A Stochastic Permeability Model for Shale Gas Reservoirs Based on Embedded Discrete Fracture Model
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摘要: 页岩储层具有不同类型的储集空间，但综合考虑不同储集空间，对页岩储层渗透率进行评价的模型未见报道.基于嵌入离散裂缝模型，建立的页岩气藏视渗透率模型包括4个步骤：（1）构建天然裂缝、有机质和无机质的空间分布模型；（2）筛选不同类型储集空间的渗透率计算方法；（3）基于嵌入离散裂缝模型，结合空间分布模型和渗透率计算方法，建立数值模拟模型；（4）在模型的入口和出口端施加压差，求得一定压差下通过该岩心的气体流量，采用达西定律得到该页岩气藏的视渗透率.其计算结果与文献报道的渗透率实验值吻合较好.通过对不同因素的探讨，结果表明，天然裂缝对页岩气藏视渗透率的贡献大于无机质和有机质孔隙.因此，计算页岩视渗透率时有必要对天然裂缝、有机质和无机质孔隙进行综合考虑.Abstract: Shale reservoirs have different types of pore spaces, however, relevant studies on measuring the apparent permeability (AP) of shale gas reservoirs with considering different pore space have not been reported. A stochastic permeability model is proposed based on the embedded discrete fracture model (EDFM) in this study, which includes four steps. (1) The spatial distribution model of natural fracture, organic matter and inorganic matter is established. (2) Different permeability calculation methods are selected for different types of pore space. (3) The numerical simulation model is established on the basis of EDFM, using the spatial distribution model and different permeability calculation methods. (4) The gas flow rate is obtained by numerical simulation method after giving different pressures at the inlet and outlet of the model. Then the AP of this shale gas reservoir can be measured through the Darcy's law. The results of the model are in good agreement with the experimental results reported in literature. The effect of different pore space types, distribution and some other characteristics were analyzed. Results show that the contribution of natural fractures to AP is greater than that of matrix pores. Therefore it is crucial to take the effect of different pore space types into account in the process of calculating shale gas AP.
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图 1 有机质方块尺寸概率密度分布函数
Fig. 1. Probability density function for patch-size distribution of organic matter
图 3 四种随机生成的天然裂缝、有机质和无机质的空间分布模型
红色实线代表天然裂缝
Fig. 3. Four stochastic spatial distribution models for natural fracture, organic matter and inorganic matter
图 4 孔隙尺寸的概率密度分布函数
a.氮气吸附实验测得的双峰孔隙尺寸分布特征曲线(美国鹰滩页岩样品)；b.有机质孔隙；c.无机质孔隙
Fig. 4. Probability density function for pore size distribution
图 6 渗透率分布场
a.完整模型(200 μm×200 μm)；b.局部放大模型(40 μm×30 μm)
Fig. 6. Permeability distribution model
图 9 两个页岩样品的孔隙尺寸分布特征曲线
Fig. 9. Bimodal pore size distribution curve of two shale samples
图 10 不同类型储集空间对渗透率的影响.
a.考虑天然裂缝，有机质和无机质孔隙对渗透率的影响；b.考虑有机质和无机质孔隙对渗透率的影响；c.只考虑有机质孔隙对渗透率的影响
Fig. 10. The effect on permeability of different types of pore space
图 11 单条天然裂缝对视渗透率的影响
a.存在一条天然裂缝；b.不存在天然裂缝；c.裂缝倾角(θ)示意；d.天然裂缝倾角对视渗透率的影响；模型尺寸为200 μm×200 μm
Fig. 11. The effect of single natural fracture to shale gas AP
图 12 天然裂缝条数对视渗透率的影响
模型尺寸为200 μm×200 μm；红色直线代表天然裂缝
Fig. 12. The effect of natural fracture number to shale gas AP
图 13 天然裂缝开度对视渗透率的影响
a.分析天然裂缝开度影响的基础模型(红色直线代表天然裂缝)；b.天然裂缝开度对视渗透率的影响规律；模型尺寸为200 μm×200 μm
Fig. 13. The effect of natural fracture aperture to shale gas AP
图 14 页岩气藏视渗透率的参数敏感性分析
a.迂曲度对视渗透率的影响；b.系统压力对视渗透率的影响；c.有机质孔隙孔径分布特征(均值和标准差)对视渗透率的影响；d.无机质孔隙孔径分布特征(均值和标准差)对视渗透率的影响
Fig. 14. Sensitivity analysis for shale gas AP
表 1 天然裂缝参数
Table 1. Natural fracture parameters
参数 数值 平均走向 北偏东60° Fisher常数K 120 最小天然裂缝长度lmin 10 μm 最大天然裂缝长度lmax 160 μm 天然裂缝条数nf 10 幂律分布指数α 0.8 孔隙度φf 0.02 迂曲度τf 1 开度h 1 μm 
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表 3 页岩样品属性
Table 3. The properties of shale samples
岩石样品属性 皮埃尔页岩 曼科斯页岩 孔隙尺寸分布 图 9 图 9 孔隙度 0.06 0.06 体积TOC 18.00% 1.36% 系统压力 13.8 MPa 13.8 MPa 实验测量的渗透率 0.017 0 μD 0.016 0 μD 模型计算的渗透率 0.016 9 μD 0.016 3 μD τm估计值 56 68 Df估计值 2.6 2.8 注：据Kuila and Prasad(2013).
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表 2 示例模型中所用的属性
Table 2. Properties used in the sample model
属性 数值 孔隙尺寸分布 图 4 孔隙度φm 0.1 体积TOC 12.00% 平均压力 10 MPa τm 10 Df 2.2
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表 4 天然裂缝的属性
Table 4. The properties of natural fractures
参数 数值 平均走向 北偏东60° Fisher常数K 120 最小天然裂缝长度lmin 20 μm 最大天然裂缝长度lmax 60 μm 天然裂缝条数nf 2 幂律分布指数α 0.8 孔隙度φf 0.002 迂曲度τf 1 开度h 1 μm
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