Experimental Investigation of Grout Nonlinear Flow Behavior through Rough Fractures

This research experimentally analyzed the impacts of various water cement (W/C) ratios of ultrafine cement grout material and normal loads FN applied to fractures on grout nonlinear flow behavior through a rough plexiglass fractured sample. An effective self-made apparatus was designed and manufactured to conduct the stress-dependent grout flow tests on the plexiglass sample containing rough fractures. At each W/C ratio, the grout pressure P increased from 0 to 0.9 MPa, and the normal loads FN ranged from 666.3 to 1467.8 N. The results of the experiments indicate that (1) the Forchheimer’s law can be used to express the results of grout nonlinear flow through rough fractures. Moreover, both nonlinear coefficient a and linear coefficient b in Forchheimer’s law decreased with the increase of the W/C ratio, but increased with the increase of the FN value. (2) For normalized transmissivity, with the increase of Re, the decline of the T/T0–Re curves means that the grout flow behavior through the fracture mainly went through three stages: the viscosity effect, then the weak inertia effect, and finally the strong inertia effect. The three stages showed that with the increase of Re, the grout flow state changed from linear to nonlinear. Moreover, with the increase of the W/C ratio, the Forchheimer coefficient β decreased. (3) At a given FN, the critical grout hydraulic gradient Jc decreased, but the critical Reynolds number Rec increased as the W/C ratio increased; at a given W/C ratio, Jc increased, but Rec decreased as FN increased.

Experimental Investigation on Nonlinear Flow Anisotropy Behavior in Fracture Media

A series of flow experiments were performed on matched fractures to study the problem of non-Darcy flow in fractured media. Five rock fractures of different roughness were generated using indirect tensile tests, and their surface topographies were measured using a stereo topometric scanning system. The fracture was assumed to be a self-affine surface, and its roughness and anisotropy were quantified by the fractal dimension. According to the flow tortuosity effect, the nonlinear flow was characterized by hydraulic tortuosity and surface tortuosity power law relationships based on Forchheimer’s law. Fracture seepage experiments conducted with two injection directions (0° and 90°) showed that Forchheimer’s law described the nonlinear flow well. Both the proposed model and Chen’s double-parameter model gave similar results to the experiment, but the match was closer with the proposed model. On this basis, a new formula for the critical Reynolds number is proposed, which serves to distinguish linear flow and Forchheimer flow.

Nonlinear Flow Characteristics of a System of Two Intersecting Fractures with Different Apertures

The nonlinear flow regimes of a crossed fracture model consisting of two fractures have been investigated, in which the influences of hydraulic gradient, surface roughness, intersecting angle, and scale effect have been taken into account. However, in these attempts, the aperture of the two crossed fractures is the same and effects of aperture ratio have not been considered. This study aims to extend their works, characterizing nonlinear flow through a system of two intersecting fractures with different apertures. First, three experiment models with two fractures having different apertures were established and flow tests were carried out. Then, numerical simulations by solving the Navier-Stokes equations were performed and the results compared with the experiment results. Finally, the effects of fracture aperture on the critical pressure difference and the ratio of hydraulic aperture to mechanical aperture were systematically analyzed. The results show that the numerical simulation results agree well with those of the fluid flow tests, which indicates that the visualization techniques and the numerical simulation code are reliable. With the increment of flow rate, the pressure difference increases first linearly and then nonlinearly, which can be best fitted using Forchheimer’s law. The two coefficients in Forchheimer’s law decrease with the increasing number of outlets. When increasing fracture aperture from 3 mm to 5 mm, the critical pressure difference increases significantly. However, when continuously increasing fracture aperture from 5 mm to 7 mm, the critical pressure difference changes are negligibly small. The ratio of hydraulic aperture to mechanical aperture decreases more significantly for a fracture that has a larger aperture. Increasing fracture aperture from 5 mm to 7 mm, that has a negligibly small effect on the critical pressure difference will however significantly influence the ratio of hydraulic aperture to mechanical aperture.

Permeability and Inertial Coefficients of Porous Media for Air Bearing Feeding Systems

In porous resistances, Darcy’s law provides a good approximation of mass flow rate when the differences between upstream and downstream pressures are sufficiently small. In this range, the mass flow rates are proportional to the porous resistance’s permeability. For gas bearings, the pressure difference is normally higher, and it is known experimentally that the mass flow rates are lower than would result from Darcy’s law. Forchheimer’s law adds an inertial term to Darcy’s law and, when an appropriate coefficient is selected for this term, provides a good approximation of flow rates for the same applications even with the highest pressure differences. This paper presents an experimental and theoretical investigation of porous resistances used in gas bearing and thrust pad supply systems. The porous resistances considered in the investigation were made by sintering bronze powders with different grain sizes to produce cylindrical inserts that can be installed in bearing supply devices. The paper describes the test setup and experimental results obtained for: (i) mass flow rate through single porous resistances at different upstream and downstream pressures and (ii) mass flow rate and pressure distribution on a pneumatic pad featuring the same porous resistances. The theoretical permeability of the chosen porous resistances was calculated, and the results from setup (i) were then used to obtain experimental permeability and to determine the inertial coefficients. The results, which are expressed as a function of the Reynolds number, confirmed the validity of using Forchheimer’s law. The mass flow rates from setup (ii) were compared to those from setup (i) at the same pressure differentials across the resistance.

Un modèle Darcy-Forchheimer pour un écoulement dans un milieu poreux fracturé

International audience We propose a numerical model for the flow of a single phase,incompressible fluid in a porous medium with fractures. In this model, the flow obeys Forchheimer's law in the fracture and Darcy's law in the rock matrix. Nous proposons un modèle numérique d'un écoulement monophasique d'un fluide incompressible dans un milieu poreux fracturé. Les lois d'écoulement sont celle de Forchheimer dans la fracture et de Darcy dans la matrice rocheuse.

Feeding System of Aerostatic Bearings With Porous Media

In porous resistances, Darcy’s law provides a good approximation of mass flow rate when the differences between upstream and downstream pressures are sufficiently small. In this range, the mass flow rates are proportional to the porous resistance’s permeability. For gas bearings, the pressure difference is normally higher, and it is known experimentally that the mass flow rates are lower than would result from Darcy’s law. Forchheimer’s law adds an inertial term to Darcy’s law and, when an appropriate coefficient is selected for this term, provides a good approximation of flow rates for the same applications even with the highest pressure differences. This paper presents an experimental and theoretical investigation of porous resistances used in gas bearing supply systems. Cylindrical sintered bronze inserts featuring lengths, diameters and particle sizes commonly used in gas bearings and thrust pads were examined. The paper describes the test set-up and experimental results obtained for: a) Mass flow rate through single porous resistances at different upstream and downstream pressures; and b) Mass flow rate and pressure distribution on a pneumatic pad featuring the same porous resistances. The theoretical permeability of the chosen porous resistances was calculated, and the results from set-up a) were then used to obtain experimental permeability and to determine the inertial coefficients. The results, which are expressed as a function of the Reynolds number, confirmed the validity of using Forchheimer’s law. The mass flow rates from set-up b) were compared with those from set-up a) at the same pressure differentials across the insert.