張 園,邸 元,張 允,張冬麗

(1.中國地質(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.中國石油化工股份有限公司 石油勘探開發(fā)研究院,北京 100083)

10.3969/j.issn.1671-8798.2017.05.002

2017-03-25

國家自然科學(xué)基金項目(51674010)；國家科技重大專項 (2016ZX05014)；中國地質(zhì)大學(xué)(北京)基本科研啟動基金項目(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.中國石油化工股份有限公司 石油勘探開發(fā)研究院,北京 100083)

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

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

非常規(guī)油氣藏的特點是低孔、低滲,孔隙尺寸大多在2.5～103nm,儲集層中納米級孔隙發(fā)育[1-2]。大量研究表明,納米級孔隙中的高毛細管力不僅影響油氣在孔隙中的流動過程,也影響油氣的相態(tài)平衡,進而影響油氣的最終采收率。

Sigmund等[3]以實驗儀器來研究C1-C4和C1-nC5混合物的泡點及露點壓力,發(fā)現(xiàn)界面效應(yīng)會影響平衡壓力及各相的組分含量。理論分析也顯示出泡點壓力會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越遠,泡點壓力下降得越顯著。由于傳統(tǒng)的PVT(pressure-volume-temperature)分析無法對毛細管力效應(yīng)的相態(tài)問題給出準確的預(yù)測,因此,需要改進傳統(tǒng)的計算方法來計算流體性質(zhì),從而對非常規(guī)油氣藏進行產(chǎn)能預(yù)測[9]。Wang等[10]通過加入孔隙壓實效應(yīng)項,研究了該效應(yīng)對油藏產(chǎn)量的影響。Teklu等[11]引入了流體組分臨界性質(zhì)的轉(zhuǎn)換因子來計算流體的相平衡,結(jié)果表明,毛細管力效應(yīng)對相包絡(luò)線的影響顯著。Rezaveisi等[12]將毛細管力項的相平衡計算模型與組分模擬器相結(jié)合,用來預(yù)測非常規(guī)油藏的產(chǎn)能變化。在前人研究的基礎(chǔ)上,筆者提出了一個能夠考慮毛細管力效應(yīng)的計算儲層流體相平衡的數(shù)值方法,將此法對某多組分混合物的相平衡進行計算,并把計算結(jié)果與實驗結(jié)果進行對比;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管力對油藏產(chǎn)量預(yù)測的影響。

1 理論模型

1.1 相平衡計算模型

當液相和氣相中各組分的逸度相等時,體系達到相平衡[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)相平衡計算中的平衡常數(shù);Pc為毛細管力。采用Young-Laplace方程[13]來計算:

(6)

式(6)中:r為毛細管半徑,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)的計算

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

溶解氣油比的計算公式如下:

(7)

式(7)中:nV和nL分別為氣體和液體的摩爾分數(shù);VmV和VmL分別為氣體和液體的摩爾體積;SC表示標準狀態(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)的計算可參見文獻[17]。

2 相平衡計算方法的驗證

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

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

3 相平衡算法的應(yīng)用

3.1 毛細管力效應(yīng)對流體性質(zhì)的影響

本研究中將油相作為潤濕相,油相的壓力設(shè)為參考壓力。分別計算了Bakken致密油藏中,孔隙半徑為10、30、50 nm及無毛細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 ℃。計算結(jié)果如圖1所示。

圖1 孔隙半徑為10、30、50 nm時和無毛細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

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

3.2 生產(chǎn)數(shù)據(jù)歷史擬合

歷史擬合作為油藏數(shù)值模擬過程中的重要環(huán)節(jié),通過數(shù)值模擬的方法及油藏的動態(tài)數(shù)據(jù)對油藏參數(shù)進行修正,并通過不斷修改地層的靜態(tài)參數(shù),使模擬計算結(jié)果達到允許的誤差范圍,以提高數(shù)值模擬的準確性。

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、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,以便準確描述基質(zhì)到裂縫之間的流體流動。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)實驗測得的實際孔隙分布數(shù)據(jù)[20]最終將孔隙半徑劃分為5個區(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分布示意(1～5分別表示5個不同的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],首先對油的產(chǎn)量進行擬合,結(jié)果如圖5(a)所示。保持油的產(chǎn)量不變,考慮毛細管力對相平衡的影響,分別將井底流壓和氣的產(chǎn)量作為擬合對象進行擬合,結(jié)果如圖5(b)和(c)所示。由圖5(b)和(c)可知,在不考慮毛細管力對相平衡影響的情況下,當基質(zhì)滲透率調(diào)整為0.037 mD(毫達西),裂縫傳導(dǎo)率為50 mD-ft(毫達西英尺)時,與生產(chǎn)數(shù)據(jù)能夠較好地擬合;而考慮毛細管力對相平衡的影響,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(毫達西英尺)變?yōu)?8 mD-ft(毫達西英尺)。

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

通過3.2節(jié)的生產(chǎn)歷史擬合過程,對油藏的數(shù)值模擬模型進行了修正,現(xiàn)采用黑油模型研究毛細管力效應(yīng)影響的相平衡對致密油藏實際開發(fā)的影響。如圖6所示,計算結(jié)果表明,毛細管力效應(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%。這是因為考慮毛細管力效應(yīng)時,泡點壓力降低,兩相區(qū)的區(qū)域變小,從而使單一油相的生產(chǎn)時間變長,產(chǎn)量提高。此外,油相黏度降低,也是產(chǎn)量升高的另一個原因。

圖6 有無考慮毛細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管力效應(yīng)的相平衡計算及產(chǎn)能預(yù)測的方法。通過某混合物平衡常數(shù)計算值與實驗值的對比,驗證了本研究方法計算相平衡的準確性。計算結(jié)果表明,考慮毛細管力的影響時,原油體積系數(shù)和溶解氣油比升高,而黏度降低。對Bakken致密油藏某生產(chǎn)井進行產(chǎn)能預(yù)測的計算表明,毛細管力效應(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%。這說明在致密油藏的產(chǎn)能預(yù)測中,應(yīng)當考慮毛細管力對相平衡的影響,否則會對產(chǎn)能預(yù)測造成誤差。

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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