开发煤层气的多分支水平井形态多样且在对开发过程中割理的作用认识不清，有必要探究煤层中离散割理分布特征和多分支水平井形态对气井产能的影响。根据煤层中面割理和端割理的发育情况和正交特性，采用随机方法在煤层中分别构建了低密度、中密度和高密度的离散割理系统，并与等长型、纺锤型、交错型和哑铃型4种不同形态的多分支水平井结合，构建出多分支水平井开发煤层气的物理模型。在考虑开发过程中煤层有效应力变化和基质收缩效应的条件下建立了煤层基质和割理系统的应力敏感模型，并采用Langmuir定理计算煤层气的解吸附，建立了一种可压缩煤层气在煤层基质–割理系统–多分支水平井耦合中流动的开发模型，进而研究了多分支水平井形态和割理密度对煤层气开发的影响。结果表明：煤层中的离散割理可以极大地增加多分支水平井在短时间内对煤层的动用范围，但是仅限于与多分支水平井直接联通的割理及周围基质区域，未与多分支水平井联通的部分则需要较长的开发时间，这也是气井在较短的时间获得峰值产量并迅速减产的重要原因；等长型多分支水平井控制的储层范围最大，交错型、哑铃型和纺锤型的控制范围依次减小；在煤层中割理密度相同时，等长型多分支水平井的煤层气峰值日产量和20 a内的累积产量均高于其他3种类型的多分支水平井，可以取得更好的开发效果；增大多分支水平井主次井筒的夹角，等长型多分支水平井开发效果更好，同时纺锤型分支水平井的峰值日产量提高显著；交错型和哑铃型多分支水平井的峰值日产量对分支数量更加敏感，纺锤型多分支水平井的分支数量应不少于8条，而哑铃型多分支井的分支数量不多于6条。

There are various forms of multilateral horizontal wells for developing coalbed methane, and the role of cleats in the development process is unclear. It is necessary to investigate the impact of the discrete cleat distribution in coal seams and the multilateral horizontal well configuration on gas well productivity. Based on the density and orthogonal characteristics of face and butt cleats in coal seams, the low density, medium density, and high density discrete cleat systems in coal seams are constructed using random methods. Combined with four different forms of multilateral horizontal wells, namely equal-length type, spindle type, staggered type, and dumbbell type, a physical model for developing coalbed methane using multilateral horizontal wells is constructed. The stress sensitive model of coal matrix and cleat system is established considering the effective stress change of coal seams and the matrix shrinkage effect in the development process. The desorption of coal-bed methane is calculated using Langmuir theorem, and a development model of compressible coal-bed methane flowing in the coupling of coal matrix, cleat system and multi branch horizontal wells is established. Furthermore, the influence of the cleat density and the configuration of multilateral horizontal wells on the development of coal-bed methane is studied. The results show that the discrete cleats in coal seams can greatly increase the drainage area of multilateral horizontal wells in a short period of development time, but are only limited to the cleats directly connected to multilateral horizontal wells and surrounding matrix areas. The parts that are not connected to multilateral horizontal wells require longer development time, which is also an important reason for gas wells to achieve peak production in a short period of time and quickly reduce production. The drainage area controlled by equal-length multilateral horizontal wells is the largest, while the drainage area of staggered type, dumbbell type, and spindle type decreases sequentially. When the cleat density is the same in the coal seams, the daily peak production and cumulative production within 20 years of the equal-length multilateral horizontal wells are higher than those of the other three types of multilateral horizontal wells, which can achieve better development results. By increasing the angle between the main and secondary wellbore of multilateral horizontal wells, the development effect of equal-length multilateral horizontal wells becomes much better, and the peak daily production of spindle multilateral horizontal wells is significantly improved. The peak daily production of staggered and dumbbell multilateral horizontal wells is more sensitive to the number of branches. The number of branches in spindle multilateral horizontal wells should not be less than eight, while the number of branches in the dumbbell multilateral wells should not be more than six.