| 壁面局部接触裂隙岩体水流-传热的一种理论模型及计算分析 |
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| 引用本文： | 项彦勇,任鹏.壁面局部接触裂隙岩体水流-传热的一种理论模型及计算分析[J].岩土力学,2014,35(10):2845-2854. |
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| 作者姓名： | 项彦勇 任鹏 |
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| 作者单位： | 北京交通大学 土木工程学院，北京 100044 |
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| 基金项目： | 高等学校博士学科点专项科研基金(No.20120009110022)；国家自然科学基金(No.50778014，No.51378055)。 |
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| 摘 要： | 核废物地质处置、地热开发、石油开采等工程领域都可能涉及稀疏裂隙岩体中的水流-传热过程。现有的裂隙岩体水流-传热理论模型和计算方法基本上都是以平行光滑壁面裂隙模型为基础的，没有考虑裂隙的壁面局部接触对水流、水-岩热交换以及岩体传热的影响。针对粗糙壁面裂隙水流过程，阐述了基于Stokes方程的Reynolds润滑方程及Hele-Shaw裂隙模型，采用MATLAB软件中的PDE工具求解，并与Walsh的等效水力开度公式进行对比；分析壁面局部接触裂隙水流-传热与填充裂隙水流-传热的相似性，提出了瞬时局部热平衡假设的适用条件，并在裂隙局部接触体传热满足Biot数条件的前提下，计算分析裂隙局部接触体与水流之间的局部热平衡时间及其影响因素；在裂隙局部接触体与水流之间满足瞬时热平衡假设的前提下，利用填充裂隙水流-传热的解析解，计算了壁面局部接触裂隙水及两侧岩石的温度分布，并分析了裂隙局部接触面积率、裂隙开度、裂隙水平均流速对岩石温度和裂隙水温度的影响特征，结果表明：（1）在设定条件下，由于裂隙局部接触体与裂隙水流之间的热交换，裂隙水流对其两侧岩石温度的影响范围随接触面积率的增大而减小，裂隙两侧岩石对裂隙水流温度的影响程度随接触面积率的增大而增大；（2）裂隙开度和裂隙水流速对岩石温度和裂隙水温度的影响方式的影响是一致的，即由于裂隙水流量随裂隙开度和裂隙水流速的增大而增大，裂隙水流对其两侧岩石温度的影响范围随裂隙开度和裂隙水流速的增大而增大，裂隙两侧岩石对裂隙水流温度的影响程度随裂隙开度和裂隙水流速的增大而减小。
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| 关 键 词： | 壁面局部接触裂隙 Hele-Shaw模型 水流-传热 瞬时局部热平衡 参数分析 |
| 收稿时间： | 2013-06-25 |
A theoretical model and its calculation analysis of water flow and heat transfer in a fractured rock with local fracture wall asperity contacts |
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| XIANG Yan-yong,REN Peng.A theoretical model and its calculation analysis of water flow and heat transfer in a fractured rock with local fracture wall asperity contacts[J].Rock and Soil Mechanics,2014,35(10):2845-2854. |
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| Authors: | XIANG Yan-yong REN Peng |
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| Institution: | School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China |
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| Abstract: | Water flow and heat transfer processes in fractured rocks may be encountered in several engineering disciplines, such as geological disposal of radioactive waste, geothermal development, petroleum exploration, etc. Currently existent theoretical models and calculation methods for water flow and heat transfer in fractured rocks are almost exclusively based on the assumption of parallel smooth fracture walls, without considering the effects of local fracture wall asperity contacts on water flow, water-rock heat exchange and heat transfer. The following studies are presented in this paper. Firstly, dealing with water flow in a fracture with rough walls, the Reynolds lubrication equation and the Hele-Shaw model of a fracture with local wall asperity contacts based on the Stokes equations are expounded; solutions are sought by using the PDE tool of the MATLAB software, and compared with the Walsh formula of the effective hydraulic aperture of a rough walled fracture. Secondly, the similarity between the water flow and heat transfer in a fractured rock with local fracture wall asperity contacts and the water flow and heat transfer in a fractured rock with fills is analyzed; the condition for applicability of the instantaneous local thermal equilibrium is proposed; and the time and its influencing parameters for local thermal equilibrium between the local fracture wall asperity contacts and the flowing water in the fracture are computationally analyzed under the premise that the Biot number condition can be satisfied by the local fracture wall asperity contacts. Lastly, assuming instantaneous local thermal equilibrium between the local fracture wall asperity contacts and the flowing water in the fracture, the distributions of temperatures in the flowing water and the rock matrix are calculated using an existing analytical solution for water flow and heat transfer in a fractured rock with fills, and the effects of the ratio of local asperity contact area, the fracture aperture and the averaged water velocity on the temperature distributions are analyzed, which indicate, under the prescribed conditions, (1) that due to the heat exchange between the local fracture wall asperity contacts and the flowing water in the fracture, the range of influence of the flowing water on the temperature of the rock matrix decreases with the increase of the ratio of local asperity contact area, whereas the degree of influence of the rock matrix on the temperature of the flowing water in the fracture increases as the ratio of local asperity contact area increases; (2) the influences of the fracture aperture and the water velocity on the temperatures of the rock matrix and the flowing water in the fracture are consistent in that the range of influence of the flowing water on the temperature of the rock matrix increases with the increases of the fracture aperture and the water velocity, whereas the degree of influence of the rock matrix on the temperature of the flowing water decreases as the fracture aperture and the water velocity increase. |
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| Keywords: | fracture with local wall asperity contacts Hele-Shaw model water flow and heat transfer instantaneous local thermal equilibrium parametric analysis |
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