Non-Darcy Flow: Laboratory Measurements in Unconsolidated Porous Media

In recent years, the petroleum industry has shown a renovated interest in Non-Darcy flow, in order to better understand reservoir performances. Non-Darcy flow is typically observed in gas wells when the fluids converging to the wellbore attains the velocity peculiar of turbulent flow. As a consequence, pressure drop around the wellbore cannot be estimated from the classic Darcy equation, where the pressure gradient is a linear function of the flow velocity. In that case, in fact, the use of Darcy equation would lead to inaccurate production performances evaluation. In order to describe correctly this phenomenon, the well-known Forchheimer equation is normally used, where the inertial coefficient  is defined. In gas wells this coefficient is usually determined by the analysis of multi-rate pressure tests performed on site. Unfortunately, such data are not easily available (or not economical) in many cases. So, it is a common practice to use particular theoretical and empirical correlations that can be derived by exploiting experimental values of the inertial coefficient. This paper reports a laboratory study in which the inertial coefficient  can be correlated to the structure of the porous media, and, in particular, of its grain size distribution. Gas flow laboratory experiments have been performed on laboratory models of glass beads and natural sands of different sizes. Moreover, porosity and permeability, together with the Klinkenberg constant, have been determined on natural sand cores with both flat and peaked grain size distribution, and a correlation with the Forchheimer equation has been checked. Forchheimer’s number has been calculated and correlated to the superficial velocity as well. In the light of the above, specific laboratory equipment has been devised in order to rely on a wide range of flow rate under appropriate pressure gradients.