Numerical analysis of fluid flow properties in a partially perforated horizontal wellbore

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1 Amercan Journal of Energy Engneerng 2014; 2(6): Publshed onlne December 23, 2014 ( do: /jajee ISSN: (Prnt); ISSN: X (Onlne) Numercal analyss of flud flow propertes n a partally perforated horzontal wellbore Mohammed Abdulwahhab Abdulwahd 1, *, Sadoun Fahad Dakhl 2, I N Nranjan Kumar 3 1 Marne Engneerng Department, Andhra Unversty, Vsakhapatnam, Inda 2 Fuel & Energy Department, Basrah Techncal College, Basrah, Iraq 3 Marne Engneerng Department, Andhra Unversty, Vsakhapatnam, Inda Emal address: Mohw2002@yahoocom (M A Abdulwahd), drsadoun2@gmalcom (S F Dakhl), neeru9@yahoocom (I N N Kumar) To cte ths artcle: Mohammed Abdulwahhab Abdulwahd, Sadoun Fahad Dakhl, I N Nranjan Kumar Numercal Analyss of Flud Flow Propertes n a Partally Perforated Horzontal Wellbore Amercan Journal of Energy Engneerng Vol 2, No 6, 2014, pp do: /jajee Abstract: The pressure drops n horzontal wellbores, acceleraton, wall frcton, perforaton roughness, and flud mxng are analyzed n a partally perforated wellbore It was demonstrated that the perforaton nflow actually reduced the total pressure drop The pressure drop due to perforaton roughness was elmnated by the perforaton nflow when the rato of radal perforaton flow to axal ppe flow rate reached a certan lmt Three dmensonal numercal smulatons on a partally perforated ppe wth 150 perforatons, geometrcally smlar wth wellbore casng (12 SPF, and 60 phasng) were presented and analyzed Numercal smulatons by commercal code CFX were also conducted wth Reynolds numbers rangng from 28,773 to 90,153 and nflux flow rate rangng from 0 to 899 lt/hr to observe the flow through perforated ppe, measure pressure drops, frcton factors and pressure loss coeffcents The acceleraton pressure drop mght be mportant compared wth the frctonal pressure drop The numercally calculated results usng k-ε model were compared wth the expermental results The numercal solutons agreed well wth the expermental data Keywords: Pressure Drop, Perforaton, Numercal, Radal Flow, Wellbore 1 Introducton Over the last decade, flows through horzontal wells have become a well-establshed technology for the recovery of ol and gas A consderable amount of analytcal and expermental work has been publshed on varous aspects of horzontal-well producton, ncludng transent flow, stablzed nflow models, productvty ndces, conng and crestng behavor Although these methods provde nsght nto the behavor of horzontal wells, only a few of them are consdered the pressure drop along the wellbore assumng the nfnte conductvty essentally Horzontal well productvty s lmted by the pressure drop wthn the wellbore, especally when the pressure drop s compared wth the reservor drawdown A better understandng of the factors affectng the total pressure drop wthn the wellbore s essental Knowledge of dfferent pressure drops that effects the horzontal wellbores s crucal n desgnng successful horzontal wells and optmzng well performance In 1990, [1] proposed the frst sem analytcal model to evaluate the producton performance of a horzontal well wth the consderaton of the wellbore-pressure drop resultng from turbulent flow Later the study contnued by others [2-9] who have presented dfferent couplng models for wellbore flow and reservor nflow through perforatons However, n certan case studes the pressure drop along a wellbore was studed just by consderng only the frctonal component In most crcumstances; the pressure drop s studed takng the acceleraton nto consderaton by neglectng the other effects lke nflow, mxng etc Reference [10] n ther study revealed that, because of the exstence of perforaton nflow, acceleraton pressure drop s an mportant factor relatve to the frctonal component Ths sgnfcantly wll nfluence the well-flow rates under certan condtons Wth the ncrease n flow velocty, the momentum nfluences the pressure drop n addton to the frcton pressure drop Ths part of the pressure drop has been addressed by several authors n recent years [5, 8, 11, and 12] Apart from that the perforaton holes act lke roughness elements whch ncrease the frcton factor of the wellbore [13] Reference [14] performed expermental studes of turbulent

2 134 Mohammed Abdulwahhab Abdulwahd et al: Numercal Analyss of Flud Flow Propertes n a Partally Perforated Horzontal Wellbore ar flow n a porous crcular ppe wth unform ar njecton through the ppe wall The fully developed turbulent ar flow, at Reynolds numbers of 28,000 to 82,000, entered the ppe whle ar was njected unformly through the wall at dfferent ratos rangng from to of njecton velocty to the average velocty at the entrance It s qute nterestng to note that the characterstcs of ppe flow wth wall mass transfer are dfferent from those of channel flow or flow past a flat plate For example, consderng the lamnar flow case, the local frcton factor ncreases wth an ncrease of wall Reynolds number for ppe flow but decreases for the channel flow [15] Reference [16] studed flow resstance n a perforated ppe, both wth and wthout flow njecton through the ppe wall, by conductng experments on a ppe of 6 5/6 nch outsde dameter and 17 ft n length Reference [11] stated that the total pressure drop along a perforated ppe s made up of wall frcton and nflow acceleraton and computed the wall frcton factor n the same way for a regular, unperforated ppe Reference [17] studed channel flow wth contnuous nflux nto the horzontal channel from an ol-reservor model They stated that the pressure gradents ncreased almost unformly n the test channel because of the confluence of nflux and axal flow, and the resultng pressure drop ncreases lnearly wth nflux velocty A careful set of sngle-phase experments n a perforated ppe wth radal nflow has been conducted by [18 and 19] In these experments, water s used as the workng flud References [18 and 19] attempt to account for the effects of radal nflow by assumng that the pressure drop n a perforated ppe s the sum of three contrbutons: the frctonal pressure drop, the pressure drop assocated wth the acceleraton of the flud n the ppe, and fnally, a mxng pressure drop References [18 and 19] showed that most of the pressure drops n the perforated ppe s due to frctonal and acceleratonal effects However, the mxng pressure drop s sgnfcant and ts contrbuton to the pressure drop s often negatve It s, therefore, suggested that the radal nflow lubrcates the ppe flow Although ths seems reasonable n the case where the velocty enterng through the radal perforatons s small compared wth the axal velocty n the ppe, they would not expect lubrcaton to occur when the radal velocty s of the same order of magntude as the axal velocty Namely, when radal and axal veloctes are of the same magntude, a jet wll penetrate the axal ppe flow resultng n a certan degree of blockage of the ppe Ths would lead to an ncrease of the pressure drop n the ppe In ths paper, the theoretcal that study of the pressure drop n a partally perforated wellbore s presented That ncorporates not only frctonal, acceleratonal pressure drops but also the pressure caused by nflow The man dfferences between the theoretcal study n ths paper wth the experments carred out by [18 and 19] are the dameter of perforatons and the perforaton densty of the ppe SG has used a perforaton dameter of 3mm and 158 perforatons, where as n ths present study, a perforaton of 4mm dameter and 150 perforatons have been used The objectve of ths paper s to determne theoretcally the varous factors that contrbute to the total pressure drop n a perforated ppe In addton to the pressure profles along a blank secton downstream of a perforated secton were measured, and new wall-frcton-factor correlatons for ppe flow wth perforaton nflux were calculated In lne wth [18 and 19], t was notced that the lubrcaton of the ppe flow occurred when the rato of the total perforaton flow rate to the total flow rate at the ppe outlet was small 2 Theoretcal Model Theoretcal analyss was carred out to determne the total pressure drops, frctonal, acceleraton and addtonal pressure drops Flud flow n a wellbore s consdered as shown n Fg 1 and assumed sngle-phase flow of an ncompressble Newtonan flud under the sothermal condtons wth no heat transfer to and from the flud to the envronment The test ppe s a partly perforated one and the rest s a plan ppe wthout perforaton Ppe and perforaton geometry for expermental and theoretcal study s lsted n Table 1 The computatonal doman taken up n ths study s same as that of the dmensons consdered n the expermental rgs [18 and 19] The geometry has been analyzed usng three dmensonal Computatonal Flud Dynamcs (CFD) Fg 2 s the structured computatonal grds; the mesh conssts of nodes and elements wth fve boundary layers The calculatons were carred out wth commercal fnte volume code ANSYS FLUENT 14 CFX5 usng a frst scheme and turbulent wth k epslon model Table 1 Geometry of the test ppe Item Expermental Theoretcal Outer Dameter 30 mm - Inner Dameter 2194 mm 22 mm Perfo Dameter 30 mm 40 mm Total perfo number Perfo phasng Perfo densty 12 SPF 12 SPF Fgure 1 Confguraton of partly perforated test ppe (not to scale) Fgure 2The unstructured mesh for partly perforated ppe

3 Amercan Journal of Energy Engneerng 2014; 2(6): Smulaton Parameters The flud consdered for the smulatons s water wth constant densty of 9982 kg/m 3 and dynamc vscosty of 0001 kg/m s Three tests were carred out wth Reynolds number of the nlet flow rangng from 28,773 to 90,153 In each of the tests, flow rate through the perforatons was ncreased from zero to maxmum value The roughness of the test ppe wall was 003 mm; the type of the test ppe was PVC Table 2 Parameters of partly perforated ppe tests Test detals are summarzed n Table 2 Unform water mass flow s ntroduced at the nlet of a partally perforated ppe Two boundary condtons are consdered At the nlet mass flow s taken nto consderaton both axally and radally where as at the ext outlet pressure s consdered as the boundary condton It s assumed that no-slp boundary condtons occur along the walls Water enters at a unform temperature (T) of 25 C For the symmetry lnes both velocty and pressure s kept constant Test Inlet Flow Rate (lt/hr) Perforaton nlet Flow Rate (lt/hr) Inlet Flow(Re) Test 1 5,157 to 5, ,756 to 90,153 Test 2 3,361 to 3, ,935 to 61,557 Test 3 1,793 to 2, ,773 to 37,198 4 Pressure Drop n a Ppe wth Radal Inflow Over a long perod of tme the pressure drop n a fully developed turbulent ppe flow s beng studed by several researchers and nvestgators The pressure drop n a straght ppe has been determned n numerous experments The total pressure drop n a perforated horzontal wellbore can be dvded nto a reversble pressure drop and an rreversble pressure drop The reversble pressure drop s due to the momentum change (flow acceleraton) as where more flud enters the wellbore through perforatons Whle the rreversble pressure drop s that due to the ppe wall frcton, perforaton roughness and mxng effects The followng relatonshp gves the four pressure drop terms that make up the total pressure drop n a perforated horzontal well p = p (1) acc wall perfo mx The last two terms of Equaton (1) combne nto one term p add, whch s the pressure drop due to the combned effects of flud mxng and perforaton roughness Equaton (1) can then be rewrtten as p = p (2) acc wall add Applyng the conservaton of lnear momentum to the control volume n the axal drecton for each perforaton unt has equal length L, results n the sum of the forces actng on the control volume surfaces towards the downstream drecton of the ppe axs where the mass flow rate s F = moutuout mnun (3) m = ρau When radal nflow occurs, the statc pressure n the ppe s not unform, and the velocty profle s not fully developed In addton to the force contrbuted by the pressure dfference (4) across the control volume and wall shear force, the sum of the forces actng on the control volume surface ncludes a force due to the combned effects of the rreversble process of flud mxng and the presence of the perforaton hole, ncludng the effect of non-unformly dstrbuton of statc pressure and non-fully developed velocty profle, F = ( pn A pout A) w ( πd L) Fadd τ (5) From the above equatons, ths can be rearranged to get the followng total pressure drop, p n out 2 2 ( uout un ) wall add p = ρ (6) Equaton (6) ndcates that the total pressure drop conssts of three dfferent components: The pressure drop due to knematc energy change (acceleraton effects) Ths demonstrates the frst term on the rght sde of Equaton (6) The frctonal pressure drop due to wall frcton n a perforaton unt, p, s based on the average velocty out wall u downstream of the perforaton, and can be calculated from the Darcy-Wesbach equaton Whte [20], f L 2 pwall = ρu out (7) 2 D When the relatve roughness of the ppe s known, an accurate and convenent relatonshp for the frcton factor n the turbulent ppe flow s the Haaland equaton f = 18 log ε + Re 37D 111 For a hydraulcally smooth ppe, surface roughness ε should be set to zero Ths equaton apples to both lamnar and turbulent flow The pressure drop due to perforaton roughness, p perfo, s the extra pressure drop due to the presence of the perforatons It represents the extra frcton caused by the perforatons 2 (8)

4 136 Mohammed Abdulwahhab Abdulwahd et al: Numercal Analyss of Flud Flow Propertes n a Partally Perforated Horzontal Wellbore actng as roughness elements n the ppe wall The pressure drop due to perforaton roughness s most mportant when there s no flow through the perforatons It has been shown that the magntude of the pressure drop due to perforaton roughness depends on the ppe-perforaton geometry and the perforaton densty [21] The pressure drop due to mxng effects, p mx, s an rreversble pressure drop whch cannot be further classfed Ths pressure effect arses from the complex nteracton between perforaton flow and wellbore flow, whch causes dsturbances n the boundary layer and hence affects the pressure drop The rreversble pressure drop due to mxng needs to be determned by experments [21] The analytcal results were examned n terms of the total pressure drop, as shown n Fg 3 The ndvdual tests had an average outlet flow Reynolds number n the range of 37,460 to 108,940 The total flow rate rato (q) s the total perforaton flow rate dvded by the total flow rate at ppe outlet 5 New Wall-Frcton-Factor Correlatons [10] Mass transfer through the ppe wall affects the wall-frcton shear The nfluence of ether nflow or outflow depends on the regme present on the wellbore The nflow (producton well) ncreases the wall frcton for lamnar flow whle decreasng t for turbulent flow In contrast, outflow (njecton well) decreases the wall frcton for lamnar flow whle ncreasng t for turbulent flow In other words, the wall frcton s dfferent from that of ppe flow wth no nflow or outflow Therefore, frcton factor correlatons for ppe flow wthout nflow or outflow cannot be used for wellbore flow wth both axal flow n the ppe and nflow or outflow through perforatons [10] A new correlaton for the local wall frcton factor for turbulent flow has been developed n [10] usng Olson and Eckert s expermental data[14] for turbulent ar flow n a porous ppe wth unform ar njecton through the ppe wall The new correlaton s of the form [10] Re w f = f o (9) Re It was found that the rato between the local frcton factor and the no-wall flow frcton factor does not depend on the wall Reynolds number to axal Reynolds number rato; nstead, t depends only on the wall Reynolds number Therefore, a new correlaton for the local frcton factor was developed [10] f [ 00153Re ] = (10) f o 1 w Fgure 3Total pressure drop across perforated secton The total pressure drop was found to be hgher for hgher Reynolds numbers Ths effect was caused by the larger wall frctonal pressure drop under hgher flow velocty As the rate of flow through the perforatons ncreases, the flow rate rato ncreases and the total pressure drop ncreases The man reason s that a hgher flow rate through the perforatons gvng a larger acceleraton pressure drop In addton, t was found that greater wall frcton was due to larger average flow velocty n the ppe, whch was caused by nflow through the perforatons and ncreased mxng effect The pressure drop due to momentum change (acceleraton pressure drop) was calculated from Equaton (6) (the frst term of the rght sde) It was notced that the values of acceleraton pressure drop for partly perforated wellbore were hgher than the values of the frctonal pressure drop Eq 10 s a satsfactory correlaton for local wall frcton factor for sngle-phase turbulent wellbore flow [10] 6 Results and Dscussons 61 Pressure Drops n Perforated Secton In ths paper, theoretcally were carred out on the ppe that was smulated wth the expermental ppe Three tests wth dfferent ppe flow rate were carred out for the perforated ppe Fgure 4 Pressure drops across perforated secton for Test3

5 Amercan Journal of Energy Engneerng 2014; 2(6): The acceleraton pressure drop s also very mportant and cannot be neglected from the nference of Fg 4 Reference [10] explaned that for partly perforated wellbore, the rato of the acceleraton pressure drop to the frctonal pressure drop R af s hgher and changes from 127 to 071 The cumulatve acceleraton pressure drop from startng pont of the perforatons s more or less the same as the cumulatve frctonal pressure drop It s shown that the acceleraton pressure drop may or may not be mportant compared to the frctonal component dependng on the specfc ppe geometry, flud propertes and flow condtons The ncrease n total flow rate rato q leads to an ncrease n the pressure drop and further ths leads to ncrease n the axal pressure drop Fg 5 represents the total pressure drop and acceleraton pressure drop for three tests For tests 1 and 2 the acceleraton pressure drop s approxmated to zero value but test 3 has values greater than values of test 1 and test 2 at zero value of total flow rate rato The acceleraton pressure drop contrbutes to the mportant part of the total pressure drop for all the three tests The acceleraton component contrbutes n the range of 366% to 999% for test 1, from 13% to 999% for test 2, and for test 3 from 93% to 598% From Equaton (6), subtractng the acceleraton pressure 2 2 drop from the total pressure drop p ρ ( u out u n ), the results are equal to the summaton of pressure drop due to wall frcton and addtonal pressure drop The addtonal pressure ncludes pressure drop due to perforaton roughness and mxng flow p add Fg 6 depcts the behavor of the remanng pressure drop The remanng pressure drop decreases wth ncrease n total flow rate rato As the rate of flow through the perforatons ncreases, the flow rate rato ncreases correspondngly and the total pressure drop ncreases It s due to the larger acceleraton pressure drop for hgher flow rate through the perforatons The remanng pressure drop decreases wth the ncreasng value of the total flow rate rato Due to ths, the acceleraton pressure drop ncreases wth the ncrease n the total flow rate rato Fgure 6 Pressure drop due to wall frcton, perforaton roughness, and flow mxng 62 Addtonal Pressure Drop n Perforated Secton The addtonal pressure drop s the resultant of the mxng effect and the perforaton roughness The addtonal pressure drop s obtaned by subtractng the frctonal pressure drop from the remanng pressure drop The wall frcton pressure drop of a perforated secton was calculated usng Equaton (7) for a unt perforaton The frcton factors were calculated from Equaton (8) for perforated ppe usng 003 mm The roughness of the ppe was taken nto consderaton because the ppe was made of PVC The wall frcton pressure drop for unformly perforated secton was calculated Equaton (11) Usng Equaton (8), the frcton factor was calculated The frcton factor can also be found from Equaton (9) because t depends on the rato of Re w or from Equaton (10) because t depends only on the Re wall Reynolds number [10] p wall = N 1 = 1 L ρu f D 2 2 (11) where N s the total number of perforatons and D s the ppe dameter The value of L s the dstance n the axal drecton of the ppe between two adjacent perforatons mnus the equvalent length that s occuped by a perforaton For a unformly perforated ppe, L s a constant, calculated as 2 L d L = N 1 4 (12) D Fgure 5 Total and acceleraton pressure drops for the three tests where d s the perforaton dameter and Lthe total length between the frst and the last perforaton of the perforated secton Fg 7 represents the addtonal pressure drop wth total flow rate rato for all the tests The addtonal pressure drop

6 138 Mohammed Abdulwahhab Abdulwahd et al: Numercal Analyss of Flud Flow Propertes n a Partally Perforated Horzontal Wellbore decreases as the flow rate rato ncreases When the flow rate rato s zero, the addtonal pressure drop s caused by perforaton roughness only When the total flow rate rato reaches a certan lmt, whch s about 0045 for test 1 and 2, the pressure drop caused by the perforaton s elmnated by the smoothng effect Beyond ths lmt of the flow rate rato, the addtonal pressure drop has a negatve value, whch means that the pressure drop due to wall frcton s reduced by the smoothng effect For test 3, we show that all the addtonal pressure drop values are negatve because of ncreases n radal flow, except for the value at zero flow rate rato Fgure 7 Addtonal pressure drop 64 Pressure Drop Coeffcents Pressure drop n a perforated ppe s the functon of the flow rate n the ppe A pressure drop coeffcent s defned as the pressure drop across the perforated secton dvded by the knetc energy at the outlet of the ppe p K = 2 (13) 05 * ρ * u out where u out s the average flow velocty at the outlet of the test ppe The pressure drop coeffcents were calculated for total and addtonal pressure drops for perforated secton for all the three tests The data ponts for each test follow a straght lne as shown n Fg 9 Data ponts of the three tests for total pressure drop followed parallely and closely except for some ponts of those tests conducted wth Reynolds number range from 62,000 to 80,400 and from 37,460 to 56,840 The pressure drop coeffcents ncrease lnearly wth ncreasng total flow rate rato Data ponts of dfferent tests for addtonal pressure are shown n Fg 10 Here also the graphcal lnes follow closely and parallel at low Reynolds number except for the tests conducted wth Reynolds number ranges from 90,800 to 108,940 ( due to hgh effect of pressure drop wth hgh Re) So ncrease Re range ncrease the pressure drop, ncrease of mass flow wth hgh Re and low knetc energy at the perforated secton The data ponts decrease wth ncreasng total flow rate rato as shown n Fg 6 63 Total Pressure Drop n Blank Secton Total pressure drop was calculated for plan ppe secton wthout perforatons wth flow rate rato as shown n Fg 8 The perforated secton s followed by the plan secton The values of the total pressure drop n the plan secton are lower than the values of total pressure drop for the perforated secton because the pressure drop n the plan secton of the ppe s manly due to the ppe wall frcton Pressure Loss Coeffcent Re out=90, ,900 Re out=62,000-80,400 Re out=37,460-56, Total Flow Rate Rato Fgure 9 Pressure drop coeffcent for total pressure drop Fgure 8 Total pressure drop for blank secton

7 Amercan Journal of Energy Engneerng 2014; 2(6): local frcton factor rato for a perforated ppe wth flud njecton for all the tests conducted above decreases when the radal flow ncreases For test 1, the values of the local frcton factor rato s hgher than tests 2 and 3 From Equaton (9), t was observed that wth the ncrease n the value of the radal flow, the local frcton factor rato decreased Fgure 10 Pressure drop coeffcent for addtonal pressure drop Fg 11 depcts the Numercal Smulaton results n ths paper and the expermental results conducted n tests[21] were used for the comparson of the total pressure drop n the perforated secton between the frst perforaton and the last perforaton Fgure 12 Wall frcton factor correlaton for turbulent ppe flow wth nflow Fg 13 represents the new correlaton predcton by Equaton (10) for local frcton factor rato f / f o wth njecton Reynolds number Re w It was observed that all the data ponts of the three tests pertanng to the frcton factor for a perforated ppe wth flud njecton were close to each other because the results depended on Rewonly Fgure 11 Comparson of numercal and expermental data[21] It further shows that there s a dfference for all the tests especally when the total flow rate ncreases and the curves are dvergng from the expermental tests The reason for ths s at the range of values of the Reynolds numbers s dfferent and hgher than from the expermental tests 65 Frcton Factor Frcton factor s a dmensonless parameter extensvely used n ppe flows to express the pressure drop due to frctonal effect Fg12 represents the new correlaton predcton by Equaton (9) for local frcton factor rato f / f o wth njecton Reynolds number Re It was observed that the w Fgure 13 Wall frcton factor correlaton for turbulent ppe flow wth nflow 7 Conclusons Numercal smulatons have been carred out on the flow n a partly perforated ppe wth nflow through perforatons The geometry of the ppe used was smlar to the ppe used n the

8 140 Mohammed Abdulwahhab Abdulwahd et al: Numercal Analyss of Flud Flow Propertes n a Partally Perforated Horzontal Wellbore expermental tests [18, 19 and 21] The total pressure drop n a horzontal wellbore s the sum of the pressure drops due to momentum change (acceleraton), wall frcton, perforaton roughness, and flud mxng The acceleraton pressure drop cannot be gnored compared wth the frctonal pressure drop The total pressure drop for perforated secton was larger than the total pressure drop n the plan secton wthout perforatons The addtonal pressure drop caused by the perforaton roughness was elmnated by the smoothng effect once the flow rate rato reached a certan lmt It was observed that the local frcton factor rato for a perforated ppe wth flud njecton decreased wth ncrease of the radal flow References [1] Dkken, BJ, Pressure Drop n Horzontal Wells and ts Effect on Producton Performance, JPT (November 1990) 1426 [2] Islam, MR and Chakma, A, Comprehensve Physcal and Numercal Modelng of a Horzontal Well, paper SPE presented at the 1990 SPE Annual Techncal Conference and Exhbton, New Orleans, September [3] Folefac, AN et al Effect of pressure Along Horzontal Wellbore on Well Performance, Aberdeen, 3-6 September [4] Ozkan, E, Sarca, C, and Hacslamoglu, M: Effect of Conductvty on Horzontal Well Pressure Behavor, paper SPE presented at the 1992 SPE Annual Techncal Conference and Exhbton, Washngton, Dc, 4-7 October [5] Ihara, M and Shmzu, N, Effect of Acceleraton Pressure Drop n a Horzontal Wellbore, paper SPE presented at the 1993 SPE Annual Techncal Conference and Exhbton, Houston, 3-6 October [6] Senes, K et al, Consderng Wellbore Frcton Effects n Plannng Horzontal Wells, JPT (October 1993) 994 [7] Landman, MJ, Analytcal Modelng of Selectvty Perforated Horzontal Wells, J Petroleum Scence and Engneerng (1994) 10, 179 [8] Sarca, C et al, Influence of Wellbore Hydraulcs on Pressure Behavor and Productvty of Horzontal Wells, paper SPE presented at the 1994 SPE Annual Techncal Conference and Exhbton, New Orleans, September [9] Novy, RA, Pressure Drops n Horzontal Wells: When Can They be Ignored? SPERE (1995) 29 [10] Ouyang, LB et al, A Sngle-Phase Wellbore-Flow Model for Horzontal, Vertcal, and Slanted Wells, SPE Journal 3(2), 1998, pp [11] Ashem, H et al, A Flow Resstance Correlaton for Completed Wellbore, J Petrol Sc Eng, 1992, 8 (2), pp [12] Marett, BP, Landman, MJ, Optmal Perforaton Desgn for Horzontal Wells n Reservor wth Boundares, paper SPE presented at the 1993 SPE Asa Pacfc Ol and Gas Conference and Exhbton, Sngapore, February 8-10 [13] Su, Z, Gudmundsson, JS, Frcton Factor of Perforaton Roughness n Ppes, SPE presented at the 1993 SPE 68 th Annual Techncal Conference and Exhbton, Houston, TX, USA, October 3-6 [14] Olson, RM and Eckert, ERG, Expermental Studes of Turbulent Flow n a Porous Crcular Tube wth Unform Flud Injecton through the Tube Wall, J Appled Mechancs (1966) 33, No 1, 7 [15] Rabthby, G, Lamnar Heat Transfer n the Thermal Entrance Regon of Crcular Tubes and Two-Dmensonal Rectangular Ducts wth Wall Sucton and Injecton, Intl J Heat and Mass Transfer (1971) 14, No 2, 223 [16] Kloster, J, Expermental Research on Flow Resstance n Perforated Ppe, Master thess, Norwegan Int of Technology, Trondhem, Norway (1990) [17] Ihara, M et al, Flow n Horzontal Wellbores wth Influx through Porous Walls, paper SPE presented at the 1994 SPE Annual Techncal Conference and Exhbton, New Orleans, September [18] Su, Z and Gudmundsson, JS, Pressure Drop n Perforated Ppes, PROFIT Projected Summary Reports, Norwegan Petroleum Drectorate, Stavanger (1995) [19] Su, Z and Gudmundsson, JS, Pressure Drop n Perforated Ppes, report, Department of Petroleum Engneerng and Appled Geophyscs, U Trondhem, Norway (1995) [20] Whte, FM, Flud Mechancs, McGraw-Hll, Inc 1986 [21] Su, Z and Gudmundsson, JS: Perforaton Inflow Reduces Frctonal Pressure Loss n Horzontal Wellbores, J Petrol Sc Eng, 1998, 19, pp