The Open Petroleum Engineering Journal

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1 Send Orders for Reprints to Te Open Petroleum Engineering Journal, 16, 9, Te Open Petroleum Engineering Journal Content list available at:.bentamopen.com/topej/ DOI: 1.174/ RESEARCH ARTICLE Layer Selection Metod of Ultra-Sort Radius Horizontal Wells Erlong Yang 1,, Huan Li 3,*, Huijuan Gao 1, Juquan Jia 1 and Meng Qi 1 1 Key Laboratory on Enanced Oil and Gas Recovery of te Ministry of Education, Norteast Petroleum University, Daqing, Heilongjiang, , Cina Post Doctoral Scientific Researc Workstation, Beijing Deeijiaye Science and Tecnology Corporation Ltd., 1, Cina 3 Second Oil Production Plant of Daqing Oilfield of CNPC, Daqing, Heilongjiang, Cina Received: November 9, 15 Revised: January 18, 16 Accepted: June 6, 16 Abstract: Study on te tecnology tat sidetracking orizontal ells it ultra-sort radius to select boundary layer as certain practical meaning. But recently tis kind of researc, especially te study on sidetracking position for orizontal ell, is less or even none. In tis paper, on te basis of te potential superposition metod and te equivalent floing resistance metod, te cumulative oil production calculation model of te orizontal ell after sidetracking is establised. Ten te dimensionless eigt from te top is introduced to modify te model it te means of numerical simulation. Terefore set up te relationsip beteen te cumulative oil production and six factors suc as cumulative oil production, effective tickness, te dimensionless eigt from te top, average permeability, oil and ater ells, te average remaining oil saturation and completeness of drilling stage for orizontal ell. By combining break-even analysis, layer selection metod of ultra-sort radius orizontal ells is determined. A relevant cart is also obtained. Te metod establised in tis paper can elp to coose te optimal layer of sidetracking orizontal ell it ultra-sort radius. Keyords: Horizontal ells it ultra-sort radius, Numerical simulation, Te layer selection metod, Te dimensionless eigt from te top. 1. INTRODUCTION Digging te side of sand body and te remaining oil in imperfect injection-production area troug sidetracking te old ell it ultra-sort radius orizontal ell as good advantage [1]. Te target locations are mainly for lo yield ell, sutdon ell, casing damage ell and abandoned ell, etc. But once tese kinds of ells sidetracking, tey ill not be able to restore to use [, 3]. Due to te ig risk, te study of layer selection metod of ultra-sort radius orizontal ells is necessary. Bot in Cina and overseas, at present, researces on layer selection metod of ultra-sort radius orizontal ells are rare. To determine te layer selection metod, it s necessary to calculate side-tracking orizontal ell productivity and development indicators. Scolars suc as Borisov [4], Giger [5], Josi [6] and Renard [7] ave given te calculation metods in forecasting productivity in steady flo state, and Cinese scolars ave predicted productivity of orizontal ells mostly based on stable or pseudo-steady flo. Te productivity formula as mostly provided by analytical solution [8, 9]. Te scolars ad not systematically studied te prediction of orizontal ell productivity in te nonsteady-state flo. Researces on te productivity and indicators prediction of te orizontal ells it ultra-sort radius are fe. In order to determine te layer selection metod, productivity index and productivity prediction metod for te * Address correspondence to tis autor at te Second Oil Production Plant of Daqing Oilfield of CNPC, Daqing, Heilongjiang, Cina; Tel: ; lzuikuaile@163.com /16 16 Bentam Open

2 17 Te Open Petroleum Engineering Journal, 16, Volume 9 Yang et al. ultra-sort radius orizontal ell need to be studied. Relationsip beteen te cumulative oil production and te effective tickness, te dimensionless eigt from te top, te distance beteen oil ells and ater ells, te average permeability, sidetrack drilling time (namely te average remaining oil saturation) and te degree of perfection in te recovery process of orizontal ells. By te potential superposition metod and te equivalent floing resistance metod te oil production rate formula of different time and ater breaktroug time for te production ells can be determined. Tus indirectly establis te relationsip beteen te oil production and te effective tickness, te distance beteen oil ells and ater ells, te average permeability, sidetrack drilling time (namely te average remaining oil saturation) and te degree of perfection in te recovery process of orizontal ells. But te matematical model establised troug tis metod cannot reflect te relationsip beteen te dimensionless distance top eigt and oil production, terefore te matematical model need a furter correction [1].. ESTABLISH THE MATHEMATICAL MODEL OF CUMULATIVE OIL PRODUCTION Te actual ell pattern of te target oilfield is five spot. Fig. (1a) is te conventional five-spot pattern it vertical ells. Fig. (1b) is te netork after te producing ell is sidetracked. Te orizontal section lengt is L. L (a)well pattern it vertical ells (b)well pattern after sidetracked Fig. (1). Well spacing scematic before and after te producing ell is sidetracked..1. Oil Production Speed of Vertical Producing Well According to te principle of potential superposition, te ell bottom potential of injection ell and production ell can be respectively obtained [11]: φ q 1 ln π r D if = + φ q r ln π jd f = + 4 C C (1) () Production fluid velocity for vertical ell is as follo: p q = µ ln πk r (3).. Oil Production Speed After Sidetracking Flo itin te pattern can be divided into tree parts, namely te vertical part of orizontal ell, te part beteen productive gallery and orizontal ell and te part beteen external boundary and productive gallery [1]. By using te equivalent floing resistance metod, rate of oil production after sidetracking can be calculated as follo: (1) Te initial oil production velocity q( = µ o ( ln πk () Oil production velocity before ater breaktroug K + ln + jr L K p H Z ln ) L πr

3 Layer Selection Metod of Ultra-Sort Radius Horizontal Wells Te Open Petroleum Engineering Journal, 16, Volume Fig. () is te ater content and its derivative. f df ds Fig. (). Water content and its derivative [13]. S W ere, q( o ln K jr p K 1 Et ln L K H Z ln L r (3) Oil production velocity after ater breaktroug (4) Te time for ater breaktroug According to te cumulative ater injection, te folloing equation can be establised: ere, dt r dr q. Wen r r D, ater breaktroug appened. So: o o / qot t V p f S s E k ro s Te cumulative oil production can be calculate as follo: q( o ln K sf ' ( s ) ) ds ( s ) sm k k ( c f ro o r p E ( sf ) K ln jr ( s ) L K ro Q( q( dt o D t ln K p t o e H jr L K Z L Q( t q( dt e 1 Et ln Wit tis model te cumulative oil production of orizontal ell under te conditions it different values of te effective tickness, te distance beteen oil ells and ater ells, te average permeability, te average remaining oil saturation and te degree of perfection in te recovery process of orizontal ells can be calculated. Te result is son in Table (correspond to te scenarios in Table 1). But tis model cannot present te influence of te dimensionless eigt from te top on te cumulative production. So te numerical simulation metod is need to be used for correction. K H Z ln L r ln r

4 17 Te Open Petroleum Engineering Journal, 16, Volume 9 Yang et al. 3. EFFECT OF DIMENSIONLESS HEIGHT FROM THE TOP ON 1-YEAR CUMULATIVE OIL PRODUCTION By establising numerical simulation conceptual model, te impact of te effective tickness, te dimensionless eigt from te top, te distance beteen oil ells and ater ells, te average permeability, te average remaining oil saturation and te degree of perfection in te recovery process of orizontal ells on te 1-year cumulative oil production can be studied [14]. In tis paper, te same numerical simulation model and te ortogonal design scenario ere used to do te researc. Table 1. Te design of numerical simulation scenario. No. Reservoir tickness (m) Dimensionless eigt from te top Distance beteen oil ells and ater ells (m) Average permeability (1-3 um ) Average remaining oil saturation Degree of perfection in te recovery process of orizontal ells (%) Table. Te results of different metods. No. Dimensionless eigt from te top Numerical simulation result Matematic model result Correction result

5 Layer Selection Metod of Ultra-Sort Radius Horizontal Wells Te Open Petroleum Engineering Journal, 16, Volume (Table ) contd... No. Dimensionless eigt from te top Numerical simulation result Matematic model result Correction result On te foundation of five-point metod for perfect vertical ells, te ater flooding to te average remaining oil saturation in accordance it te scenario requirements as conducted (according to te reserve and recovery degree of te model). Ten some or all of te ater ells ere closed, based on te degree of perfection of orizontal ells. Finally te 1-year cumulative oil production of orizontal ells can be predicted. Table sos te compared 1-year cumulative oil production calculated results of numerical simulation and matematical model calculation. By comparing te results of numerical simulation and matematical model calculation results, te dimensionless distance top eigt coefficient H p is introduced. Te revised formula is as follo: t Q( q( dt H Correction result can be obtained according to te correction formula, as son in Table. Te average error is 6.68%, ic meet te calculation precision (as son in Fig. 3). p 6 5 y = x Correction result Numerical simulation result Fig. (3). Te numerical simulation result and te correction result. 4. BREAK-EVEN ANALYSIS Under te condition tat logging investment, tecnology development costs, production costs of a ton of oil, crude oil commodity rate, oil prices, taxes, and oter parameters ere knon, according to te input-output balance principle, te economic limit cumulative oil production as calculated as follos. Q lim R ( P C ) ( C C )(1 R) e c o p f Wen calculating te cumulative oil production under te control of economic limit: te drilling investment value C as 39, yuan/t; logging investment as 14, yuan/t; tecnology development cost as 5, yuan/t; te costs of logging and tecnology development C f as 39, yuan/t; te cost of a ton of oil C p as 3yuan; oil price

6 174 Te Open Petroleum Engineering Journal, 16, Volume 9 Yang et al. P o as 4$/bbl, namely 1844yuan/t; crude oil commodity rate R c as 96%; evaluation period Γ as 1 years; te loan rate of investment R as 5.75%. According to te parameters mentioned above, te 1-years cumulative oil production after calculating as tons. 5. LAYER SELECTION METHOD As son in Figs. (4-7). Combined it te 1-years cumulative oil production under te control of economic limit, te reasonable value range of te effective tickness, te distance beteen oil ells and ater ells, te average remaining oil saturation, and te dimensionless eigt from te top can be determined, according to te formula of te cumulative oil production for orizontal ells it sort radius. Fig. (4). Te remaining oil saturation vs. different dimensionless eigt from te top and ell spacing (effective tickness is m). Wit te sensitivity analysis, tere existed a specific permeability value. Wen te average permeability as iger tan te value, te reasonable value range of te corresponding effective tickness, remaining oil saturation, and ell spacing ill be sligtly iger tan tat determined in te figure; And tere existed a specific degree of perfection value. Wen te degree of perfection in te recovery process of orizontal ells as iger te value, te reasonable value range of tese indicators sould be sligtly loer tan tat determined in te figure. Wile determining te reasonable value range of every indicator in tis paper, te specific average permeability as regarded as μm, and te specific degree of perfection in te recovery process of orizontal ells as regarded as 5%, namely tere ere to ater injection ells. Fig. (5). Te remaining oil saturation vs. different dimensionless eigt from te top and ell spacing (effective tickness is 3m). From te figure e can obtain tat en te dimensionless eigt from te top and te effective tickness ere uniform, te average remaining oil saturation decrease it te distance beteen oil ells and ater ells. Wile te

7 Layer Selection Metod of Ultra-Sort Radius Horizontal Wells Te Open Petroleum Engineering Journal, 16, Volume dimensionless eigt from te top and te distance beteen oil ells and ater ells ere uniform, te average remaining oil saturation decrease it te increase of effective tickness. And en te distance beteen oil ells and ater ells and te effective tickness ere uniform, te average remaining oil saturation as smaller ile te value of dimensionless eigt from te top as larger, ic could allo side-tracking it sort radius at larger distance from te top. Steps to determine te layer for sidetracking are as follos: Firstly, te value of te effective tickness, te distance beteen oil ell and ater ell, te average permeability, te average remaining oil saturation and te degree of perfection in te recovery process sould be collected for calculating. Secondly, te 1-year cumulative oil production can be calculated according to te formula (1), and te oil ell it te largest 1-year cumulative oil production can be cosen as te direction for sidetracking. Ten, te value of te distance beteen te oil ell and ater ell, te effective tickness of reservoir and te average remaining oil saturation of tis oil ell sould be determined. Finally, according to te figure, te sidetrack point, ic meet te condition tat te remaining oil saturation of tis point is iger tan tat corresponding to te dimensionless eigt from te top of tis point, can be determined. For example, ile te distance beteen oil ell and ater ell is 35m, te effective tickness is 4m, and te remaining oil saturation is beteen.35 and.383. According to Fig. (6), te dimensionless eigt from te top of te sidetrack point is 1/. Fig. (6). Te remaining oil saturation vs. different dimensionless eigt from te top and ell spacing (effective tickness is 4m). Fig. (7). Te remaining oil saturation vs. different dimensionless eigt from te top and ell spacing (effective tickness is 5m). CONCLUSION Te oil production prediction model is establised, and te model s calculation precision meet te requirements. Te cumulative oil production after sidetracking it sort radius orizontal ell can be predicted it te parameters

8 176 Te Open Petroleum Engineering Journal, 16, Volume 9 Yang et al. of te purpose ell. Ten te layer selection metod of side-tracking orizontal ells it ultra-sort radius can be determined by combining it break-even analysis. LIST OF ABBERIVIATIONS = Dimensionless production time; C = Constant; C f = Te costs of logging and tecnology development, million/ell; C = Te drilling cost, ten tousand yuan; C p = Te crude oil production and operating expenses, ten tousand yuan/t; D = Te distance beteen oil ell and ater ell, meter; f = Water content, %; = Te effective tickness, meter; j = Number of injection ells; K H = Average permeability on orizontal direction, um ; k ro = Relative permeability of ater-pase, um ; K Z = Average permeability on vertical direction, um ; L = Horizontal section lengt, meter; P o = Te crude oil prices after tax, ten tousand yuan/t; q = Oil production speed,ton/a; Q = Te cumulative oil production, ton; Q elim = Te cumulative oil production under te control of economic limit, ton; R = Te loan rate of investment,%. r = Radius of ater oil frontal, meter; R c = Te crude oil commodity rate, %; r = Wellbore radius of injection ell, meter; S = Water saturation; S c = Irreducible ater saturation; S f = Water saturation of ater oil frontal; S m = Water saturation ile x=; t = Production time, a; V p = Pore volume of te reservoir,m 3 ; ΔP = Differential pressure of production,kpa; μ o = Oil viscosity,mpa s; Φ if = Te bottom potential of ater injection ells; Φ f = Te bottom potential of ater production ells; CONFLICT OF INTEREST Te autors confirm tat tis article content as no conflict of interest. ACKNOWLEDGEMENTS Te support of te key project of te National Natural Science Foundation of Cina for Yout (No ), Postdoctoral Science Foundation Project of Cina (No.14M56135) and Postdoctoral Work Foundation Project of Beijing. REFERENCES [1] J. Wang, Application Analysis of Horizontal Wells in Cina., Petroleum Industry Press: Beijing, 3, pp [] X. Cang, Corpus for Development Tecniques of Horizontal Well in Complex Fault Block Reservoir., Petroleum Industry Press: Beijing, 8, pp. -3.

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