聚合物驱试井分析叠加原理适用性的探索

doi:10.19596/j.cnki.1001-246x.8262

摘要/Abstract

摘要：

建立考虑聚合物剪切变稀特性的聚驱试井数学模型，基于矩形网格和井筒周围径向加密的复合网格。采用有限体积方法求得数值解，将数值解与叠加原理得到的注聚井停注压降进行对比。结果表明：叠加原理计算得到的注聚井关井井底压力值远低于数值解，说明叠加原理不能用于聚合物驱试井解释。在实测注聚井压降资料解释中，叠加原理得到的渗透率明显偏低，进一步证明了叠加原理不适合非线性聚驱试井模型，数值方法更加适用于聚驱试井解释。研究结论适用于类似的非线性试井问题。

关键词: 聚合物驱, 非牛顿流体, 叠加原理, 数值解, 关井压降

Abstract:

A mathematical model for pressure transient analysis in polymer-flooding system was established, in which the shear thinning effect of non-Newtonian polymer solution is considered. The governing equations were discretized by finite volume method with a hybrid grid consisting of Cartesian meshes with radial refinement around well positions. The shut-in pressures from numerical solution were compared with those obtained with the superposition principle method. It shows that shut-in bottom-hole pressure computed with superposition principle method is much lower than the numerical result for polymer-flooding system, which indicating that the superposition principle cannot be used for pressure transient analysis in polymer-flooding system. Shut-in pressure data of an injection well in a polymer-flooding system was interpreted. It is found that the permeability obtained with superposition principle method is very small, which shows that the superposition principle method cannot be used to solve the nonlinear model for pressure transient analysis in polymer-flooding system. The numerical method is more suitable for polymer-flooding system. The conclusions are applicable to similar nonlinear problems in pressure transient analysis.

Key words: polymer-flooding, non-Newtonian fluid, superposition principle, numerical solution, shut-in pressure drawdown

中图分类号:

TE357

张佳, 程时清, 曾杨, 张满, 于海洋. 聚合物驱试井分析叠加原理适用性的探索[J]. 计算物理, 2021, 38(3): 324-332.

Jia ZHANG, Shiqing CHENG, Yang ZENG, Man ZHANG, Haiyang YU. Applicability Exploration of Superposition Principle for Pressure Transient Analysis in Polymer-flooding System[J]. Chinese Journal of Computational Physics, 2021, 38(3): 324-332.

图/表 10

图1 不同聚合物浓度和剪切速率的聚合物溶液黏度曲线

Fig.1 Polymer solution viscosity at different polymer concentration and shear rate

图2 基于矩形网格和井筒周围径向加密的复合网格

Fig.2 Hybrid grid consisting of Cartesian meshes with radial refinement around well positions

图3 注聚井关井压降试井与叠加原理示意图(a)注聚井的开井与关井过程; (b) 叠加原理及其虚拟生产井

Fig.3 Schematic of shut-in pressure drawdown testing of an injection well and superposition principle (a) injecting and shut-in procedure of a polymer injection well; (b) superposition principle and virtual production well

图4 (a) 注入时间和(b)注入速度对聚合物溶液黏度分布的影响

Fig.4 Polymer solution viscosity distributions at different (a) injection time and (b) flooding rate

表1 油藏基础参数

Table 1 Basic parameters of the reservoir

基础参数	值
初始地层压力/MPa	20
注聚浓度/(g·L^-1)	0.5
井筒半径/m	0.1
井储系数/(m³·MPa^-1)	0.1
表皮系数	0.1
渗透率/μm²	0.1
孔隙度	0.3
岩石压缩系数/MPa^-1	0.001
初始含水饱和度	0.5
初始含油饱和度	0.5
原油黏度/(mPa·s)	0.9
原油压缩系数/MPa^-1	0.001
原油体积系数	0.9
水黏度/(mPa·s)	0.9
水压缩系数/MPa^-1	0.000 2
水体积系数	1

图5 相渗曲线

Fig.5 Relative permeability curves

图6 数值解与叠加原理的注聚井关井压力试井曲线

Fig.6 Shut-in pressure curves of an injection well in numerical solution and superposition principle method

图7 聚驱试井复合模型与均质模型曲线

Fig.7 Shut-in pressure curves of an injection well in composite model and homogeneous model

图8 两种方法拟合实例(a) 数值方法；(b) 叠加原理方法

Fig.8 Matching examples with (a) numerical method and (b) superposition principle method

表2 压力降落试井解释结果

Table 2 Interpretation results of pressure drawdown well testing

	井储系数/(m³·MPa^-1)	表皮系数	复合半径/m	内区渗透率/(10^-3μm²)	外区渗透率/(10^-3μm²)
数值解	0.34	-3.10	15.20	15.25	1.01
叠加原理	0.31	-1.50	15.06	5.12	0.71

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