張 園,邸 元,張 允,張冬麗

(1.中國(guó)地質(zhì)大學(xué)(北京) 能源學(xué)院,北京 100083;2.北京大學(xué) 工學(xué)院,北京 100871;3.中國(guó)石油化工股份有限公司 石油勘探開(kāi)發(fā)研究院,北京 100083)

10.3969/j.issn.1671-8798.2017.05.002

2017-03-25

國(guó)家自然科學(xué)基金項(xiàng)目(51674010)；國(guó)家科技重大專項(xiàng) (2016ZX05014)；中國(guó)地質(zhì)大學(xué)(北京)基本科研啟動(dòng)基金項(xiàng)目(53200759016)

邸 元(1968— )，男，陜西省西安人,副教授，博士，主要從事多孔介質(zhì)多相流數(shù)值模擬、巖土力學(xué)研究。E-mail：diyuan@mech.pku.edu.cn。

納米孔隙中毛管力效應(yīng)對(duì)致密油藏產(chǎn)能的影響

張 園1,邸 元2,張 允3,張冬麗3

(1.中國(guó)地質(zhì)大學(xué)(北京) 能源學(xué)院,北京 100083;2.北京大學(xué) 工學(xué)院,北京 100871;3.中國(guó)石油化工股份有限公司 石油勘探開(kāi)發(fā)研究院,北京 100083)

傳統(tǒng)的相平衡計(jì)算模型無(wú)法準(zhǔn)確計(jì)算納米孔隙中的油氣相態(tài)變化,因此須對(duì)傳統(tǒng)的閃蒸計(jì)算模型進(jìn)行改進(jìn)。今通過(guò)計(jì)算油氣兩相壓力不相等情況下油氣的相平衡,得到考慮毛細(xì)管力效應(yīng)的油氣黏度、密度及溶解氣油比等物性。毛細(xì)管力采用Young-Laplace公式進(jìn)行計(jì)算,計(jì)算了某多組分混合物的相態(tài)平衡常數(shù),結(jié)果與實(shí)驗(yàn)值符合良好,從而驗(yàn)證了本文算法計(jì)算相平衡的準(zhǔn)確性。還以Bakken致密油藏為例,基于黑油模型研究毛細(xì)管力對(duì)相平衡影響時(shí)的油藏產(chǎn)量預(yù)測(cè),結(jié)果表明忽略毛細(xì)管力的影響,會(huì)使預(yù)測(cè)的油氣產(chǎn)量低于實(shí)際的油氣產(chǎn)量。本研究較好地解釋了毛細(xì)管力對(duì)油氣的相態(tài)平衡及其對(duì)致密油藏產(chǎn)能預(yù)測(cè)的影響。

毛細(xì)管力;Peng-Robinson狀態(tài)方程;油氣相態(tài)平衡;致密油藏

非常規(guī)油氣藏的特點(diǎn)是低孔、低滲,孔隙尺寸大多在2.5～103nm,儲(chǔ)集層中納米級(jí)孔隙發(fā)育[1-2]。大量研究表明,納米級(jí)孔隙中的高毛細(xì)管力不僅影響油氣在孔隙中的流動(dòng)過(guò)程,也影響油氣的相態(tài)平衡,進(jìn)而影響油氣的最終采收率。

Sigmund等[3]以實(shí)驗(yàn)儀器來(lái)研究C1-C4和C1-nC5混合物的泡點(diǎn)及露點(diǎn)壓力,發(fā)現(xiàn)界面效應(yīng)會(huì)影響平衡壓力及各相的組分含量。理論分析也顯示出泡點(diǎn)壓力會(huì)隨著孔隙尺寸的減小而降低[4-8],并且油藏條件距離臨界點(diǎn)越遠(yuǎn),泡點(diǎn)壓力下降得越顯著。由于傳統(tǒng)的PVT(pressure-volume-temperature)分析無(wú)法對(duì)毛細(xì)管力效應(yīng)的相態(tài)問(wèn)題給出準(zhǔn)確的預(yù)測(cè),因此,需要改進(jìn)傳統(tǒng)的計(jì)算方法來(lái)計(jì)算流體性質(zhì),從而對(duì)非常規(guī)油氣藏進(jìn)行產(chǎn)能預(yù)測(cè)[9]。Wang等[10]通過(guò)加入孔隙壓實(shí)效應(yīng)項(xiàng),研究了該效應(yīng)對(duì)油藏產(chǎn)量的影響。Teklu等[11]引入了流體組分臨界性質(zhì)的轉(zhuǎn)換因子來(lái)計(jì)算流體的相平衡,結(jié)果表明,毛細(xì)管力效應(yīng)對(duì)相包絡(luò)線的影響顯著。Rezaveisi等[12]將毛細(xì)管力項(xiàng)的相平衡計(jì)算模型與組分模擬器相結(jié)合,用來(lái)預(yù)測(cè)非常規(guī)油藏的產(chǎn)能變化。在前人研究的基礎(chǔ)上,筆者提出了一個(gè)能夠考慮毛細(xì)管力效應(yīng)的計(jì)算儲(chǔ)層流體相平衡的數(shù)值方法,將此法對(duì)某多組分混合物的相平衡進(jìn)行計(jì)算,并把計(jì)算結(jié)果與實(shí)驗(yàn)結(jié)果進(jìn)行對(duì)比;還以Bakken致密油藏中一口生產(chǎn)井為例,基于黑油模型研究了毛細(xì)管力對(duì)油藏產(chǎn)量預(yù)測(cè)的影響。

1 理論模型

1.1 相平衡計(jì)算模型

當(dāng)液相和氣相中各組分的逸度相等時(shí),體系達(dá)到相平衡[11],即:

(1)

根據(jù)質(zhì)量守恒定律,可得式(2)～(4)：

(2)

Fzi=xiL+yiV,i=1,…,Nc,

(3)

(4)

(5)

式(5)中:Ki為傳統(tǒng)相平衡計(jì)算中的平衡常數(shù);Pc為毛細(xì)管力。采用Young-Laplace方程[13]來(lái)計(jì)算:

(6)

式(6)中:r為毛細(xì)管半徑,目前的研究中,常將r近似為孔隙半徑[7];θ為接觸角;σ為氣相與液相間的界面張力,采用Macleod-Sugden方程[13]計(jì)算。

利用Peng-Robinson狀態(tài)方程[14]可求得液相和氣相的壓縮因子。采用Newton-Raphson迭代來(lái)解式(2)～(4)的非線性方程組,可求得組分i在氣相和液相中的逸度,最終求得xi,yi等參數(shù)[15]。

1.2 流體性質(zhì)的計(jì)算

采用前述相平衡計(jì)算方法,可求得考慮毛細(xì)管力效應(yīng)時(shí)的溶解氣油比、體積系數(shù)、黏度等物性參數(shù)(均為壓力的函數(shù))。

溶解氣油比的計(jì)算公式如下:

(7)

式(7)中:nV和nL分別為氣體和液體的摩爾分?jǐn)?shù);VmV和VmL分別為氣體和液體的摩爾體積;SC表示標(biāo)準(zhǔn)狀態(tài)(20 ℃,101.3 kPa)。

地層油的體積系數(shù)Bo用公式表示為:

(8)

式(8)中,RC表示油藏條件。

黏度[16]的計(jì)算如下:

(9)

式(9)中：μ為原油在地層條件下的黏度;μ*為低壓下混合物的黏度；ξ為混合物的黏度;參數(shù)a0～a4分別為0.102 3、0.0233 64、0.058 533、-0.040 758和0.009 332 4;ρr為視摩爾密度；各參數(shù)的計(jì)算可參見(jiàn)文獻(xiàn)[17]。

2 相平衡計(jì)算方法的驗(yàn)證

表1 某混合物各組分平衡常數(shù)(K值)的計(jì)算值與實(shí)驗(yàn)值Table 1 Caculation and experimental data of K-values for each component of the fluid

通過(guò)計(jì)算某混合物在71.7 ℃、426.1 kPa條件下的平衡常數(shù),來(lái)驗(yàn)證本文相平衡計(jì)算方法的準(zhǔn)確性。具體的計(jì)算結(jié)果如表1所示,由此可知，計(jì)算而得的平衡常數(shù)值的平均誤差為2.5%,計(jì)算值與實(shí)驗(yàn)值[10]的誤差較小,從而驗(yàn)證了本文相平衡計(jì)算方法的準(zhǔn)確性。

3 相平衡算法的應(yīng)用

3.1 毛細(xì)管力效應(yīng)對(duì)流體性質(zhì)的影響

本研究中將油相作為潤(rùn)濕相,油相的壓力設(shè)為參考?jí)毫?。分別計(jì)算了Bakken致密油藏中,孔隙半徑為10、30、50 nm及無(wú)毛細(xì)管力情況下地層油的體積系數(shù)與油的黏度及溶解氣油比,油藏溫度為115.6 ℃。計(jì)算結(jié)果如圖1所示。

圖1 孔隙半徑為10、30、50 nm時(shí)和無(wú)毛細(xì)管力情況下地層油的性質(zhì)Fig.1 Black-oil properties of the Middle Bakken formation with pore sizes of 10, 30, 50 nm, and infinity (the infinite pore size means there is no capillary pressure), respectively

由曲線的拐點(diǎn)可以看出,當(dāng)孔隙半徑降低為10 nm時(shí),受毛細(xì)管力的影響,泡點(diǎn)壓力降低約1 379 kPa,毛細(xì)管力對(duì)相態(tài)平衡影響顯著?？紫栋霃綖?0 nm時(shí),計(jì)算地層油的性質(zhì)與不考慮毛細(xì)管力條件下的計(jì)算結(jié)果基本相同。因此,對(duì)于本算例的情況,當(dāng)孔隙半徑大于50 nm時(shí),可忽略毛細(xì)管力對(duì)相平衡的影響。

3.2 生產(chǎn)數(shù)據(jù)歷史擬合

歷史擬合作為油藏?cái)?shù)值模擬過(guò)程中的重要環(huán)節(jié),通過(guò)數(shù)值模擬的方法及油藏的動(dòng)態(tài)數(shù)據(jù)對(duì)油藏參數(shù)進(jìn)行修正,并通過(guò)不斷修改地層的靜態(tài)參數(shù),使模擬計(jì)算結(jié)果達(dá)到允許的誤差范圍,以提高數(shù)值模擬的準(zhǔn)確性。

表2 Middle Bakken油藏模型的相關(guān)參數(shù)Table 2 Parameters of Middle Bakken reservoir model

油藏三維模型如圖2所示,長(zhǎng)、寬、高分別為3 200.4、792.5、15.2 m。油藏中心有一口水平井,并伴有30條人工裂縫,裂縫寬度設(shè)為0.003 m,井底流壓為6 894.8 kPa。油藏及裂縫的性質(zhì)[19]如表2所示。網(wǎng)格采用了局部加密方法,以便準(zhǔn)確描述基質(zhì)到裂縫之間的流體流動(dòng)。由于地層中孔隙分布并非單一的孔隙半徑分布,因此,根據(jù)實(shí)驗(yàn)測(cè)得的實(shí)際孔隙分布數(shù)據(jù)[20]最終將孔隙半徑劃分為5個(gè)區(qū)域,即小于10 nm(27%),10～20 nm(26%),20～30 nm(30%),30～50 nm(13%)及大于50 nm(4%)的區(qū)域。不同區(qū)域的流體具有不同的PVT性質(zhì),并將其隨機(jī)分布于油藏模型中,結(jié)果如圖3所示。該油藏模型的滲透率分布如圖4所示。

圖2 油藏的三維模型(x、y和z方向的網(wǎng)格尺寸為12.2 m×12.2 m×15.2 m)Fig.2 A three-dimensional(3D) reservoir model for the base case(The block size is set to 12.2 m×12.2 m×15.2 m in x, y, and z directions, respectively)

圖3 油藏模型中孔隙半徑隨機(jī)分布示意(1～5分別表示5個(gè)不同的PVT區(qū)域)Fig.3 Random distribution of pore sizes in the reservoir model(Color bar of 1—5 respresents five different PVT regions, respectively)

利用Kurtoglu和Kazemi提供的Bakken致密油藏450 d的生產(chǎn)數(shù)據(jù)[18],首先對(duì)油的產(chǎn)量進(jìn)行擬合,結(jié)果如圖5(a)所示。保持油的產(chǎn)量不變,考慮毛細(xì)管力對(duì)相平衡的影響,分別將井底流壓和氣的產(chǎn)量作為擬合對(duì)象進(jìn)行擬合,結(jié)果如圖5(b)和(c)所示。由圖5(b)和(c)可知,在不考慮毛細(xì)管力對(duì)相平衡影響的情況下,當(dāng)基質(zhì)滲透率調(diào)整為0.037 mD(毫達(dá)西),裂縫傳導(dǎo)率為50 mD-ft(毫達(dá)西英尺)時(shí),與生產(chǎn)數(shù)據(jù)能夠較好地?cái)M合;而考慮毛細(xì)管力對(duì)相平衡的影響,擬合后基質(zhì)滲透率調(diào)整為0.032 mD,裂縫傳導(dǎo)率由50 mD-ft(毫達(dá)西英尺)變?yōu)?8 mD-ft(毫達(dá)西英尺)。

圖5 Bakken致密油藏生產(chǎn)歷史擬合的結(jié)果Fig.5 History matching results of the Bakken tight oil reservoir

3.3 單井產(chǎn)能預(yù)測(cè)

通過(guò)3.2節(jié)的生產(chǎn)歷史擬合過(guò)程,對(duì)油藏的數(shù)值模擬模型進(jìn)行了修正,現(xiàn)采用黑油模型研究毛細(xì)管力效應(yīng)影響的相平衡對(duì)致密油藏實(shí)際開(kāi)發(fā)的影響。如圖6所示,計(jì)算結(jié)果表明,毛細(xì)管力效應(yīng)使累積產(chǎn)油量、累積產(chǎn)氣量和最終采收率分別提高7%、8%和6%。這是因?yàn)榭紤]毛細(xì)管力效應(yīng)時(shí),泡點(diǎn)壓力降低,兩相區(qū)的區(qū)域變小,從而使單一油相的生產(chǎn)時(shí)間變長(zhǎng),產(chǎn)量提高。此外,油相黏度降低,也是產(chǎn)量升高的另一個(gè)原因。

圖6 有無(wú)考慮毛細(xì)管力影響相平衡情況下生產(chǎn)井30年的累積產(chǎn)量變化Fig.6 Comparison of well performance in a 30-year period with and without the capillarity effect

4 結(jié) 論

本研究給出了考慮納米孔隙中毛細(xì)管力效應(yīng)的相平衡計(jì)算及產(chǎn)能預(yù)測(cè)的方法。通過(guò)某混合物平衡常數(shù)計(jì)算值與實(shí)驗(yàn)值的對(duì)比,驗(yàn)證了本研究方法計(jì)算相平衡的準(zhǔn)確性。計(jì)算結(jié)果表明,考慮毛細(xì)管力的影響時(shí),原油體積系數(shù)和溶解氣油比升高,而黏度降低。對(duì)Bakken致密油藏某生產(chǎn)井進(jìn)行產(chǎn)能預(yù)測(cè)的計(jì)算表明,毛細(xì)管力效應(yīng)使累積產(chǎn)油量、產(chǎn)氣量及最終采收率分別提高7%、8%和6%。這說(shuō)明在致密油藏的產(chǎn)能預(yù)測(cè)中,應(yīng)當(dāng)考慮毛細(xì)管力對(duì)相平衡的影響,否則會(huì)對(duì)產(chǎn)能預(yù)測(cè)造成誤差。

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Investigationintoeffectsofnanoporouscapillarypressureonwellperformanceoftightoilreservoirs

ZHANG Yuan1, DI Yuan2, ZHANG Yun3, ZHANG Dongli3

(1.School of Energy Resources, China University of Geosciences(Beijing), Beijing 100083, China;2.College of Engineering, Peking University, Beijing 100871, China;3.Exploration and Production Research Institute, SINOPEC, Beijing 100083, China)

In response to failure of the conventional phase equilibrium calculation model to precisely evaluate the vapor-liquid phase behavior of nanopore, the conventional flash calculation model was modified to calculate the vapor-liquid phase equilibrium in case of inequalities between liquid and vapor phases, which subsequently obtained values of properties including viscosity, density and solution gas-oil ratio. Afterwards, the Young-Laplace equation was employed to evaluate the capillary pressure by calculating the phase equilibrium constants of a multicomponent mixture. And the calculated results fairly accorded with the experimental data, which verified accuracy of this calculation. Finally, the black oil model was applied to predict the effects of capillary pressure upon well performance for an actual well from the Bakken tight oil reservoirs. Results show that the predicted well performance is lower than the actual one when the nanoporous capillary pressure is neglected. This study has provided a better understanding of the effects of capillary pressure upon vapor-liquid phase equilibrium and well performance of tight oil reservoirs.

capillary pressure; Peng-Robinson equation of state; vapor-liquid phase equilibrium; tight oil reservoirs

TE348

A

1671-8798(2017)05-0328-06