 4095.122
𝑃𝑆𝑂3 = 𝑦𝑆𝑂3 =
159.868 = 0.0390 𝑎𝑡𝑚 4095.122
Table 13: Calculations of First Catalytic Bed
T(K)
XSO2
NSO2
NO2
683
0
417.501
459.249
688
0.0172
407.674
725
0.1452
748
NSO3
NN2
TOTAL
PSO2(atm)
PO2(atm)
PSO3(atm)
0
3298.306
4175.056
0.099
0.1099
0
454.335
9.826
3298.306
4170.143
0.097
0.108
0.0023
338.649
419.823
78.851
3298.306
4135.63
0.081
0.1015
0.0190
0.2252
298.726
399.861
118.77
3298.306
4115.669
0.072
0.0971
0.0288
773
0.3125
257.633
379.315
159.86
3298.306
4095.122
0.062
0.0926
0.0390
793
0.382
226.33
363.664
191.16
3298.306
4079.472
0.055
0.0891
0.0468
798
0.400
218.711
359.854
198.78
3298.306
4075.661
0.053
0.0882
0.0487
823
0.488
181.753
341.375
235.74
3298.306
4057.182
0.044
0.0841
0.0581
848
0.576
146.579
323.788
270.92
3298.306
4039.595
0.036
0.0801
0.0670
856.4
0.606
135.132
318.064
282.36
3298.306
4033.871
0.033
0.0788
0.07
873
0.665
113.026
307.011
304.47
3298.306
4022.819
0.028
0.0763
0.0756
875
0.6726
110.408
305.702
307.09
3298.306
4021.51
0.027
0.0760
0.0763
44
Sample Calculation: 𝑘1 = 𝑒𝑥𝑝 (12.07 −
31000 ) = 3 × 10−4 (1.987 × 773)
𝑘2 = 𝑒𝑥𝑝 (22.75 −
536000 ) = 5.3 × 10−6 (1.987 × 773)
((3 × 10−4 ) × 0.062 × 0.0926) − ((5.3 × 10−6 ) × 0.0390 × 0.09260.5 ) −𝑟𝐴 = 0.0620.5 −𝑟𝐴 = 6.71 × 10−6 𝑘𝑚𝑜𝑙 ⁄𝑠𝑒𝑐 − 𝑘𝑔 𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡 1⁄−𝑟𝐴 = 149047.3 𝑠𝑒𝑐 − 𝑘𝑔 𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡⁄𝑘𝑚𝑜𝑙 Table 14: Rate Calculations of First Catalytic Bed
k1
k2
(-rA) (kmol/s-kg catalyst)
1/(-rA)
2.09E-05
5.34E-08
7.27E-07
1375530
2.47E-05
7.12E-08
8.41E-07
1188741
7.87E-05
5.26E-07
2.27E-06
439566
1.53E-04
1.65E-06
3.94E-06
253862.4
3.00E-04
5.30E-06
6.71E-06
149047.3
4.98E-04
1.28E-05
9.7E-06
103124.2
5.64E-04
1.58E-05
1.05E-05
94832.17
1.02E-03
4.42E-05
1.47E-05
68182
1.79E-03
1.16E-04
1.57E-05
63794.88
2.14E-03
1.59E-04
1.38E-05
72398.6
3.02E-03
2.88E-04
2.76E-05
362480.6
3.15E-03
3.10E-04
2.98E-05
378674.7
45
Figure 16: Plot of 1/-RA V/S XA for first bed
FA0 = 417.501 kmol/hr = 417.501/3600 kmol/s = 0.1159725kmol/s W = FA0 * Area under the curve= 0.1159725*250920 Weight of catalyst in first catalyst bed =29103.3 kg 13.2.2 Second Catalytic Bed Sample Calculation: For T = 715 K, T0 = 711 K, 𝑋𝑆𝑂2 = 0.672 715 =
711 + 307.158 × (𝑋𝑆𝑂2 − 0.672) 1 + 0.0248 × (𝑋𝑆𝑂2 − 0.672)
𝑋𝑆𝑂2 = 0.686 𝑁𝑆𝑂2 = 417.501
(1 − 0.686) 683 (1 − 0.05 × 0.686) 715
𝑁𝑆𝑂2 = 129.523 𝑘𝑚𝑜𝑙 𝑁𝑆𝑂2 𝑟𝑒𝑎𝑐𝑡𝑒𝑑 = 417.501 − 129.523 = 287.978 𝑘𝑚𝑜𝑙 𝑁𝑆𝑂3 = 287.978 𝑘𝑚𝑜𝑙 𝑁𝑂2 = 459.249 − (287.978 ⁄2) = 315.26 𝑘𝑚𝑜𝑙 46
𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 = 129.523 + 287.978 + 315.26 + 3298.306 = 4031.067 𝑘𝑚𝑜𝑙 𝑃𝑆𝑂2 = 𝑦𝑆𝑂2 = 𝑃𝑂2 = 𝑦𝑂2 =
129.523 = 0.03213 𝑎𝑡𝑚 4031.067
315.26 = 0.0782 𝑎𝑡𝑚 4031.067
𝑃𝑆𝑂3 = 𝑦𝑆𝑂3 =
287.978 = 0.0714 𝑎𝑡𝑚 4031.067 Table 15: Calculations of Second Catalytic Bed
T(K)
XSO2
NSO2
NO2
NSO3
NN2
TOTAL
PSO2(atm.)
PO2(atm)
PSO3(atm)
711
0.672
110.408
305.702
307.09
3298.306
4021.51
0.027454
0.076017
0.076363
715
0.686
129.523
315.260
287.97
3298.306 4031.067
0.032131
0.078208
0.07144
718
0.696
124.784
312.890
292.71
3298.306 4028.697
0.030974
0.077665
0.072658
723
0.714
116.957
308.977
300.54
3298.306 4024.784
0.029059
0.076769
0.074673
728
0.731
109.22
305.108
308.28
3298.306 4020.915
0.027163
0.07588
0.076669
733
0.748
101.57
301.283
315.93
3298.306
4017.09
0.025284
0.075
0.078647
738
0.766
94.005
297.501
323.49
3298.306 4013.308
0.023423
0.074129
0.080606
743
0.783
86.523
293.760
330.97
3298.306 4009.567
0.021579
0.073265
0.082547
748
0.800
79.124
290.060
338.37
3298.306 4005.868
0.019752
0.072409
0.08447
753
0.818
71.805
286.401
345.69
3298.306 4002.208
0.017941
0.071561
0.086376
758.3 0.836
64.132
282.564
353.36
3298.306 3998.372
0.01604
0.07067
0.088378
763
0.85
57.4009
279.19
360.10
3298.306 3995.006
0.014368
0.069887
0.090138
768
0.87
50.312
275.654
367.18
3298.306 3991.462
0.012605
0.069061
0.091994
771
0.88
46.094
273.545
371.40
3298.306 3989.353
0.011554
0.068569
0.093099
778
0.90
36.355
268.676
381.14
3298.306 3984.483
0.009124
0.067431
0.095658
47
Table 16: Rate Calculations of Second Catalytic Bed
k1
k2
(-rA) (kmol/s-kg catalyst)
1/(-rA)
5.16E-05
2.53E-07
6.11585E-07
1635095
5.83E-05
3.13E-07
7.8216E-07
1278512
6.38E-05
3.66E-07
8.36552E-07
1195383
7.42E-05
4.75E-07
9.34367E-07
1070243
8.61E-05
6.14E-07
1.0383E-06
963113
9.96E-05
7.89E-07
1.14852E-06
870687.1
1.15E-04
1.01E-06
1.26386E-06
791225.4
1.33E-04
1.30E-06
1.38501E-06
722018.9
1.53E-04
1.65E-06
1.28608E-06
777554.9
1.75E-04
2.10E-06
1.31821E-06
758606.4
2.03E-04
2.69E-06
1.3143E-06
760864
2.29E-04
3.36E-06
1.25102E-06
799348
2.63E-04
4.42E-06
1.08457E-06
922027.9
2.84E-04
4.85E-06
9.94423E-07
1005608
3.41E-04
6.94E-06
3.92238E-07
2549474
Sample Calculation: 𝑘1 = 𝑒𝑥𝑝 (12.07 −
31000 ) = 5.828 × 10−5 (1.987 × 715)
𝑘2 = 𝑒𝑥𝑝 (22.75 −
536000 ) = 3.1278 × 10−7 (1.987 × 715)
((5.828 × 10−5 ) × 0.03213 × 0.0782) − ((3.1278 × 10−7 ) × 0.0714 × 0.07820.5 ) −𝑟𝐴 = 0.032130.5 −𝑟𝐴 = 7.8216 × 10−7 𝑘𝑚𝑜𝑙 ⁄𝑠𝑒𝑐 − 𝑘𝑔 𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡 48
1⁄−𝑟𝐴 = 1278512 𝑠𝑒𝑐 − 𝑘𝑔 𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡⁄𝑘𝑚𝑜𝑙
Figure 17: Plot of 1/-RA v/s XA for second bed
FA0 = 110.408kmol/hr = 110.408/3600 kmol/s= 0.036688 kmol/s W = FA0 * Area under the curve = 0.036688*161430 Weight of catalyst in first catalyst bed = 4950.878 kg
49
13.2.3 Third Catalytic Bed Table 17: Calculations of Third Catalytic Bed
T(K)
XSO2
NSO2
NO2
NSO3
NN2
TOTAL
PSO2(atm)
PO2(atm)
PSO3(atm)
705
0.905
36.355
268.67
381.14
3298.306
3984.483
0.00912
0.0674
0.09565
707
0.912
37.152
269.07
380.34
3298.306
3984.882
0.00932
0.0675
0.09544
708
0.915
35.648
268.32
381.85
3298.306
3984.13
0.00894
0.0673
0.09584
710
0.922
32.652
266.82
384.84
3298.306
3982.632
0.00819
0.0669
0.09663
712
0.929
29.669
265.33
387.83
3298.306
3981.14
0.00745
0.0666
0.09741
714
0.936
26.700
263.84
390.80
3298.306
3979.656
0.00670
0.0662
0.09819
715
0.939
25.221
263.10
392.27
3298.306
3978.916
0.00633
0.0661
0.09859
716
0.943
23.745
262.37
393.75
3298.306
3978.178
0.00596
0.0659
0.09897
717
0.946
22.272
261.63
395.22
3298.306
3977.442
0.0056
0.0657
0.09936
Sample Calculation: For T = 708 K, T0 = 705 K, 𝑋𝑆𝑂2 = 0.905 708 =
705 + 307.158 × (𝑋𝑆𝑂2 − 0.905) 1 + 0.0248 × (𝑋𝑆𝑂2 − 0.905)
𝑋𝑆𝑂2 = 0.915 𝑁𝑆𝑂2 = 417.501
(1 − 0.915) 683 (1 − 0.05 × 0.915) 708
𝑁𝑆𝑂2 = 35.648 𝑘𝑚𝑜𝑙 𝑁𝑆𝑂2 𝑟𝑒𝑎𝑐𝑡𝑒𝑑 = 417.501 − 35.648 = 381.85 𝑘𝑚𝑜𝑙 𝑁𝑆𝑂3 = 381.85 𝑘𝑚𝑜𝑙 𝑁𝑂2 = 459.249 − (381.85 ⁄2) = 268.32 𝑘𝑚𝑜𝑙 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 = 35.648 + 268.32 + 381.85 + 3298.306 = 3984.13 𝑘𝑚𝑜𝑙 50
𝑃𝑆𝑂2 = 𝑦𝑆𝑂2 = 𝑃𝑂2 = 𝑦𝑂2 =
35.648 = 0.00894 𝑎𝑡𝑚 3984.13
268.32 = 0.0673 𝑎𝑡𝑚 3984.13
𝑃𝑆𝑂3 = 𝑦𝑆𝑂3 =
381.85 = 0.09584 𝑎𝑡𝑚 3984.13 Table 18: Rate Calculations of Third Catalytic Bed
k1
k2
(-rA) (kmol/s-kg catalyst)
1/(-rA)
4.27E-05 1.83E-07
2.27E-07
4396699
4.55E-05 2.04E-07
2.44E-07
4094072
4.69E-05 2.15E-07
2.42E-07
4129794
4.99E-05 2.39E-07
2.37E-07
4224889
5.32E-05 2.67E-07
2.28E-07
4383353
5.65E-05 2.96E-07
2.15E-07
4641287
5.83E-05 3.13E-07
2.07E-07
4825010
6.01E-05 3.29E-07
1.98E-07
5053386
6.19E-05 3.47E-07
1.87E-07
5361426
Sample Calculation: 𝑘1 = 𝑒𝑥𝑝 (12.07 −
31000 ) = 4.69 × 10−5 (1.987 × 708)
𝑘2 = 𝑒𝑥𝑝 (22.75 −
536000 ) = 2.15 × 10−7 (1.987 × 708)
((4.69 × 10−5 ) × 0.00894 × 0.0673) − ((2.15 × 10−7 ) × 0.09584 × 0.06730.5 ) −𝑟𝐴 = 0.008940.5 −𝑟𝐴 = 2.42 × 10−7 𝑘𝑚𝑜𝑙 ⁄𝑠𝑒𝑐 − 𝑘𝑔 𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡 1⁄−𝑟𝐴 = 4129794 𝑠𝑒𝑐 − 𝑘𝑔 𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡⁄𝑘𝑚𝑜𝑙
51
Figure 18: Plot of 1/-RA v/s XA for third bed
FA0 = 36.355kmol/hr = 36.355/3600kmol/s = 0.0100986kmol/s W = FA0 * Area under the curve= 0.0100986*181425 Weight of catalyst in first catalyst bed = 1832.14kg 13.2.4 Fourth Catalytic Bed Table 19: Calculations of Fourth Catalytic Bed
T(K)
XSO2
NSO2
NO2
NSO3
NN2
Total
PSO2(atm)
PO2(atm)
PSO3(atm)
700
0.946
22.27
261.63
395.22
3298.306
3977.442
0.0056
0.06578
0.099367
701
0.950
21.350
261.17
396.15
3298.306
3976.981
0.005369
0.065671
0.099611
702
0.953
19.851
260.42
397.64
3298.306
3976.231
0.004993
0.065495
0.100007
704
0.960
16.864
258.93
400.63
3298.306
3974.738
0.004243
0.065144
0.100796
705
0.963
15.376
258.18
402.12
3298.306
3973.994
0.003869
0.064969
0.101189
707
0.970
12.409
256.70
405.1
3298.306
3972.51
0.003124
0.06462
0.101974
708
0.97
10.931
255.964
406.57
3298.306
3971.771
0.002752
0.064446
0.102365
52
Sample Calculation: For T = 704 K, T0 = 700 K, 𝑋𝑆𝑂2 = 0.96 704 =
700 + 307.158 × (𝑋𝑆𝑂2 − 0.96) 1 + 0.0248 × (𝑋𝑆𝑂2 − 0.96)
𝑋𝑆𝑂2 = 0.96 𝑁𝑆𝑂2 = 417.501
(1 − 0.96) 683 (1 − 0.05 × 0.96) 704
𝑁𝑆𝑂2 = 16.864 𝑘𝑚𝑜𝑙 𝑁𝑆𝑂2 𝑟𝑒𝑎𝑐𝑡𝑒𝑑 = 417.501 − 16.864 = 400.63 𝑘𝑚𝑜𝑙 𝑁𝑆𝑂3 = 400.63 𝑘𝑚𝑜𝑙 𝑁𝑂2 = 459.249 − (400.63 ⁄2) = 258.93 𝑘𝑚𝑜𝑙 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑜𝑙𝑒𝑠 = 16.864 + 258.93 + 400.63 + 3298.306 = 3974.738 𝑘𝑚𝑜𝑙 𝑃𝑆𝑂2 = 𝑦𝑆𝑂2 = 𝑃𝑂2 = 𝑦𝑂2 =
16.864 = 0.004243 𝑎𝑡𝑚 3974.738
258.93 = 0.065144 𝑎𝑡𝑚 3974.738
𝑃𝑆𝑂3 = 𝑦𝑆𝑂3 =
400.63 = 0.100796 𝑎𝑡𝑚 3974.738 Table 20: Rate Calculations of Fourth Catalytic Bed
k1
k2
(-rA) (kmol/s-kg catalyst)
1/(-rA)
3.65E-05
1.39E-07
1.32E-07
7557000
3.76E-05
1.47E-07
1.3E-07
7713771
3.89E-05
1.55E-07
1.24E-07
8072529
4.14E-05
1.73E-07
1.07E-07
9315462
4.27E-05
1.83E-07
9.67E-08
10343043
4.55E-05
2.04E-07
6.97E-08
14342480
4.69E-05
2.15E-07
5.19E-08
19276120
53
Sample Calculation: 𝑘1 = 𝑒𝑥𝑝 (12.07 −
31000 ) = 4.14 × 10−5 (1.987 × 704)
𝑘2 = 𝑒𝑥𝑝 (22.75 −
536000 ) = 1.73 × 10−7 (1.987 × 704)
((4.14 × 10−5 )0.004243 × 0.065144) − ((1.73 × 10−7 ) × 0.100796 × 0.0651440.5 ) −𝑟𝐴 = 0.0042430.5 −𝑟𝐴 = 1.07 × 10−7 𝑘𝑚𝑜𝑙 ⁄𝑠𝑒𝑐 − 𝑘𝑔 𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡 1⁄−𝑟𝐴 = 9315462 𝑠𝑒𝑐 − 𝑘𝑔 𝑐𝑎𝑡𝑎𝑙𝑦𝑠𝑡⁄𝑘𝑚𝑜𝑙
Figure 19: Plot of 1/-RA v/s XA for fourth bed
FA0 = 22.27kmol/hr = 22.27/3600 kmol/s = 6.18611*10-3kmol/s W = FA0 * Area under the curve = 6.18611*10-3*2474750 Weight of catalyst in first catalyst bed = 15309.078 kg
54
14. SUMMARY SHEET 1. Diameter of converter = 6 m. 2. Heat load for heat exchanger after first bed = -6361.36 kW 3. Heat load for heat exchanger after second bed = -231.106 kW 4. Heat load for heat exchanger after third bed = -554.68 kW 5. Design Pressure for reactor = 0.1114 N/mm2 6. Design Temperature for reactor =610ºC =883 K 7. Material of Construction =SS 304 14.1 First Catalytic Bed
Inlet temperature = 410°C
Effluent temperature = 602°C
Conversion = 0.66
Weight of catalyst = 29103.3 kg.
Heat duty required= -728.67 kW
14.2 Second Catalytic Bed
Inlet temperature = 438°C
Effluent temperature = 498°C
Conversion = 0.85
Weight of catalyst = 4950.878
Heat duty required= -192.1755 kW
14.3 Third Catalytic Bed
Inlet temperature = 432°C
Effluent temperature = 444° C
Conversion = 0.96
Weight of catalyst = 1832.14 kg
Heat duty required= -7.7903 kW
55
14.4 Fourth Catalytic Bed
Inlet temperature = 427°C
Effluent temperature = 435°C
Conversion = 0.985
Weight of catalyst = 15309.078 kg
Heat duty required = -1.69 kW
56
15. CONCLUSION The next step to the Contact Process is DCDA or Double Contact Double Absorption. In this process the product gases (SO2) and (SO3) are passed through absorption towers twice to achieve further absorption and conversion of SO2 to SO3 and production of higher grade sulfuric acid. SO2-rich gases enter the catalytic converter, usually a tower with multiple catalyst beds, and are converted to SO3, achieving the first stage of conversion. The exit gases from this stage contain both SO2 and SO3 which are passed through intermediate absorption towers where sulfuric acid is trickled down packed columns and SO3 reacts with water increasing the sulfuric acid concentration. Though SO2 too passes through the tower it is unreactive and comes out of the absorption tower. This stream of gas containing SO2, after necessary cooling is passed through the catalytic converter bed column again achieving up to 99.8% conversion of SO2 to SO3 and the gases are again passed through the final absorption column thus resulting not only achieving high conversion efficiency for SO2 but also enabling production of higher concentration of sulfuric acid. The industrial production of sulfuric acid involves proper control of temperatures and flow rates of the gases as both the conversion efficiency and absorption are dependent on these.
57
16. REFERENCES
[1] Hill, Charles G. (1977). An Introduction to Engineering Kinetics and Reactor Design, Third Edition, 506,507,509-513. [2] Douglas K. Louie, (2005). Handbook of Sulphuric Acid Manufacturing , Second Edition, 3-3, 3-8, 310, 3-11, 3-14, 3-28, 3-78, 4-5 − 4-11, 4-58,6-1−6-3. [3] Matt King, Michael Moats and William G.I. Davenport (2013). Sulfuric Acid Manufacture (Second Edition) Analysis, Control and Optimization, 11-14, 19-21, 73-80, 91-99, 229-234, 262-271. [4] Levenspiel, Octave, (1999). Chemical Reaction Engineering, Third Edition, 208, 209, 212, 394. [5] Christie John Geankoplis, (2003). Transport Processes and Separation Process Principles (Includes Unit Operations) Fourth Edition, 22. [6] Central Pollution Control Board Ministry of Environment and Forests (May 2007). Comprehensive Industry Document on Sulphuric Acid Plant, 3, 6-7, 10-14, 22, 25-28, 35-36, 38. [7] Fogler, H.S., 1999. Elements of chemical reaction engineering, Third edition. Prentice Hall, New York. [8] Bhatt, B.I., Vora, S.M., 1996. Stoichiometry. Third edition. Mc-Graw Hill, New Delhi. [9] Austin G.T., Shreve, 1984 Chemical process industries, Fourth edition.Mc-Graw Hill, Singapore.
58
17. APPENDIX (DERIVATIONS)
17.1 Derivation of relationship between equilibrium conversion and temperature. Reaction taking place in the reactor: SO2 (g) + ½ O2 (g)
V2O 5
SO3 (g)
Rate Equation: The kinetic data are represented by a rate expression of the form
−𝑟𝐴 =
𝑘1 𝑃𝑆𝑂2 𝑃𝑂2 − 𝑘2 𝑃𝑆𝑂3 𝑃𝑂0.5 2
(21)
0.5 𝑃𝑆𝑂 2
that may be regarded as a degenerate form of typical Hougen-Watson kinetics. At equilibrium, the rate of forward reaction becomes equal to the rate of backward reaction.
−𝑟𝐴 =
𝑘1 𝑃𝑆𝑂2 𝑃𝑂2 − 𝑘2 𝑃𝑆𝑂3 𝑃𝑂0.5 2 0.5 𝑃𝑆𝑂 2
=0
(22)
Therefore at equilibrium, 𝑘1 𝑃𝑆𝑂2 𝑃𝑂2 = 𝑘2 𝑃𝑆𝑂3 𝑃𝑂0.5 2
(23)
The partial pressures of the various species are numerically equal to their mole fractions since the total pressure is one atmosphere. These mole fractions can be expressed in terms of a single reaction progress variable-the degree of conversion-as indicated in the following mole table.[8]
59
Table 21: Table for mole fractions expressed in terms of conversion
Initial moles Component
(kmol/hr)
SO2
417.501
Mole fraction at fractional Moles at conversion XA conversion XA
417.501 (1 − 𝑋𝐴 )
417.501 (1 − 𝑋𝐴 ) 4175.056 − 208.7505 𝑋𝐴 459.249
(417.501 𝑋𝐴 )
− 208.7505 𝑋𝐴
O2
459.249
459.249 −
N2
3298.306
3298.306
3298.306 4175.056 − 208.7505 𝑋𝐴
SO3
0.0
417.501 𝑋𝐴
417.501 𝑋𝐴 4175.056 − 208.7505 𝑋𝐴
Total
4175.056
4175.056 − 208.7505 𝑋𝐴
1.0
2
4175.056 − 208.7505 𝑋𝐴
At equilibrium, 𝑘1 𝑃𝑆𝑂2 𝑃𝑂2 = 𝑘2 𝑃𝑆𝑂3 𝑃𝑂0.5 2
(24)
417.501 (1 − 𝑋𝐴𝑒 ) 459.249 − 208.7505𝑋𝐴𝑒 𝑘1 ( )( )= 4175.056 − 208.7505 𝑋𝐴𝑒 4175.056 − 208.7505 𝑋𝐴𝑒 417.501 𝑋𝐴𝑒 459.249 − 208.7505𝑋𝐴𝑒 0.5 𝑘2 ( )( ) 4175.056 − 208.7505 𝑋𝐴𝑒 4175.056 − 208.7505 𝑋𝐴𝑒
60
(25)
𝑘1 𝐾= = 𝑘2
417.501 𝑋
𝐴𝑒 (4175.056−208.7505 ) 𝑋 𝐴𝑒
417.501 (1−𝑋𝐴𝑒 )
459.249−208.7505 𝑋𝐴𝑒
0.5
(26)
(4175.056−208.7505 𝑋 ) (4175.056−208.7505 𝑋 ) 𝐴𝑒
𝐾=
𝐴𝑒
𝑘1 𝑋𝐴𝑒 20 − 𝑋𝐴𝑒 √ = 𝑘2 (1 − 𝑋𝐴𝑒 ) 2.2 − 𝑋𝐴𝑒
(27)
17.2 Derivation of relationship between conversion and temperature. The differential form of energy balance equation for one-dimensional, plug flow model, for adiabatic operation is as follows, [9] 𝐺
𝜕(𝐶𝑝 𝑇) 𝜕𝑧
= 𝑟𝑣 (−∆𝐻) = 𝑟𝑚 𝜌𝐵 (−∆𝐻)
(28)
where, 𝐺 = 𝜌𝑢𝑧 = superficial mass velocity, which does not vary along the length of reactor. 𝜌 = fluid density 𝑢𝑧 = superficial velocity in axial direction. 𝑟𝑣 = reaction rate expressed in pseudo homogeneous form (i.e. number of moles transformed per unit time per unit of total reactor volume) ∆𝐻 = enthalpy change for the reaction at the indicated conditions. 𝜌𝐵 = bulk density of the catalyst (total mass of catalyst / total volume of reactor) 𝑟
𝑟𝑚 = 𝑝𝑣 = global reaction rate per unit mass of catalyst. 𝐵
The equation for material balance is as follows: 𝜕(𝐶𝐴 𝑢𝑧 ) = 𝜈𝐴 𝑟𝑣 = 𝑣𝐴 𝑟𝑚 𝜌𝐵 𝜕𝑧 where 𝜈𝐴 = stoichiometric coefficient for reactant A (negative for reactants) = −1 in this case
61
(29)
𝑢𝑧 = 𝑢𝑜 (1 + 𝜀𝐴 𝑥𝐴 )
𝑇 𝑇𝑜
(30)
(1 − 𝑥𝐴 ) 𝑇𝑜 (1 + 𝜀𝐴 𝑥𝐴 ) 𝑇
(31)
𝜕(𝐶𝐴 𝑢𝑧 ) 𝜕𝑥𝐴 = −𝐶𝐴𝑜 𝑢𝑜 𝜕𝑧 𝜕𝑧
(32)
𝐶𝐴 = 𝐶𝐴𝑜 Therefore
𝑟𝑣 = 𝐶𝐴𝑜 𝑢𝑜 𝐺
𝜕𝑥𝐴 𝜕𝑧
(33)
𝜕(𝐶𝑝 𝑇) 𝜕𝑥𝐴 (−∆𝐻) = 𝐶𝐴𝑜 𝑢𝑜 𝜕𝑧 𝜕𝑧
(34)
Table 22: Mole percent of gases entering the converter Inlet Moles
Molecular
(Percent )
Weight
SO2
10
64
O2
11
32
N2
79
28
Component
Average molecular weight of the inlet gas: Mavg = 0.10*64+ 0.11*32+0.79*28 = 32.04 For the temperature range of interest (875K to 683K), the heat capacity per unit mass is substantially independent of the conversion level. Hence, we take the heat capacity as constant at 0.250 cal/gm-ºK. 𝐺𝐶𝑃 (𝑇 − 𝑇𝑜 ) = −∆𝐻𝐶𝐴𝑂 𝑢𝑂 (𝑋𝐴 − 𝑋𝐴𝑂 ) Diameter of Converter is taken as 6m. [1]
62
(35)
𝑀𝑎𝑠𝑠 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑎𝑡 𝑡ℎ𝑒 𝑖𝑛𝑙𝑒𝑡 𝑜𝑓 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑒𝑟 (𝐺) =
𝐺=
4175.056 × 32.04 𝜋(62 )
= 4731.1033
𝑀𝑎𝑠𝑠 𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒 𝑎𝑟𝑒𝑎
𝑘𝑔 𝑘𝑔 = 1.314 2 ℎ𝑟 − m 𝑠𝑒𝑐 − 𝑚2
4
𝑀𝑜𝑙𝑎𝑙 𝑚𝑎𝑠𝑠 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑆𝑂2 = 𝐶𝐴𝑜 𝑢𝑜 =
417.501 × 103 3600 ×
𝜋(6)2
= 4.101688
𝑔𝑚𝑜𝑙 𝑠𝑒𝑐 − 𝑚2
4
Heat of reaction at temperature T = (∆H) = –24.60 + 1.99 x 10-3T kcal/gmol for T in degrees Kelvin. 1.314 × 0.250 × (𝑇 − 𝑇𝑜 ) = (24.60 − 1.99 x 10−3 T) × 4.101688(𝑋𝐴 − 𝑋𝐴𝑂 )
𝑇=
𝑇𝑜 + 307.158(𝑋𝐴 − 𝑋𝐴𝑂 ) 1 + 0.0248(𝑋𝐴 − 𝑋𝐴𝑂 )
63
(36)
