Description rule

When replacing variables identified by the application of the description rule it is important to ensure that those selected are truly independent, and that the values assigned to them lie within the range of possible, practical, values. 

The number of independent variables that have to be specified to define a problem will depend on the type of separation process being considered. Some examples of the application of the description rule to more complex columns are given by Hanson et al. (1962). 

The description of any operation or design problem in a multistage separation process requires assigning numerical values to, or setting, a certain number of independent variables. The number of variables to be set depends on the process, and is usually determined easily by the method the authors have called the description rule (HI). Alternatively the number of variables to be set may be determined by writing all of the independent equations which define the process, then counting the number of variables and the number of equations. In order to solve the equations, a sufficient number of independent variables must be set so that the number of dependent variables remaining equals the number of equations. 

The result just obtained by writing the equations defining the process and counting both equations and variables could have been obtained much more easily by means of the description rule. The description rule states that the number of independent variables is equal to the number of variables that can be arbitrarily set in construction or through operation. For the same example, n and m can be arbitrarily set in construe-... 

This list of variables completely describes any problem in the system of interlinked columns which can be solved by Program genvl. Following the description rule, (3), (6), and (8) are set by construction, the others by operation. 

Fire prevention and response information may be covered in other written facility documents (such as job descriptions, rules, or procedures) and communicated to employees on the same schedule as the fire prevention plan. 

By taking an inventory of equations and variables for the above column, it was determined that two or three variables (depending on whether or not the number of stages is fixed) must be specified in order to define the column performance. An alternative to this mathematical analysis is to apply the description rule (Hanson et al., 1962), which can be a less tedious method for determining the number of independent variables, based on a practical evaluation of the process. 

The description rule states that the number of independent variables that are... 

The description rule introduced in Section 5.2.1 may be used to check the degrees... 

The number of independent variables required to define the operation of an absorber or stripper may also be determined by applying the description rule, stated in Section 5.2.1. The number of trays or the column height is set by construction and may, in the design phase, be used as design variables. Since, by definition, the feeds are introduced at the top and bottom of the column, the feed locations are not variable. The feed compositions and thermal conditions are set outside the column region and are therefore beyond the operator s control. The operator can, however, control the valves on the two feeds and the two products. One of these four valves, usually the bottoms product valve, cannot be controlled independently since it must be set at steady state such as to maintain the required liquid level in the bottom of the column. The overhead valve is usually used to control the column pressure. The two feed valves may be controlled independently one controls the main process stream rate and the other controls the solvent or stripping gas flow rate. 

Each side product provides one additional independent column variable. To define the column performance, the flow rate of each side product must be known. Alternatively, a side product flow rate may be allowed to vary in order to meet a performance specification such as the concentration of a component in that product. The side product flow rate becomes a dependent variable which must be calculated to satisfy the performance specification. It has been established in Chapter 7 that a fixed-feed, fixed-configuration, fixed-pressure column with a partial condenser (having only a vapor distillate) and a reboiler has two degrees of freedom. Two variables, such as the condenser and reboiler duties, may be varied independently. Each side product adds to the column one degree of freedom. Hence, a column as defined above with S side products has 2 + S degrees of freedom. The duties and side product flow rates can each be varied independently, allowing 2 -i- S performance specifications. This conclusion can be reached by applying the description rule since each additional product rate can be controlled independently by external means. 

Reference again is made to Figure 17.1 for a degrees of freedom analysis and a study of possible control strategies. The description rule (Section 5.2.1) is applied here to an existing system. The variables that can be set by external independent means include the steam rate to the reboiler, the cooling water rate to the condenser, and the reflux and product valve positions. At a given time, only one product receiver is active, and the valves of all the other receivers are closed. 

Thus, in order to define the column operation uniquely, two specifications are required, as already concluded using the description rule (Section 17.1.3). These could be the reflux rate and distillate rate, Lg and D. Note that a subcooled condenser is assumed so that no phase equilibrium equation is written for stage 0 and no Foi variables exist. The column pressure profile is assumed fixed or determined independently from hydraulics calculations and is not included in the column variables. Also, the enthalpies and phase equilibrium coefficients are, in general, functions of the temperature, pressure, and composition (Chapter 1) and are therefore not considered as additional unknown variables. 

An attractive alternative to counting variables and equations is to use the Description Rule of Hanson, Duifin, and Somerville. ... 

In applying either the Description Rule of Section 6.7 or the enumeration algorithm of Section 6.6 to complex multistage separators that have auxiliary heat exchangers, boilers, stream mixers, stream dividers, and so on, a considerable amount of physical insight is required to develop a feasible list of design variables. This can best be illustrated by a few examples. 

To help analyze the characteristics of a single-stage separator, information flow diagrams were prepared for four commonly encoumered situations (Fig. 20.6-4). Notations used in the following discussion ate summarized at the end of this section. Following the principles of the description rule, there are N -1) -F 4 degrees of freedom for an Al-component system whenever the membrane is chosen and the operation is assumed to be isothermal. 

The description rule introduced in Section 5.2.1 may be used to check the degrees of freedom or the number of variables that must be set to define the column operation. For an existing column, the variables that can be set by construction determine the column configuration. The variables that can be controlled by external means include those variables that define the feed, the column pressure, and the condenser and reboiler duties. With a fixed feed and a pressure usually controlled to maintain an acceptable column temperature level, two variables are left for the purpose of controlling the separation— the condenser and reboiler duties. The product rates are controlled to maintain liquid levels in the condenser and reboiler and as such are not independent variables. The condenser and... 

Once the generalisations have been made, the user may employ the descriptive rules to specify new sounds, different from those that were originally picked out as typical of the sounds that the system already knows. 

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