Fluid and Energy Transport

Based on these principles, the concentrations of hydrocarbon contaminants in vapor extracted from a thermal treatment zone will increase with temperature. Further, the relative proportion of each component in the vapor phase is dependent on its volatility (Henry s law constant) and its concentration in the liquid phase. 

Volatilization of a chemical compound is controlled by its vapor pressure, ambient pressures (which vary with depth), and the partial pressures of associated chemicals and dissolved gases in groundwater. Vapor pressure increases with temperature (see Fig. 24.9), and ebullition occurs when the sum of the partial pressures of the chemical compound, water, and associated dissolved gases exceeds hydrostatic plus capillary pressures (Amos et al., 2005). That is, for ebullition to occur, bubbles must form under sufficient vapor pressure to rise to the water table and then overcome the capillary pressures to enter the vadose zone. As a result, evaporation or vaporization may occur below the pure-component boUtng point. 

Hydrolysis involves the chemical reaction with water, without regard to redox conditions, dissolved minerals, or the presence of soil microbes. For the reaction to take place, the organic compound needs to be dissolved in water, and the reaction can be modified by pH and/or temperature. The general hydrolysis reaction, involves the exchange of some functional group X (e.g. chloride, CT) with the hydroxide group in water  

While pH influences the rate of some hydrolysis reactions, there are few environmental situations where it can be used, resulting in temperature adjustment to be the most practical means to modify the reaction. Heating the subsurface from ambient temperatures to 80 °C will increase the hydrolysis rates of most organic compounds by a factor of greater than 1000. Heating to 100 °C will increase the rate of hydrolysis by a factor of over 10,000. 

Thermally enhanced hydrolysis is generally the most cost-effective remediation method for halogenated alkanes, and many funaigants and pesticides. A listing of common compounds with their hydrolysis half-lives at 100 °C is shown in Table 24.4. In situ thermal methods have been successfully used to hydrolyze 1,1,1-trichloroethane (TCA), 1,1,2,2-tetrachloroethane (TeCA), dichloromethane (methylene chloride), and ethylene dibronaide to remediate groundwater. 

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Other properties related to fluid and energy transport are viscosity, sorption, vapor transport, and hydrolysis. Gas viscosities will increase about 30 % with an increase of the temperature around 100 °C [28], facilitating transport through porous media. 

If we can expect that the eddy momentum and energy transport will both be increased in the same proportion compared with their molecular values, we might anticipate that heat-transfer coefficients can be calculated by Eq. (5-56) with the ordinary molecular Prandtl number used in the computation. It turns out that the assumption that Pr, = Pr is a good one because heat-transfer calculations based on the fluid-friction analogy match experimental data very well. For this calculation we need experimental values of C/ for turbulent flow. 

Bredehoeft, J.D. and D.L. Norton, 1990. Mass and energy transport in a deforming earth s crust. In The role of fluids in crustal processes. Studies in geophysics. National Academy Press, Washington, D.C., pp. 27-41... 

Problem 2-15. Derivation of Transport Equation for a Sedimenting Suspension. There are many parallels among momentum, mass, and energy transport because all three are derived from similar conservation laws. In this problem we derive a microscopic balance describing the concentration distribution (x, t) of a very dilute suspension of small particles suspended in an incompressible fluid undergoing unsteady flow. [Note cj>(. t) is the local volume fraction of particles in the fluid (i.e. volume of particles/volume of fluid) and hence is dimensionless. ... 

P. R. Greene, A Useful Approximation to the Error Function Applications to Mass, Momentum, and Energy Transport in Shear Layers, J. Fluids Engineering Vol. Ill, pp. 224-226,1989. 

Pollock, D., 1986. Simulation of fluid flow and energy transport processes associated with high-level radioactive waste deposal in unsaturated alluvium. Water Resources Research, Vol 22, N . 5, p. 765-775. 

All subchannel codes are used to solve mass, momentum and energy transport equations for turbulent fluid flow. Since the governing equations are very complicated, in each code simplifying assumptions are made to expedite solutions. Empirical input by either experimental data or analytical results is required for the codes to obtain reliable computer results. The correlations strongly depend on the geometry considered, the spacer concept (grids or wire-wraps), etc. 

FIGURE 1.13 Mass and energy transport processes (surface, line, and point membranes) (a) processes through surface membrane A — mass transport, B — energy transport, C — coupled mass transport, Vi,2 — bulk fluids. Pi, Cl, Ti, si, 0 2, Cb2 > P2. C2, T2, E2, C i, Cbi (b) processes over line membrane (two-dimensional gasses) Line membrane. Si and S2 — liquid surfaces (liquids 1.2) (c) processes over point membrane (one-dimensional gasses). Si, S2, S3 — surface membranes, Li, L2, L3 — line membranes. Pi — point membrane (foam), Pli, Cli, Tli, eli > Pl2, Cl2, Tl2, el2-... 

A chaotic flow produces either transverse homocHnic or transverse heterocHnic intersections, and/or is able to stretch and fold material in such a way that it produces what is called a horseshoe map, and/or has positive Liapunov exponents. These definitions are not equivalent to each other, and their interrelations have been discussed by Doherty and Ottino [63]. The time-periodic perturbation of homoclinic and heteroclinic orbits can create chaotic flows. In bounded fluid flows, which are encountered in mixing tanks, the homoclinic and heteroclinic orbits are separate streamlines in an unperturbed system. These streamhnes prevent fluid flux from one region of the domain to the other, thereby severely limiting mixing. These separate streamlines generate stable and unstable manifolds upon perturbation, which in turn dictate the mass and energy transports in the system [64-66]. 

In the thermal conduction sublayer near solid walls, a linear law can be used. In the turbulent near-wall region, Reynolds analogy between momentum and energy transport allows to derive a logarithmic law for the mean temperature, similar to (12.5-8). In general, the thickness of the thermal conduction layer differs from the thickness of the viscous sublayer and depends on the physicochemical properties of the fluid. The thermal sublayer thickness can be estimated from the intersection between the linear law and the logarithmic law. 

The general fluid properties can be described quite accurately in this way, but even the most sophisticated models are not able to describe or predict all cell properties precisely. This is because not all parameters are known well enough, and because particular porous materials often have anisotropic properties with respect to their structure and therefore also for their effective mass- and energy-transport properties. 

In this section we first review general modeling principles, emphasizing the importance of the mass and energy conservation laws. Force-momentum balances are employed less often. For processes with momentum effects that cannot be neglected (e.g., some fluid and solid transport systems), such balances should be considered. The process model often also includes algebraic relations that arise from thermodynamics, transport phenomena, physical properties, and chemical kinetics. Vapor-liquid equilibria, heat transfer correlations, and reaction rate expressions are typical examples of such algebraic equations. 

The moments form of the PBE is of the same dimensionality as the local fluid mechanical transport equations and can be solved side by side with the equations of continuity, momentum and energy transport to yield a complete mathematical description of the dispersion process [106]. However, the moment form of the PBE corresponds to an average macroscopic form of the PBE thus the microscopic phenomena are not resolved. Thus, for systems where the microscopic phenomena are important, it might be useful to chose a more fundamental modeling framework. 

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. 

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

Active Transport. Maintenance of the appropriate concentrations of K" and Na" in the intra- and extracellular fluids involves active transport, ie, a process requiring energy (53). Sodium ion in the extracellular fluid (0.136—0.145 AfNa" ) diffuses passively and continuously into the intracellular fluid (<0.01 M Na" ) and must be removed. This sodium ion is pumped from the intracellular to the extracellular fluid, while K" is pumped from the extracellular (ca 0.004 M K" ) to the intracellular fluid (ca 0.14 M K" ) (53—55). The energy for these processes is provided by hydrolysis of adenosine triphosphate (ATP) and requires the enzyme Na" -K" ATPase, a membrane-bound enzyme which is widely distributed in the body. In some cells, eg, brain and kidney, 60—70 wt % of the ATP is used to maintain the required Na" -K" distribution. 

Turbulent Diffusion FDmes. Laminar diffusion flames become turbulent with increasing Reynolds number (1,2). Some of the parameters that are affected by turbulence include flame speed, minimum ignition energy, flame stabilization, and rates of pollutant formation. Changes in flame stmcture are beHeved to be controlled entirely by fluid mechanics and physical transport processes (1,2,9). 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

Lipoprotein metabolism is the process by which hydrophobic lipids, namely triglycerides and cholesterol, are transported within the interstitial fluid and plasma. It includes the transport of energy in the form of triglycerides from intestine and liver to muscles and adipose, as well as the transport of cholesterol both from intestine and liver to peripheral tissues, as well as from peripheral tissues back to the liver. 

The Chemkin package deals with problems that can be stated in terms of equation of state, thermodynamic properties, and chemical kinetics, but it does not consider the effects of fluid transport. Once fluid transport is introduced it is usually necessary to model diffusive fluxes of mass, momentum, and energy, which requires knowledge of transport coefficients such as viscosity, thermal conductivity, species diffusion coefficients, and thermal diffusion coefficients. Therefore, in a software package analogous to Chemkin, we provide the capabilities for evaluating these coefficients. ... 

GHG emissions for milk packaging are mainly CO2 and arise from the energy used to process and produce the raw materials, container formation which is done on site in fluid milk plants and from transportation of the raw material (Irmovation Center for U.S. Dairy, 2008 Keoleian and Spitzley, 1999 Spitzley et ah, 1997). 

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