LOWERING UNCERTAINTY IN CRUDE OIL MEASUREMENT BY SELECTING OPTIMIZED ENVELOPE COLOR OF A PIPELINE

Transcription

1 LOWERING UNCERTAINTY IN CRUDE OIL MEASUREMENT BY SELECTING OPTIMIZED ENVELOPE COLOR OF A PIPELINE by Mahmd FARZANEH-GORD, Alireza RASEKH, Mrteza SAADAT, Amin NABATI 1. Intrductin Lwering uncertainty in crude il vlume measurement has been widely cnsidered as ne f main purpses in an il exprt terminal. It is fund that crude il temperature at metering statin has big effects n measured vlume and may cause big uncertainty at the metering pint. As crude il flws thrugh an abvegrund pipeline, pick up the slar radiatin and heat up. This causes the il temperature at the metering pint t rise and higher uncertainty t be created. The amunt f temperature rise is depended n exterir surface paint clr. In the Kharg Island, there is abut 3 km distance between the il strage tanks and the metering pint. The il flws thrugh the pipeline due t gravity effects as strage tanks are lcated 60m higher than the metering pint. In this study, an analytical mdel has been cnducted fr predicting il temperature at the pipeline exit (the metering pint) based n climate and gegraphical cnditins f the Kharg Island. The temperature at the metering pint has been calculated and the effects f envelpe clr have been investigated. Further, the uncertainty in the measurement system due t temperature rise has been studied. Key wrds: abvegrund pipeline, envelpe clr, il vlume measurement, slar energy, uncertainty Accurate measurement f crude il in an il exprt terminal is primary bjective. Any type f measurement errr can result in a financial lss, whether it is t the buyer r the seller. Such errrs are due inaccuracies that ccur during the custdy transfer prcess and results in the buyer receiving mre r less prduct than cntracted. Three primary surces f errr in crude il measurement include a) Vlume measurement b) Sediment and water c) temperature rise. Accurate temperature cmpensatin f grss measured vlume is critical t verall vlume measurement accuracy. Tday paint clr is cmmnly utilized in cntrl f absrbed slar radiatin by surfaces and much wrk has been carried ut in this field (e.g. [1-5]). In thermal manner, each clr has specific absrptivity and emissivity cefficient. While sun radiate t surface, absrbed and reflected energy will change with absrptivity and emissivity cefficient f surface paint clr. Fr surveying effect f surface radiative parameters, esfahani and abdlabadi [6] studied the effect f radiative parameters such as, surface reflectivity and absrptivity n thermal degradatin f plyethylene. Here, by cnsidering the Kharg Island climate cnditins, slar radiatin has predminantly effect n crude il temperature rise inside pipeline. As the Kharg Island is main Iran il exprt terminal, the accuracy f measurement is very imprtant issue. Cnsidering the fact that, the pipeline exterir surface paint

2 clr has effect n crude il temperature rise; their effects n accuracy f the measurement system have been investigated. At the fields f effect slar radiatin n temperature variatin in pipe flw, there have been previus studies such as Kwsary and Purshaghaghy [7]. They have cnsidered a mre realistic situatin in which dissipatin f the heat thrugh the uter surface t the ambient has been cnsidered. They cmputed temperature develpment in pipe flw with cnsidering thermal leakage by heater element that was shwn bulk temperature tends t a limiting value alng pipe. Yaghubi et al. [8] estimated temperature f il inside cylindrical receiver fr the Shiraz slar pwer plant; they suppsed unsteady state cnditin and neglected cnductin variatin alng pipe and btained nnlinear partial differential equatin system then slved by numerical methd. Madani [9] calculated temperature distributin f water inside the cylindrical tube with black cver by simple mdel f verall cefficient f heat lsses. At this wrk, we suppse hurly steady state situatin in pipe flw that temperature f il and pipe vary in the directin f flw. Kim et al. [10] btained thermal perfrmance f a slar system cmpsed f parallel, all-glass (duble skin) vacuum tubes by using a nedimensinal analytical mdel; they suppsed cnstant heat flux arund tube under unsteady state cnditin; Han et al. [11] cntinued same wrk with three-dimensinal mdel and cmpared results with ne-dimensinal mdel and shwed that there are gd agreement with each ther. Luminsu et al. [1] studied analytically the prcess f preheating bitumen using slar energy t ptimize cnnectin between several slar cllectrs. In the present research, a practical analytical mdel fr incmpressible flw inside an abvegrund pipeline has been cnstructed and presented. The uter surface f the pipeline is expsed t slar radiatin and wind stream. The radiatin heat exchange with ambient is als taken int accunt. Further, the effects f exterir surface paint clr which represented by emissivity and absrptivity have been studied. It is assumed that each paint clr has its specific absrptivity and emissivity and these indices have been cnsidered cmpatible with cmmn paints in industry. The mdel has been develped t study temperature develpment f crude il flw within a specific pipeline. Fr simplifying the mdel, hurly steady state situatin in pipe flw has been assumed. In mst studies because f using thermal resistance f radiatin t sky, pipe surface temperature is assumed cnstant [13, 1]; while at this paper pipe surface temperature variatin alng flw is taken int accunt. The mdel has been applied t a specific crude il pipeline. The pipeline is lcated in the Kharg Island, main Iran exprt terminal and delivers the crude il frm strage tanks t the exprting ship. The effects f pipeline paint clr in varius vlume flw rate are investigated theretically and experimentally under the relative weather cnditins f Kharg Island. The effects f paint clr have been represented by absrptivity and emissivity f the exterir surface. By cnsidering the fact that absrptivity and emissivity f the exterir surface has the primary effects and knwing the prperties f available paints in industry, ne culd select the best pipeline surface cating in accrd with its emissivity and absrptivity. Initially amunt f absrbed slar energy by pipeline surface has been estimated fr the Kharg Island climate cnditin. Then by cmputing cnvectin heat transfer cefficient the utlet il temperature was calculated by emplying energy balance alng the pipe line fr a day (5th August 007). Finally by catching relatinship between temperature and errr, the uncertainty in crude il vlume measurement has been calculated. It is fund that pipe paint clr is imprtant parameter n alteratin f il temperature and caused big uncertainty in il measurement.

3 . prblem descriptin The prblem under investigatin is heat transfer frm hrizntal pipe with incmpressible fluid flw inside. Figure 1 shws the gemetry and the cnfiguratin f the prblem which is based n the actual cnditin f the Kharg Island il terminal. Crude il flws frm the strage tank (lcated 60m higher than the pipeline) int the pipeline which its length is abut 3 Km as shwn in fig. 1. At pipeline exit, il reached t the metering statin fr measuring and the custdy transfer prcess. It is bvius that il temperature was affected by slar radiatin as il travels thrugh the pipeline. The main bjective f this paper is t determine utlet il temperature. By knwing the utlet temperature, it is pssible t cnstruct a relatinship between temperature and uncertainty then estimate errr in crude il vlume metering. Fig. 1. Schematic diagram f il pipeline system with strage tank in Kharg Island. Slar radiatin ver pipeline increase the heat lad during the day, but wind n the ther side has an effective rle t remve heat lad frm the pipe. The inlet temperature f the fluid, T fi, is assumed t be equal t il strage tank temperature and the utlet temperature is T f. As pipeline length is much higher than its diameter, the prblem is assumed t be ne-dimensinal s temperature variatin alng the pipe (x directin) is nly cnsidered. The parameters which are kept cnstant during the investigatin are the pipe's diameter D and pipeline length L. A picture f the pipeline and a schematic diagram f adpted thermal mdel are shwn in fig.. (a) (b) Fig.. a)the Kharg il pipeline, b) a schematic diagram f cnsidered prblem under investigatin.

4 3. Mathematical mdeling The slar radiatin is the primary phenmena which affects temperature variatin f surfaces. T be able t estimate pipe and fluid temperature, slar radiatin shuld be calculated in first step. Fr estimating slar radiatin many engineering mdels have been develped and prpsed. In all f these mdels, the weather cnditin and lcatin are imprtant factrs. Kamali and Mradi [15] suggested that Angstrm mdel is mre suitable fr the Kharg Island. Therefre, the Angstrm mdel has been emplyed in this study t calculate slar radiatin. Based n Angstrm mdel, slar radiatin can be estimated using the fllwing equatin as [16], I s = a + b (1) I s Where fr the Kharg Island, a=0.37 and b=0.35 in spring & summer, and a=0.37 and b=0.38 in autumn & winter [15]. The slar declinatin (δ), the main sunshine hur angle (ω s ) and the maximum pssible sunshine duratin day length (S ) was calculated frm Cper [17]: 360 δ = 3.5 sin [ (8 + n)] () 365 ωs = Arc cs( tan φ.tan δ ) (3) s = ωs () 15 The cludless hurly extraterrestrial radiatin n hrizntal surface can be calculated using the fllwing equatin as [18], I n π ( ω ω1 ) = I sc( cs )[csφ csδ (sinω sinω1) + sinφ sinδ ] π (5)

5 Fig. 3. Slar intensity n hrizntal surface at the Kharg Island in 5 th August 007. In this equatin I sc has adpted a value f 1367 W/m accrding t the wrld radiatin center and ω is slar hur as given by fllwing equatin [18], ω = 15( t 1) (6) The pipeline in the presented study is lcated at the Kharg island (Latitude: 9 and Lngitude 51 ). As slar energy can be varied by gegraphical situatin, the mdel was slved fr the climatic cnditins f the Kharg, representing the suthern Iran fr the typical days (5th August 007) f summer. Figure 3 shws amunt f slar radiatin n hrizntal surface and ambient temperature n 5th August 007. Slar radiatin is manifested between sunrise and sunset. It culd be realized that the radiatin is highest at abut 11:30 am and is negligible utside f the cnsidered time interval fr the cnsidered day. Fig.. Amunt f slar radiatin striking the pipeline surface. We estimated slar radiatin in hrizntal surface already; fr calculatin slar radiatin n pipe surface, fllwing steps is taken int accunt. Figure gives a graphical representatin f the amunt f slar radiatin striking the pipe surface. As shwn, the intensity f slar radiatin varies depending n the angle f incidence (γ), which changes accrding t the daily mvement f the sun. Sunlight, hwever, always hits half f the pipeline area because f its circular shape. The fllwing

6 equatins are btained by integrating the nrmal cmpnent f slar radiatin alng the circumference f a semi-circle, which yields the ttal slar energy absrbed by the pipeline: I p = I csγ (7) π π D π I cs( β ).. L. dβ 0 I I p = = sin β. dβ πd L π (8) 0 Here I p culd be interpreted as the slar energy absrbed per unit area f pipe surface, W/m : I I p = (9) π The ttal radiatin n pipeline surface cnsists f beam radiatin and grund-reflected radiatin. The ttal radiatin calculated by: I T = I I ρg π + (10) While reflectance f grund is cnsidered as ρ g = 0. [19]. In rder t estimate the cnvective heat transfer in utside pipe, the cncept f mixed cnvectin shuld be emplyed. The directins f air mtin due t natural and frced cnvectin are apprximately perpendicular. Fr cmbined free and frced cnvectin frm hrizntal tube several crrelatins fr varius flw regins and flw Reynlds number are prpsed. Such crrelatins can be fund in [0]. The mst widely used crrelatin t estimate cnvectin cefficient ver f a hrizntal pipe in crss flw is, m n Pr 0.5 Nu = C Re Pr ( ) 0.7< Pr <500 & 1< Re <10 Pr 6 (11) Where all prperties are evaluated at T, except Pr s, which is evaluated at T s, cylinder surface temperature. Values f C and m are given in [0]. If Pr 10, n= 0.37; if Pr > 10, n = Figure 5 shws variatins f cnvectin heat transfer cefficient utside f the Kharg il pipeline (h ) n 5th august 007. Gemetrical characteristics f the Kharg Island il pipeline are brught in tab. 1. Cnvectin cefficient can be btained frm eq. (11) and with cnsidering wind velcity at the Kharg Island n studied day. s

7 Fig. 5. Cnvectin cefficient fr Kharg il pipeline in 5th August 007. The schematic diagram f pipe flw under investigatin was shwn in fig. 1. As dimensins in radial directin are much smaller than the x (alng flw directin), ne dimensinal flw is cnsidered. The paint clr pipe surface reflects and absrbs nrmal slar radiatin flux. Absrbed slar radiatin flux increases the surface temperature and it is transferred by cnductin t the inside f the pipe then temperature f fluid is increased. In rder t btain the temperature prfile f fluid inside, a differential energy balance was carried ut. The fllwing assumptins fr energy balance equatins are cnsidered: 1. Temperature gradient acrss the thickness f the pipe is insignificant.. Steady state situatin assumed and heat transfer cefficients are cnsidered t be cnstant at the selected time interval (hurly here). 3. The surface clr is paque with cnstant absrptivity and emissivity.. The variatins in the absrptivity and emissivity f the clr surfaces with the variatin in angle f the incming radiatin are neglected. 5. Fluid prperties are independent f temperature and mean amunt is cnsidered. 6. Heat cnductin variatin alng fluid flw is neglected. Fig. 6. Pipe and fluid cntrl vlumes fr analytical study.

8 The energy balance equatins fr pipe, cntrl vlume 1, and fluid, cntrl vlume, as shwn in fig. 6 culd be written and presented as: Fr vlume cntrl (1): Q cnductin_ x + QRadiatin = Qsky + Qcnductin_ x+ dx + Qcnvectin_ ambient + Qcnvectin_ fluid (1) In the abve equatin, Q Radiatin indicates the incming energy in cnsequence with slar radiatin and reflectance f grund int pipe surface which is btained frm eq. (10). With substitutin ther related equatins, dts dts d Ts ka + αit ( πd ) = εσ ( πd )( Ts Tsky ) + ( ka ka ) + h ( )( ) ( )( πd Ts T + hi πdi T dx dx dx s T f ) (13) π( D ) That D A = i, where the sky temperature is given by Sharma and Mullick [1] as, T sky = T (1) After simplificatin we have, k ( D Di d Ts Di Di ) ( h ) + hi Ts + hi T f D dx D D Ts = εσ α εσ (15) IT ht Tsky The pipe surface temperature differences within the flw are assumed t be sufficiently small s that T s may be expressed as a linear functin f temperature. This is dne by expanding T s in a Taylr series abut the free-stream temperature T and neglecting higher-rder terms t yield, 3 T Ts 3T Ts (16) Substitutin eq. (16) int eq. (15) we have, k ( D i Ts D d ) D dx ( h Di Di + hi ) Ts + hi T f D D 3 sky εσ (T Ts 3T ) = αi T ht εσt (17) After simplificatin, eq. (17) can be written as: k ( D i D D Ts d ) dx ( h + h i D D i 3 Di + εσ T ) Ts + hi T f = αi T ht εσtsky 3εσT (18) D Fr vlume cntrl (): dt f ρ QCp = hiπdi ( Ts T f ) (19) dx Where T s can be written as,

9 ρqcp dtf T s = + T h πd dx i i f (0) With substitutin eq. (0) int eq. (18) then eq. (18) can be written as, 3 d Tf d Tf dtf a1 + a + a3 + at f = d (1) 3 dx dx dx In which, D i D ρqcp( D ) k k( D i D ) a 1 =, D ρqcp D a =, a 3 3 = ( h + i h i + εσt ), πd i h i πdihi D a ( 3 = h + εσt ) and d = α h T 3 T T εσ εσ. I T sky Eq. (1) is nnhmgeneus rdinary differential equatin frm third rder; bundary cnditins fr this differential equatin are as: 1. Inlet fluid temperature is defined: T f (0) = defined.. Inlet pipe surface temperature is defined then frm eq. (19): dtf h ( ) iπdi x= 0 = [ Ts (0) Tf (0)] dx ρqcp 3. Fluid temperature at infinite cnditin is finite: T f ( ) = finite. The ttal slutin f eq. (1) is given as, d T f = c1 exp( λ 1x) + cexp( λx) + c3exp( λ3x) + () a C 1, C and C 3 can be gained by upper bundary cnditins, λ i cefficients can be cmputed by fllwing equatin as, = a λ + a λ + a λ + a 0 (3) T Pipe Surface temperature can be gained by eq. () as, ρqcp [ c λ exp( λ x) + c λ exp( λ c exp( λ x) ] d λ () a s = x ) c1exp( λ1x) + cexp( λx) + c3exp( λ3x) + hiπdi Equatins () and () are the gverning equatins fr variatins f the hurly bulk temperature and pipe surface temperature alng the flw respectively, the prfile is in an expnential frm, hwever, fr mst practical cases, it is very clse t a linear functin. Hurly utlet il temperature frm pipeline is dminant parameter that we need. Fr catching this, we slved eq. () at each hur f day that sun radiate n pipeline. Relative parameters fr the case study are shwn in tab. 1. Table 1. Parameters used in case study.

10 Parameter Value L(m) 3000 D (m) D i (m) K pipe (W/m.K) 30 T fi (C) 5 T si (C) 5 The wrking fluid is chsen t be light crude il. Oil carries the maximum heat frm the pipe due t its thermal and physical prperties. Table gives the thermal and physical prperties f the selected fluids. The flw is assumed t be fully develped and turbulent. Table. Thermal prperties f crude il at 15.5 C. Ρ Cp K µ Fluid (kg/m 3 ) (KJ/kg C) (W/m.K) (Pa.s) Light il The fllwing sectin will try t discuss the effects f the surface paint clr n transferring crude il thrugh the Kharg pipeline using the previus described mdel. This may help engineers in their design t determine and select the ptimum envelp clr. The selectin may be the prime interest f many engineering applicatins. There are five different envelp clr in this analysis as shwn in tab. 3. The crrespnding absrptivity and emissivity fr each clr are als listed the fllwing table as, Table 3. Sample fr varius envelpe clr. Clr Black Green Brwn Off-white White Absrptivity Emissivity Figures 7, 8 and 9 shw variatins utlet il temperature frm pipeline fr varius vlume flaw rates during daytime. As expected, the black painted envelpe caused higher temperatures than the ther painted ne during the day time. Higher absrptivity f the exterir surface may result in a significant amunt f absrbed slar radiatin and, therefre, its inward transmissin int the il inside space; eventually result high heat lad. By cmparing figures, it culd be realized at lwer vlume flw rate (e.g bbl/hr), utlet il temperature is higher than the ther (larger) vlume flw rate. S increasing vlume flw rate is ne simple and practical way fr lwering utlet il temperature.

11 Fig. 7. Outlet il temperature frm the pipeline at 1000 barrel/hr n 5 th August 007. Fig. 8. Outlet il temperature frm the pipeline at 000 barrel/hr n 5 th August 007.

12 Fig. 9. Outlet il temperature frm the pipeline at 3000 barrel/hr n 5 th August 007. T verify validity f the mathematical mdel and numerical results, a cmparisn has been made between the numerical results and measured values f pipeline surface temperature. The experimental temperatures have been measured using infrared thermmeter frm pipeline surface n 5th august 007. The pipeline, shwn in fig., is cnsidered t have ff-white paint clr. At that particular day, light crude il flws thrugh pipeline with vlume flw rate at 1000 bbl/hr. The utlet surface temperature has been measured hurly during the day at distance f 300 m and 750 m frm pipeline entrance. The numerical results are btained by slving eq. () at each hur during f same day at crrespnding distances then cmpared with measured values. Cmparisn between the theretical and experimental results is depicted in fig. 10. In this wrk, it is fund that the results f the develped mathematical mdel are in gd agreement with the measured values.

13 Fig. 10. Temperature f the Kharg il pipeline n 5th august 007 in distance f a) 750m b) 300m frm pipe entrance.. Temperature effect n uncertainty f the metering system There are standard methds t quantify errrs assciated with any type f measurements such as the prpsed methd f Mffat []. The maximum pssible errrs in varius measured parameters were estimated frm the minimum values f utput and the accuracy f the instruments. This methd is based n careful specificatin f the uncertainties in the varius experimental measurements. In current study such methd is nt applicable as the aim is t quantify errrs assciated with temperature rise. Fr this purpse, it is assumed that there is n uncertainty in temperature measurement r ther measured parameters. T quantify errrs assciated with temperature rise, tw wrldwide acceptable methds fr crrecting the measured vlume t the vlume at the standard cnditin are utilized and cmpared. The difference between the values reprted by each methd is assumed t be uncertainty. Turbine flw meter is used at metering statin f the Kharg Island fr measuring vlume f transferred il. As it is knwn, base f buying il in internatinal market is transferred vlume at standard cnditin (1 atm and 15.5 C). Fr cnvert the measurement vlume t standard cnditin, CTL (temperature cefficient liquid) and CPL (pressure cefficient liquid) are used. Als is clear the amunts f these cefficients at standard cnditin are equal ne. Tw wrldwide acceptable methds t calculate the amunt f CTL are a) calculated frm API tables [3] b) frm belw equatin: β ΔT ( βΔT ) CTL = e (5) That, Δ T = bserved temperature 60 F(15.5 C), β = ( ρ ) standard cnditin CPL is cnstant versus temperature alteratins; therefre CTL is nly reasn making errr f metering. The CTL cefficients versus temperature fr light crude il are shwn in tab. It culd be cncluded that the difference between CTL values calculated frm the tw utilized methds increase as temperature rise.

14 Table. Variatin f CTL uncertainty with temperature fr light il. T ( C) CTL API CTL CTL API CTL T ( C) CTL API CTL CTL API CTL Here eq. (6) is utilized t quantify uncertainty in il vlume measurement. uncertainty = errrctl CPL V (6) Uncertainty in vlume measurement is cmputed by eq. (6) accrding t pipeline utlet il temperature tward metering statin and CTL values in tab. Daily uncertainty has been estimated by adding hurly uncertainty during a day. The uncertainty percent is calculated based n the fllwing relatin, Daily Vlume errr uncertaint y% = 100 (7) Daily transprte d vlume Fig. 11. Effects f exterir surface paint clr and vlume flw rate n daily errr uncertainty Figure 11 shws daily uncertainty percent in metering system at the Kharg il terminal n 5th August 007. These data were btained frm eq. (7) and results in Figs. 7, 8 & 9. It culd be realized that black clr makes higher uncertainty than ther clrs. This is due t higher pipeline utlet temperature (see Figs. 7, 8 & 9) and the values f CTL in tab. As difference between standard

15 il temperature (15.5 C) and bserved (here cmputed) temperature increases, uncertainty in metering will increase t. As Black paint makes highest utlet il temperature then uncertainty is biggest fr this clr envelp. S using lighter clr (white clr) fr painting exterir surface is ne practical way t reduce uncertainty. The ther result which culd be cncluded frm fig. 11 is psitive effect f vlume flw rate n uncertainty reductin. S by increasing vlume flw rate, the ther simple way fr reducing uncertainty percent culd be utilized. Ostensibly, it may be released frm fig 11 that uncertainty is nt significantly different fr different cnditins and therefre it will be negligible. Since the vlume f exprted il reach t several millin barrels per year, this infinitesimal difference culd be induced very big uncertainty in il vlume measurement. 5. Cnclusins At this wrk a mathematical mdel fr temperature develpment in an abvegrund crude il pipeline which expsed t slar radiatin and wind stream was presented. Based n climate and gegraphical cnditins f the Kharg Island and utilizing the mathematical mdel, the temperature at pipeline utlet (the metering pint) has been calculated and the effects f main pipe line flw rate and exterir surface paint clr n temperature rise have been investigated. Tw wrldwide acceptable methds fr crrecting the measured vlume t the vlume at the standard cnditin are utilized and the difference between the values reprted by each methd is assumed t be uncertainty. By cnsidering relatin between temperature and uncertainty and the ther results btained in this wrk, the fllwing pints may be cncluded: (1) The results f the prpsed mathematical mdel are in gd agreement with the field measured values in the Kharg il pipeline with ff white as envelpe clr. () Outlet il temperature frm the pipeline increase either by lwering vlume flw rate r using darker painting (higher absrptivity and lwer emissivity) fr pipeline exterir surface. (3) Uncertainty in measurement culd be reduced by painting exterir surface with lightest clr (lwer absrptivity and higher emissivity; white here) which seems a practical way. () One simple and feasible way f reducing uncertainty is t transprt crude il with maximum allwable vlume flw rate thrugh the pipeline. Hwever, by a glance at uncertainty variatins in different cnditins, it may be cncluded the uncertainty remains cnstant in different situatins; but due t the fact that il is generally exprted in very high values and afterwards brings abut almst big uncertainly in il vlume measurement prvided that can t be neglected. Finally, utilizing paint clr with lwer absrptivity and higher emissivity (white here) has been recmmend as pipeline surface clr which can reduce uncertainty in il vlume measurement. Acknwledgements The financial supprt fr this study by Natinal Iranian Oil Cmpany (NIOC)-Iranian Oil Terminals Cmpany (IOTC), is gratefully acknwledged.

16 Nmenclature C p specific heat f crude il, [Jkg -1 K -1 ] Subscripts D pipe Diameter, [m] h cnvectin cefficient, [Wm - K -1 ] T ttal I slar radiatin, [Wm - ] p pipe K cnductivity f pipe, [Wm -1 K -1 ] f fluid K T daily average clearness index, [ ] i inner n number f day f the year, [ ] uter Nu Nusselt number (=hd/k), [ ] s surface Pr Prandtel number (=ν/α),[ ] ambient value Q vlume flw rate, [KgS -1 ] Re Reynlds number (=ρud/μ),[ ] S daily measured sunshine duratin, [hr] t time f day, [hr] T temperature [ C] V il vlume, [barrel] x axial distance, [m] Greek letters α absrptivity, [ ] ε emissivity, [ ] σ Stefan Bltzmann cnstant, [W/m - K - ] ρ density, [Kgm -3 ] ø latitude, [ ] β,γ angle, deg References [1]. Takebayashi, H., Mriyama, M., Surface heat budget n green rf and high reflectin rf fr mitigatin f urban heat island, Building and Envirnment, (007),, pp []. Wang, X., Kendrick, C., Ogden, R., Maxted, J., Dynamic thermal simulatin f a retail shed with slar reflective catings, Applied Thermal Engineering, 8 (007), pp [3]. Smith, G. B., Gentle, A., Swift, P. D., Earp, A., Mrnga, N., Clured paints based n irn xide and silicn xide cated flakes f aluminium as the pigment, fr energy efficient paint: ptical and thermal experiments, Slar Energy Materials & Slar Cells, 79 (003), pp []. Baneshi, M., Maruyama, S., Nakai, H., Kmiya, A., A new apprach t ptimizing pigmented catings cnsidering bth thermal and aesthetic effects, Jurnal f Quantitative Spectrscpy & Radiative Transfer, 110 (009), pp [5]. Berger, O., Inns, D., Aberle, A., Cmmercial white paint as back surface reflectr fr thin-film slar cells, Slar Energy Materials & Slar Cells, 91 (007), pp [6]. Esfahani, J. A., Abdlabadi, A. G., Effect f char layer n transient thermal xidative degradatin f plyethylene, THERMAL SCIENCE, 11 (007),, pp [7]. Kwsary, F., Purshaghaghy, A., Temperature develpment in pipe flw with unifrm surface heat flux cnditin cnsidering thermal leakage t the ambient, Energy Cnversin and Management, 8 (007), pp [8]. Yaghubi, M., Azizian, K., Kenary, A., Simulatin f Shiraz slar pwer plant fr ptimal assessment, Renewable Energy, 8 (003), pp [9]. Madani, H., The perfrmance f a cylindrical slar water heater, Renewable Energy, 31 (006), 3, pp

17 [10]. Kim, J. T., Ahn, H. T., Han, H., Kim, H. T., Chun, W., The perfrmance simulatin f all-glass vacuum tubes with caxial fluid cnduit, Internatinal Cmmunicatins in Heat and Mass Transfer, 3 (007), pp [11]. Han, H., Kim, J. T., Ahn, H. T., Lee, S. J., A three-dimensinal perfrmance analysis f all-glass vacuum tubes with caxial fluid cnduit, Internatinal Cmmunicatins in Heat and Mass Transfer, 35 (007), pp [1]. Luminsu, I., De Sabata, C., But, A., Slar equipment fr preheating bitumen, THERMAL SCIENCE, 11 (007), 1, pp [13]. Suehrcke, H., Petersn, E., Selby, N., Effect f rf slar reflectance n the building heat gain in a ht climate, Energy and Buildings, 0 (007), pp. 35 [1]. Sahin, A. Z., Kalyn, M., Maintaining unifrm surface temperature alng pipes by insulatin, Energy 30, (005), pp [15]. Kamali, G. A., Mradi, E., Slar radiatin fundamentals and applicatin in farms and new energy, Ferdwsi., Tehran, Iran, 005 [16]. Zekai, S., Slar Energy Fundamentals and Mdeling Techniques, Springer., Lndn, 007 [17]. Cper, P. I., The absrptin f slar radiatin in slar stills, Slar Energy, 1 (1969), pp [18]. Duffie J. A., Beckman, W. A., Slar Engineering f Thermal Prcesses, Willy., New Yrk, USA, [19]. ASHRAE, Handbk f Fundamentals, American Sciety f Heating, Refrigeratin and Air Cnditining Engineers Inc., Atlanta, 1993 [0]. Incrpera, F. P., Dewitt, D. P., Intrductin t heat transfer, Wiley., New Yrk, USA, 1990 [1]. Sharma, V. B., Mullick, S. C., Estimatin f heat transfer cefficients, the upward heat flw, and evapratin in a slar still, ASME Jurnal f Slar Engineering, 113 (1991), pp []. Mffat, R. J., Using Uncertainty Analysis in the Planning f an Experiment, ASME Jurnal f Fluids Engineering, 107 (1985), pp [3]. Ferry, R., Vlume crrectin factr Fr the Manual f Petrleum Measurement Standards, American Petrleum Institute., Washingtn, D. C., 1995 Authrs affiliatins: M. Farzaneh-Grd, A. Rasekh, M. Saadat, A. Nabati Faculty f Mechanical Engineering, Shahrd University f Technlgy Shahrd, Iran Crrespnding authr: M. Farzaneh-Grd mahmd.farzaneh@yah.c.uk