A comprehensive study of the effect of Brinkman flow on the performance of hydraulically fractured wells

Teng, Bailu; Luo, Wanjing; Chen, Zhuo; Kang, Botao; Chen, Ling; Wang, Tian-Yi

doi:10.1016/j.petrol.2022.110355

Cited by 7 publications

(3 citation statements)

References 20 publications

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“…The results revealed that the discrepancy is the largest in medium sands, coarse sands, and gravel, where the Brinkman Equation is required. An extreme condition is in fractured aquifers, and several studies have supported that the Brinkman Equation is more accurate for related study [45,46]. In addition, hierarchical porous media, like large-scale study domains with distinct aquifers, also result in rapid changes in velocities [28].…”

Section: Discussionmentioning

confidence: 99%

Comparing Darcy’s Law and the Brinkman Equation for Numerical Simulations of Saltwater Intrusion

Yao,

Zhang

2023

Sustainability

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Saltwater intrusion into coastal aquifers presents a significant global challenge to fresh groundwater resources. Numerical modelling represents a valuable tool to study this phenomenon. Darcy’s Law is widely applied to groundwater studies and is extended into the Brinkman Equation to account for kinetic dissipations due to viscous shear. However, their comparative performance and accuracy in density-driven flows remain unclear. To determine the circumstances where the Brinkman Equation is required, numerical simulations with both models were implemented in hypothetical coastal aquifer scenarios. The results revealed that the largest discrepancies between the two models occur inside the dispersion zone during the break-through period, with concentration differences of up to 2.5%. The mixing of freshwater and saltwater induces rapid density and velocity variations. Brinkman’s viscous term moderates the rate of change and decreases the intrusion length by up to 6.1 m in a 180 m intrusion case. Furthermore, higher permeability and a lower recharge rate both strengthen the viscous effects in most sandy coastal aquifers. The Brinkman Equation excels at capturing intricate flow patterns with large variations. Therefore, it is necessary to be employed for studies on freshwater–saltwater interfaces and other similar conditions including groundwater–surface water interfaces, non-isothermal flows, and complex geological conditions.

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Section: Discussionmentioning

confidence: 99%

Comparing Darcy’s Law and the Brinkman Equation for Numerical Simulations of Saltwater Intrusion

Yao,

Zhang

2023

Sustainability

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“…Their research also revealed that as the number of fractures increases, so does production, and when the fracture permeability increases, production also increases. Teng et al (2020) and Teng et al (2022) studied the effect of Brinkman flow on the performance of hydraulically fractured wells. They showed that the Stokes-Brinkman equation is more accurate in characterizing the fracture flow than the Darcy-Darcy model because it adaptively accounts for fractures or cavities where porosity approaches one and produces a smooth solution field.…”

Section: Introductionmentioning

confidence: 99%

Modeling fluid flow in fractured porous media: a comparative analysis between Darcy–Darcy model and Stokes–Brinkman model

Dudun,

Feng

2024

J Petrol Explor Prod Technol

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There are limited comparative studies on modeling fluid transport in fractured porous media. Hence, this paper systematically compares the steady-state creeping flow Stokes–Brinkman and Darcy–Darcy models for computational efficiency and accuracy. Sensitivity analyses were also conducted on the effect of fracture orientations, fracture sizes, mesh resolution, and fractures with Local Grid Refinement (LGR) under the FEniCS computational framework. Both models were validated numerically, and the accuracy of their solution is compared using the R-squared metric and L2 norm estimates. Key results showed that both models have similar pressure and velocity field solutions for a given fracture orientation. The computational time required for solving the Stokes–Brinkman models for a single fracture case was unusually lower than that of the Darcy–Darcy model when the pressure and velocity terms in the Darcy–Darcy model were solved simultaneously using two equations, contrary to where only one equation solves for the pressure and the velocity is obtained by projecting the gradient of pressure onto a vector space. The Stokes–Brinkman model is more sensitive to mesh resolution, and as a result, the Darcy–Darcy model tends to be more accurate than the Stokes–Brinkman model at low resolutions. Local Grid Refinement (LGR) can improve the Stokes–Brinkman model's accuracy at low mesh resolution. Furthermore, both models showed similar results when compared for complex fracture systems such as multiple fracture cases: interconnecting and isolated fractured porous media systems under low-velocity and steady-state creeping flow conditions. The FEniCS code in this paper is shared for future researchers to reproduce results or extend the research work.

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“…[1][2][3]. Compared with rock fracture, the permeability of tight matrix is negligibly due to the permeability of a fracture conventionally being several higher magnitudes than that of rock matrix, and the fracture controls the predominant pathways of fluid flow and solute transport through fractured rock masses [4][5][6]. Individual fractures are the basic element that constitutes the fracture network, and quantitative estimation of the permeability of single fractures is the foundation for understanding the fluid flow through complex natural fractured rock masses [7,8].…”

Section: Introductionmentioning

confidence: 99%

The Effect of Fracture Surface Roughness and Mechanical Aperture on the Onset of Nonlinear Flow Behaviors in 3D Self-Affine Rough Fractures

et al. 2022

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Equivalent hydraulic aperture and fracture surface roughness are two significant factors affecting the fluid flow behaviors in rock fractures. To understand the role of fracture surface roughness and aperture in the fluid flow through 3D self-affine rough fractures, roughness fracture surfaces with joint roughness coefficients equal to 2.5, 7.5, 12.5, and 17.5 were established, and the Navier–Stokes equation was used to compute the fluid flow in these 3D self-affine rough fractures with a mechanical aperture increase from 0.2 mm to 0.8 mm with a gradient of 0.2 mm. The results show that when the fracture mechanical aperture is 0.2 mm, the impact of fracture surface roughness on fluid flow is considerable, while this effect decreases obviously with the increase of fracture mechanical aperture. Comparing the permeability obtained by the Navier–Stokes equation with the cube law under different hydraulic gradients, we found that their deviation increased with the increase of hydraulic gradients. This allows for the definition of a critical hydraulic gradient ( J c ), below which the permeability can be properly predicted using the cubic law for its simplicity, and above which Forchheimer’s equation should be applied, and Forchheimer’s coefficients A , B , and J c can be calculated by the prediction equations established in this study.

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A comprehensive study of the effect of Brinkman flow on the performance of hydraulically fractured wells

Cited by 7 publications

References 20 publications

Comparing Darcy’s Law and the Brinkman Equation for Numerical Simulations of Saltwater Intrusion

Comparing Darcy’s Law and the Brinkman Equation for Numerical Simulations of Saltwater Intrusion

Modeling fluid flow in fractured porous media: a comparative analysis between Darcy–Darcy model and Stokes–Brinkman model

The Effect of Fracture Surface Roughness and Mechanical Aperture on the Onset of Nonlinear Flow Behaviors in 3D Self-Affine Rough Fractures

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