Reactors forReactors forFluidFluid Fluid ReactionsFluid ReactionsFluidFluid--Fluid ReactionsFluid Reactions

Pertemuan 19Pertemuan 19

Pada bab ini, kita mempertimbangkan aspek Pada bab ini, kita mempertimbangkan aspek perancangan proses reaktorperancangan proses reaktor reaktor untukreaktor untukperancangan proses reaktorperancangan proses reaktor--reaktor untuk reaktor untuk reaksireaksi--reaksi multiphase di mana masingreaksi multiphase di mana masing--

masing tahap adalah suatu fluida. Inimasing tahap adalah suatu fluida. Inimasing tahap adalah suatu fluida. Ini masing tahap adalah suatu fluida. Ini termasuk reaksitermasuk reaksi--reaksi gasreaksi gas--cair dan caircair dan cair--cair. cair.

TYPES OF REACTORSTYPES OF REACTORSTYPES OF REACTORSTYPES OF REACTORS

The types of reactors used for fluidThe types of reactors used for fluid--fluid fluid reactions may be divided into two main reactions may be divided into two main yytypes:types:

1) tower or column reactors, and1) tower or column reactors, and1) tower or column reactors, and 1) tower or column reactors, and 2) tank reactors.2) tank reactors.

To e o Col mn Reacto sTo e o Col mn Reacto sTower or Column ReactorsTower or Column ReactorsTower or column reactors without mechanical agitationTower or column reactors without mechanical agitationTower or column reactors, without mechanical agitation, Tower or column reactors, without mechanical agitation, are used primarily for gasare used primarily for gas--liquid reactions. liquid reactions. If used for a liquidIf used for a liquid--liquid reaction, the arrangement liquid reaction, the arrangement involves vertically stacked compartments, each of whichinvolves vertically stacked compartments, each of whichinvolves vertically stacked compartments, each of which involves vertically stacked compartments, each of which is mechanically agitated. is mechanically agitated. In either case, the flow is countercurrent, with the less In either case, the flow is countercurrent, with the less dense fluid entering at the bottom, and the more densedense fluid entering at the bottom, and the more densedense fluid entering at the bottom, and the more dense dense fluid entering at the bottom, and the more dense fluid at the top. fluid at the top. In the case of a gasIn the case of a gas--liquid reaction without mechanical liquid reaction without mechanical agitation, both interphase contact and separation occur agitation, both interphase contact and separation occur g , p pg , p punder the influence of gravity. under the influence of gravity. In a liquidIn a liquid--liquid reaction, mechanical agitation greatly liquid reaction, mechanical agitation greatly enhances the contact of the two phases. enhances the contact of the two phases. ppWe consider here primarily the case of gasWe consider here primarily the case of gas--liquid liquid reactions.reactions.

Types of tower or column reactors for gasTypes of tower or column reactors for gas--liquid liquid reactions: (a) packed tower; (b) plate tower;reactions: (a) packed tower; (b) plate tower;reactions: (a) packed tower; (b) plate tower; reactions: (a) packed tower; (b) plate tower;

(c) spray tower; (d) falling(c) spray tower; (d) falling--film tower; (e) bubble film tower; (e) bubble columncolumn

(1) Packed tower(1) Packed tower(1) Packed tower(1) Packed towerA packed tower (Figure 24.1(a)) A packed tower (Figure 24.1(a)) contains solid shapes such as ceramiccontains solid shapes such as ceramiccontains solid shapes such as ceramic contains solid shapes such as ceramic rings or saddles to ensure appropriate rings or saddles to ensure appropriate flow and mixing of the fluids. flow and mixing of the fluids. The flow is usually countercurrent, with The flow is usually countercurrent, with the less dense fluid entering at the the less dense fluid entering at the bottom of the tower Both phases arebottom of the tower Both phases arebottom of the tower. Both phases are bottom of the tower. Both phases are considered to be continuous and ideally considered to be continuous and ideally in PF. in PF. GasGas--liquid interfacial area is enhanced liquid interfacial area is enhanced by contact of gas rising through the by contact of gas rising through the void space between particles ofvoid space between particles ofvoid space between particles of void space between particles of packing with a liquid film flowing down packing with a liquid film flowing down over the packing surfaceover the packing surface

(2) Plate tower.(2) Plate tower.(2) Plate tower.(2) Plate tower.A plate tower (Figure 24.1(b)) contains, A plate tower (Figure 24.1(b)) contains, f l b bblf l b bbl i l ti l tfor example, bubblefor example, bubble--cap or sieve plates cap or sieve plates at intervals along its height. at intervals along its height. The flow of gas and liquid is counterThe flow of gas and liquid is counter--The flow of gas and liquid is counterThe flow of gas and liquid is countercurrent, and liquid may be assumed to be current, and liquid may be assumed to be distributed uniformly radially on each distributed uniformly radially on each plateplateplate. plate. On each plate or tray, gas is dispersed On each plate or tray, gas is dispersed within the continuous liquid phase.within the continuous liquid phase.q pq pThe gasThe gas--liquid interfacial area is relatively liquid interfacial area is relatively large, and the gaslarge, and the gas--liquid contact time is liquid contact time is typically greater than that in a packedtypically greater than that in a packedtypically greater than that in a packed typically greater than that in a packed tower.tower.

(3) Sp a to e(3) Spray tower

A spray tower (Figure 24.l(c)) is an “empty” vessel with liquid sprayed (as in a “shower”) from the top as(as in a shower ) from the top as droplets to contact an upward-flowing gas stream. g gThe liquid phase is dispersed within the continuous gas phase, and ideal fl f h h i PFflow for each phase is PF. The gas-liquid interfacial area is relatively large but the contact timerelatively large, but the contact time is small.

(4) Falling(4) Falling Film col mnFilm col mn(4) Falling(4) Falling--Film columnFilm columnA fallingA falling film column (Figure 24 1(d)) isfilm column (Figure 24 1(d)) isA fallingA falling--film column (Figure 24.1(d)) is film column (Figure 24.1(d)) is also an “empty” vessel, with liquid, also an “empty” vessel, with liquid, introduced at the top, flowing down the introduced at the top, flowing down the wall as a film to contact an upwardwall as a film to contact an upward--flowingflowingwall as a film to contact an upwardwall as a film to contact an upward flowing flowing gas stream. gas stream. Ideal flow for each phase is PF. Ideal flow for each phase is PF. Since neither liquid nor gas is dispersedSince neither liquid nor gas is dispersedSince neither liquid nor gas is dispersed, Since neither liquid nor gas is dispersed, the interfacial area developed is relatively the interfacial area developed is relatively small, and gassmall, and gas--liquid contact is relatively liquid contact is relatively inefficient. inefficient. This type is used primarily in the This type is used primarily in the experimental determination of mass experimental determination of mass transfer characteristics, since the interfacial transfer characteristics, since the interfacial ,,area is well defined.area is well defined.

(5) Bubble column(5) Bubble column(5) Bubble column(5) Bubble columnA bubble column (Figure 24.1(e)) is also an A bubble column (Figure 24.1(e)) is also an “empty” vessel with gas bubbles“empty” vessel with gas bubblesempty vessel with gas bubbles, empty vessel with gas bubbles, developed in a sparger (see below) rising developed in a sparger (see below) rising through a downwardthrough a downward--flowing liquid flowing liquid stream.stream.stream. stream. The gas phase is dispersed, and the liquid The gas phase is dispersed, and the liquid phase is continuous; the assumed ideal phase is continuous; the assumed ideal flow pattern is PF for the gas and BMF forflow pattern is PF for the gas and BMF forflow pattern is PF for the gas and BMF for flow pattern is PF for the gas and BMF for the liquid.the liquid.Performance as a reactor may be affected Performance as a reactor may be affected by the relative difficulty of controlling axial by the relative difficulty of controlling axial y y gy y gand radial mixing. and radial mixing. As in the case of a packed tower, it may As in the case of a packed tower, it may also be used for catalytic systems, with also be used for catalytic systems, with y y ,y y ,solid catalyst particles suspended in the solid catalyst particles suspended in the liquid phase.liquid phase.

Tank Reacto sTank Reacto sTank ReactorsTank Reactors

Tank reactors usually employ mechanical agitation to Tank reactors usually employ mechanical agitation to bring about more intimate contact of the phases, with bring about more intimate contact of the phases, with one phase being dispersed in the other as the one phase being dispersed in the other as the

ti hti hcontinuous phase.continuous phase.The gas phase may be introduced through a “The gas phase may be introduced through a “spargersparger” ” located at the bottom of the tank; this is a circular ring located at the bottom of the tank; this is a circular ring of closedof closed end pipe p o ided ith a n mbe of holesend pipe p o ided ith a n mbe of holesof closedof closed--end pipe provided with a number of holes end pipe provided with a number of holes along its length allowing multiple entry points for the along its length allowing multiple entry points for the gas.gas.Tank reactors are well suited for a reaction requiring aTank reactors are well suited for a reaction requiring aTank reactors are well suited for a reaction requiring a Tank reactors are well suited for a reaction requiring a large liquid holdup or a long liquidlarge liquid holdup or a long liquid--phase residence timephase residence timeTank reactors equipped with agitators (stirrers, Tank reactors equipped with agitators (stirrers, impellers turbines etc ) are used extensively for gasimpellers turbines etc ) are used extensively for gasimpellers, turbines, etc.) are used extensively for gasimpellers, turbines, etc.) are used extensively for gas--liquid reactionsliquid reactions

CHOICE OF TOWER OR TANK CHOICE OF TOWER OR TANK REACTORREACTOR

The choice between a towerThe choice between a tower--type and a type and a tanktank--type reactor for a fluidtype reactor for a fluid--fluid reaction fluid reaction ypypis determined in part by the kinetics of the is determined in part by the kinetics of the reaction. reaction. As described by the twoAs described by the two--film model for film model for gasgas--liquid reactionsliquid reactionsgasgas liquid reactions liquid reactions

Typical values of gasTypical values of gas--liquid interfacial arealiquid interfacial areaTypical values of gasTypical values of gas liquid interfacial area liquid interfacial area (a(aii and aand aii’) for various types of vessels’) for various types of vessels

The two extremes for a nonvolatile liquidThe two extremes for a nonvolatile liquid--phase phase reactant, are virtually instantaneous reaction in the reactant, are virtually instantaneous reaction in the liquidliquid--film,film,

aaii interfacial area based on unit volume of liquid interfacial area based on unit volume of liquid phase, mphase, m22 mm--33 (liquid) (liquid) aaii’ interfacial area based on ’ interfacial area based on p ,p , ( q )( q ) iiunit volume of vessel (occupied by fluids), munit volume of vessel (occupied by fluids), m2 2 mm33

(vessel)(vessel)

aiai interfacial area based on unit volume of liquid interfacial area based on unit volume of liquid phase, mphase, m22 mmPP

--33 (liquid)(liquid)phase, mphase, m mmPP (liquid)(liquid)Ai’ interfacial area based on unit volume of Ai’ interfacial area based on unit volume of vessel (occupied by fluids), mvessel (occupied by fluids), m22 mm--33 (vessel)(vessel)( p y ),( p y ), ( )( )The two quantities The two quantities aaii and are related byand are related by

TOWER REACTORSTOWER REACTORSTOWER REACTORSTOWER REACTORS

PackedPacked--Tower ReactorsTower ReactorsWe consider the problem of determining the height, We consider the problem of determining the height, h of a tower (i e of the packing in the tower) and itsh of a tower (i e of the packing in the tower) and itsh, of a tower (i.e., of the packing in the tower) and its h, of a tower (i.e., of the packing in the tower) and its diameter, D, for a reaction of the model type:diameter, D, for a reaction of the model type:

in which A transfers from the gas phase to react within which A transfers from the gas phase to react within which A transfers from the gas phase to react with in which A transfers from the gas phase to react with nonvolatile B in the liquid phase.nonvolatile B in the liquid phase.The height h is determined by means of appropriate The height h is determined by means of appropriate

t i l b l f f tht i l b l f f thmaterial balances or forms of thematerial balances or forms of thecontinuity equation.continuity equation.

For simplification, we make the following assumptions:assumptions:

(1) The gas and liquid flow rates are constant throughout the column;throughout the column;

(2) Each phase is in PF.(3) T is constant.(4) P is constant.(5) The operation is at

steady state.steady state.(6) The two-film model is

applicable

In Figure 24.3, the other symbols In Figure 24.3, the other symbols g , yg , yare interpreted as follows:are interpreted as follows:

G = total molar mass flow rate of gas, mol mmG = total molar mass flow rate of gas, mol mm22 ss--11

L = total liquid volumetric flow rate, mL = total liquid volumetric flow rate, m3 3 mm2 2 ss--11

(b h G d L l d i(b h G d L l d i i li l(both G and L are related to unit cross(both G and L are related to unit cross--sectional sectional area A, of the unpacked column)area A, of the unpacked column)

cc = liquid= liquid--phase concentration of A mol mphase concentration of A mol m--33ccAA = liquid= liquid--phase concentration of A, mol mphase concentration of A, mol m 33

ccnn = liquid= liquid--phase concentration of B, mol mphase concentration of B, mol m--33

yy = mole fraction of A in gas= mole fraction of A in gasyyAA = mole fraction of A in gas= mole fraction of A in gasppAA = partial pressure of A in gas = y= partial pressure of A in gas = yAAPPNote that h is measured from the top of theNote that h is measured from the top of theNote that h is measured from the top of the Note that h is measured from the top of the

column.column.

Continuity equation for A in the gas Continuity equation for A in the gas y q gy q gphase (PF):phase (PF):

The second term on the right is the flux of A at the li id i t f NA( 0)gas-liquid interface, NA(z = 0).

Thus, the continuity equation may be written as

(24.4-1)

which becomes, with yA = pA/P, (24.4-2)

Continuity equation for A in the Continuity equation for A in the y qy qbulk Liquidphase (PF):bulk Liquidphase (PF):

For A in the bulk liquid, with reference to the For A in the bulk liquid, with reference to the control volume in Figure 24.3, in which the input control volume in Figure 24.3, in which the input f A i t th b ttf A i t th b ttof A is at the bottom,of A is at the bottom,

The second term on the left is the flux of A at the fictitious liquid film-bulk liquid interface, NA (z = 1). That is,

(24.4-3)

where (where (-- rrAA))intint, in mol m, in mol m--33 (liquid) s(liquid) s--11, is the intrinsic , is the intrinsic rate of reaction of A in the liquid phase as givenrate of reaction of A in the liquid phase as givenrate of reaction of A in the liquid phase, as given rate of reaction of A in the liquid phase, as given by a rate law for a homogeneous reaction. by a rate law for a homogeneous reaction. Equation 24.4Equation 24.4--3 becomes3 becomesEquation 24.4Equation 24.4 3 becomes3 becomes

(24.4-4)

Continuity equation for B in the bulk liquid phase (PF):With f t th t l l i Fi 24 3 iWith reference to the control volume in Figure 24.3, in which the input of B is at the top,

That is, since the rate of diffusion of B in the liquidThat is, since the rate of diffusion of B in the liquidThat is, since the rate of diffusion of B in the liquid That is, since the rate of diffusion of B in the liquid film is Nfilm is NBB = = --bNbNAA, for counter, for counter--diffusion,diffusion,

(24.4-5)

or

(24.4-6)That is,

Overall material balance around Overall material balance around column:column:

For A: rate of moles entering in gas + rate ofFor A: rate of moles entering in gas + rate ofFor A: rate of moles entering in gas + rate of For A: rate of moles entering in gas + rate of moles entering in liquid = rate of moles leaving moles entering in liquid = rate of moles leaving in gas + rate of moles leaving in liquid + rate of in gas + rate of moles leaving in liquid + rate of moles lost by reaction:moles lost by reaction:moles lost by reaction:moles lost by reaction:

which can be written

(24.4-7)

where “rA” is the total rate of consumption of A (in liquid film and bulk liquid) over the entire column.

Similarly, for B:Similarly, for B:Similarly, for B:Similarly, for B:

(24.4-8)

Combining 24.4Combining 24.4--7 and 7 and --8, we obtain8, we obtain

(24.4-9)b(

a o nd the toparound the top,

(24.4-9a)

around the top,

( )

(24.4-9b)

Determination of the tower diameter D depends Determination of the tower diameter D depends h t i ifi d f th t Th thh t i ifi d f th t Th thon what is specified for the system. Thus, the on what is specified for the system. Thus, the

crosscross--sectional area issectional area is

(24.4-10)

where qg,usg, and Ftg are the volumetric flow rate, superficial linear velocity and molar flow rate of gassuperficial linear velocity, and molar flow rate of gas, respectively, and ql is the volumetric flow rate of liquid. The gas flow rate quantities are further interrelated by an

ti f t t Th f id lequation of state. Thus, for an ideal gas,

(24 4 11)(24.4-11)

E ample 24 1E ample 24 1Example 24.1Example 24.1

If, for the situation depicted in Figure If, for the situation depicted in Figure 24.3, the partial pressure of A in the gas 24.3, the partial pressure of A in the gas phase is to be reduced from Pphase is to be reduced from PA,inA,in to Pto PAA,,outoutat a specified gas flow rate G and total at a specified gas flow rate G and total p ess e P hat is the minim m liq idp ess e P hat is the minim m liq idpressure P, what is the minimum liquid pressure P, what is the minimum liquid flow rate, Lflow rate, Lminmin, in terms of G, P, and the , in terms of G, P, and the partial pressures/ concentrations of A andpartial pressures/ concentrations of A andpartial pressures/ concentrations of A and partial pressures/ concentrations of A and B? Assume that there is no A in the liquid B? Assume that there is no A in the liquid feed.feed.feed.feed.

SOLUTIONSOLUTIONSOLUTIONSOLUTION

The criterion for L Lmin is that CB,out 0. That is, there is just enough input of B to react with A to lower its partial pressure to pA,out and to allow for an outlet liquid-phase concentration of CA, out. From equation 24 4 9 with C C 0 andFrom equation 24.4-9, with CB,out = CA,in = 0 and L = Lmin,

(24.4-12)

For reaction in the liquid film only, CA,out = 0, and ,equation 24.4-12 reduces to

( )PPbG( )( )inB

outAinA

CPPPbG

L,

,,min

−= (24.4-13)( ),

Then,,(24.4-14)

To establish α (i.e., L), it is necessary to take flooding and wetting of packing into account (see Zenz, 1972).

B bbleB bble Col mn Reacto sCol mn Reacto sBubbleBubble--Column ReactorsColumn Reactors

In a bubbleIn a bubble--column reactor for a gascolumn reactor for a gas--liquid liquid reaction, Figure 24.1(e), gas enters the bottom reaction, Figure 24.1(e), gas enters the bottom of the vessel, is dispersed as bubbles, and flowsof the vessel, is dispersed as bubbles, and flowsof the vessel, is dispersed as bubbles, and flows of the vessel, is dispersed as bubbles, and flows upward, countercurrent to the flow of liquid. upward, countercurrent to the flow of liquid. We assume the gas bubbles are in PF and the We assume the gas bubbles are in PF and the liquid is in BMF although nonliquid is in BMF although non ideal flow modelsideal flow modelsliquid is in BMF, although nonliquid is in BMF, although non--ideal flow models ideal flow models (Chapter 19) may be used as required. (Chapter 19) may be used as required. The fluids are not mechanically agitated. The fluids are not mechanically agitated. y gy gThe design of the reactor for a specified The design of the reactor for a specified performance requires, among other things, performance requires, among other things, determination of the height and diameterdetermination of the height and diameterdetermination of the height and diameter.determination of the height and diameter.

Continuity Equations for BubbleContinuity Equations for Bubble--y qy qColumn ReactorsColumn Reactors

Continuity equation for A in the gas phase (PF):Continuity equation for A in the gas phase (PF):

(24.4-2)

Continuity equation for A in the bulk liquid phase Continuity equation for A in the bulk liquid phase (BMF):(BMF):(BMF):(BMF):

(24.4-15)(24.4 15)

The integral on the left side of equation The integral on the left side of equation 24 424 4 15 i i d i lth h15 i i d i lth h ((24.424.4--15 is required, since, although c15 is required, since, although cAA( = ( = ccA,outA,out) is constant throughout the bulk ) is constant throughout the bulk li id f t t b tt (BMF f li id)li id f t t b tt (BMF f li id)liquid from top to bottom (BMF for liquid), liquid from top to bottom (BMF for liquid), PPA A decreases continuously from bottom to decreases continuously from bottom to tttop. top. These quantities are both included in NThese quantities are both included in NAA(z (z = 1) (see Example 24= 1) (see Example 24--2, below).2, below).

Overall material balance around column:Overall material balance around column:Overall material balance around column:Overall material balance around column:

(24 4-9)- - (24.4 9)

Correlations for Design Parameters for BubbleCorrelations for Design Parameters for Bubble--Correlations for Design Parameters for BubbleCorrelations for Design Parameters for BubbleColumn ReactorsColumn ReactorsGas holdup, Gas holdup, εεgg::p,p, ggFor a nonelectrolyte liquid phase, the correlation For a nonelectrolyte liquid phase, the correlation of Hikita et al. (1980) isof Hikita et al. (1980) is

(24.4-16)

Mass transfer coeficient kMass transfer coeficient kMass transfer coeficient, kMass transfer coeficient, kAlAl

The liquidThe liquid--film mass transfer coefficient may be film mass transfer coefficient may be l fl f kk ((kk l fl fgiven as a correlation for given as a correlation for kkAlAl ((kkii in general for in general for

species i, or often denoted simply by species i, or often denoted simply by kkLL.), or for .), or for kk aa ’ the product of the mass transfer coefficient’ the product of the mass transfer coefficientkkAlAlaaii , the product of the mass transfer coefficient , the product of the mass transfer coefficient and the interfacial area based on vessel volume and the interfacial area based on vessel volume (often denoted simply as(often denoted simply as kkLLaa).).(often denoted simply as (often denoted simply as kkLLaa).).

ForFor kkAlAl, the correlation of Calderbank and Moo, the correlation of Calderbank and Moo--For For kkAlAl, the correlation of Calderbank and Moo, the correlation of Calderbank and MooYoung (1961) for small bubbles isYoung (1961) for small bubbles is

(24.4-17)

where DA= molecular diffusivity of A in the liquid phase, m2 s-1 and kAl is in m s-1,p , Al ,

For kAlai’, the correlation of Hikita et al. (1981) is

(24.4-18)( )

With units given above, With units given above, kkAlAlaaii’ is in s’ is in s--11 as derived as derived g ,g , AlAl iifrom the factor from the factor g/ug/usgsg since the other factors are since the other factors are dimensionless.dimensionless.

Interfacial area, Interfacial area, aaii’’::

An expression forAn expression for aaii’’ given by Froment andgiven by Froment andAn expression for An expression for aaii given by Froment andgiven by Froment andBischoff (1990, p. 637) may be writtenBischoff (1990, p. 637) may be written

(24.4-19)

With units given above, ai’ is in mWith units given above, ai’ is in m--11 (i.e., m(i.e., m22

interfacial area (minterfacial area (m33 reactor)reactor)--11))interfacial area (minterfacial area (m33 reactor)reactor) 11).).

M t f ffi i t kM t f ffi i t k

Shah et al (1982) made no recommendation forShah et al (1982) made no recommendation for

Mass transfer coefficient, kMass transfer coefficient, kAgAg::

Shah et al. (1982) made no recommendation for Shah et al. (1982) made no recommendation for the determination of kthe determination of kAgAg; in particular, no ; in particular, no correlation for kcorrelation for kAA in a bubble column had beenin a bubble column had beencorrelation for kcorrelation for kAgAg in a bubble column had been in a bubble column had been reported up to that time. reported up to that time. If the gas phase is pure reactant A, there is noIf the gas phase is pure reactant A, there is noIf the gas phase is pure reactant A, there is no If the gas phase is pure reactant A, there is no gasgas--phase resistance, but it may be significant phase resistance, but it may be significant for a highly soluble reactant undergoing fast for a highly soluble reactant undergoing fast reaction.reaction.

TANK REACTORSTANK REACTORSTANK REACTORSTANK REACTORS

Continuity Equations for Tank ReactorsContinuity Equations for Tank ReactorsContinuity Equations for Tank ReactorsContinuity Equations for Tank ReactorsContinuity equation for A in the gas phase Continuity equation for A in the gas phase (BMF):(BMF):(BMF):(BMF):

Since the gas phase is in BMF, the continuity Since the gas phase is in BMF, the continuity equation corresponding to 24.4equation corresponding to 24.4--1, and1, andbased on the enti e essel of ol mebased on the enti e essel of ol mebased on the entire vessel of volumebased on the entire vessel of volume

24.5-1

(24.5-2)

Continuity equation for A in the bulk liquid phase (BMF): Since the liquid phase is in BMF the(BMF): Since the liquid phase is in BMF, the continuity equation for A in the bulk liquidphase is similar to equation 24.4-15,phase is similar to equation 24.4 15,

Thus, we have

(24.5-3)( )

Overall material balance around tank: is again given by equation 24.4-9:

(24.4-9)

Correlations for Design Parameters for Correlations for Design Parameters for Tank ReactorsTank Reactors

Power input, PI:

Michell and Miller (1962) proposed the following correlation for PI (in kW):

(24.5-4)

(24 5 5)(24.5-5)

where ubr is the rise velocity of a bubble through a quiescent liquid (equation 23.3-2).

The correlations of Meister et al. (1979) for kAl ai’ for one and two impellers per stage, respectively, are:

(24.5-6)( )

(24.5-7)

Chandrasekharan and Calderbank (1981) proposed the following correlation, whichshows a much stronger inverse dependence on vessel diameter:

(24.5-8)

It was shown to be accurate to within 7.5% over a range of vessel diameters.

The correlations of Hassan and Robinson (1977) for gas holdup, εg, for both non-electrolyte and electrolyte liquid phases are:

(24 5 9)

(24.5-10)

(24.5-9)

These two correlations were based on laboratory-l d il t l t l t (D 1 ) dscale and pilot-plant-scale reactors (D < 1 m), and

do not take into account vessel and impeller geometrygeometry.