煤基质收缩对裂隙渗透率影响的新数学模型

NEW MATHEMATICAL MODEL FOR EFFECT OF COAL MATRIX SHRINKAGE ON FRACTURE PERMEABILITY

煤基质收缩使储层裂隙孔隙度和渗透率发生很大变化,目前的研究方法普遍存在测量费用昂贵和计算误差大的问题。文章基于固体变形理论与固体表面能理论,建立了一个新的煤基质收缩变形对煤裂隙渗透率和孔隙度影响的数学模型,消除了直接用煤体收缩系数来计算煤裂隙孔隙度和渗透率所引起的误差。研究结果表明,煤基质收缩引起裂隙渗透率变化经历了一个先降低后升高的趋势;裂隙的渗透率增大与储层压力的降低呈对数变化关系;煤层气中Langmuir体积大的气体所占的相对密度越大,解吸后煤储层裂隙的孔隙度和渗透率的变化越大。最后,通过实例计算分析对比,模型能准确合理地反映煤基质收缩变形对煤裂隙渗透率和孔隙度变化的影响。

Coal matrix shrinkage makes the porosity arid permeability of reservoir fractures changing a lot. There are disadvantages of high measuring cost and big calculating error commonly for the current using methods. Based on the solid deformation theory and the solid surface theory, a new mathematical model is developed for the effect of shrinkage and deformation of coal matrix on permeability and porosity of coal fractures to eliminate the error caused by calculating permeability and porosity of coal fractures directly with the coal shrinkage factor. The study results show the change of the fracture permeability caused by the matrix shrinkage experiences the process of descending first and then ascending. It presents logarithm relationship that the fracture permeability increases as the reservoir pressure decreases. The larger the relative density of the gas with big Langmuir volume in the coal-bed gas is, the greater the change of porosity and permeability of the reservoir fractures after desorption is. With real cases calculating, analyzing and comparing, it is found that the model can reflect the effect of shrinkage and deformation of coal matrix on permeability and porosity of coal fractures properly and accurately.