陳志海,董廣為,廉培慶
(中國(guó)石化 石油勘探開(kāi)發(fā)研究院,北京 100083)
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穿透非均質(zhì)儲(chǔ)層的復(fù)雜軌跡井產(chǎn)量計(jì)算新方法
陳志海,董廣為,廉培慶
(中國(guó)石化 石油勘探開(kāi)發(fā)研究院,北京 100083)
解析法和半解析法計(jì)算水平井產(chǎn)量的公式一般要求油藏儲(chǔ)層均質(zhì),且井軌跡平行于油藏邊界,難以準(zhǔn)確地計(jì)算復(fù)雜軌跡井的產(chǎn)量。根據(jù)井軌跡和儲(chǔ)層滲透率把油藏劃分為若干區(qū)域,不同區(qū)域滲透率取值不同,且井軌跡可不平行邊界。通過(guò)引入點(diǎn)源函數(shù)法,基于定壓油藏邊界建立了非均質(zhì)性?xún)?chǔ)層復(fù)雜軌跡井的產(chǎn)量分段積分相似解,利用Ouyang模型計(jì)算了井筒內(nèi)流動(dòng)的沿程壓力損失。該方法避免了數(shù)值模擬中數(shù)值彌散的發(fā)生,只需輸入較少的參數(shù)就可以對(duì)復(fù)雜軌跡井進(jìn)行快速產(chǎn)能評(píng)價(jià)。實(shí)例計(jì)算結(jié)果表明:①?gòu)?fù)雜軌跡井井筒內(nèi)的流量從指端到跟端逐漸增大;②由于儲(chǔ)層的非均質(zhì)性,各段流量分布并不均勻,滲透率高的部位流量也高;③井筒壓降從指端到跟端同樣逐漸增大,由于流量分布不均勻,因此不同軌跡段在井筒內(nèi)壓降也不相等。該方法計(jì)算結(jié)果與Eclipse數(shù)模方法一致,表明該方法是可行的。應(yīng)用該方法計(jì)算的油井產(chǎn)量與油田現(xiàn)場(chǎng)生產(chǎn)對(duì)比,預(yù)測(cè)油井產(chǎn)量相對(duì)誤差小于5%,能滿足現(xiàn)場(chǎng)油藏工程研究的需要。
非均質(zhì)儲(chǔ)層;點(diǎn)源函數(shù);復(fù)雜軌跡井;產(chǎn)量計(jì)算
近十年來(lái),復(fù)雜軌跡井開(kāi)發(fā)技術(shù)在油氣田開(kāi)發(fā)領(lǐng)域取得突飛猛進(jìn)的發(fā)展,已經(jīng)由單一的水平段發(fā)展為極大限度接觸油藏面積的復(fù)雜軌跡井段(又稱(chēng)復(fù)雜結(jié)構(gòu)井技術(shù))。該技術(shù)不僅在常規(guī)油氣藏開(kāi)發(fā)的剩余油挖潛應(yīng)用廣泛,而且已成為包括頁(yè)巖油氣、致密油氣、深水油田等非常規(guī)油氣藏開(kāi)發(fā)不可或缺的主導(dǎo)技術(shù)之一[1-3]。現(xiàn)場(chǎng)實(shí)踐表明,復(fù)雜軌跡井技術(shù)不僅能提高單井產(chǎn)量,而且能提高油田的采收率,使很多無(wú)法開(kāi)發(fā)的油田獲得經(jīng)濟(jì)有效地開(kāi)發(fā)。復(fù)雜軌跡井與油藏接觸面積大,克服油藏儲(chǔ)層非均質(zhì)性對(duì)油井產(chǎn)量的制約,實(shí)現(xiàn)單井經(jīng)濟(jì)效益最大化[4]。
目前,水平井已具有較為配套的單井產(chǎn)量計(jì)算公式包括計(jì)算定壓邊界油藏的穩(wěn)態(tài)法和計(jì)算封閉邊界油藏的擬穩(wěn)態(tài)法。對(duì)于定壓邊界油藏水平井產(chǎn)量的經(jīng)典公式主要包括Joshi 模型[5]、Bulter模型[6]、范子菲模型[7]和Furui模型[8]。Joshi 模型要求水平段長(zhǎng)度相對(duì)于油藏邊界長(zhǎng)度小,即低穿透比能滿足壓力等勢(shì)線呈橢圓形。其余幾個(gè)模型要求水平段的穿透比為1,即滿足垂直于水平段的流線相互平行地流入井筒。國(guó)內(nèi)很多學(xué)者在這些模型基礎(chǔ)上進(jìn)一步推導(dǎo)了一些改進(jìn)公式[9-12],這些公式的多假設(shè)油藏呈箱型、均質(zhì),且水平段與某一邊界平行。
復(fù)雜軌跡井與傳統(tǒng)水平井有很大的差異,主要體現(xiàn)在長(zhǎng)井眼段與油藏接觸,穿透多段非均質(zhì)性?xún)?chǔ)層,且在油藏內(nèi)的井身軌跡復(fù)雜多變,此類(lèi)井的產(chǎn)量計(jì)算未能得到較為滿意地解決。國(guó)內(nèi)很多學(xué)者也開(kāi)展了很多探索,主要集中在結(jié)構(gòu)簡(jiǎn)單水平井的井筒摩阻計(jì)算、多分支井間干擾、射孔方式對(duì)產(chǎn)量的影響等方面,但大多考慮單一因素對(duì)產(chǎn)量的影響[13-14]??紤]多因素對(duì)計(jì)算復(fù)雜軌跡井產(chǎn)量的方法在文獻(xiàn)中比較少見(jiàn)。
假定油藏形狀為箱型,油藏上、下邊界封閉,其余4個(gè)外邊界定壓(圖1)。復(fù)雜結(jié)構(gòu)井井眼軌跡在油藏內(nèi)可以為任意曲線形狀,沿程流動(dòng)阻力不斷發(fā)生變化。為精確地描述油藏流入井筒的滲流和井筒內(nèi)的流體管流分布,依據(jù)油藏非均質(zhì)性和井眼軌跡,將復(fù)雜軌跡井的井筒分段計(jì)算,使得每一微段井筒近似為直線并且考慮微井段對(duì)應(yīng)儲(chǔ)層的非均質(zhì)性。
假定連續(xù)的井眼曲線軌跡可離散為N個(gè)微井段,第1個(gè)微段為復(fù)雜軌跡井的指端,而第N個(gè)微段為復(fù)雜軌跡井的跟端(圖2)。每個(gè)微井段都能穿越對(duì)應(yīng)油藏的非均質(zhì)儲(chǔ)層段,微井段的節(jié)點(diǎn)壓力受井筒內(nèi)沿程摩阻分布的影響,假設(shè)第i個(gè)井筒微段所在儲(chǔ)層x,y,z方向滲透率分別為Kx,i,Ky,i,Kz,i,微段長(zhǎng)度為L(zhǎng)i,應(yīng)井筒內(nèi)流量為qi,井筒壓力為pi。
每一微井段相當(dāng)于一個(gè)獨(dú)立的線匯,由一系列點(diǎn)匯連接而成。點(diǎn)匯位于井筒橫截面圓心位置,并且過(guò)點(diǎn)匯的井筒橫截面上壓力均相等。因而點(diǎn)匯處的壓力代表了和油藏接觸的井筒外邊界的油藏壓力。在進(jìn)行空間上的壓力疊加時(shí),考慮各微井段間相互干擾,則i個(gè)微井段的壓力降為:pR-pi
圖1 油藏與井筒物理模型示意圖Fig.1 Reservoir and wellbore trajectory model
圖2 非均質(zhì)儲(chǔ)層內(nèi)復(fù)雜軌跡井的管流模型Fig.2 Pipe flow model of complex trajectory well in heterogeneous reservoirs
(1)式中:pR為油藏初始?jí)毫?,MPa;pi為第i個(gè)微井段中心點(diǎn)壓力,MPa;B為原油體積系數(shù),m3/m3;qj為第j個(gè)微井段的流量,m3/d;a,b,h分別為模擬油藏的長(zhǎng)、寬、高,m;Lj為第j個(gè)微井段的長(zhǎng)度,m;Φ為孔隙度,%;Ct為綜合壓縮系數(shù),MPa-1;xi,yi,zi為第i個(gè)微井段的中點(diǎn)坐標(biāo);lj為第j個(gè)微井段軌跡;t為生產(chǎn)時(shí)間,d;τ為時(shí)間積分變量。
公式(1)中G[(xi,yi,zi),lj,τ]為Green函數(shù),根據(jù)Newmann積原理可以表示
(3)
(4)
以y方向?yàn)槔?,介紹Green函數(shù)的簡(jiǎn)化過(guò)程。把Green函數(shù)代入公式(1),可得:
(6)
對(duì)于擬穩(wěn)態(tài)狀態(tài)下的流動(dòng),令t→∞,可得:
(7)
方便起見(jiàn),令A(yù)ij為第j個(gè)微井段對(duì)第i個(gè)微井段中心點(diǎn)的影響因子:
(8)
則公式(7)可表達(dá)為:
(9)
公式(9)矩陣表達(dá)式為:
井筒內(nèi)流體流動(dòng)存在摩阻,考慮重力、粘滯摩阻和加速度摩阻的影響,目前許多學(xué)者開(kāi)展了井筒壓降模型的研究[17-19]。本文采用Ouyang單相模型計(jì)算由重力、摩擦、加速度3部分構(gòu)成的壓降,并通過(guò)摩擦系數(shù)經(jīng)驗(yàn)修正公式融入了射孔粗糙度造成的壓降。壓降方程表達(dá)式為:
譯者是翻譯的主體,也是民族文化建構(gòu)的重要參與者。從功能角度看,中國(guó)文化外譯屬于外宣翻譯。在外宣翻譯中,譯者的主體性體現(xiàn)尤為重要,因?yàn)橹袊?guó)在國(guó)際社會(huì)的形象很大程度上取決于外宣翻譯的質(zhì)量(張健,2013)。為達(dá)到傳播和接受效果,需要譯者在翻譯過(guò)程中時(shí)刻考慮目標(biāo)讀者的閱讀感受。在中國(guó)文化外譯過(guò)程中,譯者主體性影響、制約和支配著文化翻譯的效果。
(11)
fj為第j微井段摩阻因子,無(wú)因次,可表示如下:
(12)
式中:f0為沒(méi)有流體流入時(shí)摩阻因子,無(wú)因次;qI為單位長(zhǎng)度的流量,m2/d;D為井筒直徑,m;NRe,NRe,w分別為雷諾數(shù)和流入雷諾數(shù),無(wú)因次。
因此,井筒內(nèi)部每?jī)蓚€(gè)相鄰微井段中心點(diǎn)之間的壓降,可以由Ouyang模型算得,數(shù)學(xué)表達(dá)式為:
(13)
代入前一方程組可得以下矩陣形式:
(14)
當(dāng)井底流壓給定,此方程組為關(guān)于(q1,q2,…,qN)的非線性方程組,可由Newton-Raphson迭代法求解。
安哥拉某深水油田濁積巖油藏為滲透率各向異性的非均質(zhì)油藏,油藏上、下邊界封閉,四周為邊底水定壓邊界,壓力值為16.55 MPa。油藏長(zhǎng)度1 524 m,寬度為610 m,有效厚度為61 m。復(fù)雜軌跡井在油藏內(nèi)裸眼段井筒長(zhǎng)1 219 m,跟端井底流壓為13.79 MPa,沿井筒軌跡穿越油藏儲(chǔ)層的滲透率分布如表1所示,井筒粗糙度0.000 6,其他參數(shù)見(jiàn)表1。
2.1井筒流量及壓力分布
表1 各井段長(zhǎng)度和滲透率
對(duì)于長(zhǎng)井段復(fù)雜軌跡井,考慮滲透率差異性,分段賦值計(jì)算從油藏流入井筒的流量,并沿程計(jì)算井筒摩阻壓降對(duì)產(chǎn)量的影響是必要的。該計(jì)算方法能夠更準(zhǔn)確地計(jì)算復(fù)雜軌跡井的產(chǎn)量,更好地考慮工程和地質(zhì)的需要。
2.2與Eclipse結(jié)果對(duì)比
采用相同油藏、流體和復(fù)雜軌跡井參數(shù),對(duì)比了該方法計(jì)算結(jié)果和Eclipse軟件計(jì)算結(jié)果,由圖5可知,各節(jié)點(diǎn)的流量與滲透率值呈現(xiàn)正相關(guān)性,計(jì)算結(jié)果與Eclipse模擬結(jié)果基本一致,井筒中間段較好吻合,兩端吻合稍差,Eclipse結(jié)果偏低,這是因?yàn)镋clipse設(shè)定的邊界條件難以滿足定壓邊界,更接近于封閉邊界。
點(diǎn)源函數(shù)法的優(yōu)勢(shì)在于避免了數(shù)值模擬中數(shù)值彌散的發(fā)生,只需輸入較少的參數(shù)就可以對(duì)復(fù)雜軌跡井進(jìn)行快速產(chǎn)能評(píng)價(jià)。而油藏?cái)?shù)值模擬方法的數(shù)值發(fā)散現(xiàn)象,以及需要輸入較為準(zhǔn)確的油藏參數(shù),限制了該方法在油藏評(píng)價(jià)階段的應(yīng)用。
圖3 分段流入量及累計(jì)流入量分布Fig.3 Inflow rate of different segments and cumulative pipe flow rate
圖4 分段井筒摩阻壓降及累計(jì)壓降分布Fig.4 Pipe flow pressure drop of different segments and cumulative pressure drop
圖5 點(diǎn)源函數(shù)與數(shù)模方法結(jié)果對(duì)比Fig.5 Results comparison between point source function method and Eclipse simulation
2.3計(jì)算結(jié)果與油田現(xiàn)場(chǎng)對(duì)比
應(yīng)用該方法計(jì)算了安哥拉某深水油田A1井在不同井底流壓下的產(chǎn)量(圖6),井底流壓越小,生產(chǎn)壓差越大,單井日產(chǎn)油量也就越高。通過(guò)與油田現(xiàn)場(chǎng)測(cè)量的產(chǎn)量數(shù)據(jù)進(jìn)行對(duì)比可以看出,預(yù)測(cè)的油井產(chǎn)量稍低于實(shí)際產(chǎn)量,這主要是模型做了簡(jiǎn)化造成的,但總體相對(duì)誤差小于5%,能滿足現(xiàn)場(chǎng)油藏工程研究的需要。
圖6 新方法計(jì)算產(chǎn)量與現(xiàn)場(chǎng)產(chǎn)量對(duì)比Fig.6 Comparison of the calculated well production rate with the metered oil production in oilfield
應(yīng)用點(diǎn)源函數(shù)方法計(jì)算復(fù)雜軌跡井產(chǎn)量,不僅考慮了油藏儲(chǔ)層的非均質(zhì)性和沿程井筒的壓降損失,而且適用條件和應(yīng)用范圍更廣,克服了傳統(tǒng)水平井產(chǎn)量計(jì)算方法的不足。通過(guò)計(jì)算實(shí)例表明,該方法能準(zhǔn)確地計(jì)算復(fù)雜軌跡井的產(chǎn)量,在油藏評(píng)價(jià)階段能發(fā)揮快速便捷的作用。通過(guò)與油藏?cái)?shù)值模擬結(jié)果對(duì)比,表明該方法是切實(shí)可行的。
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(編輯張亞雄)
A new method for production calculation of complex trajectory wells in heterogeneous reservoir
Chen Zhihai, Dong Guangwei, Lian Peiqing
(Exploration&ProductionResearchInstitute,SINOPEC,Beijing,100083,China)
Analytical and semi-analytical formulas for production calculation of horizontal wells generally require the reservoirs being homogeneous and well trajectory parallel reservoir boundary,which make them unsuitable for complex trajectory wells.In this paper,the reservoir is divided into several regions based on well trajectory and permeability.Each region has different permeability,and the well trajectory within the region may be unparallel with the boundary.The point source function method is introduced to establish the segmented integral similarity solution for the production of complex-trajectory well in heterogeneous and constant-pressure-boundary reservoir,and the Ouyang model is used to calculate the pressure loss along the wellbore.This method can avoid numerical dispersion in simulation,and provide a fast production evaluation with fewer input parameters.Case study result shows that flow rate in wellbore with complex trajectory increases from toe to heel,the reservoir inflow rate is different in each segment due to reservoir heterogeneity and is high in the high permeability reservoir region,the pressure drop within the wellbore also increases from toe to heel and is different in each wellbore segment due to the uneven distribution of flow rate.The result of this method is consistent with that of Eclipse,confirming its feasibility.In comparison with the metered oil production in field,the calculated production of complex trajectory well has an error of less than 5%,showing that it can satisfy the demand of real-field reservoir engineering research.
heterogeneous reservoir,point-source function,complex-trajectory well,production calculation
2015-02-13;
2016-04-15。
陳志海(1970—),男,博士、教授級(jí)高級(jí)工程師,油氣藏滲流理論及數(shù)值模擬。E-mail:chenzh.syky@sinopec.com。
國(guó)家科技重大專(zhuān)項(xiàng)(2016ZX05033-003);中石化科技部項(xiàng)目(P12100)。
0253-9985(2016)03-0444-06
10.11743/ogg20160319
TE312
A