Pulse testing

One of the most useful and practical methods for obtaining experimental dynamic data from many chemical engineering processes is pulse testing. It yields reasonably accurate frequency-response curves and requires only a fraction of the time that direct sine-wave testing takes. 

An input pulse of fairly arbitrary shape is put into the process. This pulse starts and ends at the same value and is often Just a square pulse (i.e., a step up at time zero and a step back to the original value at a later lime t ). See Fig. 14.3. The response of the output is recorded. It typically returns eventually to its original steadystate value, If C(,j and m, are perturbations from steadystate, they start and end at zero. The situation where the output does not return to zero will be discussed in Sec. 14.3.4, 

The input and output functions are then Fourier-transformed and divided to give the system transfer function in the frequency domain The details of one procedure for accomphshing this Fourier transformation are discussed in the following sections, and a little digital computer program that does this job is given in Table 14.1. Alternative methods include the use of Fast Fourier Transforms, which are available in most computing centers. 

In theory only one pulse input is required to generate the entire frequency-response curve. In practice several pulses arc usually needed to establish the required size and duration of the input pulse. Some tips on the practical aspects of pulse testing are discussed in Sec. 14.3.3. 

Consider a process with an input m, and an output x, . By definition, the transfer function of the process is 

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A frequency response technique was tried first and some results were received. The useful frequency domain was less than one order of magnitude, while in electrical problems five orders of magnitude can be scanned. The single pulse technique was more revealing, but evaluation by moments had the usual accumulation of errors. Fourier transform of the pulse test results was the final method. 

The flow through a reaetor is 10 dm /min. A pulse test gave the following eoneentration measurements at the outlet. 

J6. The frequency response data given below were obtained by pulse-testing a closed-loop system that contained a proportional-only controller with a proportional band of 25. Controller setpoint was pulsed and the process measurement signal was recorded as the output signal. 

The numerator is the Fourier transformation of the time function The denominator is the Fourier transformation of the time function m, . Therefore the frequency response of the system G(j ) can be calculated from the experimental pulse test data x, and as shown in Fig. 14.3. 

The experimental data from a pulse test are usually two continuous curves of x and m recorded as functions of time. A reasonable number of points are selected from these curves and fed into the digital computer. We will discuss later what a reasonable number is. 

The input disturbance for a pulse test begins and ends at the same value. In terms of perturbation variables, the input m ) is initially zero and is returned to zero after some time, ... 

Since the operations to get frequency response from step-test data involve numerical differentiation of the data, the results are less reliable than pulse test data as frequency is increased. 

Pulse testing does not work well on processes that are highly nonlinear because the pulse tends to drive the process away from the steadystate into a nonlinear region unless the pulse height is made very small. 

Pulse testing also has problems in situations where load disturbances occur at the same time as the pulse is being performed. These other disturbances can effect the shape of the output response and produce poor results. The output of the prt)cess may not return to its original value because of load disturbances. 

We are trying to extract a lot of information from one pulse test, i.e., the whole frequency response curve. This is asking a lot from one experiment. 

Astrom s autotune method has several distinct advantages over openloop pulse testing ... 

Accurate information is obtained around the important frequency, i.e., near phase angles of —180". In contrast, pulse testing tries to extract information for a range of frequencies. It therefore is inherently less accurate than a... 

Write a digital computer program that will calculate G(( , from pulse test data when the process contains an integrator. 

When developing a liquid phase adsorptive separation process, a laboratory pulse test is typically used as a tool to search for a suitable adsorbent and desorbent combination for a particular separation. The properties of the suitable adsorbent, such as type of zeolite, exchange cation and adsorbent water content, are a critical part of the study. The desorbent, temperature and liquid flow circulation are also critical parameters that can be obtained from the pulse test. The pulse test is not only a critical tool for developing the equilibrium-selective adsorption process it is also an essential tool for other separation process developments such as rate-selective adsorption, shape-selective adsorption, ion exchange and reactive adsorption. 

A pulse test procedure [6] begins with an injection of a small pulse of the feed mixture to be separated into a desorbent stream flowing through a packed adsorbent column at a fixed flow rate and temperature. The on-line column effluent composition is then determined as a function of time or volume of desorbent passed by gas or liquid chromatography. Particularly important is the sequence and time when each of the feed components exit the packed adsorbent column because these characteristics describe the specific adsorbate and adsorbent interactions. By determining the interactions using the pulse test, the separation process can be optimized. 

Figure 6.3 Schematic pulse test two components and paraffin tracer.

The adsorbent and adsorbate interaction obtained using the pulse test is at a diluted feed condition. So, the interaction information might not fully represent the actual interaction since the commercial feed concentration is normally much higher. To be more representative, the breakthrough technique is introduced. 

The breakthrough procedure is similar to the pulse test procedure except a large amount of high feed concentration is used. The breakthrough procedure can be described as follows ... 

Acid-base interactions between zeolitic adsorbents and adsorbates do not always correctly predict the trend of adsorbent selectivity. This is illustrated by the adsorptive separation of durene from isodurene. Pulse test experiments indicated that the adsorbent selectivity for durene/isodurene increases from KX < NaX < LiX, shown in Table 6.6 [32], Because isodurene is a stronger base than durene (Table 6.5), one would expect that the results for adsorbent selectivity... 

Table 6.8 Separation of p-xylene using KY and BaX adsorbents with various desorbents [38, 39] by pulse tests.

Selectivity is a relative term and is defined in the Molex process as the adsorbent s preference for desired component (in this case, normal paraffins) over the undesired feed components (cyclic paraffins, iso-paraffins, aromatics) while employing a particular desorbent. One can easily determine an adsorbent and desorbent combination selectivity using a pulse test screening apparatus. This apparatus consists of a known volume of adsorbent placed in a fixed bed. A stream of desorbent is then passed over the bed to fill the pore and interstitial volume of the bed. A known quantity of feed is introduced to the feed at the top of the adsorbent bed and passed across the column as a pulse of feed. This pulse of feed is then pushed through the adsorbent bed using a known desorbent flow rate. Effluent from the column is monitored for the various feed components and the concentrations of each component noted (with respect to time) as they elude from the... 

In the case of the Molex process, the pulse test separation between the desired normal paraffins and the non-normal feed components produces discrete and separate peaks. This high degree of separation means a Molex unit can achieve high degrees of purity and recovery but the ultimate purity and recovery are dictated by non-ideal conditions such as back mixing or flow mal-distributions. 

The second adsorbent characteristic is capacity. Capacity is defined as the quantity of desired component for example normal paraffins adsorbed from the feed while the adsorbent is exposed to the feed. Capacity is reported either as a weight or volume of the desired component retained by the adsorbent per volume or weight of adsorbent. It is desirable to have capacity values as great as physically practical. Capacity, just like selectivity, is measured using the pulse test apparatus. 

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