油基鉆井液環(huán)境下電成像測(cè)井響應(yīng)分析及定量反演

高建申, 孫建孟, 姜艷嬌, 于其蛟, 劉彥萍

(1.西安石油大學(xué)光電油氣測(cè)井與檢測(cè)教育部重點(diǎn)實(shí)驗(yàn)室,陜西西安 710065;2.中國(guó)石油大學(xué)(華東)地球科學(xué)與技術(shù)學(xué)院, 山東青島266580; 3.東北石油大學(xué)地球科學(xué)學(xué)院,黑龍江大慶 163318; 4.中國(guó)石化勝利石油工程有限公司測(cè)井公司,山東東營(yíng) 257061)

電成像測(cè)井起源于20世紀(jì)80年代,在油氣勘探和儲(chǔ)層精細(xì)評(píng)價(jià)過(guò)程中發(fā)揮著重要作用。最初開(kāi)發(fā)的電成像測(cè)井儀器,以FMS和FMI為代表,適用于低電阻率水基鉆井液[1-2]。然而,隨著勘探開(kāi)發(fā)的不斷深入,深水儲(chǔ)層中高溫高壓環(huán)境,大斜井、水平井中復(fù)雜鉆井條件,以及頁(yè)巖儲(chǔ)層中的水敏效應(yīng)等問(wèn)題對(duì)鉆井液類(lèi)型提出挑戰(zhàn)。油基鉆井液具有潤(rùn)滑性好、耐高溫、保持井壁穩(wěn)定和提高鉆井效率等優(yōu)點(diǎn),因此在鉆井過(guò)程中常使用油基鉆井液替代水基鉆井液[3-5]。但是,常規(guī)的電成像測(cè)井儀器難以適用于高電阻率油基鉆井液,因此需要發(fā)展適用于油基鉆井液環(huán)境下的電成像測(cè)井儀器。進(jìn)入21世紀(jì)以來(lái),第一代適用于油基鉆井液的電成像測(cè)井儀器及其應(yīng)用報(bào)道相繼出現(xiàn)[6-10],研究表明這些儀器存在諸多問(wèn)題,例如對(duì)較厚泥餅、高角度地層和低阻地層響應(yīng)不靈敏,成像效果較差,難以進(jìn)行定量解釋等[11-14]。第二代油基鉆井液電成像測(cè)井及定量反演是目前的研究熱點(diǎn)之一[12-13,15-16]。為此,筆者利用垂直耦合處理方法和支持向量回歸算法[17-21],開(kāi)展油基鉆井液電成像測(cè)井參數(shù)的反演研究,以期解決泥餅厚度和地層電阻率的定量評(píng)價(jià)問(wèn)題。

1 測(cè)量方法及響應(yīng)特征

1.1 測(cè)量方法

如圖1所示,測(cè)量極板采用單發(fā)雙收裝置。為使電流能夠穿過(guò)高阻泥餅層,位于極板中心位置的雙排鈕扣電極,發(fā)射兆級(jí)頻率的電流穿過(guò)高阻泥餅層進(jìn)入地層,回流到位于極板兩端對(duì)稱(chēng)分布的返回電極。同時(shí),為減少漏電流影響,增加對(duì)測(cè)量電流的聚焦效果,位于鈕扣電極陣列周?chē)钠帘坞姌O與鈕扣電極等電位發(fā)射同頻率的電流,同樣回流到返回電極。同時(shí)測(cè)量鈕扣電極電壓U、電流I的幅度和相位,得到測(cè)量總阻抗Z為

(1)

Z=Zm+Zf.

(2)

式中,三者在阻抗矢量圖版[8]中構(gòu)成三角形關(guān)系。一般情況下,泥餅阻抗遠(yuǎn)高于地層阻抗,在阻抗矢量圖版中,泥餅阻抗與地層阻抗近似保持垂直關(guān)系,滿(mǎn)足

Re(Zm)Re(Zf)+Im(Zm)Im(Zf)=0 .

(3)

式中,Re和Im分別為阻抗的實(shí)部、虛部符號(hào)。

圖1 油基鉆井液電成像測(cè)井原理示意圖Fig.1 Schematic of electrical imaging logging in oil based drilling fluid

在高頻電流影響下,泥餅阻抗可以等效為

(4)

式中,rm為泥餅等效電阻;Cm為泥餅等效電容。

根據(jù)式(2)～(4)可以得出地層視電阻率Raf,即

(5)

式中,Rm、εmr分別為油基鉆井液電阻率和相對(duì)介電常數(shù);ε0為真空介電常數(shù),其值為8.85×10-12F/m;ω為儀器工作角頻率;K為儀器常數(shù)。

從式(5)可以看出,計(jì)算地層視電阻率需要的參數(shù)包括儀器常數(shù)K,儀器工作頻率f,油基鉆井液電阻率Rm和相對(duì)介電常數(shù)εmr,總阻抗實(shí)部Re(Z)和虛部Im(Z)。利用實(shí)驗(yàn)或數(shù)值模擬方法可以確定儀器常數(shù),通過(guò)處理電壓、電流信號(hào)可以得到頻率、阻抗實(shí)部和虛部,通過(guò)地面或井下儀器測(cè)量可以得到油基鉆井液電阻率和相對(duì)介電常數(shù)[22-23],但未考慮井溫、鉆井液與地層相互作用等因素的影響,地面測(cè)量得到的參數(shù)與井下實(shí)際情況存在差異。

1.2 響應(yīng)特征

根據(jù)測(cè)量原理,利用三維有限元數(shù)值模擬方法計(jì)算不同條件下的地層視電阻率。值得注意的是,式(5)忽略了極板與地層之間的間隔(等效為泥餅厚度)對(duì)測(cè)量響應(yīng)的影響,為此需要研究不同間隔下的測(cè)量響應(yīng)。

據(jù)調(diào)研,油基鉆井液電阻率通常是水基鉆井液的104～107倍,一般大于10 kΩ·m[24]。當(dāng)頻率高于0.1 MHz時(shí),不能忽略鉆井液和地層的相對(duì)介電常數(shù)對(duì)測(cè)量結(jié)果的影響[25]。油基鉆井液相對(duì)介電常數(shù)范圍一般為3～10[26],地層相對(duì)介電常數(shù)與地層電阻率近似滿(mǎn)足冪函數(shù)關(guān)系或取定值10[27-28]。

從圖2中可以看出,當(dāng)?shù)貙与娮杪市∮?00 Ω·m時(shí),利用式(5)得到的地層視電阻率曲線近似為斜率為45°的直線,基本上可以定量反映地層電阻率變化;當(dāng)?shù)貙与娮杪蚀笥?00 Ω·m時(shí),曲線斜率逐漸降低,偏差增大,失去定量表征地層電阻率變化的能力;地層電阻率繼續(xù)增大,曲線反轉(zhuǎn),此時(shí)一個(gè)地層視電阻率對(duì)應(yīng)兩個(gè)地層電阻率,即存在雙解現(xiàn)象。反轉(zhuǎn)點(diǎn)對(duì)應(yīng)的地層電阻率值(以下稱(chēng)反轉(zhuǎn)值)受多個(gè)因素影響。例如,當(dāng)Rm為20 kΩ·m,Dm分別為1和5 mm時(shí),反轉(zhuǎn)值分別為5和2 kΩ·m。間隔不變,油基鉆井液電阻率越大,反轉(zhuǎn)值也越大。另外研究表明,反轉(zhuǎn)值還受工作頻率的影響,頻率越大,反轉(zhuǎn)值越小。

另外,圖2中總視電阻率曲線在低阻地層中基本保持平直,難以反映出地層電阻率變化;在高阻地層中,曲線斜率逐漸增大,能夠定性表示地層電阻率變化,這為高阻地層中地層電阻率定量反演提供主要的參考依據(jù)。

圖2 不同條件下的視電阻率曲線Fig.2 Apparent resistivity curves under different conditions

2 SVR應(yīng)用

支持向量機(jī)(support vector machine,簡(jiǎn)稱(chēng)SVM)是一種基于統(tǒng)計(jì)學(xué)理論中結(jié)構(gòu)風(fēng)險(xiǎn)最小化準(zhǔn)則的機(jī)器學(xué)習(xí)新方法,具有良好的范化能力,能夠解決“維數(shù)災(zāi)難”問(wèn)題,理論上可以得到全局最優(yōu)解。支持向量回歸(support vector machine for regression,簡(jiǎn)稱(chēng)SVR)是一種以SVM為基礎(chǔ)的非線性回歸算法,其基本思想是為解決低維空間線性不可分的問(wèn)題,利用核函數(shù)將數(shù)據(jù)樣本映射到高維空間,尋找一個(gè)最優(yōu)擬合面使得所有樣本數(shù)據(jù)離該最優(yōu)擬合面誤差最小。

SVR算法求解過(guò)程可表述為如下約束問(wèn)題:

(6)

本研究中,已知的參數(shù)有儀器工作頻率、測(cè)量阻抗實(shí)部和虛部,需要反演的參數(shù)為地層電阻率和極板與地層之間的間隔。另外,還需要掌握油基鉆井液電阻率和相對(duì)介電常數(shù),為此制定如圖3所示的反演流程,具體表述為:

(1)數(shù)據(jù)預(yù)處理,包括數(shù)據(jù)對(duì)數(shù)變換和歸一化。

(2)根據(jù)測(cè)量數(shù)據(jù)和經(jīng)驗(yàn),初始化油基鉆井液電阻率和相對(duì)介電常數(shù),分別記為Rm0、εmr0,利用式(5)計(jì)算地層視電阻率。

圖3 油基鉆井液電成像測(cè)井參數(shù)反演流程Fig.3 Inversion workflow for electrical imaging logging in oil based drilling fluid

(3)選擇總視電阻率、地層視電阻率及測(cè)量阻抗實(shí)部、虛部作為輸入?yún)?shù),地層電阻率和間隔作為輸出參數(shù),利用SVR算法反演得到地層電阻率Rt0,極板與地層之間的間隔Dm0。

(4)根據(jù)油基鉆井液電阻率和相對(duì)介電常數(shù)初值Rm0、εmr0和反演得到的地層電阻率Rt0和間隔Dm0,利用查表插值方法[29-30]求得對(duì)應(yīng)的測(cè)量阻抗實(shí)部、虛部,分別記為Re(Z′)、Im(Z′)。

(5)計(jì)算目標(biāo)函數(shù)O,如果O>δ,則返回步驟(2)重新計(jì)算;如果O<δ,則輸出此時(shí)對(duì)應(yīng)的地層電阻率和間隔。目標(biāo)函數(shù)表示為

(7)

式中,w1、w2、w3分別為阻抗實(shí)部、虛部和模值的權(quán)系數(shù)。

3 應(yīng)用舉例及效果分析

3.1 隨機(jī)地層模型驗(yàn)證

建立地層模型,井眼直徑為0.2 m,油基鉆井液電阻率為10 kΩ·m,相對(duì)介電常數(shù)為6,地層電阻率范圍為0.2 Ω·m～20 kΩ·m,極板與地層之間間隔范圍為1～10 mm,隨機(jī)改變地層電阻率和間隔,利用有限元數(shù)值模擬方法得到測(cè)量數(shù)據(jù),然后利用上述反演方法反演地層電阻率和極板與地層之間間隔,結(jié)果如圖4所示。圖4中含有320組測(cè)量數(shù)據(jù),從圖中可以看出反演值與實(shí)際值相吻合,準(zhǔn)確率超過(guò)90%,尤其是當(dāng)?shù)貙与娮杪手岛芨呋蚝艿蜁r(shí),也能夠達(dá)到良好的反演效果,驗(yàn)證了上述數(shù)據(jù)選擇和反演方法的正確性。

圖4 隨機(jī)地層電阻率和間隔反演結(jié)果Fig.4 Inverted results for a formation model with random resistivity and standoff

3.2 地層模型成像反演結(jié)果

不失一般性,建立層狀地層模型,地層厚度為1 m,地層中含有低阻、高阻層段,井眼直徑為0.2 m,極板與地層之間間隔為1 mm。為貼近實(shí)際測(cè)井情況,油基鉆井液電阻率變化范圍為10～100 kΩ·m,相對(duì)介電常數(shù)變化范圍為3～8。為增加對(duì)比和驗(yàn)證效果,選擇水基鉆井液環(huán)境下的成像結(jié)果作為參照對(duì)象。圖5給出了模擬及反演的電阻率曲線,圖6給出了對(duì)應(yīng)的成像結(jié)果。

圖5中,第一道為深度道,符號(hào)RW表示水基鉆井液井內(nèi)視電阻率數(shù)據(jù)(第二道),ROC、ROVC、ROIN分別表示油基鉆井液井內(nèi)常規(guī)視電阻率數(shù)據(jù)、垂直耦合方法處理和反演地層電阻率數(shù)據(jù)(第三道至第五道),下同。從圖5可以看出,以水基鉆井液井內(nèi)測(cè)量結(jié)果作為參考,油基鉆井液井內(nèi)常規(guī)視電阻率曲線動(dòng)態(tài)變化范圍較小,電阻率值大于100 Ω·m,只能定性表征地層電阻率變化。整體上,垂直耦合處理結(jié)果與水基鉆井液井內(nèi)測(cè)量曲線變化一致,但在高阻層段相差較大,甚至出現(xiàn)了反轉(zhuǎn)現(xiàn)象(0.05和0.35 m處),測(cè)量結(jié)果遠(yuǎn)低于實(shí)際值,造成低阻假象。反演處理結(jié)果與水基鉆井液井內(nèi)測(cè)量曲線基本一致,擴(kuò)大了曲線動(dòng)態(tài)變化范圍,消除了垂直耦合處理造成的反轉(zhuǎn)現(xiàn)象,達(dá)到定量表征地層電阻率變化的目的。

圖5 層狀地層電阻率曲線Fig.5 Processed resistivity curves for a layered formation

圖6中,反演地層電阻率成像與水基鉆井液井內(nèi)成像基本相同,印證了上述分析。另外,在低阻層段,反演得到的間隔曲線(第六道)與實(shí)際值相吻合;在高阻層段,地層電阻率與鉆井液電阻率相差較小,增加了鉆井液、泥餅與地層之間的區(qū)分難度,反演值大于實(shí)際值,但反映出地層電阻率的變化,高值對(duì)應(yīng)高阻層段,低值對(duì)應(yīng)低阻層段。

圖6 層狀地層模擬成像結(jié)果Fig.6 Simulated imaging results for a layered formation

建立低阻地層模型,地層電阻率范圍為1～10 Ω·m,極板與地層之間間隔為2 mm,其他條件與圖5一致,成像結(jié)果如圖7所示。圖7中,與水基鉆井液井內(nèi)成像相比,受極板與地層之間高阻鉆井液、泥餅的影響,常規(guī)視電阻率成像質(zhì)量很差,難以分辨出地層電阻率的變化。垂直耦合處理和反演成像結(jié)果與水基鉆井液井內(nèi)成像相符,間隔反演值與實(shí)際值相差很小。進(jìn)一步,取極板與地層間隔變化范圍為1～10 mm,其他條件不變,成像結(jié)果如圖8所示。反演成像不受間隔變化影響,與水基鉆井液井內(nèi)成像保持一致,而且間隔反演值與實(shí)際值變化也一致。說(shuō)明了該反演方法解決了低阻地層中常規(guī)成像不清晰的問(wèn)題,而且能夠定量反映出極板與地層間隔變化,從而可以了解井眼形狀和地層滲透性。

圖7 固定間隔低阻地層模擬成像結(jié)果Fig.7 Simulated imaging results for a formation with constant standoff

圖8 改變間隔低阻地層模擬成像結(jié)果Fig.8 Simulated imaging results for a formation with changed standoff

4 結(jié)束語(yǔ)

針對(duì)油基鉆井液環(huán)境下電成像測(cè)井中存在的問(wèn)題,基于數(shù)值模擬和SVR方法進(jìn)行了油基鉆井液電成像測(cè)井響應(yīng)分析及定量反演。研究表明,垂直耦合處理得到視電阻率和常規(guī)視電阻率能夠分別反映出中低阻地層和高阻地層的電阻率變化,可以作為油基鉆井液電成像測(cè)井參數(shù)定量反演的主要依據(jù)。提出的基于SVR反演方法不僅可以定量地反映出地層電阻率變化,還能夠定量反映出低阻地層中極板與地層的間隔變化;高阻地層增加了高阻鉆井液、泥餅與地層之間的區(qū)分難度,反演間隔偏大,高值對(duì)應(yīng)高阻地層,低值對(duì)應(yīng)低阻地層。該反演方法擺脫了油基鉆井液電參數(shù)的限制,為油基鉆井液電成像測(cè)井?dāng)?shù)據(jù)處理提供支持。

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