Relationships design

The difference between the number of variables involved in a design and the number of design relationships has been called the number of degrees of freedom similar to the use of the term in the phase rule. The number of variables in the system is analogous to the number of variables in a set of simultaneous equations, and the number of relationships analogous to the number of equations. The difference between the number of variables and equations is called the variance of the set of equations. 

If Nv is the number of possible variables in a design problem and Nr the number of design relationships, then the degrees of freedom Nd is given by ... 

How the number of process variables, design relationships, and design variables defines a system can be best illustrated by considering the simplest system a single-phase, process stream. 

For many design calculations it will not be possible to select the design variables so as to eliminate the recycle of information and obviate the need for iterative solution of the design relationships. 

Exact analytical solutions of the design relationships are rarely possible semi-empirical methods based on the analysis of idealised reactors will normally have to... 

Tubular reactors are normally used in the chemical industry for extremely large-scale processes. When filled with solid catalyst particles, such reactors are referred to as fixed or packed bed reactors. This section treats general design relationships for tubular reactors in... 

Table 8.1 summarizes the fundamental design relationships for the various types of ideal reactors in terms of equations for reactor space times and mean residence times. The equations are given in terms of both the general rate expression and nth-order kinetics. 

Tiller and Huang(13) give further details of the problem of developing a usable design relationship for filter equipment. Studies by Tiller and Shirato 14-1, Tiller and Yeh 15-1 and Rushton and Hameed(16) show the difficulty in presenting practical conditions in a way which can be used analytically. It is very important to note that tests on slurries must be made with equipment that is geometrically similar to that proposed. This means that specific resistance is very difficult to define in practice, since it is determined by the nature of the filtering unit and the way in which the cake is initially formed and then built up. 

Scaleup involves determining the controlling factors in a process, the role that mixing plays, and the application of a suitable scaleup technique. In this section, the general scaleup relationships will be presented, and the particular types of processes involved will be covered. Section X will cover pilot planting, how runs are made to determine the controlling factor, and how to choose a suitable design relationship for that situation. 

The distribution of temperature of the material between the cylinder and mold zoneswill have a stepped character. Such a model of the temperature profile enables us to obtain the requisite design relationships for a coordinated choice of both the temperature and the time that the material being treated in the various zones of the inj rtion cylinder and the mould is present. 

Radiation targeting involved exposing proteins to (OH/e g) or exclusively OH radical attack and then correlating activity loss with radiation dose. This correlation, using a set of empirically designed relationships, allowed a determination of protein size. It was, however, dependent upon a number of parameters such as temperature and protein concentration. Recent research carried out by Houee-Levin and co-workers as well as other groups have shown this technique to be dependent upon the judicious choice of protein and the empirical correlations fail in a wide number of systems. 

Tower Height / Height of Transfer Unit, Z/HTU Fig. 9. Example of design relationship of Z HTU vs X/Xj for ammonia stripping tower (15). 

---