A small work has been done on the mass transportation with chemical reaction in jet ouster. The chief focal point of research in this chapter is to develop some important experimental and patterning techniques for efficient design of multi nose jet ousters. To accomplish this end the recent literature on mass transportation with and without chemical reaction along with experimental informations developed for different gas liquid contactors are required to be adopted. An effort is made for necessary alteration and development to bing theories which can be used for our survey.
On the footing of the assortment of generated experimental informations, multi nozzle-single nose, laboratory scale-industrial graduated table, horizontal installation-vertical installing etc. , were utilized to develop general mathematical theoretical accounts. These developed theoretical accounts may be utilized to plan multi nose jet ouster without experimental informations on the basic available physicochemical belongingss like diffusivities, rate invariable, equilibrium invariable, Henerys ‘ jurisprudence changeless etc.
A In this chapter the mathematical theoretical account for soaking up of Cl in aqueous Na hydrated oxide system were developed by doing usage of package like STATGRAPHICS and MATLAB. With the aid of recent mathematical techniques the job of gas-liquid mass transportation reduces to mathematical job and solved by good mathematical theoretical accounts.
4.1 Prediction of soaking up rate and reaction rate invariable of Cl into aqueous Na hydrated oxide solution
The rate invariable of Cl soaking up in aqueous solution reported by different research workers has been summarized and presented in table 4.1.1 given below:
Table 4.1.1: Rate invariable for reaction as reported by different research workers
Ashour et Al. ( 1996 ) studied the soaking up of into aqueous hydrogen carbonate and aqueous hydrated oxide solutions both by experimentation and theoretically. They estimated the reaction rate coefficient of reaction between and over the temperature scope of 293 – 312K:
It is observed that there is dissension in the literature about the value of the forward rate coefficient of soaking up of into aqueous solution of.
In this subdivision, correlativity to gauge the rate invariable for soaking up of in to aqueous solution of Na hydrated oxide in jet ouster is developed utilizing incursion theoretical account. The consequences obtained by this theoretical account are compared with the experimental values. Apart from this a mathematical theoretical account is besides developed to gauge rate of soaking up and sweetening factor which may be utilized to gauge farther interfacial country in the subdivision 4.4.
4.1.1 Model for the soaking up of Cl into aqueous solution based on incursion theory
When is absorbed in aqueous solution, the undermentioned reactions may take topographic point:
In this theoretical account, all reactions are assumed to be reversible. However reaction ( 4.1.2 ) and ( 4.1.3 ) have finite reaction rates, whereas reaction ( 4.1.4 ) and ( 4.1.5 ) are assumed to be instantaneous.
Here three equilibrium invariables and are independent and staying can be obtained by following equation:
The concentrations of chemical species that are present in aqueous solutions are renamed as follows:
220.127.116.11 Concentration of an single chemical species in majority of liquid
Assuming all the reactions are at equilibrium the undermentioned equations can be derived by overall mass balance.
where is the molar ratio of Cl to ab initio.
As the reactions are at equilibrium the independent equilibrium invariables are:
We have 7 terra incognitas and 7 algebraic independent equations.
These equations are additive system of equations and may be solved by minimum residuary technique utilizing MATLAB to acquire which converge to the solution ) .
It may be noted that in instance of aqueous solution do non incorporate any Cl ab initio ( means L=0 ) so
18.104.22.168 Mass balance at interface using Higbie ‘s incursion theoretical account
In jet ouster liquid jet resulting at high speed from noses situated at top, pulls the gaseous stage in to the jet. The gaseous watercourse is broken into little bubbles due to high kinetic energy of liquid jet and the gas-liquid comes in contact for a short clip at approximately 1/10 2nd. The mass transportation takes topographic point from the interface of bubble to the encircled liquid. To follow incursion theoretical account Lashkar-e-Taiba, , be the distance from the interface of the bubble. So ten = 0 denotes the gas-liquid interface. The liquid coming out of jet travel as free jet from mercantile establishment of multi nose to entry of pharynx where the environing gas gets entrained in it through its exposed outer surface. This liquid watercourse with bubbles so travels in unvarying cross subdivision of pharynx and at the terminal it passes through a conelike diffusor subdivision. Let Z be the length along the axis of liquid jet Z = 0 at the out Lashkar-e-Taiba of noses and at the mercantile establishment of the jet ouster. Let, be the clip of and may be computed by
To calculate volume between mercantile establishments of noses to inlet of pharynx, it is assumed that fluid travels through cylindrical transition holding diameter equal to inside diameter of nose and length
By presuming all reactions reversible, the undermentioned reaction rate look may be written.
The reactions ( 4.1.4 ) and ( 4.1.5 ) are instantaneous holding big values of rate of reaction therefore are eliminated. We besides assume that:
Chemical reactions are at equilibrium.
The diffusivity of ionic spices are equal.
The fluxes of the nonvolatilizable species at interface are equal to zero.
By sing the mass balance following differential equation are derived:
Entire Cl balance
As it is assumed all reactions are reversible hence the instantaneous reactions are besides at equilibrium and their equilibrium invariable may be written as follow:
There are 6 terra incognitas and 6 partial differential equations/algebraic equations which can be solved for the concentrations of all chemical species.
Initial status and boundary conditions
the concentration of chemical species are equal to bulk concentrations in liquid.
Boundary conditions at interface
At the interface of gas-liquid
For not volatile species
for all except =1 ( )
For volatile species ( ) , the rate of soaking up per unit interfacial country may be written as
Here in our system there is merely one volatile species i.e. Cl and therefore So we may compose and =
The equation ( 4.1.27 ) may be re-written as
The value of the true gas side mass transportation coefficient, for Cl required in equation ( 4.1.27 ) was predicted from the correlativity reported by Lydersen ( 1983, pp. 129 ) which is about 0.000432.
Where is the physical equilibrium invariable ( Henry ‘s jurisprudence invariable ) of
For chlorine-aqueous solution the equation ( 4.1.28 ) may be re-written as
Therefore is negligible.
The boundary status for pure at the gas liquid illation reduces to
22.214.171.124 Numeric solution and its execution
Equation ( 4.1.19 ) – ( 4.1.29 ) represents a mathematical theoretical account to obtain the values of It is non possible to obtain analytical solution and therefore we have used Finite Difference Method ( FDM ) to transform each partial differential equation of the theoretical account into the system of ordinary differential equations in
We choose following finite difference looks to come close the partial derived functions:
where refer to the chemical species, refers to the spacial node figure and
. Typical values for the initial nodal spacing at the gas-liquid interface are about. The transformed system of ordinary differential equation in T can be solved by MATLAB package by utilizing ODE15 convergent thinker with preconditioning technique and with particular Jacobi pre-conditioner.
This simulation gives and at the same time and which gives the mean rate of soaking up of per unit interfacial country ( flux ) . This may be written as
The gas liquid exposure clip for the jet ouster may be stated as
Similarly, the enhancement factor of may be determined from the undermentioned equation
where are interfacial and bulk concentrations of in the liquid severally and is the liquid stage mass transportation coefficient for physical soaking up of and is given by
To work out the mathematical theoretical account the diffusivities of different species and Henry ‘s jurisprudence invariable of are required which are tabulated in Table ( 4.1.2 ) . We besides need the equilibrium invariables and the forward rate coefficients of all chemical reactions ( 4.1.2 ) through ( 4.1.5 ) , which are tabulated in Table ( 4.1.3 ) .
Table 4.1.2: Henery ‘s jurisprudence invariable of and diffusion coefficients of ( ) , ( ) , and ( ) ( Ashour et al. , 1996 )
* rate of reactions and are instantaneous holding big value of and are eliminated.
Table 4.1.3: Valuess for Equilibrium invariables of Reactions ( 4.1.2 ) and ( 4.1.5 ) at assorted temperatures, ( Ashour et al. , 1996 )
4.1.2 Consequences and treatment
The incursion theoretical account has been used to develop mathematical theoretical account for soaking up of in to aqueous solution of Na hydrated oxide. The mathematical theoretical account to foretell absorpaiton rate is presented by equation ( 4.1.19 ) – ( 4.1.29 ) .
To work out this theoretical account the value of and were required. The value of was determined by the correlativity given by Brian et Al. ( 1966 )
The reaction and are instantaneous therefore eliminated.
There is big fluctuation in the value of in the literature as clear from Table ( 4.1.1 ) . Hence effort has been made to gauge value of by utilizing informations obtained for soaking up of in aqueous Na hydrated oxide solution in the jet ouster. The value of was adjusted until the theoretically predicted rate of soaking up was within 1 % of the by experimentation measured rate of soaking up of
Therefore following correlativity is developed to foretell the value of:
The predicted value of from equation ( 4.1.1 ) reported by Ashour et Al. ( 1996 ) and predicted value of from equation ( 4.1.37 ) by proposed theoretical account, along with the value obtained from the experimental consequence of present work are presented in tabular array ( 4.1.4 ) and plotted in figure ( 4.1.1 ) and ( 4.1.1b ) .
Table 4.1.4: The values of rate invariables for reaction 4.1.3, , at atmospheric force per unit area for -Aqueous system
Figure 4.1.1: Comparison of obtained by Ashour et Al. ( 1996 ) , proposed mathematical theoretical account and experimental consequence by Ashour et Al. ( 1996 ) with present experimental consequence over the temperature scope of 293-312 K
Figure 4.1.1a: Detailed position of Figure 4.1.1 at a temperature T-1 =3.3×10-3
Figure 4.1.2: Mistake estimations for K2 and Ashour et Al. ( 1996 )
The experimental value and value predicted by present theoretical account ( equation 4.1.37 ) are comparable. The value estimated by Ashour et Al. ( 1996 ) are a small higher for which mistake is estimated. The mistake in-general may be defined as the absolute value of difference between estimated or measured value and existent value. Here mistake is defined as follow:
The mistake estimates for Ashour et Al. ( 1996 ) and proposed theoretical account along with mistake between proposed theoretical account and present experimental value are presented in figure ( 4.1.2 ) . The mistake between proposed theoretical account and Ashour et Al. ( 1996 ) are less than 5.2 ten 10-4 and the mistake between proposed theoretical account and experimental value is about 0.8 ten 10-4. As the mistake is really less it may be concluded that the proposed theoretical account is good.
The figure ( 4.1.3 ) nowadayss V, ( as parametric quantity ) . The values obtained by experiment and by proposed theoretical account are in good agreement.Thus the chemical soaking up mechanism proposed in the present work may be considered to be right.
Figure 4.1.3: Comparison between the values for rate of soaking up obtained by experimentation and predicted by proposed theoretical account with regard to at different
The value obtained by experiment and predicted from the proposed theoretical account are in good understanding. Hence, the proposed mathematical theoretical account may be used to foretell the value of reaction rate, These values may be farther utilised to foretell enhancement factor and interfacial country utilizing following co-relations:
The correlativity obtained to gauge rate invariable for forward portion of soaking up of Cl in aqueous is
4.2 Consequence of the diffusivities on soaking up of Cl into aqueous Na hydrated oxide solution
The soaking up of Cl into aqueous Na hydrated oxide solutions is one of the of import systems holding industrial importance and besides is of theoretical involvement.
Danckwerts ( 1950a and 1950b ) and Sherwood and Pigford ( 1952 ) showed that soaking up rate could be predicted by the incursion theory for soaking up accompanied by an instantaneous irreversible reaction of the type
Spalding ( 1962 ) studied the soaking up rate of into H2O and aqueous solutions of and utilizing liquid-jet column. They have besides established that the soaking up rate of will be affected by the reactions ( 4.2.1 ) and /or ( 4.2.2 ) :
depending upon the value of the solution.
Further, they have observed that when value was higher than 12.6 ( i.e. concentration more than the forward portion of reaction ( 4.2.2 ) was rate-controlling and the consequence of this reaction on the soaking up rate could be predicted by the incursion theory for soaking up accompanied by an instantaneous irreversible reaction.
Brian et Al. ( 1965 ) studied gas soaking up accompanied by a two-step chemical reaction,
followed by. They have considered both stairss irreversible and of finite reaction rates and presented the theoretical analysis based on both, the movie theory and the incursion theory, with numerical solutions for the enhancement factor, .
Takahashi et Al. ( 1967 ) used two different types of absorbers viz. liquid-jet column and a
stop-cock type absorber to analyze the soaking up rates of into aqueous ( . The predicated soaking up rate utilizing incursion theory was in good understanding with experimental consequences.
Hikita et Al. ( 1972 ) studied gas soaking up of two-step chemical reaction, followed by, accompanied by They have studied the consequence of ratio of chemical equilibrium invariables, P ( which is defined as ) , on enhancement factor, I? . They have developed mathematical theoretical accounts for finite value and a?z , for equal diffusivity and unequal diffusivities of species on the footing of incursion theory.
Hikita et Al. ( 1973 ) stated that in instance of strong hydroxide solution the forward portion of reaction ( 4.2.2 ) is non merely reaction which governs the soaking up rate of but the rapid reaction
besides affects the soaking up rate of as the equilibrium invariable of this reaction is really big.
In this subdivision, the writer has developed a mathematical theoretical account to analyze the consequence of diffusivities on the enhancement factor and analyzed the experimental informations obtained by him and Hikita et Al. ( 1973 ) on the footing of the incursion theory for gas soaking up accompanied by a two measure instantaneous chemical reaction. In this work, the rate of soaking up in the jet ouster is studied by utilizing – aqueous system at.
4.2.1 Mechanism of chemical soaking up
Spalding ( 1962 ) mentioned that, when concentration is more than the forward portion of reaction ( 4.2.2 ) is rate-controlling which affects the soaking up rate.
Hikita et Al. ( 1973 ) stated that ( hypochlorous acid ) formed by reaction ( 4.2.2 ) can respond once more with ions consequences in rapid reaction ( 4.2.3 ) holding equilibrium invariable
Therefore sing two measure mechanism of the reaction ( soaking up ) between and an aqueous hydrated oxide solution, may be written as follows:
The values of the equilibrium invariables of reactions ( 4.2.2 ) and ( 4.2.3 ) are and. They are stated as follows:
The values of and at is given by ( Connick et al. , 1959 ) and
( Morris, 1966 ) severally.
The hydrolysis of dissolved with H2O takes topographic point harmonizing to the reaction
The equilibrium invariable of this reaction is given by
and holding value ( Connick et al.,1959 ) at.
The values of is really low compared to the value of, and therefore reaction ( 4.2.1 ) will non hold a important part to the entire reaction rate of
Therefore, the soaking up of into aqueous hydroxide solutions can be considered as an instantaneous two-step reaction, which is tantamount to state that reaction ( 4.2.4 ) followed by reaction ( 4.2.5 ) and holding over all reaction ( 4.2.6 ) .
4.2.2 Mathematical theoretical accounts related to soaking up
Enhancement factor, I?
The rate of soaking up of reactant ( gas ) with instantaneous chemical reaction can be predicted by summing
( a ) Sum of diffuse off unreacted and
( B ) Sum of reacted ( in the signifier of ) diffuse off from the gas-liquid interface.
The integrating of equation ( 4.2.7 ) from clip zero to the entire exposure timegives the mean soaking up rate and which may be written as:
The mean soaking up rate of in absence of the chemical reaction is given by the well-known Higbie equation
It is known that the enhancement factor is the ratio of mean rates of soaking up with chemical reaction and without chemical reaction. Therefore from equation ( 4.2.8 ) and ( 4.2.9 ) :
Desorption of the
Lahiri et Al. ( 1983 ) studied the procedure of desorption of the intermediate merchandise hypochlorous acid, , during the procedure of soaking up of in aqueous alkaline hydrated oxides. They gave correlativity for the rate of desorption of the merchandise:
Therefore, mean rate of desorption over a entire exposure clip, is given by
= sweetening factor for desorption
= true liquid side mass transportation coefficient without chemical reaction.
The equation ( 4.2.10b ) will go:
One reaction-plane theoretical account
Hikita et Al. ( 1972 ) developed the theoretical account based on incursion theory for soaking up with instantaneous chemical reaction and found that for there exists merely one reaction plane, where the over-all reaction of reactions and is, returns irreversibly. The mean rate of soaking up of the solute gas can be calculated by following equations which were derived by Danckwerts ( 1950 ) and Sherwood and Pigford ( 1952 ) .
Where is root of the equation
This soaking up mechanism is called a “ one reaction-plane theoretical account ” .
Two reaction plane theoretical account
Hikita et Al. ( 1972 ) developed a two reaction plane theoretical account when and established the fact that two reaction planes are formed within the liquid, which are as follows:
The reaction which is the amount of forward portion of the first-step reaction
) and the backward portion of 2nd measure reaction take topographic point irreversibly at the first reaction plane ( which is located closer to the gas-liquid interface )
The reaction take topographic point irreversibly at the 2nd reaction plane.
Further, the soaking up rate may be calculated by equation ( 4.2.11 ) and following equation:
where is the root of following equations.
Two reaction plane theoretical account for soaking up ofinto aqueous solution
The reaction strategy for the system studied in this work is similar to the work of Hikita et Al. ( 1972 ) . The present reaction system ( Equation ( 4.2.4 ) and ( 4.2.5 ) ) may be described in the signifier
The present system is different than the work of Hikita et Al. ( 1972 ) due to presence of which was non present in Hikita et Al. ( 1972 ) . However the species is non-reactive. Hence it does non impact reactive mechanism.
Figure 4.2.1: Concentration profiles for soaking up of into aqueous solution
Since, the equilibrium changeless ratio is really high, so we can use the two reaction plane theoretical account to the present system.
The diffusion coefficients of all species, based on the incursion theory is modeled by partial differential equations. The concentration profile for each species which will be derived by work outing the developed theoretical account will be similar to that as shown in Figure 4.2.1.
with the undermentioned initial and boundary conditions:
where and are the locations of the first and the 2nd reaction planes, severally, and and stand for the values of when attacks from part 2 and from part 3, severally.
This proposed theoretical account is more general.
Specifically, when the consequence of are negligible and therefore removed from the equations, the proposed theoretical account will cut down to pattern of Hikita et Al. ( 1973 )
The analytical solution of this job ( i.e. concentration profile in the liquid ) was given by Hikita et Al. ( 1973 ) and is every bit follows:
Proposed mathematical theoretical account I: This theoretical account is represented by equations ( 4.2.17 – 4.2.27 ) , when are non zero.
Proposed mathematical theoretical account II: This theoretical account is represented by equations ( 4.2.17 – 4.2.22 ) when consequence of are negligible with modifying boundary conditions which are as follows:
In proposed mathematical theoretical account II, we have consider the consequence of leap at and The two plane theoretical account theory suggest us that at there is a instantaneous reaction between species ( ) and ( ) and causes leap in concentration of species. Similarly, at there is a sudden reaction between species ( ) and ( ) and causes leap in concentration of species ( ) . This leap values are defined by the last term of the Equation ( 4.2.42 ) and Equation ( 4.2.43 ) severally.
The soaking up rate for proposed mathematical theoretical account I can be calculated by equation ( 4.2.11 ) and
where the invariable can be determined by work outing the following brace of coincident equations.
Similarly the soaking up rate for proposed mathematical theoretical account II can be calculated by equation ( 4.2.11 ) and
where the invariable can be determined by work outing the following brace of coincident equations.
The equations ( 4.2.45 ) , ( 4.2.46 ) ( 4.2.47 ) ( 4.2.48 ) ( 4.2.49 ) and ( 4.2.50 ) are solved by the test and mistake process based on Newton – Raphson technique to measure and. In this technique the first conjecture values of and was calculated by sing equal diffusivities i.e. .
There are several numerical methods like finite difference method, finite volume method, finite component method etc. to work out proposed mathematical theoretical account I and proposed mathematical Model II. Looking to the nature of the mathematical theoretical account ( clip dependant and in one dimension ) FDM is the best suited technique. Other methods are expensive from clip point of position. Hence, we have used the numerical technique, finite difference method, to work out the theoretical account utilizing Matlab package.
4.2.3 Discussion of consequences
The consequence of the diffusivity ratio on sweetening factor
Figure 4.2.2 shows the secret plan of the enhancement factor versus the concentration ratio for different diffusivities ratio of with changeless and The value of are taken to be 2.43, 1 and 0.1. In this figure the secret plans of Hikita ( 1972 ) , proposed mathematical theoretical account I [ equations ( 4.2.17 – 4.2.27 ) with are non zero ] and proposed mathematical theoretical account II [ equations ( 4.2.17 – 4.2.22 and 4.2.40 – 4.2.44 ) with are zero ] are presented.
Figure 4.2.2: Variation in enhancement factor with regard to at different, 1, 0.1 and changeless and for soaking up of into aqueous solution
The undermentioned consequences may be drawn from figure ( 4.2.2 ) .
The lines in the figure holding higher are at higher place for the same
. This indicates that at higher ratio of diffusivities of reactants ( liquid and gas ) , the enhancement factor is higher. It can be concluded that higher the diffusivity of liquid reactant with regard to gaseous reactant, higher is the enhancement factor. This may because as is higher the thickness of movie reduces due to travels faster toward the interface so
For same secret plans shows that enhancement factor additions with addition in the reactant ratio. The addition in enhancement factor is steeper at initial addition of. After that the rate of rise in enhancement factor with regard to rate of rise in reactant ratio is cut downing and after certain value of there is barely any rise is enhancement factor with regard to reactant ratio. It can be concluded that there is addition in enhancement factor with addition in liquid reactant concentration up to certain bounds. This may be interpreted that at higher sweetening factor is higher. The decrease of at higher may be due to high viscousness of solution at higher.
For the same ratio of the value of enhancement factor derived from proposed mathematical theoretical account II is higher than the value from proposed mathematical theoretical account I. The value derived from Hikita ( 1972 ) is the lowest. The predicted values from proposed mathematical theoretical account I and proposed mathematical theoretical account II are higher than Hikita ( 1972 ) as the consequence of spreading out have been considered. Furthermore, the consequence of have been considered in the proposed mathematical theoretical account I.
Figure 4.2.3: Mistake estimates between experimental informations and proposed
mathematical theoretical account at different, 1, 0.1 and changeless and.
Figure 4.2.3 shows the mistake estimates between Hikita ( 1972 ) theoretical account and proposed mathematical theoretical account I. Here mistake is defined as follow:
It is observed that the lower value of for different, the proposed mathematical theoretical account I and Hikita ( 1972 ) theoretical account are comparable. However, for higher values of, the comparing shows that there is a numerical instability in Hikita ( 1972 ) theoretical account ( higher value of mistake ) . Therefore, we conclude that the proposed theoretical account I is well-posed.
Comparison of experimental consequences with fake consequences
Figure 4.2.4 is a comparing of predicted by the fake consequences of Hikita ( 1973 ) , proposed mathematical theoretical account I and proposed mathematical theoretical account II with by experimentation determined values ( for ) at existent value of diffusivity ratio: and ( Postpone A 3.4 ) . It may be observed that the values obtained by experiment, Hikita ( 1973 ) theoretical account and proposed theoretical account I are comparable. Equations ( 4.2.17 ) to ( 4.2.22 ) and ( 4.2.45 ) to ( 4.2.50 ) indicate that is a map of rate of reactions and three diffusivity ( in liquid ) ratios, and The predicted values by proposed mathematical theoretical account I are higher to some extent than Hikita ( 1973 ) theoretical account which is due to the consequence of reaction on, have been consider in mathematical theoretical account I. It may be do out that the influence of rate of reaction are fringy that may be because being instantaneous reaction diffusivity ratio of species are rate controlling.
Figure 4.2.4: Comparison of experimental observation and proposed
mathematical theoretical account
The values predicted by proposed mathematical theoretical account II for are higher than experimental values. It may be concluded that the consequence of jumping in the concentration of and which have been considered in the theoretical account at the interface 1 and 2 are non appreciable. Hence the values predicted by theoretical account II are higher. So exemplary II is non appropriate under runing conditions of the experiment.
The enhancement factor depends on the five independent dimensionless parametric quantities i.e. , three diffusivity ratios, and, and two concentration ratios and
The enhancement factor additions as the value of with regard to additions.
The value of enhancement factor additions as the value increases, and the consequence becomes big at low values and low at high values
The proposed mathematical theoretical account I is more appropriate to experimental consequences at operating conditions i.e. at 300C.
4.3 Numeric theoretical account of rate of soaking up in multi nozzle jet ouster ( chlorine- aqueous solution )
High speed jet from the noses entrains the gas and due to really high turbulency in the pharynx, gas is split into bubbles. In the diffusor subdivision partial separation of the gas and liquid may happen. The high interfacial country formed by bubbles is desirable for increasing rate of mass transportation. Different research workers, including Kuznetsov and Oratovskii ( 1962 ) , Boyadzhiev ( 1964 ) , Volgin et Al. ( 1968 ) and Beg and Taheri ( 1974 ) , attempted to imitate the operation of the jet ouster for gas soaking up.
Johnstone et Al. ( 1954 ) reported a jet ouster survey in which was absorbed in solution, and the sum of S dioxide absorbed in the liquid, was measured at assorted distances from the point of liquid injection. It was found that the mass transportation increased well as the liquid injection rate increased.
Kuznetsov and Oratovskii ( 1962 ) developed a mathematical theoretical account for foretelling soaking up of by responding with solution in the pharynx and the divergent subdivision of a venturi scrubber.
removal efficiency of a jet ouster was investigated by Talaie et Al. ( 1997 ) utilizing a 3-dimensional mathematical theoretical account based on a non unvarying droplet concentration distribution predicted from a scattering theoretical account in the gas flow where the gas-phase mass transportation coefficient was calculated by empirical equations.
Mandal et Al ( 2003 ) studied the jet ouster followed by bubble column and developed two simple correlativities of and as a map of superficial gas speed. This correlativity can be combined to cipher liquid-side mass transportation coefficient.
Utomo et Al. ( 2008 ) investigated the influence of operating conditions and ouster geometry on the hydrokineticss and mass transportation features of the ouster by utilizing 3-dimensional CFD mold. The CFD consequences were validated with experimental informations.
Taheri et Al. ( 2010 ) studied the 3-dimensional mathematical theoretical account, based on annulate two-phase flow theoretical account for the anticipation of the sum of removed in a venturi scrubber.
We have made an effort to foretell mass transportation features by numerical mold. Here, the writer has described the mathematical theoretical account for the anticipation of the sum of Cl removed in jet ouster. The consequences of simulation are compared with the experimental information.
4.3.1 Mathematical mold
In this survey the theoretical account developed by Taheri et Al. ( 2010 ) is modified to accommodate the jet ouster used in the present work. Taheri et Al. ( 2010 ) developed a 3-dimensional mathematical theoretical account based on annulate two-phase flow theoretical account in rectangular geometry of the venturi scrubber. They develop a theoretical account to foretell interfacial country by foretelling bead size and droplet concentration. Alternatively in this work an effort is made to foretell the alteration in concentration of reactant, , through the ouster.
The concentration of bubbles has been assumed unvarying across the cross subdivision of the scrubber.
The continuity equation of bubbles is solved to obtain bubble concentration distribution sing the consequence of gas turbulency.
For developing the theoretical account, the pollutant concentration distribution in gas stage was obtained by the undermentioned theoretical account utilizing aggregate balance.
The general equation can be obtained by composing differential mass balance for pollutants over a differential control volume.
The rate of reaction of pollutant per unit volume at clip for changeless volume system may be written as
The may be calculated by utilizing rate of mass transportation per unit country as
where = interfacial country per unit volume
= ( figure of bubble / volume ) ten ( interfacial country / bubble )
may be computed from speed in instance of traveling gas as
equation ( 4.3.1 ) may be written as
Boundary conditions for Equation ( 4.3.1 ) are as follows:
The value of may be estimated by utilizing the undermentioned equation ( Ogawa et al. , 1983 )
Substituting equation ( 4.3.3 ) in equation ( 4.3.1 ) it will cut down to
In order to measure the bubble concentration distribution, in the above equations, the undermentioned unidimensional scattering equation, showing stuff balance for bubble in a differential control volume, must be solved:
with the boundary conditions of:
In Equation ( 4.3.3 ) , the bubbles are convected in the ten way.
It is assumed that for each nozzle the beginning of bubbles is limited to one component. The beginning strength, S, is the figure of bubbles generated per unit volume per unit clip. Bubbles are carried from component to component and are dispersed by convection and eddy diffusion effects. Number of bubbles per second is defined by the undermentioned equation:
where is the entire gas flow rate.
Substituting equation ( 4.3.3 ) and ( 4.3.7 ) in equation ( 4.3.4 ) it will cut down to
The bubble speed can be obtained by work outing the undermentioned equation. This is obtained by composing a force balance for bubbles.
The modified retarding force coefficient, , can be calculated by utilizing the undermentioned looks given by Taheri et Al. ( 2010 ) adopted for bubbles:
Here can be obtained by the expression given by Tahari et Al. ( 2010 ) adopted for bubbles:
Substituting Equation ( 4.3.11 ) ( 4.3.12 ) and ( 4.3.13 ) in Equation ( 4.3.10 ) it will cut down to
The gas speed is computed by the undermentioned equation:
The equation ( 4.3.1 ) can be solved at the same time with equation ( 4.3.3 ) , ( 4.3.5 ) , ( 4.3.7 ) , ( 4.3.9 ) , ( 4.3.16 ) and ( 4.3.17 ) .
The mass transportation rate, , in each component can be evaluated by theoretical account developed in old subdivision presented by equation 4.1.32.
When pollutants undergo a really fast reaction into the liquid stage such as soaking up of into aqueous solution, the majority concentration of gas in the liquid stage can be considered equal to zero.
4.3.2 Consequences and treatments
Figure 4.3.1 is a secret plan of fluctuation of gas stage concentration along the axis of ouster for different values of initial gas concentration for nozzle N1 holding figure of orifice1. For comparing of the experimental consequences and predicted consequences obtained by the proposed theoretical account are plotted in the same figure. From both the profiles shown in the figure, it is clear that the proposed theoretical account is in good understanding with experimental consequences.
Figure ( 4.3.2 ) shows the fluctuation of gas stage concentration along the axis of the ouster for different noses N5 ( no. of orifice 1 ) , N6 ( no. of orifice 3 ) and N7 ( no. of orifice 5 ) . The consequences predicted by the theoretical account are in good understanding with the experimental consequences. Thus the theoretical account is applicable for multi nozzle jet ouster.
It is besides shows that the transition in the jet ouster first increases so lessenings and eventually becomes about changeless. The figure of opening in the nozzle affects the gas transition in the jet ouster with three opening ( N6 ) the transition obtained is maximal with five openings ( N7 ) lower limit and with one opening ( N5 ) in between upper limit and lower limit.
Figure 4.3.1: Variation of gas stage concentration along the axis of ouster for different values of initial gas concentration at ( comparing between proposed theoretical account and experimental value )
Figure 4.3.2: Variation of gas stage concentration along the axis of ouster for different noses N5 ( no. orifice 1 ) , N6 ( no. of orifice 3 ) and N7 ( no. of orifice 5 ) for apparatus 3 at and initial gas concentration ( comparing between proposed theoretical account and experimental value )
The figure 4.3.3 shows the fluctuation of bubble speed along the axis of the ouster. It indicates that the bubble speed all of a sudden increases to a maximal value and so it remains changeless.
Figure 4.3.3: Speed profiles of gas and droplet along axial way
The proposed theoretical account is in good understanding with experimental values for individual nose every bit good as for multi noses. Hence the proposed theoretical account may be used for planing the industrial ousters.
The figure of nose ( opening ) affects the gas transition. In present work the maximal transition is obtained for no. of nozzle 3 ( N6 ) .
4.4 Mass transportation features in multi nose jet ouster
In this subdivision a mathematical theoretical account to foretell keep up, mass transportation coefficient and interfacial country has been proposed for multi nose jet ouster and compared with experimental informations obtained.
Many research workers have published their work on jet ousters ( Jackson, 1964 ; Volmuller and Walburg, 1973 ; Nagel et al. , 1970 ; Hirner and Blenke, 1977 ; Zehner, 1975 ; Pal et al. , 1980 ; Ziegler et al. , 1977 ) because of the high energy efficiency in gas liquid contacting.
The kinetic energy of a high speed liquid jet is used for acquiring all right scattering and intense commixture between the stages in the jet ousters.
Zlokamik, ( 1980 ) has reported that O soaking up efficiency is every bit high as 3.8 kilogram O2/kwh in ousters as compared to 0.8 kilograms O2/kwh in a propellor sociable. The higher gas scattering efficiency of the ouster type can be understood from the well known fact: “ gas scattering is possible merely if the fraction of micro turbulency is high ” ( Schugerl, 1982 ) .
Radhakrishnan et Al. ( 1984 ) have used a perpendicular column fitted with a multi jet ouster for gas-dispersion for analyzing the force per unit area bead, armed robbery and interfacial country.
Agrawal ( 1999 ) has reported interfacial country, approximately 13000 m2/m3 in horizontal individual nose jet ouster. The mensural values of the interfacial country in the jet ouster are in the scope of 3000 to 13000 m2/m3.
4.4.1 Hold up
Yamashita and Inoue ( 1975 ) , Koetsier et Al. ( 1976 ) and Mandal ( 2004 ) reported the armed robbery features with regard to gas flow rate in the jet ouster. At lower scope of gas flow rate, gas hold up additions with addition in gas flow rate but at higher scope of gas flow rates the addition in gas flow rate decreases the gas keep up or it remain changeless depending on the tallness of liquid in the follow up column is high or low severally. At lower gas flow rates little bubbles produced are in big figure and at higher gas flow rate due to coalescence the bubbles of larger size are produced which lead to diminish in figure of bubbles.
Hills ( 1976 ) has reported that the armed robbery is non affected by liquid flow rate. Mandal ( 2004 ) observed that for the same gas flow rate the addition in liquid flow rate decreases the gas hold up.
The variables and impact the liquid armed robbery in a jet ouster.
Radhakrishnan et Al. ( 1984 ) obtained following correlativity by using multi additive arrested developments analysis on their experimental informations:
A new mathematical theoretical account has been attempted to foretell the gas hold up every bit follows:
It is assumed that the theoretical account is of the signifier:
Using experimental informations and multi additive arrested development analysis the values of and were obtained. The values obtained are and
Figure 4.4.0: Comparison of liquid armed robbery predicted by Radhakrishnan ( 1984 ) , present theoretical account and experimental value at different ratio.
Therefore mathematical theoretical account for liquid hold up is as follows.
Liquid armed robbery may be determined by following equation.
The consequences predicted from Radhakrishnan ( 1984 ) theoretical account and present theoretical account ( equation – 4.4.3 ) is compared with existent experimental value at different in figure ( 4.4.0 ) .
4.4.2 New theoretical account to foretell mass transportation features, and
To foretell mass transportation characteristics the value of and are required to be predicted. Here a mathematical theoretical account is developed to foretell the value of and utilizing chlorine-aqueous Na hydrated oxide solution.
Doraiswamy and Sharma ( 1984 ) have reported that if
so the reaction is considered to be pseudo first order and in the fast reaction government.
As soaking up of in aqueous solution of studied in the present work satisfy the status ( 4.4.4 ) and ( 4.4.5 ) , it is treated as imposter foremost order fast reaction.
Levenspiel ( 1999 ) presented a simplified solvable imposter first order rate look as a replacing for 2nd order reaction rate equation when the value of is so high that it do non alter appreciably, which is presented here as follows:
Substituting equation ( 4.4.7 ) , ( 4.4.8 ) in equation ( 4.4.6 ) we have:
By rearranging equation ( 4.4.9 ) and incorporating between will give the equation:
Sharma and Danckwerts, ( 1970 ) stated that when
Then gas stage opposition is negligible.
But for chlorine-aqueous system
Therefore, to foretell interfacial country few experiments were carried out for -aqueous system.
-aqueous system satisfies the status as of equation ( 4.4.12 ) . Therefore gas stage opposition is negligible. Hence equation ( 4.4.11 ) will turn to
And equation ( 4.4.10 ) may be written for ciphering interfacial country as follows:
True gas side mass transportation coefficient for Cl
For aqueous system
# Merely a sample is shown. Run No. 110
Table 4.4.1: Typical scope of experimental values
That implies that gas stage opposition controls the rate of reaction ( Levenspiel, 1999 ) .
Therefore the rate of soaking up of may be written as
The true gas side mass transportation coefficient, , is given by,
The theoretical account presented by the equations ( 4.4.10 ) , ( 4.4.14 ) and ( 4.4.17 ) are the theoretical accounts to foretell the value of and
4.4.3 New mathematical theoretical account related to interfacial country for multi nose ousters
Radhakrishnan et Al. ( 1986 ) have suggested the undermentioned correlativities to estimations interfacial country i.e.
Mandal et Al. ( 2003 ) have suggested the undermentioned estimations for interfacial country of system i.e.
, where is gas superficial speed
In this work a new theoretical account has been proposed for appraisal of ” This theoretical account is easy to use and necessitate minimal input informations.
is determined by experimentation and is equal to.
can be estimated by the theoretical account developed in subdivision 4.1 given by look ( 4.1.32 ) .
So can be determined
This mathematical theoretical account is employed for multi noses ouster with figure of orifice 3, 5 and 7. The dimensions of multi noses ouster are given in chapter 3. The consequences obtained with this theoretical account for multi nozzle ouster are compared with experimental informations.
4.4.4 Consequences and treatments
A new mathematical theoretical account has been proposed as per experiment ( 4.4.16a ) , ( 4.4.17 ) and ( 4.4.20 ) to foretell mass transportation features by finding the value of and. The predicted values by utilizing this proposed theoretical account is presented diagrammatically in the figures ( 4.4.1 ) to ( 4.4.16 ) . The figures show the consequence of on predicted value of, and for different noses and different values of. The fluctuation in the rate of soaking up of with chemical reaction in aqueous solution is discussed below.
126.96.36.199 Factors impacting rate of soaking up ( ) in liquid jet ouster
is higher for higher ( figure – 4.4.13 ) . This is because the liquid jet spray country in the free jet subdivision is higher for more figure of noses and will ensue in more entrainment of gas and high rate reaction due to high interfacial country. The high liquid jet exposed country counters the consequence of addition in viscousness of aqueous solution due to increase in its concentration.
Figure ( 4.4.1 ) , ( 4.4.5 ) , ( 4.4.9 ) and ( 4.4.13 ) show the consequence of on utilizing different noses. The undermentioned decisions can be derived from the survey of the figures.
A common tendency has emerged that as additions the besides increases in all apparatuss for all noses. This is because rate of reaction is map of concentration of both reactants i.e. Cl ( ) and ( ) .
lessenings with addition in.
The concentration of aqueous solution in is unbroken high to keep imposter foremost order status. So that rate of reaction is independent of viscousness of. The decrease in soaking up rate is due to increase in aqueous solution with addition in concentration, which leads to less diffusivity coefficient ( Stokes-Einstein equation ) and besides decrease of physical solubility of ( Krevelen and Hoftijzer theory, 1948 ) .
This is due to ( I ) the addition in viscousness of aqueous solution, ( two ) decrease of physical solubility of and ( three ) diffusivity of in aqueous solution when concentration of is increased. But for lower concentration of, the value of is maximal for nozzle N6 ( three nose ) . The value of is minimal for nozzle N5 ( individual nose ) .
The maximal soaking up obtained is in perpendicular installing holding three nozzle that is setup 3 holding nozzle N6.
188.8.131.52 Effect of different parametric quantities on mass transportation features ( and ) in jet ousters.
Consequence of on and
Volumetric mass transportation coefficient ( ) : Figure ( 4.4.2 ) , ( 4.4.6 ) , ( 4.4.10 ) and ( 4.4.11 ) are the secret plans of predicted by proposed theoretical account versus for apparatus 1, 2 and 3. It is observed that by increasing maintaining other parametric quantities constant the value of volumetric mass transportation coefficient additions.
Interfacial Area ( ) : Figure ( 4.4.3 ) , ( 4.4.7 ) and ( 4.4.11 ) are the secret plans of interfacial country, predicted by proposed theoretical account against different values of for apparatus 1 and 3. These figures show that interfacial country lessening with addition in. The decrease in interfacial country is due to higher viscousness of the solution at higher concentration.
The higher concentrations have inauspicious consequence on diffusivity and physical solubility of in solution.
Mass transportation coefficient ( ) : The figures ( 4.4.4 ) , ( 4.4.12 ) and ( 4.4.16 ) are the secret plans of predicted by proposed theoretical account against different values of for apparatus 1, 2 and 3.
The mass transportation coefficient ( ) is higher at higher exclusion for the apparatus 1 ( with nozzle N1 ) the highest value of is observed for lower ( ) with.
Consequence of figure of noses on and
Volumetric mass transportation coefficient ( ) : Variation of with figure of noses for different, in jet ouster are shown in figures ( 4.4.6 ) and ( 4.4.14 ) . It is observed in figure ( 4.4.14 ) that is highest for nozzle N7. ( no. of orifice 5 ) for all. is less for nozzle N6 ( no. of orifice 3 ) than nozzle N7 ( no. of orifice 5 ) . is minimal for N5 ( no. of orifice 1 ) . In figure ( 4.4. ) similar form is shown for nozzle N2 and N3 in set up 2 i.e. is higher for nozzle N3 ( no. of opening ( 3 ) than nozzle N2 ( no. of orifice 1 ) .
Hence obtained is higher for big figure of noses for the same sum flow country.
So we may infer that as the figure of noses are more the value of is more.
Interfacial country ” :
The interfacial country generated in jet ouster by changing for aˆ¦aˆ¦aˆ¦aˆ¦aˆ¦.. figure of noses ( opening ) and at different are presented in figure ( 4.4.7 ) and ( 4.4.15 ) .
Interfacial country produced in jet ouster decreases with addition in figure of noses ( openings ) for all values of that were studied. This seems to be due to coalescency of bubbles at the junction where jets meets near the pharynx.
Mass transportation coefficient ( ) : Figure ( 4.4.8 ) and ( 4.4.16 ) are the comparing of values obtained by proposed theoretical account for for different noses ( N2, N3, N5, N6 and N7 ) at different.
In the apparatus 3 where industrial multi nose ouster was used for experiment shows that the value of is more for the noses holding more orifice merely a little fluctuation is seen in figure ( 4.4.16a ) where at higher the value is less for nose N7 ( 5 opening ) so for nozzle N6 ( 3 opening ) .
Similar tendency is observed in figure ( 4.4.8 ) plotted for apparatus 2, where the value of for nozzle N3 ( no. of orifice 3 ) is higher than for nozzle N2 ( no. of orifice 1 ) .
So we may reason that the as figure of nozzle additions the value of additions.
The predicted by the proposed theoretical account for different noses ( N2, N3, aˆ¦ . & A ; N7 ) at different are presented in figures ( 4.4.8 ) and ( 4.4.16 ) . The is higher for higher figure of noses ( openings ) holding the same flow country. Both setup 2 and setup 3 shows similar treach.
Consequence of on and
The fluctuation of and is shown in figure ( 4.4.1 ) to ( 4.4.16 ) .
Volumetric mass transportation coefficient ( ) : The consequence of on at different conditions is shown in figures ( 4.4.2 ) , ( 4.4.6 ) , ( 4.4.10 ) and ( 4.4.14 ) . All the figures are similar qualitatively i.e. as the value of additions the value of lessenings. The lessenings is really crisp at initial values of. Afterwards the lessening in with regard to is reduced. This is because of decrease in value of higher
Interfacial country ” : The consequence of on interfacial country for different noses and at different. It is shown in figures ( 4.4.3 ) , ( 4.4.7 ) , ( 4.4.11 ) and ( 4.4.15 ) . It is observed that there is merely a small fluctuation in interfacial country with alteration in. This is because the interfacial country generated depends on viscousness of the liquid and aˆ¦aˆ¦to gas ratio. In the present experiment the liquid to gas ratio is kept changeless and really low concentration of has been used. Under these conditions the viscousnesss of liquid and gas will non alter significantly.
From figures it is seen that at higher the value of reduces with addition in. While at lower ( 0.525 & A ; 0.11 ) there is non much fluctuation in with regard to increase in. This is because of higher the viscousness of liquid is more and that causes the decrease in diffusivity and physical solubility of Cl.
Mass transportation coefficient ( ) : The consequence of on is shown in figures ( 4.4.4 ) , ( 4.4.8 ) , ( 4.4.12 ) and ( 4.4.16 ) . From the figures it is seen that at higher ( 0.79 ) and orifice 1 and 3 the value of reduces with regard to. This is because at higher viscousness of solution is higher.
Correlations for anticipation of the armed robbery and interfacial country in a multi-jet ouster contactor system have been proposed by the equation ( 4.4.3 ) and ( 4.4.14 ) .
Two theoretical accounts have been proposed for the appraisal of interfacial country. Hence, a new theoretical account is developed by equation ( 4.4.14 ) and ( 4.4.20 ) to foretell interfacial country. The consequences are presented in figure ( 4.4.17 ) . The anticipations are good fitted with experimental informations.
The figures ( 4.4.1 ) to ( 4.4.16 ) are plotted on the footing of the anticipation from proposed new theoretical account presented by equations ( 4.4.20 ) .The behaviour of are shown against different initial concentration of gases for different noses and in these figures.The consequences may be analyzed as summarized in the undermentioned tabular array.
Table 4.4.2: Summary of analysis of consequences for different and noses
4.5 Removal efficiency of Cl in jet ouster ( Chlorine aqueous solution )
The major factors which affect the efficiency of jet ouster are liquid flow rate, gas flow rate, the concentration of absorbing liquid and the concentration of the solute in the gas.
Ravindram and Pyla ( 1986 ) proposed a theoretical theoretical account for the soaking up of and in dilute based on coincident diffusion and irreversible chemical reaction for foretelling the sum of gaseous pollutant removed.
Many research workers ( Volgin et al. , 1968 ; Ravindram and Pyla, 1986 ; Cramers et al. , 1992, 2001 ; Gamisans et al. , 2001, 2002 ; Mandal, 2003, 2004, 2005 ; Balamurugan et al. , 2007, 2008 ; Utomo et al. , 2008 ; Yadav, 2008 ; Li and Li, 2011. ) have reported different theories and correlativities to foretell scouring efficiency of jet ousters.
Uchida and Wen ( 1973 ) developed a mathematical theoretical account to foretell the remotion efficiency of 2 into H2O and alkali solution. The fake consequences of their theoretical account were compared with experimental consequences and they found that there is a good understanding with the experimental consequences. They have besides found enhancement factor to foretell rate of the chemical soaking up.
Gamisans et Al. ( 2001 ) evaluated the suitableness of an ejector-venturi scrubber for the remotion of two common stack gases, sulfur dioxide and ammonium hydroxide. They studied the influence of several runing variables for different geometries buildings of Venturi tubing. A statistical attack was presented by them to qualify the public presentation of scrubber by changing several factors such as gas pollutant concentration, gas flow rate and liquid flow rate. They carried out the calculation by multiple arrested development analysis doing usage of the method of the least squares method. They have used commercial package bundle, STATGRAPHICS, to find the multiple arrested development coefficients.
Less attending has been paid in the country of mathematical and statistical mold. The statistical theoretical accounts have edge over other theoretical accounts due to their capacity to manage random informations right. There are several techniques available to associate the governable factors and experimental facts.
In this chapter, we have made an effort to develop statistical theoretical account based on non-linear non additive quadratic multiple arrested development analysis to foretell removal efficiency of jet ouster for -aqueous system.
4.5.1 Statistical mold
We have used the non additive quadratic relation between independent variables and dependent variables and is every bit follows:
Here, is a response variable, is the chief factor ; is the changeless value of the arrested development ; is the additive coefficient ; is the quadratic coefficient and is the interaction coefficient. When. ; and.
The calculation was carried out by non additive arrested development analysis doing usage of the generalized minimum residuary method.
The non additive arrested development coefficients determined by calculation with the package bundle, STATGRAPHICS Plus 4.0, were used to find the optimum theoretical account adjustment.
4.5.2 Consequences and treatments
The factors which affect the soaking up efficiency are gas concentration and the scouring liquid concentration. In this work the jet ouster is operated on critical value of liquid flow rate. For a given geometry, decrease in the liquid flow rate will take to decrease of induced gas flow rate. Therefore, in the present work the liquid flow rate is kept changeless. Consequence of and on the remotion efficiency ) of the ouster have been investigated in this work.
The experimental values for the operating variables used in the present work are presented in Table 4.5.1 and the experimental informations are tabulated in Table 4.5.2, 4.5.3.
Table 4.5.1: Codification of the operating variables for the statistical analysis
Table 4.5.2: Experimental matrix for Cl remotion efficiency utilizing setup – 1
Table 4.5.3: Experimental matrix for Cl remotion efficiency utilizing setup – 3
184.108.40.206 Statistical analysis
STATGRAPHICS Plus 4.0 is used to foretell the remotion efficiency ( Y ) utilizing statistical theoretical account ( 4. 5. 1 ) for the noses N1, N5, N6 and N7.The consequences are summarized in table 4.5.4 and 4.5.5. Table 4.5.4 demonstrates the parametric quantities as result of fake consequences of STATGRAPHICS plus 4.0. The arrested development coefficients of fitted theoretical accounts are summarized in table 4.5.5.
The analysis of discrepancy ( ANOVA ) for the operational variables and indicate that remotion efficiency is good described by nonlinear quadratic theoretical accounts. The convergence is obtained successfully after 4 loops for appraisal of arrested development coefficients.
Furthermore, the statistical analysis showed that both factors ( and ) had important effects on the response ( ) and the liquid concentration is more important between two.
It may be observed that fitted theoretical accounts do non incorporate the independent term ( ) . This implies that the remotion efficiency ( ) is a map of the factors considered merely.
Trials are run to find the goodness of tantrum of a theoretical account and how good the non additive arrested development secret plan approximates the experimental information. As the consequences are multi numerical they are presented in figure ( 4.5. ) and table ( 4.5. ) . Statistical trials like R-squared, R-squared ( adjusted for d.f. ) , standard mistake of estimation, average absolute mistake and Durbin-Watson statistic are covered. The tabular arraies incorporating assurance interval, analysis of discrepancy ( ANOVA ) and residuary analysis are besides reported.
Consequences of statistical analysis in STATGRAPHICS Plus 4 for different noses:
220.127.116.11 Interpretation of the consequences of statistical analysis in STATGRAPHICS Plus 4 for different noses
The consequences of fitted theoretical account, R-squared trial, R-squared ( adjusted for d.f. ) trial, standard mistake of estimations, mean absolute mistake and Durbin-Watson statistic trial are summarized in tabular array ( 4.5.6 ) and may be interpreted as follow.
The R-Squared statistic indicates that the theoretical account as fitted explains 85.84 % , 86.55 % , 88.27 % and 48.59 % of the variableness in Y for N1, N5, N6 and N7 severally.
The adjusted R-Squared statistic which is more suited for comparing theoretical accounts with different Numberss of independent variables are 77.75 % ,78.86 % , 80.46 % and 0.0 % for N1, N5, N6 and N7 severally
The standard mistake of the estimation shows the standard divergence of the remainders to be 9.79, 7.69, 7.08 and 32.60 for N1, N5, N6 and N7 severally. This value can be used to build anticipation bounds for new observations.
The average absolute mistake ( MAE ) of 6.18, 5.15, 4.43 and 17.94 is the mean value of the remainders for N1, N5, N6 and N7 severally
Table 4.5.6: Summary of statically consequences
The Durbin-Watson ( DW ) statistic tests the remainders to find if there is any important correlativity based on the order in which they occur. Since, the DW value is less than 1.4 for N1 there may be some indicant of consecutive correlativity. Similarly, since, the DW value is greater than 1.4 for N5, N6, N7 there is likely non any serious autocorrelation in the remainders.
The end product besides shows asymptotic 95.0 % assurance intervals for each of the unknown parametric quantities.
After analysis the consequences it may be concluded that the theoretical account developed is non fit for nozzle N7.
18.104.22.168 Interpretation of figure ( graph )
For each set of experiment a mathematical theoretical account depicting the consequence of related variables on removal efficiency were derived and plotted in the figures ( 4.5.1 ) to ( 4.5.20 ) .These figures may be analyzed as follows:
Figures ( 4.5.2 ) , ( 4.5.7 ) , ( 4.5.12 ) and ( 4.5.17 ) show the response surfaces for the remotion of Cl with fluctuation in gas concentration ab initio and the scouring liquid concentration. The response surface shows removal efficiency varies from 50 % to maximal value of 96 % . It is observed that the consequence of liquid concentration is greater than the gas concentration on.
Dependence of removal efficiency ( ) on gas concentration ( ) and on initial concentration of liquid ( )
Figures ( 4.5.1 ) , ( 4.5.6 ) , ( 4.5.11 ) and ( 4.5.16 ) are demonstrative curve of the fitted theoretical account demoing the consequence of on at constant.The similar curve may be obtained and plotted for other value of.
Figures ( 4.5.3 ) , ( 4.5.8 ) , ( 4.5.13 ) and ( 4.5.18 ) show the contours of estimated response surface for nozzle N5, N6, N7 and N1 severally. The presentation of contours is for visual image of the best part where the is maximal.
A common tendency ( except little fluctuation for nozzle N6 ) may be observed that at higher concentration of there is lessening of with addition in initial concentration of. But a rearward tendency is observed at lower i.e. is increasing with addition in. The ground for this behaviour is that at higher the viscousness of liquid additions. The higher viscousness has inauspicious consequence on diffusivity and physical solubility. And this consequence becomes more appreciable at higher because of higher scouring burden due to higher initial concentration of ( ) .
The figures ( 4.5.3 ) , ( 4.5.8 ) , ( 4.5.13 ) and ( 4.5.18 ) screening contours have significance that they show the correlativities of all the parametric quantities.The counters are utile to place the parts of maximal efficiency The following tabular array shows the parts of the maximal efficiency.
Analysis of the contours suggests the undermentioned parts to hold upper limit.
Table 4.5.7: Summary of analysis of contours for remotion efficiency
Observed versus Predicted
The figures ( 4.5.4 ) , ( 4.5.9 ) , ( 4.5.14 ) and ( 4.5.19 ) show the ascertained versus predicted secret plan for N1, N5, N6 and N7 severally. The Y axis shows the ascertained value of and X axis show the predicted value by fitted theoretical account of. It may be observed that the points are indiscriminately scattered around the diagonal line bespeaking that theoretical account tantrums good. It may besides be observed that the secret plan is consecutive line holding no curve that means no demand to seek for higher order multinomial.
Remainders versus Predicted
The figures ( 4.5.5 ) , ( 4.5.10 ) , ( 4.5.15 ) and ( 4.5.20 ) show of the residuary analysis. The Y axis shows Studentized residuary and X axis shows the predicted from the fitted theoretical accounts. It may be observed that there is uni