Consolidation with threshold gradients

Pascal, F.; Pascal, H.; Murray, David

doi:10.1002/nag.1610050303

Cited by 31 publications

(25 citation statements)

References 7 publications

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“…The time-dependent load presented in Eq. (8) is different from previous loads including the constant load [15], the ramp load [34], and the exponential-type load [35]; however, this time-dependent load still has practical meaning, and there is no evidence that previous loads are more rational.…”

Section: Deduction Of the Mathematical Equations For A Special Implicmentioning

confidence: 90%

“…Practical applications of the issue include the consolidation of clayey soils, the design of oil reservoirs, etc. In on study, Pascal et al [15] studied one-dimensional soil consolidation with a threshold gradient using the finite difference method, and they considered instantaneously applied constant load. In addition, Xie et al [28] investigated the condition of general time-dependent load, and constructed a solution using the separation of variables technique; however, their solution does not present the location of the seepage front in an analytical form, thus it can not be seen as an analytical solution.…”

Section: Introductionmentioning

confidence: 99%

“…The physical background of the Stefan problem lies in many aspects, such as the solidification of the alloy melt [6], the melting and ablation during the laser heating process [7,8], the shore-line movement problem [9,10], the freeze and thaw of humid porous media [11,12], the hydration process of the soybean [13,14], and the flow in porous media [15,16]. In most situations, the Stefan problem can only be solved numerically; however, finding analytical solutions for the problem has always been of great interest to the researchers.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

Zhou

Shi

2017

Acta Mech. Sin.

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One-dimensional non-Darcy flow in a semiinfinite porous media is investigated. We indicate that the non-Darcy relation which is usually determined from experimental results can always be described by a piecewise linear function, and the problem can be equivalently transformed to a multiphase implicit Stefan problem. The novel feature of this Stefan problem is that the phases of the porous media are divided by hydraulic gradients, not the excess pore water pressures. Using the similarity transformation technique, an exact solution for the situation that the external load increases in proportion to the square root of time is developed. The study on the existence and uniqueness of the solution leads to the requirement of a group of inequalities. A similar Stefan problem considering constant surface seepage velocity is also investigated, and the solution, which we indicate to be uniquely existent under all conditions, is established. Meanwhile, the relation between our Stefan problem and the traditional multiphase Stefan problem is demonstrated. In the end, computational examples of the solution are presented and discussed. The solution provides a useful benchmark for verifying the accuracy of general approximate algorithms of Stefan problems, and it is also attractive in the context of inverse problem analysis.

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Section: Deduction Of the Mathematical Equations For A Special Implicmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

Zhou

Shi

2017

Acta Mech. Sin.

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“…It is assumed that the CBM desorption starts at the initial formation pressure. According to the S-D adsorption and stress calculation method (Pascal et al 1981) (Zhang et al 2012), the volumetric strain caused by desorption of CBM can be written as:…”

Section: Stress Induced By Desorptionmentioning

confidence: 99%

Mechanism of shear failure near fracture face during drainage process of CBM well

Xiong

et al. 2018

J Petrol Explor Prod Technol

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In this paper, whether the coal fines can be induced by shear failure during drainage process has been discussed in detail. By coupling with the percolation theory, the elasticity mechanics were used to construe the extra stresses in the formation surrounding with the hydraulic fracture. The safe window of the bottom hole pressure was also calculated from the failure envelope. The research shows that the formation pressure on the fracture surface of the coal seam is negatively related with the bottom hole pressure, and the induced stress is positively related with the bottom hole pressure during the drainage process of fractured CBM wells. The pore pressure around the fracture changed due to pore-elastic effects, which also caused a significant change of the in situ stresses. In order to avoid the breakout of the coal seam around hydraulic fracture during drainage process, the model of the reasonable bottom hole pressure is also built.

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“…In 1973, the consolidation problem with initial gradient was investigated, and the approximate solution of the moving boundary model with threshold pressure gradient was obtained (Schmidt and Westman, 1973;Pascal, 1973). Then several modified expressions of Darcy's law were developed (Huang, 1998), based on the flow rate-pressure gradient curves of core flood experiments.…”

Section: Introductionmentioning

confidence: 99%

Variable-Permeability Well-Testing Models and Pressure Response in Low-Permeability Reservoirs with non-Darcy Flow

et al. 2016

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This paper proposes the concept of variable-permeability effect and sets up the one-dimensional and two-dimensional non-Darcy well testing models. The finite difference algorithm is employed to solve the differential equations of the variable-permeability model, and the non-convergence of the numerical solutions is solved by using the geometric mean of permeability. The type curves of pressure and pressure derivative with variable-permeability effect are obtained, and sensitivity analysis is conducted. The results show that the type curves upturn in the middle and late sections, and the curves turn more upward with the severer of the variable-permeability effect. The severer the non-Darcy effect is, the less obviously the curve upturns caused by boundary effect. Furthermore, the boundary effect is increased by increasing the number of impermeable boundaries or decreasing the distance between the well and boundary. EARTH SCIENCES RESEARCH JOURNAL

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Consolidation with threshold gradients

Cited by 31 publications

References 7 publications

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

One-dimensional non-Darcy flow in a semi-infinite porous media: a multiphase implicit Stefan problem with phases divided by hydraulic gradients

Mechanism of shear failure near fracture face during drainage process of CBM well

Variable-Permeability Well-Testing Models and Pressure Response in Low-Permeability Reservoirs with non-Darcy Flow

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