摘要
针对水平井地层渗透率各向异性的特性 ,文章假设地层为水平均质 ,水平方向渗透率相同 ,但不同于垂向渗透率 ,酸液为不可压缩流体 ,建立了酸液在稳态流动下的渗流微分方程。根据所建立的渗流微分方程 ,通过中间变量的变换、分离变量等数学手段 ,导出了水平井在渗透率各向异性情况下的压力场与流速场的计算公式。该计算公式具有物理意义明确 ,实用性强等优点。实例计算表明酸液等压线为一族同心椭圆 ,而流速场呈平面椭圆辐射状 ,越靠近水平井筒 ,等压线越密集 ,酸液流速越大 ,压力降落主要集中在井筒附近的地层中。渗透率各向同性地层酸液的压力场与流速场只是它的一个特殊情况。文中所建模型为水平井酸化模拟及酸化设计提供了依据。
In light of the anisotropic property of formation permeabilities of horizontal well, a percolation differential equation of acidizing fluid at steady state flow was set up through assuming that the formation- is level and homogeneous, i. e. the horizontal permeabilities are identical but different from the vertical permeabilities: and the acidizing fluid is incompressible. On the basis of the percolation differential equation, the formulas of calculating acidizing pressure and flowing velocity fields under the anisotropic condition of formation permeabilities of horizontal well were derived by use of these mathematic methods as the transform of intermediate variable and the separation variable, etc. These formulas are of the advantages as clear physical significance and strong practicability. Through the calculation of an example, it was indicated that the isobaric lines of acidizing fluid are a group of concentric ellipses but the flowing velocity field shows up radial plane ellipses; the closer to horizontal borehole the position, the denser the isobaric line, the greater the flowing velocity; and the pressure drop is mainly concentrated in the formation nearby the borehole. The pressure and flowing velocity fields under the isotropic condition of formation permeabilities are their special cases. The model set up in the paper has provided a basis for the acidizing simulation and design of horizontal well.
出处
《天然气工业》
EI
CAS
CSCD
北大核心
2004年第8期56-58,共3页
Natural Gas Industry
基金
国家 8 6 3项目"石油勘探开发分布式集成应用系统"(编号 :86 3- 30 6 -ZT0 4 - 0 3- 3)成果之一
关键词
水平井
酸化工艺
压力场
流速场
计算方法
井筒
数学模型
Differential equations
Flow patterns
Gases
Mathematical models
Oil wells
Percolation (computer storage)
Pressure effects
