Estimation of the Non‐Darcy Coefficient Using Supercritical CO₂ and Various Sandstones

Abstract

Non-Darcy flow (also known as high-velocity flow, inertial flow, etc.) often occurs in the near-well region of a reservoir during injection or production. This flow needs to be characterized and its origins fully understood, as it is a critical factor in reducing well productivity. The Forchheimer equation, which describes fluid flow considering an inertial effect, can be adopted to analyze non-Darcy flow. In particular, the non-Darcy coefficient in the equation represents inertial resistance in a porous medium and is an empirical value that depends on the pore geometry and fluid properties. This study, as part of research on geological CO 2 storage, reports non-Darcy flow tests with a high flow rate and examines the non-Darcy coefficient by using supercritical CO 2 and various sandstones. The dependence of the coefficient on the properties of the supercritical CO 2 was also assessed in a series of non-Darcy tests under different pore pressures. The coefficient varied with the properties of the supercritical CO 2 and sandstone. As the permeability of sandstone increased, the non-Darcy coefficient decreased nonlinearly and converged to a value. The results also indicate that the coefficient is reduced with a decreasing ratio of density to viscosity for the supercritical CO 2 . An equation predicting the coefficient was derived, having the advantage that both the hydraulic properties of rock and the fluid properties can be considered simultaneously in a dimensionally correct analysis.

Teach Second Law of Thermodynamics via Analysis of Flow through Packed Beds and Consolidated Porous Media

“…The experimental procedure to determine β involves two steps: In the first step, the permeability k of the porous sample is determined from Darcy's law by restricting the experiments to low flow rates, and in the second step, the experiments are conducted at high flow rates and β is evaluated directly from the Forchheimer equation from the knowledge of pressure drop versus flow rate. The non-Darcy flow coefficient decreases with the increase in the permeability of the porous medium [20].…”

“…When the permeability k of the porous medium is decreased (keeping µ the same), the porous medium becomes less permeable to fluid flow resulting in larger resistance to fluid motion and hence larger rates of mechanical energy dissipation and entropy generation. Note that k is typically in the range of 10 −15 to 10 −12 m 2 for porous sandstones [20]. In turbulent flow through consolidated porous medium, the key factor governing the vs. behavior is where is the non-Darcy flow coefficient.…”

“…With the increase in ρβ, the entropy generation rate increases at any given V s , as shown in Figure 19. Note that the non-Darcy flow coefficient is inversely related to the porous medium permeability [20]. For sandstones, β is typically in the range of 10 8 to 10 12 m −1 .…”

Equivalent Pore Channel Model for Fluid Flow in Rock Based on Microscale X-ray CT Imaging

“…The system allows a maximum of 320 kV radiation energy output and has a minimum focal spot size of 400 nm with a digital flat panel detector. Each sandstone specimen had already been characterized for hydraulic properties through a mercury intrusion porosimetry (MIP) test in this laboratory [16]. The measured pore median diameter and porosity are described in Table 1.…”

“…Katz and Thompson [32,33] proposed a permeability prediction method using the P t and a corresponding characteristic length (L t ). Many previous studies have examined the validity of the proposed method and highlighted the importance of the P t , because the L t is a unique representative length scale for fluid flow and dominates the permeability [16,[32][33][34]. With this representation of the P t , a criterion for deciding the threshold intensity value in micro-CT-images to distinguish between P ap and P indis was suggested in this study.…”