Dynamic method, input-response

It is well known that the measurement of residence time distribution usually employs the dynamic method [54], the so-called input-response technique. However, for measuring RTD of solid particles the input signal is a difficult and troublesome problem. The author of the present book employs an arbitrary known function as the input signal so that this problem is solved. This procedure is also applicable, in principle, to the measurements of RTD of solid materials in other devices. 

The dynamic methods used are a modal analysis with a spectrum as an input and a space-time history analysis which needs one or more accelerograms for inputs. Analyses of the first type are the most common ones the second type is used in particular cases or for the accurate study of the response of a plant component placed at a specific place in a structure. 

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

Let us deal with the transient response method. The transient response method is a method of measuring the characteristics of a system in particular, this method is effective when the dynamic characteristics of the system are investigated. In order to clarify the characteristics of the system, a comparison between the input and the output wave forms is useful. In general, the following three input wave forms have been widely used (Figure 2.1) ... 

Step response method The input signal is changed stepwise from the steady-state value to some specific value. This method is mainly used to discuss the dynamic characteristics of a system. 

Since this work deals with the aggregated simulation and planning of chemical production processes, the focus is laid upon methods to determine estimations of the process models. For process control this task is the crucial one as the estimations accuracy determines the accuracy of the whole control process. The task to find an accurate process model is often called process identification. To describe the input-output behaviour of (continuously operated) chemical production plants finite impulse response (FIR) models are widely used. These models can be seen as regression models where the historical records of input/control measures determine the output measure. The term "finite" indicates that a finite number of historical records is used to predict the process outputs. Often, chemical processes show a significant time-dynamic behaviour which is typically reflected in auto-correlated and cross-correlated process measures. However, classic regression models do not incorporate auto-correlation explicitly which in turn leads to a loss in estimation efficiency or, even worse, biased estimates. Therefore, time series methods can be applied to incorporate auto-correlation effects. According to the classification shown in Table 2.1 four basic types of FIR models can be distinguished. 

Another new method for the dynamic measurement of ki a uses gas phase dynamics and consists of continuously measuring the composition of the outlet gas in response to a step input of a nonreactive tracer such as CO2 in the inlet gas stream (Andre et al., 1981). This method is especially useful under particular conditions for application to high viscosity media and solid-substrate fermentations. 

In a chromatographic experiment a small packed adsorption column is subjected to a perturbation in the inlet concentration of an adsorbable species and the dynamic response at the column outlet is measured. Such measurements provide, in principle, a simple and rapid means of studying adsorption kinetics and equilibria. This method has been widely applied to gaseous sorbates but similar techniques are in principle applicable with liquids. In practice it is usual to employ either a pulse or a step input although other types of perturbation may also be used. The choice between step or pulse depends entirely on practical convenience since exactly the same information may be obtained from either experiment. 

As shown in Table 4.2, large break LOCA events involve the most physical phenomena and, therefore, require the most extensive analysis methods and tools. Typically, 3D reactor space-time kinetics physics calculation of the power transient is coupled with a system thermal hydraulics code to predict the response of the heat transport circuit, individual channel thermal-hydraulic behavior, and the transient power distribution in the fuel. Detailed analysis of fuel channel behavior is required to characterize fuel heat-up, thermochemical heat generation and hydrogen production, and possible pressure tube deformation by thermal creep strain mechanisms. Pressure tubes can deform into contact with the calandria tubes, in which case the heat transfer from the outside of the calandria tube is of interest. This analysis requires a calculation of moderator circulation and local temperatures, which are obtained from computational fluid dynamics (CFD) codes. A further level of analysis detail provides estimates of fuel sheath temperatures, fuel failures, and fission product releases. These are inputs to containment, thermal-hydraulic, and related fission product transport calculations to determine how much activity leaks outside containment. Finally, the dispersion and dilution of this material before it reaches the public is evaluated by an atmospheric dispersion/public dose calculation. The public dose is the end point of the calculation. 

The reaction-curve method is based on the open-loop response of the process to a step input. This response curve can be used to derive the dynamic characteristics of the process. If the process can be described by a first-order lag and dead time, the controller setting can be calculated. 

Stochastic identification techniques, in principle, provide a more reliable method of determining the process transfer function. Most workers have used the Box and Jenkins [59] time-series analysis techniques to develop dynamic models. An introduction to these methods is given by Davies [60]. In stochastic identification, a low amplitude sequence (usually a pseudorandom binary sequence, PRBS) is used to perturb the setting of the manipulated variable. The sequence generally has an implementation period smaller than the process response time. By evaiuating the auto- and cross-correlations of the input series and the corresponding output data, a quantitative model can be constructed. The parameters of the model can be determined by using a least squares analysis on the input and output sequences. Because this identification technique can handle many more parameters than simple first-order plus dead-time models, the process and its related noise can be modeled more accurately. 

In the dynamic optimization method [234-236], Eq. (2.9) is taken as a mathematical model of the calorimeter, and thus appropriate zero initial conditions are assumed. This method assumes the existence of one input function T(t) and one output function P(t). The impulse response H(t) is determined as a derivative with respect to time of the response of the calorimetric system to a unit step. As a criterion of accordance between the measured temperature change T(t) and the estimated course of temperature x(t), the integral of the square of the difference between these two courses is taken ... 

It is essential to draw a distinction between Unear and nonlinear responses of the system. To correct the response of the system the linearity has to be confirmed by the experimental facts. When we look for the correct answer, the best method is to analyze the response of each forcing input function in the system To achieve this, it would be helpful to use the dynamic time-resolved characteristics for the typical input function, given earUer ( 2.3). 

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