  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): $\textbf{I}. Stationary ; \textbf{II}. Pseudo \ Stationary(PSS) ;
\textbf{III}. Boundary \ Dominated(BD).$
