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：本文对非均匀多孔介质中互溶驱替过程里粘性指进生长速率进行了随机分析。描述储层渗透率分布的统计参数在较宽范围内变化。指进的形成源于不同粘度流体（水与聚合物溶液）的混合。通过数值方法确定并可视化了粘性指进生长速率的分布函数。精细的数据处理揭示了混合区前端对储层渗透率相关长度（描述介质颗粒度）依赖性的非单调性质。研究表明，颗粒度增大至某一特定值会引发分布形态的扩展，并将分布最大值向更高速度区域偏移。此外，渗透率标准差的增加对粘性指进生长速率密度分布的形态与特征影响微弱。基于横向流平衡近似与Koval模型的理论预测与数值计算的速度分布进行了对比。