retrofitting columns by the installation of...

$: Retrofitting Columns by the Installation of Packingssu.ac.ir/cms/fileadmin/user_upload/Daneshkadaha/... · 12.1 Advantages of retrofitting 295 known. Yet another means by which r\c$
12 Retrofitting columns by the installation of packing

On the strength of the advantages that they offer in process engineering, packed columnsare progressively encroaching upon territory that was formerly the exclusive domain of platecolumns. A well-known example is the industrial-scale vacuum separation of ethylben-zene/styrene mixtures, for which purpose bubble-cap plates were initially used in compliancewith tradition. They were subsequently superseded by special slotted-sieve and valve plates;and these, in turn, are now losing ground to structured sheet-metal packing.

At the present time, packing is attracting attention not only for new installations but alsofor retrofitting existing columns. The aims of substituting modern, high-performance packingwith a low pressure drop for the former column internals are to save energy, increase thecapacity, and improve the product quality. This applies particularly to separation processes inrefineries, to chemical and petrochemical production plants, and to food processing.

12.1 Advantages of retrofitting

The relationship between energy costs and the expenditure on equipment is evident inFig. 1.7. The pressure drop per theoretical stage Ap/nt causes the relative volatility todecrease in the direction from the top to the bottom of the column. In other words, themean value am is less than that in theoretically isobaric rectification aiso, i.e. in the bound-ary case when Ap/nt = 0. The minimum number of theoretical stages ntymin and the mini-mum reflux ratio are correspondingly greater; thus nt>min > nt>minyiso, and rmin > rmin>iso. As isevident from Figs. 1.7 and 1.8, the number of theoretical stages in real rectification, whenAplnt > 0, is also greater, i.e. nt > nt>iso; and, according to Eqn (1-52), the reflux ratio aswell, i. e. r > riso.

The procedure outlined below permits calculation of the savings in energy and the reduc-tion in the number of theoretical stages that can be achieved by retrofitting and makes dueallowance for the specific pressure drop Aplnt. The steps (a)-(p) can be deduced from Figs.1.7, 1.8 and 12.1 and the thermodynamic fundamentals and relationships that describe recti-fication processes.(a) The nature of the task implies that the mole fractions of the more volatile component in

the feed xF, overhead product (distillate) xD, and bottom product xB are given. The pres-sure pT at the top of the column is also given and can theoretically be optimized to allowminimum separation costs. Known parameters are the molar enthalpy of the feed hF andh'F at the inlet and boiling temperatures, respectively, and the molar condensationenthalpy Ahv of the vapour stream in the inlet cross-section. Hence the factor / thatdescribes the thermal state of the feed can be calculated from Eqn (1-12).

(b) The relative volatility aIjiso of a molar mixture with a concentration x*tso, yfjso at theintersect / of the equilibrium curve and the g-line can be determined by iteration fromphase equilibrium equations. Thus, the following applies for an ideal binary mixture:

Packed Towers in Processing and Environmental Technology. Reinhard BilletCopyright © 1995 VCH Verlagsgesellschaft mbH, WeinheimISBN: 3-527-28616-0

SOFTbank E-Book Center Tehran, Phone: 66403879,66493070 For Educational Use.

292 12 Retrofitting columns by the installation of packing

1

XF / f Xp

Liquid mole fraction xxn1

Fig. 12.1. Qualitative diagram represent-ing the minimum number of theoreticalstages and the enrichment curve required toobtain the minimum reflux ratio in isobaricand real rectification

where Au A2, Bj, B2, C7, and C2 are the Antoine constants for a given boiling point Tand the corresponding pressures of the more volatile Pj and less volatile P2 components1 and 2. The phase equilibrium concentration of the more volatile fraction x*iso canthen be obtained from the following equation, which is valid for a = aI>iso, y = y*iso,x = x*iso and a pressure /?/ = pT:

xUso (a[Jso -f XF

' • - / _ !

(12-2)

(c) Once aItiso and x*iso have been obtained, the phase equilibrium concentration of the lessvolatile component y*iso can be calculated from the following equation:

xUso (aUso -(12-3)


12.1 Advantages of retrofitting 293

There is no need for iteration if the feed is admitted into the column at the boilingpoint, i.e. if hF = hF and / = 1, in which case x*iso = xF. Under these circumstances,a*wo = a*- corresponding to pt = pT and T(xF) can be determined direct from Eqn(12-1); and thus yfJso = yFJso, from Eqn (12-3).

(d) It is evident from Fig. 12.1 that the minimum reflux ratio in isobaric rectification is givenby

(12-4)

(e) Thus the reflux ratio r in real rectification can be obtained from Eqn (1-49) by assuminga value for the factor vg\ and the energy parameter e can therefore be calculated fromEqn (1-47). In Fig. 1.8, the value of s, the stage-number parameter, can then be read offon the axis of ordinates against this value of e and the corresponding pressure drop pertheoretical stage Ap/nt. This step is demonstrated in the qualitative diagram shown inFig. 1.7. A knowledge of the parameter s is essential for determining the number of theo-retical stages in real rectification from Eqn (1-45).

(f) The term nt>min>iso in Eqn (1-45) applies to the minimum number of theoretical stages inisobaric rectification. It can be defined by the Fenske. equation if the mean relative vola-tility amJso in the range of concentrations under consideration can be accepted, withoutreservation, as being sufficiently accurate for practical purposes. Thus

InxD l-xB

- xD xB Jnt,min,iso = J - 1 ( 1 2 " 5 )

In a.m,iso

The minimum number of theoretical stages required in the enriching zone of thecolumn, in which the mean relative volatility is am}enr!iso, is given by

In

^t,min,enr,iso

XD l-XF

-xD xF - 1 (12-6)

(g) Eqn (1-45) can be rearranged to give the total number of theoretical stages nt in realrectification, i. e.

(12-7)

The number of these stages that is accounted for by the enriching zone is given by

^ t, min, enr, iso ' $ , . _ .

n,,enr = \ s (12-8)

(h) The pressure pF in the cross-section of the feed inlet can now be obtained from nlenr, i. e.

(12-9)



(i) The relative volatility a7 applies to the intersect of the curves that are valid for the feedinlet cross-section. As described in step (b), it can be determined by means of Eqn(12-1), but applies in this case to real rectification. Therefore, x7*can be obtained fromthe following relationship:

r imi + * ; ( « , - ! ) * ' / - i / - I ( 1 2 1 0 )

(j) Now that Jt*and a7 are known, the phase equilibrium concentration yf can be determinedfrom

Again, iteration is unnecessary if the mixture is at the boiling point when it flows intothe column, because x*= xF and a7 = aF at /?7 = pF and T(xF).

(k) The minimum reflux ratio rmin for the real column can then be obtained from

-y*

The following relationship ought to exist between rmin and the minimum reflux ratio inan isobaric column rminjiso

r - (r • i \ y*'™ Xl'iso i Xl>iso ±L i n? ITl'mm ~ \rmin,iso ^ l) * * ^ * * — 1 V1^"1"3/

(1) The reflux ratio in isobaric rectification can be obtained by rearranging Eqn (1-52). Thus

Fmin, iso / 1 /-» 1 A \

riso = r = vrmin>iso (12-14)

The factor v in Eqns (1-48) and (1-50) can then also be determined.

(m) Since rmin>iso and v are now known, the energy parameter for isobaric rectification eiso, asrepresented on the axis of abscissae in Fig. 1.7, can be calculated from Eqn (1-46).

(n) The value for siso corresponding to eiso on the isobaric (Apfnt = 0) curve in Fig. 1.8 canbe read off on the axis of ordinates. Rearranging Eqn (1-44) and inserting this value forsiso then gives the number of theoretical stages in the isobaric column, i.e.

nUlso = H t ~ + Siso (12-15)1 $iso

(o) The values obtained for nt and nt>iso in steps (g) and (n) can be taken to calculate thetheoretical column efficiency r\c from Eqn (1-42). Alternatively, r\c can be calculatedfrom Eqns (1-53), (1-54) or (1-55), because the terms in these equations are now also


12.1 Advantages of retrofitting 295

known. Yet another means by which r\c can be obtained is to determine the increase inthe number of theoretical stages Ant that is caused by the specific pressure drop Ap/nt,i.e.

Ant = nt- nt>iso = _ * ~ i " ° T Km,*™ + 1) (12-16)^1 S) {L Siso)

In this case, the theoretical column efficiency, i. e. the number of theoretical stages ina theoretical isobaric column, expressed as a ratio of that in a column with pressuredrop, is given by

= n,Mo + An, An,1 +

(p) The amount Ar by which the reflux ratio in a real column exceeds that in an isobariccolumn is defined by

Ar = r- riso = * ~ 6iso (rminMo + 1) (12-18)yi - e) {i - eiso)

It allows an expression to be obtained for the efficiency in terms of energy r\e, i. e. theenergy consumption in a theoretical isobaric column to be expressed as a ratio of that ina real column. Thus

= riso + 1 = 1_u riso + Ar + 1 l + Ar v ;

riso + 1

Relationships for the relative increase in the energy consumption QIQiso and in the num-ber of theoretical stages Ant/nt)iso can be obtained by following the steps (a)-(p) in the pro-cedure outlined above. With the aid of Fig. 1.8, they can be expressed as functions of thepressure drop per theoretical stage Aplnt, i.e.

4 ^ — - 1 = f (Ap/n,) (12-20)Qts

An, 1- 1 = f(Ap/nt) (12-21)

nt,iso T\C

Both relationships are presented graphically in the numerical example given in Fig. 12.2.The diagram convincingly demonstrates the advantages that can be derived from installingpacking instead of plates. The upper curve was plotted from the sole aspect of achieving theutmost savings in energy, i.e. for a constant number of theoretical stages (nt = const.), andthe parameters that were taken into consideration were nt>min>iso, riso and s. The two lowercurves represent the case in which the intention was both to save energy and to reduce the



number of theoretical stages, i. e. the minimum reflux ratio factor was constant (v = const.)and the parameters were rminJso, ntMnMo and ntJso. The headings on the diagram indicate theranges of pressure drops that apply to arranged packing, random packing, and plates.

12.2 Potential for retrofitting with low-pressure-drop packing

It is clearly evident from Fig. 12.2 that the energy consumption and the number of theo-retical stages in intensive-rectification columns can be substantially reduced by substitutinglow-pressure-drop packing for fractionating plates.

Theoretically, it is also feasible to retrofit the column so that the number of theoreticalstages remains unchanged. In this case, the severity or the fineness of the cut can beincreased, and purer products can be obtained.

e:DCO

0.30

0.20

0.15

0.100.08

0.06

0.04

0.03

0.02

0.015

Regular or corrugated-sheet packing

/

r

3—-/

y

3—-

y

11Mt min.is

ntr,ss

!

ft

A

/+

y

k-.

Tt1o=27.4= 58

0-4-4

- 0.5,

/

/

/

)

/

?y

/

/\y

/

//

/

Dumpedpack ag

/si —

y

/y y

A /

n

y

y

/

/

/

min.iso = ^- "11 Q

t m i n . i s o " L '-J

nt, iso=52

v = 1.3

Trays

- ^

y

-i

j

y /

A

s

W

y

y

y

y

/

3 4 6 8 10 15 20 40 60 80

Specific pressure drop A p / n t [mm WG ]

0.30

0.20

0.15

0.100.08

0.06

0.04

0.03

0.02

0.015

CD

Fig. 12.2. Increase in energy consumption and in the number of theoretical stages as a function ofthe specific pressure drop in vacuum rectification involving a large number of theoretical stages.Evaluated with the aid of Fig. 1.8.


72.2 Potential for retrofitting with low-pressure-drop packing 297

The condition for equilibrium at the point y = yt\ x = xj is

— (12-22)

Consequently, the minimum reflux ratio rmin is given by (cf. Fig. 12.1)

a,^"min

a7 1-x?

The rate of heat emission Q is described by

Q =xD - xB

h'B-h'F

(12-23)

(12-24)

where v is the factor for the minimum reflux ratio {cf. Eqn (1-50)} and rmin depends on thepressure pF in the feed cross-section and thus, according to Eqn (12-9), on the pressure dropper theoretical stage Ap/nt.

Another means of determining the effect of Ap/nt on Q arises from the following equa-tion, which can be obtained by rearranging Eqn (1-47):

r • • -\- p' min,iso ' c

1 -e(12-25)

Consequently, the following relationship can also be derived from Eqn (1-57); and it canbe evaluated with the aid of Fig. 1.8:

CD

a

IDC=

Fig. 12.3. Application of Fig. 1.8 forretrofitting estimates

Hnin.iso t V g " " i )

Energy parameter



XF - XB -*-

1-eAhv + h'D - h'B\ + h'B - h'F (12-26)

The significance of the pressure drop per theoretical stage Ap/nt in retrofitting anddesigning separation columns is further demonstrated in Figs. 12.3 and 12.4. These diagramsrepresent a method of comparing column internals with different pressure drops per theoret-ical stage, i.e. (Ap/nt)j and (p/nt)2. The two types of column compared are denoted by thesubscripts 1 and 2, and the method permits a comparison in the following five cases:(A) The minimum reflux ratio factor v, as defined by Eqn (1-50), remains constant.(B) The reflux ratio r {Eqn (12-25)} and thus the energy parameter e remain constant.(C) The number of theoretical stages nt {Eqn (12-7)} and thus the stage-number parameter s

remain constant.(D) The product vapour load V remains constant.(E) The column is operated at a constant pressure drop per theoretical stage Ap/nt.

In Cases (A) and (B), the difference in the number of theoretical stages is given by

An't = nh - nh = ^ " ^ (nt,min,iso + 1) (12-27)

In Cases (A) and (C), the difference in reflux ratio is given by

Ar' = r2 - n = (1_ee22~^_ei) (rminjso + 1) (12-28)

Eqns (12-27) and (12-28) can be solved numerically with the aid of Fig. 1.8.The percentage reduction in the number of theoretical stages that can be achieved by in-

stalling the internals denoted by the subscript 1 instead of those denoted by the subscript 2can be determined from the following equation:

100 = ^ 100 (12-29)nh nt.

The corresponding savings in energy can be calculated from the following equation:

Ql~QQl 100 = y ^ y y 100 (12-30)

In Case (A), the reduction achieved in the number of theoretical stages is less than thatin Case (B), and the savmgs in energy are less than those in Case (C). On the other hand,no energy is saved in Case (B), and no reduction in the number of theoretical stages iseffected in Case (C).

In Case (D), the opportunity of retrofitting with stacked packing with a low pressure dropcan be exploited to increase the capacity F. If the vapour flow rate V is the same in bothcases, i. e. V = const., the distillate flow rate D in a real column can be compared to that ina theoretical isobaric column Diso by means of the following equation:

V = Diso (riso + 1) = D (riso + 1 + Ar) (12-31)



The inlet capacity in the isobaric case is given by Eqn (12-32); and that in the real case,by Eqn (12-33):

F = D1 ISO J-^lSt

F = DxF-xB

The efficiency in terms of capacity is therefore given by

XD

XF

xD-

-xB-xB

xB

(12-32)

(12-33)

F1 ISO

1(12-34)

1 +

where Ar is as defined by Eqn (12-18). In other words, the efficiency is the same in terms ofcapacity r\F as it is in terms of energy r\e, as defined by Eqn (12-19). The lower the value ofAp/nt, the greater that of v]F. As a consequence of the pressure drop in a theoretical stageAp/nt, the capacity in real rectification is less than that in theoretical isobaric i.e.

AF

F iso

F - Friso r

Fx ISO

= 1 -x\F = i(Ap/nt) (12-35)

Hence, the following equation applies if column internals with a specific pressure drop(Ap/nt)2 are replaced by internals with a lower value (Ap/«,)/ and the vapour flow rate isassumed to be the same, i.e. Vj = V2 = const, (cf. Fig. 12.4):

= D2 (r2 (12-36)

Product vapour rate V

Fig. 12.4. Qualitative comparison ofcolumn internals with various specificpressure dropsCase D: if the vapour load is keptconstantCase E: if the specific pressure drop iskept constant

<O

CDd .

CO

Capacity factor Fv



The inlet capacity F2 in Case 2 and that Fj in Case 1 are given by

F2-

F, -

The percentage increase in capacity is

Fj-F2

D XD~xF-

D XD~xF-

therefore

-xB• X B

-xB

• X B

(12-37)

i 100 (12-38)F2 r2 + 1

in which Ar ' is as defined by Eqn (12-28).

In Case (E) , an increase in capacity F can also be achieved by retrofitting, because the

loads permit ted by modern packing of appropriate dimensions are higher than those

obtained by plates of equivalent Ap/nt. It is evident from the qualitative diagram shown in

Fig. 12.4 that the increase in capacity in this case is given by

Fi ~ F2 FVi - Fy2—P-— 100 - — 100 (12-39)

r2 tv2

where FVl and Fy2 are the vapour capacity factors at which the value Ap/nt = constant inpackings 1 and 2.

The benefits offered by high-performance packing with small values of Ap/nt arereviewed in Table 12.1. They apply to both the planning of new and the retrofitting of exis-ting columns. It is evident from the table that advantages can be obtained in the number oftheoretical stages nt and thus the column height i7, the reflux ratio r and thus the columndiameter ds, the energy consumption Q, and the capacity F.

If the calculations reveal that the height of the column to be retrofitted Hj is less than theoriginal height H2, i.e. Hi < H2l full exploitation of the available height H2 will give rise tomore clean-cut separation, i.e. to improved product quality.

An impression of the advantages that modern packing has over conventional sieve platescan be obtained from Table 12.2. The example taken was the vacuum rectification of a mix-ture with a thermally unstable bottoms product. The principle of the heat pump was appliedby compressing the overhead vapour to heat the bottoms. There is no mistaking the consid-erable improvement that was achieved in the economics of the process by the installation ofpacking.



Table 12.1. Characteristics for planning new columns and retrofitting existing columns with low-pressure-drop packing

V =

ntl

An

H,

r ' '

Ar

dsi

Q i

F,

A

= const.

< nt2

;

< H2

< r 2

< d S 2

< Q 2

= F2

e =

ntint]

An

r i <

Ar'

dSidSi-d-d

F, :

B

(Ap/nt)i -

- const.

< nt2

> ntl (v)

; > An|(v)

< H 2

= r2

C r i (v)

1 - 0

= ds2

< dSi (v)

<S(v)= F2

< (Ap/n t)2

s = const.

n t l = nt2

nti < ntl (v)

An; = 0

H, < H 2TT ^ - IT / \

Hi < H, (Vjri < r2

ri > ri (v)

Ar' > Ar'(v)

dSi < ds2

dSi > dSi (v)

Q, < Q 2

Qi > Qi W

Fi = F2

c

V =

ntl <

An;

const.

= nt2:n t , (v)

= 0

Hi < H2

H, < H, (v)

ri <

ri >

Ar' :

ds, -dsi -

P-P-

\/ »

Fi >

D

r2

r,(v)

> Ar'(v)

: d s 2

> dSi (v)

>S(v)F2

Ap/n t = const.

ntl = nt2

nti < ntl(v)

An; = 0

Hi < H2

H, < H, (v)

ri = r2

r, < r, (v)

Ar' = 0

dSi = ds2

dSi < dsl (v)

Q, > Q 2

Qi < Qi(v)

Fi > F 2

E

Table 12.2. Economics of applying the principle of the heat pump. Valid for the separation of amixture consisting of equal parts by weight of ethylbenzene and styrene fed at a rate of 30tons/hour into the following columns:(a) fitted with perforated plates(b) packed with Mellapak 250 Y.Based on the following prices:electricity 0.06 SFr/kWh, steam 12 SFr/ton, cooling water 0.6 SFr/kWh (SFr = Swiss Francs).With the courtesy of Sulzer AG, Winterthur

Operating data Sieve tray Mellapak

Pressure at head of column [mbar]

Temperature at head of column [°C]

Number of theoretical stages

Reflux ratio

Pressure at foot of column [mbar]

Temperature at foot of column [°C]

Reboiler temp, difference [°C]

Compression ratio

Compressor costs

Energy savings [%]

67

58

54

8.25

310

106

15

9.9

100

30

67

58

54

6.5

127

81

15

4.5

60

60



12.3 Advantages of packing in steam rectification

Even if a vacuum is applied, it is not always possible to separate unstable mixtures at tem-peratures that are low enough to avoid thermal decomposition. This applies particularly tomixtures of fatty acids, and an example is the separation of palmitic and stearic acids inindustrial-scale rectification columns equipped with 20-40 plates. If the pressure at the headof the column is 7 mbar, pressure drops of 43-85 mbar occur under normal operating condi-tions and are responsible for boiling points of between 267 °C and 279 °C.

In separation tasks of this nature, it is absolutely essential to restrict the residence time ofthe products and the pressure drop to the minimum possible values. Even if this demand ismet and even if the vacuum applied is justifiable from the engineering and economicaspects, substances that are unstable to heat cannot always be separated under conditionsthat preclude thermal decomposition. Thermally unstable substances that are encountered inthermal separation practice include higher fatty acids, unsaturated and high-molecular-weightorganic compounds, and essential oils. They can be separated under very favourable condi-tions by rectifying with an inert vapour as carrier. Steam is mostly used for this purpose,because many of the organic substances that have to be separated in practice are insoluble inwater. An example of the reduction in temperature that can be achieved by this means arisesin the distillation of palmitic acid. Thus, if the mass fraction of steam is about 15%, theboiling point at a pressure of 13.3 mbar can be lowered by about 19°C; and at a pressure of133 mbar, by about 36 °C.

Rectification with an inert vapour under vacuum is also resorted to for crude oils thatmay undergo thermal decomposition at elevated temperatures. For instance, the temperatureabove which Near East crudes may thermally decompose is about 390 °C.

The advantages of steam or inert vapour rectification are offset by the high steam con-sumption and the extent to which the column cross-section must be enlarged to accommo-date the steam fraction additionally imposed. This is evident from the following theoreticalconsiderations.

Let a mixture's instability to heat entail that the temperature at a given theoretical stage /,as counted from the head of the column, must not exceed a given value th Then the equilib-rium pressure corresponding to this temperature th i.e. the sum of the partial pressures ofthe mixture's components c = 1 to c = n in the product vapour with a molar flow rate V, isgiven by (cf. Fig. 12.5):

c = n

Pv,i = 2 Pa = const (12-40)c = l

This equilibrium pressure can be attained and maintained at a constant value if the molarflow rate of steam S is correspondingly large. If the vapour pressure curves for the individ-ual components Pc = f(t) are known, the pressures at the boiling points of the pure compo-nents Pi,i,Pc,i,Pn,i can be obtained as is indicated by the qualitative diagram presented in Fig.12.6. Hence, if the composition of the liquid product phase Xjti,xcj,xn>i leaving the /'th theo-retical stage is given, the corresponding partial vapour pressures can be calculated from

Pa = la xa Pa (12-41)


12.3 Advantages of packing in steam rectification

pT=const.

Pressure p

303

Stage 1

Stage j

Stage nt

Fig. 12.5. Scheme for describing theproduct temperature within the column insteam rectification

S ' V Lm

PJ. tj

mS.V [

Top

Ap

Botto

p B = f ( p T ( n t l A p / n t )

t B = f ( S / V , p p )

Top

Fig. 12.6. Qualitative boilingpressure curves in steam rectification

Pi

PHJ Pvj'Pcj

H V

(xc)Stage j

Boiling temperatureJ

A simplifying assumption that can be made for mixtures that obey Raoult's law is that theactivity coefficient y is unity. It is valid for most hydrocarbon systems subjected to steam rec-tification, and considerably simplifies the calculation of phase equilibria.

The value thus determined for the equilibrium pressure pv,i of the product vapour at atotal pressure pt above the f th theoretical stage allows the partial pressure of the steam atthis stage to be determined as a function of the pressure pT at the top of the column and thepressure drop per theoretical stage Ap/nt for the type of packing concerned under the givenloading conditions, i.e.



Ps,i = Pi ~ Pv,i =PT+ (i - 1) — - Pv,i (12-42)\ fi I

The total vapour flow rate is the sum of the flow rate of steam and that of the productvapour, i.e.

Vtot = S + V (12-43)

If it assumed that the modified Dalton's law of partial pressures applies, the molar frac-tion of steam will be given by Eqn (12-44); and that of the product vapour, by Eqn (12-45):

<12-44>

Hence, if the molar flow rate of product vapour V is known, the molar flow rate of steamcan be calculated from the partial vapour pressures pSi and pVi, i. e.

S = V^~ (12-46)Pv.t

If the individual components each have roughly the same molar vaporization enthalpy,the molar flow rate V of the product vapour and thus its molar fraction yv in the totalvapour mixture must be constants, i.e.

(yv) v = const = const (12-47)

In this case, the partial pressure of the product vapour can be determined at any giventheoretical stage. Thus,

Pv,t = yvPt = yvAp (12-48)

Consequently, the phase equilibrium temperature corresponding to the composition xc>i inthe liquid phase at that particular stage can be obtained.

Now suppose that the thermal instability of the substances to be separated entails that acertain upper operating temperature limit may not be exceeded, e. g. the temperature tt laiddown for the fth stage. In this case, the partial pressure pVi exerted by the molar volumeabove the f th stage must remain constant; its relationship to the total pressure is given by

Pi = Ps,i + Pv.i (12-49)

The partial pressure of the steam pSi can be regulated by means of the steam molar flowrate S.


12.3 Advantages of packing in steam rectification 305

The total pressure pt at the /'th theoretical stage is fixed by the pressure pT at the head ofthe column and the pressure drop per theoretical stage Ap/nt for the packing concerned(cf. Fig. 12.5). Thus,

(12-50)

The partial pressure of the product vapour pVi can be derived by combining Eqns (12-49)and (12-50). Thus,

Pv,i=Pr+(i-l) — -Ps,i (12-51)

The following relationship must apply for the partial pressure of the steam:

S(12-52)

It therefore follows that the volume flow rate of steam required per unit flow rate ofproduct vapour is given by

The condition for steam rectification must be adhered to, i. e.

(Pv,i)ti = const. = const. (12-54)

Consequently, the lower the pressure drop per theoretical stage Aplnt for the packing,the less the flow rate S of steam required.

The lowest steam flow rate occurs in an isobaric column, i.e. for Ap/nt = 0, in whichcase the following applies:

% - = -£ZL-l (12-55)y Pv.t

If Ap/nt > 0, Siso must be increased by a corresponding amount AS. Since AS is directlyproportional to Ap/nt, the pressure drop in an actual column must be compensated byadmitting steam at a higher flow rate. This additional rate of steam is given by

It follows from this equation that the lower the pressure drop per theoretical stage, theless the amount of steam that has to be admitted in steam rectification.



The ratio of the cross-sectional areas of steam rectification columns, the one with Aplnt

= 0 and the other with Ap/nt > 0, is equal to the ratio of the squares of their diametersdSyiso and ds. The temperature is the same in both cases, and the density of the steam is thusdirectly proportional to the pressure. In other words, Eqn (12-57) applies for steam rectifica-tion with Ap/nt > 0; and Eqn (12-58), for Ap/nt = 0:

(Qs.dtt = const. ~ Ps,i

\Qs,i,iso)ti = const. ~ PS,i,iso

(12-57)

(12-58)

Therefore, the increase in the column diameter necessitated by the pressure drop withinthe bed of packing can be described by

"•S, ISO

ds - ds,iso)2

Ps,i (12-59)

PS,i,is

Another fact to be taken into consideration is that the ratio of the steam partial pressurein isobaric rectification to that in nonisobaric is equal to the corresponding ratio of theirmolar flow rates, i.e.

(12-60)

Rearranging Eqn (12-59) to solve for ds and substituting from Eqn (12-60) yields

d5 = ds>iso + Ads = dS}iso + d5>iso \ —lhH£- 7 — = ds>iso 1 + \ / —T—V Ps,i Siso V S

(12-61)

Substituting from Eqns (12-52) and (12-53) then gives

\/ „ T> S'lS° \l ps. l

Hf(12-62)

This equation states that the amount Ads, by which the diameter dStiso of an isobaric recti-fication column has to be increased, is directly proportional to the square root of the pres-sure drop per theoretical stage Aplnt, provided that the vapour load is constant in thecolumn. It also clearly reveals the advantages of replacing existing column internals by low-pressure-drop packing. Consider, for instance, the case in which the pressure drop per theo-retical stage of the existing internals is greater than that of the packing intended as a re-placement, i.e.

nt /2(12-63)



According to the previous remarks, this replacement would result in a savings of AS insteam. Eqn (12-64) would then apply for the original internals 2; and Eqn (12-65), for thereplacement packing 1:

P T + d - l ) ( ^

V Pvj(12-64)

. p T + ( i - l ) - ^ -pVJ

^ = ^ d2-65)

The molar flow rate of steam, expressed in terms of the molar flow rate of productvapour, can then be obtained by substracting Eqn (12-64) from Eqn (12-65), i. e.

In other words, the savings ASIV in the molar flow rate of steam is directly proportionalto the amount (k -1), by which the pressure drop per theoretical stage of the replacementpacking 1 is less than that for the existing internals 2.

It can be easily verified by dividing Eqn (12-65) by Eqn (12-66) that the correspondingrelative savings in steam is given by

AS S2-S, k-1= —r = (12-67)

2̂ S2 ,, , PT-PVJ

If the total vapour load is kept constant in both cases, the reduction in column diameterthat can be achieved by substituting the packing 1 for the existing internals 2 is given by

as2

A reduction in capital investment entails that the costs per unit column volume (cf. Chap-ter 11) for Column 7, as expressed by Eqn (12-69), are also less than those for Column 2, asexpressed by Eqn (12-70):

= (dS2 -Adsf

df2

CS2 = vV2 C2 (12-70)

where vV2 is the column volume per unit of separation efficiency for Column 2,C2 is the cost per unit volume (m3) for Column 2, andC\ is the cost per unit volume (m3) for Column 1.



Packing 1 is considered to be more economical only if the total costs CT>1, i. e. capital andrunning costs, are less than those for the original internals 2. It is quite feasible that, if thecosts for the shell and bed of packing are very high, Column 1 may involve the higher acqui-sition costs, despite the smaller diameter ds>1, yet the total costs may still be less, i.e. CTJ <CT,2- However, if the costs for the shell and packing are extremely high, i.e. Cj ^> C2, CTJmay exceed CTa, even if dsJ < dSy2-

A flow chart for an oil refinery is shown in Fig. 12.7 to illustrate steam rectification.

WaterHigh-pressure steam

Vacuumcolumn /

Vacuum station

Saturated steamHeater

Fig. 12.7. Crude oil inert steam rectification plant

Fuel ? oil

The five valve-ballast plates in the distillation zone of a FCC fractionating column werereplaced by a bed of Montz Packing Bl/250.60 of 2.6 m total height. A schematic diagramof the upper section of the column is shown in Fig. 12.8. As a result, the separation effi-ciency was increased from 3 to 4.5 theoretical stages with an associated improvement in theproduct quality. The packing was arranged in parallel layers, as is shown in Fig. 12.9.Utmost care in stacking the packing is essential in order to maintain the efficiency through-out the height of the bed.

Data characteristic of a plant for the distillation of fatty acids before and after changingover from plates to packing are presented in Table 12.3. The advantages achieved from the



change-over are immediately evident: the reduction in the pressure drop per theoretical

stage allowed a 40 % increase in capacity, a reduction of 25 °C in the temperature at the foot

of the column, and 15 % savings in energy. In addition, the column could be operated

without carrier steam.

Fig. 12.8. Example for retrofitting aFCC fractionating column by substitut-ing Montz packing for five valve-ballastplates in order to improve separation

I I I I I I I I I I

Liquiddistributor

Distillation

zone

Liquidcollector

Table 12.3. Data relating to the rectification of coconut oil fatty acid in a column formerly fittedwith bubble-cap plates and after retrofitting with Mellapak packing.With the courtesy of Sulzer AG, Winterthur

Characteristic data Trays Mellapak

Column diameter ds [m]

Effective column height H [m]

Pressure at head of column pr [mbar]

Pressure at foot of column pB [mbar]

Temperature at head of column tD [°C]

Temperature at foot of column tB [°C]

No. of theoretical stages nt

Capacity increase AF [%]

Carrier steam S [%]

Energy savings AQ/Q [%]

90

255

26

10

2.5

18.6

5

173

23

230

32

40

15



Fig. 12.9. Montz Pak Bl-250 packing elements for a column of 4-m diameter. The beds of packingwere charged through manholes

12.4 Improvement in product purity caused by restricting the pressure drop inbeds of packing

The total pressure drop between the head and the foot of the column will obviously behigh in rectification processes that involve a large number of theoretical stages. Hence, if itmay not exceed a given value owing to the product or the process conditions, undesirablelimits may be imposed on the separation efficiency and thus on the purity of the product inplate columns. Examples of the limits that may be set by the process conditions arise in theseparation of thermally unstable mixtures; in coupled columns with an integrated heatingsystem, e.g. if the heat content of the bottoms in the one column is utilized for the indirectcondensation of the overhead product in the other; or if the overhead vapour in the onecolumn is used to heat the bottoms in another that operates under reduced pressure.

In cases of this nature, more theoretical stages can be realized by substituting low-pressure-drop packing for the plates (trays), i.e. nuP > ntJ. This is evident from the qualita-tive diagram in Fig. 12.10. According to this, the pressure drop must be the same in bothcases, i. e.

Ap = f-^-1 ntJ = \^2-\ nttP = const. (12-71)nt IT \ nt JP

In other words, the ratio of the number of theoretical stages to the specific pressure dropin the packed column {Eqn (12-72)} is greater than that in the plate column {Eqn (12-73)}:


12.4 Improvement in product purity caused by restricting the pressure drop in beds of packing 311

u v = c o n s t , a n d A p = c o n s t . — n t p > n t T — - ( x D P - x B p ) > ( x D

X D , T

n t , I

XB,I

1

Ap= const.

X D , P

M1888

XB,P

Trays Packing Vapour load uv

Fig. 12.10. Schematic diagram demonstrating the advantages of packing over plates for improvingproduct quality in separation processes with constant total pressure drop

(12-72)

rAp =

, nt ITnt,p = 7——r— nuT

AEAnt Jp

AE]nt JT

p = const.AE)

nt jp

(12-73)

Thus the degree of separation is also increased.A measure for the fraction of high boilers AB remaining in the overhead product D is

*B _ _• ^ l *>D)xB = const., Ap = const. (12-74)

It can be expressed in the following form:

(12-75)

This function can be evaluated in the light of the above remarks, to obtain the minimumnumber of theoretical stages from Eqn (1-60). Information can thus be derived on theimprovement in product quality that can be achieved if the plates are replaced by packing.

Likewise, the fraction of low boilers AD remaining in the bottoms B is given by

BA — (XB)XD = const., Ap = const. (12-76)



and information on the improvement in the quality of the bottoms can be derived, by ana-logy, from the following function:

(12-77)

If the overhead and bottom products are of very high purity, the term xD(l - xB) tendstowards unity. In other words, if the relative volatility is given, the term xB(l - x^) decidesthe minimum number of theoretical stages nUmin. This is clearly demonstrated in Fig. 12.11,in which xB(l - xD) is shown as a function of nt and r^p with a as parameter. The followinglinear relationships are obtained by plotting on semilogarithmic paper:

- xD) xB •1

(12-78)

Thus if xB = const., xD is given by

XD ~ 1 -

or, if xD = const., xB is given by

xB «

xB a '

1 11 -xD an, + 1

(12-79)

(12-80)

o= 3

Ratio of specif ic pressure drops r A p ( n t I = 5 0 )

1.5 2 2.5 3 3.5 4

10

e 10'1

i 10-2s 10-3

ioJ

10"

\

\

s

\\

• \

\

s

N

\

\

\

\

N"i

\ \1%,

50 100 150Number of theoretical stages nt

200

Fig. 12.11. The advantage of low-pressure-drop packing in improving product quality by the schemeillustrated in Fig. 12.10.


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