The paper presents a stochastic analysis of the growth rate of viscous fingers in miscible displacement in a heterogeneous porous medium. The statistical parameters characterizing the permeability distribution of a reservoir vary over a wide range. The formation of fingers is provided by the mixing of different-viscosity fluids -- water and polymer solution. The distribution functions of the growth rate of viscous fingers are numerically determined and visualized. Careful data processing reveals the non-monotonic nature of the dependence of the front end of the mixing zone on the correlation length of the permeability (describing the medium graininess) of the reservoir formation. It is demonstrated that an increase in graininess up to a certain value causes an expansion of the distribution shape and a shift of the distribution maximum to the region of higher velocities. In addition, an increase in the standard deviation of permeability leads to a slight change in the shape and characteristics of the density distribution of the growth rates of viscous fingers. The theoretical predictions within the framework of the transverse flow equilibrium approximation and the Koval model are contrasted with the numerically computed velocity distributions.
翻译:本文对异相可混淆位移过程中粘性指状物生长速率进行了随机分析,研究中注重描述一个储层的渗透率分布的统计参数。通过水和聚合物溶液的混合提供了指状物生成的条件。数值确定和可视化了生长速率的分布函数。数据处理揭示了混合区前端与储层渗透率相关长度(描述储层的粒度)之间依赖关系的非单调性。研究结果表明,在粒度增加到一定值时,会导致分布形状扩展并将最大值移动到速度更高的区域。此外,孔隙度标准差的增加导致生长速率密度分布的形状和特征略微改变。本文还对横向流动平衡近似与Koval模型进行了理论预测,并将其与数值计算得到的速度分布进行了对比。