Study on the Determination of Separated Layer Water Injection Based on Grey Correlation Analysis Method

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1 Research Joural of Appled Sceces, Egeerg ad Techology 5(16): , 2013 ISSN: ; e-issn: Maxwell Scetfc Orgazato, 2013 Subtted: March 23, 2012 Accepted: Deceber 13, 2012 Publshed: Aprl 30, 2013 Study o the Deterato of Separated Layer Water Iecto Based o Grey Correlato Aalyss Method 1, 2 Jutg Zhag, 1, 2 Hogu Y, 1, 2 Ye Zhag, 1, 2 Huahua Zhag ad 3 Jafeg Teg 1 Accuulato ad Developet of Ucovetoal Ol ad Gas, State Key Laboratory Cultvato Base Jotly-costructed by Helogag Provce ad the Mstry of Scece ad Techology, Northeast Petroleu Uversty, Daqg, Cha, Key Laboratory of Ehaced Ol ad Gas Recovery Mstry of Educato, Northeast Petroleu Uversty, Daqg, Cha, Yushul Olfeld Co. Ltd., Daqg Olfeld Copay Ltd., Daqg, Cha, Abstract: How to detere the separated layer water ecto s a proble whch reservor egeers cocer flood developet ol feld. These varous fluetal factors of dvdg coeffcet ethod are aalyzed ths study. Grey correlato aalyss ethod s used to detere the doat fluetal factors. Ad the weght of dfferet doat fluetal factors s deteredhch realzes the quattatve coparso aog the dvdg coeffcet forula. Ths ethod cosders the pact of these factors whch are cosst of the easure trasforato coeffcet, perforato thckess, ector producer dstace, locato coeffcet ad the uber of ector ad producer. The separated layer water ecto forula s detered. The scetfc ad reasoable ecto allocato s realzed. The proble whch the cotradcto exsts the sae layer or betwee the layer ad the layer s obvous the S block through cobg wth the curret water ecto developet. The separated layer water ecto ethod s proposed ecessarly. The forula for water ecto s detered by grey correlato aalyss ethod Block S. These factors cosdered are ore wth the actual stuato. Ad the reasoable ecto allocato s realzed. It s drectve ad refereced for other ol feld or block. Keywords: Dvdg coeffcet, grey correlato, separated layer water ectoeght INTRODUCTION At preset, doestc water dstrbuto ethods s aly dvded to two types whch are acrodstrbuto ad cro-dstrbuto. Macro-dstrbuto ethod s based o the whole ol feld or block as the research obect ad accordg to the developet patter of the ol feld or block to get the water dstrbuto of the ol feld or block (Xog et al., 2004). Mcro-dstrbuto ethod s based o well group, the sgle well or layer seget as the research obect, fro the cro cosderato cted correcto coeffcet to accout the ecto water quatty of sgle well or well group (Hog ad J, 1992). Or usg dvdg coeffcet to splt wth the shut ecto wells coected to all the producto wells the drecto of the flow of lqud (Ya ad Che, 2007). Through the ecto-producto balace, the water ecto of sgle water well s coputed, or to splt sgle water well of the water ecto well to get layer seget dstrbuto water (L et al., 2005). But study o ecto s relatvely less foreg. Ad Uted States J.L. Athoy ad so oho propose the ethod of dsplaceet volue to dstrbute water ecto ad detere the large well group water floodg of optocs aster's thess Research of water ecto rate (Athoy, 1992). Uted States P.M. Jarer ad others apply Hear ad Hall curve o the ew coverso well study of water ecto rate (Jarre et al., 1992). The forer Sovet Uo P.M. cattapboho has used statstcal ethods to study the effect of ecto rate o flud wthdrawal rate (Cattapbo et al., 1991). Abroad ost of these ethods are cro-ecto ethod. These ethods are ostly reflected badly the specfc forula for calculatg the geologcal codto factor less ad faled to ake full use of exstg otorg data ad producto perforace data ad dvdg coeffcet of adaptablty ad practcalty s worse. I ths studye cosder the geologcal codtos, the cobato of dyac ad statc data to detere the a factors of affectg the dvdg coeffcet ad the weght of each factor (Zhao, 2007), reasoable dvdg coeffcet of block s establshed, a reasoable stratfed water ecto forula of block ecto wells s got, achevg ratoal dstrbuto of Correspodg Author: Hogu Y, College of Petroleu Egeerg, Northeast Petroleu Uversty, Daqg , Cha, Tel.:

2 sgle well of water ecto well ad creasg adustet effect of water floodg. THE THEORY OF GREY CORRELATION ANALYSIS METHOD Grey correlato aalyss ethod s a ethod of ultvarate statstcal aalyss, by solvg key relatoshps betwee varous factors the syste, detfes portat factors affectg target values ad so as to aster the a features of thgs. It s a quattatve descrpto of a syste developet tred ad coparso ethods (La et al., 2006). It s based o the saple data for each factor, by gray correlato degree to descrbe the stregth, the sze ad order of the relatoshp betwee varous factors. If the saple data seres reflects that the chaged tred (drecto, sze, speed, etc.) of two factors are bascally the sae, the correlato degree betwee the s larger; coversely, t s saller. Deg ulog put forward the grey syste theory that has wde applcatos areas such as ol ad atural gas explorato ad developet (Deg, 1990). Grey correlato aalyss of grey syste theory s a quattatve descrpto ad coparso of ethods of dyac developet treds. The dvdg coeffcet s as a grey syste ths ethod, based o the saple data of varous factors, by the correlato degree to descrbe the relatoshp betwee factors assocated wth stregth, sze ad order. It ay deped o chaos ad tg sequetal of the syste to search for the evoluto law of the syste the case of less data, so as to better detere the a factors, provdg a theoretcal bass for predcto ad cotrol of syste. Grey correlato aalyss geerally requres the followg fve steps. Detere the sequece of aalyss: O the bass of aalyss of the target varable of the research questos, to detere a depedet varable ad ultple depedet varables factors. The depedet varable data costtute the referece sequece, varable data costtute the coparatve sequece, s expressed, respectvely as forula (1): y0 y0 y0 y0 y1 y1 y1 y1 y y y y 1, 2,, 1, 2,, 1, 2,, Res. J. Appl. Sc. Eg. Techol., 5(16): , 2013 (1) ad = Respectvely as a referece sequece ad copared sequece = The sequece's legth = Fro 1 to = The uber of coparatve sequece 4078 The desoless of sequece: Because the physcal sgfcace of the varous factors s dfferet the systehch wll s lead to that the orgal varable sequece s wth a dfferet uber of desos or levels. I order to esure that all factors have rak ad of equal weght, t s eeded to be desoless. Desoless ethod s cooly used s tal value ethod ad average ethod. Desoless sequece by applcato tal value ad ea value ethod s expressed as forula (2): x x k k y y k 1 k 1 k y k (2) y 1 (3) s fro 0 to, k = Fro 1 to. The ew sequece after desoless s x 0 ad x 1 Calculatg correlato coeffcet: Correlato coeffcet s the data pots of the -th coparso sequece ad referece sequeces the k-th degree of correlato, ts expresso s show as forula (4): k ax k ax (4) The Δ o (k) ca be calculated by forula (5): ξ o (k) Δ o (k) k x k x k 0 (5) = Correlato coeffcets = The absolute value of the -th coparso sequece ad referece sequeces the k-th degree of correlato Δ ad Δ ax = Respectvely the u ad axu absolute dfferece of each data pot ρ = Resoluto rato ρ = Fro 0 to 1, values fro 0.1 to 0.5, usually s 0.5. Resoluto coeffcet s creased sgfcace of dfferece betwee the correlato coeffcet. Calculatg correlato degree: Because the uber of correlato coeffcet s ay, the forato s too scattered, for ease of copare, to copute a average of correlato coeffcet, the correlato degree s the forula (6):

3 Res. J. Appl. Sc. Eg. Techol., 5(16): , 2013 Table 1: The correlato degree of a factors Classfcato These a factors Sort Correlato degree II The easures trasforato coeffcet I Perforato thckess II Iector producer dstace II Locato coeffcet II The uber of ector ad producer Table 2: The weght of a factors These a factors Weght values These a factors Weght values The easures trasforato coeffcet Locato coeffcet 0.2 Perforato thckess The uber of ector ad producer Iector producer dstace k1 r k (6) r s correlato degree, the value s fro 0 to 1 MAIN INFLUENCE FACTORS OF DIVIDING COEFFCIENT DETERMINED I vew of the curret ethod of dvdg coeffcet calculato of ay at hoe ad abroad, detfy the factors fluecg the dvdg coeffcet values. It s foud through aalyss that ay paraeter (pact factor) troduced dvdg coeffcet forula ad there s o ufed stadard. Therefore, order to better detfy ad dvde the level of effect factors o the effect of dvdg coeffcet ad how dvdg coeffcet, these fluecg factors wll be classfed, cludg geologcal factors (I), cotrollable factors (II) ad tegratve factors (III). Geologcal factors related to the status of the geologcal features, such as the pereablty of layers, coectvty coeffcet, the coeffcet of terlayer terferece, the affect coeffcet of sedetary faceses, the coeffcet of pereablty asotropy, perforato thckess ad so o. Cotrollable factors s the factor that s geerated for the operato of people, such as the uber of ector ad producer, ector producer dstace, the easures trasforato coeffcet, g wdth coeffcet ad the locato coeffcet. The tegratve factors s to cosder the perforace of the factors of ecto wells ad the surroudg characterstcs of producg wells coected wth t, such as the drecto forato capacty. These a factors are detered by grey correlato aalyss ethod. Dvdg coeffcet s establshed whch cosders the effect of varous factors. Therefore the splt result s ore realstc. Gray correlato aalyss ethod to detere the a factors ad weghts: Accordg to the actual water ecto profle data of S well feld, the layer water absorpto s chose as the referece sequece. Ad pereablty of layers, perforato thckess, coectvty coeffcet ad the coeffcet of terlayer terferece, ector producer dstace, the easures 4079 trasforato coeffcet, g wdth coeffcet, the locato coeffcet, the uber of ector ad producer ad the drecto forato capacty are as coparso sequeces. Usg ea ethod to desoless, resoluto rato s 0.5 ad the correlato degree of varous factors s calculated. The a fluecg factors are effectve thckess, ectoproducto wells, ector producer dstace, the easures trasforato coeffcet ad the locato coeffcet through sortg. The values are Table 1. Accordg to the correlato degree, the weght values are detered through oralzato. It s show Table 2. SINGLE-LAYERED WATER INJECTION FORMULA DETERMINED The plae dvdg coeffcet ad vertcal dvdg coeffcet are establshed whch takg to accout all factors of weght depedg o the selected a factors of S well feld. Plae dvdg coeffcet: Plae dvdg coeffcet to cosder the weght of varous factors s set up based o the selected fve paraeters. The forula s forula (7): M M N N 1 M M N N 1 1 H H /ld D H H /ld D (7),,l respectvely s the total uber of layer of I water ecto well, the total uber of ecto wells ad the uber of water ecto wells coected wth I well. M, α, N respectvely s the easures trasforato coeffcets of of I water ecto well, locato coeffcets ad the uber of ector ad producer, they are desoless. H s the perforato thckess of layer of I water ecto well, the ut s eter, γ s dvdg

4 Res. J. Appl. Sc. Eg. Techol., 5(16): , 2013 coeffcet of I water ecto well, t s desoless ad exstg the forula (8): 1 (11) 1 1 (8) 1,, respectvely s the correcto of the easures trasforato coeffcets, locato coeffcets ad the uber of ector ad producer weght correcto, they are desoless, respectvely s perforato thckess ad ector producer dstace weght correcto, the ut s eter. The correcto forula for varous weghts s forula (9): 1 M M M wm 1 w 1 N N N wn 1 H H H wh 1 D D DwD (9),,,, respectvely s the average of easures trasforato coeffcets, the average of locato coeffcets, the average of the uber of ector ad producer, the average of perforato thckess ad the average of ector producer dstace. Ad s the uber of fluecg factors for the costructo of dvdg coeffcet w M α N H D respectvely s the weght of the easures trasforato coeffcets, locato coeffcets, the uber of ector ad producer, perforato thckess ad ector producer dstace after oralzato based o the correlato degree value of each paraeter. Vertcal dvdg coeffcet: Accordg to the costructo process of plae dvdg coeffcet, vertcal dvdg coeffcet s establshed accordace wth the S water ecto wells. The forula s show as forula (10): M M N N M M N N 1 H H /ld D H H /ld D (10) β s vertcal dvdg coeffcet of layer of I water ecto well ad t s exstg the forula (11): 4080 The Forula of Sgle Well Iecto Allocato: After obtag the well of plae dvdg coeffcet, water ecto of sgle well ecto allocato ca be evaluated accordg to the plae dvdg coeffcet. The forula s show as forula (12): w w M M N N 1 M M N N 1 1 H H /ld D H H /ld D (12) = The uber of sgle othly ecto of Well I ecto well, the ut s w = The uber othly ecto of total ecto well, the ut s Whe ecto allocato aout of each ecto s detered, dvded by total perforato effectve thckess of each ecto wells ad the forula of water testy of water ecto well ca be obtaed, the forula s forula (13): wh 30 hk k1 (13) wh = The stregth of well I ecto well, the ut s 3 /(d) h k = Effectve thckess of k layer of well I ecto well, the ut s eter The forula of layer ecto allocato: Whe gettg sgle well ecto allocato of water ecto wells, the layer ecto allocato ca be coputed accordg to vertcal dvdg coeffcet, the forula s forula (14): q M M N N M M N N 1 H H /ld D H H /ld D (14)

5 Res. J. Appl. Sc. Eg. Techol., 5(16): , 2013 q s ecto othly volue of layer of ecto well, the ut s CONCLUSION Based o geology ad developet of the S well feld, these fluecg factors of dvdg coeffcet are aalyzed, by grey correlato aalyss ethod to detere the a pact factors. They are the easure reforato coeffcet, perforato thckess, ector producer dstace, locato coeffcet ad the uber of ector ad producer. At the sae te the weght values of varous factors the dvdg coeffcet are detfed. Accordg to the weght value of a fluece factors ad the varous factors, the plae dvdg coeffcet ad vertcal dvdg coeffcet are establshed. Costructg dvdg coeffcet s ore le wth the actual stuato of S well feld. Depedg o the water ecto rate of S well feld, these forulas of sgle well ad layer seget ecto allocato are detered, to acheve the ratoalty of separate layer water ecto; Through the study o ths ethod, the deterato of the stratfed water ecto after water floodg work provdes a quattatve stadard. It has practcal plcatos. ACKNOWLEDGMENT Ths author gratefully ackowledges facal support fro Helogag Provcal Scece ad Techology Pla Proect (Grat No: GZ09A407) ad Research Progra of Iovato Tea of Scece ad Techology Ehaced Ol ad Gas Recovery (Grat No: 2009td08). REFERENCES Cattapbo, et al., Coprehesve Applcato of Varous Statstcal Methods to Study o Iecto Rate ad Effect Speed o the Aout of Ol Producto. L F. (Ed.), Traslato by Ol ad Gas Feld Developet Egeerg. Deg, J., Grey Syste Theory Tutoral. Huazhog Uversty of Scece ad Techology Press, Cha, pp: Hog, C. ad H. J, A study of the aalyss of the ecto-producto perforace ad ts applcato o the prorato of ecto rate. Petrol. Explor. Develop., 19(2): Jarre, et al., Applyg Hear ad Hall Curve Method to Icrease the Iecto of New Coverso Well. J, P., (Ed.), Traslato of Ol ad Gas Feld Developet Proect. L, F., L. Lu, J. Dg, et al., A study o calculato of accuulatve water? I take rate of separate layer. Hea Petrol., 19(5): La, C., J. Zhog, F. Ca ad J. Zhag, Ifluecg factors aalyss of ol feld output based o grey correlato aalytcal ethod. Nat. Gas Geosc., 17(6): Xog, X., J. Yag ad K. Lu, Deterato of water ecto rate for sgle ecto well eployg dvdg coeffcet approach. Fault- Block Ol Gas Feld, 11(3): Ya, C. ad. Che, Applcato of ecto well cotrastg test ecto proect adustet. Drll. Prod. Techol., 31(2): Zhao, J., Take weghts of lad evaluato odel based o grey correlato degree. Poeerg Sc. Techol. Mothly, 8: Athoy, J.L., Detere How Well Large Water Floodg the Best Ecooc Methods for Water Iecto ad Ol Producto. J, P. (Ed.), Traslato by Ol ad Gas Feld Developet Egeerg. 4081