Darcy’s experiment

The term flow velocity sounds simple the distance the water moves in a unit of time. In this sense it is also handled by Darcy s experiment ... 

The term groundwater age sounds simple as well the time that has passed since a water parcel was recharged into the saturated water system. Or, in terms of travel time, the time that has passed since the water entered the ground until it reaches the point at which it is observed, for example, at a spring or a well. In a simplistic way one could compute the age of water (/) in Darcy s experiment by dividing the length of the flow path (Al) by the measured flow velocity (V) ... 

This brief discussion of the flow regime of an unconfined system emphasizes its three-dimensional nature and the large variety of water fluxes, velocities, and ages that prevail in each case study. The unconfined groundwater regime differs fundamentally from the one-dimensional tube of Darcy s experiment, with its particular properties (section 14.6). 

Lange, J.L. and Antohe, B.V. 2000. Darcy s experiments and the deviation to nonlinear flow regime. ASME Journal of Fluids Engineering, 122 619-25. 

The theory of laminar flow through homogeneous porous media is based on a classical experiment originally performed by Darcy in 1856. Darcy s experiment is described in Fig. 10. The total volume of the fluid percolating through the fixed bed, Q, can be expressed in terms of the height of the bed and the bed area as... 

In this equation ut should be interpreted as the volumetric flux density (directional flow rate per unit total area). The indexes range from 1 to 3, and repetition of an index indicates summation over that index according to the conventional summation convention for Cartesian tensors. The term superficial velocity is often used, but it is in our opinion that it is misleading because n, is neither equal to the average velocity of the flow front nor to the local velocity in the pores. The permeability Kg is a positive definite tensor quantity and it can be determined both from unidirectional and radial flow experiments [20], Darcy s law has to be supplemented by a continuity equation to form a complete set of equations. In terms of the flux density this becomes ... 

The steady-state flow numerical experiment was primarily designed to evaluate the phasic relative permeability relations. The numerical experiment is devised within the two-phase lattice Boltzmann modeling framework for the reconstructed CL microstructure, generated using the stochastic reconstruction technique described earlier. Briefly, in the steady-state flow experiment two immiscible fluids are allowed to flow simultaneously until equilibrium is attained and the corresponding saturations, fluid flow rates and pressure gradients can be directly measured and correlated using Darcy s law, defined below. 

Experiments were conducted by Darcy (1856) to study viscous flows through homogeneous porous media, which resulted in the well-known Darcy law. There are various models from which Darcy s law may be derived to describe gas flow through a packed bed... 

Figure 5.13. Schematic diagram of Darcy s filtration experiment (from Darcy, 1856).

The mean free path, /, of the C02 molecules at the temperatures and pressures of the permeation experiment are by far smaller than the membrane pore size, d, that is, d, /.. Then, Knudsen flow is not possible since the determining process is gaseous laminar flow through the membrane pores [18]. It is therefore feasible to apply Darcy s law for gaseous laminar flow (Equations 10.19 through 10.23). 

The purpose of this study is to develop a simple model which retains some of the features of the above complex process to predict the lay-up thickness as a function of time during the squeeze-flow lamination of circular prepreg lay-ups. The prepreg of interest is of the type commonly adopted in the board manufacturing industry. It is composed of two outer resin layers and a fabric core constructed of interlaced yarns oriented in two directions perpendicular to each other (Figure 1). The fabric core is treated as a porous slab characterized by a constant Darcy permeability coefficient (see k in Darcy s law% i.e.. Equation 2 below) which can be estimated from fabric parameters such as the yarn diameter and the pitch distances. The lay-up thickness predictions provided by this model have been found to be in reasonable agreement with experiment for the lamination of up to five epo.xy prepreg layers. 

The population balance simulator has been developed for three-dimensional porous media. It is based on the integrated experimental and theoretical studies of the Shell group (38,39,41,74,75). As described above, experiments have shown that dispersion mobility is dominated by droplet size and that droplet sizes in turn are sensitive to flow through porous media. Hence, the Shell model seeks to incorporate all mechanisms of formation, division, destruction, and transport of lamellae to obtain the steady-state distribution of droplet sizes for the dispersed phase when the various "forward and backward mechanisms become balanced. For incorporation in a reservoir simulator, the resulting equations are coupled to the flow equations found in a conventional simulator by means of the mobility in Darcy s Law. A simplified one-dimensional transient solution to the bubble population balance equations for capillary snap-off was presented and experimentally verified earlier. Patzek s chapter (Chapter 16) generalizes and extends this method to obtain the population balance averaged over the volume of mobile and stationary dispersions. The resulting equations are reduced by a series expansion to a simplified form for direct incorporation into reservoir simulators. 

Note that even though the velocity distribution is known, the corresponding permeability values cannot be computed directly from Darcy s law (Eq. 2), since the pressure gradient at locations within the medium is not known. Nevertheless, the permeability distribution can be determined as that function for which calculated velocity values corresponding to the mathematical model of the experiment most closely match those values actually obtained. In this section, we describe this inverse problem. 

RF transmission and reception of the NMR signal. For the stimulated pulse sequence, three hard pulses were used with the spin-warp sequence as discussed in Section 3.1. It is also necessary to obtain images corresponding to the porosity distribution as described in Section 2, in addition to the velocity images. This is because the images obtained in the velocity experiment are measures of the intrinsic velocity, the actual velocity of the fluid within the pore space. Darcy s law, however, is written in terms of the superficial velocity. The two velocities are simply related by the porosity ... 

Darcyf" carried on a series of experiments involving the flow of water through sand placed in a vertical iron pipe and found the flow rate to be proportional to the head of pressure, which is called Darcy s law as expressed by the following equation... 

Another measure of length is the equivalent hydraulic radius, rh, determined inversely from saturated or unsaturated flow experiments. By comparing Darcy s equation with Poiseuille s law, and invoking a capillary bundle model, one obtains the following definition of rh (Kutflek Nielsen, 1994),... 

Thus, the units of this effective viscosity are centipoises (Pa-s). The effective viscosity is not the actual viscosity of any real fluid, it is the viscosity of a virtual fluid simulating the combined flow of C02 and surfactant—brine through reservoir rock. The effective viscosity is a number that can be used in Darcy s law, along with the absolute permeability of the rock, to give the ratio of pressure gradient to superficial flow rate. In particular, the effective viscosity defined previously is not to be used with any assumed value of the relative permeability of dense C02 in the rock. As will be seen, experiments show that this effective viscosity is not constant, but changes in value as a number of other parameters of the flow are varied. 

It has been well established by experiment that for low Reynolds number flow through porous media the pressure drop follows Darcy s law. In one dimension Darcy s law may be written... 

ABSTRACT In order to investigate the effect of coal particle size on gas desorption and diffusion law at constant temperature, the constant temperature dynamic coal particle gas adsorption and desorption experiment with different particle sizes was conducted in the coal gas adsorption and desorption experiment system. The results suggest that gas desorption laws of different particle size of coal samples show a good consistency at different pressures, and the cumulative desorption of gas coal particle is linear with time. For the same particle, the higher the initial pressure, the more the maximum gas desorption the smaller the coal particle is, the more quickly the gas desorption rate is at the same initial pressure. Then, the gas spherical flow mathematical model is built based on Darcy law and is analysed with finite difference method. At last, the gas spherical flow mathematical model is constructed with Visual Basic. The contrast between numerical simulation and experimental results shows that the gas flow in the coal particle internal micropore accords with Darcy s law. 

The fluid di lacement experiments were conducted under different conditions of gas injection and types of the porous media. In order to be consistent in the analysis of the results, the flow of the injected gas has been treated according to Darcy s law. Darcy s law for the gas phase flowing in a linear system is given as follows (43). 

Sonicated emulsion results at 35 C as a function of phase ratio and salt concentration further show that the behavior of these emulsions in the porous media is different from those at 25°C. Even three phase systems give relatively more stable emulsions and possess non-Newtonian behavior. Hysteresis effect shown by some emulsions in porous media experiments is highlighted. The nature of emulsions produced by sonication and by the shearing of liquids in the porous media is contrasted. Extensive physical property data for these emulsions are also given. The applicability of Darcy s law for the present situation is discussed. 

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