水力压裂技术是高效开发多层叠置煤层的一种方式。在多层叠置煤层中，各层地应力、岩石力学性质等都存在差异，而这些差异会对水力裂缝纵向扩展产生较大影响。因此针对多层叠置煤层中水力裂缝纵向延伸问题，基于孔弹性理论和损伤力学建立了多层叠置煤层压裂裂缝纵向扩展模型，该模型假设仅当单元应变超过岩石的临界应变时才会造成损伤;通过对岩石的初始渗透率和裂缝渗透率进行加权求和来计算单元渗透率，其权重系数是裂缝宽度和单元尺寸的函数;在初始状态下，除裂缝单元外，其他单元均无损伤。采用有限元数值离散方法和Newton-Raphson(NR)迭代法建立了相应的数值求解迭代格式，并基于MATLAB软件编写了相应数值计算程序。基于建立的模型，研究了原位应力差、砂煤岩界面强度、砂岩层(盖层)弹性模量和泊松比以及压裂液黏度对水力裂缝纵向延伸的影响。结果表明:原地应力差、界面强度越大，压裂缝穿过砂煤岩界面并在砂岩层中扩展延伸的可能性越大;砂岩层弹性模量越大，裂缝穿层后延伸高度越大;压裂液黏度越大，压裂缝越容易穿过层间界面延伸到上下隔层;如果水力裂缝沿砂煤层界面扩展，则界面处的裂缝宽度远小于煤层中的裂缝宽度;沿砂煤层界面扩展时的水力裂缝缝内压力高于穿过砂煤层界面在砂岩层中扩展时的水力裂缝缝内压力。

Hydraulic fracturing technology is a way to efficiently develop multi layer superimposed coalbed reservoirs.Among the multi layer coalbed superimposed reservoirs,compared with other rock layers,the interlayer stress,interface properties,and lithology of coal layer are quite different,which will have a great impact on hydraulic fracture propagation.Therefore,aiming at the problem of hydraulic fracture longitudinal propagation,a multi layer superimposed coal layer hydraulic fracture longitudinal expansion mechanism model was developed based on the theory of pore elasticity and damage mechanics.In this approach,it assumes that the damage will only be caused when the element strain exceeds the critical strain of the rock.The element permeability is the weighted summation of initial rock permeability and fracture permeability,and the weight coefficient is a function of fracture width and element size.In the initial state,all elements except the fracture elements have no damage.The finite element numerical discretization method and Newton Raphson (NR) iterative method were used to establish the corresponding numerical solution iteration format,and the corresponding numerical calculation program was written by MATLAB.The model was used to examine the influences of in situ stresses difference,interface strength,modulus of elasticity and Poisson’s ratio of sandstone layer (cap layer),and fracturing fluid viscosity on the longitudinal propagation of hydraulic fracturing.The results demonstrate that the larger in situ stress difference,interface strength,and modulus of elasticity(sandstone layer),the higher probability of hydraulic fracture penetrates the sand coal layer interface and extends in the sandstone layer.High viscosity of the fracturing fluid will make it possible that the fracture extends through the interlayer interface to the upper and lower barriers.If the fracture propagation along the sand coal layer interface,the fracture width in the interface is much smaller than that in the coal.The pressure in the fracture that propagates along the sand coal layer interface is higher than the pressure of hydraulic fractures that cross the sand coal interface.

1 模型建立与求解

   1.1 损伤演化模型

   1.2 控制方程

   1.3 数值求解

2 模型稳定性与正确性分析

   2.1 模型收敛性与稳定性验证

   2.2 模型正确性验证

3 算例分析

   3.1 原位应力差对裂缝扩展的影响

   3.2 界面强度对裂缝扩展的影响

   3.3 杨氏模量和泊松比对裂缝扩展的影响

   3.4 压裂液黏度对裂缝扩展的影响

4 结论