non-Darcy Flow Research Articles

Analyses of entropy generation and Hall influence in the Cattaneo–Christov double diffusive radiative Non-Darcy flow of a Casson nanofluid within rotating disks

The present research work interprets the entropy generation in the magnetohydrodynamic multiple slip flow of Casson nanofluid initiated due to stretching and coaxially rotating surfaces of two disks inside a non-Darcy porous medium under the dominance of the diacritic Hall current and heat generation. The energy field is explored by incorporating the consequences of distinctive thermal radiation, viscous dissipation, and Joule heating. The present study overcomes the barrier of heat and mass transport by annexing Cattaneo–Christov double diffusion effects. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with multiple slip boundary conditions. A compatible similarity transformation comprised in the current study is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via dispensing the successive linearization method. The present article deals with an in-depth exploration of diagnostic flow parameters’ attributes against the flow field and efficient physical quantities with the help of distinctive graphs and tables. As per regression analysis, the maximum relative error for the regression model on the skin friction coefficient in the radial direction ranging from .0097236 to .017225% is less than that of the other physical quantities. Besides, augmenting the thermophoretic diffusion boosts diluting the concentration of nanoparticles.

A reinterpreted discrete fracture model for Darcy–Forchheimer flow in fractured porous media

We propose a novel hybrid-dimensional model for the Darcy–Forchheimer flow in fractured rigid porous media, with a natural applicability to non-conforming meshes. Motivated by the previous work on the reinterpreted discrete fracture model (RDFM) for Darcy flows, we extend its key idea to non-Darcy flows. Coupling the Darcy’s law in the matrix and the Forchheimer’s law in the fractures through the introduction of the Dirac-δ functions to characterize the fractures, we derive a relationship between the total flow velocity in the porous media and the fluid velocity in the fractures. With this relation, it is natural to model the Darcy–Forchheimer flow in the whole computational domain by one equation. The local discontinuous Galerkin (LDG) method is applied for numerical discretization of the steady-state single-phase flow problem and a time-marching method is adopted to find the solution of the resulting nonlinear system. Besides, we construct a direct solver for the nonlinear equation of the fluid velocity in fracture to save computational cost. As an application, we discuss a simple transport model coupled with the flow equation. Several numerical experiments validate the performance of the model with its effectiveness on non-conforming meshes. We observe that the Darcy–Forchheimer model effectively reduce the flow rates and make the predictions more realistic in case of excessive fracture velocities.

An XFEM-based hydro-mechanical model to consider the non-Darcy flow in complex fracture networks

Geotechnical instability and failure are closely related to the hydro-mechanical coupled behavior of fractured rocks, and the existing studies often regard the fracture seepage as linear Darcy flow. Due to the neglect of non-Darcy effect caused by rough rock wall and high flow velocity, the estimated rock deformation and seepage flow can lead to incorrect assessment of geotechnical risks. Hence, this study proposed an efficient and robust hydro-mechanical (HM) coupled model to consider non-Darcy flow in complex fracture networks. The fractured rock mass's mechanical response, including the fracture surface's frictional contact, was calculated using the XFEM solver, and the widely used Forchheimer's law was adopted to describe the non-Darcy flow along the fractures. The fracture segments cut by mechanical element edges are considered one-dimensional flow elements, and the Newton-Raphson iteration method is adopted to solve the Forchheimer equation directly. To consider the influence of fracture deformation on the conductivity of fractures, the Barton-Bandis model was adopted to determine the hydraulic aperture of the fractures when the fracture was closed. Subsequently, a staggering Newton-Raphson method can be developed to decouple the fracture deformation and fluid flow process. Experimental results were adopted to validate the accuracy of the numerical model, and several numerical cases were used to illustrate the efficiency and robustness of the proposed model. The effects of inlet pressure, confining stress, and non-Darcy effect on the HM-coupled behavior of fractured rock were investigated. Numerical results suggested that the distribution of fluid pressure and failure process of rock mass based on Darcy assumption could be dramatically changed after considering the nonlinear seepage behavior.

Well Test Analysis for a Well in Gas Storage Reservoirs With the Formation Containing High Salinity Water

Abstract The production capacity of the gas wells is seriously affected by salt deposition during the injection and production process for underground gas storage with high salt content, so it is necessary to predict the production performance through well test technology. However, the existing well test analysis methods cannot be reliably used to interpret the well test data affected by salt deposition phase change and high-speed non-Darcy flow during the injection and production process. Therefore, this paper first determines the relationship between salt deposition and temperature and pressure through flash calculation of phase equilibrium of saltwater and hydrocarbon system, then establishes a porosity and permeability model considering the effect of salt deposition, and further establishes a high-speed injection-production well test analysis model considering the effect of salt deposition in combination with Forchheimer’s percolation law. Finally, the model is solved by numerical method, and the dynamic changes of reservoir pressure and salt deposition are simulated and calculated. The results show that the higher the salinity of formation water is, the greater the risk of salt deposition in the reservoir is, and the permeability of the reservoir will significantly decrease after salt deposition occurs; the non-Darcy flow effect will aggravate the risk of salt deposition in the reservoir. The research results provide a theoretical method for the evaluation of reservoir parameters and production performance prediction of salt gas storage reservoirs.

Injectivity assessment for CCS field-scale projects with considerations of salt deposition, mineral dissolution, fines migration, hydrate formation, and non-Darcy flow

This paper aims to review the main mechanisms identified in the lab scale that impact CO2 injectivity during CCS projects in saline aquifers and evaluate their relevance in field scale through numerical models. They may include water vaporization, salt precipitation in the dry-out zone, mineral dissolution, which can result in fines migration in porous media, CO2 hydrate formation, and effects of non-Darcy flow. All those mechanisms are observed from lab experiments and significantly impact reservoir petrophysical properties such as porosity and permeability and consequently on injectivity in field operations. This study includes these mechanisms in numerical models to quantify their impacts on the CO2 injectivity well index in synthetic and real field cases. In addition, a sensitivity analysis was performed for a range of brine compositions of seawater and higher salinities. This analysis shows an additional injectivity reduction as the salinity increases due to the halite scale, in agreement with the lab data from the literature. Another dependence evaluated in this study is when the ratio between capillary and viscous forces is decreased, reducing the injectivity. Additionally, when mineral reaction dissolution is considered in our modeling, it is possible to observe two occurring competitive phenomena, where the mineral dissolution can compensate for part of the injectivity loss due to salt deposition in the dry-out zone. That is especially relevant when the reservoir rock matrix is rich in reactive minerals, such as calcite and dolomite. However, mineral dissolution may lead to fines, and the risk of fines migration can lower the injectivity by at least 10% within five years of CO2 injection, according to our results. The mineral dissolution is also considered in these calculations, and the loss in injectivity is the net result of dissolution and fines migration. The gain in porosity–permeability as the results of mineral dissolution was modeled using the Kozeny-Carman equation. The results show the importance of considering the uncertainty of injectivity loss in CCS projects, where the amount of CO2 captured for storage must be injected often with no other alternatives, highlighting the need to provide flexibility in project planning to deal with such risks.

Three-dimensional non-Darcy free convective heat transfer flow in a bidisperse porous medium within a cubical cavity

Heat transport in porous media, especially in a bidisperse porous matrix, has recently received considerable attention due to its diverse real-life applications in applied science and engineering. In the current study, we employ the Darcy-Brinkman-Forchheimer model and three temperature equations incorporating the local thermal nonequilibrium conditions among the fluid and the porous matrix to examine the three-dimensional free convective heat transfer flow in a bidisperse permeable matrix inside a cubical cavity. The Galerkin weighted residual finite element method simulates the model's non-dimensional governing equations. We examine the effects of the significant model parameters on the flow and heat domains considering (104 ≤ Raf ≤ 106), (103 ≤ Rap ≤ 106), (10−3 ≤ Daf ≤ 10−1), (10−4 ≤ Dap ≤ 10−2),(0.7 ≤ ϕ ≤ 0.9) and (0.4 ≤ ε ≤ 0.7). It is found that the average Nusselt number in the macrophase, microphase, and solid matrix increased with the increase of the macro porosity for about 7.18%, 7.06%, and 9.86%, respectively, when it rises from 0.7 to 0.9. Furthermore, increasing the micro-porosity enhances the rate of heat transfer. As the Raleigh number advances, there is a noticeable increase in heat transfer in both the macrophase and the microphase.

New correlations for non-Darcy flow in porous media

New correlations for non-Darcy flow in porous media

Investigation of unsteady non-Darcy flow through rockfill material using Saint–Venant equations and particle swarm optimization (PSO) algorithm

Investigation of unsteady non-Darcy flow through rockfill material using Saint–Venant equations and particle swarm optimization (PSO) algorithm

Influence of 3D Fracture Geometry on Water Flow and Solute Transport in Dual-Conduit Fracture

The geometry of the fracture exerts an important impact on the flow of the fractures and the transport of the solutes. Herein, Forchheimer’s law and the weighted-sum ADE (WSADE) model were alternatively employed, and the obtained pressure gradient versus discharge curves for the fitting reveal that Forchheimer’s law adequately described the non-Darcy flow behavior and the robust capability of WSADE in capturing the non-Fickian transport in dual-conduit fractures (DCFs). Different boundary layer effects brought about obvious differences in water flow and solute transport trends between 2D and 3D fractures. Moreover, with the change in the distance between the main conduit and the diversion conduit, the hydraulic parameters were correlated with the fitting parameters in Forchheimer’s law and WSADE. The solute mixing process is dramatically altered by the results, which directly demonstrate major flow patterns at the intersection. The prediction of solute transport in naturally fractured rocks depends primarily on the depicted flow and its effects on mixing. The findings help to increase the understanding of transport processes in such systems, especially for characterizing the dual-peaked BTCs obtained in aquifers.

A three-dimensional numerical pressure transient analysis model for fractured horizontal wells in shale gas reservoirs

Shale gas development has greatly contributed to the world's energy supply. Pressure transient analysis (PTA) has extremely helped the development of shale gas. In this paper, a three-dimensional numerical model for transient pressure analysis of multi-stage fractured horizontal wells (MFHWs) in shale gas reservoirs was proposed, which was based on the embedded discrete fracture model (EDFM). The adsorption effect of shale gas, stress sensitivity of shale reservoir, and high-velocity non-Darcy flow in fractures were considered in this model, and the model was solved by Matlab Reservoir Simulation Tool (MRST). The discrete process of governing equations is described in detail, the typical MFHW pressure transient response curve of a shale gas reservoir was obtained, different flow regimes were divided, and three-dimensional pressure distribution profile of different flow stages were drawn to clearly understand the flow states of shale gas in the reservoir. The effects of different flow mechanisms and fracture properties on the log–log curves of the MFHW pressure transient response were analyzed in detail. The numerical PTA model proposed in this paper not only considers a variety of complex flow mechanisms of shale gas, but also accurately describes the characteristics of complex fracture network of shale reservoirs in three-dimensional conditions through EDFM. In addition, the problems of the incomplete description of shale gas flow stages by conventional analytical methods and semi-analytical methods were avoided through the numerical solution. The pressure response behavior of fluid in shale gas reservoir can be better explained by using this model, which helps to reduce the uncertainty of shale reservoir development.

One‐dimensional nonlinear creep consolidation of soft soils with time‐dependent drainage boundary under construction load

AbstractTo further investigate the nonlinear creep properties of soft soils and the effect of variable loading, a one‐dimensional (1D) nonlinear creep consolidation system of soft soils under construction load is established, including time‐dependent drainage (TDD) boundary, elastic‐viscous‐plastic deformation, non‐Darcy flow (NDF), and self‐weight stress. The consolidation problem is presented by virtue of the finite volume method, and the associated calculation program is compiled. The efficiency of the numerical solutions is validated by comparing the degenerated solution against analytical, semi‐analytical, and numerical solutions. Then the influences of construction load and nonlinear creep model parameters on consolidation are studied. The results show that TDD boundary and construction load significantly affect consolidation, and the larger the loading rate and interface parameter, the faster soil's overall dissipation process of excess pore‐water pressure (EPP). Meanwhile, at the earlier consolidation stage, considering the secondary consolidation effect will cause an increase in excess pore‐water pressure (EPP). Prolonging the construction period, decreasing the interface parameter, considering the self‐weight stress, or increasing the non‐Newtonian index will all aggravate this phenomenon. Additionally, the TDD boundary, construction load, and non‐Newtonian index flow (NNIF) are not a determinant for final soil settlement.

Potential influences of leakage through a high permeability path on shallow aquifers in compressed air energy storage in aquifers

The potential leakage influences of compressed air energy storage in aquifers, especially on the overlying shallow aquifer environment, need more attention, but there is still a lack of relevant studies. In this research, a coupled wellbore-reservoir underground anticline model is simulated using T2Well/EOS3. Two-phase non-Darcy flows, different from the multiphase Darcy flow in porous media, are considered in both the central working wellbore and a highly permeable leakage path. In an anticline, the results show that the leakage rate will decline and reach a relatively steady state as the cycles continue. The final continuous small periodic oscillations of leakage rate occur with a hysteresis effect with respect to cycle injection-production. When air leakage occurs in the initial gas bubble process, it gradually disappears and gets replaced by brine leakage. A decrease in the reservoir permeability can result in a larger initial leakage rate, but a smaller rate and fluctuation during the cycle process. However, in a horizontal reservoir, strong gas fingering increases the risk of air leakage, which, once occurs, can last during the rest of the process. This research can deepen the understanding of the leakage process and help evaluate and prevent incidents of environmental contamination in gas storage in aquifers.

Numerical simulation of single-phase two-component non-Darcy flow in naturally fractured reservoirs for enhanced gas recovery and carbon dioxide storage

Numerical simulation of single-phase two-component non-Darcy flow in naturally fractured reservoirs for enhanced gas recovery and carbon dioxide storage

Entropy generation in magnetohydrodynamic radiative non-Darcy slip flow of a Casson nanofluid with Hall effects and activation energy

The present research work examines the entropy generation in the magnetohydrodynamic second-order slip flow of Casson nanofluid surpassing a horizontal stretching sheet inside a non-Darcy porous medium under the dominance of Hall current and nonlinear thermal radiation. The present model is made more realistic by taking second-order velocity slip flow. The energy field is pursued by incorporating the consequences of distinctive viscous dissipation and Joule heating. The chemical reaction incited by activation energy is comprised in the current exploration. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with second-order velocity slip and convective boundary conditions. A compatible similarity transformation comprised is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via the spectral quasi-linearization method. The present article deals with an in-depth exploration of the characteristics of diagnostic flow parameters against the-flow field and other efficient physical quantities with the help of distinctive graphs and tables. As per the regression analysis, the maximum relative error for the reduced Nusselt number ranging from .000090231% to .00015936% is less than that of the other physical quantities. Magnetic force, thermophoresis, and Brownian motion assist in lessening the heat transport rate, but it gets enriched under the Hall current effects. For the increasing Casson parameter, fluid movement tends to rise near the sheet’s surface and gets decelerated afterwards. The intense Hall current accelerates the Casson fluid’s motion. But the velocity components in xandz-directions become abated across the flow region due to increasing the first-order velocity slip parameter. Besides, the enhancement in the magnitude of the second-order velocity slip parameter undermines the velocity components in xandz-directions.

RSM-based sensitivity analysis of hybrid nanofluid in an enclosure filled with non-Darcy porous medium by using LBM method

The emphasis of this study is the numerical analysis via D2Q9-based Lattice Boltzmann Method of free convection MHD non-Darcy flow in hybrid nanofluid (TiO2/Cu–water) occupying a differentially heated square enclosure. A key novelty of the work is the inclusion of a response surface methodology (RSM)-based sensitivity analysis. The current investigation has been done considering the variation in Rayleigh number (103 ≤ Ra ≤ 106), Darcy number (0.0001 ≤ Da ≤ 0.1), and Hartmann number (0 ≤ Ha ≤ 50). From RSM, high Darcy parameter, low volumetric fraction, and low Hartmann number are identified as the optimum functioning conditions for heat transfer rates.

Investigating to chemically reactive and radiative Darcy/non-Darcy stagnation point flow of ternary composite nanofluids with moderate Prandtl numbers

ABSTRACT In this study, the Darcy or non-Darcy stagnation point flow and thermal analysis of ternary composite nanofluids with modest Prandtl numbers across stretched surfaces that are susceptible to slip or no-slip environments are examined. The concept of non-linear thermal radiation is brought into play. It has been decided to apply non-linear slip. Homogeneous and heterogeneous chemical reactions, or HHCRs, make the flow problem harder to solve. Along with the shooting method, the Runge–Kutta method of the fourth order is an important part of the numerical solution needed for the non-dimensional and non-linear system of partial differential equations. In slip and no slide, both the amplified porosity parameter and the Forchheimer number work to slow down the speed of the fluid. In a medium that may be Darcy or non-Darcy, an increase in the slip parameter causes the fluid velocity and temperature to sputter and stop. When Darcy and non-Darcy media and slip and no-slip conditions are taken into account, surface viscous drag goes down as the strength of the porous matrix goes up, heat transfer rate goes down as the Brinkman number goes up, and mass transfer rate goes up as the homogeneous reaction rate parameter goes up.

Mass-loss effects on the non-Darcy seepage characteristics of broken rock mass with different clay contents

A seepage testing system was designed and a series of seepage experiments on broken rock was conducted using different original porosity conditions and clay contents. The mass-loss process of the broken rock and the change in water flow velocity were investigated. After the mass-loss test, the non-Darcy seepage characteristics of the broken rock were tested through a step-by-step pressure-reduced seepage test. The experimental results show that the mass-loss and water velocity evolution during the water inrush could be divided into four stages: acceleration, stable with slight fluctuations, reacceleration, and stable. The lost-mass and change in water velocity were positively correlated with the clay contents and negatively correlated with the original porosity. By introducing the evolution equation of the Kozeny-Carman equation and the liquid limit index which characterises the effective particle size, the prediction model of the permeability coefficient was built. Six prediction models of the non-Darcy coefficient were verified against the testing results. The prediction model of the critical flow velocity from a Darcy flow to a non-Darcy flow using the Forchheimer number was also established. The results could provide an important reference for understanding water inrush mechanisms, adopting effective control measures for water inrush events, and calculating the water influx of tunnels.

One-Dimensional Nonlinear Consolidation for Soft Clays with Continuous Drainage Boundary Considering Non-Darcy Flow

Adopting the non-Darcy flow presented by Hansbo and considering the nonlinear compression and permeability characteristics of soils, the one-dimensional nonlinear consolidation problem of soft clays is investigated by means of a continuous drainage boundary. The numerical solutions of average consolidation degrees defined by settlement and excess pore water pressure are derived by using the finite difference method, and the correctness of these solutions is verified by comparing them with existing analytical and numerical solutions. Based on the proposed solutions, a parametric study is conducted to study the influence of interface parameter, non-Darcy flow parameter and soil nonlinearity on the consolidation behavior of soft clays. The results show that the solutions based on the continuous drainage boundary can be degenerated into the solutions based on the Terzaghi drainage boundary if the interface parameter is taken as a reasonable value. The soil consolidation behavior considering both non-Darcy seepage and nonlinear characteristics of soil is very complex.

Adoption of Homotopy Perturbation Method (HPM) for non-Darcy Flow in Porous Media

For non-Darcy flow in coarse porous media, an analytical solution based on the Homotopy Perturbation Method (HPM) is proposed. Subsurface water profile data of a laboratory model are used for six different inlet discharges in both rounded and crushed coarse porous media types. The model slope is S = 0.00001 close to the horizon. Different upstream and downstream water level boundary conditions are considered. The results of the analytical solution of non-Darcy flow by the HPM method are compared with experimental data. The normal objective function (NOF) is used for better comparison between the results of analytical solutions and experimental data. Results depict that the HPM method provides acceptable solutions in both rounded and crushed media types. The analytical results of flow rates q = 26.25 lit/s with NOF of 0.000294586 percent in rounded porous media and q = 30 lit/s with NOF of 0.00028660 percent in crushed one are the most consistent with the experimental data. The proposed HPM solution performs very well, particularly at higher flow rates, in both rounded and crushed porous media.

A Negative Value of the Non-Darcy Flow Coefficient in Pore-Fracture Media under Hydro-Mechanical Coupling

The Forchheimer equation is widely used in studying non-Darcy flow. Non-Darcy flow coefficient β in the Forchheimer equation is generally thought to be positive, and there are few studies on negative values. In this work, we performed seepage tests on sandstone samples with single, T-shaped, and Y-shaped fractures under different confining pressures, water pressures, and angles to analyze the nonlinear seepage behaviors and the features of Forchheimer’s coefficients of water flow in pore-fracture media. At the same time, the flow trajectory of the fluid inside the sample is studied by numerical simulation. The results showed that β was negative in the seepage test in pore-fracture media. The angle of the single-fracture sandstone sample had a greater influence on the seepage characteristic of the pore-fracture media; angles of the sandstone samples with T-shaped and Y-shaped fractures had a relatively small impact. The relationship between β and inherent permeability k was following a power function, and the differences in the seepage characteristics between the three fractures were compared. The use of the normalized hydraulic conductivity method is used to evaluate the applicability of Darcy’s law. Finally, we explained the primary cause of non-linear seepage behaviors with negative β in fractured sandstone samples.