﻿ 考虑动态克林伯格系数的煤储层渗透率预测模型
 地球物理学报  2018, Vol. 61 Issue (1): 304-310 PDF

Prediction model of permeability in coal reservoirs considering the dynamic Klinkenberg coefficient
LI LiGong, KANG TianHe, LI YanBin
Mining Technology Institute, Taiyuan University of Technology, Taiyuan 030024, China
Abstract: With pressure decreasing, the Klinkenberg effect plays an more and more important role in permeability of coal reservoirs. While existing prediction models of this issue neglect the change of the Klinkenberg coefficient, which may be responsible for the difference between the prediction results and actual data, especially at low pressure. This paper presents a further demonstration to this issue. Assuming a constant volume and using the Matchstick Model, this work has established a novel prediction model of the permeability and the calculation formula for the process of pressure reduction. We also analyzed the changing rules of the permeability and Kinkenberg coefficient when the pressure in reservoir decreased.The results show that with decreaing reservoir pressure, the Klingberg coefficient shows a trend of increase first and then of decrease.Under a constant reservoir pressure, this coefficient exponentially decreases with increasing permeability but linearly increases with rising temperature.The novel model presented in this paper is simple and its parameters are easy to obtain. The prediction results match well with the actual data from production, especially at the stage of low reservoir pressure. Therefore this model permits to predict the change of permeability in coal reservoirs with a fairly good accuracy.
Key words: Klinkenberg coefficient    Permeability    Constant volume    Matchstick model
0 引言

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 图 1 克林伯格系数实验测量方法 Fig. 1 Experimental measurement method of Klinkenberg coefficient

1 渗透率模型的建立 1.1 模型基本假设

(1) 体积不变假设(Massarotto et al., 2009).所谓体积不变假设是指在煤层气开采过程中，储层压力降低，煤储层的整体体积保持不变，即水平应变为零，垂直应力、应变也为零.

(2) 煤基质体孔隙对渗透率不产生影响，即煤储层渗透率主要取决于微裂隙的影响.

(3) 不考虑基质体与裂隙之间压力传递损耗，即煤基质体中压力与裂隙压力相等

(4) Matchstick群假定(Reiss, 1980).煤层被理想化为一个火柴棍的集合体，火柴棍模型中的有效空间代表煤的孔隙，每一个火柴棍体代表煤基质，如图 2.

 图 2 Matchstick模型 Fig. 2 Matchstickmodel

(5) 假设火柴棍块体为弹性体.

1.2 模型理论推导 1.2.1 孔隙率随储层压力变化关系

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 图 3 火柴棍模型中微裂隙变化示意图 Fig. 3 Sketch of micro-crack change in Matchstick model

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1.2.2 克林伯格系数b的动态变化模型

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1.2.3 考虑动态克林伯格系数的渗透率模型

1941年克林伯格通过实验证明多孔介质中气体流动存在克林伯格效应，并给出了考虑克林伯格效应渗透率表达式(式(1)).在考虑动态克林伯格系数b时，式(1)可写为

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2 模型验证

 图 4 渗透率随储层压力变化曲线 Fig. 4 Variation of permeability with reservoir pressure

 图 5 不同固定克林伯格系数下渗透率随储层压力变化曲线 Fig. 5 Variation of permeability with increasing reservoir pressure under different Klinkenberg coefficients

3 动态克林伯格系数影响因素分析

 图 6 不同初始渗透率下克林伯格系数随储层压力变化关系 Fig. 6 Relationship between Klinkenberg coefficient and reservoir pressure under different initial permeability values

 图 7 储层压力为5 MPa时克林伯格系数与渗透率关系曲线 Fig. 7 Curve of Klinkenberg coefficient versus permeability at 5 MPa reservoir pressure

 图 8 储层压力为5 MPa时克林伯格系数随温度变化关系曲线 Fig. 8 Relationship between Klinkenberg coefficient and temperature with reservoir pressure 5 MPa
 图 9 不同温度下克林伯格系数随储层压力变化关系曲线 Fig. 9 Curves of Klinkenberg coefficient versus reservoir pressure at different temperatures
4 结论

(1) 考虑在储层压力降低过程中克林伯格系数b的动态变化，给出了动态克林伯格系数b的计算公式，并建立考虑动态克林伯格效应的渗透率预测模型.该模型只用基本物理学参数，实现对煤储层渗透率预测，该模型实用性和操作性强，具有更高的理论和实用价值.

(2) 以圣胡安盆地基础工程数据为背景，分别采用新模型和P & M模型对其渗透率进行预测，并与实际工程数据进行比较.结果表明：高储层压力阶段(大于2 MPa)两者预测结果差异不大，均与实测数据符合良好；在低储层压力阶段(小于2 MPa)，新模型考虑了动态考虑伯格效应的影响，其预测结果与实测结果符合度高于P & M模型，进而验证了新模型的正确性及优越性.

(3) 以圣胡安盆地煤储层数据为基础，分析了克林伯格系数的影响因素.结果表明随储层压力的降低，克林伯格系数呈先增大后减小变化趋势；在储层压力相同时，克林伯格系数随渗透率的减小呈指数形式变化，随温度的升高呈线性变化趋势.

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