◎边水推进的精确公式-Derived By Qi-Chengwei

虚度

Accurate Formula for the Advance of the Edge Water - Derived By Qi-Chengwei
Rate Topic:本文遵循Lagrange方法，成功地解析了无限大平面地层中每一流体质点流向有限长裂缝的运动规律。
By using Lagrangian method, the author successfully derived the formula which depicts the kinematic law of fluid particle flowing into a straight crack with finite length in infinite plane stratum.
地层中任一流体质点流入裂缝需要经历的时间——
The time of motion can be expressed in the presentation of curvilinear orthogonal coordinates generated byΦ andΨ .
Any particle flowing into the crack needs time——[πL2/(8q)][sinh(4πΦ/q)-(4πΦ/q)cos(4πΨ/q)]

其中，(Φ,Ψ )为流体质点的曲纹坐标，与直角坐标(x, y)一一对应；q为单位厚度内裂缝的产能，m2/s；L为裂缝长度，m。
运用该公式可以绘出从同一条等势线上同时出发的各流体质点在以后不同时刻的流动动态
The kinestate at the same time in the future of any partical flowing from the same equipotential line can be drawn as the following graphic by using this formula.

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图注：q=128m2/s，L=56m。★不论q取值如何变化，上图中各点位置不动，即推进线形状不变。
当“产层厚度/生产段长度<<1”时，水平井激发的渗流场可近似为裂缝激发的渗流场。
这个图从数学上显示了在忽略油水流度差异的情况下生产段两端先见水的现象。
该公式采用渗流网的曲纹坐标为自变量，形式简洁对称，定量反映了流动动态。
详细推导过程见《裂缝激发的渗流场之运动学分析》内蒙古石油化工2010年第6期。
欢迎感兴趣者交流，我的邮箱：qcw_128@163.com ；QQ：383785237 。

Kinematic Analysis of Seepage Field Excited by a Straight Crack with Finite Length
Chengwei Qi
(China University of Petroleum – Beijing , Changping District of Beijing 102249)
Abstract：By using Lagrangian method, the author successfully derived the formula which depicts the kinematic law of fluid particle flowing into a straight crack with finite length in infinite plane stratum.
Key words：ring cracks group; general complex potential formula; velocity field; kinematics; kinestate; water breakthrough time; curvilinear orthogonal coordinates

Detailed derivation see, "Kinematic Analysis of Seepage Field Excited by a Straight Crack with Finite Length" Inner Mongolia Petrochemical No. 6 in 2010.
Interested to share, my email: qcw_128@163.com; QQ: 383785237.

南明之水

无限大地层的假设是不是能不能改进一下