Numerical simulation of hydro-mechanical coupling in fractured vuggy porous media using the equivalent continuum model and embedded discrete fracture model

Yan, Xiangqiao; Huang, Zhaoqin; Ye, Jun; Zhang, Zhao; Liu, Piyang; Yang, Li; Fan, Dongyan

doi:10.1016/j.advwatres.2019.02.013

Cited by 76 publications

(42 citation statements)

References 30 publications

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“…A composite high resolution scheme, known as the MINMOD scheme (Li et al, 2015;Moukalled et al, 2016), is used to reduce the undershoot and overshoot around the interface when the density ratio is large. A BICGSTAB method is used to solve the above variables (Yan et al, 2019;Zeng et al, 2019;Sheng et al, 2020). For variable-coefficient equations, matrices for the corresponding constant-coefficient systems are used as preconditioners.…”

Section: Governing Equationmentioning

confidence: 99%

Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities

Zhu

2020

Adv. Geo-Energ. Res.

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In this work, we present a hydrodynamics coupled phase-field surfactant model with variable densities. Two scalar auxiliary variables are introduced to transform the original free energy functional into an equivalent form, and then a new thermodynamically consistent model can be obtained. In this model, evolutions of two phase-field variables are described by two Cahn-Hilliard-type equations, and the fluid flow is dominated by incompressible Navier-Stokes equation. The finite difference method on staggered grid is used to solve the above model. Then a classical droplet rising case and a droplet merging case are used to validate our model. Finally, we study the effect of surfactants on droplet deformation and merging. A more prolate profile of droplet is observed under a higher surfactant bulk concentration, which verifies the effect of surfactant in reducing the interfacial tension. Increases in surface Péclet number and initial surfactant bulk concentration can enhance the non-uniformity of surfactant distribution around the interface, which will arise the Marangoni force. The Marangoni force acts as an additional repulsive force to delay the droplet merging.

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Section: Governing Equationmentioning

confidence: 99%

Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities

Zhu

2020

Adv. Geo-Energ. Res.

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“…A preconditioned biconjugate gradient stabilized method (BICGSTAB) is used to solve the above variables (Yan et al 2019;Zeng et al 2019).…”

Section: Dimensionless Governing Equation and Numerical Schemementioning

confidence: 99%

Thermodynamically consistent modelling of two-phase flows with moving contact line and soluble surfactants

et al. 2019

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Droplet dynamics on a solid substrate is significantly influenced by surfactants. It remains a challenging task to model and simulate the moving contact line dynamics with soluble surfactants. In this work, we present a derivation of the phase-field moving contact line model with soluble surfactants through the first law of thermodynamics, associated thermodynamic relations and the Onsager variational principle. The derived thermodynamically consistent model consists of two Cahn–Hilliard type of equations governing the evolution of interface and surfactant concentration, the incompressible Navier–Stokes equations and the generalized Navier boundary condition for the moving contact line. With chemical potentials derived from the free energy functional, we analytically obtain certain equilibrium properties of surfactant adsorption, including equilibrium profiles for phase-field variables, the Langmuir isotherm and the equilibrium equation of state. A classical droplet spread case is used to numerically validate the moving contact line model and equilibrium properties of surfactant adsorption. The influence of surfactants on the contact line dynamics observed in our simulations is consistent with the results obtained using sharp interface models. Using the proposed model, we investigate the droplet dynamics with soluble surfactants on a chemically patterned surface. It is observed that droplets will form three typical flow states as a result of different surfactant bulk concentrations and defect strengths, specifically the coalescence mode, the non-coalescence mode and the detachment mode. In addition, a phase diagram for the three flow states is presented. Finally, we study the unbalanced Young stress acting on triple-phase contact points. The unbalanced Young stress could be a driving or resistance force, which is determined by the critical defect strength.

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“…Based on the above advantages, 23,29-40 many scholars have performed numerous simulations using the EDFM, demonstrating its good adaptability for simulating fractured reservoirs. 23,[29][30][31][32][33][34][35][36][37][38][39][40] The EDFM can describe the interporosity flow between different media, so each cell is connected with different numbers and types of cells. To understand and record these connections 30 proposed the non-neighboring connection (NNC) method, and Jiang et al 31 proposed the connection list, but they did not study their methods further.…”

Section: Introductionmentioning

confidence: 99%

“…The EDFM uses an orthogonal structured grid for the mesh matrix, and the fractures are divided into a series of segments based on the boundary of the matrix cell. Based on the above advantages, 23,[29][30][31][32][33][34][35][36][37][38][39][40] many scholars have performed numerous simulations using the EDFM, demonstrating its good adaptability for simulating fractured reservoirs. The EDFM is very flexible for handing various kinds of intersections, such as fracture-fracture and fracture-well intersections 28 .…”

mentioning

confidence: 99%

“…These segments are the fracture grids in the EDFM. 23,[29][30][31][32][33][34][35][36][37][38][39][40] The EDFM can describe the interporosity flow between different media, so each cell is connected with different numbers and types of cells. The interporosity between two systems is calculated using the Peaceman-like formulation, which appears as the source/sink term in the governing equations.…”

mentioning

confidence: 99%

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Simulation of a multistage fractured horizontal well in a tight oil reservoir using an embedded discrete fracture model

Zhao

Liu

Zhang

et al. 2019

Energy Science & Engineering

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As an unconventional resource, tight oil reservoirs hold abundant geological reserves and great development potential. However, tight oil reservoirs suffer from high heterogeneity and low permeability. To obtain commercial oil and gas flow, multistage hydraulically fractured horizontal well technology is often adopted. In this paper, an embedded discrete fracture model (EDFM) is adopted to study the fractured reservoir. First, the relationship between the EDFM connection list is studied and its coefficient matrix of the equation system is solved. EDFM connection list is a method to record the connections between the grids. Thereafter, the reasons for the sparsity of the coefficient matrix and the symmetry of the locations of nonzero elements in the matrix are explained, and a simple method to establish and assemble the coefficient matrix is proposed. Using this method, a simulator for tight oil reservoir with EDFM is developed. By comparing the simulation results of the self‐programming simulator with the commercial software SAPHIR, the usefulness of the simulator is verified. Finally, several simulations and sensitivity analysis are performed to determine the key factors affecting production. Modeling studies show the influence of fractures, the horizontal well, and stress sensitivity, providing very useful information for the design of hydraulic fracturing and production development programs.

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Numerical simulation of hydro-mechanical coupling in fractured vuggy porous media using the equivalent continuum model and embedded discrete fracture model

Cited by 76 publications

References 30 publications

Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities

Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities

Thermodynamically consistent modelling of two-phase flows with moving contact line and soluble surfactants

Simulation of a multistage fractured horizontal well in a tight oil reservoir using an embedded discrete fracture model

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