Cement Grout Nonlinear Flow Behavior through the Rough-Walled Fractures: An Experimental Study

This research experimentally studied the effects of various fracture roughness (characterized by the fractal dimension D) and normal stress (normal loads FN) applied to fracture on ultrafine cement grout nonlinear flow behavior through rough-walled plexiglass fractured sample. A high-precision and effective sealing self-made apparatus was developed to perform the stress-dependent grout flow tests on the plexiglass sample containing rough-walled fracture (fracture apertures of arbitrary variation were created by high-strength springs and normal loads according to design requirements). The real-time data acquisition equipment and high-precision self-made electronic balance were developed to collect the real-time grouting pressure P and volumetric flow rate Q, respectively. At each D, the grouting pressure P ranged from 0 to 0.9 MPa, and the normal loads FN varied from 1124.3 to 1467.8 N. The experimental results show that (i) the Forchheimer equation was fitted very well to the results of grout nonlinear flow through rough-walled fractures. Besides, both nonlinear coefficient (a) and linear coefficient (b) in Forchheimer’s equation increased with increase of D and FN, and the larger the FN was, the larger the amplitude was. (ii) For normalized transmissivity, with the increase of Re, the decline of the T/T0−β curves mainly went through three stages: viscous regime, weak inertia regime, and finally strong inertia regime. For a certain D, as the normal load FN increased, the T/T0−β curves generally shifted downward, which shows good agreement with the single-phase flow test results conducted by Zimmerman. Moreover, with the increase of D, the Forchheimer coefficient β decreased. However, within smaller FN, β decreased gradually with increasing D and eventually approached constant values. (iii) At a given FN, Jc increased with increasing D.

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

Under certain flow conditions, fluid flow through porous media starts to deviate from the linear relationship between flow rate and hydraulic gradient. At such flow conditions, Darcy’s law for laminar flow can no longer be assumed and nonlinear relationships are required to predict flow in the Forchheimer regime. To date, most of the nonlinear flow behavior data is obtained from flow experiments on packed beds of uniformly graded granular materials (Cu = d60/d10 < 2) with various average grain sizes, ranging from sands to cobbles. However, natural deposits of sand and gravel in the subsurface could have a wide variety of grain size distributions. Therefore, in the present study we investigated the impact of variable grain size distributions on the extent of nonlinear flow behavior through 18 different packed beds of natural sand and gravel deposits, as well as composite filter sand and gravel mixtures within the investigated range of uniformity (2.0 < Cu < 17.35) and porosity values (0.23 < n < 0.36). Increased flow resistance is observed for the sand and gravel with high Cu values and low porosity values. The present study shows that for granular material with wider grain size distributions (Cu > 2), the d10 instead of the average grain size (d50) as characteristic pore length should be used. Ergun constants A and B with values of 63.1 and 1.72, respectively, resulted in a reasonable prediction of the Forchheimer coefficients for the investigated granular materials.

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.

Manipulation and analysis of an optofluidic multiphase microlens

We show the underlying physics governing the shape of a multiphasic microlens by exploiting nonlinear flow behavior at the interface.