Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow

LIU Jian; YANG Qiaoyan; BAI Xue; SONG Kai; LUO Chengjie; SA Yongfang

doi:10.3969/j.issn.0258-2724.20180756

Volume 55 Issue 1

Jan. 2020

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Journal of Southwest Jiaotong University > 2020 > 55(1): 218-224.

LIU Jian, YANG Qiaoyan, BAI Xue, SONG Kai, LUO Chengjie, SA Yongfang. Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756

Citation:

LIU Jian, YANG Qiaoyan, BAI Xue, SONG Kai, LUO Chengjie, SA Yongfang. Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756

Citation:

LIU Jian, YANG Qiaoyan, BAI Xue, SONG Kai, LUO Chengjie, SA Yongfang. Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756

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Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow

doi: 10.3969/j.issn.0258-2724.20180756

Received Date: 04 Sep 2018
Rev Recd Date: 08 Oct 2018

Available Online: 21 Dec 2018

Publish Date: 01 Feb 2020

Abstract

Abstract

In order to explore the movement law of water flow in rock mass fissures, a fracture seepage flow model was established with real rock mass materials to study the seepage flow state and parameters. The single-fracture seepage flow model was constructed using natural marble blocks, instead of the common non-stone materials such as cement, glass, acrylic, and steel. Based on the model, seepage experiments with different fissure widths (0.77, 1.18, 1.97, 2.73 mm) were conducted to investigate the relationship between pressure loss and flow rate, the critical point of transition from Darcian to non-Darcian flow, and the quantification of parameters in the Forchheimer equation. Results show that the relationship between pressure gradient and flow rate is governed by linear Darcy’s law when the fracture width is 0.77 mm, but obvious non-Darcy characteristics are observed with the increase of the fracture width and flow rate, which can be described by Forchheimer equation. The coefficient of viscosity and inertia term of the Forchheimer equation can be expressed as a power function of fracture width, and the error can be reduced by introducing Reynolds number to correct the inertia coefficient. Besides, the method of judging the critical point of transition from Darcian to non-Darcian flow via the slope characteristics of pressure gradient-flow curve proved feasible in this experiment.
- fracture,
- non-Darcy,
- Forchheimer equation,
- Reynolds number,
- critical point

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References(29)

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Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow

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