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Simulation and Optimization of NOx AbsorptionSystem in Nitric Acid Manufacture

N. J. Suchak and J. B. JoshiDept. of Chemical Technology, University of Bombay, Matunga, Bombay 400 019, India

A mathematical model has been developed for the prediction of the optimumdesign of packed and plate columns for the manufacture of nitric acid. The effectsof inlet NOr composition, extent of oxidation and extenl of absorption in each stage,temperature, and pressure have been included in the model. The optimization ofthe preoxidizer and the condenser has also been discussed.

IntroductionAbsorption of NOx is an important step in the manufacture

of nitric acid. Absorption of NOx gas is probably the mostcomplex when compared with other absorption operations.This is for several reasons. First, the NOx gas is a mixture ofseveral components consisting of NO, N02, N20J, N204' andso on. The absorption of NOx gas in water results into twooxyacids, nitric acid, and nitrous acid. Secondly, several re-versible and irreversible reactions occur in both gas and liquidphases. Thirdly, simultaneous absorption of many gases occursfollowed by chemical reaction. Also, simultaneous desorptionof many gases occurs preceded by chemical reaction. For ex-ample, the absorption of N02, N20J, and N204 is accompaniedby chemical reaction whereas the desorption of NO, N02, andHN02 is preceded by chemical reaction. Finally, heterogeneousequilibria prevail between gas-phase and liquid-phase com-ponents. Sherwood et al. (1975) and Joshi et al. (1985) havereviewed these aspects of NOx absorption.

For the process design of NOx absorption towers, it is nec-essary to understand the combined effects of several equilibria,including the rates of mass-transfer and chemical reaction.Further, sUbstantialheat effects are associated with NOx ab-sorption; therefore, temperature variations need to be takeninto account in the process design. There have been outstandingattempts in this direction. For instance, Koval and Peters (1960),Andrew and Hanson (1961), Koukolik and Marek (1968),Carleton and Valentin (1968), Hoftizer and Kwanten (1972),Makhotkin and Shamsutdinov (1976), Holma and Sohlo (1979),Emig et al. (1979), Counce and Perona (1979, 1980, 1983),Joshi et al. (1985), Miller (1987), and Wiegand et al. (1990)have reported various aspects of ~he process design of packed

Correspondenceconcerning thi~ aniele ~hould be addressed 10 J. B. Joshi.Current odd,e" of N. J. Suehak: Cannon Technologies. Ine.. P. B. Box I. New Kensington.

PA 15068.

944

columns, plate columns, and packed bubble columns used forthe manufacture of nitric acid. These attempts will be strength-ened if the following important features are included in theprocess design.

(I) The rates of absorption of N02, N20J' and N204 in nitric

acid are different from those in water. The rates decrease withan increase in the concentration of nitric acid.

(2) It is known that for a given set of partial pressures ofNO, N02, and N204' there exists a certain limiting concentra-tion of nitric acid beyond which no absorption of N204 andN02 occurs (Carberry, 1958). This heterogeneous equilibriumsubstantially reduces (even three to four times) the rates ofabsorption of N02, N20J' and N204' and the extent of reduc-tion increases as the nitric acid concentration approaches theequilibrium value.

(3) A substantial quantity of nitric acid is formed in the gasphase, particularly at high temperatures and high partial pres-sure of NOx' Therefore, HNO) formation needs to be includedin the mathematical model.

(4) A detailed energy balance also needs to be incorporatedin the model.

Table I summarizes the earlier work. Though the mathe-matical model of Suchak et al. considers all the above aspects,it was developed for a case of a four-stage absorption system.In the commercial process of nitric acid manufacture, a largenumber (exceeding 50) of absorption and oxidation stages areused. Under these conditions, there are several aspects whichneed to be considered for the reliable and optimal design. Theseare:

(1) For every mole of NOx absorber, 1/3 mol is desorbed inthe form of NO. Thus, the oxidation rates are linked with theabsorption/desorption rates.

(2) The rate of absorption of N02 as such is negligible.

June 1994 Vol. 4O,\No. 6 AIChE Journal

"".~::~:e::~... -

Dependence Role of Heter-of H.JkD ogeneous Formationon HNO] EquiI. on HNO] in

Cone. Abs. Rate Gas Phase

NC NC NCNC NC NCC NC NCC NC NCC C C

r

jif

Table 1. Summary of Previous Work

Mass Transferof H,O, HNO]and/or HN02from/to Gas

Phase from/toLiquid Phase

NCNCNCNCC

CC

NCNCC

Emig et aI. (1979)'-

Holma & Sohlo (1979)"Miller (1987)Wiegand et aI. (1990)"Suchak et aI. (1991)

CompleteEnergyBalance

'The mechanism of absorption with chemica] reaction needs to be included in the overaJl rate equation."The plate efficiency needs to be calculated for the case of NO, absorption.C = Considered

NC = Not considered

However, in the presence of NO, NO, forms N20) and HN02in the gas phase. The rate of N20] and HN02 absorption arevery high. Thus, the presence of sufficient NO enhances therate of absorption.

(3) The maximum permissible concentration of HNO) (1)decreases with an increase in mole fraction of NO. As theabsorption continues, the mole fraction of NO increases be-cause of the absorption of N204' N20), and HNO) (g). There-fore, the multistage operation is needed for getting the desiredconcentration of HNO) (1). Each stage consists of an absorp-tion section and an oxidation section. For instance, in the caseof a sieve plate column, the absorption occurs on the plateand the NO oxidation occurs in the empty space between thetwo plates. The plate spacing depends upon the extent of de-sired oxidation. The extent of absorption on a plate is also avariable.

(4) The effect of temperature is multi fold. The rate of NOoxidation decreases whereas the rate of absorption increaseswith an increase in temperature. The conversion of N02 toN204 is favorable at lower temperature. Further, for a givenNO, composition in the gas space, the maximum permissibleHNO) (1) concentration increases with a decrease in temper-ature.

(5) Total pressure is a very strong' parameter. The rate ofNO oxidation is proportional to the cube of pressure and therates of absorption also increase with an increase in total pres-sure.

Since all the above parameters strongly interact, detailedunderstanding is needed for the selection of optimum designand operating parameters.

Mathematical Model

In the commercial nitric acid plant, the mixture of ammoniawith air is passed over catalyst gauze at temperature and pres-sure in the range of 800-850°C and 0.3-2 MPa, respectively.The following is a major reaction:

4NH) (g) + 502 (g) - 4NO (g) + 6H~0 (g)

This is an exothermic oxidation reaction with a short resi-dence time. Heat liberated is advantageously removed in heatrecovery section to produ~e superheated steam, to preheat air,and in certain cases to preheat the tail gas. The gas streamleaving the heat recovery section is at a temperature above dew

AIChE Journal June 1994

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point (in a typical case 200°C) and is further cooled in a cooler/condenser before feeding it to an absorber.

The condensate is a weak nitric acid solution which is addedup at an appropriate location in the absorption column.

Model for the cooler/condenser

In the cooler, the gas stream is directly contacted to weakaqueous solution of nitric acid. Mainly two types of coolersare employed: (i) spray type, where an aqueous weak acidsolution is sprayed in the gas stream; (ii) bubble column typewhere the gas is bubbled through a pool of liquid. In bothtypes of coolers, the weak nitric acid solution is directly broughtin contact with the gas stream.

Condensers employed are generally large surface area heatexchangers. The hot gas from the heat recovery stream is passedover the cooler surface where part of water vapor condenses.

In cooler as well as condenser, during cooling, many chem-ical reactions and chemico-physical phenomena occur. Theyare: (i) oxidation of nitric oxide; (ii) formation of higher ni-trogen oxides; (iii) condensation of water and oxy acids; (iv)absorption of nitrogen oxides.

In the process design of a nitric acid plant, the design ofcooler/condenser is very important for obtaining the desiredconcentration of the product acid from the absorption section.Therefore, a mathematical model for the l:ooler/condenser ispresented below.

Gas-phase reactions and equilibria

The gas entering the mndenser mnsists of NO, gases, ni-trogen, oxygen, and water \'apor. Nitric oxide undergoes ir-reversible oxidation with oxygen in the gas phase.

The oxidation reaction is expressed as:

kl2NO (g) + O~ (g) -- 2NO, (g) (2)

(I)

Joshi et al. (1985) have reviewed the published literature onNO oxidation. It is believed that NO oxidation proceeds bydimerization of NO is followed by oxidati0!1 by oxygen toform N20J' The oxidation reaction is second-order with respectto NO and first-order with respect to oxygen.

The gas phase l:onsists of "10, NO" N,O" and N,OJ' In the

Vol. 40. 'Jo. 6 945

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Table 2a. Gas-Phase Reactions

A

Eqs.

I2345

(kN/m')-'.s-1(kN/m2)-1(kN/m')-1(kN/m')-1(kN/m2)-1

Equilibrium and Rate Constants

. log" k,=652.I/T-4.747loginK,= 2,993/ T - 11.232log,o K, = 2,072/T - 9.2397log" K,=2,051.17/T-8.7385log,o K, = 2,OO3.8iT - 10.763

presence of water vapor (which is generaIJy the case) oxyacids(HNO, and HNO) are also present in the gas phase. Complexequilibria prevail in the gas phase which can be described bythe following equations:

K,2NO, (g) ~ N,O. (g)

K)NO (g) + NO, (g) ~ N,O) (g)

K4NO (g) + NO, (g) + H,O (g) ~ 2HN02 (g)

Kj3N02 (g) + H,O (g) ~ 2HNO) (g) + NO (g)

The reaction rate constant k] and the gas-phase equilibriaconstants K2 . . . Kj were reported by Joshi et aI. (1985) andare presented in Table 2a.

The total number of moles in the gas per mole of inerts isobtained by adding ratios of all gaseous species to one moleof inerts:

Yr= YNO+ YNO, + YN,o, + YN,o, + YHNO,

+ YHNO,+ YH,o+ Yo, + 1.0 (7)

where,

Table 2b. Heats of Reaction

Reactions

Std. Heat ofReaction (25°C)

kcal x 10-)

Reactions in Gas Phase2NO(g)+02(g) - 2N02(g) ~H] = -13.64

"per kmol NO oxidized

2N02(g) - N20O(g] ~H) = - 13.69per kmol N20. formed~H.= -9.55perkmol N20) formed

3N02{J) + H20{J) - 2HNO)(J) + NO{J) ~H6 = - 4.23per kmol HNO) formed

NO{J) + N02(g) + H20(J) - 2HN02(g) ~H7 = - 4.905per kmol HN02 formed

Reactions in the Liquid Phaseper kmol N02 absorbed ~Hg= -12.82per kmol N20. absorbed ~H9= -12.04per kmo1 N20) absorbed ~H]o= -9.55per kmol HN02 absorbed ~HI3= +5.71per kmol HNO) absorbed ~H II= - 9.36per kmol HN02 absorbed ~H12 = - 9.9

NO{J] + N02(g] - N20)(g)

946

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--'-"""""'-

YN,o,= K,( YNO)2P1IY1 (8)

Y",o, = K'YNoYNo,PrIYT (9)

YHNO, = [K. YNOYNO: YH,oPrIYr)]/,

(10)

. - (Kj( YNO,»)YH,o pr

)]/,

}HNO, -

Y YNO r(II)

All the components of NOx can be expressed in terms of:(a) Total reactive nitrogen (YN"), mole of reactive nitrogen

per mole of inerts:

Y,," = YNO + YNO, + 2( YN,o,) + 2( YN,o,) + YHNO, + YHNO, (12)

(3).(b) while extent of oxidation at any instance is expressed in

the form of YNO' , moles of divalent nitrogen per mole of inerts:

(4) YNO" = YNO + YN,o) + 0.5 (YHNO) - 0.5 ( YHNO,) (13)

(5)

(c) YH,o' is moles of water in the form of oxyacids and freewater vapor per mole of inerts. It is expressed as:

YH,o' = YH,o + 0.5 (YHNO,) + 0.5 (YHNO,) (14)(6)

Condensation and liquid-phase reactions

In the cooler/condenser, due to reduction in temperature,water vapor from the gas phase condenses with simultaneousabsorption of nitrogen oxides thus further altering the equi-libria. Nitrogen oxides when absorbed in an aqueous acid so-lution form nitrous and nitric acid. The following reactionsoccur in the liquid phase:

2N02 (I) + H20 (I) + HNO) (I) + HN02 (I) (15)

N20) (I) + H20 (I) + 2HN02 (I) (16)

N20. (I) + H20 (I) + HN02 (I) + HNO) (I) (17)

HN02 in the bulk of liquid phase is considered to decomposeto form nitric acid:

3HN02 (I) + HNO) (I) + 2NO (I) + H20 (I) (18)

HNO) and H20 are at their saturation concentrations in thegas phase. Vapor pressure of H20 or HNO) over the aqueousnitric acid solution is a function of temperature and nitric acidconcentration:

PH,O =I( T, Conc(HNO)) (19)

PHNO,= I( T, Conc(HNOJ» (20)

Condensate concentration and heterogeneous equilibria

For a known composition of NOx in the gas phase the max-imum attainable concentration of nitric acid (in the liquidphase) is described by Carberry (1958):

June 1994 Vol. 40, No.6

\AIChE Journal

AIfl1

.

PNO~- (p )312N20.

(21)

Holma and Sohlo (1979) have given the following correlationfor the equilibrium constant:

log KH=30.086- 0.0693T - (0.197 - 3.27 x 10-4 T) W

-. + L227 10g[(100- W)/W2] (22a)

and for less than 5 percent by weight

log KH=31.96-0.0693T-(3.27x 10-4 T-0.4193)W (22b)

where

KH = Kf2K6 (101.3W (23)

and W is the maximum attainable HN03 concentration inweight percent. K6 is given by Eq. 21.

Material balance over condenser/cooler

Here we make the following rational assumptions:(1) All reacted nitrogen oxide entering the condenser is in

the form of nitric oxide.(2) Gases leaving the condenser are in equilibrium with con-

densate.(3) Gases leaving the condenser are saturated with nitric acid

and water vapor.Water enters the condenser in the form of water vapor.

Partly it condenses and partly it reacts to form nitric andnitrous acid in both liquid and gas phases. Equating the in-coming and outgoing streams of condenser for H20':

G( YH,o',,) = G( YH,o',C>+ Lc(1 + 0.5Xd

As stated in the assumption, NO, entering the condenser isin the form of nitric oxide while due to oxidation, gas-phaseequilibrium, condensation, and absorption in the condenser,it is present in both gas and liquid phases. The balance forreactive nitrogen gives:

G( YN',,) = G( YN',C> + Lc(XC>

Due to oxidation of nitric oxide to nitrogen dioxide, oxygenconcentration in the gas phase reduces. The material balancefor oxygen is given by:

G( Yo,,;) =G( Yo"C> + Lc(O.75XC>

+ G( YN',c- YNO',C>

The second term on righthand side needs some explanation.It has been assumed earlier that all the NO, entering the cooler /condenser is in the form of NO. This NO is converted to HNO,through several stages: (a) NO oxidation to NO: according toEq. 2; (b) conversion of NO and NO: to N~O" N:O~, andHNO~ according to Eq. 3, 4, and 5: (c) absorption of N02,N20h and HN02 to form HNO, and HN02; (d) decompositionof HNO~ and desorption of NO. The desorbed NO need to beoxidized again. Thus, the stoichiometric oxygen requirement


~';,,:j~Jif~"':t'liiL~,;

is greater than that indicated by Eq. 2. All the above stepsmay be combined to give the following equation:

2NO + 1.502 + H20 -- 2HN03

Thus, it can be seen that, for the formation of 1 mol ofHN03, 0.75 mol of oxygen is needed.

Method of solution

For the estimation of gas-phase composition and quantityof condensate (at specified temperature and concentration ofcondensate), we need to solve Eqs. 7-14 and 19-26. Usingsubstitutions in Eqs. 7, 19, 24, 25, and 26 a system of fivenonlinear algebraic equations having five unkd()wns namelyYr, YNO"Yo" Lc, and YH,owas formulated. Under most prac-tical conditions these five variables possess large positive value.The Newton-Raphson method in conjunction with the Gauss-Jordan method was employed. The objective behind reducingthese equations was to achieve single finite solution with min-imum numerical iterations.

(24)

Model for oxidizer

The gases leaving the condenser are in equilibrium with thecondensate concentration. In order to produce the productacid of desired concentration it is necessary to further oxidizethe nitric oxide. This is achieved by providing additional vol-ume between the condenser and the absorber. The extent ofoxidation required depends on many factors such as the desirednitric acid concentration, temperature, and pressure. The ox-idation volume is usually provided at the bottom of the ab-sorption column. Here essentially an increase in the molefraction of tetravalent oxides occurs. Temperature in this sec-tion is maintained in the range similar to the absorption tem-perature of the product acid. For modeling the oxidationsection, we make following assumptions: (1) gas-phase flowsin the plug, flow manner; (2) the oxidizer is operating at thesteady state; (3) gases follow ideal gas behavior.

(25)

Gas-phase reactions and equilibria

The gas-phase reactions and equilibria have been describedin the previous section. The set ::>fEqs. 7-16 is a mathematicalformulation for establishing composition of the gas phase.Suchak et al. (1991) have reduced these eight equations to fourequations expressed in YNO' Yr. YH,o, and YNO,.

For a known molar concentration of inerts, oxygen, totalNOn and NO' to N' ratio, equilibrium partial pressures inthe gas phase can be estimated.(26)

Model for the oxidizer section

Mass balance across a differential height dh at height h fromthe bottom is given as:

(a) Divalent nitrogen balance:

dY"o' S ,

;;;:;-= -c (kdpNO)"PO,cli) (27)

Vol. 40, ~o.() 947

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(b) Oxygen balance:

IdYo, S ,

dh '= - 2G(k, (PNO)"PO,tc)

Equations 27 and 28 are- nonlinear differential equations.The overall oxygen and NO. balance (across the oxidizer) isestablished on solving these equations.

Heat balance

Oxidation of NO, formation of N10),N204' HN01, andHNO) in the gas phase are exothermic. Because of these re-

actions significant heat changes Occur. The values of reactionrate constant and equilibrium constants depend upon temper-ature. Heat liberated because of various reactions in the gasphase has been included in Table 2b.

If QT is the total heat change per unit time in the differentialelement then the temperature change under adiabatic condi-tions is given by:

Te= (QT+mrCp71i)/m~Cp~

where Te and T, are the temperature at the exit and the inletof differential element.

(a) Contribution to the heat changes from the gas phase aredue to the following steps:.The rate of formation of N20) from NO and N02 in the

differential element is given by:

(N203)j= (N203)e - (N103)'

(N20J)j= G( YN,O,.e- YN,o,)

The rate of heat generation due to N20) formation is:

QI =«N20J)j)~H4 (32)

. The rate of formation of N204 from N02 in the differential

element is given by:

(N204)j= (N204)e- (N104)' (33)

(N204)j= G( YN,O..e- YN,O..i) (34)

The rate of i}.eatgeneration due to N204 formation is:

Q2 = «N204)j).1H3 (35)

. The rate of formation of HN03 in the differential elementis given by:

(HN03)j= (HN03). - (HN03); (36)

=G( YHNO,..- YHNO,) (37)

The rate of heat generation due to HN03 formation is:

Q3 =(HN03)p1~ (38)

JUDe 1994 Vol. 40, No.6 AIChE Journal948

.. ,:.<...,,~'f~#~

. The rate of formation of HN01 in the differential elementis given by:

(28)(HN02)r= (HN02)e - (HN02)i

= G ( Y HNO,.e - Y HNO,.,)

(39)

(40)

The rate of heat liberated due to HN01 formation is:

Q4 = (HN02)j.1H7 (41)

. The rate of heat generation due to the oxidation of NO

is estimated from the knowledge of the rate of NO oxidation.It may be noted that NO is consumed in the N103 and HN01formation and liberated during HNO) formation.

The mass balance for NO across the differential element isgiven by:

NOD= (NO,- NOe) - N203J- 1I2HN02J+ 1/2HNOJJ(42)

= G ( YNO.' - Y NO.e - Y N,O,.e + Y N,O).i- 1/2 Y HNO,.e

(29) + 1/2YHNo,.i+ 1I2YHNo).e-1I2YHNo,,;) (43)

The rate of heat generation due to NO oxidation is givenby:

Qs = (NO>o)~H, (44)

Total heat change in the differential volume is summationof all the heat changes:

(30)QT=Q, +Q2+Q)+Q4+QS (45)

(31)

Method of solution

Estimation of Gas-Phase Composition. Solution proce-dure described by Suchak et al. (1991) has been used.

Solution of Ordinary Differential Equations. The solutionof Eqs. 27 and 28 is a boundary value problem. The flow rateand composition of the gas phase entering the oxidizer areknown. The equations were solved simultaneously by thefourth-order Runge-Kutta method. Integration was carried outuntil the exit of the oxidizer.

Solution of Heat Balance Equations. From the above twosteps the concentrations of all species are known at the inletand exit of the differential height. Assuming all the heat isutilized as sensible heat, temperature of the gas at the exit ofthe differential height is estimated. For this purpose Eqs. 29-45 were used. The effect of step size for integration was ex-amined and it was selected in such a way that the oxidizervolume is independent of the step size.

Model for the absorption column

The absorption column employed for the manufacturingnitric acid is a plate or a packed column. The configurationis shown in Figure la. The cool gas stream (NO..)is introducedat the bottom of the column in the first empty section. NO inthe gas phase irreversibly oxidizes to form N02 affecting theequilibrium concentrations of all the other constituents of NO...In the case of a packed column, the empty section is followed

~'

i,~,'

t~

GAS OUT WATER IN

-----

-----"

-----

-----

PRODUCT liNO,

-----

COOLER/CONDENSER -----OXIDATIONSECTION

CONDENSATE

Figure 1a. NO. absorption system for the manufactureof nitric acid.

by a packed section, which is further followed by an emptysection and a packed section until desired removal of NOr isachieved. Usually one set of empty and packed sections arehoused in one column. In order to ensure complete wetting ofthe packings, a recirculation of loop is set up as shown inFigure Ib. A heat exchanger is provided in the external loopto remove the heat of reaction. In the case of plate columns,heat-transfer coils are placed in the peol of liquid over theplate. Two plates are separated by an empty section as shownin Figure Ic. A material balance is given by the followingequations.

(I) Reacted nitrogen balance over the entire column:

O( YN*,/- YN*,F) =L,,)(p (46)

where YN*,Fis mole ratio of reacted nitrogen to inerts at thecolumn outlet.

(2) Water and water vapor balance over the entire column:

O( YH,o*.,- YH,O*,F) =Lp(1 +Xp/2)-Fw (47)

YH,O*.Fis a molar ratio of saturated water vapor to inert gasat the outlet.

(3) Oxygen balance over the entire column:

O( Yo", - Yo,*,p) = a.75L,,)(p+ a.50( YN*.r- YNO*,p) (48)

For the explanation of first term on the righthand side, kindlyrefer to the text below Eq. 26.


OVERFLOWFROM IN.t)THSECTION

OVERFLOWTO (N-1ITH

SECTION

OVERFLOWTOIN-2)TH

SECTION

PACKEDSECTI ONIN th)

EM PTYSECTION(N th)

PACKEDSECTION(N -1) th

Figure 1b. One oxidation.absorption section in a packedcolumn.

Model for empty section/space between plates

Model for empty section or the space between two consec-utive plates is identical to that of an oxidizer already describedin detail in the section discussing the model for oxidizer.

~

N th PLATE

000 0COOLING SURFACE

IN-I) th PLAfE

Figure 1c. One oxidation-absorption section in a platecolumn.

949

c.

III

OXIDATIONSECTION

------

-- - - ---

~

Vol. 40. :'I/o. (J

I

Model for absorption stage and material balance overan absorption stage

The following equations establish material balance over anabsorption stage.

(1) Reacted nitrogen balance:

G( Y~ ',1'-1 - Yr-;',r-;)'=LNXr-; -Lr-;+,Xr-;+, -LsXs

For the stage where the condensate (from cooler/condenser)is introduced Ls=Lc and Xs = Xc, otherwise, Ls=O.

(2) Water and Water vapor balance:

G( YH,o',r-;-, - YH,O',N) =LN(1 +XNI2)-LN+,(1 + XI' +,12)

+ Ls(1 + Xsl2) (50)

Model for a packed section

A detailed model of the packed column has been presentedby Suchak et al. (1991). The same model was used in the presentwork where the correlation for KH values suggested by Holmaand Sohlo (1979) was used. A schematic representation of oneset of packed/empty sections is shown in Figure 1b.

Model for sieve plate

The liquid phase on a plate was assumed to be completelybackmixed. For mass-transfer coefficients, holdup, and gas-liquid interfacial area on a sieve plate, the following correla-tions suggested by Zuiderweg (1982) were used:Gas side mass-transfer coefficient:

kc =0.13/ Pc - 0.065/ pb (51)

Liquid side mass-transfer coefficient:

kL = 2.6 x 10- 5/'1Z.25 (52)

Gas-liquid interfacial area:

~=43/P')( VbPch?P/u)0.5)/H", (53)

€L =0.6HWp~25b-o.25 (FP)0.25 /Hw (54a)

where:

'" FP=L' /V'(PC/PL)0.5 (54b)

h'=€LH", (54c)

The absorption section model of Suchak et al. (1991) wasused with design parameters of sieve plate obtained from theequations given above.

Method of solution

Computations of absorptiol1column begins with the bottommost absorption stage. The gas-phasecomposition of the streamentering this absorption stage is known from the oxidizer cal-culations. Concentration and flow rate of product acid with-

950

.",.~~ -~

(49)

drawn are also considered to be known. From the detailedmodel of an absorption stage, concentrations of water vaporand reacted nitrogen in the exit stream is obtained. Concen-tration and the flow rate of liquid overflow from the subse-quent absorption stage are the two remaining unknowns. Forthis purpose Eqs. 49-50 were solved by substitUting Eq. 49 in50. These calculations were repeated for all the absorptionstages until the condition (Y~' < YN'.F) was satisfied. Heatbalance was also established for each differential volume ac-cording to the procedure described earlier. The differentialheight for integration was 0.01 m for packed column and 0.002m for plate column. There was no effect of step size belowthese values. Therefore, each differential volume can be con-sidered to be isothermal. As a result, energy and species equa-tions can be treated separately.

Results and Discussions

Simulation of a commercial plate column

Suchak et al. (1991) have shown a good agreement betweenmodel predictions and experimental observations for the caseof multiple packed columns in series. It was thought desirableto simulate a sieve plate column manufacturing 750 ton/d(100070basis) of nitric acid having 58.5% concentration. Thisstep was considered necessary before undertaking the opti-mization exercise. The design and operating parameters of thecolumn are summarized in Tables 3a and 3b, respectively. Theliquid submergence on each sieve plate was 50 mm. The drypressure drop was calculated using the procedure of Fair (1984).Comparison between the predicted and the experimental con-centration profiles of nitric acid are shown in Figure 2. It canbe seen that the agreement is very good. The predicted outletNOx concentration was 1,210 ppm whereas the concentrationin the commercially operating plants was 1,260 ppm. Thisagreement can be considered to be excellent.

Table 3a. Design Parameters of Commercial Plate ColumnProducing 750 tons/d Nitric Acid

Column diameter =5.5 mNumber of plates =73Plate spacing = 700 mmLiquid submergence =50 mmPercent free area = 3.6070Hole diameter = 4 mm

Table 3b. Operating Parameters of Commercial PlateColumn Producing 750 tons/d Nitric Acid'

(I) Total gas flow rate before the cooler-condenser

= 1.69 kmolls(2) Total NOx flow rate before the cooler-condenser

=0.1392 kmolls(3) Oxygen flow rate before the cooler-condenser

=0.1356 kmolls(4) Condensate temperature=48'C(5) Condensate concentration =42% (w/w)(6) Oxidizer volume=49.9 m)(7) Oxidizer temperature = 38' C(8) Inlet HNO) concentration = 00/0

(9) Outlet HNO) concentration = 58070 (w/w)(10) Total pressure at the inlet of column =0.46 MPa

'Capacity is on the basis of 100"1. concentration.

June 1994 Vol. 40, No.6\

AIChE Journal

II

U-"~~:'I",

'~"':/:;,:,~~'~f j;-~~-"~~~_~;0£;~d~ ",,'>

,)t:."',\,, '",'",. >,¥f". .,.f'~" ''i1,'~.?:.}f,;~s~~.:...\.

,J~,..;..

>- 50~

~ 40

v<t

~ 30a:...z... 70ozo;: 10«a:...zI.1JuZou

Figure 2.

60

D EXPERIMENTAL

- PREDICTED

78 65 57 494' 33 75 17

PLA TE N UMBER FROM BOTTOM

Simulation of a commercial nitric acid towerproducing 750 ton/d.For the design and operating parameters, refer to Table 3a.

Optimum design

(I) It has been pointed out earlier that heterogeneous equi-

librium prevails between the liquid phase and the gas phase.As a result of this, for a given NO, composition, there is amaximum permissible concentration of HNO) which can beproduced. The concentration of HNO) increases with an in-crease in the mole fraction of tetravalent nitrogen oxides inthe gas phase. Therefore, the gas phase entering the absorptioncolumn must possess sufficiently high mole fraction of tetra-valent nitrogen oxides so that the absorption can occur. Thiscondition of gas-phase composition is achieved in the oxidi~eras shown in Figure la. Obviously, the oxidizer volume increaseswith an increase in the desired concentration of nitric acid.

(2) The effect of oxidation temperature on the oxidizer vol-ume is shown in Figure 3. At any given nitric acid concentra-tion, the oxidation volume incr~ases with an increase intemperature. The extent of increase is very high in the tem-perature range of 30-450 C.

: 25...r~ 20r-~ I~

151

-' I8 10~

isI-

al5.

.0

35

TOTAL PRESSURE = 0..5 MPoCONOENSATE TEMPERATURE

= 50°CCONOENSATE CONCENTRATION. SO 'I, (WT)EXCESS OXYGEN. 30 'I,

30

!

SYMBOLI

iII

i 6.

OXIOATION iTEMPERATURE .0:

j

5 i1530.5

ooo

/

~58 60 62 6.CONCENTRATI?N OF PRODUCT NITRIC ACID,WT

'/,

Figure 3. Effect of oxidation temperature and productnitric acid concentration on oxidizer volume.


'4

12

OXIDATION TEMPERATURE =30.C

CONDENSATE TEMPERATURE" 50"cCONDENSATE CONCENTRATION" SO .1. (WT)EXCESS OXYGEN" 30 'I.

e10

SYMBOL TOTAL PRESSURE(MPo)

0..50.71,. 31

2'02

....

~ 8w:r

~ 6

"-JoU .

aooA

o5.

Figure 4.

6 58 60 62'" 64

CONCENTRATIONOF PRODUCTNITRIC ACID,WT'I.

Effect of total pressure and product nitric acidconcentration on oxidizer volume.

66

(3) The effect of pressure on oxidation volume is shown inFigure 4. The oxidation volume is nominal at 1.32 and 2.03MPa. The volume increases with a decrease in pressure. Theextent of increase is substantial when the pressure is reducedfrom 0.71 to 0.45 MPa.

(4) The effect of excess oxygen is shown in Figure 5. Whenthe percentage excess is in the range of 10-30010, the oxidationvolume decreases marginally. However, a further increase inthe excess oxygen results into an increase in the oxidationvolume. Such a behavior occurs because of two opposing fac-tors. With an increase in excess oxygen, the residence timedecreases due to an increase in the oxygen partial pressure.However excess oxygen is accompanied by an increase in theoxidation volume due to increase in volumetric flow rate. FromFigure 5 it can be seen that 30% excess is an optimum numberas far as the oxidizer volume (before the absorber) is concerned.

(5) Effects of condenser temperature and condensate con-

centrations are shown in Figures 6a and 6b. It can be seenfrom Figure 6a that the oxidation volume is negligible whenthe desired HNO) concentration is less than 60% and the con-densate temperature is greater than 60.C. However, at thehigh temperatures of 60° and 70°C, the oxidation volume

I

i66

161I TOTAL PRESSURE" 0.45 MPo

14~ OXIDATION TEMPERATURE" JOoCI CONDENSATE TEMPERATURE" 50°C

12~CONDENSATE CONCENTRATION" SO OJ. (WT)

E. : I PERCENT EXCESS i~ 10f- I

SYMBOLOXYGEN:

~ i j 0 10 !r at- I 0 20z ,~ i I 0 30

~6:I

A 40u

JI

2~

o54 56 sa 60 62 64

CONCENTRATIONOF PRODUCTNITRIC ACID, WT'I.

Figure 5. Effect of excess oxygen and product nitricacid concentration on oxidizer volume.

66

Vol. 40. :"io. 6 951

...""-'

99.9 99.66,0......100 PPIroA

100

",80

'""c

~60

0'0~..:r; 70

-1-0 -o.s

1+E II; 10r

~ 8~::t: I

I t4.

1 b

14

TOTAL PRESSURE = 0'" MPoOXIOATION TEMPERATURE = 30cCCONOENSATE CONCENTRATION = 50 '/, (WT )

EXCESS OXYGEN = 30 '/,

SYMBOL CONOE NSATETEMPERATURE ,cc

40

50

60

70

oo

<>

£:.

o51. 58 60 62 61.

CONCENTRATION OF PROOUCT NITRIC ACIO, WT '/,

Figure 6a. Effect of condensate temperature and prod.uct nitric acid concentration on oxidizer vol.ume.

6

TOTAL PRESSURE = 0'45 MPoOXIDATION TEMPERATURE = 1S'tCONDENSATE TEMPERATURE = 40"cEXCESS OXYGEN = 30 '/,

ECONDENSATE

CONCEN TRAT I ON

'10(WT )

30

40

50

SYMBOL

~ 4

'"'"::t: 3z~:>

-'o 2u

oo

<>

o54 56 58 60 62 64

CONCENTRATION OF PRODUCT NITRIC ACID, WT '10

Figure 6b. Effect of condensate concentration andproduct nitric acid concentration on oxi.dizer volume.

increases sharply when the desired HNO) concentration in-creases.

When the condensate temperature is less than 50'C, theoxidation volume smoothly increases with an increase in HNO)concentration. It may be noted, however, that all the linescross each other and there is a possibility of selecting an op-timum oxidation"volume by selecting proper condensate tem-perature.

From Figure 6b it can be seen that the oxidation volume. increases with an increase in the condensate concentration and

desired HNO) concentration.In order to get an overall view regarding the number of

stages needed with respect to the extent of absorption, theparameters such as pressure, temperature, and heights ofpacked and empty sections were varied over a wide range. Themodel results are given in Figures 7,8, and 9. The capacity ofabsorber was 750 ton/d and '30070 excess oxygen was used.Values of other parameters are listed in Table 4. From Figures7,8, and 9, it can be seen that the required number of stages

952

/,..~._."' ~.".::.t:~'~"-,!,,'7~",\. .:.

. ."

'.'., .'.'.' .'.';2~-:;-\'

PE:.~CE:.N~ REMOVAL

99.9 9 S.6E"

96.{; 66 -"

-20::'pp~

]50

1.~, ].0

PA.CKE.D HE.IGHT ~ 07 ~ m

-1]OOPP..,. TE.MPERA1WH.-

JO~C

~ 200

'"4

~ 150

PUo/AMETEr< ~ E.MPTY HEIGHT

:0~ 100CD:ri 50

0.,:,/0.7,

.I 1,.5

1.0-1,0 -0., 0,0 05

LOG (100- -I. REMOVAL)

66 Figure 7. Effect of extent of absorption on the numberof stages with pressure and height of emptysection as parameters.

66

increases rapidly with an increase in the extent of absorption.In order to emphasize this point, the extent of conversion isshown on the top axis. Also shown are the two lines when theNO,. composition in the gas phase becomes 1,200 and 200 ppm.

The effect of total pressure and the height of empty sectionon the number of stages is shown in Figures lOa to IOc forpacked heights of 0.25, 1.0, and 3.0 m, respectively. In all thecases, the number of stages decreases with an increase in pres-sure. The decrease is dramatic in the pressure range of 0.4 to0.71 MPa. This is because the rate of oxidation varies as thecube of the pressure. However, a similar reduction is not ob-served when the pressure is increased from 0.71 to 1.31 MPaand further to 2.02 MPa. This is because the overall absorptionbecomes increasingly controlled by equilibria and the rate ofoxidation is not important. This is a useful result. The oxi-dation volume is needed for getting sufficient tetravalent oxidesso that the positive driving force prevails in the subsequentsection. Such a desired composition is achieved in a smalloxidation volume. In fact, at high pressures the number ofstages were found to be independent of the oxidation volume(in the range covered).

From Figures lOa to IOc it can be seen that, at total pressureof 0.4 and 0.71 MPa, the number of stages decreases with anincrease in the oxidation volume. Though, the number of stages

PER CENT REMOVAL

99.0 96-6 68-'9C

--1100 PPM PRE.SSURE. ~ 0 7,",PA.

PA.CKED I-I£,I(,"'T : 0 lS m

100

80

60

/30'C

5 'c'0

()oS

LOG(

100--I. AE.MOVAL)

,-, ].0,.00,0

Figure 8. Effect of extent of absorption on the numberof stages with temperature and height ofempty space as parameter.

June 1994 Vol. 40, No.6 AIChE Journal

j;~'~f~;-i.'\~'~~"",'.,-

":'.","..

:,:~:';.c'

. .-~.,.. ",-.,.Jo.. ...,. ..

,;-~

99.9

150

PEA CEN T RE.MOVAL

99.0 96'8 G8..t.9g.6a 90.0

o

~ 100.,~:JZ

1200 PPM PRE.SSURE.:0"

MPo

TEWPERATURE-= 30.C

PAAAt,4E.TER= EMPty HE.IGHT100

'"w

'"ctn 150

50

Hp= 1 m

a-100 0.5 ',0-0.5 0.0

LOG(

100- '1. REMOVAL.)

Figure 9. Effect of extent of absorption on the numberof stages with the height of packed and emptysections as parameters.

decreases, it does not necessarily mean that the total heightdecreases. In fact, in almost all the cases, the total height wasfound to increase with an increase in the height of empty section(Table 5a). The increase is nominal when the empty height isincreased from 0.4 to 0.7 m. This result is useful because thecost associated with a large number of stages can be reduced.However, a similar result is not obtained when the empty heightis increased to 4 m and 10 m. The total height substantiallyincreases at these empty heights. From these results it can beseen that there is an optimum level of NO oxidation per stage.A very high level of conversion needs more oxidation volumeand it is not useful since some NO is liberated in the subsequentabsorption section. An empty height of 0.7 m looks favorable.

The effect of packed height is shown in Figure!! and Table5b. It can be seen that the effect of packed height is not asdramatic as the empty height. The optimum packed height liesin the range of 0.25 to 0.5 m. The effect of temperature onthe number of stages and total height is shown in Figure J2and in Table 5c. In this case also the optimum empty heightcan be considered as 0.7 m and the optimum packed height isin the range of 0.25 to 0.5 m.

Though the total height is substantially low at lower tem-peratures, it may not be economically' advantageous to operatethe absorption column at low temperatures due to high re-frigeration costs. However, the liquid ammonia feedstock pro-

Table 4. Values of Parameters

Values of Parameters for Figures 3 to /2Capacity = 750 ton/dTotal gas-flow rate before cooler condenserTotal NO, flow rate before cooler condenserOxygen flow rate before cooler condenserSuperficial liquid velocityColumn diameterPackingPacking sizePacking voidage

= 1.69 kmolls=0.1352 kmol/s

= 0.1356 kmol/s

= 5 mm/s=5.5 m= Intalox saddles

= 37 mm=0.77

Additional Parameters for Figures 7 to 12Condensate temperature = 50°CCondensate concentration = 50070(WI.)Concentration of product nitric acid = 58070(wI.)

Additional Parameter for Figures 10 to 12I Outlet NO, = 700 ppm


180

160

"0

1.0

110v>UJ

'"~100v>u.080a:UJID:r:::J60z

TEMPERATUqE,:; 30.(

PACKED HEIGHT:; 0.25m

SYMBOLHEIGHT OF EMPTY

SECTION, m

0.,0.7,.5

'0

10

80

70

60

v>UJ

'""

50V,u.o '0a:UJID:r 30:::JZ

10

10

36

30

"'UJ

'""~ 20u.o

a:UJID:r:::JZ

,0

oooto.

,.010.0

..

8 10 12 11. 16 18PRESSURE. P, X 10'1 IkN/ml)

(a)

10 11

TEMPERATURE:; JO°C?ACKED HEIGHT:: 1.0 m

SYMBO LHEIGHT OF

EM PTY SEC T ION, m

O.,J.7

.oo '-5"<7to

4.010.0

10 121'-

15~PESSURE, ?T X 10' : kN/m"

)10'8 II

(b)

TEMPERATURE:: ]O"C

PACKED HEIGHT:: ].Om

SYMBOLHEIGHT OF

EMPTy SECTION. ,11

J.4

J.71--0-

I---6-,---"7--

, .5,

'0-<>-----0- ,0.0

10 11

°RESSUREl' 16 18

Pr x 10-' (kN/m"II10

(C),

Figure 10. Effect of total pressure and the height ofempty section on number of stages.Packed height: A = 0.25 m; B = 1.0 m: C = 3.0 m.

953Vol. 40, No.6

Table 5a. Total Column Height"

Height of Total Column Height, mEmpty Packed

Pressure, MPaSection Height

HE' m Hp, m 0.4 0.71 1.31 2.02

0.4 0.25 105.95 29.90 13.65 10.400.7 0.25 112.10 37.05 19.00 14.251.5 0.25 138.25 56.00 33.25 26.254.0 0.25 225.25 119.00 72.25 63.75

10.0 0.25 430.25 266.50 184.50 143.50

0.4 1.00 103.60 26.60 11.20 7.000.7 1.00 103.60 28.90 13.60 8.501.5 1.00 107.50 35.00 17.50 12.504.0 1.00 135.00 55.00 35.00 25.00

10.0 1.00 198.00 110.00 66.00 55.00

0.4 3.00 112.20 30.60 13.60 10.200.7 3.00 I I 1.00 29.60 14.80 11.101.5 3.00 112.50 36.00 18.00 13.504.0 3.00 119.00 49.00 28.00 21.00

10.0 3.00 156.00 78.00 52.00 39.00

'Parameters are listed in Table 4; temperature = 3D'C.

Table 5b. Total Column Height"

Height of Total Column Height, mEmpty Packed Pressure, MPaSection HeightHE>m Hp, m 0.4 0.71 1.31 2.02

0.7 0.10 128.00 62.40 38.40 30.400.7 0.25 90.25 36.10 13.65 16.150.7 0.50 79.20 27.60 14.40 10.800.7 1.00 76.20 25.50 11.90 10.200.7 3.00 81.40 25.90 14.80 1l.l0

'Parameters are listed in Table 4; temperatUre= 15'C.

Table 5c. Total Column Height"

Height of Total Column Height, mEmpty Packed

Temperature, .CSection HeightHE, m Hp, m 5 15 30 40

0.4 0.25 72.15 79.95 105.95 131.950.7 0.25 84.55 90.25 112.10 140.601.5 0.25 120.75 120.75 138.25 168.000.7 0.10 130.40 128.00 144.80 172.800.7 0.50 72.00 79.20 103.20 133.200.7 .. 1.00 68.00 76.50 103.70 134.30

"Parameters are listed in Table 4; pressure = 0.4 MPa.

vides for some refrigeration load. The rate of heat removaldue to vaporization of liquid ammonia can be used advanta-geously in the top section where the rate of oxidation is verylow. Most of the heat is usually removed by the am bient water.Hence, the operating temperature is decided by the ambienttemperature. Some refrigeration may, however, be used afterestablishing a clear economic advantage.

From Figures lOa to lOe and Table Sa it can be seen thatthe total height substantially decreases with an increase in thetotal pressure. The equipment cost will decrease with an in-

954

'bO TEMPERATURE=

ISO(

IoiEIGHTOF EMPTY SECTION "O.7m

ILOSYMBOL PAC KED

HEIGHT, m

0.10

0.75

0.50

\-00).00

VI 110OJ

'""~ 100

--0---0---<>----0--u.

o

~ 60

'":>::0Z 60

LO

10

8 10 11 IL'b

PRESSURE. PT X '01 I k N Iml)1018 12

Figure 11. Effect of total pressure and the packed heighton number of stages.

crease in pressure. This is because the reduction in volume andan increase in wall thickness with pressure results into an overalldecrease in the metal requirement. However, this should betraded off with operating expenses for compression (after giv-ing due credit to the energy recovery in the turbine).

From the foregoing discussion it can be seen that the op-timum heights for empty section and packed section can beselected directly. However, the optimum temperature and pres-sure depend upon the geographical location and the cost ofpower.

The results on packed columns are presented in Figures 7to 12 and Table 5 and are for the design and operating pa-rameters listed in Table 4. For a plate column (% free area,hole diameter, and column diameter are given in Table 3a), asimilar exercise resulted into the following correlations:

PRESSURE:. 0.10 MPo

PACKED HIGHT=-

0.15 m

SVM BOl HEIGHT OF EMPTY SECTION1m)

HO co

'"(I

.X PH.;:1.0

O.L0.7

1.5VI 110OJ

'""~ 130u.o0: ISOOJ

'"%~ 120

PH: 0.,

PH:. Q.5l1f'ight 01

f'rnpty

5f't hon: 0 7m

90 ~~60

~30

10 10 30TEMPERATURE,.C

LO

Figure 12. Effect of temperature and the height of emptysection and the packed height on the numberof stages.

June 1994 Vo\. 40, No.6 AIChE Journal

:_~~":{:;~""-'-~~"':;'.'-'..:.~*~;;:~',-~~,~\-:~~-:?<.._:-

- "

. ,,:~-~',~

. :;u~~:f~~~~-'~~;;~r~'~:,;l~,:j

~;~r!",:'.~!'.'V;-~~)~":-:,' -~

"

-

"

--~;;"~'.":",".:'1>;'

::~,;','--~','.".,':.',- """.0,-'-.." -- :"\'.""'~-;,':~:,-'~.

"'"

{!:::_~-:-:~;'-~'i;.:~;:t!i~

~:i~J:;2aI,:;.~>-

.,

'¥'f:"<,

1

;1

O.2<HE< 1.5 m

N =482. 74Hio.4J4Hwo.l44exp( - 1,221.6/ PT)

x exp( - 1,563.1/1) (55a)

1.5 <HE< 10 m

N =28.0IHio.I77Hwo'9gexp(658.8/ PT)exp( - 555.7/1) (55b)

where

O.4<HE< 10 m, 0.025<Hw<0.1 m,

0.4<PT<2.02 MPa and 278< T<318 K

Conclusions

(1) A mathematical model has been developed for the pre-

diction of optimum design of packed and plate columns. Theeffects of inlet NOx composition, temperature, pressure, vol-ume of pre-oxidizer, volume of interstage oxidizers, and extentof absorption per stage have been included in the model.

(2) The concentration of product nitric acid strongly dependsupon the inlet NO, composition, temperature, pressure, andexcess oxygen. For a given concentration of product nitric acid,the optimum design of preoxidizer has been presented.

(3) The extent of oxidation per stage strongly influences thenumber of stages. The overall equipment volume was foundto increase with an increase in the extent of oxidation. How-ever, the number of stages increases with a decrease in theextent of oxidation.

(4) The optimum design depends nominally on the extent ofabsorption per stage.

(5) Correlations have been developed for the number ofstages for plate and packed absorption columns.

Notationa = interfacialarea, m2/m3b weir length per unit bubbling area, m - I

~ = average specific heat of liquid phase, kcal/kmol'.K'D = diffusivity, m2/sF = fraction of hole area per unit bubbling area

FP = flow parameter, L'IV' ~PGlPL

F", = feed water, kmol/sG = flow rate of inerts, kmol/sh = height from bottom of the spray column, mhi = volume of liquid per unit plate area, m2/m3H = total height of the column, m

He = Henry's low coefficient, kmol/m2 (kN/m2)HE = height of empty section, mHp = height of packed section, mH", = weir height, m

k = reaction rate constant, s -,

k, = forward reaction rate constant for Eq. Ikc = gas-side mass-transfer coefficient, kmol/[m2. s(kN/m2)]k, = liquid-side mass-transfer coefficient, m/sk. = forward reaction rate constant for reaction nK, = heterogeneous equilibrium constant defined by Eqs. 21

and 23, (kN/m2)-05KH = heterogeneous equilibrium constant, Eqs. 22a and 22b,

atm .2

K. = equilibrium rate constant for reaction nL = molar flow rate of liquid, kmol/s


L' = mass-flow rate of liquid, kglsLp = flow rate of water in the product acid, kmollsmO

= mass-flow rate of liquid, kmollsN' = total moles of NO.

NO' = total moles of divalent nitrogen oxidesPH = pitch of holes, mPn = partial pressure of component n, kN/m2PT = total pressure of gas, kN/m2Q, = heat changes due to formation of N20J in bulk gas,

kcallsQ2 = heat changes due to formation of N204 in bulk gas,

kcallsQJ = heat changes due to formation of HNO) in bulk gas,

kcal/sQ4 = heat changes due to formation of HN02 in bulk gas,

kcal/ sQ5 = heat changes due to formation of NO in bulk gas,

~~/s ~QT = total heat changes, kcal/s

S cross-sectional area of the column, m2T = temperature, K

V' = mass-flow rate of gas, kg/sVG = superficial gas velocity, m/sW = weight fraction of HNOJ in aqueous nitric acid solutionX = moles of nitric acid per mole of water

YH,o' = kmol of water in form of oxyacids and free water in gasphase per kmol of inerts

Y~' = kmol of reactive nitrogen per kmol of inertsY~..F = moles of reaction nitrogen per mole of inerts in the gas

stream leaving absorberY~.., = moles of reacted nitrogen per mole of inerts in the gas

stream from NHJ oxidizerY~o. = kmol of divalent nitrogen per kmol of inerts

Y~O..F = moles of divalent nitrogen oxides per mole of inerts in thegas stream leaving absorbermoles of oxygen per mole of inerts

moles of oxygen per mole of inerts in the gas stream leavingabsorber

Yo, .., = moles of oxygen per mole of inerts in the gas stream fromNH J oxidizer

YT = total moles of gas per mole of inertsY, = moles of gaseous component x per mole of inerts

v . -10, -YO,.F =

Greek letters

.lH, = heat of reaction for reaction given by Eq. xEC = fractional gas holdupE, = fractional liquid holdup'�L = kinematic viscosity of liquid, m2/sP = density, kg/m!(]

= surface tension, N/m

Subscripts

a =C =e =f=F =G =

absorptioncondensateexit conditionformationoutletgas phaseinlet conditionliquid phasenth stageside stream from condenser to columntotal

i =L =N =S =T =

Literature CitedAndrew, S. P. S., and D. Hanson. "The Dynamics of Nitrous Gas

Absorption," Chem. Eng. Sci.. 14, 105 (1961).Carberry, J., "Some Remarks on Chemical Equilibrium and Kinetics

in the Nitrogen Dioxide-Water System." Chern. Eng. Sci.. 9, 189(1958).

Vol. 40, No.6

".;iA.'.y ,.."<~~~~":""",,,,,..

955

"",'~..:'~ ~,""",,--,-'~rt.. ~~~

Carleton, A, J., and F. H. Valentin, Proc. Eur. Symp. Chem. ReactionEng., Pergamon, Oxford, p. 361 (1968).

Counce, R. M.. and J. J. Perona, "Gaseous Nitrogen Oxide Ab-sorption in a Sieve Plate Column," Ind. Eng. Chern. Fund., 18,400 (l979b).

Counce, R. M., and J. J. Perona, "A Mathematical Model for Ni-trogen Oxide Absorption in a Sieve Plate Column," Ind. Eng. Chem.Proc. Des. Dev., 19,426 (1980).

Counce, R. M., and J. J. Perona, "Scrubbing of Gaseous NitrogenOxides in Packed Towers," AIChE J., 29, 26 (1983).

Emig, G., K. Wohlfahrt, and U. Hoffmann, "Absorption with Si-multaneous Complex Reactions in Both Phases, Demonstrated bythe Modeling and Calculation of Counter-Current Flow Columnsfor the Production of Nitric Acid," Comput. Chem. Eng., 3, 143(1979).

Fair, J. R., "Gas-Liquid Contacting" in Chemical Engineers' Hand-book, R. H. Perry and C. H. Chilton, eds., McGraw Hill Koga-kusha, Tokyo (1984).

Holma, H., and J. Schlo, "A Mathematical Model for an AbsorptionTower of Nitrogen Oxides in Nitric, Acid Production," Comput.Chern. Eng., 3, 135 (1979).

Hoftizer, P. J., and F. J. G. Kwanten, "Absorption of Nitrous Gases,"

.".,..-::,:.;.~[",,~::,;,::~.

. -

G. Nonhabel, Gas Purification Processes for Air Pollution Control,Butterworths, London (1972).

Joshi, J. B., V. V. Mahajani, and V. A. Juvekar, "Absorption ofNO, Gases," Chem. Eng. Commun., 33, I (1985).

Koukolik, M., and J. Marek, Proc. 4th Eur. Symp. Chem. React.Eng., Pergamon, Oxford, p. 347 (1968).

Koval, E. J., and M. S. Peters, "Reaction of Aqueous Nitrogen Diox-ide," Ind. Eng. Chem., 52, 1011 (1960).

Makhotkin, A. F., and A. M. Shamsutdinov, Khim. Khim. Tekhnol.,19(9), 1411 (1976).

Miller, D. N., "Mass Transfer in Nitric Acid Absorption," AIChEJ., 33, 1351 (1987).

Sherwood, T. K., R. L. Pigford, and C. R. Wilke, Mass Transfer,McGraw-Hill, New York (1975).

Suchak, N. J., K. R. Jethani, and J. B. Joshi, "Computer AidedDesign of NO, Gases in Water, Nitric Acid and Mixed Solution ofNitric and Sulphuric Acids," AIChE J., 36, 323 (1991).

Wiegand,K. H., E. Scheibler, and M. Thiemann, "Computations forPlate Columns for NOx Absorption by a Stage to Stage Method,"Chern. Eng. Technol., 13,289 (1990).

Zuiderweg, F. J., "Sieve Trays," Chem. Eng. Sci., 37,1441 (1982).

Errata

. In the article titled "Memory-Integral Mass-Transfer Models for Adsorption Process Simulation" (March1993, p. 422) by G. M. Harriott, the following corrections are made:.On p. 425, fifth full paragraph, the last sentence should read: "Galer kin projection forces the error to beorthogonal to the basis function. . .".On p. 426, Table 2, the solution for Galerkin Projection: Linear Basis should contain a term of 7r/3, not 7r/6

as reported..On p. 428, the coefficients Ia, b} in the formulae for harmonic forcing (Eq. 28) should be multiplied by 2. Thephase lag is ct>= tan -I (bla), and the asymptotic form of the amplitude A at large frequency CJ)is: A -3/~..On p. 432, sentences 6 and 7 of the first paragraph should read: "On desorption, however, the pellet does not

unload until concentration drops below II H, and since the driving force for diffusion is then 0(1/ H), a time ofO(H) is required to clean out the pellet. The ratio of timescales for desorption to adsorption is simply the isothermslope at low concentration: H.".The title of the article by Glueckauf (1955) is "Theory of Chromatography: 10. Formulae for Diffusion IntoSpheres and Their Application to Chromatography."

. Correct affiliations of the authors of the article titled' 'Two Methods of Selecting Smoothing Splines Appliedto Fermentation Process Data," (April 1994, p. 716) are as follows: .

.. Nina F. ThornhillDept. of Electronic and Electrical Engineering

Mauro Manela and John A. CampbellDept. of Computer Science

Karl M. StoneAdvanced Centre for Biochemical Engineering,

University College London, Gower Street, London WClE 6BT

956 June 1994 Vol~ 40, No.6 AICbE Journal

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