Modeling of Non-isothermal CSTR Adsorption Tower for Sulphur Trioxide Hydration Using Vanadium Catalyst

Transcription

1 rticle International Journal of Modern Engineering Sciences, 4, 3(): 39-6 International Journal of Modern Engineering Sciences Journal homepage: ISSN: Florida, US Modeling of Non-isothermal CSTR dsorption Tower for Sulphur Trioxide Hydration Using Vanadium Catalyst *M.F.N bowei, T.O Goodhead Department of Chemical Petrochemical Engineering, Rivers State University of Science and Technology, Nkpolu, Port Harcourt, Rivers State, Nigeria * uthor to whom correspondences should be addressed; fiboweng@yahoo.com; Tel.: rticle history: Received 5 July 4, Received in revised form 7 September 4, ccepted September 4, Published 5 September 4. bstract: The design of a continuous stirred tank reactor (CSTR) in form of adsorption tower for the production of, metric tonne per annum of sulphuric acid have been carried out. Model performance equation were developed to determine the functional parameters of the reactor. These parameters include reactor volume, reactor height, space time, space velocity, and rate of heat generation per reactor volume. The developed performance models were simulated using Matlab R7B within the operational limits of conversion degree, X=.95 to.99. The relationship between these parameters and the degree of conversion are presented graphically. Keywords: Modelling, Non-isothermal, CSTR, Performance, Equations, Sulphuric cid.. Introduction Sulphuric acid is a very important commodity chemical and indeed, a nation s sulphuric acid production is a good indicator of its industrial strength (Chenier, 987) and York etal (968). The search for the modification in sulphuric acid production is a global concern (Green Wood et al, 984). This is due to the importance attached to the use of the acid particularly in the area of manufacturing industrial chemicals (ustin, 984) and Fair (968). Previous works of Goodhead and bowei (4) focused on development of design models for H SO4 production based on

2 4 semi batch, isothermal plug flow (IPF) and non-isothermal plug flow (NIPF). Therefore, in this present paper we considered development of design equations for the simulation of non-sothermal continuous stirred tank reactor (CSTR) in form of adsorption tower primarily to evaluate the performance as a function of kinetic parameters. Interestingly, design and operation of such equipment, require rates of both physical and chemical process. Hence, principles governing such physical process such as energy and mass transfer including chemical kinetics were exploited to develop the design equations. Industrial chemical reactors are used to carryout chemical reactions in commercial scale. Often times in reactor design we want to know the size, type of reactor and method of operation that are best for a given reaction. Industrial scale production of sulphuric acid is dependent on the oxidation of sulphur dioxide to sulphur trioxide in fixed bed catalytic reactors. [Charles, 977]. The Chemistry for the production of sulphuric acid is presented as follows Duecker and West (975) and Faith (965). S O SO SO O SO3 () HO S O H SO 3 4 Through the years, several catalyst formulations have been employed, but one of the traditional catalytic agents has been Vanadium pentoxide (VO5). Its principal applications include; ore processing, fertilizer manufacturing, oil refining, waste water processing, chemical synthesis etc. [Faith, 965]. The general schematic presentation for the production of sulphuric acid is given below. Figure : Contact process for making sulfuric acid and Oleum from sulfur

3 4 It is worthwhile to continue to research on the best hypothetical reactor unit for the production of sulphuric acid. That actually formed the basis of this thesis. The task of this thesis is to design ideal fluid- fluid contactor units that would produce sulphuric acid in commercial quantity at the lowest possible cost from gaseous sulphur trioxide and water as absorbent. The production of the acid is considered on the three principal types of reactor semi-batch reactor, continuous stirred tank reactor and plug flow absorption reactor in a view of selecting the best absorption reactor with the best operating condition that would give the minimum capital and operational cost to achieve maximum output. In the industrial chemical process, heterogeneous fluid-fluid reactions are made to take place for one of three reasons. First, the product of reaction may be a desired material. Such reactions are numerous and can be found in practically all areas of the chemical industry where organic and inorganic synthesis are employed [Octave levenspiel, 97]. Fluid-fluid reactions may also be made to take place to facilitate the removal of an unwanted component from a fluid. Thus the absorption of a solute gas by water may be accelerated by adding a suitable material to the water which will react with the solute being absorbed. The third reason for using fluid-fluid systems is to obtain a vastly improved product distribution for homogeneous multiple reactions than is possible by using the single phase alone. The area of interest in this study is of absorption with chemical reaction. bsorption is the process of removing one or more constituents of a gaseous mixture by treating it with a liquid. The necessary condition is the solubility of these constituents in the absorbing liquid. The soluble constituents of the gas mixture are called active components and the others, being practically insoluble, are called inert components [Salil et al, 4 & Warren et al, ]. The reverse process of removing a gas from a solution is called stripping or desorption. The direction of mass transfer depends on the way the liquid- gas composition deviates from the mutual equilibrium state. If the concentration of the active component in a gas is higher than its concentration when it is in equilibrium with the liquid, mass transfer occurs from the gas phase to the liquid phase. On the other hand, when its concentration in the gas is lower than that corresponding to its equilibrium with the liquid, mass transfer occurs from the liquid phase to the gas phase. bsorption or stripping processes may be handled in two ways. a) Statically: This is done in order to know the equilibrium state between the phases and the deviation of the actual compositions of the two phases from the equilibrium state. b) Kinetically: This indicates the rate of the process under the given conditions or helps find conditions for running the process economically [Salil et al, ].

4 4 Gas absorption with reaction is usually carried out in columns. The process column requirement could be single unit, two units or multiple units, depending on choice and mixture composition. bsorption columns are vertical, cylindrical vessels containing devices that provide intimate contacting of the rising vapour (or gas) with the descending liquid. This contacting provides opportunity for the two streams to achieve some approach to thermodynamic equilibrium. Depending on the type of internal devices used, the contacting may occur in discrete steps called plates or trays, or in a continuous differential manner on the surface of a packing material [Octave Levenspiel,97]. The fundamental requirement of the column is to provide efficient and economic contacting at the required mass transfer rate. Individual column requirements vary from high vacuum to high pressure, from low to high liquid rates, from clean to dirty systems and so on. s a result a large variety of internal devices have been developed to fill these needs. [Warren et al, ]. For the case under investigation - gas absorption with chemical reaction, the following factors will determine the design method used. The overall rate expression: Since materials in the two separate phases must contact each other before reaction can occur, both the mass transfer and the chemical rates will enter the overall rate expression. Equilibrium solubility: The solubility of the reacting components will limit their movement from phase to phase. This factor will certainly influence the form of the rate equation since it will determine whether the reaction takes place in one or both phases. The contacting scheme: In gas-liquid systems semi-batch and counter current contacting schemes predominate. In liquid-liquid systems mixed flow and batch contacting are used in addition to counter and co-current contacting. [Octave Levenspiel,97]. Many possible permutations of rate, equilibrium, and contacting pattern can be imagined; however, only some of these are important in the sense that they are widely used on the technical scale. Interestingly, the aspect of development of model equation for plug flow reactor in sulphuric acid production was discussed well in the works Goodhead and bowei (4). However, present work is aimed at developing design equations for the performance evaluation of non-isothermal CSTR in hydration of sulphur trioxide using vanadium catalyst.. Kinetic nalysis The reaction mechanism as presented in equation showed chain reaction character is tics [ustin, 984]. Gibney and ferracid (994) reported on the photo-catalysed oxidation of SO3 - by (dimethyl-glyoximato) (SO3) 3- and its (Co(dimethyl-glyoximato) (SO3) 3.

5 43 The work adopted inverse reaction for the kinetic data generation, thus. SO3 H O H SO () 4 is described as irreversible bimolecular chain reaction. Further research into the works of Erikson, [974] and Corma [5] established the reaction as second order reaction with rate constant K =.3 mole/sec Duecker, (975),Froust (96 and nchera (997) performed abinitio calculation and determined the energetic barrier and established conclusively that the irreversible biomolecular nature of the reaction have Hr = -5kcal/mol at 5 C. Following the outcome of the work of Chenier (987) and Fogler (994) as cited above, the rate expression for the formation and production of sulphuric acid is summarized as in equation 3. presented as; -R = K H O SO3 (3) Hence from equation (.33) the amount of SO3 and HO that have reacted at any time t can be C C X C C X (4) R K Bo Where Co = Initial concentration of SO3 (moles/vol) CBo = Initial concentration of HO ( moles/vol) X = Fractional conversion of SO3 (%) -R = Rate of disappearance of SO3 (mole/ Vol/t) In this work, the rate expression (-R) as in equation 4 will be used to develop the hypothetical semi-batch reactor, continuous stirred tank reactor and plug flow reactor design equations with inculcation of the absorption coefficient factor as recommended in the works of Van-Krevelen and Hoftyger cited in ustein (984). This is achieved by modifying equation 4 as illustrated below. The hypothetical concentration profile of the absorption of sulphur trioxide by steam (HO) is represented in figure Concentrati Gas (SO 3 ) C i Inter face Liquid C Bi Liquid Gas Film Z L C BL r Distance normal to phase boundary Figure : bsorption with chemical Reaction

6 44 Sulphur trioxide () is absorbed into the steam (B) by diffusion. Therefore the effective rate of reaction by absorption is defined by rdl R C CL rkl ( C CL ) i i Z (5) L Invoking the works of Krevelen and Hoftyzer cited in ustein (984), the factor r is related to Ci, DL and KL to the concentration of steam B in the bulk liquid CBL and to the second order reaction rate constant K for the absorption of SO3 in steam solution. Thus r = D C K Substituting equation (5) into (6) results in L BL K (6) L - R = (C) C K D (7) BL L Previous reports[octave levenspiel (999) and Danner (983) showed that the amount of SO3 (C) and steam (CBL) that have reacted in a bimolecular type reaction with conversion X is CO X. Hence equation (7) can be rewritten as - R = D C C X C C X Where K L BO O K D C ( m 3 = ) m = L C C B m = initial molar ratio of reactants -R = Rate of disappearance of SO3 K = bsorption reaction rate constant DL = Liquid phase diffusivity of SO3. KL = Overall liquid phase mass transfer coefficient X ) ( X r = Ratio of effective film thickness for absorption with chemical reaction. 3. Materials and Method (8) 3.. Development of Performance Model 3... Reactor volume For non-isothermal operation of the continuous stirred tank reactor, the reactor volume model is obtained from the auto-thermal balance principle (Conlson & Richardson,978 and 979), which is expressed mathematically as:

7 45 But, rate of heat production by reaction = ( -HR) RVR () rate of heat removal by out flow of product = GPCP (T-To) () rate of heat removal by heat transfer = Ut (T-Tc) () Which upon substitution into equation (3.4) gives ( -HR) RVR = GPCP (T-T) + U t (T-Tc) (3) From which, Recall that G VR = PCP T T Ut T Tc H R (4) R 3 - R = K D C m X X (5) L Putting equation 4 into 5 yields VR = GpC p T T Ut T Tc H K D C 3 m X X R L (6) Where, GP = Mass flow rate of product, (Kg/sec) CP = Specific heat of product, (KJ/Kg K) U = Overall heat transfer coefficient of material, (KJ/Sec m 3 K). t = Effective area of heat transfer, (m ) X = Conversion degree T = Operational temperature of reaction, (K) T = Initial temperature of reaction, (K) Tc = Temperature of cooling fluid, (K) HR = Heat of reaction, (KJ/mol) C = Initial concentration not SO3, (mol/m 3 ) K = bsorption reaction rate constant, (/sec)

8 46 DL = Liquid phase diffusivity of SO3, (m /sec) m = Initial molar ratio of reactants Reactor height Considering a reactor with cylindrical shape we have VR = r h (7) h = V R r (8) Putting equation 7 into equation 6 results in h = r G T T U T T H K D C 3 m X X R p C p L t c (9) Space time The space time Ts is mathematically defined (octave levenspiel, 986 and coulson & Richardson, 979) as Ts = Volume of Volumetric reactor flow rate = V R V () But V = Mass flow rate of reaction Mixture Density of reaction mixture = G p () Putting equation into results in p Ts = VR G p () Substituting equation 6 into gives Ts = p GpCp T T Ut T Tc H G K D C m X X R P L (3) Space velocity This is the reciprocal of the space time, Ts and expressed mathematically as Vs = V (4) T s V R Then, from equation 3 it is possible that,

9 47 Vs = 3 H R GpK D L C m X X G C T T U T T p p p t c (5) Heat Generation per reactor volume The steady state heat generation model for reactor is given (Rase, 977) as Q = (-Hr) F X (6) The heat generation per reactor volume is obtained by dividing both sides of equation 6 by the reactor volume, i.e Rq = Q H R F X (7) V V R Putting equation 6 into 7 results in R Rq = H R F X K D C 3 m X X G C T T U T T p P t c (8) Presented in figure 3 is a typical hypothetical non-isothermal CSTR unit Figure 3: Hypothetical model of a non-iso-thermal CSTR 3.. Computational Method The developed models as presented in section 3. were programmed using MTLB, and the flow chart describing the computational procedure is given in Fig 3.. Performance dimensions such as reactor volume, length, space time, space velocity, heat generation per unit volume, and heat

10 48 exchanger functional parameters capable of maintaining non-isothermal conditions were cleverly inculcated into the computer algorithm. The equations of these performance measures were expressed as a function of fractional conversions and characteristic operational temperature. The computational algorithm exploited for the evaluation of performance parameters as a function of kinetic data is presented in figure 4. Figure 4: Flow chart describing the computational procedure of non-isothermal CSTR performance dimension

11 Input Parameter Evaluation The reactor performance models were evaluated with variables obtained from stoichiometric calculations from the reaction mechanism presented in section equation. Such functional variables inculcated into the computer algorithm for the purpose of simulation of the performance dimensions include molar flow rate, concentration etc. Table. Design functional variables Quantity Symbol Value Unit Effective Heat Transfer rea t.5 m Specific Heat of product (Conc HSO4) Cp.38 KJ/KgK Specific Heat of cooling fluid Cpc 4. KJ/KgK Initial concentration of SO C 6,759 mol/m 3 Fractional change in volume -.5 Product mass flow rate Gp.3858 Kg/sec Operational temperature of reaction T 33 to 363 K Initial temperature of reactants T 33 K Initial temperature of cooling fluid T 98 K Heat of reaction HR -88 Kj/mol Overall Neat Transfer coefficient U Kj/Secm Product Density (HSO4) p.64x 3 Kg/m 3 bsorption reaction rate constant K.3 /sec Conversion degree X % Reactant molar flow rate F mol/sec Cooling fluid density c Kg/m 3 Diameter of tubular reactor Di. to. m Molar ratio of reactants m. to.5 Radius of CSTR and SBR r. to. m Liquid phase diffusivity of SO3 DL 7 m /Sec Volumetric flow rate of reactants V.35 x -4 m 3 /Sec Specific heat capacity of HO Cpw 4. KJ/KgK Viscosity of HSO4 at 9 o C µa 5 x -3 Kg/m.sec Viscosity of HO at 6 C µw 5 x -4 Kg/m.sec Thermal conductivity of HO at C Kw.6 w/mk Thermal conductivity of HSO4 at 7 C Ka.5 W/mK Thermal conductivity of Hastelloy KH. W/mK

12 5 4. Results and Discussion 4.. Results of the Computation Industrial reactors for the production of sulphuric acid over a range of reaction time t = 6 to 8 Sec, degree of conversion X =.95 to.99 and operating temperature T = 33 to 363K have been investigated and designed. The reactors have a capacity of.389x 3 Kg/hr of sulphuric acid. These reactors were designed with hastelloy because it has excellent corrosion and sulphuric acid resistance properties. The reactors performance models developed in chapter three were simulated with the aid of MTLB R7b. The results provided information for the functional reactors parameters viz: the reactor volume, the rate of heat generation per unit volume, length, space time, and space velocity. The functional parameters of the reactors and the heat exchanger are tabulated in appendices and. The results showed that the reactor volume is dependent on operating temperature T and degree of conversion X. The volume of the reactor would tend to infinity at % conversion. The variation of the reactor volume, as a result of sulphur trioxide addition to water, with reaction time, operating temperature and degree of conversion is illustrated in figures 5-. From the results it was observed that volume of the reactors increases with increasing reaction time and degree of conversion and decreases with increasing operating temperature. This obvious characteristic behavior is well demonstrated in figures 5- Conversely figures - illustrated the variation of heat generation per unit volume of the reactors as a function of reaction time t, operating temperature T and degree of conversion within the limits t, T and X as specified. plot of heat generation RQ versus operating temperature T was observed to be curvilinear. The rate of heat generation per reactor volume RQ was found to be increasing with increasing operating temperature T within the range of X =.95 to.99. Similar plots were made RQ versus X within the range of T = 33 to 363K. The graphs were also curvilinear with negative gradient. t fairly above 99% conversion of sulphur trioxide, there was a sharp drop tending to the abscissa of the graph. This behavior explains the infinity of the rate of heat generation per unit reactor volume at % degree of conversion of sulphur trioxide. Finally the rate of heat generation per unit reactor volume decreases with increasing reaction time and degree of conversion within the range of temperature as specified. Figures 7 and 8 illustrated the variation of space time with operating temperature and degree of conversion X as specified within the range of T = 33 to 363K and X =.95 to.99. The plots were curvilinear within the range of T and X investigated. However, for the addition of sulphur trioxide to

13 5 water, the highest conversion was observed for the highest space time with the lowest operating temperature. The space time TS, was observed to be increasing with increasing degree of conversion and decreases with increasing operating temperature within the range specified. In the same vain, space velocity exhibited the obvious reciprocal behavior of space time as reflected in figures 9 and..4 x -3. RECTOR VOLUME (m3) x=95 x=96 x=97 x=98 x= TEMPERTURE (K) Figure 5: Plots of Reactor Volume against Temperature for Non-Isothermal CSTR RECTOR VOLUME (m3).8 x CONVERSION DEGREE Figure 6: plot of Reactor Volume against Conversion Degree for Non-Isothermal CSTR

14 5 6 5 SPCE TIME (sec) 4 3 x=95 x=96 x=97 x=98 x= TEMPERTURE (K) Figure 7: Plots of Space Time against Temperature for Non-Isothermal CSTR SPCE TIME (sec) CONVERSION DEGREE Figure 8: Plot of Space Time against Conversion Degree for non-isothermal CSTR 35 SPCE VELOCITY(sec-) x=95 x=96 x=97 x=98 x= TEMPERTURE (K) Figure 9: Plots of Space Velocity against Temperature for Non-Isothermal CSTR

15 53 SPCE VELOCITY (sec-) CONVERSION DEGREE Figure : plot of Space Velocity against Conversion Degree for non-isothermal CSTR 4.5 x 7 HET GENERTED PER UNIT VOLUME(kJ/sec.m3) x=95 x=96 x=97 x=98 x= TEMPERTURE (K) Figure : Plots of Heat Generated per unit Volume against Temperature for Non-Isothermal CSTR HET GENERTED PER UNIT VOLUME (kj/sec.m3) 4.5 x CONVERSION DEGREE Figure : Heat Generated per Unit Volume against Conversion Degree for non-isothermal CSTR

16 Discussions The consideration of non-isothermity of the reactors is a reasonable assumption as long as the operation of the reactors is within the sonic limit. n observation deduced from this work is that the operating temperature tends to influence the reactor performance. Generally the operation is favoured by low temperature. This confirms the reason why heat exchangers should be incorporated in the design. The consideration of the optimum limit of degree of conversion X from.95 to.99 is reasonable because at % conversion of sulphur trioxide, the functional parameters of the reactors will all tends to infinity. In this case the dimensions of the reactors have no limit. Work free days of 65 is allowed to produce the specified quantity i.e..389 x 3 Kg/hr of sulphuric acid. Sulphur trioxide, SO3 can be produced by catalytic oxidation of sulphur dioxide using vanadium pentoxide as catalyst. From the results of the computation for the non-isothermal CSTR it was found that; if the degree of conversion, X was.95, the operational temperature, T was 33K, the reactor volume, VR were.5957e-5m 3 and 7.863E-6m 3 when the reactant molar ratio, m=. and.5 respectively but increase of X, and T resulted in increase of the reactor volume up to.43e-4 to.78e-3m 3 when m=., T=363K and X=.95 to.99 and E-5 to.7897e-4m 3 when m=.5. Critical examination of the results of the reactor types gives the following analysis: (a) t the same operating temperature, change in degree of conversion, X from.95 to..99 curvilinearly increases the reactor volume and space time of the non-isothermal CSTR, while the rate of heat generation per reactor volume and space velocity decreases by the same proportion. (b) t the same degree of conversion, change in operating temperature from 33 to 363K linearly increases the reactor volume and space time of the non-isothermal CSTR, while the rate of heat generation per reactor volume and space velocity decreases curvilinearly by the same proportion. 5. Conclusion Reactors have been designed for the production of ten thousand metric tons per year of sulphuric acid. Computer programs were developed and utilized to simulate the reactors performance models over a temperature interval of T=33 to 363K, and conversion degree, X=.95 to.99. For the plug flow reactors and the semi-batch reactor, additional variable of reactor diameter of. to.m and reaction time of 6 to 8sec respectively were used. From the results of computation, it is clearly established that:

17 55 (a)when the degree of conversion, X=.95, operational temperature, T=33K, the reactor volume, VR are.5957e-5m 3 and 7.863E-6m 3, the space time, TS are.36e-sec and 3.375E- sec, and the rate of heat generation per reactor volume, RQ are.68e7kj/sec.m 3 and 4.55E7KJ/sec.m 3 for the reactant molar ratio, m=. and.5 respectively. (b)when the degree of conversion, X=.99 for the same lower operational temperature as specified above, the reactor volume, VR are.9e-4m 3 and 4.637E-5m 3,the space time, TS are.339sec and.778e-sec, and the rate of heat generation per reactor volume, RQ are.89e6kj/sec.m 3 and 8.444E6KJ/sec.m 3 for the reactant molar ratio, m=. and.5 respectively. (c) When the degree of conversion, X=.95,at the upper limit of operational temperature, T=363K the reactor volume, VR are.43e-4m 3 and E-5m 3,the space time, TS are E-sec and.4655e-sec, and the rate of heat generation per reactor volume, RQ are.879e6kj/sec.m 3 and E6KJ/sec.m 3 for the reactant molar ratio, m=. and.5 respectively. (d)when the degree of conversion, X=.99, operational temperature, T=363, the reactor volume, VR are.78e-3m 3 and.7897e-4m 3, the space time, TS are sec and 7.695E-sec, and the rate of heat generation per reactor volume, RQ are.6835e5 KJ/sec.m 3 and.964e6 KJ/sec.m 3 for the reactant molar ratio m=. and.5 respectively. (e)from (a) (d) above, the volume of the reactor and the space time were greater at the upper limits of conversion degree, while the rate of heat generation per reactor volume decreases as conversion degree increases. References bowei, M. F.N.. Computer-aided design of heat exchanger for P.F. reactor in the addition of ethylene oxide. Part : Design equation development. Modeling, simulation and control, B., 5(4)(989): 5-4. ncheya Juarez, J. C.,.(997) Strategy for Kinetic Parameter Estimation in the Fluid Catalytic Cracking Process, Ind. Eng. Chem. Res., 36()(997): ustin, G. T., Shreve s Chemical process industrial. Fifth edition, publisher McGraw-Hill, (984), p Blanding, F. H., Reaction Rates in Catalytic Cracking of Petroleum, Industrial and Engineering Chemistry, 45(6)(953): Charles G. Hill, jr, n Introduction to chemical engineering Kinetics & Reactor design, st edition, John Wiley & Sons US, (977), p5-6, p Chenier, P. J., Survey of industrial chemistry, John Wiley & Sons, New York, (987), p45-47.

18 56 Christenson, G., pelian, M. R., Hickey, K. J., Jaffe, S. B., Future Directions in Modeling of the FCC Process: n Emphasis on Product Quality, Chemical Engineering Science, 54(999): Corma,., Melo, F. V., Sauvanaud, L., Kinetic and Decay Cracking Model for a Micordowner unit, pplied Catalysis : General, 87 ()(5): Coulson, J. M., Richardson, J. F., Chemical Engineering, vol., 3 rd Edition, Pergamon press Inc., New York, (978), p59-53, Coulson J. M., Richardson J. F, Chemical Engineering, Vol. 3, nd Edition, Pergramon Press Inc. New York..(979), p3 -, Danner and Daubert, Manual for predicting Chemical Process design data, lche, New York, (983). Duecker and West, Manufacture of Sulphuric acid, Reinhold, New York, (975). Erikson, T. E., Chem Soc, Faraday Trans. I, 7(974): 3. Faith, K. C., Industrial Chemistry, Third edition, John Wiley & Sons New York, (965), p Fair, G. M. Geyer, J.C.; and Oken D.. (968): Water Purification and waste water treatment, and disposal, volume. Water and waste water Engineering, New York Wiley. Fogler, H. S. (994) Elements of Chemical Reaction Engineering. nd edition Prentice-Hall Inc., India. Gibney, S. C., and Ferracid, G., Photocatalysed Oxidation, Journal of organic Chemistry, 37(994): Goodhead T.O and bowei M.F.N, sign of Isothermal Plug Flow Reactor dsorption Tower for Sulphur Trioxide Hydration using Vanadium Catalyst, International Journal of Innovative Science and Modern Engineering (IJISME), (9)(4): 9-6. Goodhead T.O and bowei M.F.N, Modeling of Semi Batch Reactor dsorption Tower for Sulphur Trioxide Hydration using Vanadium Catalyst, International Journal of Scientific and Engineering Research, IJTEEE, 5(8)(4). Goodhead T.O and bowei M.F.N, Modelling of Non-Isothermal Plug Flow Reactor dsorption for Sulhur Trioxide Hydration Using Vanadium Catalyst, International Journal of Technology Enhancement and Emerging Engineering Research, IJTEEE, (9)(4). Octave Levenspiel, Chemical Reaction Engineering Third Edition, John Wiley & Sons; New York Chichester Weinheim Brisbane Singapore Toronto, (999)

19 57 PPENDIX : NON- ISOTHRML CSTR T (K) X m V R (m 3 ) h (m) T s (sec) V s (sec - ) R q (kj/sec.m 3 ) e-5.3e-.36e- 9.6e+.68e e-5.e-.855e e e e-5 3.e-.664e e e e-5 4.e e-.978e e e-5 4.9e- 4.9e-.4336e e e e e-.574e+.879e e e-.543e e e e e-.594e e e e e e-.7453e+ 3.88e e-4 5.6e e-.3e+ 3.35e e e e-.743e+.464e e e e-.47e+.88e e e-.3746e- 4.3e+ 6.7e e e e-.554e e e e- 5.68e-.783e+.5478e e e- 7.48e-.384e+.9777e e-4.59e e-.3e+.66e e-4.58e-.458e e-.366e+6

20 e e e-.93e+ 3.39e e e e-.3638e+.9687e e-4.34e-.33e e-.4e e e-.373e e-.876e e e-.643e e e e-4.35e-.93e+ 5.48e e e-4.478e-.339e+ 8.46e-.89e e e-.739e+ 4.87e- 7.35e e e-.94e e- 5.44e e e e+.6638e e e e e+.767e- 3.74e e e e+.84e-.6835e+5

21 59 PPENDIX : NON -ISOTHERML CSTR T(K) X m V R (m 3 ) h (m) Ts (sec) Vs (sec - ) Rq (kj/sec.m 3 ) e e e- 3.53e+ 4.55e e e e-.7879e+.5e e e e-.75e+.787e e-5.7e-.4e e+.38e e-5.484e-.39e- 8.73e+.95e e e-.4655e e e e e e-.383e e e e e-.473e+.4e e-5.875e e-.87e+.464e e-5.599e-.77e e+.7e e-5.87e-.563e e e e-5.46e-.8488e- 5.49e e e e e-.77e+.59e e-5.375e e-.53e+.547e e-5.598e-.334e e+.79e e-5.59e-.789e e+ 8.36e e-5.597e-.35e e e e-5.985e-.488e- 4.9e e e-5.48e e-.689e+.6873e+7

22 e-5.76e-.438e e+.39e e-5.43e-.5e e e e-5 3.8e-.63e e e e e e- 3.39e e e e e-.6539e+ 3.83e e-5.696e-.778e e e e e-.94e e+ 5.5e e e- 4.84e-.457e e e e e-.93e+.774e e e e-.5545e+.669e e-4 9.5e e-.34e+.964e+6