Process-scale models

Process-scale models represent the behavior of reaction, separation and mass, heat, and momentum transfer at the process flowsheet level, or for a network of process flowsheets. Whether based on first-principles or empirical relations, the model equations for these systems typically consist of conservation laws (based on mass, heat, and momentum), physical and chemical equilibrium among species and phases, and additional constitutive equations that describe the rates of chemical transformation or transport of mass and energy. These process models are often represented by a collection of individual unit models (the so-called unit operations) that usually correspond to major pieces of process equipment, which, in turn, are captured by device-level models. These unit models are assembled within a process flowsheet that describes the interaction of equipment either for steady state or dynamic behavior. As a result, models can be described by algebraic or differential equations. As illustrated in Figure 3 for a PEFC-base power plant, steady-state process flowsheets are usually described by lumped parameter models described by algebraic equations. Similarly, dynamic process flowsheets are described by lumped parameter models comprising differential-algebraic equations. Models that deal with spatially distributed models are frequently considered at the device... 

Industrial scale polymer forming operations are usually based on the combination of various types of individual processes. Therefore in the computer-aided design of these operations a section-by-section approach can be adopted, in which each section of a larger process is modelled separately. An important requirement in this approach is the imposition of realistic boundary conditions at the limits of the sub-sections of a complicated process. The division of a complex operation into simpler sections should therefore be based on a systematic procedure that can provide the necessary boundary conditions at the limits of its sub-processes. A rational method for the identification of the subprocesses of common types of polymer forming operations is described by Tadmor and Gogos (1979). 

Scale- Up of Electrochemical Reactors. The intermediate scale of the pilot plant is frequendy used in the scale-up of an electrochemical reactor or process to full scale. Dimensional analysis (qv) has been used in chemical engineering scale-up to simplify and generalize a multivariant system, and may be appHed to electrochemical systems, but has shown limitations. It is best used in conjunction with mathematical models. Scale-up often involves seeking a few critical parameters. Eor electrochemical cells, these parameters are generally current distribution and cell resistance. The characteristics of electrolytic process scale-up have been described (63—65). 

Physical modeling involves searching for the same or nearly the same similarity criteria for the model and the real process. The full-scale process is modeled on an increasing scale with the principal linear dimensions scaled-up in proportion, based on the similarity principle. For relatively simple systems, the similarity criteria and physical modeling are acceptable because the number of criteria involved is limited. For complex systems and processes involving a complex system of equations, a large set of similarity criteria is required, which are not simultaneously compatible and, as a consequence, cannot be realized. 

For a new process plant, calculations can be carried out using the heat release and plume flow rate equations outlined in Table 13.16 from a paper by Bender. For the theory to he valid, the hood must he more than two source diameters (or widths for line sources) above the source, and the temperature difference must be less than 110 °C. Experimental results have also been obtained for the case of hood plume eccentricity. These results account for cross drafts which occur within most industrial buildings. The physical and chemical characteristics of the fume and the fume loadings are obtained from published or available data of similar installations or established through laboratory or pilot-plant scale tests. - If exhaust volume requirements must he established accurately, small scale modeling can he used to augment and calibrate the analytical approach. 

Scale models are a real asset in the effective and efficient layout and sometimes process development of a plant. Although any reasonable scale can be used, the degree of detail varies considerably with the type of process, plant site, and overall size of the project. In some instances cardboard, wooden, or plastic blocks cut to a scale and placed on a cross-section scale board will serve the purpose. Other more elaborate units include realistic scale models of tlie individual items of equipment. These are an additional aid in visualizing clearances, orientation, etc. 

The introduction of computers to many companies allows proprietary software to be used for layout design. Spreadsheet, mathematical modeling and computer-aided design (CAD) techniques are available and greatly assist the design process, and have added to the resources available to planners. However, the traditional scale models described above will still be useful to present the result to management and shop floor personnel. 

Since electrochemical processes involve coupled complex phenomena, their behavior is complex. Mathematical modeling of such processes improves our scientific understanding of them and provides a basis for design scale-up and optimization. The validity and utility of such large-scale models is expected to improve as physically correct descriptions of elementary processes are used. 

Ideally, a mathematical model would link yields and/or product properties with process variables in terms of fundamental process phenomena only. All model parameters would be taken from existing theories and there would be no need for adjusting parameters. Such models would be the most powerful at extrapolating results from small scale to a full process scale. The models with which we deal in practice do never reflect all the microscopic details of all phenomena composing the process. Therefore, experimental correlations for model parameters are used and/or parameters are evaluated by fitting the calculated process performance to that observed. 

The second process, that of RGHg deposition together with particulate matter, has been addressed in various regional scale modeling studies for some time, but only recently has it been considered for direct measurement. Reactive gaseous Hg exhibits the characteristics of a so-called sticky gas and is cotmnonly modeled in the same fashion as nitric acid vapor (e.g., USEPA 1997 Bullock and Brehme 2002). 

System Representation Errors. System representation errors refer to differences in the processes and the time and space scales represented in the model, versus those that determine the response of the natural system. In essence, these errors are the major ones of concern when one asks "How good is the model ". Whenever comparing model output with observed data in an attempt to evaluate model capabilities, the analyst must have an understanding of the major natural processes, and human impacts, that influence the observed data. Differences between model output and observed data can then be analyzed in light of the limitations of the model algorithm used to represent a particularly critical process, and to insure that all such critical processes are modeled to some appropriate level of detail. For example, a... 

Since both the temperature dependence of the characteristic ratio and that of the density are known, the prediction of the scaling model for the temperature dependence of the tube diameter can be calculated using Eq. (53) the exponent a = 2.2 is known from the measurement of the -dependence. The solid line in Fig. 30 represents this prediction. The predicted temperature coefficient 0.67 + 0.1 x 10-3 K-1 differs from the measured value of 1.2 + 0.1 x 10-3 K-1. The discrepancy between the two values appears to be beyond the error bounds. Apparently, the scaling model, which covers only geometrical relations, is not in a position to simultaneously describe the dependences of the entanglement distance on the volume fraction or the flexibility. This may suggest that collective dynamic processes could also be responsible for the formation of the localization tube in addition to the purely geometric interactions. 

As already indicated, a physical description in terms of a process with a single time constant is fair but an assessment on the basis of two time-scales gives even improved results. Therefore, more research has to be carried out to determine the characteristics of the most important additional phenomena. As an example a two time-scale model is applied to the previously reported measurements of Fig. 8.3 and displayed in Fig. 8.4. Clearly, the release is governed by two rates, typically a smaller and a larger time scale appear compared with the single rate case. However, the single rate results are still very valuable because they describe the apparent rate very well and this would be the only thing that can be described in coarse scale models of devolatilization, e.g., in CFD of biomass conversion. 

Matthews et al. (2000a) have developed a field-scale model of emissions based on the above approach. In addition to the processes discussed above, the field-scale model allows for added organic matter and soil organic matter separately, and for the effects of inorganic terminal electron acceptors. Figure 8.4 shows that the model was capable of predicting seasonal emissions at a particular site from model parameter values measured independent of the emission data. 

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