Chemical Absorption: Fluid-Fluid Reactions and Liquid Phase Behavior

Fluid-Fluid Reactions

Franco GrisafiFluid-Fluid Reactions O. Levenspiel,"Chemical Reaction Engineering", 3rd ed., Wiley 1999 Heterogeneous fluid-fluid reactions are made to take place for one of three reasons.

A) First, the product of the reaction may be a desired material. Such reactions are numerous and can be found in practically all areas of the chemical industry where organic syntheses are employed. An example of liquid-liquid reactions is the nitration of organics with a mixture of nitric and sulfuric acids to form materials such as nitro-glycerine. The chlorination of liquid benzene and other hydrocarbons with gaseous chlorine is an example of a gas-liquid reaction.Fluid-Fluid Reactions: Kinetics

B) Fluid-fluid reactions may also be made to take place to facilitate the removal of an unwanted component from a fluid. Thus, the absorption of a solute gas by water may be accelerated by adding a suitable material to the water which will react with the solute being absorbed. Table 23.1 shows the reagents used for various solute gases.

C) The third reason for using fluid-fluid systems is to obtain a vastly improved product distribution for homogeneous multiple reactions than is possible by using the single phase alone. Let us turn to the first two reasons, both of which concern the reaction of materials originally present in different phases.

Factors Determining Process Approach

The Overall Rate Expression. Since materials in the two separate phases must contact each other before reaction can occur, both the mass transfer and the chemical rates will enter the overall rate expression.

Equilibrium Solubility. The solubility of the reacting components will limit their movement from phase to phase. This factor will certainly influence the form of the rate equation since it will determine whether the reaction takes place in one or both phases.

The Contacting Scheme. In gas-liquid systems semibatch and countercurrent contacting schemes predominate. In liquid-liquid systems mixed flow (mixer-settlers) and batch contacting are used in addition to counter and concurrent contacting.

Many possible permutations of rate, equilibrium, and contacting pattern can be imagined; however, only some of these are important in the sense that they are widely used on the technical scale.Factors determining how to approach this process

The Overall Rate Expression. Since materials in the two separate phases must contact each other before reaction can occur, both the mass transfer and the chemical rates will enter the overall rate expression.

Equilibrium Solubility. The solubility of the reacting components will limit their movement from phase to phase. This factor will certainly influence the form of the rate equation since it will determine whether the reaction takes place in one or both phases.

The Contacting Scheme. In gas-liquid systems semibatch and countercurrent contacting schemes predominate. In liquid-liquid systems mixed flow (mixer-settlers) and batch contacting are used in addition to counter and concurrent contacting.

Many possible permutations of rate, equilibrium, and contacting pattern can be imagined; however, only some of these are important in the sense that they are widely used on the technical scale.

Example of Fluid-Fluid Reaction Systems

Solute Gas Reagent

CO2 Carbonates

CO2 Hydroxides

CO2 Ethanolamines

CO Cuprous amine complexes

CO Cuprous ammonium chloride

SO2 Ca(OH)2

SO2 Ozone-H2O

SO2 HCrO4

SO2 KOH

Cl2 H2O

Cl2 FeCl2

H2S Ethanolamines

H2S Fe(OH)3

SO3 H2SO4

C2H4 KOH

C2H4 Trialkyl phosphates

Olefins

NO Cuprous ammonium complexes

FeSO4

NO Ca(OH)2

NO H2SO4

NO2 H2O ª Adapted from Teller (1960).

The Rate Equation for G/L Reactions

For convenience in notation let use talk of G/L reactions, even though what we say holds equally for L/L reactions. Further, let us assume that gaseous A is soluble in the liquid, but that B does not enter the gas. Thus, A must enter and move into the liquid phase before it can react, and reaction occurs in this phase alone.

Now the overall rate expression for the reaction will have to account for the mass transfer resistance (to bring reactants together) and the resistance of the chemical reactions step. Since the relative magnitude of these resistances can vary greatly, we have a whole spectrum of possibilities to consider.

Our analysis considers the following second-order reaction: A(g-l) + bB(I) - R(s or lor g), -TA= KCACB (Eq.1) present in gas, but soluble in liquid with solubility given by PAi = HACAi present in liquid and unable to enter the gas phase reaction occurs in liquid only, maybe close to the interface (in the liquid film), maybe in the main body of liquid

The Rate Equation: Contactor Notation

For notation consider a unit volume of contactor V, with its gas, liquid, and solid:

G . L in contact in this volume S = gas-liquid interfacial area 1 fi = Vi V' S fg=VB, E = fit fg, r a1 = ~ S V, r Vr = volume of contactor Vi = volume of liquid Solid may be present

The Rate Equation: Different Expressions

The rate of reaction is usefully written in a number of ways, as follows (NA=kmoles of A):

-" = - „ !!! 1 dNA V, dt A

-r" = - S dt 1 dNA

Vi dt 1 dNA A

r"V, = rVi = r"S

These rates are related by r" = fri = ar"

Since reactant A must move from gas to liquid for reaction to occur, diffusional resistances enter the rate.

The Rate Equation: Two-Film Theory

The rate of reaction is usefully written in a number of ways, as follows (NA=kmoles of A):

-" = - „ !!! 1 dNA V, dt A

-r" = - S dt 1 dNA

Vi dt 1 dNA A

r"V, = rVi = r"S

These rates are related by r" = fri = ar"

Since reactant A must move from gas to liquid for reaction to occur, diffusional resistances enter the rate. Here we will develop everything in terms of the two-film theory. Other theories can and have been used; however, they give essentially the same result, but with more impressive mathematics.

Two-Film Model for Mass Transfer Kinetics

The two-film model for the mass transfer kinetics assumes the existence of a thin film in each phase where all the mass transfer resistance is concentrated. The thickness & is of the order of few tenths of millimeter, and it depended on the flu dynamics of the system: the higher the velocity the smaller it is.

Under this assumption, the flux JA should be directly proportional to DA and inversely proportional to 8.

JA = - DA,L aCA as E DA,L CAi - CA

The experimental evidence is that JA is proportional to DA0.5!

Gas side Liquid side Interface Liquid film Gas film PA

JA = r"A= dNA Sdt

PAi

Assume equilibrium at interface, or PAi = HAi CAi and take HAi = constant, thus PAi = HA CAi

Main body of gas CAi CA

Higbie Penetration Theory (1935)

A more realist model for mass transfer is that proposed by Higbie. It is assumed that all lumps of fluid are continuously moving approaching the interphase for a small amount of time texp during which each lump releases or adsorbs mass to or from the other phase. Each lump therefore exchanges mass in a transient time regime.

CA,b liquid lump t=0 GAS CAi CA LIQUID CA, b

Solution: CAi - CA CAi - CA,b = erfc Χ 2 DAt =)

erf z = 21® et dt VTI

erfc(z) = 1 - erf(z)

CAi CA

JA(t) = - DA OCA) x=0 = (CAi - CA,b) 1 DA Tt

t=texp

CA

UA) = 1 texp Jo JA(t)dt = (CAi - CA,b) texp V 4DA Ttexp

kı. = V 4DA Ttexp

Lump mass balance equation: aCA at = DA 02CA 2 x2

B.Cs. t=0 CA=CA,b x=0 CAFCA¡ X=00 CAF CA,b

Error function: CAi CA t=t1 JA

Rate Equation for Straight Mass Transfer (Absorption) of A

Here we have two resistances in series, of the gas film and of the liquid film. Thus, the rate of transfer of A from gas to liquid is given by the rate expressions, for the gas film

mol mol m2 · Pa · s - m3 contactor · Pa · s 1 - ... or -r"" = KAga (PA - PAi) 1 (Eq.2)

For the liquid film it is: rÄ= KAI(CA ¡- CA) ... or -r" = kAla (CAi- CA) (Eq.3)

m3 liquid m3 liquid m2 surface · s m3 contactor · s

Gas-Liquid Mass Transfer

The mass transfer of A from the gas phase to the liquid one is the result of two series combined resistances, that related to the gas phase and that relevant to the liquid. Usually G-L equilibrium is assumed at interface CAiFfeq(PAi) = PAi/HA.

Gas side Liquid side Interface Liquid film Gas film 8 PA L - JA = r"A = dNA Sdt

PAI

Assume equilibrium at interface, or PAi = HAi CAi and take HAi = constant, thus PAi = HA CAi

Main body of gas CAi CA

Gas-Liquid Mass Transfer: Physical Absorption

(physical absorption with no reaction) Combining Eqs 2 and 3 with the equilibrium equation at G/L interphase CAi=PAi/HA the mass transfer overall equation can be derived:

JA = T"A = KAg (PA - PAi)

PAi CAL = HA

JA = T"A = KAL(CAi - CA)

Gas side Liquid side Interface Liquid film Gas film SLI PA

PAi

Assume equilibrium at interface, or PAi = HAi CAi and take HAi = constant, thus PAi = HA CAi

Main body of gas CAi CA

1 1 1 JA = "A= - % 0 (PA - HACA) = KGPtot (YA - yA) -+ KAg KAL

Where KG is the global mass transfer coefficient referred to the gas phase , Ptot is the total gas pressure and YA* is the equilibrium mole fraction of A in the gas phase corresponding to the liquid bulk concentration of A (CA).

∗ = HACA Ptot

KG = 1 HA kAg + KAI

HA

Reaction Inside the Liquid Phase

Once absorbed in the liquid phase A may react with B following kinetics of the chemical reaction.

A + bB > R

Interface PA CB

PA

dNA CAi

JA = r"A = Sdt

CA

CBi

Gas film

Liquid film

Main body of liquid

Reaction can take place in both the liquid film and in the main body of liquid. Fast reactions occur in a narrow zone within the film, slow reactions spread through the film and main body of liquid.

JB = dNB Sdt = -bJA

Interface Behavior for Liquid-Phase Reaction

The combination of mass transfer and reaction kinetics may give rise to different regimes of chemical absorption as follows:

• Case A: Instantaneous reaction with low C,
• Case B: Instantaneous reaction with high CB
• Case C: Fast reaction in liquid film, with low CB
• Case D: Fast reaction in liquid film, with high CB,
• Case E and F: Intermediate rate with reaction in the film and in the main body of the liquid
• Case G: Slow reaction in main body but with film resistance
• Case H: Slow reaction, no mass transfer resistance