SuccessfullySpecify Three-Phase Separators Hereis a stepwise procedure for designing
liquid/Iiquid/vapor separutors.
WayneD.Monnery andWilliam Y.Svrcek, University of Calgary
t is often necessaryto separatetwo immiscible liquids, the light and heavy phases,and a vapor. A typical example in petroleum refining is the separationofwater, and a hydrocarbon liquid and vapor. Little has been published on three-phase (liquid/liquid/vapor) separarion, with most information available only in corporate design files. This article attempts to alleviate this situation by covering the basicsofthree-phase separator design. The authors provide a Step-by-Step procedure and worked out examples. Further, the examples offer guidanceon making assumptions for the calculations.
section calm to promote the separation. There are different variations of horizontal three-phasevapor-liquid separators. The liquid separation section is usually a variationof a deviceto provide interface level control, which may include a boot or a weir. A boot typically is specifiedwhen the volume of heavy liquid is not substantial(< l5-207o of total liquid by weight), while a weir is used when the volume is substantial. Thesehorizontal separatorsare illustrated in Figure 2. The bucket-and-weir type design is used when interface level control may be difficult, such as with heavy oils or when large amounts of an emulsionor a paraffin are present(1).
Selectingthree.phareseparatore
$tokos'lawappliee
As with two-phase designs, threephaseunits can be either vertical or horizontal, althoughthey typically are horizontal (seeFigures l and2). The vertical orientation.Figure 1, is only used if there is a large amount of vapor to be separatedfrom a small amount of the light and heavy liquid (< l0-207o by weight). Unfortunately, there are no simple rules for separator selection. Sometimes,both configurationsshould be evaluatedto decide which is more economical. Further, the available plot space(footprint) may be a factor. The design of three-phaseseparators is similar to their two-phase counterparts, except that the liquid section differs. For the vertical type, a baffle commonly keeps the liquid separation
Separatinga vapor from a light liquid (two-phaseseparation)has been covered in a previous article (2) and will not be discussedhere. However, all necessary information for performing this part of the calculation is provided here. The following discussioncoversthe separation of light and heavy liquids. The flow of rising light droplets in the heavy liquid phase or settling heavy dropletsin the light liquid phaseis con- , sidered laminar and is soverned bv Stokes'law:
rt -
v T -
1,488g,fi(p,- pr) 18F
(l)
where 1,488convertsviscosityof the
pRoGREss. SEpTEMBER CHEMTcAL ENGTNEERTNG rgga . 29
MULTIPHASE FLOW
For horizontal separators with a is more diffigiven diameter,the heights of the light cult (requires and heavy liquids are assumedso that more time) to setthe cross-sectionalarea can be calcutle the droplets lated. With the vapor disengagement out of the continWire mesh area set by guidelines, the lengths uous phase with required by holdup requirements and the greater visvapor/liquid separationare calculated. cosity, since U. is + D Feed Then, with the assumedheights of the lower. Practically nozzle 1 -i n . light and heavy liquids and calculated speaking, U, is vent M a x i m u m values of settling velocities, the set* typically limited liquid tling times are calculated. in calculations H"ls"rg" I level The actual residence times for the to 10 in./min light and heavy liquids are subsemaximum. Baffle quently calculated and comparedwith sepFor vefiical -* Holdup A ^.[the required settling times. as in the arators,the diameLishtliq. Lioht r' vertical case. If the residence times ter required for tiq"uiO +r'-\ Baffleto provide are not greater than the required setvapor disengagenozzle l H ' c a l m i n gz o n ei s times, then either the diameter tling recommended is calculated ment lnterface should be increased or. for a given as in our previous SectionA-A heavyliquid Hrl diameter, the length should be article (2). In sizincreased(liquid separationis coning a separator,the trolling). In the subsequentdesign heightsof the light I procedures, the laner approach is and heavy liquids Heavy used, along with the procedures disand are assumed, liquidnozzle cussed in our previous paper for the settling velocivapor/liquid separationr2). ties and settling I Figure l.Vertical three-phase separalors are used with high The following desi-rn procedures times are then vapor loadings and heuristics are a result of a review calculated. of literature sources and accepted The residencetimes of the light and continuous phasefrom lb/(ft)(s) to cP. guidelines. design industrial heavy liquids are determinednext. For Simplifying Eq. 1 and converting Horizontal design proceduresare prethe liquids to separate,the residence the units of the terminal settling sented for the four separator types time of the light liquid must be greater velocity to in./min from fUs results in: shown in Figure l. The horizontal for the heavy than the time required design procedures incorporate optidroplets to settle out of the light liquid 2.0615l xl}-s|f,QH-pL) mizing the diameter and length by phase; and the residence time of the ,r rr = T minimizing the approximate weight heavy liquid must be greater than the of the shell and heads.To add a degree time required for the light liquid of conservatismto the design,the vol(2) droplets to rise out of the heavy liquid = ume available in the headsis ignored. phase.Ifthese conditionsarenot satiswhereDo is in microns(1 micron 6 liquid fied, then 3.28084x 10 feet) andU7,in./min. separationis conEq.2 maybe rewrittenas: trolling and the vessel diameter kt(Pu - Pr) rt (3) must be increased. u r=---T Holdup time for liquids must be where addedto residence ... xl\-sfi . 121 ks=2.0615t oi iausti, time. The height 89 or causiic of the vertical Values of ft, are given for some sys0is3' 89 Furfural 89 0.i63 Water ketone Methylethyl three-phase sepatems in Table 1. 0.163 8g Water sec-Butyl alcohol rator is calculated From Eqs. 1-3, it can be seenthat 89 0.163 Methylisobutylketone Water in the same manthe settling velocity of a droplet is 0.163 89 Water Nonylalcohol ner as for-the twoinverselyproportional to the viscosiphasecase. ty of the continuousphase.Hence, it Vapor nozzle
i I
I t
= = ! E
:
{
I
il
_T J
30 .
1994. SEpTEMBER
pRocREss ENGTNEERTNG CHEMIcAL
3. Interfacecontrol with weir Feed inlet
l,v Min.12in. Min.12in.
Heavy liquid outlet
Light liquid outlet
* l N , *l L ',l^n. * * u,n.l 2. InterJacecontrol with boot
NI*-
l
4. Bucketand weir Vapor outlet
Vapor outlet
Lightliquidholdu/surge
Heavy liquid outlet -t
|
Heavyliquid outlet
I
L,
I
-t
Light liquid outlet -t
-l
lLzlLslL4l
Note:N= 112d7,1+6in. drv= Nozzledia'
t - L -
I Figure 2. Basic designs of horizontal three-phase separators,
Vertical design.procedur€ Refer to Figure 1 for dimensions: 1. Calculate the verlical terminal vapor velocity: Pv U- = ylPt rtt2 Pv
(4)
Calculate the K value, using one of the methods in Thble 2 and set Uu = A.l5Ur for a conservativedesign. 2. Calculate the vapor volumetric flow rate:
WV Qv=
3,600pu
(s)
3. Calculate the vessel internal diameter,Dur:
140-,\"' D""=l# | \nu, )
(6)
If there is a mist eliminator, add 3-6 in. Io D, to accommodatea support ring and round up to the next 6-in. increment to obtain D; if there is no mist eliminator,D = Dur. 4. Calculate the setting velocity of the heavy liquid out of the light liquid using Stokes'law (the maximum is 10 in./min): kt(Pn - Pr) vr tH L -ltr
0\
where ft, is obtained from Table 1 or is calculated(seeEq. 3).
5. Similarly, calculate the rising velocity of the light liquid out of the heavy liquid phaseusing Stokes' law: ur ru . J-- k t ( P r - P t ) ILH
(8)
6. Calculate the light and heavy liquid volumetric flow rutes, Q* and QnL: o w-r .L-_
w-"LL
(9)
60pL
-Wrt n unr- 60pa
(10)
7. Assume Hr = I ft (minimum) and calculate the settling time for the
. sEprEMBERrggr . 31 CHEMTCALENGTNEERTNGpRocREss
MULTIPHASE
(0- .0rl\
o,in{ ^ =(t.+aeal\/oo a, r, lI--T-/\----G-/ ) Equation13
- 0.6973=2.14ftJs Ur =0' 313 53.95 I EquationEl
-*
Qv=
= : = -=
415.000lb/h
=165.32ft'ls
3.600s/hx 0.69731Vff
lEquation E2
^ 1TVT4STFIs - r0.13ft --irISHs r-\o= V
I
lEquation
2
ou -
E3
16.5000lb/h = 5.10ft'lmin 60 minthx 53.95lbtftt
a EquationE4
"=,{*t#d)
vnr=ffi
heavy liquid droplets to settle through this distance(12 is a conversionfactor for ft to in.):
-
l2H,
----------=
(11)
U,,
8. Assume Hn = | ft (minimum) and calculate the settling time for the light liquid droplets to rise through this distance: t ,LH -
L zH , ---:
(1 2 )
TI uLH
9. If there is a baffle Plate, calculate the area: a. Calculate(P. - P). b. Assume 11* (use 9 in. as a minimum) and calculate Ht+ H^. c. Use Figure 3 to obtain G. d. CalculateAr: S e eE q . ( l 3 ) i n t h eb o x . e. Assume Wo = 4 in. f. Calculate WD/D.
32,
= 0.35ft'lmin
lEquation E5
whereD"is inft. = 3.28084 x 10{ft Note:1 micron
t ,HL_
l,3o0lb/h
g. Use Table 3 to determineAo lA. h. CalculateA= (nl4)D2. i. Calculate Ar. j. Selectthe larger value ofAr. k. Calculate the area of the baffle plate - settling area for the light liquid;A.-A-Ao. 10. Calculate the residence time of each phasebased on the volumes occupied by the light and heavY phases:
s*=w
(I4a)
- HuAu A vHL-
(14b)
H.=+
If eLL < tu, or Iur 1 trr, \tctease the diameter and repeat the procedure from Step 7 (liquid separationis controlling). Note that An= A. 11. Calculate the height of the light liquid above the outlet (holdup
( 1s )
Check this r-alueu'ith that assumed in Step 9b to ensurethat the assumed value is reasonable. ft- surge is not specified, calculate the surge height basedon surgetime:
(eu* eo)r,
Hs=\---TL
Qrt
. CHEMICALENGINEERINGPRoGRESS sEprEMBERlggd
basedon the required holduP
(16)
The minimum is 6 in. 12. Calculate the vessel height using the guidelines: He= 6 in. minimum. H aio= h d. + greater of (2 ft or /1t + 0.5 f0. Ho=0.5D or a minimum of: 3 6 i n . + V z d r( w i t h o u t m i s t eliminator), or 24 in. + t/zd* lwith mist eliminator):
10,000
24in.
c
o_ o
F c
9,000
-o G
8,000
G
r.i
High liquid levelaboveinterface /= 4.0184a8 . = _ J . 9 t 6 4tt = -i.801705 = :l 1.i5348 pr- pu,lblft3 t. \, to H/D+ = HID = \/.\r = 0.00153756 ' = 16.787101 = 1.299201 : - i.2.923932 . = 1.1.353518 '= 11.844824 - = -36.999376 : = 10.529572 : = 9.892851
I Figure 3. G is found from the downconterallowableflow.
the time lbr the light liquid to rise out of the heavy liquid phase: trH=(12)(1.0) ll.lJ=6.9min 9. Calculate
2 . C a l c u l a t et h e r a p o r '\ r r l u r r - t r i " iili ti-:,r-r' :'1:ri- i1f-;1: r _ r _ i l , ) < r l n t l l l _ i l ) S flow rate,seeEq. El in the bor. 3. Calculatethe vesselinner diamlL.it' . . \ : > . r 1 .H eter,seeEq. E3 in the box. ' t -. = I ) i n . .H r + H n = 2 4 = Hn+ H, + HR+ O^* Ufii n, = 10.5fi. Use 1J i n . L ' . : r g F r , r L r r-e1 .G = 9 . 8 0 0g p h / f t z . .a - jr 4 . C a l c u l a tl h e c : e t t l i n \ge l o c i l r, r l {. = _ c a l i i t ' r r 6m 0 i n i h )( 5 . 1 0 - o.-1-i the heavyliquid out of the iight liqLrid r ii' 9..\00gph/iir = 0.25 ft2 ..\...ll ti ll It' a mist eliminatorpad is used, p h a s e .U s i n g T a b l e l , f t s = 0 . 1 6 3 = J jp.. -,-riionalheightis addedas shownin Then: \ \ . , D= - 1 l r 1xl 1 0 . 5=) 0 . 0 3 1 7 : - - l r eI . Um = 0.163(62.11 53.95)/0.630 = 2 .1 1 i n . / m i n E x a m p l e1 5. Calculatethe settlingvelocitl of Sizea verticalseparatorwith a baf'the light liquid out of the heavyliquicl ': :lltc and wire-meshmist eliminaphase: : i,.r separatethe mixture given in U r a = 0 . 1 6 3 ( 6 2 . 1-1 5 3 . 9 5 ) / 0 . 7 6 1 = l.l4 tn.lmin . -,rleJ. The operatingpressureis 165 '..,:, rrild it is necessaryto have a 6. Calculatethe light and hearr Jr'(rcarbon liquid holduptime of 25 Iiquid volumetric flow rates. see Eq. :: and a surgetime of only 5 min. E4 and E5 in the box. 1oa,r= Ar+A, ft3ls 1. Calculatethe vertical terminal 7 . A s s u m eH r = 1 f t a n d c a l c u l a t e - .iitr'. Using Table 2, calculateK the tirne fbr the heavy liquid to sertle Q , -- vr ,u : . 60 - ' i t h e Y o r k D e m i s t e re q r r r t i o n s . out of the light liquid phase: Tt:2 ,fF; . . . E q . E 1 i n t h eb o x . 4u, t n , . =( 1 2 )( 1 . 0 )l 2 . l 1 = 5 . 7m i n , : n JL ' 1= 0 . 7 5x 2 . 1 4= 2 . 0 5f t l s . 8. AssumeHn = 1 fi and calculate :.luivalent expressions, suchasH',/D
^=#6
. SEPTEMBER CHEMICAL ENGINEERING PROGRESS 1994.
33
MULTIPHASE FLOW
. Using Table 3, AD/A = 0.0095: 1= (nl4)(10.5 ft)2 = 86.59 ftz A, = (0.0095)(86.59ft2)= g.g21r2 . Use A, = 0.82 ft2. A, = 86.59- 0.82 = 85.11 ft2 10. Calculate the residencetime of eachphase: 0r. = (1.0 fI) (85.77 112115.10 ft3lmin = 16.8min lnr = (1.0 f0 (86.59 ftz)10.35 ft3lmin = 241.4 min 11. Calculate the height of the light liquid above the outlet, based on holdup: tlo = (5.10 ft3imin) (25 min)/85.77 ftz = 1.5 ft /1s = (5.10 + 0.35)(ft3/min)(5 min)i86.59 ft2 = 0.31 ft Use I/r = 0.5 ft. 12. Calculate d, according to Table 5: )"= Qrl(Qr + Q) = (5.10 + 0 . 3 5 Y ( 5 . 1 0+ 0 . 3 5 + 1 6 5 . 3 2x 6 0 ) = 0.0006 Use Eq. E6 (see box) to calculate Pr
drum F Fuelgasknock-out fuelgaslinebetween NLt andhighlevelshutdown ZOft.ilug in theincoming drum G.FlareKnock-out 20to 30minto Hll factors(optionall: Multiply bythefollowing Personnel
Factor
Instrumentation
Factor
Experienced
1.0
WellInstrumented
1.0
Trained
1.2
Instrumented Standard
1.2
Inexperienced
1.5
PoorlvInstrumented
1.5
p,=##
rbtft3 x 53.es . +ffi x62.It= 54.55
l EquationE6
=r.rrr, )'''
1994. SEpTEMBER
Horizontaldesign procedure: no boot or weir 1. Calculate the vapor volumetric flow rate, Qu, using Eq. 5.
I EquationE7
34 .
pu = pLX+ pll - l.) = (54.55) (0.0006) + (0.6913) (l - 0.0006) = 0.730 Qu = 165.32+ (5.10 + 0.35)/60= 165.4I ft3/s Use Eq. E7 (seebox) to calculated* dN > 2l in.; use dt = 24 in. Calculate Ho'. Ho = 0.5 (10.5)= 5.25ft or Ho = 24 + 2412= 36 in. = 3.0 ft (minimum) Use 11, = 5.5 ft. From Figure 1, I1t = I ft and s = 0.5 ft. Calculate Ilur: Hsw='/,(2.0 f0 + 2 ft = 3 ft Set 11, = 0.5 ft. Final dimensions: D = 10.5 ft, HH= I.0 ft^ HL = 1.0 ft, Hn= 1.5 fr, Ho = 0.5 ft. HB.,= 3.0 ft, andHo = 5.5 ft. Add 1.5ft for the mist eliminator. Hr= l4'0 ft HID=14.0i10.5=1.3 Add 2 ft to H, (Hp = 2.0 ft, Ho = 7.0 f0 so that HlD = 1.52 (HlD shouldbe in the rangeof 1.5 to 6.0).
pRocREss ENGTNEERTNG CHEMTCAL
2. Calculate the light and heavy liquid volumetric flow rates, Q' and using Eqs. 9 and 10. O711, 3. Calculate the vertical terminal velocity, Ur, using Eq. 4. (selecta K r alue from Table 2) and set Uu = 0.75Ur. 4. Select holdup and surge times t-romTable 6 and calculate the holdup and surgevolumes,V, atd Vr, (unless surgeis otherwisespecified,suchas a >lus volume): Vo= To Q,
(18)
Vs=TsQr
(19)
5. Obtain an UD from Table 7 and initially calculate the diameter accordingto:
(20)
Calculate the total cross-sectional ilea:
A _ TED' 4
(2r)
6. Set the vapor space height, 11, , rhe larger of 0.2D or 2 ft; I ft if :.-,ereis no mist eliminator. Using 1 ,/D in Table 3, obtainAr/A, andcal--llateAu. 7. Set the heightsof the heavy and ;ht liquids, Hrrand Hr, 8. Find (AnL+ AL)lAr, using (I1", - fl -tlD inTable 3,andcalculateA* 9. Calculatethe minimum length to -- -,rmmodatethe liquid holdup/surge:
V, +V,
r _
L _
tr-Au_ (our*,4rr)
(22)
Qrr=
I = H,./L't
Uw= Qr/Av
()L\
Q,,
'=
-"{
trrQ*
tntQ,
e*'(h-Av-o*)
12. Calculatethe minimum length required for vaporiliquid separation: Lum= UvlQ
(2s)
13. If L 1 Lr,,,r, then set L = Lr,* (here, vapor/liquid separation controls). This simply results in some extra holdup and residencetime. If I 11 Lr,*, then increase Hu and recalculate Au, and repeat, starting from Step 9. If L > L*n, the design is acceptable for vapor/liquid separation. If L )) Lr,,.,(liquid holdup controls). I can onlr,be reducedand l.rrr. increasedif H,, is reduced. F1, ma1' only be reducedif it is _ureater than the minimum specifiedin Step 6. (With reduced 11* recalculateAu and repeat the procedurefrom Step9.) Note: For this and other calculations, "much greater than" (>>) and "much less than" (<<) mean a variance of greater than 20Vo. 14. Calculate the settling velocities of the heavy liquid out of the light liquid phaseand the light liquid out of the heavyliquid phase,U". and U.o, using Eqs. 7 and 8 (find ft, from Thble 1). 15. Calculatethe settling times of the heavy liquid out of the light phase and the light liquid out of the heavy phase: tur= 12 (D - Hv- HH)IUHL (26)
(21)
16. Calculate the residencetimes of the light and heavy liquids:
Q3)
Ca]culate the actual vapor
1 ?| q r
/
velocity:
0ur= AorLlQu, | [.
.
17.If gHL< tLHor 0,-, < t", then increasethe vessellength (liquid separationcontrols):
tro= 12 HHL/ULH 10. Calculate the liquid dropout -:a:
I\ A ', - A , -. A 1u , l\ L '
(28)
(30) 18. CalculateUD.If UD << 1.5, decreaseD (unlessit is alreadyat its minimum), and if UD >> 6.0 then increaseD; repeatfrom Step 5. 19. Calculate the thickness of the shell and headsaccording to Table 8. 20. Calculate surface area of the shell and headsaccordingto Table 8. 21.Calculate t h e a p p r o x i m a tvee s sel weight accordingto Table 8. 22. Increaseor decreasethe vessel diameter by 6-in. increments and repeat the calculations :until the UD ratio ran-eesfrom 1.5-6.0. 23. Using the optimum vesselsize (minimum wei-eht).calculatethe normal and high liquid levels: Hau= D - H,
( 31 )
Anrr= (Am+ Arr) + Vo/L
(32)
Obtain 11r.. using Table 3 with the value of A*ro/Ar.
Horizontaldesign procedure: heavy liquid boot 1. Calculate the vapor volumetric flow rate, Q, using Eq. 5. 2. Calcrilate the light and heavy liquid volumetric flow rates, Q* and Q n r , p e rE q s . 9 a n d 1 0 . 3. Calculate the vertical terminal velocity, Ur, using Eq. 4 (the K value comes from Table 2) and set Uu = 0.15 Ur. 4. Select holdup and surge times from Table 6 and calculate the holdup and surge volumes, V, and Vr, from Eqs. 18 and 19 (unlesssurgeis other-
pRocREss. SEpTEMBER CHEMTcAL ENGTNEERTNG rgs+ . 35
?= :.:: :-= :-: -. ::
MULTIPHASE FLOW
,,,: wise specified,such as slug volume). 5. Obtain UD from Table 7 and initially set the diameter according to:
/ l?\ s
I lt 14
F F 7 E F F
Then calculate the total cross-sectional area,A, using Eq. 21. 6. Set the Yapor spaceheight, F1* to the larger of 0.2D or 2 ft (l ft if there is no mist eliminator). Using HutD in Table 3, obtainAv/Ar and calculate Au. 7. Set the light liquid heights in the vessel and boot, HrN and Hrrt. 8. Calculate the cross-sectional area of the light liquid above the bottom of the vessel,Ar., using Hrtt/D in Table 3. 9. Calculatethe minimum length to accommodatethe liquid holdup/surge:
f
"-
\ :
-
V., +V"o n Ar-Au-ArN
1994. SEpTEMBER
Approximate
'=(t+
(34)
10. Calculate the liquid droPout time, $, using Eq. 23. 1L. Calculate the actual vaPor velocity, Uuo,using Eq.24. 12. Calculate the minimum length required for liquid/vaporseparation. Lrr*, usingBq.25. 13. If L 1 Lr,*, then set L = Lr,* (vapor/liquid separation controls). This simply results in some extra holdup and residence time. If I 11Lr,*, then increaseH, and recalculateAr, thenrepeatfrom Step9.If L> Lr,*, the design is accePtable for vapor/liquid separation.If L >> LMrN, liquid holdup controls. I can only be reduced atd L*,* increased if I1u is reduced.Humay only be reducedif it is greater than the minimum specified in Step 6. With reduced Hu, recalailate A, and repeat from Step 9. 14. Calculate the settling velocity of the heavy liquid out of the light liquid phase, U"., using Eq. 7 (obtain ks from Table 1). 15. Calculate the settling time of
36 .
DishedHeads
the heavy liquid out of the light liquid phase: tm= 12 (Hrrn + D - H)IUHL Q5) 16. Calculate the residencetime of the light liquid:
ou=
(,q,,-e,)r eu
(36)
Note: This volume of light liquid ignores the light liquid volume in the boot. I7. If 1LL < to, then increase the vessellength (liquid separationcontrols):
19. Calculate the thickness of the shell and headsaccording to Table 8. 20. Calculate the surface area of the shell and headsaccording to Table 8. 21. Calculate the aPProximate weight of the shell and heads according to Table 8. 22.Increaseor decreasethe vessel diameter by 6-in. increments and repeat the calculations until 1,/D rangesfrom 1.5-6.0. 23. With the optimum vessel size (minimum weight), calculate the normal and high liquid levels: Hnu= D - Hu
(38)
Attrr= Arru + VrlL
(39)
(37)
18. CalculateUD.If UD << 1.5 then decreaseD (unlessit is already at a minimum) and if UD >> 6.0 then increaseD; rcpeatfrom SteP5.
PRocREss ENGINEERING cHEMICAL
Determine H*rrusingTable 3 from A*r/Ar. 24. Design the heavy liquid boot: Set the height of the heavY liquid, Hur; calculate the rising velocity of the light liquid out of the heavy liquid phase,Uru, using Eq. 8 (find ft, from
Table 1); set U, - 0.15 ULHicalculate the heavy liquid boot diameter:
Then calculate the settling time of the light liquid out of the heavy liquid phase: ttr=
l2Hu1/Us1
(4r)
Calculate the residencetime of the heavyliquid:
A -ndH* "ut 4en
(42)
the light liquid comparlment using Eq. 44 or read it from Table 9. Htu= 0.5D + 1
where D is in feet andHrrrin inches (round up to nearestin.). If D < 4.0 ft, then Hrm= 9 in. Using HoytD in Table 3, CalculateArrr. 8. Calculate the weir heisht: Hw=D-Hv
If eHr < tru, then diameter.
1. Calculate the vapor volumetric flow rate, Qu, using Eq. 5. 2. Calculate the light and heavl' liquid volumetric flow rates, Qu and per Eqs.9 and 10. Q11y.as 3. Calculate the vertical terminal vapor velocity, Ur, using Eq. 4 (find K tiom Table 2) and set Uv = 0.l5Ur. 4. Select holdup and surge times tiom Table 6, and calculatethe holdup and surge volumes, V, and V., from Eqs. 18 and 19 (unlesssurgeis otherir ise specified,suchas a slug volume). 5. Obtain UD from Table 7 and initially calculate the diameter accordingto:
(43)
t. { ft I u
n
(4s)
the boot
Horizontaldesign prooedure: weir
1
(44)
Then calculatethe total cross-sectiona r e aA . . . u s i n gE q . 2 l . "l 6. Set the vapor spaceheight.Hu. ro the larger of 0.2D or 2 ft (1 ft if lhere is no mist eliminator). Using H../D in Table 3, obtainAu/A, and cal;ulateAu. 7. Calculatethe low liouid level
If Hw< 2 ft, increaseD, and repeat the calculationsfrom Step 6. 9. Calculate the minimum length of the light liquid compartment to accommodate holdup/surge, 1,. in Figure 2 :
Vn+V, Ar- Ar.- AuL
(-+6)
Round to the nearest 7: ft. The minimum for Lr= d, + 12 in. 10. Set the interface at the height H,*12, obtaining the heights of the heavy and light liquids, Hrrand Hrr. 11. For the liquid settling compartment,calculatethe cross-sectional area of the heavy liquid, using Hr/D in Table 3 and calculate the cross-sectionalareaof the light liquid from:
Arr=Ar- A,- A*
(4',7)
12. Calculate the settling velocity of the heavy liquid out of the light liquid phase,Uur, andthe light liquid out of the heavy liquid phase, U"r, using Eqs 7 and 8 (find ft, from Table 1). 13. Calculate the settling times of the heavy liquid out of the light liquid phase and the light liquid out of the heavy liquid phase: (48) tur= l2Hr1/U*
tru= l2Hrx/Uro
(4e)
14. Calculate minimum I, to facilitate liquid-liquid separation as the larser of:
( t,,o-, trrQrr\ , A,, I
L1 =maxl:ff \
(50)
nur
Round to the nearest % ft. 15. Find l,: L= Lt+ Lz
( s 1)
16. Calculate the liquid dropout time, Q, using Eq. 23. 17. Calculate the actual vapor velocity. U,,.,.using Eq.24. 18. Calculatethe minimum length required for vapor/fliquid separation, 1.,rr,..using Eq. 25. 19. lf L ( Zr'.r- then set L = L*r (vapor/liquid separation controls). This simply results in some extra holdup and residence time. If L << Lr,*, then increase Hr, recalatlate A, and repeat the calculations from Step 6. If L > L*,r, the design is acceptable for vapor/liquid separation. If Z >> .Lrr, (liquid separation and holdup control), Z can only be reduced and Lr,* increased if Hv is reduced. //u may only be reduced if it is greater than the minimum specifledin Step 9. With reduced Hr, recalculate A, and repeat from Step 9. 20. CalculateUD.If UD << 1.5, then decreaseD (unlessit is already at a minimum) and repeat from Step 6. If UD >> 6.0, then increase D and repeat from Step 5. 21. Calculatethe thicknessof the shell and headsaccording to Table 8. 22. Calculate the surface area of the shell and headsaccordins to Table 8.
pRoGREss. SEpTEMBER CHEMTCAL ENGTNEERTNG 1994. 37
MULTIPHASE FLOW
there is no mist eliminator). Using Hr/D inTable 3, obtainAu/Arand calculateAu. 7. Calculatel,:
23. Calculate the approximate vessel weight according to Table 8. 24. Increase or decreasethe diameter by 6-in. incrementsand repeatthe calculations untiT UD ranges from 1.5-6.0. 25. With the optimum vessel size (minimum weight), calculate normal and high liquid levels:
(o,,e,,+o-,e-,1 -,'.''.] f L l -
Hnu=D-H,
(52)
Atrrr= Arrr+ V,1L,
(53)
Obtain Hr' ANLL|Ar.
60 min for reflnery service,or 10-15 min for chemical-plant service. For amine regeneratorfeed drums, 0o. = 10-15 min. 5. Obtain UD from Table 7 and initially setthe diameteraccordingto:
using Table 3 with
Horizontaldesign procedure: bucket and weir 1. Calculate the vapor volumetric flow rate, Qu, using Eq. 5. 2. Calculate the light and heavy liquid volumetric flow rates, Q, and Qnr,perEqs.9 and 10. 3. Calculate the vertical terminal vapor velocity, Ur, using Eq. 4 (flnd K from Table 2) and set Uv= 0.75 Ur. 4. Select residencetimes for light and heavy liquids, 0r, and 0o.. For sour water stripper feed drums, 0o. =
g,, =
,=(
+(e,,0,,re,,,O,,(s4) 0J0n(r1r)
Then calculatethe total cross-section. . u s i n gE q . 2 1. a l a r e aA 6. Set the vapor spaceheight, 11u, to the larger of 0.2D or 2 ft. (1 ft if
235'ooolblh =343.5'7ft3/s 3.600s/hx 0.190lb/ff
I EquationE8
o,,=
45'ooorblh -=18.52ft'lmin 60min/hx 40.5lb/ft'
I Equation E9
o-, =
7'5oolb/h =2.y2ft'lmin 60 min/hx62.0lblfr' tutQrt
A,,
-
8. Calculate the liquid dropout time, Q, usingEq. 23. 9. Calculatethe actualvapor velocUuo,usingEq.24. 10. Calculate the minimum length required for vapor/liquid separation, L*,r, using Eq. 25 . ll.If Ll 1 Lr,*, then set Lt = Luru (vapor/liquid separation controls). This simply results in some extra holdup and residencetime. lf Lt << LM,N,th.enincreaseIlr,. recalculateAu and repeat the calculations from Step 1. If Lt ) Lr,*, the design is acceptablefor vapor/liquidseparation. 12. Calculatethe light liquid layer thicknessbased on the heavy liquid settlins out:
Ur = 0' 175 I Equation811
7 r . 8 0 " ' ' = 11'15 ft' usel1'0ft -, ,-- ( 4 r 2xt.7 \0.6ru xr/i)
I EquationE12
- Equation813
2.0 min x2.02ft3hn1n=0.45ft
s.%ft
I Equation814
trrQo - 2.0 min x 18.52ft3lmin =2.41 ft
rs.02ff
ALL
I Equation E15
ff ls = 4.83ftls Q u = 343.51 rr ure= T 7r.08 te I Equation816
38 .
1994. SEPTEMBER
Ar-4,
4=ffi=14.54ft
I Equation810
PROGRESS ENGINEERING CHEMICAL
155)
w,D, tlni
Nomenclbture
prop€rengli
"' :, =;il;:::T:1",,-*lllllJli, ==,1'l l: = :-i;iliill,1l11;1",, "'*ftJil],."',0,'o '7\ = 0,"0,",, "'"'.'" il,,l,l,1l;; l,'.;l:l = v o l u m e t r i cf i o w . f l r / s o r l t r / m i n - vessem l l l e r i a l s t r e s sv a l u e .p s i
0 S
lne
=
^-
liquidabor.e vessel bor-
ASu = 5psqif. gravity differenceberween
:#, ?:light
I i g h ra n d h e a v yl i q u i d r
TC
TH
tut
= *' " iiii,r; i:i::';i'J' =;5.,ff::;l o u t o l l i g h t I i q u i d 'm i n
= ressel diemeler. n "r'llu'
D
of Western degreesin
ttu
3' =llJli';,ilr,.ormicrons
1s
t . .f r D , = r 3 p r l r ' J i s e n g a g e m edni a = t e f f i c i e n c yd. i m e n s i o n -
TH TS
6
V,'
: i o. r _\H=H --\r r l l - X l Pu l 1 - 1D . e s i g nt h e l i g h t l i q u i d b u c k e r : ': the top of light liquid u eir'= D , i l s s u m et h e b o t t o n rr s a t 0 . 1 l 5 D l . . r t t i e a h o l d u p / s u r g e( t 1 , p r c a l l r . ' . -i min.); assume HLL is 6 in. , rrl the weir height andLLL is 6 in. i e the bottom of the bucket. . r,c Table 3 with HrrrlD and D. calculate Au' and Arr.r. -ulateL,:
_
lro + r,)9,,
H-
= t e i , s h tl r . . = l i ; . : : i : : : : : = : :
d r o p l e i so L r o r f l i g h r l i q u i d .i n . t m i n
Un Up
o u t o f h e a v yl i q u i d ,i n . i m i n = mixture velocity, tVs = boot velocitr'.in.lmin = l c f r n i l r Jilg l 6 . i 1 _ 1 r i.. ' .c r i n . / r r i n = \ i - L p i \rre l . r c i t r .f L l :
f L ii li
: , z z : : .: ' i: -. H,,;
,
a,
= ---
.-.-:.:.
:'
H,,H,,,u
- - - :-- - : - - - . . ' - _ - . = :::::::::-::::, ::-
HP.
= heiSi:t:i,'::r iiir:
Hs
=
g
= totai vertical separarorheight.ii = vapor disengagementareaheighi. ir = weir height. ft
H,..
fle. 11
nv H,,,
irrroe heiohr
= ri
-
::-::
ailrdenaa time. min
::'.:::,i:. liquid ifaction
=
l\:.:::\. !-P
=
:::.:::.lbr'ft]
=
:, :: j irLrloui time- s
= h e i g h ld r f l e r e n c eb e l i i e e nl i g h i u n J
(58)
\ssume 1., is the largerof D/l2 l in. t 6 , Design the heavy liquid comrnt: Set the top of the heavy liq. - i r ' = D - H v - A 1 1 ;a s s u m ea :r \Lrr_se(typically, 5-15 min); : HLL is about 6 in. below the :r,ght and LLL is about 6 in. .h- bottomof the vessel.Using : v,trh Hrrr/D and Hr,,y/D, ca7i . ...andAr_r... - L L l . i t eL . , :
H.
leed nozzle.ft = disengagementheight. fi = htrldupheisht. fi
H;,
= s e t t l i n qr e l o c i t vu f h e r v r l i o u i d
u,., = r i s i n g v e l o c i t )o f l i g h r l i q u i d d r o p l e r s
= h e i g h r .f t H.. = liquid level above baffle, in. or ft HB,. = liquid height from abor.ebaffle to
heavy iiquid weirs. in. = S t o k e s l' a u .t e r m i n a lr e l o c i r r c o n -
fts
(Ar,'r_ Arr,') l : .
vHL
H
,.hereD" is in microns. 13. Calculate the differenc- rl :rsht betweenthe light and he;:,,., quid weirs:
T
= c f a \ i t a r i o n acl o n s t a n tJ, 2 . 1 7 f r , / s r = baffle liquid toad.gph/fr)
-'
0.00128e'(AsG)Dpr r-i6,
= \ u r g et r m r .m i n . = a l l o r l a b l eb o r i z o r r n lv c l o c i t l . f r l s
Y:,
;::]o.oLoint
u
r p r e l so u l
l
s r a n t .r i n . / m i n )cr P r i t l b / f r r = t e r m i n a lr e l o c i t yc o n s L a n fl .r , i s = vessellengrh.ft = v a p o r , 4 i q u isde p a r a r i o m n irrrrnum
K L
L*,*
;'':liilr,r-Hj I
_
(r, + rr)9,,
(5e)
lAorr- Arrr) 17. CalculateL = L, + Lr+ L. + L^. 1 8 . C a l c u l a t eU D . I f U D < < 1 . 5 .
)lr'-:li. l';L
I
- , ; i
;JL:
:.::: l;;iri,l ;evei
L, L;
i:i:i .;;iriti
LLL
: , , . r , r q l i i i e re l
1/ -:.
.\ lI
r
I
',:a.tI
I li.','i,l l-. ^l
then decreaseD trndlepeatfi'onl Step 5 Ii UD >> 6.0. then increaseD and repeatfi'om Step-5. 19. Calculatethe thicknessof the shel1and headsaccordingto Table8. 20. Calculate tl're surf'acearea of
pRocnEss. sEpTEMBER cHEMTCAL ENGTNEERTNG 1994. 39
MULTIPHASE FLOW
w h e r eP: = d e s i g p n r e s s u raen dD = d r u md i a ,
shell and headsaccordingto Table 8. 21. Calculatethe approximatevessel weight according to Table 8. 22. Increase or decreasethe diameter by 6-in. incrementsand repeatthe calculations until UD ranges from t.5-6.0.
Example2 Design a three-phasehorizontal separatorwith a weir to separatethe mixture in Table 10. The operating pressure and temperature are 25 psig and 100, respectively,and it is necessary to have a liquid holdup and surge time of 15 min. 1. SeeEq. E8, box, p. 38 2. SeeEqs.E9 and E10, box, p. 38 3. K = 0.175 (the Gas Processors Suppliers'Associationvalue in Table 2 was divided by 2 since there is no mist eliminator). S e eE q . E 1 1 ,b o x , p . 3 8 U v = 0 . 7 5 x 2 . 5 5 = 1 . 9 1f t l s 4. Holdup + surgeas specified= 15 min. Vu+ V, = (15 min) (18.52ft3lmin) = 211.80 ft3 Assume 10 min holdup, 5 min surge. 5 . A s s u m eU D = l . l . SeeEq. El2, box, p. 38 Ar=n/4 (11.0f|'z = 95.03ft2 6. Since the mass rate of vaoor is
1_ "-2xl7M
55xI32
about827oof theloading,setF1yto be much greaterthan the minimum. AssumeHv = 0.70D= (0.70)(1 1.0f0 = 7.70 ft. Using Table 3, Av/Ar = Av= 71.08ft2 0.148, 7 , H r r r =( 0 . 5 ) ( 1 1 .+07) = I 2 . 5 i n . , use13in. Hrr/D = 13/(11.0 x 12)= 0.098 = 0.051 UsingTable3, ALLrj/Ar (0.051X95.03 Aur= fP) = 4.95112 8. H, = 11.0- 1.10= 3.30ft 9. SeeEq.El3, box,p. 38 Usel,r = 15.0ft. = 1.65ft 10.HHL- Hrr= 3.3012 = 0.150 ll. HH//D= 1.65111.0 FromTable3, AH/A, = 0.094 Aur= (0.094X95.03 ft2)= 8.93ft2 - 8.93= 15.02 Au=95.03- 71.08 ftl 12.FromTable1, ks= 0.333 - 40.5)/0.24 = Uur= (0.333)(62.0 29.83in./min Use 10in./min(maximum) - 40.5)10.682 = Uro= (0.333)(62.0 10.50in./min Use 10in./min(maximum) 13, tHL = Q2 in./ft)(1.65ft)ilo in./min= 1.98min, use2.0mins tr, = tnr = 2.0 min 14. SeeEqs.E14 and E15. box, p .3 8 Uselr = 3.0ft. 1 5 .L = 3 . 0+ 1 5 . 0= 1 8 . 0f t '7.10 16.0 = ftll.gI ftls = 4.03s 17.SeeEq.El6, box.p. 38
*l|rc= 0.307in.
I Equation 817
. .-= = , = 0 . - -x8l=! f8 1-10?. 1? - - * r , 1=60 . 4 9i5n . 'rH 2 x 1 7 . 5 0x00 . 8 5 x 55 I EquationE18
we11.
t = ff'ltff#(on.at
rt2 +2x r0r.88 n')= ' 7.s20tb
I EquationE19
40 .
sEpTEMBER 1994.
18. LurN = (4.83 ftls)(4.03 s ) = 19.5fr 19. Since L 1 Lr,*, set -L = 19.5 ft (setZ, = 16.0ft, lr = 3.5 ft) 20. UD = 19.5/11.0= L78 21. Assume dished heads per Table11. AssumeE = 0.85 Use SA-516 70 carbon steel, design temperature= 650o S = 17,500psi; from Ref. (3). Corrosionallowance= Vrsin. P=25+30=55psig SeeEq. E17, box on this page. Use r, - 7s in. SeeEq. E18, box on this page. Use /" = Vz in; use t = Vzin. 2 2 . A s = ? I ( 1 1 . 0f 0 ( 1 9 . 5 f 0 = 673.81ftz Au= (0.842)(11.0fO'z= 101.88ft2 23. SeeEq. E19, box on this page. 24. In this example, calculations were performed for only one diameter. However, nearly the minimum UD corcespondedto a diameter of 11.0 fU therefore. the next diameter should be smaller, resulting in a laryer UD. Also, calculationsshould be performed using a diameter of I 1 . 5f t . 25. For the light liquid compartment: Hnrr= Hw= 3'3 ft - 3 ft, 4 in' A x L r = 4 . 8 5+ 1 8 5 . 2 0 1 1 6=.106 . 4 3 f P = 0.713 A*t/Ar= 16.43/95.03 Using Table 3, HNLrt/D= 0.229 Htrrr= (0.229)(11.0)= 2.52 ft - 2 ft, 6 in. HLLL= 13 in' Comment: Due to the small amount of heavy liquid and large amount of vapor, a better design would have used a boot. A vertical vessel should be comoared. as
pRocnEss CHEMTCAL ENGTNEERTNG
@
Toreceivea free copyof this article, sendin theReader Inquirycardin this issuewith the number 153circled,
