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Evaluation of Inclined-Pipe, Two-Phase Liquid Holdup and Pressure-Loss Correlations Using Experimental Data G.A. Payne, * SPE-AIME,U. of Tulsa C.M. Palmer, ● * SPWWME, u. of Tdsa J.P. Brill, SPE-AIME,U. of Tulsa H.D. Beggs, SPE-AIME,u. of Tulsa

.

Introduction

Literature Review

Two-phase flow in pipelines located in hilly terrain is encountered in the petroleum industry frequently. In oilfield gathering systems, two-phase mixtures must be transported from the wells to the separation facility. Because of the problems associated with oil and gas production offshore, it is usually necessary to have a common pipeline for the liquid and the gas streams. It is especially important to have good design methods for sizing these pipelines. When designing two-phase pipelines, pressure losses and liquid holdup must be predicted. The liquid holdup is defined as the fraction of pipe OC- “ cupied by liquid durhtg two-phase flow. A value of liquid holdup also is an important consideration when designing separation equipment, slug catchers, and pumps. A great deal of research has been conducted in horizontal and vertical two-phase flow, and several good correlations exist for these cases. However, only limited research has been performed in inclined two-phase flow. The main objective of this study was to design and construct an experimental facility that could be used to investigate two-phase flow phenomena in pipeiines laid in hilly terrain. The secondary objective of this study was to evaluate several existing correlations for ‘predicting liquid holdup and pressure losses using data obtained from the test facility.

Several authors have investigated inclined two-phase flow to some degree. An actual field study of a 16-in. pipeline was conducted by Flaniganl in 1958. Pressure drops over various sections of the line were measured. He concluded that the inclination of the hills had no effect on the pressure drop and that no pressure recovery existed in the downhill sections. Flanigan’s design method included using the Panhandle equation to calculate friction loss and an elevation factor to determine the loss caused by elevation. It is possible that Fhmigan’s elewitior: factor could include some pressure recovery in the downhill sections. This is because any pressure loss, not accounted for by the friction term, is assumed to be elevation loss on the uphill side. The overall pressure drop was used in the development of this correlation; consequently, any pressure recovery that might have been present is included in the elevation term. A two.phase inclined flow study was conducted in 1967 by Guzhov et al. 2 Them data were taken in 2-in. pipe inclined at angles between 3=9“ from horizontal. In development of the correlation, two flow regimes were considered — plug and stratified. A mixture Froude number and the gas input fraction were used to predict flow pattern. In stratified flow, there is one liquid holdup expression for uphill flow and one for downhill flow. This holdup is use(: to find a two-

●NOWa

consultant, Denver. ““h ow with Mapco Ino., Tulsa.

014S-21W7WO02.0874 S00.25 @1979 Scdetyof Petroleum Engineers of AIME

A 2-in. (5. l-cm) diameter, 550-ft (168-m) long pipeline was designed and constructed in a hiily terrain configuration. Two-phase-flow liquid holdup and pressure10SScorrelations were evaluated using gas/ water data obtained from experiments. Accurate predictions were obtained using the Beggs and Brill correlation and a combination of Beggs and Brill and Guzhov et aL correlat~ons. 1198

JOURNALOFPETROLEUM TECHNOLOGY

.

phase density that will determine elevation pressure loss. In plug flow, the stratified uphill holdup expression is used for holdup in both uphill and downhill flow. This results in complete recovery of the elevation pressure loss. A friction loss expression is given. Evaluation of the acceleration term requires an iterative solution. Beggs and Bri113investigated two-phase flow at several inclinations between +90 and -90° from horizontal. Test sections of 1- and 1.5-in. pipe were used. Holdup and pressure drop were measured, and holdup and friction factor correlations were proposed. A horizontal flow pattern map consisting of segregated, intermittent, and distributed flow regimes is used to determine a horizontal holdup. The horizontal holdup is corrected for inclination and then used to determine the d~v~ti~il pressure loss. Friction and acceleration terms also are provided. Recently, Robinson4 showed that the accuracy of the Beggs and Brill correlation could be improved when applied to directional wells by using a transitional zone between the segregated and intermittent flow regimes. When the flow is in this region, a weighted average of the segregated and intermittent holdup values is used. Sometimes, horizontal flow correlations are used with Flanigan’s elevation factor to design pipelines in hilly terrain. The American Gas Assn. Design Manual recommends using Dukler’sc horizontal correlation with Flanigan’s elevation factor. Dukler’s correlation is based on a large amount of experimental data. Dukler developed a holdup

correlation that requires an iterative procedure. The holdup is used to determine friction and acceleration pressure drops. The two-phase friction factor is a function of no-slip holdup and a smooth pipe friction factor. Eaton’s7 correlation also is used for pipeline design. ‘!’hismethod is based on data taken in 2-,4-, and i7-in. pipe under field conditions. Eaton proposed a holdup correlation that is a function of several dimensionless groups. This holdup is used to determine the acceleration component of the pressure drop. The fricticn factor is also a function of several dimensionless groups, but this must be used with caution because the friction. factor becomes unbounded as single-phase flow is approached.

Experimental Facility A schematic diagram of the hilly-terrain-pipeline test facility is shown in Fig. 1. The test facility consisted of 1,200 ft of 2-in. Schedule 40 line pipe (ID= %067 in.) with associated gas compressor, water p~mp, meter runs, and separator. The entire systeni was closed —i.e., both gas and liquid were recircl~lated. The test section was 400 ft long and amanged h three hills. Entrance and exit e~fects were avc,ided by extending the pipe about 7S ft (450 pipe f~iameters) on each end of the test section. Fig. 2 is a profile of the test section, and Table 1 gives data about that section. GeneralProcedure for Two-Phase Flow Testing The system was pressurized initially to 400 or 500 psia with a three-stage Worthington compressor.

Fig. 1- Schematic diagram of hilly terrain facillty.

SEPTEMBER1979

1199

.

TABLE1 -TEST SECTION DATA Length (ft)

Section*

Elevation Change (ft)

Angle (degrees)

3.69 -3.75 6.11 -3,31 0.24 6.59 -5.56

4.23 -4.30 7.02 -3.60 -0.14 6,24 -5.91

50 50 60 1: 46 54

“Note that See. 5 contalna two Inollnatlone over the total length correepondlng to the pressure drop data.

This provided the necessary volume to start a twostage Knight compressor. The gas was circulated with the gas bypass valve fully open. After the desired meter run was opened, the bypass valve was closed until the desired g= flowrate was achieved. Whh the flow controller set on the desired liquid rate and the correct meter run open, the pump was started and the water bypass valve was closed partia~y. The pump pressure had to be about 200 psi greater than the system pressure for the flow controller to function properly. After water reached the separator, the liquid-level control valve was set to maintain the desired liquid level. Once the liquid level was stabilized, the gas rate was set more exactly. When the syst m had stabilized completely and all temperatures, J ressures, and flow-rate data were recorded, transducer equalizhg valves were opened and the ball valves were shut. The liquid was drained from each segment and then weighed. The ball valves were opened and the equalizing valves were shut. If only pressure loss data were desired, the holdup procedure was omitted. A cornple% discussion of the experimental equipment, includlng pressure traverse and holdup measurement procedure, is found in Refs. 8 and 9. The holdup data taken by Palmers and the pressure drop data taken by Payne9 are presented in Tables 2 and 3.

Evaluation Techniques PVT Properties Because the liquid used here was water, we did not

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1

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? 4 6A

00 so 100 4s S4

2

06 o

00

800

400

(FT)

a.os -a.7s e.tt -a.al 0.R4 6.0s -s.

s6

Fig. 2-Test section profile.

4.aa -4. ao 7.02

have to consider mass transfer between phases. We assumed the water had a constant density of 62.4 lbrn/cu ft. The gas/water surface tension was assumed to be a constant 60 dyne/cm for the range of pressures and temperatures encountered in this study. Water viscosity was determined from the correlation of water viscosity as a function of temperature presented by Beal.10 Specific gravity of the natural gas was 0.64. The gas compressibility factor was calculated using a subroutine provided by Brill and Beggs,’1which is an acceptable approximation to the Standing-Katz zfactor chart. The Lee et al. 12correlation was used to calculate the gas viscosity. Statistical Analysis The statistical parameters used to evaluate the experimerwal data were average percent error and standard deviation. These parameters are defined as follows: LYOE=

~

oi’oE=

~~

‘=‘

%E, N’

To make any statistical inference from experimental data, the data usually must be distributed normally. For this reascm, the actual values of percent errur for predicted pressure drop in the total test sect;on were sorted into ranges, and the cumulative relative frequency of the percent error was plotted vs the value of percent error on normal probability paper. A normal distribution will plot as a straight line intersecting the 50th percentile at the mean. It also will intersect the 16th percentile and the 84th percentile one standard deviation on either side of the mean. Figs. 3 and 4 show that the errors do approximate a normal distribution. Because the average percent error is based on a finite sample, we cannot expect it to coincide exactly with the actual population mean. However, since the percent errors approximate a normal distribution, it is possible to determine an interval that will bracket the true value of the average percent error, given specified odds. For a normal distribution where the sample variance is used as an estimator of the population variance, this interval is given by the following expression: IT’o~ *

-3.00 -0.14 0.!24 -0.81

calculated value - measured value ~ lM 9 . measured value

(i,-a,2 ;N - 0

($)“

Using the above confidence limits and a = 0.01 (i.e., a 999’0confidence intewal), we can show that the Beggs and Brill correlation true average percent error lies between -20.51 and -28.53%’o. Consequently, at best this correlation underpredicts JOURNALOF PETROLEUM TECHNOLOGY

TABLE 2- HOLDLIP DATA RECORDEDBY PALMER8 Temp$#ure

Pressure (psla)

Run Inlet Outlet Inlet —— —— 12304 526 514 98 20404 570 572 93 12105 518 512 100 12709 395 378 102 12907 533 521 84 12205 401 390 83 20401 665 659 70 20402 616 609 81 20403 575 568 88 21401 547 541 75 21402 547 541 78 21403 548 542 66 21404 549 543 94 21405 548 542 103 545 110 21406 551 21407 549 542 110 21408 469 462 104 466 105 21409 473 465 103 21410 472 21301 604 584 80 21302 575 555 93 21303 555 542 100 21304 537 528 105 21305 518 510 109 21306 513 506 110 21307 504 500 98 21308 446 442 98 21309 440 435 106 21310 443 435 112

Llquld Rate

Gas

Rate

(BID)

Uphill Holdup

(scf/D) Sec.1 —— 505.0 640831 0.2225 234.6 677479 Ot21W 330.4 905634 0.2010 864.5 6289180.2852 703.8 520402 0.3934 799311 0.1718 345.9 743081 0.2294 234.6 %?34.6 1164866 0.1520 754148 0.1967 234.6 130150 0.4510 323.8 123028 0.4175 323.8 109593 0.4372 323.8 90434 0.5214 323.6 230.6 74635 0.5669 130174 0,5506 457.3 457.3 Vxt48 0.5506 457.3 204937 0.3067 166058 0.4982 457.3 187631 0.4948 457.3 595.1 1745730 0.1787 1399844 0.2190 595.1 1015462 0.2483 595.1 595,1 775024 0.2895 578.1 561458 0.3505 274798 0.4226 590.8 253418 0.3280 132.3 131.8 204474 0.3419 131.6 140991 0.3780 285.0 141260 0.3049

Outlet 90 :: 95 76 68 68 78 :? 54 :: 78 z 84 75 74 76 87 85 93 86 99 78 70 70 66

DownhillHoldup

Sec. 3

sec. 5B Sec. — 2

0.2448 0.2413 0,2040 0.3385 0.3993 0.1684 0.2396 0.1553 0.2022 0.5182 0.3966 0.4826 0,6041 0.5954 0.5442 0.5242 0.6076 0.4$%5 OO~A16 0,1606 0.1779 0.2491 0.2873 0.3602 0.3897 0.3081 0.3142 0.3576 0.4999

0.2483 0.2445 0.2190 0.3181 0.3096 0.1718 0.2473 0.1339 0.1888 0.4163 0.5551 0.5277 0.5796 0s494 0.5107 0.5230 0.4267 0.3115 0.4191 0.1520 0.1860 0.2332 0.2615 0.3710 0.48W 0.3087 0.2851 0.3965 0.3106

Sec.6 .Sec. 4 0,2101 D.1847 0,1302 0.1199 0.1510 0.1527 0.2213 0.2614 0.3949 0.1639 0.0833 0.1439 0.1050 0.1319 0.0781 0.1127 O.0000* 0.1279 0.3645 0.2126 0.4157 0.0584 0,3263 0.1974 0.3524 O,Y91O 0,1767 0,3255 0.1823 0.4010 0.2926 o.507r 0.1979 0.1727 0.3263 0.2182 0,2413 0.2526 0,1423 0.1751 0.1639 0.1510 0.1871 0.1771 0.2046 0.25$6 0.1974 0.2578 0.4062 0.0951 0.1259 0.1097 0.1632 0.0879 0.2040 0.0520 0.2181 0.1886

0.2136 0.1484 0.1875 0.2821 0.1510 0.1562 0.1588 0.1163 0.1406 0.1701 0.3029 C,2751 0.2W9 0.1883 0.2300 0.3764 0.1892 0.1883 0.2448 0.1649 0.1623 0.2317 0.2291 0.2639 0.2048 0.1285 0.1111 0.0929 0.2717

..

“Llquld holdup waa not measured.

Os. ss

I

I

I

I

I

I

1

I

1

I

I

1

I

1

7

I

““”~

I

/ so

09

96 -

96

i

●

80

80

60

eo

40

40 I

20

20

//

6

r! -

1

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1 0.1

-80

-60

-40

-30

-20

-lo

0

10

~/

I

I

I -30

1

I

-20

SEFTEMBER1979

I

-lo

1

I

0

t

I

10

I

I

20

I

*

30

t

9

1

J

40

!41?RROR

%ERROR

Fig. 3-Cumulative frequency of percent errors in pressuredrop(total test section) usingthe Beggs and 13rillcorrelation.

1

Fig. 4-Cumulative

frequency of pf3rCf)nt errors in pressuredrop (total test section)usingthe Eato~ Dukler-Flanlgancombination. 1201

,

.

TABLE 3-PRESSURE DROP DATA RECORDEDBY PAYNE8

Run —— 12101 12103 12202 12203 12204 12205 12302 12303 12304 12702 12703 12704 12705 12708 12707 12708 12709 12902 12803 12904 12905 12906 12307 22001 22002 22003 22004 22005 22006 22007 22008 22009 22010 22011 22012 22502 22503 2254)4 22505 22505 22507 22508 22509 22510 22511 22512 22513 22514 22515 22516 22517 22518 22519 32002 32003 32004 32005 32008 32007 32008 32009 32010 32011 32012 32013 32014 32015 32016 32017 32018

120’2

Average Inlet Preesure Temperature (peia) VF)

Llquld Rate (BID)

528

84

92

532 426 423 411 401 516 535 526 378 384 405 385 387 387 427 395 635 611 805 571 546

69 74 79 70 76

:: 857 617 338

412 391 385 347 308 291 289 % 284 431 432 430 430 428 430

431 432 435 439 440 440 439 440 439 405 408

511 470 477 489 488 435 433 435 420 425 421 431 450 455 491 510

: 94

% 505 231

z :: : 99 98 ; 80 78 80 80 71 2 84 88 % 88 89 91 90 67 62 67 % z 91 89 95 96 98 100 ,W 101 1:; 99 89 75 79 85 87 92 91 97 98 102 107 109 109 105 97 102 100 100

1% 1077 1080 887 884 664 128 421 515 808 703 703 331 331 331 331 331 331 331 331 331 415 415 415 515 515 512 512 515 604 604 604 604 604 703 703 703 703 805 805 8(I5 805 233 233 233 130 131 131 131 131 131 131 131 85 85 85 85 84 84

Gas Rate (scflD) 1793716 1708329 1401284 857840 038779 831174 1335187 1361592 66W04 844802 814955 780271 459842 288922 288111 326655 653008 1494170 837792 793896 947422 985878 542509 1007089 780274 580427 291464 251880 228044 149998 113882 71148 71148 260946 365469 319909 283475 218097 159957 95000 91806 175836 239541 261048 326608 311346 253889 i 77556 110171 107612 167495 242558 2!31122 1788601 1319003 651544 608329 1383708 1779416 344198 282284 219788 173545 118403 115796 171136 246550 IF% 1649585

Sec.1 —— -3.0 -1.8 -3.6 -3.2 -2.4 -Ice -1.4 -2.0 -2.0 -0.8 -1.6 -3.0 -2.0 -1.4 -1.2 -2.4 -2,0 -1.0 -1.2 -1.6 -2.6 -3.4 -2.6 -1.4 -1.2 -0.8 -1.0 -0,8 -0.7 -0.7 -0.6 -0.6 -0.9 -0.7 -1.0 -1,0 -1.1 -1.3 -1.3 -1.3 -1.5 -1.3 -1.1 -1.3 -1.3 -1.3 -1.4 -1.3 -1.4 -1,4 -1.3 -1,3 -1.6 -2.1 -1.4 -~:J -0.7 -0.6 -1.8 -0.5 -1.3 -0.4 -0.8 -0.6 -0.7 -0.3 -r13 -0.3 -0.5 -0.6

Preseurtr,Drop P t Sec.2 —— Sec.3 Sec.4 —. Sec,5 -0.6 -1.4 -0.4 -5,0 -1.4 -2.2 -1.2 -5.4 -2.8 -11,2 -4.2 -3.0 -2.0 -4.0 -2.4 -10.6 -1.0 -1.6 -7.6 -3.2 -0.2 -2.2 -1.0 -4.6 -1,2 -1.6 -1.0 -4.8 -0.2 -2.6 -1.6 -7.8 -0.6 -1.6 -0,4 -4.5 -0.4 -1.2 -2,8 -0.6 -0.6 -1.2 -2.0 -4,6 -1.8 -3.6 -2.2 -9.0 -1.0 -3.0 -1.4 -6.2 -0.2 -2.6 -0.6 -5.2 -0.2 -2.2 -0.2 -4.2 -1.2 -3.2 -2.0 -9,8 -0.6 -1,0 -2.6 -7.8 -0.8 -0.6 , -1.6 -3.0 0.4 -1.4 -0.6 -4.4 0,2 -1.8 -0.8 -5.2 0.2 -2.6 -0.8 -6.4 -0.2 -3.0 -1.2 -7.6 0.8 -2,6 -5.6 -0.4 -1.8 -0.8 -0.9 -4.0 -0.7 -1.4 -1.1 -3.2 -0.5 -1.3 -2.6 -0.6 -0.3 -1.7 -2.2 -0.1 -0.3 -1.4 -2.0 -0.2 -0.2 -1.3 0.1 -2.0 -2.0 -0.2 -1.2 0.1 -0.2 -1.9 -0.9 -0.1 -0.2 -1.0 -0.2 -2.0 -0.3 -0,9 -0.1 -2.1 -0.2 -1,2 0,1 -2.4 -2.7 -0.3 -1.4 -0.1 -1.8 -2.6 -0.3 -0.1 -2.8 -0.4 -1.8 -0.1 -0.3 -1.7 -2.4 -0.1 -0.1 -2.0 -0.3 -2.1 -0.2 -2.0 -0.4 -1.8 -0,1 -1.9 -0.5 -0.8 -0,3 -1.8 0.1 -0.9 -1.1 -0.2 -1.8 -0.2 -1.6 -1.3 -0.3 -0.2 -0.4 -2.0 -0.1 -1.8 -1.9 -0.7 -2.1 -0.1 -0.2 -1.7 -2.5 -0.1 -1.3 -0,5 -0.2 -1.9 -2,2 -C,5 -2.0 -0.3 -2.5 -0.4 -2.1 -0.3 -1.5 -1,8 -0.6 -0.3 -1.6 -0.7 -1.9 -0.5 -2.3 -0.5 -0.7 -2.1 -1.4 -1.5 -5.0 -1.6 -3.6 -0.8 -1.7 -0.7 -2.0 -0.2 -1.5 -0.1 -0.1 -1.5 -0.2 -1.0 -1.0 -0.2 -2.9 -0.5 -1.3 -1.0 -5.0 -2.2 -1.4 -0.3 -0.9 -0.1 -1.4 -0.1 -0.1 -0.9 -1.4 -0.3 -0.2 -0.7 -1.5 -1.4 -0.2 -0.1 -0.6 -1.6 -0.6 -1.0 -1.6 -0.4 -1.4 -0.7 -1.4 -0.1 -1.6 -0.6 -1.2 -0.1 -0.4 -0.6 -1.2 -O.l -0.6 -0.3 -2.4 -1.2 -0.6 -0.3 -1.5 -1.0 -3.3 -0.6

Sec,6 -1.0 -1.8 -2,8 -2,6 -1,2 -0.8 -1.0 -1.6 -0,4 -0.6 -1.2 -2.4 -1.4 -0.6 -0.4 -2.0 -1.2 -1.4 -0.8 -1,0 -1.2 -1,6 -0,8 -0.8 -0.5 -0.4 -0.2 -0.2 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.2 -0.1 -0.2 -0.5 -0.8 -1.0 -1.9 -2,0 -1.6 -1.9 -1.7 -1,9 -1.9 -2.2 -1.1 -1.0 -2.1 -2.2 -2.2 -1.3 -0.7 -0.1 -O.1 -0.3 -1.5 -0.5 -0.3 -0.4 -0.3 -0.4 -0.4 -0.2 -0.4 -0.4 -1.2 -1.1

JOURNALOF PETROLEUM TECHNOLOGY

.

TABLG4- CUMULATIVE FREQUENCY DISTRIBUTIONOF PERCENT ERRORSIN PRESSUREDROP (TOTALTESTSECTION) ’10E

-50 4 0 0 o

Beggsand Brili (modified by Robinson) Beggsand Briii (neglect pressurerecovery) 13eggsand Briii (roughpipe friction factor) Dukier(HL), Dukier(FF), Fianigan (EF) Eaton (Hi.), Eaton (FF), F!anigan(EF) Guzhovet al.

7:

-20 -lo 0 —— —— 8704100 61 %HHlnhro 0 0 :E

10

20 —— ---

11 31 84 44847Q981OO 6Q8990981OO

80

100 —

07

100

HL = Ilquld holdup. FF = frlctlon factor. EF = olevatlon faotor.

pressure 10ssat least 20V0for 2-in. pipe. A similar analysis for the Eaton-Dukler-Flanigan combination gives a %Woconfidence interval of 1.16 to 10.8OVO.Table 4 gives the percent error distribution of the other methods used to compare calculated pressure drop with the measured pressure drop. Holdup &ldySiS Liq~id holdup was measured in three uphill and three downhill sections for each experiment. Calculated values of liquid holdup corresponding to the measured values were determined from the Beggs and 13rill$Flanigan,l and Guzhov et al.z correlations. The re$ults of this analysis are provided in Table S and in Figs. 5 through 10. Examination of the individual percent errors for the uphill sections indicates that the correlations predict the holdup more accurately in some sections than others. This fluctuation could result from the presence of slugs in some parts of the test section. As can be seen in Table 5, the Beggs and Brill correlation was the most accurate in predicting the liquid holdup in the uphill sections. In downldll flow, the fluctuation of the holdup percent error in individual sections is similar to that found in the uphill sections. This also could be

caused’ by slugging. The Guzhov et al. correlation gave the lowest average percent error of the three correlations. Using the Guzhov et al. criteria for stratified flow, liquid holdup in dowrtill flow is predicted most accurately by Guzhov et af. in stratified flow and by Beggs and Brill elsewhere. Statistics for this combination also are shown in Table 5. The Beggs and Brill correlation was used in a modified form to see if the downhill holdup could be predicted more accurately. The correlation was forced to a segregated flow condition for those experiments where stratified flow was indicated, according to the Guzhov et af. criteria. This modified form proved to be less accurate than the original Beggs and Brill correlation for downhill flow. The consistently large positiv~ percent errors for liquid holdup in the downhill section indicates that the correlation is overpredicting the downhill holdup. Table 5 shows that the Fkmigan correlation was the least accurate of the three correlations. As Flanigan stated, the correlation was a crude approximation, but this was one of the first steps taken to predict liquid holdup. Flanigan’s correlation was developed for uphill flow, and holdup in downhill flow was ignored. 1.0

0.8

O.lt

0.8

O.*”

0.4

0.4

..

0.2

0.0

0.0 0.0

O.a

0.4 CALCULATED

0.0 UPHILL

0.s

1.0

HOLDUP

Fig. 5-Measured uphill holdup vs calculated uphiii hoidupusingthe i3eggsand Brill method.

sE!PrEMBER1979 .“.

0.’2

0.0

0.9

0.4

OALCULATEO

O.a UPHILL

0.8

1.0

HOLDUP

Fig. 6-Measured uphiii holdup vs calculated uphili holdupusingthe Flanldan method.

12,03

PressureLees Analysis The calculation procedure used to determine pressure loss in the test section is given in Ref. 9. Six different correlations or combinations of correlations were compared with the experimental data. Table 6 and Figs. 11 through 18 give the results of this comparison. The statistics in Table 6 are based on the total pressure drop tor the entire test section. A positive value of average percent error indicates an overprediction of pressure loss. The Guzhov et al. correlation was significantly worse than the others. This was attributed to the downhill holdup beinb equal to the uphill holdup in plug flow. This results in complete recovery of the elevation term in downhill flow. The majority of the data are in this flow regime, according to the Guzhov

TABLE 5- STATISTICS FROM HOLDUP ANALYSIS Downhill

Uphill Method

O/oE —.

S

%E ——

s

Beggsand Bril” Flanigan Guzhov et al. Begge-Guzhov*

9.2 16.3 14.3 .

15.0 30.1 19.5 “

61.0 . 36.6 17.9

60.8 57.4 46.7

‘Oomblnatlon of Begg@and Brlll correlation with the (3uzhov ct el. Correletlon for downhill only.

et al. criteria. The acceleration term in thh corre-

lation was neglected. The combination of Dukler holdup, Dukler friction factor, and the Flanigan elevation factor did not predict pressure loss as well as the Eaton holdup, 1.0

0.8

0.s

e

0.4

e

0.2

0.0

0.0

0.0

0.0

0.2

0.4

0.0

O.a

0.2

0.4

1.0

CALCULATED OAI.CULATEO

UPHILL

0.0

0.8

1.0

OOWNHILL HOLQUP

HOLOUP

Fig. 7-Measured uphill holdup vs calculated uphill holdup using the GuzhovetaL method.

Fig. 9-Measured downhiii hoidupvs calculated downhiil hoidup usingthe Guzhovet al. method. 1.0

0.8 0.0

0.8 0.0

0.4 0.4 ee 0.2 a

0.2

0.0 0.0

0.0

0.0

0.2

0.4

0.0

0.s

0.2

0.4 CALCULATED

CALCULATE

O.n

1.0

DOWNHILL HOLOUP

130WNHlLL HOI.OUP

Fig. 8-Measured downhill holdupvs calculated downhill holdup usingthe Beggsand Brill method.

1204

0.6

1.0

Fig. 10- Measureddownhiii holdupvs calculated downhili holdup using the Begge and BriiilGuzhovet al. method.

JOURNALOFPETROLEUM TECHNOLOGY

TABLE6-STATISTICS FROM PRESSUFiE.LOSSANALYSiS Downhill

Uphill

.—

sec.3 ms ——

sec. 5 ms ——

26.21

3.39 4353

6.34 55.66 -125.07

26.21

0.2640.04 4.46

26.21

3.3S 43.62

8.03 57.03

29.34

18,43 51.95

25.56 66.06

-91.67

236.26

-24.20

42.74

12.61 61,73

14.20 53.85

21.87

269.81

62.56

41.79

22.19 63.28

26.40 52.03

40,66

260.38 .

Sec. 1 ~s

Method

Beggsand Brllt -0.62 Beggsand Brlll (modlfiadby Robinson) -2.44 Beggsand Brill (rregleotpressure raoovery) -0.62 BeggsandBrill (roughpipe friotlonfactor) 15.61 Eaton(HL), Dueler, Flanagan 10.89 Dueler, Dueler, Flanlgan(EF) 22.17 Eaton(HL), Eaton(FF), 11.36 Flar,!gan(EF) Guzhovet eL -11.66

See. 2

sec. 4

~lox s ——

m

56.55 -121.02

176.76 -66.20

s %7?s— ——

120.32 -133.66 163.66 -24.52 12.65 162.63 -25.75

14.45

30.86

123.64

-1.45

15.91

-92.77

174.41

-4S6

21.79

224.5S

35S)9

122.24

79.68

266.66

62.97

146.36

207.60 46.15 161.44 -140.06

221.81 240.05

41.44 -22.06

173.96

-66.66

16.95 203.64

47.70 12.23 63.11 14.92 66.70 28.18 65.60 -11.56 66.21 -22.05 42S6 -178.02

~ s ——

Total Test Section

S00. 6

118.03 -131.32

42.16 221.lQ 152.40

5.S8 15.23

19.43

14.63

125.95 6.87 42.s6 -sea

20.64 41.43

HL = Ilquid holdup. FF = friction factor. EF = elevation factor.

Dukler friction factor, and Fktnigan elevation factor combination. This must be a direct result of the Dukler holdup correlation. This agrees with a previous evaluation of Dukler’s holdup correlation by MarcanolJ wherg the Dukler correlation underpredicted by 33qo. Underprediction of liquid holdup would result in overprediction of friction loss. The combination using. Eaton’s friction factor V@ fairly accurate since the correlation was developed with data taken in 2-in. pipe. The original Beggs and Brill correlation and the version modified by Robinson4 gave essentially the

same results for these data. The Beggs and Erill correlation next is analyzed in detail. Beggs and Brill Method Whe~: analyzing the holdup data, we found that the Beggs and Brill correlation overpredicted holdup in downhill flow. This would result in too much pressure recovery and a corresponding underprediction in overall pressure loss. In view of this, the Beggs and Brill correlation was evaluated with the elevation term set at zero in downhill flow. This resulted in conside.. :bly better performance. The average percent error was reduced to - 1.45T0 with a I

1

I

I

e

I

I

1

1

e ●

e

eo

‘% ea Oo

ii

I

1

-4 -a

-4

-1s

-lo

-20

-a

PRaaa

URa

DROP

-10

-20

PRESSURE

DROP

I 1

-24 (PSID)

(PSID)

Fig. 11- Measured w calwlated pressure drop (total test section) usingthe keggs and Briiicorrelation. SEFTEMSER1979

-12

t

-24 OALOULATaO

CALCULATED

t

Fin. 12- Measured vs calculated rxessure drOP(tOtal test section) using the f3egg8and Brlll correlation as modified by Robinson. 1205

!l!M40 confidence interval of -6.49 to 3.59Vo. Fig. 13 shows the improved performance of the correlation. However, to conclude that the downhill holdup is the only error source in this correlation could be an oversimplification. Possibly, some error exists in the friction component of the total pressure drop. The Beggs and Brill correlation was developed in plastic pipe, and roughness was not a parameter in the friction factor. In the original correlation, the Drew et al.14equation was used to calculate a smooth-pipe friction factor multiplier. This was replaced with another

equation,15 which is a function of relative roughness and which resulted in an average percent error for the total test section of -4.38%’owith a 99qo confidence interval of -11.28 to 2.52Vo. Fig. 14 shows the improved performance of the correlation. Table 5 gives the uphill and downhill statistics for this variation of the Beggs and Brill method. It seems that using a rough-pipe friction factor provided too much friction Ioss. However, the overprediction of pressure recovery compensates for this. Note that the roughness used was that of commercial steel or wrought iron (0.00015 ft). This value resulted in good agreement I

1

1

I

I

a

●

-24

-84

d

● ●

-s9

●

-2a w

✍

w -la

-10

a ● *O

a a

o

o

1% -la u

-12

a

0

-a

-a * -4

-4

-4

-B 9ALOULATED

-19

-lo

PREOOURE

-20 DROP

~

-!24

-4

(PSID)

Fig. 13- Measured vs calculated pressure drop (total test section) using the Beggs and Brlll correlation with no preseurerecovery.

OAL,0ULA7E0

6

PRE8SURS

DROP

(PelD)

Fig. 14- Measured vs calculated pressuredrop (total test ssction) using the Beggs and Brlll correlation with a rough-pipefrlct!on factor multiplier, 12)6

-lo

-20

PRE8SURS

DROP

-24 (PSID)

Fig. 15- Measured vs calculated pressuredrop (total test section) using the Eaton-Dukler-Flanlgan cornbinatlon. -

1

0ALCULA7E0

-12

I

I

I

I

PRESSURE

DROP

1

I

“’c+

I

CA LO ULATMD

(PSID)

@

between calculated and measured pressure drops in single-phase gas flow. The Beggs and Brill correlation seems to be affected primarily by an overprediction of holdup in downhill flow. This results in too much pressure recovery. It is possible that the friction loss is not as great as it should be. However, neglecting pressure recovery and using a rough-pipe friction factor would result in an excessive pressure loss. An interesting analysis would be to use the Beggs and Brill/Guzhov et al. combination discussed previously for downhill holdup with a rough-piW friction factor. We did not do this because our paper is a combination of two independent research projects (see Refs. 8 and 9). Results of the holdup analysis were not available before completion of the pressure loss analysis.

Several conclusions can be drawn from the experimental data analyzed in this study. 1. The Beggs and Brill correlation accurately predicts holdup in uphill flow. 2. The Beggs and Brill correlation overpredicts liquid holdup in downhill flow. 3. Liquid holdup prediction in downhill flow can be improved by using the Guzhov ef al. correlation when stratified flow 1s indkated and by using the Beggs and Brill correlation at all other times. 4. The combination of Eaton holdup, Dukler friction factor, and the Flanigan elevation factor accurately predicted pressure loss. 5. The Beggs and Brili correlation underpiedicted pressure loss by nearly 25V’o. This is primarily because of an overprediction of liquid holdup in downhill flow. 6. Neglecting pressure recovery in downhill flow to

I

.,

Acknowledgment

The sponsorship of these projects by the U. of Tulsa Fluid Flow Projects is gratefully acknowledged.

Nomenclature !lolZ= T7E = N = S =

percent error .. average percent error number of data points deviation about the average percent error . t = variate of the t distribution a = confidence coefficient

References 1. Fhudgan, o.: “Effect of Uphill F1OWon Pressure Drop in

Dcsii of Two-PhaseGatheringSystems,”Oil and GasJ.

Conclusions

I

compensate for the overprediction of holdup with the Beggs and Brill correlation gave excellent r~ults.

1

I

10

1

1

(March10,1958)S6,132. (luhov, A.L., MamaYcv, V.A.,and Odishariys,G.E.: “A Studyof Transportation inGasSystems,”paperIGV/C19-67 prcscntcdat the loth IntcmationalGas UnionConfcrcncc, Hamburg,hU)C 610, 1%7. H.D.andBrill,J.P.: “A Studyof Two-PhaseFlowin 3. BCSSS, lnclincdPips,” J. Pet. Tech. (May 1973)607-617;7hwJs., 2.

AIME, 25s. 4. Itobmson, J.R.:

“&vclOpmcnt of a Two-PhaseWell DSI& Eank and an Evaluation Study of Pressure Lass Methods APPlkdto DirectionalOd Wells,”MSthesis,U. of Tulsa, OK

(19?4). 5. Baker, O.: “Gas-Liquid Flow in Pipelines, II. Design

Manual,” API-AGA Projcst NX-28, Ncw York City (Oct. 1970). 6. Duklcr, A.E.: “Gas-LiquidFlow in Pipelines, Part I, ResearchRcsuks,” API-AGAProject NX28, NewYorkCity (May1969). 7. Eaton, B.A.: “’The Prediction of Flow Pattcms, Liquid Holdup and Pressure LOSSCS OccurringDuring Continuous Twe-PhaseFlowin HorizontalPipolincs,”PhD dissertation, U. of Texas,Austin(1966). 8. Palmer, C.M.: “Evaluation of Inclined Pipe Two-Phase

A

o ..84

r7’”’”/ 1-

/

,/

e

:

/

00

— ~ -1$ a a m a

*O

@

-la

&

n

w = a a * w

s

●

-a

-4

-4

-s CA I. GUI.ATED

-16

-20

-24

PRESSURE

DROP

(PO ID)

-$!2

v

I

-4

I

-0 GA!. GULATED

Fig. 17- Measured vs calculated pressure drop (total test eectlon) using the Eatort-Eaton-Flartlgan cont. bination.

SEPTEMBER1979

I

t

I

t

-lo

-20

-%4

PRESSURE

RROP

-12

(PSIO)

Fig. 18- Measured vs calculated prestsuredrop (total test section) usingthe Guzhovet al, correlation. 1207

“

Liquid Holdup CorrelationsUsingExperimentalData,” MS thesis,U. of Tulsa, OK (1975). 9. Payne, G.A.: “Experhnentsl Evaluation of llvo-Phase PressureLossCorrelationsfor InclinedPipe,” MS thesis,U. of Tulsa,OK(1975). 10. B@ C.: “Vkosity of Air, Water, Natural Gas, Crude 011 and Its Associated Gases at Oil-Field Temperatures and Pressures,” ?hrns. AIME(1946)16S,94-115. 11. Brill,J.P. and Beggs,H.D.: 7ivo-Phase Flow in Pi”, U, of TulsaPress,Tulsa, OK (1975). 12. Lee,A.L., Gonzales;M.H., and Ealdrt, B.E.: “The Viscosity of Natural Gas,” A Pet. Tech. (Aug.1966)997-1~, ~ans., AIME, 237. “ 13. Marcano, N.I.L.: “Comparisons of Liquid Holdup Correlationsfor Gas Liquid Flow in Hoizcmtal Pipes,” MS thesis,U. of Tulsa,OK(1973). 14. Drew,T.B., Koo, E.C., and McAdams,W.H.: “The Friction Factor for CleanRoundpipes,” Thins., AIChE(i932]28,56. London(1938)11,133. 15. J. hi. CitrilEirgm,

S1Metric Conversion Factors B/D X @ne/cm x “F (eF-32)/l.8 ft X in. x lbm/cu ft X X scf/D

1.589873 1.000” 3.048* 2.540’ 1.601846 2.863640

‘

E-01 = E+OO = = E-01 = E-02 = Ei-01 = E-02 =

ins/d mN/m

“c m m kg/m9 std ms/ms

●Conver810nfactor la exact.

Or;glnal manuscript r~elved In Society of Petroleum Englneere offloe July 13, 1977. Paper ●ccepted for publication Jan. 18, 1979. Revlaed menuacrlpt received July 17, 1978. Paper (SPE 6374) flrat presented at the SPE-AIME 52nd Annual Fall Technical Conference and ExtNbltlon, held In Denver, Oct. 9-12, 1877. Thle paperwill be Included In the 197S TtsrrrsaotkIrr8volume.