Porous media flows

The framework for the solution of porous media flow problems was estabUshed by the experiments of Henri Darcy in the 1800s. The relationship between fluid volumetric flow rate, hydraulic gradient, and cross-sectional area, yi, of flow is given by the Darcy formula ... 

S. Sheppard, M. D. Mantle, A. J. Seder-man, M. L. Johns, L. F. Gladden 2003, (Magnetic resonance imaging study of complex fluid flow in porous media flow patterns and quantitative saturation profiling of amphiphilic fracturing fluid displacement in sandstone cores), Magn. Reson. Imag. 21, 365. 

Physical Parameters Affecting Particle Migration in Porous-Media Flow... 

Injection of highly acid or alkaline wastes has the potential to dissolve some reservoir rock to create channels that would allow more distant transport of small particles. Table 20.11 summarizes the various physical parameters that affect particle migration in porous-media flow. 

Porous media, flow through, 11 330-332, 766-767 25 290-291 Porous pipes, cross-flow filtration in,... 

Bolton EW, Lasaga AC, Rye DM (1996) A model for the kinetic control of quartz dissolution and precipitation in porous media flow with spatially variable permeability Eormulation and examples of thermal convection. J Geophys Res 101 22,157-22,187 Bolton EW, Lasaga AC, Rye DM (1997) Dissolution and precipitation via forced-flux injection in the porous medium with spatially variable permeability Kinetic control in two dimensions. J Geophys Res 102 12,159-12,172... 

With the average elongational strain rate of the flow field between the eddies and the relaxation time of the polymer molecules, one can define a dimensionless characteristic number, the Deborah number, which represents the ratio of a characteristic time of flow and a characteristic time of the polymer molecule, and thus one can transfer considerations in porous media flow to the turbulent flow region. 

Fig. 6. Schematic representation of examples of the elongational flow between two eddies in turbulent flow in comparison with porous media flow (Durst 1982)...

As Hashemzadeh s measurements in porous media flows have shown, the co-acrylates have a smaller elongational viscosity portion than the polyacrylamides, i.e., they are more easily deformed and their drag-increasing mechanism first comes into effect at smaller Reynolds numbers, although the value of the drag increase at this point is far smaller than for the polyacrylamides. 

Hassanizadeh, S.M. and Gray, W.G. (1980) General conservation equations for multiphase systems 3. Constitutive theory for porous media flow, Adv. Water Resources 3, 25-40... 

Gray, W.G. (1999) Thermodynamics and constitutive theory for multiphase porous-media flow considering internal geometric constraints, Advances in Water Resources 22(5), 521 -547... 

If a plane drawn in a porous media flow is considered, the velocity will not be uniform over the plane. There will be no flow where this plane intersects the solid particles,... 

The velocity component in the x-direction shown in Fig. 10.9 can, because the boundary layer is assumed to be thin, be taken as equal to the velocity at the surface, i.e., as equal to the velocity that would exist at the surface at the value of x considered in inviscid flow over the surface (see discussion in Section 10.3 above). The boundary layer form of the full energy equation for porous media flow is derived using the same procedure as used in dealing with pure fluid flows, this procedure having been discussed in Chapter 2. Attention will be restricted to two-dimensional flow. 

Because in the porous media flow model being used, the effects of viscosity are assumed to be negligible, the velocity will be uniform across the duct, i.e., the velocity will be equal to um everywhere and the cross-stream velocity component, v, will, therefore, be zero everywhere. It will further be assumed that the temperature gradients across the flow, i.e., in the v-direction, will be much greater than those in the z-direction because W < L, L being the length of the duct. With these assumptions, the governing equation, i.e., Eq. (10.34), reduces to ... 

Flow through a solid matrix which is saturated with a fluid and through which the fluid is flowing occurs in many practical situations. In many such cases, temperature differences exist and heat transfer, therefore, occurs. The extension of the methods of analyzing convective heat transfer rates that were discussed in the earlier chapters of this book to deal with heat transfer in porous media flows have been discussed in this chapter. Both forced and natural convective flows have been discussed. 

The book provides a comprehensive coverage of the subject giving a full discussion of forced, natural, and mixed convection including some discussion of turbulent natural and mixed convection. A comprehensive discussion of convective heat transfer in porous media flows and of condensation heat transfer is also provided. The book contains a large number of worked examples that illustrate the use of the derived results. All chapters in the book also contain an extensive set of problems. 

For incompressible and porous media flows we may follow the approaches of [239, 200] wherein the variations of the factor PkCp k within the averaging volume are neglected to enable application of the Leibnitz and Gauss averaging rules on the temperature and apparent flux terms. For this particular case the modified volume averaged enthalpy equation in terms of temperature can be deduced from (3.176) as follows ... 

Ligguet, J. A., P. L. F. Liu The boundary integral equation method for porous media flow, Allen Unwin, London (1983). 

Fig. 5. Arbitrarily generated porous media, flow paths and permeability bands in lattice units for non- Newtonian fluid (n=0.529) and different pressure gradients (F) are shown. We study porosities 64.8, 66.6%, 68.7%, 70.1%, 71.9%.

Characterization of dilute polyacrylamide and polystyrene solutions by means of porous media flow. 

Viscoelastic flow behaviour of dilute polymer solutions in porous media is described as a method for characterization of polymer-solvent-temperature systems. Porous media flow tests provide information on the solution state of polymer solutions and the molecular weight of the polymers used. Furthermore, flow-induced and thermally induced degradation effects - frequently observed in polymer solutions - can be characterized by the measurement of viscoelastic effects in flow through porous media. Decrease of molecular weight and changes of the conformation of macromolecules in solution are important parameters in these processes. 

For the present fluid-mechanical tests a homologous series of polyacrylamide (PAAm) samples was used whose mean weights, of the molar masses were determined by means of a low-angle laser-light-scattering photometer. The PAAm samples exhibit virtually the same molecular weight distribution Myy/Mn = 2.5 the intrinsic viscosity [ 7 1 was deter-minded in a Zimm-Crothers rotational viscometer, since the polymer solutions are subjected to a very low shear rate in this instrument. The porous media flow tests were carried out with the aid of an instrument such as described in Refs. [1, 2]. Reference is also made to these studies as regards the test procedure and evaluation of the measured data. 

Fig. 1 Porous-media flow behaviour of dilute PAAm solutions with different molecular weights...

If modified coefficients, Tjg and Deg, are used, as suggested in Refs. [1, 2] on the basis of the FENE dumbbell model. Fig. lb is obtained. The onset behaviour is described by the onset Deborah number, De o e,0 " with g 0 critical elongation rate of the porous media flow and T = relaxation time of the polymer solution, whilst the maximum value of the attainable increase of the extensional viscosity in normalized form only depends on the... 

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