Analytical Solution of Unsteady-state Forchheimer Flow Problem in an Infinite Reservoir: The Boltzmann Transform Approach

For several decades, attempts had been made by authors to develop models suitable for predicting the effects of Forchheimer flow on pressure transient in porous media. However, due complexity problem, they employed numerical and/or semi-analytical approach, which greatly affected accuracy and range applicability their results. Therefore, order increase applicability, a purely analytical approach solving this problem is introduced applied. objective paper mathematical model quantifying turbulence media employing approach. The partial differential equation (PDE) that governs unsteady-state under turbulent condition obtained combining with continuity equations state. then presented dimensionless form (by defining appropriate variables) enhance more generalization application method Boltzmann Transform obtain an exact solution equation. Finally, logarithms approximation (for larger times) derived. Moreover, after rigorous modeling analysis, novel relationship between time, pressure, radius was infinite reservoir dominated flow. It observed bears some similarities laminar conditions. Their logarithm approximations also share similarities. In addition, results show efficiency kind complex problem. Doi: 10.28991/HEF-2021-02-03-04 Full Text: PDF