考虑动力学扩散作用的煤系气储层渗透率模型

张宏学; 刘卫群; 李盼

doi:10.11858/gywlxb.20210709

考虑动力学扩散作用的煤系气储层渗透率模型

doi: 10.11858/gywlxb.20210709

张宏学^1,,
刘卫群^{2, 3},
李盼¹

1.
安徽理工大学力学与光电物理学院，安徽淮南　232001
2.
中国矿业大学（徐州）力学与土木工程学院，江苏徐州　221116
3.
中国矿业大学（徐州）深部岩土力学与地下工程国家重点实验室，江苏徐州　221116

基金项目: 安徽省教育厅科研基金（KJ2020A0329，KJ2016A207）

详细信息

作者简介:
张宏学（1982－），男，博士，副教授，主要从事裂隙岩体渗流研究. E-mail：hxzhang@aust.edu.cn

中图分类号: O354.9; TE371
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出版历程
- 收稿日期: 2021-01-15
- 修回日期: 2021-03-24

Permeability Model of Coal Measure Gas Reservoirs Considering Dynamic Diffusion

1.
School of Mechanics and Optoelectronics Physics, Anhui University of Science & Technology, Huainan 232001, Anhui, China
2.
School of Mechanics and Civil Engineering, China University of Mining and Technology (Xuzhou), Xuzhou, 221116, Jiangsu, China
3.
State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology (Xuzhou), Xuzhou, 221116, Jiangsu, China

摘要

摘要: 为了预测煤系气开采过程中储层渗透率的演化规律，考虑气体在基质中的动力学扩散作用，基于储层的应力-应变本构关系和渗透率-孔隙率的立方关系，提出了储层的有效应力-渗透率模型，分别建立了储层在常体积和单轴应变条件下的渗透率解析模型。利用现场和实验室测试的渗透率数据，探讨了两种模型的有效性。结果表明，与常体积条件下的渗透率模型和C-M模型相比，单轴应变条件下的渗透率模型能够较好地拟合现场和实验室的渗透率数据，建立渗透率模型须考虑气体在基质中的动力学扩散作用。研究了模型参数对渗透率的影响，结果表明模型参数对渗透率的演化规律以及反弹压力有显著的影响。
- 煤系气储层 /
- 渗透率 /
- 动力学扩散 /
- 基质收缩 /
- 裂隙压缩
Abstract: In order to predict evolution of permeability for reservoir in the process of coal measure gas exploitation, based on the stress-strain constitutive of reservoir and the cubical relation of permeability and porosity, the model of the effective stress-permeability of reservoir was presented, which considers the kinetic diffusion of gases in the matrix. The analytical models of reservoir under constant volume and uniaxial strain conditions were established respectively. Furthermore, the effectiveness of the two models are investigated using permeability data from field and laboratory tests respectively. The results show that, compared with the model under constant volume condition and C-M model, the permeability model under uniaxial strain condition can better fit the permeability data from the field and laboratory. It is very important to take the dynamic diffusion of gas in the matrix into consideration during establishing the permeability model. Besides, the effect of model parameters on permeability was studied. It is shown that the model parameters have a significant influence on the permeability evolution and rebound pressure.
- coal measure gas reservoirs /
- permeability /
- dynamic diffusion /
- matrix shrinkage /
- cleat compressibility

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图 1 双孔单渗模型

Figure 1. Dual-porosity and single-permeability model

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图 2 反弹压力的演化规律

Figure 2. Evolution of rebound pressure

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图 3 渗透率模型的有效性

Figure 3. Effectiveness of permeability model

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图 4 渗透率随基质压力（裂隙压力不变）的演化规律

Figure 4. Evolution of permeability with matrix pressure (fracture pressure is constant)

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图 5 渗透率随裂隙压力（基质压力不变）的演化规律

Figure 5. Evolution of permeability with fracture pressure (matrix pressure is constant)

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图 6 模型参数对渗透率的影响

Figure 6. Effects of model parameters on permeability

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表 1 渗透率数据^[15–16]

Table 1. Permeability data^[15–16]

Field experiment		Laboratory experiment
Reservoir pressure/MPa	$k/{k_{0}}$	Reservoir pressure/MPa	$k/{k_{0}}$
0.10	7.30	0.38	12.99
0.35	6.62	0.68	10.51
0.79	5.65	1.39	3.93
1.10	4.95	2.04	2.49
1.38	4.25	3.06	1.68
2.07	3.20	4.11	1.36
2.76	2.45	5.14	1.20
3.45	1.75	6.26	1.04
4.14	1.35
4.83	1.05
5.52	1.02

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表 2 模型参数^{[8, 16]}

Table 2. Model parameter^{[8, 16]}

Fitting data	$\;\mu $	p_f0/MPa	p_L/MPa	$\varepsilon _{\rm{L}} $	E_m/MPa	a₀/mm	k₀/md
Field	0.36	7.20	7.20	0.013 00	5 000	5	2
Laboratory	0.30	6.20	4.16	0.010 75	3 000	5	2

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