Unit models heat exchangers

Finally the kiln type and design has to be included in the model size, insulation, operating temperatures and throughput in order to correctly dimension operational units (fans, heat exchanges) to optimize mill drying - and this involves a trade-off between flexibility, costs and befits. 

The job is not finished with steady state controllability analysis. Only dynamic simulation enables a reliable assessment of the control problem. The solution of the dynamic modelling depends on the dynamics of units involved in the control problem. Detailed models are necessary for the key units. The simplification of the steady-state plant simulation model to a tractable dynamic model, but still able to represent the relevant dynamics of the actual problem, is a practical alternative. Steady-state models can be used for fast units, as heat exchangers, or even chemical reactors with low inventory. 

These measurements can be made on actual operating units on line but they may also be done using model heat exchanger units or instrumented pipe loops run in parallel to system flow. Figure 10.12 shows such an instrumented pipe loop test unit with five parallel, instrumented pipe runs. Water flow from the target system is diverted through this unit, so that conditions are representative of the actual operating system [18]. 

At the first level of detail, it is not necessary to know the internal parameters for all the units, since what is desired is just the overall performance. For example, in a heat exchanger design, it suffices to know the heat duty, the total area, and the temperatures of the output streams the details such as the percentage baffle cut, tube layout, or baffle spacing can be specified later when the details of the proposed plant are better defined. It is important to realize the level of detail modeled by a commercial computer program. For example, a chemical reactor could be modeled as an equilibrium reactor, in which the input stream is brought to a new temperature and pressure and the... 

Suppose the overall heat transfer coefficient of a shell-and-tube heat exchanger is calculated daily as a function of the flow rates in both the shell and tube sides (ws and wt, respectively). U has the units of Btu/(h)(°F)(ft2), and ws and wt are in lb/h. Figures E2.3a and E2.3b illustrate the measured data. Determine the form of a semiempirical model of U versus ws and wt based on physical analysis. 

The formulation of objective functions is one of the crucial steps in the application of optimization to a practical problem. As discussed in Chapter 1, you must be able to translate a verbal statement or concept of the desired objective into mathematical terms. In the chemical industries, the objective function often is expressed in units of currency (e.g., U.S. dollars) because the goal of the enterprise is to minimize costs or maximize profits subject to a variety of constraints. In other cases the problem to be solved is the maximization of the yield of a component in a reactor, or minimization of the use of utilities in a heat exchanger network, or minimization of the volume of a packed column, or minimizing the differences between a model and some data, and so on. Keep in mind that when formulating the mathematical statement of the objective, functions that are more complex or more nonlinear are more difficult to solve in optimization. Fortunately, modem optimization software has improved to the point that problems involving many highly nonlinear functions can be solved. 

According to the three-step model (Figure 4), PBC system can ideally be defined as a complex process consisting of three consecutive subsystems (unit operations, functions) the conversion system (furthest upstream), the combustion (chamber) system, and the heat exchanger system (boiler system). The conversion system... 

Step (i) was proved in Appendix A of Floudas et al. (1986), and hence the minimum number of matches predicted by the MILP transshipment model can always be represented with an equal number of heat exchanger units in a feasible HEN network. 

Remark 3 Note that since we do not partition into subnetwork but treat the HEN problem as one network we may not have one-to-one correspondence between matches and heat exchangers units in the case of pinch point(s) taking place. In this case one match may have to take place in more than one (e.g., two) heat exchangers. This, however, can be remedied by simply postulating in the possible set of matches two heat exchangers for the matches that can take place across the pinch point(s) and let the optimization model identify whether there is a need for one, two or none of these units. 

FEHE Model There are no phase changes or small pinch temperatures in the heat exchanger. Therefore a 10-lump model is used for this unit. The steady-state exit temperatures predicted by the lumped model are close to those calculated by the rigorous countercurrent model used in the steady-state design. Table 7.2 compares the steady-state conditions for the process obtained from the dynamic model with those obtained in the steady-state design. 

Figure 2. Flow Sheet of the HPLC Unit for Rapid Protein Analysis. A binary gradient system with gradient controller, Model 21500 pumps,Model 2152 controller, Pharmacia, Piscataway, NJ, U.S.A. (A), Variable wavelength UV-Visible detector, Model LC 95, Perkin Elmer, Norwalk, CT, U.S.A (B), Constant temperature circulating bath, Model DL-8 Haake Buchler, Saddlebrook, NJ, USA (C), Heat exchangers (D), Sampling valve,...

Computer simulation models have been formulated for cascade and Stratco sulfuric acid alkylation units. These complete models incorporate mathematical descriptions of all the interacting parts of the units, including reactors, distillation columns, compressors, condensers, and heat exchangers. Examples illus-strate diverse model applications. These Include identifying profitable unit modifications, comparing cascade to Stratco performance, evaluating optimal unit capacity and determining optimal deisobutanizer operation. 

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