Process variables, classification

In this chapter, the mathematical formulation of the variable classification problem is stated and some structural properties are discussed in terms of graphical techniques. Different strategies are available for carrying out process-variable classification. Both graph-oriented approaches and matrix-based techniques are briefly analyzed in the context of their usefulness for performing variable categorization. The use of output set assignment procedures for variable classification is described and illustrated. 

The idea of process variable classification was presented by Vaclavek (1969) with the purpose of reducing the size of the reconciliation problem for linear balances. In a later work Vaclavek and Loucka (1976) covered the case of multicomponent balances (bilinear systems). 

Various strategies are available for performing process variable classification. These have been briefly presented. Their application for different types of plant model... 

Sanchez, M., Bandoni, A., and Romagnoli, J. (1992). PLADAT—A package for process variable classification and plant data reconciliation. Comput. Chem. Eng. S16,499-506. 

The H AZOP leader selects an appropriate aspect of the plant s process systems (a process node) and associated systems that affect the selected process variable for the selected mode of plant operation. The selection may be made fiom the plant system classification, or it may be from the nodal analysis of the process. 

In this chapter we will present a discussion of those points, leading us directly to the decomposition of the general problem into estimable, nonestimable, redundant, and nonredundant subsystems. This allows us to reduce the size of the commonly used least squares estimation technique and allows easy classification of the process variables the topic of the next chapter. 

The concepts of structural observability are the basic tools for developing variable classification strategies. Some approaches presented in Chapter 3 are based on the fact that the classification of process variables results from the topology of the system and the placement of instruments and has nothing to do with the functional form of the balance equations. Thus, the linearity restriction will be removed and efficient reduction of the large-scale problem will be accomplished. 

Variable classification is the essential tool for the design or revamp of monitoring systems. After fixing the degree of required knowledge of the process, that is to say, the subset of variables that must be known, this technique is repeated until the selected set of instruments allows us to obtain the desired information about the process. There is a great economic incentive for robust classification because a deficient procedure will require the installation of extra instrumentation. 

An elegant classification strategy using projection matrices was proposed by Crowe et al. (1983) for linear systems and extended later (Crowe, 1986, 1989) to bilinear ones. Crowe suggested a useful method for decoupling the measured variables from the constraint equations, using a projection matrix to eliminate the unmeasured process variables. 

CHAPTER 3 CLASSIFICATION OF THE PROCESS VARIABLES FOR CHEMICAL PLANTS... 

By obtaining the output set assignment on the previous set of balances we can classify the unmeasured process variables as determinable or nondeterminable. The results are given in Table 5 this classification is coincident with those from other works cited in the literature. 

Once the process variables have been classified, a great deal of information about the process topology is also available. The question now is how to use the classification and this information to attack other problems. In a real process we will have different kind of problems to solve and the goals will vary from one process to another. Among the possible situations that may be encountered are the following ... 

Using a classification algorithm we can determine the measured variables that are overmeasured, that is, the measurements that may also be obtained from mathematical relationships using other measured variables. In certain cases we are not interested in all of them, but rather in some that for some reason (control, optimization, reliability) are required to be known with good accuracy. On the other hand, there are unmeasured variables that are also required and whose intervals are composed of over measured parameters. Then we can state the following problem Select the set of measured variables that are to be corrected in order to improve the accuracy of the required measured and unmeasured process variables. 

If A22 0, the system possesses unmeasured variables that cannot be determined from the available information (measurements and equations). In such cases the system is indeterminable and additional information is needed. This can be provided by additional balances that may be overlooked, or by making additional measurements (placing a measurement device to an unmeasured process variable). Also, from the classification strategy we can identify those equations that contain only measured variables, i.e., the redundant equations. Thus, we can define the reduced subsystem of equations... 

This chapter has shown that the analysis of the topological structure of the balance equations allows classification of the measured and unmeasured process variables, finally leading to system decomposition. 

Furthermore, a variable classification strategy based on an output set assignment algorithm and the symbolic manipulation of process constraints is discussed. It manages any set of unmeasured variables and measurements, such as flowrates, compositions, temperatures, pure energy flows, specific enthalpies, and extents of reaction. Although it behaves successfully for any relationship between variables, it is well suited to nonlinear systems, which are the most common in process industries. 

Remark 2. The permutation matrix IIU, obtained as a by-product of the Q-R factorization procedure of A2, enables an easy classification of the unmeasured process variables, as is indicated by Eq. (4.15). The variables in subset un ru correspond to the minimum number and the location of measurements needed for the system to satisfy the estimability condition, that is, that all unmeasured variables be determinable. 

In the following sections, the use of the Q-R decomposition approach is discussed within the framework of the general multicomponent and energy (bilinear) reconciliation problem. In this case the classification of the measured and unmeasured process variables involves a sequence of steps. 

From the classification it was found that, for this specific problem, there are 10 redundant and 6 nonredundant measured variables, and all the unmeasured process variables are determinable. Symbolic manipulation of the equations allowed us to obtain the three redundant equations used in the reconciliation problem ... 

Chemical reactors intended for use in different processes differ in size, geometry and design. Nevertheless, a number of common features allows to classify them in a systematic way [3], [4], [9]. Aspects such as, flow pattern of the reaction mixture, conditions of heat transfer in the reactor, mode of operation, variation in the process variables with time and constructional features, can be considered. This work deals with the classification according to the flow pattern of the reaction mixture, the conditions of heat transfer and the mode of operation. The main purpose is to show the utility of a Continuous Stirred Tank Reactor (CSTR) both from the point of view of control design and the study of nonlinear phenomena. 

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