低渗透油藏的非线性渗流模型

A New Nonlinear Model of Liquid Flows in Low Permeability Reservoirs

摘要: 工程上将多孔介质的渗透率小于50毫达西的油藏，称为低渗透油藏。长期以来，由于存在启动压力，低渗透油藏的渗流特征很难描述，至尽还没有理想的模型。本文考虑液体和固体壁面的相互吸引的性质，从微管的负滑移边界模型出发，定义固壁边界附近不流动流体的流体层为边界黏附层，采用边界黏附层与压力梯度成反比的实验经验公式，推导出了考虑边界负滑移条件下，圆管中的流速分布公式和流量公式。进而得到考虑边界黏附层的低渗透渗流模型。最后以微管和低渗透岩心的流动实验对模型进行了验证，拟合出了相应的启动压力梯度。分析表明：低渗透油层在整体上不存在启动压力，但在压力梯度较小的局部，可以认为存在拟启动压力梯度；通过对实验数据的不同次方拟合，我们可以比较出指数函数1次方拟合的相对准确。 In the petroleum development engineering, the low permeability reservoir is that the permeability of porous media is lower than 50 micro-Darcy. Because of the existence of the threshold pressure gradient (TPG), the mathematical model of liquid flow in low permeability media is difficult to describe this kind of flow. Until then there is not an ideal model, although there are several models used to fields of well testing analysis and petroleum numerical simulations. Based on force between liquid and surface solid, and the negative slip boundary model of a micro-channel, a new liquid flow model was derived for low permeability reservoirs in this paper. First we defined the no-movement liquid layer close to the solid surface as the boundary stick layer which is regarded as the negative slip length, and used the inverse proportion of the height of the boundary stick layer to the pressure drop gradient, thus the formulae of liquid velocity and the flow rate of a round channel were derived; Then the model of liquid flows in low permeability reservoirs was gotten, based on the capillaries model; Finally the flow models were tested by examples and showed how to get the TPG of the low permeability reservoirs. The results show that there is no TPG on the whole of the low permeability reservoirs, but in small local pressure gradient, the effects of boundary layer can be seen. Compared different power fittings on the experimental data, the first power exponential function fitting is relatively accurate.