Cement Grout Nonlinear Flow Behavior through the Rough-Walled Fractures: An Experimental Study
Yuhao Jin, Lijun Han, Changyu Xu, Qingbin Meng, Zhenjun Liu, Yijiang Zong
Abstract
This research experimentally studied the effects of various fracture roughness (characterized by the fractal dimension <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>D</mml:mi></mml:math>) and normal stress (normal loads <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mtext>N</mml:mtext></mml:mrow></mml:msub></mml:math>) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mi>P</mml:mi></mml:math> and volumetric flow rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mi>Q</mml:mi></mml:math>, respectively. At each <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mi>D</mml:mi></mml:math>, the grouting pressure <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mi>P</mml:mi></mml:math> ranged from 0 to 0.9 MPa, and the normal loads <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mtext>N</mml:mtext></mml:mrow></mml:msub></mml:math> 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 (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mi>a</mml:mi></mml:math>) and linear coefficient (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mi>b</mml:mi></mml:math>) in Forchheimer’s equation increased with increase of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M10"><mml:mi>D</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M11"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mtext>N</mml:mtext></mml:mrow></mml:msub></mml:math>, and the larger the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M12"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mtext>N</mml:mtext></mml:mrow></mml:msub></mml:math> was, the larger the amplitude was. (ii) For normalized transmissivity, with the increase of Re, the decline of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M13"><mml:mtext> </mml:mtext><mml:mi>T</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>β</mml:mi></mml:math> curves mainly went through three stages: viscous regime, weak inertia regime, and finally strong inertia regime. For a certain <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M14"><mml:mi>D</mml:mi></mml:math>, as the normal load <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M15"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mtext>N</mml:mtext></mml:mrow></mml:msub></mml:math> increased, the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M16"><mml:mi>T</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mo>−</mml:mo><mml:mi>β</mml:mi></mml:math> curves generally shifted downward, which shows good agreement with the single-phase flow test results conducted by Zimmerman. Moreover, with the increase of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M17"><mml:mi>D</mml:mi></mml:math>, the Forchheimer coefficient <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M18"><mml:mi>β</mml:mi></mml:math> decreased. However, within smaller <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M19"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mtext>N</mml:mtext></mml:mrow></mml:msub></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M20"><mml:mi>β</mml:mi></mml:math> decreased gradually with increasing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M21"><mml:mi>D</mml:mi></mml:math> and eventually approached constant values. (iii) At a given <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M22"><mml:msub><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mtext>N</mml:mtext></mml:mrow></mml:msub></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M23"><mml:msub><mml:mrow><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow></mml:msub></mml:math> increased with increasing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M24"><mml:mi>D</mml:mi></mml:math>.