﻿ 注气驱油藏新型气驱特征曲线推导及应用
 西南石油大学学报(自然科学版)  2018, Vol. 40 Issue (2): 135-141

Derivation and Practice of the New Gas Flooding Characteristic Curve of Reservoir with Gas Injection Flooding
YUAN Zhiwang , YANG Baoquan, YANG Li, GU Wenhuan, SHANG Fanjie
CNOOC Research Institute, Chaoyang, Beijing 100028, China
Abstract: Because the conventional gas flooding characteristic curve fails to effectively describe actual seepage fluid (injected gas) in stratum and displaced crude oil, displacement process of gas injection development is analyzed and oil and gas seepage characteristics of miscible flooding and immiscible flooding are represented, respectively. Based on the steady seepage theory, the relational expression of the actual seepage fluid (injected gas) in stratum and displaced crude oil is derived, which is a semi-logarithmic function of cumulative gas injection volume and cumulative oil output; this is termed the new gas flooding characteristic curve, and its applicable conditions are analyzed. Relevant examples are applied to study the effect of changes to the injection production pattern and displacement mechanism on the characteristics of gas flooding curve. Under the condition of a given volume of gas injection, this curve can be used to accomplish long-term and stage-yield prediction, and can be applied at the initial stages of gas injection development.
Key words: gas flooding characteristic curve     gas injection     miscible flooding     immiscible flooding     displacement mechanism

1 新型气驱特征曲线推导 1.1 假设条件

(1) 地层温度恒定；(2)忽略毛管力作用；(3)注气保压开发油藏；(4)注入气无漏失或漏失量可忽略不计；(5)天然水体能量较弱油藏；(6)在半对数坐标系中$\ln(K_{\rm{ro}}/K_{\rm{rg}})-S_{\rm{g}}$成直线关系；(7)渗流满足达西定律。

1.2 新型气驱曲线推导

 $$$\dfrac{{{K_{\rm{o}}}}}{{{K_{\rm{g}}}}} = \dfrac{{{S_{\rm{o}}}}}{{{S_{\rm{g}}}}}$$$ (1)
 图1 混相驱油气相对渗透率与含气饱和度关系曲线 Fig. 1 Gas and oil relative permeability curves as a function of $S_{\rm{g}}$ for miscible displacement of oil by gas

 $$$\dfrac{{{K_{{\rm{rg}}}}}}{{{K_{{\rm{ro}}}}}} = d{{\rm{e}}^{ - c{S_{\rm{g}}}}}$$$ (2)
 图2 非混相驱油气相对渗透率与含气饱和度关系曲线 Fig. 2 Gas and oil relative permeability curves as a function of $S_{\rm{g}}$ for immiscible displacement of oil by gas

 图3 混相驱油气渗透率比与含气饱和度半对数关系曲线 Fig. 3 Gas/oil relative permeability ratio plotted as a function of $S_{\rm{g}}$, for miscible displacement of oil by gas
 图4 非混相驱油气渗透率比与含气饱和度半对数关系曲线 Fig. 4 Gas/oil relative permeability ratio plotted as a function of $S_{\rm{g}}$ for immiscible displacement of oil by gas

 $$${Q_{\rm{g}}} = {Q_{{\rm{sg}}}} + {Q_{{\rm{injg}}}}$$$ (3)

 $$$\dfrac{{{Q_{{\rm{injg}}}}}}{{{Q_{\rm{o}}}}} = \dfrac{{{\mu _{\rm{o}}}{B_{\rm{o}}}}}{{{\mu _{\rm{g}}}{B_{\rm{g}}}}}\dfrac{{{K_{{\rm{rg}}}}}}{{{K_{{\rm{ro}}}}}}$$$ (4)

 $$${G_{\rm{i}}} = \int_0^t {{Q_{{\rm{injg}}}}} {\rm{d}}t$$$ (5)

 $$${G_{\rm{i}}} = \dfrac{{{\mu _{\rm{o}}}{B_{\rm{o}}}}}{{d{\mu _{\rm{g}}}{B_{\rm{g}}}}}\int_0^t {{Q_{\rm{o}}}{{\rm{e}}^{c{S_{\rm{g}}}}}} {\rm{d}}t$$$ (6)

 $$${N_{\rm{p}}} = \dfrac{{100Ah\phi {S_{\rm{g}}}}}{{{B_{\rm{o}}}}} \text{，其中：}{S_{\rm{g}}} = \dfrac{{{N_{\rm{p}}}{B_{\rm{o}}}}}{{100Ah\phi }}$$$ (7)

 $$${Q_{\rm{o}}} = \dfrac{{{\rm{d}}{N_{\rm{p}}}}}{{{\rm{d}}t}} = 100Ah\phi \dfrac{1}{{{B_{\rm{o}}}}}\dfrac{{{\rm{d}}{S_{\rm{g}}}}}{{{\rm{d}}t}}$$$ (8)

 $$${G_{\rm{i}}} = \dfrac{N}{{1 - {S_{{\rm{wc}}}}}}\dfrac{{{\mu _{\rm{o}}}{B_{\rm{o}}}}}{{dc{\mu _{\rm{g}}}{B_{\rm{g}}}}}({{\rm{e}}^{c{S_{\rm{g}}}}} - c)$$$ (9)

 $$$\ln ({G_{\rm{i}}} + cD) = a + b{N_{\rm{p}}}$$$ (10)

 $D = \dfrac{{N{\mu _{\rm{o}}}{B_{\rm{o}}}}}{{dc{\mu _{\rm{g}}}{B_{\rm{g}}}(1 - {S_{{\rm{wc}}}})}}, a = \ln D, b = \dfrac{{c{B_{\rm{o}}}}}{{100Ah\phi }}$

 $$$\ln {G_{\rm{i}}} = a + b{N_{\rm{p}}}$$$ (11)
1.3 新型气驱曲线适用条件分析

2 实例分析 2.1 实例1

M油藏为西非深水A油田的主力油藏之一，水深1 300~1 450 m，储层发育为深水海底扇朵叶复合沉积，为层状构造边水油藏。流体为纵向具有明显组分梯度的高挥发性油。原油地面密度平均为0.797 g/cm$^3$，原始气油比550$\sim$1 100 m$^3$/m$^3$，地层黏度平均为0.085 mPa$\cdot$s，油藏平均渗透率为831 mD，平均孔隙度为23%。该油藏于2009年全面投产，采用3口采油井，2口注气井开发，均为水平井，开发方式为顶部注伴生天然气边部采油。高峰年采油速度达9.7%，2012年5月，1口油井注气突破；2013年12月第二口油井注气突破。为了提高M油藏整体开发效果，2014年12月，油藏增加一口加密油井。油藏整体保持稳产，稳产期约5 a，日产油、生产气油比动态曲线见图 5，预测采收率超60%，达到了预期开发效果。

 图5 M油藏日产油、气油比动态曲线（2009-2017） Fig. 5 Daily oil production and gas oil ratio curve of M reservoir(2009-2017)
2.1.1 生产动态数据拟合及分析

 图6 M油藏累注气量-累产油半对数关系曲线 Fig. 6 Semi-logarithmic relationship curve between cumulative oil production and cumulative gas injection in M reservoir

2.1.2 开发指标预测结果评价

 图7 M油藏实际累产油量与预测累产油量对比曲线 Fig. 7 Cumulative oil production comparison curve between actual and forecasting in M reservoir
2.2 实例2

Pickton油田[18-20]位于美国东德克萨斯盆地，储层顶深为2 220 m，净油柱高度为69 m，海相碳酸盐构造岩性油藏，流体为挥发油，纵向流体性质有差异，原油地面密度为0.797 g/cm$^3$，原始气油比为276 m$^3$/m$^3$，地层黏度为0.21 mPa$\cdot$s，油藏平均渗透率为379 mD，平均基质孔隙度为20%，原始地质储量为542$\times$10$^4$ m$^3$。该油田于1944年投产，最大油井数为80口，高峰日产油量为850 m$^3$，油田初期为衰竭开发，从1949开始在油田西部注伴生天然气，1952年开始在油田东部注伴生天然气，1964年停止注气(如图 8)，从1965年至1968年注水开发，最后进入回收天然气阶段至废弃，油田采收率为51.4%。

 图8 Pickton油田日产油与气油比曲线（1944—1964） Fig. 8 Dailyoil production and gas oil ratio curve of Pickton Oilfield（1944-1964）
2.2.1 生产动态数据拟合及分析

 图9 Pickton油田累注气量-累产油半对数关系曲线 Fig. 9 Semi-logarithmic relationship curve between cumulative oil production and cumulative gas injection in Pickton Oilfield
2.2.2 开发指标预测结果评价

 图10 Pickton油田实际累产油量与预测累产油量对比曲线 Fig. 10 Cumulative oil production comparison curve between actual and forecasting in Pickton Oilfield
3 结论

(1) 注气混相驱油藏，含气饱和度在0.2$\sim$0.8；注气非混相驱油藏，含气饱和度在某一特定区间内(依据目标油藏相渗特征)，油气相对渗透率比值与含气饱和度呈半对数线性关系。

(2) 注气驱油藏地层中实际参与渗流的流体为注入气和被驱替地层油，而不是传统认为的产出气和被驱替地层油。

(3) 基于稳定渗流理论，建立了新型气驱特征曲线关系式，即累积注气量和累积产油半对数关系式。实例分析表明，井网加密、驱替机理变化等因素都会影响气驱特征曲线形态，调整效果的不同，曲线的斜率也会呈现不同的变化特征，可用于评价调整效果。

(4) 新型气驱特征曲线在已知注气量条件下，可用于长期以及阶段产量预测且在注气开发较早阶段便可应用。实例计算表明，该特征曲线使用简便可靠，对注气驱油藏的动态分析及开发指标预测具有一定的指导意义。

$K_{\rm{o}}, K_{\rm{g}}$—混相驱油、气渗透率mD；

$K_{\rm{ro}}, K_{\rm{rg}}$—油、气的相对渗透率，无因次；

$S_{\rm{o}}$—地层含油饱和度，无因次；

$S_{\rm{g}}$—地层含气饱和度，无因次；

$S_{\rm{wc}}$—束缚水饱和度，无因次；

$a$—方程回归截距，$\times$10$^4$ m$^3$

$b$—方程回归斜率，m$^{-3}$

$c, d$—与储层和流体物性相关的系数，无因次；

$D$—常数，$\times$10$^4$ m$^3$

$Q_{\rm injg}$—地面条件下，油藏原油日注入气量，m$^{3}$

$Q_{\rm{sg}}$—地面条件下，油藏原油溶解气量，m$^{3}$/d；

$Q_{\rm{g}}$—地面条件下，油藏原油总气量，m$^{3}$

$Q_{\rm{o}}$—地面条件下，油藏日油产量，m$^{3}$

$G_{\rm{i}}$—地面条件下，油藏累积注气量，$\times$10$^{4}$ m$^{3}$

$\mu_{\rm{o}}, \mu _{\rm{g}}$—地层原油、地层注入气的黏度，mPa$\cdot$s；

$B_{\rm{o}}, B_{\rm{g}}$—地层原油、地层气的体积系数，无因次；

$\gamma_{\rm{o}}, \gamma_{\rm{g}}$—地层原油、地层气的黏度，mPa$\cdot$s；

$t$—时间，d；

$A$—油藏气驱波及面积，km$^{2}$

$h$—油层有效厚度，m；

$\phi$—油层孔隙度，%；

$N$—地质储量，$\times$10$^{4}$ m$^{3}$

$N_{\rm{p}}$—累积产油量，$\times$10$^{4}$ m$^{3}$

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