Control volume, environmental modeling

Export processes are often more complicated than the expression given in Equation 7, for many chemicals can escape across the air/water interface (volatilize) or, in rapidly depositing environments, be buried for indeterminate periods in deep sediment beds. Still, the majority of environmental models are simply variations on the mass-balance theme expressed by Equation 7. Some codes solve Equation 7 directly for relatively large control volumes, that is, they operate on "compartment" or "box" models of the environment. Models of aquatic systems can also be phrased in terms of continuous space, as opposed to the "compartment" approach of discrete spatial zones. In this case, the partial differential equations (which arise, for example, by taking the limit of Equation 7 as the control volume goes to zero) can be solved by finite difference or finite element numerical integration techniques. 

The discussion above provides a brief qualitative introduction to the transport and fate of chemicals in the environment. The goal of most fate chemists and engineers is to translate this qualitative picture into a conceptual model and ultimately into a quantitative description that can be used to predict or reconstruct the fate of a chemical in the environment (Figure 27.1). This quantitative description usually takes the form of a mass balance model. The idea is to compartmentalize the environment into defined units (control volumes) and to write a mathematical expression for the mass balance within the compartment. As with pharmacokinetic models, transfer between compartments can be included as the complexity of the model increases. There is a great deal of subjectivity to assembling a mass balance model. However, each decision to include or exclude a process or compartment is based on one or more assumptions—most of which can be tested at some level. Over time the applicability of various assumptions for particular chemicals and environmental conditions become known and model standardization becomes possible. 

The construction of a mass balance model follows the general outline of this chapter. First, one defines the spatial and temporal scales to be considered and establishes the environmental compartments or control volumes. Second, the source emissions are identified and quantified. Third, the mathematical expressions for advective and diffusive transport processes are written. And last, chemical transformation processes are quantified. This model-building process is illustrated in Figure 27.4. In this example we simply equate the change in chemical inventory (total mass in the system) with the difference between chemical inputs and outputs to the system. The inputs could include numerous point and nonpoint sources or could be a single estimate of total chemical load to the system. The outputs include all of the loss mechanisms transport... 

The relationship of the thermal conductivities of fabrics and volume fractions of water in the interfiber spaces was expressed by a quadratic curve when the heat flow was normal to the fabric surface and by a straight line when the flow was parallel to the warp yarns. Except for hairy wool fabrics, the thermal conductivity of various wet fabrics may be calculated from the equations of Naka and Kamata (J3). An earlier investigation used an environmentally controlled room as a periodic heat source, and observed conductivities of 1-2 x 10 l cal/cm-sec °C for cotton, linen, and wool fabrics, and changes to 2-10 x 10 when the water content of these fabrics were increased ( ). After correcting for anisotropic effects, good agreement between actual conductivity measurements of wool fabrics and those calculated from a mathematical model of a random arrangement of fibers was observed. 

The fed-batch technique of cultivation is limited by fermenter volume because the volume of fermentation broth increases after each substrate addition. This disadvantage can be avoided by application a cyclic feeding strategy [9-11] which allows one to control the synchrony of individual cell development [9] by the limiting substrate concentration. The preliminary simulation results on a computer show that this type of environmental control of continuous production of exocellular hydrolytic enzymes based on our model is very promising. 

Organization and Overview. The book is divided into two volumes. The first contains 14 chapters, which cover the origin and characterization of petroleum, major processes for fuel-production, and environmental pollution control. The second volume contains 13 chapters, which focus on lubricants, hydrogen production, process modeling, automation, and refining management. 

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