论文标题
在井附近的非线性流量井层半径的和平模型中的基本面
Fundamentals in Peaceman Model for Well-Block radius For Non-Linear Flows Near Well
论文作者
论文摘要
我们考虑在有限差和以不同规模定义的分析解决方案之间进行缝制机械：流动扰动的遥远和近乎来源。该方法的本质之一是源模型代理中两个不同流动的粗略问题和边界价值问题。我们正在提出通过总通量粘合溶液的方法，该通量在粗网格上预定。重要的是要提到粗解决方案“看不到”边界。 从工业角度来看，我们的报告提供了数学工具，用于分析在多孔介质中围绕孔流体流量的模拟数据解释。它可以被认为是著名的和核心的封闭式半径公式的数学“衬衫”，用于线性（darcy）径向流动，但可以在更一般的情况下应用。 作为一个重要的情况，我们认为非线性叉状剂流。在文章中，我们严格地获得了良好的块半径，明确取决于$β-$ forchheimer因子和井上流量的总速率，并提供了Dake公式的概括以及对$ d $ fix率的评估。
We consider sewing machinery between finite difference and analytical solutions defined at different scale: far away and near source of the perturbation of the flow. One of the essences of the approach is that coarse problem and boundary value problem in the proxy of the source model two different flows. We are proposing method to glue solution via total fluxes, which is predefined on coarse grid. It is important to mention that the coarse solution "does not see" boundary. From industrial point of view our report provide mathematical tool for analytical interpretation of simulated data for fluid flow around a well in a porous medium. It can be considered as a mathematical "shirt" on famous Peaceman well-block radius formula for linear (Darcy) radial flow but can be applied in much more general scenario. As an important case, we consider nonlinear Forchheimer flow. In the article we rigorously obtained well-block radius, explicitly depending on $β-$Forchheimer factor and total rate of the flow on the well, and provide generalization of the Dake Formula and evaluation of the $D-$factor.
