Geometric multigrid methods for Darcy–Forchheimer flow in fractured porous media

Arrarás, Andrés; Gaspar, Francisco José; Portero, Laura; Rodrigo, Carmen

doi:10.1016/j.camwa.2019.04.031

Cited by 16 publications

(3 citation statements)

References 45 publications

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“…Darcy's law, which states that fluid flow rate is directly proportional to the pressure gradient, is applied to the fluid flow in the matrix of the model. As to the fluid flow within the hydraulic fracture, the Forchheimer model with the non-Darcy coefficient is implemented to simulate a turbulent flow, accounting for the inertial effects [16][17][18]. Meanwhile, local grid refinement with logarithmic spacing, discretizing the reservoir to a finer degree region around hydraulic fractures and more coarsely further away from the hydraulic fractures, is coupled with the Forchheimer model to accurately depict the detailed transient fluid flow around the hydraulic fractures [19][20][21].…”

Section: Simulation Methodology and Integrated Workflowmentioning

confidence: 99%

Well Pattern and Well Spacing Optimization of Large Volume Water Injection in a Low-Permeability Reservoir with Pressure Sensitivity

et al. 2022

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Even with the fractured wells, the primary oil recovery of low-permeability reservoirs is still poor in Block X of Shengli Oilfield. To further enhance the oil recovery, water is injected into the reservoir. Different from the conventional injection scheme, the maximum daily injection rate of the proposed scheme by Shengli Oilfield reaches 2000 m3, and the average daily injection rate is around 1500 m3. Thus, the conventional well spacing of certain well pattern is not suitable for the novel injection scheme. In the paper, the optimal well pattern and well spacing for the large volume water injection scheme to develop a pressure-sensitive low-permeability reservoir is investigated. Firstly, the CMG is employed to build the basic reservoir model developed by fractured vertical wells. To finely depict the pressure sensitivity, the dilation-recompaction geomechanical model is introduced to couple with the basic reservoir model. Based on the established coupled model, the optimal well spacing for the inverted 5-spot well pattern and the inverted 9-spot well pattern is investigated with a total of 80 sets of numerical experiments. The numerical experiments indicate that the optimal well spacing for the inverted 5-spot well pattern is 850 m/350 m and the optimal well spacing for the inverted 9-spot well pattern is 550 m/450 m. To further screen the well pattern, the normalized index of oil production per unit area of each well pattern is proposed. And it is found that the oil production per unit area of the inverted 5-spot well pattern is higher than the inverted 9-spot well pattern. For the reservoir developed with fractured vertical wells coupled with large volume water injection, compared with the inverted 9-spot well pattern, the inverted 5-spot well pattern is better, and the corresponding optimal well spacing is 850 m/350 m. The paper proposes an efficient simulation and optimization workflow for the development of pressure-sensitive low-permeability reservoirs with fractured vertical wells coupled with large volume water injection, providing practical guidance for the efficient and sustainable development of pressure-sensitive low-permeability reservoirs.

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Section: Simulation Methodology and Integrated Workflowmentioning

confidence: 99%

Well Pattern and Well Spacing Optimization of Large Volume Water Injection in a Low-Permeability Reservoir with Pressure Sensitivity

et al. 2022

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“…[37,39]. The Darcy permeability equation has been studied by many scholars [40,41]; combining the experimental data from this paper, based on previous studies, the modified Darcy permeability equation for low-temperature coal can be expressed in pressure form as follows:…”

Section: Analysis Of the Mechanism Of Water Migration During The Free...mentioning

confidence: 96%

The Temperature Field Evolution and Water Migration Law of Coal under Low-Temperature Freezing Conditions

Huang

et al. 2021

IJERPH

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This study examines the evolution law of the coal temperature field under low-temperature freezing conditions. The temperature inside coal samples with different water contents was measured in real-time at several measurement points in different locations inside the sample under the condition of low-temperature medium (liquid nitrogen) freezing. The temperature change curve was then used to analyse the laws of temperature propagation and the movement of the freezing front of the coal, which revealed the mechanism of internal water migration in the coal under low-temperature freezing conditions. The results indicate that the greater the water content of the coal sample, the greater the temperature propagation rate. The reasons for this are the phase change of ice and water inside the coal during the freezing process; the increase in the contact area of the ice and coal matrix caused by the volume expansion; and the joint action of the two. The process of the movement of the freezing front is due to the greater adsorption force of the ice lens than that of the coal matrix. Thus, the water molecules adsorbed in the unfrozen area of the coal matrix migrate towards the freezing front and form a new ice lens. Considering the temperature gradient and water content of the coal samples, Darcy’s permeation equation and water migration equation for the inside of the coal under freezing conditions were derived, and the segregation potential and matrix potential were analysed. The obtained theoretical and experimental results were found to be consistent. The higher the water content of the coal samples, the smaller the matrix potential for the hindrance of water migration. Furthermore, the larger the temperature gradient, the larger the segregation potential, and the faster the water migration rate.

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“…Study [9] numerically examined the mathematical model of filtration in a cracked-porous environment. In this case, it is believed that Darcy's law holds in a porous environment, while in the cracks, where the rate of filtration is greater, the Darcy-Forechheimer law is obeyed.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

A finite-element study of elastic filtration in soils with thin inclusions

Michuta¹,

Ivanchuk²,

Martyniuk³

et al. 2020

EEJET

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Soil environments are heterogeneous in their nature. This heterogeneity creates significant difficulties both in terms of construction practice and in terms of the mathematical modeling and computer simulation of the physical-chemical processes in these heterogeneous soil arrays. From the standpoint of mathematical modeling, the issue is the discontinuity of functions, which characterize the examined processes, on such inclusions. Moreover, the characteristics of such inclusions may depend on the defining functions of the processes studied (head, temperature, humidity, the concentration of chemicals, and their gradients). And this requires the modification of conjugation conditions and leads to the nonlinear boundary-value problems in heterogeneous areas. That is why this work has examined the impact of the existence of thin inclusions on the conjugation conditions for the defining functions of the filtration and geomigration processes on them. The conjugation condition for heads has also been modified while the mathematical model of an elastic filtration mode in a heterogeneous array of soil, which contains thin weakly permeable inclusions, has been improved. The improvement implies the modification of conjugation conditions for heads on thin inclusions when the filtering factor of the inclusion itself is nonlinearly dependent on the head gradient. The numerical solution to the corresponding nonlinear boundary-value problem has been found using a finite-element method. A series of numerical experiments were conducted and their analysis was carried out. The possibility of a significant impact on the head jump has been shown taking into consideration the dependence of filtration characteristics of an inclusion on head gradients. In particular, the relative difference of head jumps lies between 26 % and 99 % relative to the problem with a stable filtration factor for an inclusion. In other words, when conducting forecast calculations, the influence of such dependences cannot be neglected

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Geometric multigrid methods for Darcy–Forchheimer flow in fractured porous media

Cited by 16 publications

References 45 publications

Well Pattern and Well Spacing Optimization of Large Volume Water Injection in a Low-Permeability Reservoir with Pressure Sensitivity

Well Pattern and Well Spacing Optimization of Large Volume Water Injection in a Low-Permeability Reservoir with Pressure Sensitivity

The Temperature Field Evolution and Water Migration Law of Coal under Low-Temperature Freezing Conditions

A finite-element study of elastic filtration in soils with thin inclusions

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