本文研究了分形油藏无限大地层和有界地层非牛顿幂律流渗流模型，利用拉氏变换和分解的方法求得了井底定流量生产无限大地层及有界地层（包括封闭和定压地层）五种情况非牛顿幂律流的实空间解析解，通数值积分法和拉氏数值反演分析了分形油藏非牛顿幂律流的压力动态特征以及分形参数和边界对压力动态的影响。

考虑到深井、超深井中井底围压对射流流场有一定的影响，建立了井底受限射流流场的物理模型。采用к-ε模型，并对模型的主要系数进行了优选，用有限元方法对围压条件下井底受限射流的流场进行了数值模拟。给出了高围压条件下射流轴心动压力、径向速度和轴心线上湍流动能等流场参数分布，并与零围压条件下淹没自由射流的参数进行了比较，得出了高围压条件下受限射流轴心动压力衰减规律的数学模式，进一步完善了钻井水力参数设计的理论和方法。

常规的侧钻方法是利用井下动力钻具和弯接头侧钻出新井眼。在上部软地层，考虑到节约成本的需要，采用压弯钻杆法或吊打纠斜法侧钻出新井眼是相当有效的。这两种方法都是采用转盘钻钻进的，它不但节约了租用井下动力钻具的费用，而且也大大提高了机械钻速，可尽快地解除事故侧钻出新井眼。

以一种现场常用的PDC取心钻头为原型，充分考虑排屑槽和切削齿对于井底流动的影响， 建立了与实际相接近的PDC取心钻头井底流场的物理模型，运用к-ε两方程模型，采用线性六面体等参单元对取心钻头井底流动空间进行划分，用有限元方法对井底流场进行了数值模拟研究，分析了排屑槽和切削齿对PDC取心钻头井底漫流的影响，为合理进行取心钻头的结构设计及水力设计提供了依据和校验方法。

Based on analysis of existing compositional and empirical modeling method for density of drilling fluid, a novel density model is developed according to PVT characteristics of drilling fluid, furthermore modeling method is determined in the paper. The new model presents density of drilling fluid is the linear superposition of initial density, a function of temperature, and a function of pressure, i.e. it is linear with both a function of temperature and a function of pressure. The simulated experiment on density characteristics of oil-in-water drilling fluid under high-temperature and high-pressure condition is conducted in-depth. The result shows that the calculated data of model is in high agreement with the measure data, and its correlation coefficient is higher than the empirical model’s, which illustrates that the new model can more accurately predict the variation of density with temperature and pressure. This research provides a theoretical support of calculating and controlling accurately bottomhole pressure in the process of drilling.