The influence of the equivalent hydraulic diameter on the pressure drop prediction of annular test section

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1 IOP Conference Series: Materials Science an Engineering PAPER OPEN ACCESS The influence of the equivalent hyraulic iameter on the pressure rop preiction of annular test section To cite this article: A H H Al-Kayiem an M A Ibrahim 05 IOP Conf. Ser.: Mater. Sci. Eng Relate content - Force convection heat transfer from a wire inserte into a vertically-mounte pipe to liqui hyrogen flowing upwar H Tatsumoto, Y Shirai, M Shiotsu et al. - Design of micro istribution systems consisting of long channels with arbitrary cross sections S Misanitis an D Valougeorgis - Liqui flow through converging microchannels an a comparison with iverging microchannels V S Duryohan, S G Singh an A Agrawal View the article online for upates an enhancements. This content was ownloae from IP aress on 7/07/08 at 06:38

2 3r International Conference of Mechanical Engineering Research (ICMER 05 IOP Conf. Series: Materials Science an Engineering 00 ( oi:0.088/ x/00//0049 The influence of the equivalent hyraulic iameter on the pressure rop preiction of annular test section A H H Al-Kayiem an M A Ibrahim Mechanical Engineering Department, Universiti Teknologi PETRONAS, 360 Banar Seri Iskanar, Perak, Malaysia hussain_kayiem@petronas.com.my Abstract. The flow behaviour an the pressure rop throughout an annular flow test section was investigate in orer to evaluate an justify the reliability of experimental flow loop for wax eposition stuies. The specific objective of the present paper is to assess an highlight the influence of the equivalent iameter metho on the analysis of the hyroynamic behaviour of the flow an the pressure rop throughout the annular test section. The test section has annular shape of 3 m length with three flow passages, namely; outer thermal control jacket, oil annular flow an inner pipe flow of a coolant. The oil annular flow has internal an external iameters of 0.04 m an m, respectively. Oil was re-circulate in the annular passage while a col water-glycol mixture was re-circulate in the inner pipe counter currently to the oil flow. The experiments were carrie out at oil Reynols number range of 000 to 7000, covering laminar, transition an turbulent flow regimes. Four ifferent methos of equivalent iameter of the annulus have been consiere in this hyraulic analysis. The correction factor moel for frictional pressure rop was also consiere in the investigations. All methos aresse the high eviation of the preiction from the experimental ata, which justifie the nee of a suitable pressure preiction correlation for the annular test section. The conventional hyraulic iameter metho is a convenient substitute for characterizing physical imension of a non-circular uct, an it leas to fairly goo correlation between turbulent flui flow an heat transfer characteristic of annular ucts.. Introuction A commonly accepte approach to exten the pipe flow equations to annular geometry is by moification of the iameter. The equations that are use in the pipe flow to calculate the friction factor (FF an Reynols number (Re are being use in annular flow by replacing the iameter, as the characteristic geometry in pipe flow equations, by the effective iameter. Different effective iameter efinitions have been propose in the literature both for Newtonian an non-newtonian fluis. Re an FF relationship is unique to a given effective iameter efinition, De. Different values of frictional pressure rop might be obtaine accoring to the De use in characteristic geometry. Several stuies have also been propose to moify the Re efinition with shape factor while continuing to use the classical approach of equivalent iameter. Since the results from these stuies have significant eviations from each other, the selection of appropriate correlation for the respective flui an flow regime becomes very important for the accurate estimation of pressure losses in annuli Lawn an Elliott []. Dosunmu an Shah [] evelope a turbulent friction factor correlation that inclues wall roughness for straight pipe an annular flow. A systematic approach is aopte in which pipe an Content from this work may be use uner the terms of the Creative Commons Attribution 3.0 licence. Any further istribution of this work must maintain attribution to the author(s an the title of the work, journal citation an DOI. Publishe uner licence by Lt

3 3r International Conference of Mechanical Engineering Research (ICMER 05 IOP Conf. Series: Materials Science an Engineering 00 ( oi:0.088/ x/00//0049 annular pressures loss ata for two fluis (xanthan gum an guar gum are use. The first pressure loss ata with xanthan gum have been use for correlation evelopment while the secon set of ata with guar gum have been use for the correlation evaluation. They recommenation that the hyraulic iameter efinition of equivalent iameter for an eccentric annulus provie the best annular efinition for friction pressure preiction. In aition to the hyraulic iameter customarily use an accepte as equivalent iameter for the annular concentric ucts, there are many other equivalent iameter correlations suggeste in the literature. In the past, annuli have been evaluate on the basis of hyraulic iameter as equivalent iameter, but this may not always be the best way to represent the imension for flow in an annulus. Lawn an Elliott [], an Jones an Leung [3] recommene the nee of further stuies to explore the influence of ifferent equivalent iameters in the annular flows. Anifowoshe an Osisanya [4] teste seven ifferent equivalent iameters efinitions to estimate their effect on the pressure losses in wellbore hyraulics. The preicte results have been compare with experimental ata to select the best moel to fit the pressure losses preiction of power low moels. The conclue that the pressure losses estimation is significantly affecte by the equivalent iameter moel. They suggeste that the hyraulic iameter efinition provie the best estimation of the pressure losses for the power law flui in laminar flow conitions. The objective of the present paper is to emonstrate an iscuss the pressure rop results, which are preicte theoretically an measure experimentally, for the annulus oil flow using various equivalent iameter moels. This effort is part of a hyraulic characterization an correction of unjustifie flow loop for wax eposition stuies, an to introuce a correction metho to ajust the pressure rop preiction. In aition to the commonly use hyraulic iameter moel, another three moels have been checke, an the pressure rop correction factor moel. The investigate region covers all the flow regimes, laminar, transition, an turbulent with Re ranging from 000 to The results assiste in unerstaning the influencing of the equivalent iameter on the preiction of the pressure rop in the eposition section.. Experimental apparatus The experimental set-up use for this stuy, shown in figure, is a high pressure/high temperature (HPHT flow loop, evelope for wax eposition research of waxy crues. The main test section has an annular flow shape of 3 m long. The test section is fully jackete with hot glycol-water mixture recirculate in the heating system of the HPHT flow loop from the hot flui reservoir. While a col glycol-water mixture is re-circulate in the central pipe an counter-currently to the oil flowing in the annular space. The aim of the col mixture is to provie a col conitions for the flowing oil to impose the waxing eposition. Figure. Schematic of the wax eposition test loop in the HPHT flow loop.

4 3r International Conference of Mechanical Engineering Research (ICMER 05 IOP Conf. Series: Materials Science an Engineering 00 ( oi:0.088/ x/00//0049 The oil is re-circulate through the experimental flow loop by 3 3 stage gear pump. The flowrate an ensity of oil are measure by MICROMOTION flow meter installe ownstream the pump. The oil enters an leaves the test section vertically from inch pipe. A Rosemount ifferential pressure transucer is installe across the oil section to measure the pressure rop. The inlet of the oil section is equippe by pressure transmitter. The heating jacket temperature, oil temperature an col glycol-water mixture temperature are monitore at the inlet an outlet of the test section by type-t (copper-constantan thermocouple probes. 3. Equivalent iameter approaches for non-circular pipe flow Preiction of Re, FF, an the pressure loses, Δp may iffer accoring to the use of ifferent De. In this contest, several stuies have also been propose to moify the Re efinition shape factor while continuing to use the classical approach of equivalent iameter. Since the results from these stuies have significant eviations from each other, the selection of appropriate correlation for the respective flui an flow regime becomes very important for accurate estimation of pressure losses in annuli, Lawn an Elliott []... The Hyraulic Diameter Metho, Dh The common representation of iameter for flow in the non-circular conuits is the hyraulic iameter efine as: 4A D h ( P where A is the flow area an P is the perimeter. For annular configuration, D h becomes, D h In aition to the hyraulic iameter customarily given by equation ( an accepte as equivalent iameter for the annular concentric ucts [5], there are many equivalent iameter correlations also suggeste in the literature. These correlations have been checke against the hyraulic iameter to exten the criteria of the pressure rop characterization. By efining the inner an outer iameters of the annulus by an, respectively, the three methos efining the annulus equivalent iameter are as below.... The Petroleum Diameter Metho, De, p. One of the suggeste ways of calculating the pressure rop of a non-circular, concentric- annular flow cross-section name The Petroleum Engineering Metho uses equation ( for evaluating an equivalent calculation iameter to replace the circular pipe iameter Bertuzzi F [6]. 5 3 D e, p (... The Equivalent Area Diameter Metho, De, a. Equation (3, simply, is assuming an equivalent iameter of a circular pipe having the same flow area. The equivalent area iameter for annulus is calculate as: D e, a (3 3

5 ..3. The Equivalent Geometry Diameter Metho, De, g. Another criteria use to obtain an equivalent circular iameter from comparing the geometry in the pressure-loss equations for pipe flow an concentric annulus flow of Newtonian flui terms is the geometry terms is the equivalent geometry iameter given by Bertuzzi F [6]: / ln(, D g e (4.. The Correction Factor Moel, knon-c Another metho for preicting the frictional pressure rop for flow in a concentric annular conuits (long pipe stabilize flow assumption suggests the use of a correction coefficient for non-circular passages, k non-c. This factor is to be separately evaluate for laminar an turbulent flow conitions an applie to the frictional pressure rop calculations with the ai of a circular pipe stanar correlations but having a iameter equal to the hyraulic iameter, (D h = - of annular conuit Ielchik an Frie [7]. For a roune annular tube, the correction factor, which is a function of the iameter ratio, can be foun for (Re 000 from:, ln k lam c non (5 Equation (6, obtaine by Jones & Leung (3, is also propose to preict the correction factor for the laminar flow in the annular passage, as: / / ln( ( ( ( ( 4 4, k lam c non (6 Both equation (5 an (6 are not a function of Re, they are only function of the iameters of the annular flow conuits. In the case of turbulent flow, k non-c epens only slightly on the iameter ratio an lies in the range The correction factor of such a tube can be calculate from the following formula , f f k turb c non (7 where, an are the inner an outer iameters of the annulus passage. Accoring to the hanbook of Hyraulic Resistance [7], the actual frictional pressure rop in a stabilize long pipe assumption flow in an annular conuits shoul be calculate as a prouct of a correction coefficient an the frictional pressure rop calculate for the hyraulic iameter of the annular conuits. 3r International Conference of Mechanical Engineering Research (ICMER 05 IOP Conf. Series: Materials Science an Engineering 00 ( oi:0.088/ x/00//0049 4

6 3r International Conference of Mechanical Engineering Research (ICMER 05 IOP Conf. Series: Materials Science an Engineering 00 ( oi:0.088/ x/00// Results an iscussion In orer to ecie the appropriate moel of equivalent iameter, the preicte pressure rop in the test section is compare to the measure pressure rop. A Rosemount ifferential pressure transucer is installe across the oil section to monitor the pressure rop. The pressure rop is preicte using Darcy equation assuming Newtonian, incompressible an steay flow in the annulus, L U P f (8 D e Darcy friction factor, f is estimate using Churchill s equation. The Churchill equation combines expressions for friction factor in both, the laminar an the turbulent flow regimes. It is accurate to within the error of the ata use to construct the Mooy iagram. This equation also provies an estimate for the transition region. The Churchill equation shows very goo agreement with the Darcy equation for laminar flow. In the turbulent regime a ifference of aroun 0.5-% is observe between the Churchill equation an the Colebrook equation, Co [8]. f 8 8 Re A.45ln B Re 7 Re A B e D e 6 (9 Re is base on the relevant equivalent iameter, an e is the surface roughness. Knowing that the annulus inner an outer iameters are 0.04 an m, respectively, the values of the equivalent iameters, D e are obtaine from the four moels using the set of equation ( to (4. The calculate values of the equivalent iameters are shown in table. 4.. Results of the Pressure Drop using Equivalent Diameter Moels Figure isplays the measure an preicte pressure rop across the annulus versus Reynols number. The actual Re calculate from the measurement in the annulus is ranging from 3000 to The preicte ranges of Re are extene to 7000 to examine the capacity of each moel in simulating the turbulence regime. The results of pressure rop obtaine by using the various equivalent iameter moels are compare with the measure results. The equivalent iameter has significant effect on the turbulent flow regime length an the pressure rop. Different trens of the pressure rop coul be observe for ifferent equivalent iameters use in the preiction. In case of the equivalent area metho, which has the lowest values of the pressure rop estimation, the turbulence region is over estimate compare to the realistic estimation. The length of the turbulent flow regime ecrease with the increase of the value of the equivalent iameter. For this point, care must be taken in the selection of the appropriate equivalent iameter which can give a goo representation for the flow phenomenon in the annular passage. As it is clear in the figure, all the moels are unerestimate the pressure rop compare to the measure values. In fact, eeper investigation has emonstrate that the moels are correct if the losses at the inlet an outlet of the annulus test section are taken into consieration. This will be elaborate further in the coming sections. 5

7 3r International Conference of Mechanical Engineering Research (ICMER 05 IOP Conf. Series: Materials Science an Engineering 00 ( oi:0.088/ x/00//0049 Figure. The effect of the various equivalent iameter moels on the preiction of the pressure rop at various turbulent regimes. Figure 3 shows the regression analysis for the calculate an measure pressure rop using ifferent equivalent iameter moels. The equivalent area moel shows the biggest eviation of 96% between the measure an calculate pressure rop, an the values of the measure pressure rop are 3 times the calculate values with stanar error of 3.8. The equivalent geometry moel showe the smallest eviation of 9% an the measure pressure rop is times the calculate pressure rop with stanar error of Figure 3. Calculate versus measure pressure rop an linear regressions; the effect of various equivalent iameter moels use for the annulus. 6

8 3r International Conference of Mechanical Engineering Research (ICMER 05 IOP Conf. Series: Materials Science an Engineering 00 ( oi:0.088/ x/00// Results of the Pressure Drop using Correction Factor Moel For the eposition apparatus uner consieration in this stuy, the correction factor for laminar flow, k non-c, lam, accoring to equation (8, is equal to.49. The same value is obtaine by using equation (9. For turbulent flow, the correction coefficient, k non-c, turb, is epenent on Re number. This epenency is foun to be week for Re ranging from 000 to 0000, k non-c, turb = This is because of the presence of the transition zone an low turbulence level in this range of Re. Figure 4 illustrates the correction factor effect on the calculation of the pressure rop. The use of Jones & Leung (3 correction factor reuces the root mean square error between the measure an calculate values by %, while the stanar eviation from the measure values remains the same about with or without J-L correction. Therefore the correction factor prouces insignificant (positive effect for improving the calculation routine. However, the correction factor metho shoul be consiere for polishing calculation results when the hyraulic iameter approximation is use, (3, 5, 7. Figure 4. The effect of the correction factor on the calculation of the pressure rop. Although the equivalent geometry moel, equation (4, slightly reuces the iscrepancy between the measure an calculate pressure rop results compare to other equivalent iameters, the hyraulic iameter will be use as stanar for the calculations an further analysis. This ecision is justifie by the following reasons: The hyraulic iameter is a convenient substitute for the characteristic physical imension of a non-circular uct, an it leas to fairly goo correlation between turbulent flui flow an heat transfer characteristic of circular an noncircular ucts. The hyraulic iameter is also use for ucts involving laminar flow to provie a consistent basis of comparison with turbulent flow results (, 3, 4. However, for laminar flow itself, this quantity oes not lea to satisfactory correlations between circular an noncircular ucts, Ielchik et al. (7. Using a general correlation for the equivalent length in not avise as it emonstrate that the equivalent length is not sufficient for accurate escription of the observe behavior. No existing correlation or metho has yet foun with general acceptance Jones an Leung (3. 5. Conclusion Annular flow test section, esigne originally for wax eposition stuies, is investigate experimentally an theoretically to introuce acceptable hyraulic simulation moel. Four moels, an also the pressure rop correction factor moel, have been investigate. The followings are conclue. The equivalent iameter moels have significant influence on the estimation results of the pressure rop in annuli. 7

9 3r International Conference of Mechanical Engineering Research (ICMER 05 IOP Conf. Series: Materials Science an Engineering 00 ( oi:0.088/ x/00//0049 The four moels of the equivalent iameters stuie in the present work show ifferent tren in estimating the turbulence regions in the annulus. The equivalent geometry iameter moel uner-estimate the turbulence level, while the other moels over-estimate the turbulence level. The hyraulic iameter is reasonably estimate the turbulence level in the annulus. However, the theoretically obtaine results of the frictional pressure losses have shown large eviation compare to the measurement results. Accoringly, a correction metho is necessary to reuce the mathematical simulation error of the frictional pressure losses of oil flow in the annular test section in PRSB HPHT flow loop. Acknowlegement The authors acknowlege Universiti Teknologi PETRONAS, (UTP for the financial support to carry out the project. In particular, the secon author expresses his appreciation to UTP for sponsoring his stuy uner the GA scheme. Thanks are ue to PRSB/PETRONAS for proviing the HPHT flow loop apparatus an for the logistic support to carry out the experimental measurement. References [] Lawn C, Elliott C 97 Journal of Mechanical Engineering Science [] Dosunmu I T, Shah S N 03 Journal of Petroleum Science an Engineering [3] Jones O C, Leung J 98 Journal of Fluis Engineering [4] Anifowoshe O L, Osisanya S O, The Effect of Equivalent Diameter Definitions on Frictional Pressure Loss Estimation in an Annulus With Pipe Rotation. SPE Deepwater Drilling an Completions Conference; 0: Society of Petroleum Engineers. [5] Davison P 05 Turbulence: an introuction for scientists an engineers Oxfor University Press, USA [6] Bertuzzi F F M J, Poettmann F H an Thomas L K Wellbore Wellbore Hyraulics Petroleum Engineering Hanbook. Richarson TX USA: Society of Petroleum Engineers 987. [7] Ielchik I E, Frie E 986 [8] Co C 988 Flow of fluis through valves, fittings, an pipe Crane Co. 8