L 39: Fluid- Fluid Reactions Fluid- Fluid Reactions (Non catalytic)(Non catalytic)

Prof. K.K.PantDepartment of Chemical Engineering

IIT Delhi. kkpant@chemical.iitd.ac.in

Setting up the rate equation for straight mass transfer basedon the two film theory.

The Rate Equation for Straight Mass Transfer (Absorption) of AHere two resistances in series, of the gas film and of the liquid film. The rate of transfer of A from gas to liquid is given by the rate expressions, for the gas film

In the liquid film

Combining the two eqns and using Henrys’ law PAi= H CAi

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All sorts of special forms of the rate equation can result depending on the relative values of the rate constants k, kg, and k,, the concentration ratio of reactants pA /CB, and Henry's law constant HA. There are eight cases to consider, going from the extreme of infinitely fast reaction rate (mass transfer control) to the other extreme of very slow reaction rate (no mass transfer resistance need be considered)

Case A: Instantaneous reaction with low CB,Case B: Instantaneous reaction with high CBCase C: Fast reaction in liquid film, with low CBCase D: Fast reaction in liquid film, with high C,

Case E and F: Intermediate rate with reaction in the film and in the main body of the liquidCase G: Slow reaction in main body but with film resistanceCase W: Slow reaction, no mass transfer resistance

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Figure : Concentration of reactants as visualized by the two-film theory for an infinitely fast irreversible reactions of any order, A + bB products. Case A-low CB, Case B high CB,

General rate expression

The absorption of A from gas is larger when reaction occurs within the liquid film than for straight mass transfer. Thus for the same concentrations at the two boundaries of the liquid film we have

E >1

Instantaneous Reaction with Respect to Mass Transfer. : Since an element of liquid can contain either A or B, but not both, reaction will occur at a plane between A-containing and B-containing liquid. Also, since reactants must diffuse to this reaction plane the rate of diffusion of A and B will determine the rate, so that a change in p, or C, will move the plane one way or the other

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kAg, and kAl ,: mass transfer coefficients in gas and liquid phases. The liquid side coefficients are for straight mass transfer without chemical reaction and are therefore based on flow through the whole film of thickness x0.

In addition, since the movement of material within the film is visualized to occur by diffusion alone, the transfer coefficients for A and B are related by

General rate expression

The absorption of A from gas is larger when reaction occurs within the liquid film than for straight mass transfer. Thus for the same concentrations at the two boundaries of the liquid film we have

E >1

Can be correlated with HATTA MODULUS/ NUMBER (MH)

M H, stands for the Hatta modulus,

M2H= (k CA CB x0 )/ kAl CAi

MH >1 ALL REACTION IN FILM and surface area is controlling factor. MH >2 , REAXN IN FILM, INSTANTANEOUS Reaction (BUBBLE COLUMN)

MH < 1 No Reaction in Film, and bulk liquid volume is controlling

MH < 0.02 INFINITELY SLOW REACTION ( BUBBLE COLUMN )

The enhancement factor for fluid-fluid reactions as a function of MH and Ei

modified from the numerical solution of van Krevelens and Hoftijzer

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Role of the Hatta Number, MH

To identify whether reaction is fast or slow, we focus on unit surface of gas-liquid interface, assume that gas-phase resistance is negligible, and we define a film conversion parameter

If MH >>1, all reaction occurs in the film, and surface area is the controlling ratefactor. On the other hand, if MH <<1 no reaction occurs in the film, and bulk volume becomes the controlling rate factor. More precisely, it has been foundthat:

From Fig. 23.4, for MH >1000

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1. If MH > 2, reaction occurs in the film and we have Cases A, B, C, D.2. If 0.02 < MH < 2, we then have the intermediate Cases E, F, G.3. If MH < 0.02, we have the infinitely slow reaction of Case H.

To find the rate from the general expression, we need to first evaluateEi and MH. :

(a) locate the resistance to reaction (what % is in the gas film, in the liquidfilm, in the main body of liquid)(b) locate the reaction zone(c) determine the behavior in the liquid film (whether pseudo first-order reaction,instantaneous, physical transport, etc.)(d) calculate the rate of reaction (mol/m3 hr)

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Eliminating the unmeasured intermediates x, x0, pAi, CAi,

For the special case of negligible gas-phase resistance, for example, if you usedpure reactant A in the gas phase, then

= KAl CAi E , E = x0/x

Case C: Fast Reaction; Low CW The plane of reaction for case A now spreadsinto a zone of reaction in which A and B are both present. However, reaction is fast enough so that this reaction zone remains totally within the liquid film.Thus, no A enters the main body of liquid to react there.Since the last resistance term in the general rate equation, Eq. 5, (I/kfl )is negligible (large k), the rate form for this case is

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Case G: Slow Reaction with Respect to Mass Transfer. all reaction occurs in the main body of the liquid; however, the film still provides a resistance to the transfer of A into the main body of liquid. Thus, three resistances enter into the rate expression, Thus

Case H: Infinitely Slow Reaction.

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Slow reactions Case G still shows film resistance. Case H shows no film resistance.

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Factors to Consider in Selecting a Contactor(a)Contacting pattern.

•Towers approximate plug G plug L.

•Bubble tanks approximate plug G / mixed L.

•Agitated tanks approximate mixed G / mixed L.

•Towers have the largest mass transfer driving force and in this respect have

an advantage over tanks.

• Agitated tanks have the smallest driving force.

(b) kg and kL. For liquid droplets in gas kg is high, kL, is low.

For gas bubbles rising in liquid, kg is low, kL is high.

(c) If the resistance is in the gas and or liquid films : Use a large

interfacial

area "a," thus most agitated contactors and most columns. If the L film

dominates, stay away from spray contactors. If the G film dominates stay

away from bubble contactors.

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d) If the resistance is in the main body of the L you want

large fl = Vl/Vr. Stay away from towers. Use tank contactors.

(e) Solubility. For very soluble gases, those with a small

value of Henry's law constant H (ammonia, for example), gas

film controls, thus avoid bubble contactors.

For gases of low solubility in the liquid, thus high H value (O2,

N2, as examples) liquid film controls, so avoid spray towers.

(f) Reaction lowers the resistance of the liquid film, so

For absorption of highly soluble gases, chemical reaction is not

helpful. For absorption of slightly soluble gases, chemical

reaction is helpful and does speed up the rate.

Fluid Solid non catalytic Reactions