Darcy processes

Keywords compressibility, primary-, secondary- and enhanced oil-recovery, drive mechanisms (solution gas-, gas cap-, water-drive), secondary gas cap, first production date, build-up period, plateau period, production decline, water cut, Darcy s law, recovery factor, sweep efficiency, by-passing of oil, residual oil, relative permeability, production forecasts, offtake rate, coning, cusping, horizontal wells, reservoir simulation, material balance, rate dependent processes, pre-drilling. 

The flow velocity, pressure and dynamic viscosity are denoted u, p and fj and the symbol (...) represents an average over the fluid phase. Kim et al. used an extended Darcy equation to model the flow distribution in a micro channel cooling device [118]. In general, the permeability K has to be regarded as a tensor quantity accounting for the anisotropy of the medium. Furthermore, the description can be generalized to include heat transfer effects in porous media. More details on transport processes in porous media will be presented in Section 2.9. 

The physical process of melt ascent during two-phase flow models is typically based on the separation of melt and solid described by Darcy s Law modified for a buoyancy driving force. The melt velocity depends on the permeability and pressure gradients but the actual microscopic distribution of the melt (on grain boundaries or in veins) is left unspecified. The creation of disequilibria only requires movement of the fluid relative to the solid. 

Leakage through a synthetic liner is controlled by Fick s first law, which applies to the process of liquid diffusion through the liner membrane. The diffusion process is similar to flow governed by Darcy s law except that it is driven by concentration gradients and not by hydraulic head. Diffusion rates in membranes are very low in comparison with hydraulic flow rates even in clays. In synthetic liners, therefore, the factor that most influences liner performance is penetrations. Synthetic liners may have imperfect seams or pinholes, which can greatly increase the amount of leachate that leaks out of the landfill. 

The processes of infiltration and evaporation of ground water depend strongly on the vertical profile of the soil layer. The following soil layers can be selected saturated and unsaturated. The saturated layer usually covers depths >lm. The upper unsaturated layer includes soil moisture around plants roots, the intermediate level, and the level of capillary water. Water motion through these layers can be described by the Darcy (1856) law, and the gravitation term KZ(P) in Equation (4.31) can be calculated by the equation ... 

From equation (14)i we could obtain the Darcy s law, if we neglect the inertial terms and the mass exchange and make suitable constitutive hypotheses on fields m,bf and Tf. The equation of balance (15)i for the volume fraction generalize the classical Langmuir s evolution equation, while the balance (15)2 for the microstretch Us includes the Wilmanski s porosity balance as well as the equation which rules the changes of internal surfaces area of the pores (see [8, 11, 1], respectively). The energy balance equations do not appear at all because the process is assumed to be isothermal. 

Liquid infiltration into dry porous materials occurs due to capillary action. The mechanism of infiltrating liquids into porous bodies has been studied by many researches in the fields of soil physics, chemistry, powder technology and powder metallurgy [Carman, 1956 Semlak Rhines, 1958]. However, the processes and kinetics of liquid infiltration into a powdered preform are rather complex and have not been completely understood. Based on Darcy s fundamental principle and the Kozeny-Carman equation, Semlak Rhines (1958) and Yokota et al. (1980) have developed infiltration rate equations for porous glass and metal bodies. These rate equations can be used to describe the kinetics of liquid infiltration in porous ceramics preforms, but... 

Consequently, for single component gases, which are nondissociated during the process, and a linear pressure drop across the porous media, this transport process follows Darcy law [16,19] ... 

In the simplest situation of a flow through a straight cylindrical pore, Darcy s law, based on the Hagen-Poiseuille equation, describes the process with the expression [73]... 

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). 

We note that our previous descriptions of flow processes have tacitly assumed laminar flow. For example, flow in capillaries was described by balancing pressure-derived forces against viscous forces, ignoring acceleration (inertial) effects. Darcy s law, Eq. 4.18, is also based on laminar flow. With turbulence, flow resistance increases the pressure gradient is no longer linearly related to flow (see Eqs. 4.18 through 4.20) but increases more rapidly as expressed by... 

Advection is the transport of dissolved contaminant mass due to the bulk flow of groundwater, and is by far the most dominant mass transport process [2]. Thus, if one understands the groundwater flow system, one can predict how advection will transport dissolved contaminant mass. The speed and direction of groundwater flow may be characterized by the average linear velocity vector (v). The average linear velocity of a fluid flowing in a porous medium is determined using Darcy s Law [2] ... 

According to the Darcy law in laminar flow of homogeneous liquids via a porous medium with the penetration factor Kp, the process of a liquid... 

Water Flux The permeability of a UF membrane is determined by pore size, pore density, and the thickness of the membrane active layer. Water flux is measured in the absence of solute, generally on a newly made or freshly cleaned sample. The test is simple, and involves passing water through the membrane generally in dead-end flow under carefully controlled conditions. In a water flux test, the membrane behaves as a porous medium with the flow described by Darcy s law. Adjustments for viscosity and pressure are made to correct tne results to standard conditions, typically the viscosity of water at 25°C and the pressure to 50 psi (343 kPa). The water flux will be many multiples ofthe process flux when the membrane is being used for a separation. Virgin membrane has a standard water flux of over 1 mm/sec. By the time the membrane is incorporated into a device and used in an application, that flux drops to perhaps 100 pm/s. Process fluxes are much lower. 

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. 

Frequently we define a porous medium as a solid material that contains voids and pores. The notion of pore requires some observations for an accurate description and characterization. If we consider the connection between two faces of a porous body we can have opened and closed or blind pores between these two faces we can have pores which are not interconnected or with simple or multiple connections with respect to other pores placed in their neighborhood. In terms of manufacturing a porous solid, certain pores can be obtained without special preparation of the raw materials whereas designed pores require special material synthesis and processing technology. We frequently characterize a porous structure by simplified models (Darcy s law model for example) where parameters such as volumetric pore fraction, mean pore size or distribution of pore radius are obtained experimentally. Some porous synthetic structures such as zeolites have an apparently random internal arrangement where we can easily identify one or more cavities the connection between these cavities gives a trajectory for the flow inside the porous body (see Fig. 4.30). 

Because it is difficult to account for changes in the properties of the reaction medium (e.g., permeability, thermal conductivity, specific heat) due to structural transformations in the combustion wave, the models typically assume that these parameters are constant (Aldushin etai, 1976b Aldushin, 1988). In addition, the gas flow is generally described by Darcy s law. Convective heat transfer due to gas flow is accounted for by an effective thermal conductivity coefficient for the medium, that is, quasihomogeneous approximation. Finally, the reaction conditions typically associated with the SHS process (7 2(XX) K and p<10 MPa) allow the use of ideal gas law as the equation of state. 

Today two models are available for description of combined (diffusion and permeation) transport of multicomponent gas mixtures the Mean Transport-Pore Model (MTPM)[21,22] and the Dusty Gas Model (DGM)[23,24]. Both models enable in future to connect multicomponent process simultaneously with process as catalytic reaction, gas-solid reaction or adsorption to porous medium. These models are based on the modified Stefan-Maxwell description of multicomponent diffusion in pores and on Darcy (DGM) or Weber (MTPM) equation for permeation. For mass transport due to composition differences (i.e. pure diffusion) both models are represented by an identical set of differential equation with two parameters (transport parameters) which characterise the pore structure. Because both models drastically simplify the real pore structure the transport parameters have to be determined experimentally. 

Numerical models for electrochemical process performance assessment or dimensioning generally assume uniform properties or one-dimensional property variations. For example, plug flow with axial dispersion is usually assumed within fdter-press electrolysers [1], whereas a Darcy flow model is commonly used within the gas diffusion layer of PEM electrolysers and fuel cells [2],... 

Note the similarity of this equation to the form of Fick s first law as shown in Eq. [1-4] the difference is that Darcy s law is for water flow while Fick s first law is for mass transport by Fickian processes.)... 

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