Characterization of a Non-Darcy Flow and Development of New Correlation of NON-Darcy Coefficient

Abstract

Darcy’s law has long been used to describe the flow in porous media. Despite the progress that took place in oil production industry research, it became clear that there is a loss of pressure, especially in the area near the wellbore region, where Darcy’s law is not applicable. For this reason, Forchheimer presented his equation in 1910, where he added a new term to Darcy’s law dealing with pressure loss due to inertial forces by introducing a new term, the coefficient, into the equation. This paper presents a study of fluid flow through porous media, where water was used as a working fluid. Furthermore, the characteristics of the non-Darcy flow were analyzed by presenting the corresponding pressure and velocity gradient curves for each pressure. Extensive analysis indicates that many of the correlations available in the literature either have defective units or are the product of a small number of experiments. In this study, we benefit from relatively large samples, the radial flow, and the perforation in the middle of the samples. The properties of the samples were measured using mercury intrusion porosimetry. It was found that there is a direct relationship between the porosity and the grain’s size; the greater the size of the grains, the greater the porosity, and vice versa. The non-Darcy coefficient term, β, is found to be inversely proportional to the porosity and permeability. In a previous study, the β was investigated for compressible flow scenarios; however, this study calculated it for an incompressible flow. Finally, by analyzing the β values of both studies, we could deduce new novelty correlations for the β coefficient term, where the permeability, porosity, and tortuosity are included.

Revealing patterns in the influence of variable permeability of well bottomhole zones on the operational modes of underground gas storage facilities

“…The results of works [8][9][10] confirm the problematic nature of building universal models of gas inflow to well blowouts that would work reliably in the entire range of operational data changes at significant time intervals.…”

“…Works [8,9] report the study of the coefficient β, which occurs in the nonlinear model of gas inflow to wells.…”

“…In [8], it was established that there is a direct relationship between porosity and grain size -the larger the grain size, the greater the porosity, and vice versa. It was established that the coefficient β is inversely proportional to the porosity and permeability, and also that the coefficient β is correlated with the permeability, porosity, and tortuosity of reservoir layers.…”

“…Establishing the conditions under which Darcy's law is satisfied or not fulfilled depends on the flow rate of the well and the permeability of the bottomhole zone under which the given formulas ( 7), (8) hold within the accuracy of the measurements. There are no conditions that would unambiguously identify the applicability of Darcy's law under the conditions of operation of wells with variable withdrawal/injection volumes.…”

Effects of Clay Content on Non-Linear Seepage Behaviors in the Sand–Clay Porous Media Based on Low-Field Nuclear Magnetic Resonance

“…Darcy's law states that the pressure gradient is linearly proportional to the fluid velocity in porous media. However, previous research has revealed that Darcy's law is effective only within a certain range [2][3][4][5]. When the samples contain clay, their seepage behavior deviates from Darcy's law at low or high hydraulic gradients [6].…”