Laboratory Measurements of non-Darcy Flow Coefficients in Natural and Artificial Unconsolidated Porous Media

The estimation of Non-Darcy flow regime is often a critical issue in petroleum engineering, as it is a key parameter to estimate and predict the correct production performances and behavior of hydrocarbon reservoirs. 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’s law, where the pressure gradient is a linear function of the flow velocity. In fact, the use of Darcy’s law would lead to inaccurate production performances evaluation. The most commonly used tool to approximate the non-linear behavior of the flow velocity is the well-known Forchheimer equation, deploying the “inertial” coefficient Beta that can be estimated experimentally, by means of direct measurements on core samples. In gas wells the inertial coefficient Beta is usually estimated by means of indirect measurements, through the analysis of multi-rate pressure tests performed on site during the routine well testing programmed after well completion. Unfortunately, such data are not easily available in many cases, and new measurements are very expensive, since well testing is accomplished by gas production shutdown for several tens of hours or days. 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 experimental study reports Non-Darcy flow laboratory investigations performed on natural and artificial unconsolidated porous media (glass beads and loose natural sands of different grain size). The inertial coefficient Beta and permeability has been calculated for several samples (with both peaked and flat grain size distribution, obtained by sieving glass beads and sand); experimental data suggest that also Beta is to some extent affected by pore structure. Moreover, the Forchheimer’s number has been calculated and its non-linearity with respect to superficial velocity has been checked. In the light of the above, specific laboratory equipment has been devised in order to rely on a wide range of flow rates under appropriate pressure gradients.