Transport in Porous Media
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The Riemann Solution for the Injection of Steam and Nitrogen in a Porous Medium
Transport in Porous Media - Tập 81 Số 3 - Trang 505-526 - 2010
Correction to: Darcy–Brinkman–Forchheimer Model for Film Boiling in Porous Media
Transport in Porous Media - Tập 138 - Trang 695-696 - 2021
A correction to this paper has been published: https://doi.org/10.1007/s11242-021-01631-0
Experimental Investigation of Fluid Through Porous Media Packed with Single-Diameter and Multi-diameter Spheres
Transport in Porous Media - Tập 110 - Trang 449-459 - 2015
Both Newtonian fluid flow and power-law non-Newtonian fluid flow through porous media composed of single-diameter and multi-diameter spheres were studied experimentally. The pressure drop characteristics for the packed beds with single-diameter spheres were validated well by theoretical models. For the packed beds containing spheres with two different sizes and three different sizes, three types of mean diameters were examined in the theoretical model, and the mass mean diameter is recommended as the effective diameter based on the present experimental data.
Addressing the Influence of a Heterogeneous Matrix on Well Performance in Fractured Rocks
Transport in Porous Media - Tập 117 - Trang 69-102 - 2017
We address the influences of heterogeneity and complex geology of the matrix of fractured rocks on transient flow. Fractional constitutive flux laws reflect the stochastic framework that we consider. We model transient diffusion in both the matrix and fracture systems in terms of a continuous time random walk. Our procedure is particularly suited to address a complex geology that may exist on a number of scales and which may include dead ends and discontinuities. The performance of a horizontal well produced through arbitrarily located, multiple hydraulic fractures with distinct properties (length, width, permeability) forms the basis for our thesis. The pressure distribution in a rectangular drainage region where the well may be placed arbitrarily is expressed in terms of the Laplace transformation. The required solutions are obtained numerically. The focus of our work is on long-term behaviors for production at a constant pressure. In addition to numerical solutions, asymptotic results that provide information on the structure of the solutions are presented. Agreement between the asymptotic and numerical solutions is excellent. We show that long-term responses are governed by two distinct, two-parameter Mittag–Leffler functions and are an outcome of the complexities we desire to model in both the matrix and fracture systems. As a consequence, power-law behaviors that reflect the heterogeneity inherent in the system define long-time expectations. We show that the new solutions we derive do reduce to those of classical diffusion; that is, results corresponding to classical diffusion are a subset of the new results obtained here. Our results are particularly suited to model transient flow in shale reservoirs.
Stress Dependency of Permeability Represented by an Elastic Cylindrical Pore-Shell Model: Comment on Zhu et al. (Transp Porous Med (2018) 122:235–252)
Transport in Porous Media - Tập 127 - Trang 573-585 - 2018
Stress dependency of permeability of porous rocks is described by means of a theoretical elastic cylindrical pore-shell model. This model is developed based on a bundle of elastic capillary tubes representation of the preferential flow paths formed in heterogeneous porous rocks. The radial displacement caused in tubes by the pore fluid pressure applied over the surface of the elastic cylindrical flow tubes is expressed by a Lamé-type equation. The radial displacement is incorporated into the Kozeny–Carman relationship to determine the variation of the permeability of porous rocks by variation of the pore fluid pressure. The solution of this equation yields a semi-analytical equation which provides accurate correlations of the stress dependency of the permeability data of porous rocks. The errors associated with the previous formulation of this problem by Zhu et al. (Transp Porous Med 122:235–252, 2018) are explained in view of the present formulation.
Numerical Simulation of Forced Convective Heat Transfer Past a Square Diamond-Shaped Porous Cylinder
Transport in Porous Media - Tập 102 - Trang 207-225 - 2014
Fluid flow and heat transfer around and through a porous cylinder is an important issue in engineering applications. In this paper a numerical study is carried out for simulating the fluid flow and forced convection heat transfer around and through a square diamond-shaped porous cylinder. The flow is two-dimensional, steady, and laminar. Conservation laws of mass, momentum, and heat transport equations are applied in the clear region and Darcy–Brinkman–Forchheimer model for simulating the flow in the porous medium has been used. Equations with the relevant boundary conditions are numerically solved using a finite volume approach. In this study, Reynolds and Darcy numbers are varied within the ranges of
$$1
Optimization for Early-Warning Monitoring Networks in Well Catchments Should Be Multi-objective, Risk-Prioritized and Robust Against Uncertainty
Transport in Porous Media - Tập 114 - Trang 261-281 - 2015
Groundwater abstraction wells are commonly protected by zones of restricted land use. Such well protection areas typically cannot cover the entire well catchment, and numerous risk sources remain. Each risk source could release contaminants at any time, affect the well earlier or later, and thus put the quality of supplied water at risk. In this context, it seems fortunate that most well catchments are equipped with monitoring networks. Such networks, however, often grew historically while following diverse purposes that changed with time. Thus, they are often inadequate (or at least suboptimal) as reliable risk control mechanism. We propose to optimize existing or new monitoring networks in a multi-objective setting. The different objectives are minimal costs, maximal reliability in detecting recent or future contaminant spills, and early detection. In a synthetic application scenario, we show that (1) these goals are in fact competing, and a multi-objective analysis is suitable, (2) the optimization should be made robust against predictive uncertainty through scenario-based or Monte Carlo uncertainty analysis, (3) classifying the risk sources (e.g., as severe, medium, almost tolerable) is useful to prioritize the monitoring needs and thus to obtain better compromise solutions under budgetary constraints, and (4) one can defend the well against risk sources at unknown locations through an adequate model for the residual risk. Overall, the concept brings insight into the costs of reliability, the costs of early warning, the costs of uncertainty, and into the trade-off between covering only severe risks versus the luxury situation of controlling almost tolerable risks as well.
Seismic Reflection from an Interface Between an Elastic Solid and a Fractured Porous Medium with Partial Saturation
Transport in Porous Media - Tập 85 - Trang 375-396 - 2010
The theory of Tuncay and Corapcioglu (Transp Porous Media 23:237–258, 1996a) has been employed to investigate the possibility of plane wave propagation in a fractured porous medium containing two immiscible fluids. Solid phase of the porous medium is assumed to be linearly elastic, isotropic and the fractures are assumed to be distributed isotropically throughout the medium. It has been shown that there can exist four compressional waves and one rotational wave. The phase speeds of these waves are found to be affected by the presence of fractures, in general. Of the four compressional waves, one arises due to the presence of fractures in the medium and the remaining three are those encountered by Tuncay and Corapcioglu (J Appl Mech 64:313–319, 1997). Reflection and transmission phenomena at a plane interface between a uniform elastic half-space and a fractured porous half-space containing two immiscible fluids, are analyzed due to incidence of plane longitudinal/transverse wave from uniform elastic half-space. Variation of modulus of amplitude and energy ratios with the angle of incidence are computed numerically by taking the elastic half-space as granite and the fractured porous half-space as sandstone material containing non-viscous wetting and non-wetting fluid phases. The results obtained in case of porous half-space with fractures, are compared graphically with those in case of porous half-space without fractures. It is found that the presence of fractures in the porous half-space do affect the reflection/transmission of waves, which is responsible for raising the reflection and lowering the transmission coefficients.
The Onset of Convection in a Layered Porous Medium with Vertical Throughflow
Transport in Porous Media - Tập 98 - Trang 363-376 - 2013
An analytical investigation of the effect of vertical throughflow on the onset of convection in a composite porous medium consisting of two horizontal layers has been made. The cases of iso-flux and iso-temperature boundaries are both investigated. The critical Rayleigh number depends on a Péclet number
$$Q$$
, a permeability ratio
$$K_{r}$$
, a thermal conductivity ratio
$$k_{r}$$
, and a depth ratio
$$\delta $$
. For the case of small
$$Q$$
an approximate solution is obtained, which shows that in general throughflow has a stabilizing effect whose magnitude may be increased or decreased by the heterogeneity. This solution is supplemented by an asymptotic solution valid for large
$$Q.$$
Stability of Thermal Convection in a Fluid-Porous System Saturated with an Oldroyd-B Fluid Heated from Below
Transport in Porous Media - Tập 99 - Trang 327-347 - 2013
A linear stability analysis is conducted for thermal convection in a two-layer system composed of a fluid layer overlying a porous medium saturated with an Oldroyd-B fluid heated from below. It is found that the convection pattern in the system is controlled by the porous medium when the ratio of the depth of the fluid layer to that of the porous medium is small. However, the fluid layer takes a predominant role if the depth ratio exceeds a critical value. Compared with stationary convection, the switching point from a porous-dominated mode to a fluid-dominated mode for oscillatory convection is located at a lower depth ratio. The effects of different parameters on stationary convection and oscillatory convection are also investigated in detail.
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