楊尚諭,楊秀娟,閆相禎,許建國(guó),樊 恒

(1.中國(guó)石油大學(xué)(華東)油氣CAE技術(shù)研究中心,山東青島 266580;2.吉林油田公司采油工藝研究院,吉林松原 138000)

煤層氣水力壓裂縫內(nèi)變密度支撐劑運(yùn)移規(guī)律

楊尚諭1,楊秀娟1,閆相禎1,許建國(guó)2,樊 恒1

(1.中國(guó)石油大學(xué)(華東)油氣CAE技術(shù)研究中心,山東青島 266580;2.吉林油田公司采油工藝研究院,吉林松原 138000)

針對(duì)煤層氣水力壓裂有效支撐縫長(zhǎng)過(guò)短且縫內(nèi)鋪砂濃度分布不均勻的問(wèn)題,研究變密度支撐劑顆粒在裂縫內(nèi)的運(yùn)移規(guī)律。采用Pseudo Fluid模型考慮了裂縫內(nèi)支撐劑顆粒之間的相互影響,借助Visual Studio 2012設(shè)計(jì)平臺(tái)編制相應(yīng)計(jì)算軟件,并通過(guò)與現(xiàn)場(chǎng)監(jiān)測(cè)值進(jìn)行對(duì)比,校核了軟件計(jì)算的準(zhǔn)確性。討論了壓裂液黏度、裂縫壁面、排量和支撐劑密度等參數(shù)對(duì)縫內(nèi)鋪砂濃度和有效支撐縫長(zhǎng)影響規(guī)律,分析了超低密度支撐劑在不同圍壓和溫度工況下的破碎率。結(jié)果表明:堅(jiān)果殼支撐劑在圍壓為69 MPa、環(huán)境溫度為90℃工況下破碎率＜2%,滿足現(xiàn)場(chǎng)需求;隨著壓裂液黏度、施工排量增加,裂縫支撐長(zhǎng)度增加,縫內(nèi)鋪砂更加均勻;支撐劑顆粒直徑增加使得裂縫支撐長(zhǎng)度降低;采用變密度支撐劑較單一陶粒砂有效支撐半縫長(zhǎng)增加了19.5 m,且鋪砂效果更均勻。

煤層氣井;變密度支撐劑;分段壓裂;支撐劑運(yùn)移

伴隨國(guó)內(nèi)油氣需求的持續(xù)增長(zhǎng)與常規(guī)油氣產(chǎn)量的不斷下降,具有較大資源潛力的非常規(guī)油氣逐漸成為新的領(lǐng)域,受到各個(gè)國(guó)家和油氣公司的高度重視[1]。我國(guó)經(jīng)過(guò)20 a的研究探索,實(shí)際鉆完煤層氣井近萬(wàn)口,但仍存在大批煤層氣井產(chǎn)量低或者產(chǎn)出的氣不具備工業(yè)產(chǎn)能,直接影響了我國(guó)煤層氣開(kāi)采的發(fā)展[2-4]。大量現(xiàn)場(chǎng)壓裂井監(jiān)測(cè)數(shù)據(jù)結(jié)果表明,煤層氣低產(chǎn)井壓裂誘導(dǎo)裂縫內(nèi)支撐劑顆粒由于密度較高而大量沉積在近井端0～40 m范圍內(nèi),有效支撐縫長(zhǎng)較短是影響煤層氣井壓裂產(chǎn)能的主要原因之一[5-8]。

由Stokes定律可知清水?dāng)y砂顆粒以拋物線方式下沉結(jié)合砂提翻滾,攜砂距離較短,鋪砂近井厚度較大,遠(yuǎn)井厚度小,有效支撐短[9-10]。Liu和Sharma等[11-14]通過(guò)實(shí)驗(yàn)的方式對(duì)支撐劑顆粒在裂縫內(nèi)的運(yùn)移規(guī)律進(jìn)行研究,結(jié)果表明,支撐劑顆粒速度改變?nèi)Q于支撐劑顆粒直徑與該位置處裂縫寬度的比值,當(dāng)該比值接近1時(shí),支撐劑顆粒沿縫長(zhǎng)方向速度將急劇下降。Staben等[15-17]提出采用兩平行板代替裂縫壁進(jìn)行支撐劑顆粒運(yùn)移規(guī)律研究,未考慮裂縫寬度變化對(duì)顆粒運(yùn)移速度的影響。

國(guó)外學(xué)者提出的超低密度支撐劑技術(shù)可以使得攜砂距離增加,有效支撐長(zhǎng)度變長(zhǎng),裂縫導(dǎo)流能力增加,但超低密度支撐劑價(jià)格昂貴,不適合大面積投入使用。

綜上分析,針對(duì)煤層氣水力壓裂支撐劑密度較高使得縫內(nèi)攜砂距離偏短的問(wèn)題,筆者提出采用高密度支撐劑與超低密度支撐劑混合的方法進(jìn)行壓裂,研究了變密度支撐劑在壓裂裂縫內(nèi)的運(yùn)移規(guī)律,并通過(guò)實(shí)驗(yàn)驗(yàn)證了該超低密度支撐劑滿足現(xiàn)場(chǎng)抗壓性能及破碎率要求。該方法增加了裂縫有效支撐長(zhǎng)度,提高了煤層氣井產(chǎn)能,為煤層氣低產(chǎn)井、老井重復(fù)壓裂提供技術(shù)支持。

1 低密度堅(jiān)果殼支撐劑力學(xué)性能

將堅(jiān)果殼制成支撐劑首先要考慮的問(wèn)題就是當(dāng)支撐劑被輸送到誘導(dǎo)裂縫內(nèi)時(shí),該支撐劑是否能抵抗地層閉合壓力而繼續(xù)起到支撐作用,通過(guò)實(shí)驗(yàn)對(duì)其抗壓強(qiáng)度和破碎率進(jìn)行測(cè)試,圖1為堅(jiān)果殼支撐劑試樣。

本實(shí)驗(yàn)針對(duì)兩種密度的干燥支撐劑:①ULW1體積密度0.8 g/cm3(視密度1.20 g/cm3);②ULW2體積密度1.25 g/cm3(視密度1.75 g/cm3)。研究20/40目堅(jiān)果殼支撐劑顆粒在20℃和90℃時(shí)的抗擠壓強(qiáng)度及破碎率情況,ULW1支撐劑實(shí)驗(yàn)結(jié)果表明:當(dāng)閉合壓力達(dá)到100 MPa,支撐劑顆粒ULW1在 20℃時(shí)振篩10 min后支撐劑顆粒破碎率分別為1.41%,1.33%,1.59%和1.36%,由圖2(a)中支撐劑顆粒應(yīng)力-應(yīng)變關(guān)系曲線得到堅(jiān)果殼支撐劑彈性模量為172.42 MPa;當(dāng)溫度升高到90℃后,如圖3(a)所示,振篩10 min后支撐劑顆粒破碎率分別為1.47%,1.64%,1.93%和1.85%,90℃時(shí)對(duì)應(yīng)堅(jiān)果殼支撐劑彈性模量為137.93 MPa;溫度升高,ULW1破碎率增大,彈性模量降低。

ULW2支撐劑抗壓實(shí)驗(yàn)選取3組顆粒試樣進(jìn)行測(cè)試,結(jié)果表明:當(dāng)閉合壓力達(dá)到100 MPa,ULW2支撐劑在20℃時(shí)振篩10 min后顆粒破碎率分別為4.02%,6.38%和6.95%,支撐劑彈性模量為344.83 MPa,如圖2(b)所示;當(dāng)溫度升高到90℃后,振篩10 min后支撐劑顆粒破碎率分別為5.29%, 7.90%和7.32%,該工況下支撐劑彈性模量為275.86 MPa,如圖3(b)所示;溫度升高,ULW1破碎率增大,彈性模量降低。對(duì)比發(fā)現(xiàn)ULW2在閉合壓力為100 MPa工況下顆粒破碎率較大,降低閉合壓力到69 MPa,重做實(shí)驗(yàn),結(jié)果表明,3組試樣90℃時(shí)最大破碎率為2.0%,滿足現(xiàn)場(chǎng)煤層氣水力壓裂支撐劑抗壓及破碎率性能指標(biāo)。

圖1 堅(jiān)果殼支撐劑試樣Fig.1 Proppant sample of nut shell

2 變密度支撐劑在誘導(dǎo)裂縫內(nèi)運(yùn)移規(guī)律

2.1 基于Pseudo Fluid模型的裂縫等效寬度計(jì)算

煤層氣水力壓裂誘導(dǎo)裂縫中,由于支撐劑密度、壓裂液黏度的影響,支撐劑顆粒之間會(huì)存在相互拖拽的現(xiàn)象使得支撐劑在x,y方向上的速度發(fā)生改變(圖4)。

圖2 低密度支撐劑(0.8,1.25 g/cm3)20℃時(shí)的強(qiáng)度試驗(yàn)曲線Fig.2 Strength test curves of the low-density proppant(0.8,1.25 g/cm3)at 20℃

圖3 低密度支撐劑(0.8,1.25 g/cm3)90℃時(shí)的強(qiáng)度試驗(yàn)曲線Fig.3 Strength test curves in of the low-density proppant(0.8,1.25 g/cm3)at 90℃

圖4 支撐劑顆粒運(yùn)移軌跡及裂縫邊界示意Fig.4 Diagram of the proppant particle motion and fracture boundary

誘導(dǎo)裂縫內(nèi)動(dòng)力流體懸浮顆粒之間相互作用非常復(fù)雜,研究某一支撐劑顆粒周圍粒子對(duì)其影響規(guī)律只在非常有限的工況下才可以實(shí)現(xiàn)。筆者采用經(jīng)過(guò)簡(jiǎn)化的半經(jīng)驗(yàn)Pseudo Fluid模型對(duì)其求解,該模型利用等效裂縫寬度來(lái)近似模擬變密度支撐劑顆粒相互影響效果。支撐劑顆粒在誘導(dǎo)裂縫內(nèi)流動(dòng)時(shí),由于支撐劑濃度不為0而引起的附加流體拖拽力使得裂縫寬度發(fā)生變化,裂縫寬度改變量wc可通過(guò)式(1)[18]計(jì)算得到,即

式中,wc為附加拖拽力而引起的裂縫寬度變化量,m; c為t時(shí)刻攜砂液中支撐劑體積分?jǐn)?shù);dp為支撐劑顆粒直徑,m;w為支撐劑顆粒位置處裂縫寬度,m。

水力壓裂裂縫的等效寬度weff可以表述[19]為

式中,weff為Pseudo Fluid模型對(duì)應(yīng)的裂縫等效寬度,m。

2.2 裂縫內(nèi)流體流動(dòng)方程

煤層氣水力壓裂誘導(dǎo)主裂縫呈細(xì)長(zhǎng)型,忽略縫內(nèi)流體壓力在寬度方向(圖4中z向)上的變化。因此,裂縫內(nèi)的壓裂液流動(dòng)過(guò)程可以通過(guò)縫內(nèi)流體二維流

式中,vx,vy為壓裂液在x,y方向上的速度分量, m/min;qL為濾失速度,m/min。

2.3 縫內(nèi)支撐劑運(yùn)移方程

誘導(dǎo)裂縫內(nèi)攜砂液質(zhì)量守恒方程[23]為動(dòng)模型[20-22]描述,即

式中,ρ為攜砂液密度,kg/m3;v為攜砂液速度, m/min;ρF為流體密度,kg/m3;QL為濾失量,m3。

變密度支撐劑顆粒質(zhì)量守恒方程[24]為

式中,ρp為變密度支撐劑等效密度,kg/m3;vp為支撐劑顆粒速度,m/min。

在攜砂液中,由于支撐劑密度和黏性力的影響,支撐劑顆粒的水平速度小于攜砂液的移動(dòng)速度。因此,要精確的計(jì)算裂縫內(nèi)鋪砂濃度,必須分析出支撐劑在縫內(nèi)的運(yùn)移速度。

支撐劑顆粒運(yùn)移速度[25-26]為

式中,vt為修正后的Stoke顆粒沉降速度,m/min;kwc為支撐劑和壓裂液沿縫長(zhǎng)方向上平均速度的比值。

式中,vp為支撐劑顆粒x向平均速度,m/s;vf為壓裂液的平均速度m/s;

修正后的Stoke沉降速度vt通過(guò)式(8)求得

式中,vs為Stoke沉降速度,m/min;fRe為慣性效應(yīng)修正系數(shù),無(wú)因次;fc為縫內(nèi)支撐劑濃度效應(yīng)修正系數(shù),無(wú)因次;fw為壁面效應(yīng)修正系數(shù),無(wú)因次;fT為湍流擾動(dòng)修正系數(shù),無(wú)因次。

聯(lián)立方程(4)～(6)得到誘導(dǎo)裂縫內(nèi)變密度支撐劑運(yùn)移方程,即

方程(9)對(duì)應(yīng)的邊界條件(圖4)為

l2邊界上:

l1和l3邊界上:

誘導(dǎo)裂縫內(nèi)流體壓力、裂縫寬度和縫內(nèi)支撐劑濃度計(jì)算相互依存,想要同時(shí)求解難度較大。筆者在計(jì)算誘導(dǎo)裂縫內(nèi)速度場(chǎng)時(shí)忽略縫內(nèi)流體壓力和裂縫寬度變化對(duì)支撐劑運(yùn)移規(guī)律的影響,假定支撐劑在每個(gè)時(shí)間步內(nèi)的運(yùn)移過(guò)程是準(zhǔn)穩(wěn)態(tài),即在任意時(shí)間步內(nèi),支撐劑運(yùn)移速度的改變不直接影響縫內(nèi)流體速度變化。

在初始支撐劑濃度的基礎(chǔ)上對(duì)縫內(nèi)壓力和有效裂縫寬度進(jìn)行迭代求解,當(dāng)該迭代計(jì)算收斂,利用裂縫尺寸和流體速度求解變密度支撐劑運(yùn)移方程(9),得到下一步迭代計(jì)算的支撐劑濃度值,持續(xù)迭代計(jì)算,直到最終收斂,確定裂縫內(nèi)支撐劑濃度的最終分布。

3 實(shí)例分析及結(jié)果討論

以寧武盆地W8-3井為例,表1為煤儲(chǔ)層物理力學(xué)參數(shù)。

表1 W8-3井煤儲(chǔ)層基本參數(shù)Table 1 Fracturing parameters of coal reservoir

3.1 煤層氣水力壓裂裂縫形狀及幾何尺寸計(jì)算

采用自編3D-CBMulti-Fracture軟件,對(duì)該區(qū)塊W8-3煤層氣井水力壓裂裂縫幾何形狀進(jìn)行預(yù)測(cè)。壓裂設(shè)計(jì)方案:壓裂液施工排量6.5 m3/min,平均砂比12%,最高砂比25%～30%,攜砂液用量390 m3,支撐劑用量46.8 m3,前置液用量303.3 m3,頂替液17.9 m3。圖5為W8-3井第2段裂縫幾何尺寸及縫內(nèi)壓力分布云圖,裂縫有效半長(zhǎng)70.6 m,最大縫寬為9.54 mm,縫內(nèi)最大凈壓力為20.60 MPa,上半縫高9.05 m,下半縫高3.96 m,與現(xiàn)場(chǎng)微地震監(jiān)測(cè)結(jié)果對(duì)比誤差為3.06%。煤層氣水力壓裂過(guò)程中,底層與產(chǎn)層的最小主應(yīng)力相差小,裂縫向下延伸嚴(yán)重;蓋層與產(chǎn)層應(yīng)力相差大,裂縫向上延伸受阻,縫內(nèi)凈壓力增加,使得裂縫向下延伸。

3.2 縫內(nèi)變密度支撐劑鋪砂濃度影響因素

忽略壓裂施工參數(shù)的改變對(duì)誘導(dǎo)裂縫幾何形狀的影響,對(duì)比圖6計(jì)算結(jié)果表明裂縫壁對(duì)支撐劑運(yùn)移速度影響較大,對(duì)于W8-3第2段裂縫,由于裂縫壁的影響,支撐半縫長(zhǎng)度從47.67 m減小到30.85 m,支撐縫高從10.41 m減小到9.32 m。

圖5 W8-3井第2段裂縫幾何尺寸及縫內(nèi)壓力分布云圖Fig.5 Effective fracture geometry and pressure contours of W8-3 well’s the 2nd crack

圖6 壓裂液黏度為10 mPa·s,不考慮和考慮裂縫壁時(shí)縫內(nèi)支撐劑鋪砂濃度分布云圖Fig.6 Proppant concentration contour map without wall and with wall for 10 mPa·s fluid

隨著壓裂液黏度增加,裂縫支撐縫高增大,裂縫壁的存在使得支撐劑顆粒附加拖拽力減小,從而促使支撐劑平均速度大于壓裂液平均流速,即裂縫有效支撐長(zhǎng)度和支撐高度均增加,如圖7(a)所示。圖8為現(xiàn)場(chǎng)測(cè)試數(shù)據(jù)與軟件模擬結(jié)果對(duì)比發(fā)現(xiàn)當(dāng)壓裂液黏度小于255 mPa·s時(shí),軟件模擬結(jié)果偏保守,而當(dāng)壓裂液黏度大于255 mPa·s時(shí),軟件計(jì)算結(jié)果較實(shí)際情況略高,但最高誤差小于10%,計(jì)算精度滿足工程要求。

圖7 壓裂液黏度為500 mPa·s,考慮裂縫壁時(shí)縫內(nèi)支撐劑(40/70,20/40)鋪砂濃度分布云圖Fig.7 Proppant(40/70,20/40)concentration contour map with wall for 500 mPa·s fluid

圖8 壓裂液黏度與裂縫有效支撐長(zhǎng)度關(guān)系曲線Fig.8 Relationship between fluid viscosity and crack effective length

圖7對(duì)比表明:支撐劑顆粒的直徑增加促使壓裂液拖拽力增加,從而使得支撐劑阻力增加,由于支撐劑顆粒沿裂縫x方向的速度分量減小,因此,支撐劑顆粒直徑從(40/70)目增加到(20/40)目裂縫支撐長(zhǎng)度迅速降低。

忽略施工排量改變對(duì)裂縫形狀的影響,圖9為施工排量對(duì)壓裂誘導(dǎo)裂縫內(nèi)支撐劑鋪設(shè)濃度的影響,結(jié)果表明:施工排量增加1倍使得沿縫長(zhǎng)方向壓降速度增加,縫內(nèi)支撐劑分布合理且有效支撐縫長(zhǎng)增大0.41倍。

圖10為不同密度支撐劑工況下對(duì)應(yīng)誘導(dǎo)裂縫有效半縫長(zhǎng),采用變密度支撐劑有效支撐半長(zhǎng)達(dá)到44.5 m,較單一陶粒砂有效支撐半縫長(zhǎng)增加了19.5 m,且鋪砂效果更均勻,將極大的提高煤層氣產(chǎn)能。

圖9 施工排量為4,8 m3/min時(shí)縫內(nèi)鋪砂濃度Fig.9 Proppant placement concentration for the pumping rate 4,8 m3/min

圖10 不同密度支撐劑裂縫有效支撐長(zhǎng)度Fig.10 Effective support length of different fracture proppant density

4 結(jié) 論

(1)在圍壓為69 MPa、環(huán)境溫度為90℃工況下,堅(jiān)果殼支撐劑破碎率＜2%,滿足現(xiàn)場(chǎng)規(guī)定支撐劑使用要求。

(2)利用Pseudo Fluid模型研究變密度支撐劑顆粒之間相互影響,研究表明壓裂液黏度、裂縫壁面、支撐劑粒徑、排量和支撐劑密度等因素將直接影響誘導(dǎo)裂縫內(nèi)鋪砂濃度的分布,進(jìn)而影響壓裂裂縫導(dǎo)流能力。

(3)與單一陶粒砂相比,使用變密度支撐劑有效支撐半縫長(zhǎng)增加了19.5 m,且縫內(nèi)鋪砂更為均勻,極大地提升了煤層氣產(chǎn)量。

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Variable density proppant placement in CBM wells fractures

YANG Shang-yu1,YANG Xiu-juan1,YAN Xiang-zhen1,XU Jian-guo2,FAN Heng1

(1.Oil and Gas CAE Technology Research Center,China University of Petroleum,Qingdao 266580,China;2.Oil Production Technology Research Institute of Jilin Oilfield Company,Songyuan 138000,China)

The migration law in the cracks of variable density proppant particles had been researched,for effective support fracture length of CBM hydraulic fracturing was too short and seam sanding concentration distributed uneven.The mutual influence of the fracture proppant particles was considered using Pseudo Fluid model,and the corresponding calculation software was written with the Visual Studio 2012 design platform,then the accuracy of the calculations was checked through comparison with the value of field monitoring software.The effective law to seam sanding concentration and effective support slot length of the fracturing fluid viscosity,wall cracks,displacement and proppant density parameters were discussed,and the broken rate of the ultra-low density proppant was analyzed at different confining pressure and temperature conditions.The results show that broken rate of a nut shell proppant is less than 2%in the condition of confining pressure 69 MPa and the ambient temperature 90℃,which meet the site requirements;With the increase of fracturing fluid viscosity,the construction displacement and fracture bracing length,the seam sanding is more uniform;with the proppant particle diameter increases,the crack support length decreases;compared to single ceramic sand,using variable-density proppant makes effective support half-slot length increasing 19.5 m,and the sanding effect is more uniform.

coalbed methane well;variable density proppant;staged fracturing;proppant migration

P618.11;TE371

A

0253-9993(2014)12-2459-07

2013-11-15 責(zé)任編輯:韓晉平

國(guó)家自然科學(xué)基金資助項(xiàng)目(51374228,51105381);中央高?；究蒲袠I(yè)務(wù)費(fèi)專項(xiàng)資金資助項(xiàng)目(27R1315018A)

楊尚諭(1986—),男,陜西榆林人,博士研究生。E-mail:shangyuy@163.com

楊尚諭,楊秀娟,閆相禎,等.煤層氣水力壓裂縫內(nèi)變密度支撐劑運(yùn)移規(guī)律[J].煤炭學(xué)報(bào),2014,39(12):2459-2465.

10.13225/j.cnki.jccs.2013.1693

Yang Shangyu,Yang Xiujuan,Yan Xiangzhen,et al.Variable density proppant placement in CBM wells fractures[J].Journal of China Coal Society,2014,39(12):2459-2465.doi:10.13225/j.cnki.jccs.2013.1693