scholarly journals Does Rheology of Bingham Fluid Influence Upscaling of Flow through Tight Porous Media?

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 680
Author(s):  
Tong Liu ◽  
Shiming Zhang ◽  
Moran Wang
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Sample Size ◽  
Effective Permeability ◽  
Bingham Fluid ◽  
Newtonian Fluids ◽  
Absolute Permeability ◽  
Start Up ◽  
Flow Through ◽  
Tight Porous Media

Non-Newtonian fluids may cause nonlinear seepage even for a single-phase flow. Through digital rock technologies, the upscaling of this non-Darcy flow can be studied; however, the requirements for scanning resolution and sample size need to be clarified very carefully. This work focuses on Bingham fluid flow in tight porous media by a pore-scale simulation on CT-scanned microstructures of tight sandstones. A bi-viscous model is used to depict the Bingham fluid. The results show that when the Bingham fluid flows through a rock sample, the flowrate increases at a parabolic rate when the pressure gradient is small and then increases linearly with the pressure gradient. As a result, an effective permeability and a start-up pressure gradient can be used to characterize this flow behavior. By conducting flow simulations at varying sample sizes, we obtain the representative element volume (REV) for effective permeability and start-up pressure gradient. It is found that the REV size for the effective permeability is almost the same as that for the absolute permeability of Newtonian fluid. The interesting result is that the REV size for the start-up pressure gradient is much smaller than that for the effective permeability. The results imply that the sample size, which is large enough to reach the REV size for Newtonian fluids, can be used to investigate the Bingham fluids flow through porous media as well.

scholarly journals Behavior of viscoplastic rocks near fractures: mathematical modelling

2019 ◽  
Vol 489 (4) ◽  
pp. 362-367
Author(s):  
V. V. Shelukhin ◽  
A. E. Kontorovich
Keyword(s):  
Porous Medium ◽  
Pressure Gradient ◽  
Yield Stress ◽  
Bingham Fluid ◽  
Channel Width ◽  
Viscoplastic Fluid ◽  
Second Phase ◽  
Two Phase ◽  
Start Up ◽  
Flow Through

Starting from conservation laws and basic thermodynamic principles, we derive equations for a two-phase granular fluid. The first phase is the granular viscoplastic Bingham fluid and the second phase is the viscous Newtonian fluid. We perform an asymptotic analysis of the equations for the flows in the Hele-Show cell when the channel width is well much below its length. While calculating the fluid fluxes-pressure gradient relationship, we derive laws of flow of the two-phase granular viscoplastic fluid through porous media. A criterium is formulated for the start up of the granular phase flow through a porous medium. Given a yield stress, we prove that such a phase does not flow if either or both pressure gradient and channel width are small. We calculated phase flows varying phase viscosities, phase resistivities and yield stress. We reveal reasons which slow down particle intrusion into a porous medium.

A New Unified Diffusion—Viscous-Flow Model Based on Pore-Level Studies of Tight Gas Formations

SPE Journal ◽  
2012 ◽  
Vol 18 (01) ◽  
pp. 38-49 ◽  
Author(s):  
Mohammad R. Rahmanian ◽  
Roberto Aguilera ◽  
Apostolos Kantzas
Keyword(s):  
Porous Media ◽  
Viscous Flow ◽  
Flow Regime ◽  
Gas Flow ◽  
Flow Model ◽  
Molecular Flow ◽  
Single Element ◽  
Free Molecular Flow ◽  
Flow Through ◽  
Tight Porous Media

Summary In this study, single-phase gas-flow simulation that considers slippage effects through a network of slots and microfractures is presented. The statistical parameters for network construction were extracted from petrographic work in tight porous media of the Nikanassin Group in the Western Canada Sedimentary Basin (WCSB). Furthermore, correlations between Klinkenberg slippage effect and absolute permeability have been developed as well as a new unified flow model in which Knudsen number acts implicitly as a flow-regime indicator. A detailed understanding of fluid flow at microscale levels in tight porous media is essential to establish and develop techniques for economic flow rate and recovery. Choosing an appropriate equation for flow through a single element of the network is crucial; this equation must include geometry and other structural features that affect the flow as well as all variation of fluid properties with pressure. Disregarding these details in a single element of porous media can easily lead to flow misinterpretation at the macroscopic scale. Because of the wide flow-path-size distribution in tight porous media, a variety of flow regimes can exist in the equivalent network. Two distinct flow regimes, viscous flow and free molecular flow, are in either side of this flow-regime spectrum. Because the nature of these two types of flow is categorically different, finding/adjusting a unified flow model is problematic. The complication stems from the fact that the viscosity concept misses its meaning as the flow regime changes from viscous to free molecular flow in which a diffusion-like mechanism dominates. For each specified flow regime, the appropriate equations for different geometries are studied. In addition, different unified flow models available in the literature are critically investigated. Simulation of gas flow through the constructed network at different mean flow pressures leads to investigating the functionality of the Klinkenberg factor with permeability of the porous media and pore-level structure.

Cessation of Darcy regime in gas flow through porous media using LBM: Comparison of pressure gradient approaches

2017 ◽  
Vol 45 ◽  
pp. 693-705 ◽  
Author(s):  
Aliakbar Kakouei ◽  
Ali Vatani ◽  
MohammadReza Rasaei ◽  
Behnam Sedaee Sola ◽  
Hamed Moqtaderi
Keyword(s):  
Porous Media ◽  
Pressure Gradient ◽  
Gas Flow ◽  
Flow Through Porous Media ◽  
Flow Through

Oscillatory forcing of flow through porous media. Part 2. Unsteady flow

2002 ◽  
Vol 465 ◽  
pp. 237-260 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Flow Through Porous Media ◽  
Mean Flow ◽  
Two Fluids ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Numerical computations are employed to study the phenomenon of oscillatory forcing of flow through porous media. The Galerkin finite element method is used to solve the time-dependent Navier–Stokes equations to determine the unsteady velocity field and the mean flow rate subject to the combined action of a mean pressure gradient and an oscillatory body force. With strong forcing in the form of sinusoidal oscillations, the mean flow rate may be reduced to 40% of its unforced steady-state value. The effectiveness of the oscillatory forcing is a strong function of the dimensionless forcing level, which is inversely proportional to the square of the fluid viscosity. For a porous medium occupied by two fluids with disparate viscosities, oscillatory forcing may be used to reduce the flow rate of the less viscous fluid, with negligible effect on the more viscous fluid. The temporal waveform of the oscillatory forcing function has a significant impact on the effectiveness of this technique. A spike/plateau waveform is found to be much more efficient than a simple sinusoidal profile. With strong forcing, the spike waveform can induce a mean axial flow in the absence of a mean pressure gradient. In the presence of a mean pressure gradient, the spike waveform may be employed to reverse the direction of flow and drive a fluid against the direction of the mean pressure gradient. Owing to the viscosity dependence of the dimensionless forcing level, this mechanism may be employed as an oscillatory filter to separate two fluids of different viscosities, driving them in opposite directions in the porous medium. Possible applications of these mechanisms in enhanced oil recovery processes are discussed.

scholarly journals Review Of Applied Mathematical Models For Describing The Behaviour Of Aqueous Humor In Eye Structures

2015 ◽  
Vol 20 (4) ◽  
pp. 757-772
Author(s):  
M. Dzierka ◽  
P. Jurczak
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Aqueous Humor ◽  
Trabecular Meshwork ◽  
Newtonian Fluids ◽  
Flow Through Porous Media ◽  
Rheological Models ◽  
Proposed Model ◽  
Flow Through ◽  
Mathematical Equations

Abstract In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.

The Mechanism of Gas and Liquid Flow Through Porous Media in the Presence of Foam

1968 ◽  
Vol 8 (04) ◽  
pp. 359-369 ◽  
Author(s):  
L.W. Holm
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Liquid Flow ◽  
Effective Permeability ◽  
Mobility Ratio ◽  
Reservoir Rock ◽  
Porous System ◽  
Foam Flow ◽  
Surfactant Solutions ◽  
Flow Through

Abstract This study shows that in the presence of foam, gas and liquid flow separately through porous media representative of reservoir rock. These results were obtained by using tracer techniques to measure the flow of the gas and liquid comprising the foam. Foam does not flow through the porous medium as a body even when the liquid and gas are combined outside the system and injected as foam Instead the liquid and gas forming the foam separate as the foam films break and then re-form in the porous system. Liquid moves through the porous medium via the film network of the bubbles and gas moves progressively through the system by breaking and re-forming bubbles throughout the length of the flow path. The flow rates of the gas and liquid are a function of the number and strength of the films in the porous medium. There is no free flow of gas; i.e., no continuous gas phase. On the basis of these results, foam can be expected to improve a waterflood or gas drive by decreasing the permeability of the reservoir rock to a displacing liquid or gas. This improves the mobility ratio and thus the conformance of the flood. Introduction Foam is formed when gas and a solution of a surface active agent are injected into a porous medium either simultaneously or intermittently. During the past few years, several papers have been published on the subject of foam flow in porous media. Foam has been used successfully in the removal of capillary water blocks from producing formations. The use of foam in gas storage reservoirs to reduce gas leaks and to increase storage capacity has been considered in recent years. Foam has also been investigated as an oil displacing agent, and as an agent to improve the mobility ratio in a waterflood. However, the mechanism by which the gas and liquid phases comprising the foam flow through a porous medium has not been described adequately. Normally, when two immiscible phases (gas and liquid) flow concurrently through a porous medium, each phase follows separate paths or channels. At given saturations of the two phases, a certain number of channels are available to each phase, and as saturations change, the number and configuration of the channels available for each phase also change. The effective permeability of each phase is a function of the saturation of that phase only, and the flow of each phase can be described by Darcy's law. When foam is present, the effective permeability of the porous medium to each phase is greatly reduced compared with permeabilities measured in the absence of foam. Based upon the observed flow of surfactant solutions and gas in capillaries, it has been concluded that the gas and liquid may flow separately or they may flow combined as foam. At least four mechanisms have been postulated to explain how fluids flow with foam present:A large portion of the gas is trapped in the porous medium and a small fraction flows as free gas, following Darcy's law.The foam structure moves as a body; the rate of gas flow is the same as the rate of liquid flow.Gas flows as a discontinuous phase by breaking and re-forming films. Liquid flows as a free phase.A portion of the liquid and gas move as a foam body while excess surfactant solution moves as a free phase. It also has been suggested that different flow mechanisms exist for high quality (dry) foams made from dilute surfactant solutions and for foams made from more concentrated solutions. Studies conducted on the flow of foam through capillaries have shown that a plug-type flow occurs and that foam flows as a body.

scholarly journals Finite element and network electrical simulation of rotating magnetofluid flow in nonlinear porous media with inclined magnetic field and hall currents

2014 ◽  
Vol 41 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Anwar Bég ◽  
S. Rawat ◽  
J. Zueco ◽  
L. Osmond ◽  
R.S.R. Gorla
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Porous Media ◽  
Pressure Gradient ◽  
Hall Current ◽  
Shear Stresses ◽  
Inclined Magnetic Field ◽  
Current Parameter ◽  
Flow Through ◽  
Secondary Velocity

A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha), Hall current parameter (Nh), Darcy number (Da), Forchheimer number (Fs), Ekman number (Ek) and dimensionless pressure gradient parameter (Np), in addition to one geometric parameter-the orientation of the applied magnetic field (? ). Several special cases are extracted from the general model, including the non-porous case studied earlier by Ghosh and Pop (2006). A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of Ghosh and Pop (2006). for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease with an increase in Hall current parameter (Nh) with the converse observed for the secondary velocity.

scholarly journals Generalized lattice Boltzmann model for flow through tight porous media with Klinkenberg's effect

2015 ◽  
Vol 91 (3) ◽  
Author(s):  
Li Chen ◽  
Wenzhen Fang ◽  
Qinjun Kang ◽  
Jeffrey De’Haven Hyman ◽  
Hari S. Viswanathan ◽  
...  
Keyword(s):  
Porous Media ◽  
Lattice Boltzmann ◽  
Lattice Boltzmann Model ◽  
Flow Through ◽  
Tight Porous Media ◽  
Boltzmann Model ◽  
Klinkenberg’S Effect
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