Numerical investigation of heat transfer effect on flow behavior in a single fracture
- PDF / 3,444,511 Bytes
- 16 Pages / 595.276 x 790.866 pts Page_size
- 40 Downloads / 213 Views
TECHNICAL NOTE
Numerical investigation of heat transfer effect on flow behavior in a single fracture Jie Tan 1,2 & Guan Rong 1,2 & Renhui He 1,2 & Jie Yang 1,2 & Jun Peng 3 Received: 23 October 2019 / Accepted: 12 August 2020 # Saudi Society for Geosciences 2020
Abstract This study numerically investigates the effect of heat transfer between fluid and fracture walls on flow behavior in a single fracture. The process of heated flow through fracture models created with realistic rock surfaces is simulated by solving the Navier-Stokes equations and energy conservation equation. The simulation results show that the heat transfer has a significant effect on the viscosity of water in the fracture, but the effect on the density is negligible. With the influence of heat transfer, the fluid in the fracture exhibits nonlinear characteristics even though the flow rate is small. The Forchheimer equation is proven to well represent the nonlinearity induced by both the fracture geometry and the heat transfer. As the flow rate increases, the heat transfer effect gradually decreases. In addition, when the rock temperature is large enough, the fracture geometry effect becomes less prominent. The results in this study provide new insights in understanding the heat transfer–dependent fracture flow behavior and directing such experimental procedures in future. Keywords Rock fracture . Heat transfer . Nonlinear flow . Critical hydraulic gradient
List of symbols P Pressure (Pa) Q Volumetric flow rate (mL/min) A Linear coefficient B Nonlinear coefficient μ Dynamic viscosity coefficient (Pa·s) eh Hydraulic aperture (mm) w Width of the fracture (mm) ρ Fluid density (kg/m3) ρave Average fluid density (kg/m3) Responsible Editor: Broder J. Merkel * Guan Rong [email protected] 1
State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
2
Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Ministry of Education, Wuhan University, Wuhan 430072, China
3
Department of Civil Engineering, The University of Hong Kong, Hong Kong, China
β Z2 n zi △y θmax u τ I T q D K Cp T_ext T_in T_out j Q_in υ Jc Rec g
Non-Darcy coefficient (m−1) Root mean square of the slope of fracture profile Number of data points The ith asperity height (mm) Interval of the data points (mm) Maximum apparent dip angle (°) Flow velocity (m/s) Transpose operation symbol Identity matrix The temperature value (°C) Heat generation (K/s) Thermal diffusivity (m2/s) Thermal conductivity (W/m K) Specific heat capacity (J/kg K) Temperature of outer surface in the rock sample (°C) Water temperature of the inlet (°C) Water temperature of the outlet (°C) Time step Given flow rates of inlet (mL/min) Kinematic viscosity (m2/s) Critical hydraulic gradient Critical Reynolds number Gravitational acceleration (m/s2)
851
Page 2 of 16
Arab J Geosci
12μ βρ B¼ 2 2; w eh we3h
(2020) 13:851
Introduction
A¼
Rock mass is in nature composed of the rock matrix and the fractures. The presence of fractures greatly affec
Data Loading...