Flow diagrams qualitative

Using the qualitative stability analysis from the flow diagram as outlined in 1.7.3 and 6.1.5, we find the following pattern. For conditions where there is a single stationary state, it is always stable to perturbations in regions of multiple solutions, the uppermost and lowest are stable whilst the middle... 

The previous two chapters have considered the stationary-state behaviour of reactions in continuous-flow well-stirred reactions. It was seen in chapters 2-5 that stationary states are not always stable. We now address the question of the local stability in a CSTR. For this we return to the isothermal model with cubic autocatalysis. Again we can take the model in two stages (i) systems with no catalyst decay, k2 = 0 and (ii) systems in which the catalyst is not indefinitely stable, so the concentrations of A and B are decoupled. In the former case, it was found from a qualitative analysis of the flow diagram in 6.2.5 that unique states are stable and that when there are multiple solutions they alternate between stable and unstable. In this chapter we become more quantitative and reveal conditions where the simplest exponential decay of perturbations is replaced by more complex time dependences. 

The chemical engineer uses flow diagrams to show the sequence of equipment and unit operations in the overall process, to simplify visualization of the manufacturing procedures, and to indicate the quantities of materials and energy transfer. These diagrams may be divided into three general types (1) qualitative, (2) quantitative, and (3) combined-detail. 

A qualitative flow diagram indicates the flow of materials, unit operations involved, equipment necessary, and special information on operating temperatures and pressures. A quantitative flow diagram shows the quantities of materials required for the process operation. An example of a qualitative flow diagram for the production of nitric acid is shown in Fig. 2-1. Figure 2-2 presents a quantitative flow diagram for the same process. 

Qualitative flow diagram for the manufacture of nitric acid by the ammonia-oxidation process. 

Figure 2-1 presents a qualitative flow diagram for the manufaeture of nitrie acid by the ammonia-oxidation proeess. Figure 2-2 presents a quantitative flow diagram for the same proeess. With the information from these two figures, prepare a quantitative energy balanee for the proeess and size the equipment in suffieient detail for a preliminary cost estimate. 

Table 1.1 is a list of the commonly used continuous separation operations based on interphase mass transfer. Symbols for the operations that are suitable for process flow diagrams are included in the table. Entering and exit vapor and liquid and/or solid phases are designated by V, L, and S, respectively. Design procedures have become fairly well standardized for the operations marked by the superscript letter a in Table 1.1. These are now described qualitatively, and they are treated in considerable detail in subsequent chapters of this book. Batchwise versions of these operations are considered only briefly.

System Structure Analysis. After the identification of subsystems to be examined and the definition of undcsired events within the context of preliminary hazard analysis, events which lead to incidents are investigated. These event sequences can be represented as logic structure in a block diagram, a flow diagram, a fault tree, or a decision table. In the presentation which follows (Table 4.9.). a decision table was used. It contains, column by column, the combinations of system states which lead to the undesired event. The presentation permits qualitative identification of weak points in the system. In general, for example, the probability of a system state will decline with the growing number of failed components. The logic structure presentation could form the basis for further quantitative analyses. 

Problem Analysis and Quantification. Qualitative and quantitative answers are obtained through use of industrial engineering techniques such as flow diagrams, flowcharts, from-to charts, and activity-relationship charts. For the detailed application of these manual techniques see Refs. 1 to 4. 

Figure 3.6.1 (Berty 1979) is a Sankey (1898) diagram, used in power engineering, where the bandwidth is proportional (here qualitatively only) to the flowing masses. This illustrates the calculation results for a rather extreme case of an NOx reduction problem. The case is extreme because the catalyst particle has a dp=0.2mm, i.e., 200 microns. Flow resistance is very high, therefore an L=1 mm deep bend is used only. Per pass concentration drop is still high, Ci-C=1.2ppm, or Dai=0.11. This was tolerated in this case, since it is between 11.2 and 10.00 ppm concentration, and nothing better could have been achieved.

The stationary-state response curves, or bifurcation diagrams shown in Figs 1.13(b) and 1.12(f), represent two of the simplest possible patterns monotonic variation and a single hysteresis loop respectively. These are the only qualitatively different responses possible for the cubic autocatalytic step on its own. They are also found for a first-order exothermic reaction in an adiabatic flow reactor (see chapter 6). With only slightly more complex chemical mechanisms a whole array of extra exotic patterns can be found, such as those displayed in Fig. 1.14. The origins of these shapes will be determined in chapter 4. 

The influence of a commensurate lattice potential on a free density wave is considered in section 5. The full finite temperature renormalization group flow equation for this sine-Gordon type model are derived and resulting phase diagram is discussed. Furthermore a qualitative picture of the combined effect of disorder and a commensurate lattice potential at zero temperature is presented in section 6, including the phase diagram. 

Fig. 5.39. Experimental p-T diagram for CH3CHO + O2 in a flow reactor with tres = 3s showing five regions of different qualitative behaviour. (Reprinted with permission from reference [75], Royal Society of London.)...

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