Illustrative problems

The first illustrative problem comes from quantum mechanics. An equation in radiation density can be set up but not solved by conventional means. We shall guess a solution, substitute it into the equation, and apply a test to see whether the guess was right. Of course it isn t on the first try, but a second guess can be made and tested to see whether it is closer to the solution than the first. An iterative routine can be set up to cany out very many guesses in a methodical way until the test indicates that the solution has been approximated within some narrow limit. 

The purpose of these 3 volumes is to present techniques of process design and to interpret the results into mechanical equipment details. There is no attempt to present theoretical developments of the design equations. The equations recommended have practically all been used in actual plant equipment design, and are considered to be the most reasonable available to the author, and still capable of being handled by both the inexperienced as well as the experienced engineer. A conscious effort has been made to offer guidelines to judgment, decisions and selections, and some of this will be found in the illustrative problems. 

Potential problems with an ATES loop are illustrated in Figure 39 and encounter a number of events that are related to the chemical behaviour of the system. However, the figure also illustrates problems connected to a general system design, such as aeration and sand production. These types of problems may also have secondary damaging impacts on surroundings buildings and the environment. 

Secondly, the minimum amount of intermediate storage is determined with and without the PIS operational philosophy. In both cases the production goal was set to that which was achieved when the model was solved with infinite intermediate storage. In the illustrative example a 20% reduction in the amount of intermediate storage is achieved. The design model is an MINLP model due to the non-linear capital cost objective function. This model is applied to an illustrative problem and results in the flowsheet as well as determining the capacities of the required units. 

This chapter contains a discussion of two intermediate level problems in chemical reactor design that indicate how the principles developed in previous chapters are applied in making preliminary design calculations for industrial scale units. The problems considered are the thermal cracking of propane in a tubular reactor and the production of phthalic anhydride in a fixed bed catalytic reactor. Space limitations preclude detailed case studies of these problems. In such studies one would systematically vary all relevant process parameters to arrive at an optimum reactor design. However, sufficient detail is provided within the illustrative problems to indicate the basic principles involved and to make it easy to extend the analysis to studies of other process variables. The conditions employed in these problems are not necessarily those used in current industrial practice, since the data are based on literature values that date back some years. 

For the second step one establishes a solution method. The system under consideration may be static, dynamic, or both. Static cases require solving a boundary value problem, whereas dynamic cases involve an initial value problem. For the illustrative problem, we discuss the solution of a static Laplace (no sources) or Poisson (sources) equation such as... 

All of these illustrative problems have been worked in the three distinct steps, in order to emphasize the reasoning involved. With a little practice, you can combine two or three of these steps into one operation (or set-up), greatly increasing the efficiency in using your calculator. 

The polymers which have been used to illustrate problems of inorganic polymer formation have been lieteroatomic. that is, their chains are built from different atoms alternating with each other. The other structure mentioned has been homoatomic—all the atoms in the chain are the same. There aie only a few homoatomic polymers of airy promise. Most elements will form only cyclic materials of low molecular weight if they polymerize at all. In addition to the silane polymers, black phosphorus, a high-pressure modification of the element, forms in polymeric sheets. 

Due to the simplicity of this illustrative problem and of the linear equilibrium isotherm Y = aX+b we can reduce the two coupled two point boundary value differential equations (6.127) to one differential equation as follows. 

Benigni, R. and Richard, A.M., QSARs of mutagens and carcinogens two case studies illustrating problems in the construction of models for noncongeneric chemicals, Mutation Research, 37(1), 29-46, 1996. 

The exercises have been extended. As for the first edition they are designed to assist in deepening understanding. It is only when one tackles an illustrative problem that one s deficiencies as far as understanding is concerned are revealed, and this equally applies to the design of problems It is hoped that the answers... 

Figure 27 Example of real polarization data illustrating problems associated with analysis of limited or false Tafel regions.

The case studies also illustrated problems in near miss management systems with reference to the proposed framework (see Chapter 4) ... 

FIG. 5-24 Flowchart illustrating problem solving approach using mass-transfer rate expressions in the context of mass conservation. 

---