We consider sewing machinery between finite difference and analytical solutions defined at different scales: far away and near the 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. In his remarkable paper Peaceman propose a framework how to deal with solutions defined on different scale for linear \textbf{time independent} problem by introducing famous, Peaceman well block radius. In this article we consider novel problem how to solve this issue for transient flow generated by compressiblity of the fluid. We are proposing method to glue solution via total fluxes, which is predefined on coarse grid and changes in the pressure, due to compressibility, in the block containing production(injection) well. 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 compressible 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) transient flow but can be applied in much more general scenario. In the article we use Einstein approach to derive Material Balance equation, a key instrument to define $R_0$. We will enlarge Einstein approach for three regimes of the Darcy and non-Darcy flows for compressible fluid(time dependent): $\textbf{I}. Stationary ; \textbf{II}. Pseudo \ Stationary(PSS) ; \textbf{III}. Boundary \ Dominated(BD).$

翻译：我们考虑在远场和近扰动源处不同尺度上定义的有限差分解与解析解之间的拼接方法。该方法的核心在于，粗网格问题和源模型代理中的边值问题表征了两种不同的流动。Peaceman在其著名论文中针对线性**时间无关**问题，通过引入著名的Peaceman井块半径，提出了处理不同尺度上定义解的框架。本文则探讨如何解决由流体可压缩性引发的瞬态流动中的这一新问题。我们提出一种通过总通量粘合解的方法，其中总通量在粗网格上预定义，并因可压缩性而在含生产（注入）井的块内产生压力变化。需指出，粗网格解"无法感知"边界。从工业应用角度，本报告为多孔介质中井周围可压缩流体流动的模拟数据解析解释提供了数学工具。它可视为线性（达西）瞬态流动中著名的Peaceman井块半径公式的数学"外衣"，但能应用于更广泛的场景。本文采用Einstein方法推导物质平衡方程——定义$R_0$的关键工具。我们将Einstein方法扩展到可压缩流体（时间依赖）的三种达西与非达西流动模式：$\textbf{I}$. 稳态；$\textbf{II}$. 拟稳态（PSS）；$\textbf{III}$. 边界主导流（BD）。