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1.
A classification of mathematical models of laminar boundary layer suction is presented. The conditions of singular separation near the tip of a plate are analyzed and the optimal ejection rate distribution necessary for preventing this separation is found. It is shown that, by using inviscid-fluid ejection, it is possible to eliminate the pressure-gradient singularity, which is the cause of the singular separation, and the optimal ejection rate distribution near the edge necessary for this is found. With reference to an exact solution of the Navier-Stokes equations, the unseparated flow about a circle with ejection at the back holder is demonstrated. The flow structure in the presence of fluid injection into the boundary layer is discussed. 相似文献
2.
Although a lot of research has been done in modeling the oil recovery from fractured reservoirs by countercurrent imbibition, less attention has been paid to the effect of the fracture fluid velocity upon the rate of oil recovery. Experiments are conducted to determine the effect of fracture flow rate upon countercurrent imbibition. A droplet detachment model is proposed to derive the effective water saturation in a thin boundary layer at the matrix–fracture interface. This effective boundary water saturation is a function of fluid properties, fluid velocity in the fracture and fracture width. For a highly water–wet porous medium, this model predicts an increase in the boundary water saturation with increase in fracture fluid velocity. The increase in boundary water saturation, in turn, increases the oil recovery rate from the matrix, which is consistent with the experimental results. The model also predicts that the oil recovery rate does not vary linearly with the boundary water saturation. 相似文献
3.
We develop a semi-analytical model of transient fluid flow in a 2D layered permeable medium with cross-flow between adjacent layers. It is shown that the pressure satisfies a diffusion equation to leading order, even when the non-linear term and gravity are included in the mathematical model. The solution is based on an analytical expression in the transform domain for the fluid pressure in terms of interfacial flux functions; the algorithm to compute the flux functions accepts an arbitrary number of formation layers. We show some benchmark tests that validate the general model; the model is then applied to an example derived from experiments. Numerical experiments confirm the significance of the cross-flow in a particular scaling of the ratio of permeabilities and quantify the influence of the various physical parameters. 相似文献
4.
Fluid flow in a single rough-walled rock fracture has been extensively studied over the last three decades. All but few of these studies, however, have been done with Newtonian fluids and unidirectional flow in rectangular fractures. Notwithstanding the importance of such setups for theoretical understanding of fundamental issues in fracture flow, practical applications in drilling and petroleum engineering often involve radial flow of a non-Newtonian fluid. An example is a borehole intersecting a natural fracture during drilling in a fractured rock. In this study, steady-state incompressible radial flow from a circular well into a self-affine rough-walled fracture was simulated numerically using the lubrication theory approximation. The fluid rheology was power law. The flow behavior index was equal to 0.6, 0.8, 1.0 (Newtonian), 1.2, or 1.4. Asperities diverted the flow from an axisymmetric radial pattern that would be observed in a smooth-walled fracture. The extent of the deviation from radial flow was found to increase as the fluid became more shear-thickening. To reveal finer details of the flow, a tracer was introduced at the borehole wall and was transported by the flow. The front of the tracer propagating into the fracture was found to become slightly smoother with a more shear-thickening fluid. In the vicinity of contacts between fracture faces a more shear-thickening fluid could deliver the tracer closer to the contact spots. 相似文献
6.
One of the most popular models that has been applied to predict the fluid velocity inside the fracture with impermeable walls is the cubic law. It highlights that the mean flux along the fracture is proportional to the cubic of fracture aperture. However, for a fractured porous medium, the normal and tangential interface conditions between the fracture and porous matrix can change the velocity profile inside the fracture. In this paper, a correction factor is introduced for flow equation along the fracture by imposing the continuity of normal and tangential components of velocity at the interface between the fracture and porous matrix. As a result, the mean velocity inside the fracture depends not only on the fracture aperture, but also on a set of non-dimensional numbers, including the matrix porosity, the ratio of intrinsic permeability of fracture to that of matrix, the wall Reynolds number, and the ratio of normal velocity on one wall to the other. Finally, the introduced correction factor is employed within the extended finite element method, which is widely used for numerical simulation of fluid flow within the fractured porous media. Several numerical results are presented for the fluid flow through a specimen containing single fracture, in order to investigate the deviation from the cubic law in different case studies. 相似文献
7.
The pattern of the two-dimensional vortex flow of a nonhomogeneous fluid in a confined domain is studied using two-dimensional numerical calculations. It is found that in the case of a nonhomogeneous initial density distribution the kinetic energy decay rates are proportional to the square root of viscosity at the active stage of flow restructuring. The correlation functions of the velocity and the density are derived for different moments of time in the inertial range. All these results indicate the choice of the two-dimensional turbulence development scenario in a nonhomogeneous fluid. 相似文献
8.
The diffuse-interface (DI) model for the two-phase flow of a one-component fluid in a porous medium has been presented by Papatzacos [2002, Transport Porous Media 49, 139–174] and by Papatzacos and Skjæveland [2004, SPE J. (March 2004), 47–56]. Its main characteristics are: (i) a unified treatment of two phases as manifestations of one fluid with a van der Waals type equation of state, (ii) the inclusion of wetting, and (iii) the absence of relative permeabilities. The present paper completes the presentation by including the implementation of wetting in the general case of a mixed-wet rock. As a result of this implementation, some statements are made about capillary pressure, confirming similar statements by Hassanizadeh and Gray [1993, Water Resour. Res. 29, 3389–3405]. As an application of the model, we show that relative permeabilities depend on the spatial derivatives of the saturation. 相似文献
10.
The prediction of the free-surface seepage flow behavior in fractured rock mass is of significance in geotechnical engineering. There are two major issues in solving the seepage flow in complicated fractured rock mass based on the fractured porous medium (FPM) flow model, in which groundwater is assumed to flow simultaneously in both rock matrix and embedded fractures: One is the mesh generation of rock mass in the presence of the fracture network, especially when there exist a large number of stochastic fractures; the other is that a robust iteration algorithm is required since the free surface is unknown at the beginning of solution. Aiming at these two issues, this paper proposes a novel numerical method by coupling radial point interpolation method (RPIM) and finite element method (FEM), in which RPIM is utilized to model the rock matrix and FEM is utilized to model the fractures. On the basis of the variational inequality (VI) theory for free-surface seepage analysis, the computation formulations of the numerical method are derived and the corresponding computation program is developed. Three examples are solved with the present method. It is found that the VI theory can be extended to solve the free-surface seepage problem based on the FPM flow model. A crucial advantage of the present method is that the mesh generation can be greatly simplified. The present method has been verified to be a robust, efficient and reliable method for modeling the groundwater flow in complicated fractured rock mass. 相似文献
11.
The ideal fluid flow due to fluid penetration through the boundary of an infinitely long solid cylinder in contact with a
solid wall is determined. A formula is derived according to which the force exerted by a finite-length part of the cylinder
on the wall is directed into the wall and can thus have an arbitrarily large absolute value.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 82–84, January–February, 2006. 相似文献
12.
Fluid banks sometimes form during gravity-driven counter-current flow in certain natural reservoir processes. Prediction of
flow performance in such systems depends on our understanding of the bank-formation process. Traditional modeling methods
using a single capillary pressure curve based on a final saturation distribution have successfully simulated counter-current
flow without fluid banks. However, it has been difficult to simulate counter-current flow with fluid banks. In this paper,
we describe the successful saturation-history-dependent modeling of counter-current flow experiments that result in fluid
banks. The method used to simulate the experiments takes into account hysteresis in capillary pressure and relative permeabilities.
Each spatial element in the model follows a distinct trajectory on the capillary pressure versus saturation map, which consists
of the capillary hysteresis loop and the associated capillary pressure scanning curves. The new modeling method successfully
captured the formation of the fluid banks observed in the experiments, including their development with time. Results show
that bank formation is favored where the pc-versus-saturation slope is low. Experiments documented in the literature that exhibited formation of fluid banks were also
successfully simulated. 相似文献
13.
One-dimensional supersonic gas flow across an infinite permeable surface (obstacle of zero thickness) is investigated by the direct statistical simulation (Monte-Carlo) method. Both the characteristic features of the formation of a shock perturbation in the interaction between the plane supersonic flow and the permeable obstacle and the effect of the perturbation on the flow parameters behind the obstacle are found. It is concluded that the accommodation coefficient can be determined from the data on the equilibrium flow macroparameters behind the obstacle. 相似文献
14.
The paper presents the application of an advanced second moment closure (SMC) to the prediction of the flow field within stationary
and rotating square cross-sectioned ducts. The rotation number is 0.1 and the Reynolds number is 100,000. The SMC used satisfies
the two-component-limit and has been reported in literature to produce improvements in the prediction of a wide range of flows.
The computations were initially validated against existing experimental data, then used to obtain the various budget terms
for the Reynolds stresses. The aims of this work are to judge the performance of the advanced SMC and to gain insight into
the physics of rotation and its interaction with secondary flows based on the predicted Reynolds stress budgets for high Reynolds
number flows. It was found that the advanced SMC performs slightly better than a basic SMC, although neither model predicts
the flow on the suction side of the rotating duct well. On the pressure side computed budgets are similar to those obtained
in a significantly higher aspect ratio duct. On the suction side, however, the effects of the secondary flows are clearly
seen through a significant decrease of various budget terms, a feature not seen in a higher aspect ratio duct, and it thus
appears that the models do not entirely capture the interaction between the stabilizing rotation and secondary flow effects. 相似文献
15.
This work presents a similarity solution for boundary layer flow through a porous medium over a stretching porous wall. Two
considered wall boundary conditions are power-law distribution of either wall temperature or heat flux which are general enough
to cover the isothermal and isoflux cases. In addition to momentum, both first and second laws of thermodynamics analyses
of the problem are investigated. Independent numerical simulations are also performed for verification of the proposed analytical
solution. The results, from the two independent approaches, are found to be in complete agreement. A comprehensive parametric
study is presented and it is shown that heat transfer and entropy generation rates increase with Reynolds number, Prandtl
number, and suction to the surface. 相似文献
16.
We present an analysis for the process of fluid infiltration into a deformable, thin and permeable web that moves in close proximity over a rigid and stationary solid cylinder. While this is a process of significant interest in a range of coating, printing and composites pultrusion processes, its hydrodynamics have received limited attention in the open literature. The flow in the film separating the web from the cylinder is described by lubrication theory, while fluid transfer into the web is governed by Darcy’s law. The deformation of the web at each position is a linear function of the local gap pressure; this is consistent with the assumption of a thin and rigidly supported web. Our results indicate that the web/fluid interface is forced away from the cylinder surface as it approaches it and bounces back downstream from the minimum separation point. This behavior produces a non-symmetric gap between the adjacent surfaces, and this is shown to have critical influence on the final amount of penetrating fluid. The extent of fluid penetration is also found to be affected by the web elasticity (expressed by the dimensionless Ne number) and permeability (expressed in dimensionless form via \(\hat{{K}})\) where under a specific Ne and \(\hat{{K}}\) combination a maximum penetration depth is obtained. Finally, we derive a closed-form asymptotic solution for the final infiltration depth in the limit of Ne \(<<\) 1 and \(\hat{{K}}<<\)1 and test its predictions against the above-mentioned numerical results. 相似文献
17.
While it is generally assumed that in the viscous flow regime, the two-phase flow relative permeabilities in fractured and porous media depend uniquely on the phase saturations, several studies have shown that for non-Darcian flows (i.e., where the inertial forces are not negligible compared with the viscous forces), the relative permeabilities not only depend on phase saturations but also on the flow regime. Experimental results on inertial single- and two-phase flows in two transparent replicas of real rough fractures are presented and modeled combining a generalization of the single-phase flow Darcy’s law with the apparent permeability concept. The experimental setup was designed to measure injected fluid flow rates, pressure drop within the fracture, and fluid saturation by image processing. For both fractures, single-phase flow experiments were modeled by means of the full cubic inertial law which allowed the determination of the intrinsic hydrodynamic parameters. Using these parameters, the apparent permeability of each fracture was calculated as a function of the Reynolds number, leading to an elegant means to compare the two fractures in terms of hydraulic behavior versus flow regime. Also, a method for determining the experimental transition flow rate between the weak inertia and the strong inertia flow regimes is proposed. Two-phase flow experiments consisted in measuring the pressure drop and the fluid saturation within the fractures, for various constant values of the liquid flow rate and for increasing values of the gas flow rate. Regardless of the explored flow regime, two-phase flow relative permeabilities were calculated as the ratio of the single phase flow pressure drop per unit length divided by the two-phase flow pressure drop per unit length, and were plotted versus the measured fluid saturation. Results confirm the dependence of the relative permeabilities on the flow regime. Also the proposed generalization of Darcy’s law shows that the relative permeabilities versus fluid saturation follow physical meaningful trends for different liquid and gas flow rates. The presented model fits correctly the liquid and gas experimental relative permeabilities as well as the fluid saturation. 相似文献
18.
The transmissivity of a variable aperture fracture for flow of a non-Newtonian, purely viscous power-law fluid with behavior index n is studied. The natural logarithm of the fracture aperture is considered to be a two-dimensional, spatially homogeneous and correlated Gaussian random field. We derive an equivalent fracture aperture for three flow geometries: (1) flow perpendicular to aperture variation; (2) flow parallel to aperture variation; (3) flow in an isotropic aperture field. Under ergodicity, results are obtained for cases 1 and 2 by discretizing the fracture into elements of equal aperture and assuming that the resistances due to each aperture element are, respectively, in parallel and in series; for case 3, the equivalent aperture is derived as the geometric mean of cases 1 and 2. When n=1 all our expressions for the equivalent aperture reduce to those derived in the past for Newtonian flow and lognormal aperture distribution. As log-aperture variance increases, the equivalent aperture is found to increase for case 1, to decrease for case 2, and to be a function of flow behavior index n for case 3. 相似文献
19.
We present an analytical solution of axisymmetric motion for a Bingham fluid initially at rest subjected to a constant pressure gradient applied suddenly. Using the Laplace transform, we obtain expressions which allow the calculation of the instantaneous velocity, plug radius and rate of flow as a function of time. We also give a relation for the shear stress in the plug and in the region where the behaviour of the fluid is Newtonian. 相似文献
20.
In this article, we extend the work of Chakrabarti and Gupta (1979, Quart. Appl. Math., Vol. 37, pp. 73–78), and the work
of Pop and Na (1998, Mechanics Research Communications, Vol. 25, pp. 263–269) to a Darcy–Brinkman porous medium. 相似文献
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