Flooding Prognosis in Packed Columns by Assessing the Degree of

Sep 22, 2016 - Fortunately, it has been observed that the inherent distinction before and after the occurrence of flooding is the shift in the degree ...
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Flooding Prognosis in Packed Columns by Assessing the Degree of Steadiness (DOS) of Process Variable Trajectory Yi Liu,† Bo-Fan Hseuh,‡ Zengliang Gao,† and Yuan Yao*,‡ †

Engineering Research Center of Process Equipment and Remanufacturing, Ministry of Education, Institute of Process Equipment and Control Engineering, Zhejiang University of Technology, Hangzhou 310014, China ‡ Department of Chemical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan ABSTRACT: Pressure drop is a key factor that indicates flooding phenomenon in packed columns. However, it is difficult to apply statistical process control (SPC) to this variable for flooding prognosis. This is because, even if the system is operated below the flooding point, both the mean and variance of pressure drop may continue to change, because of fluctuations in either the gas or the liquid flow rate. As such, it is incorrect to represent the measured values of pressure drop with a certain distribution. Fortunately, it has been observed that the inherent distinction before and after the occurrence of flooding is the shift in the degree of steadiness (DOS) of the pressure drop trajectory. This is the motivation for the research presented in this paper. First, an assessment approach is introduced to quantify the concerned DOS of the pressure drop trajectory in each time window. Thereafter, instead of the original process variable, the DOS is monitored for flooding prognosis. Because of the lack of knowledge on the exact distribution of DOS, a nonparametric charting technique is adopted, which can be implemented in a simple and efficient manner. The feasibility of the proposed method is then illustrated using the experimental results on flooding prognosis in a packed column. column. The flooding point is determined by both gas and liquid velocities. At any given gas flow rate, there exists a definite liquid velocity above which the flooding phenomenon occurs. Similarly, a limiting gas velocity exists for any given liquid flow rate.6 The flooding phenomenon often leads to poor column efficiency, and may even shut down the entire production line. Therefore, packing columns cannot be operated or controlled under flooding conditions. On the other hand, high gas/vapor velocity often means high column capacity. The closer the column operation is to its maximum possible capacity, the smaller the column size and the less the capital investment. In order to prevent the operation of packed columns from flooding, various empirical models have been used to predict the operating limits.6−12 However, the prediction accuracy is always dependent on empirical parameters related to the packed column under consideration, which are difficult to obtain.13 The inability of accurately predicting and preventing flooding may result in a loss of operating hours, a decrease of product purity, equipment damages, safety hazards, etc. In industrial operations, a conservative setting of gas velocity is often selected for safety reasons. This being ∼70%−85% of the flooding point velocity, it leads to low production rates and high energy consumption. Therefore, in order to ensure the

1. INTRODUCTION In the chemical industry, statistical process control (SPC) techniques have been widely utilized to monitor the operation status of various production processes.1−5 Control charts are most commonly used tools in SPC, which compare the values of monitoring statistics to predetermined control limits in a graphical way. A properly selected monitoring statistic summarizes the information on process status, while the corresponding control limit is derived by making the assumption that in-control process data follow the underlying statistical distribution, irrespective of whether it is Gaussian or non-Gaussian. If the monitoring statistic is outside of the control limit, a fault is usually registered. However, this assumption may not be satisfied in certain specific industrial applications. A typical case that motivates the research in this paper is that of packed columns. Packed columns have been widely used in chemical separation processes, including absorption, stripping, and distillation. Gas and liquid flow rates in packed towers are known to be limited by the tendency of the columns to flood.6 With the increase in either the liquid flow rate or the gas flow rate, the liquid holdup in the column increases, causing a decrease in the free area available for gas flow. As a consequence, the pressure drop in the column increases. The so-called flooding point is finally reached, when gas bubbles rise violently through the liquid. In such a situation, the pressure drop in the column increases sharply, even with the slightest increase in gas flow rate. At the same time, some liquid may be transported outside by the gas leaving through the top of the © 2016 American Chemical Society

Received: Revised: Accepted: Published: 10744

August 29, 2016 September 21, 2016 September 22, 2016 September 22, 2016 DOI: 10.1021/acs.iecr.6b03315 Ind. Eng. Chem. Res. 2016, 55, 10744−10750

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Industrial & Engineering Chemistry Research

Figure 1. Variable trajectory of pressure drop with a liquid flow rate of 0.89 × 10−4 m3/s and a continuously adjusted gas flow rate.

Figure 2. Variable trajectory of pressure drop with a liquid flow rate of 1.45 × 10−4 m3/s and a stepwise adjusted gas flow rate.

the occurrence of flooding. However, in their method, for every operating condition, different types of filters and indicator functions are required. These are difficult to determine. Moreover, a statistical control limit for detecting the changes in the signal is also lacking. To the best of our knowledge, to date, no SPC strategy for flooding prognosis has been developed. In a conventional SPC, the in-control state is defined by the historical data collected under normal operating conditions (NOC). By assuming that the NOC data follow a certain statistical distribution, control limits are calculated for process monitoring. Any operating data

efficient and safe operation of packed columns, research on flooding prognosis and detection becomes necessary. Although there are several process variables that can be measured in packing columns, it is generally recognized that the pressure drop inside the column is the most crucial variable for flooding prognosis. For this reason, Pihlaja and Miller14 developed a univariate flooding detection method, comprised of the following steps: sensing of the differential pressure signal, signal filtering, generation of the flooding indicator, and identification of the onset of flooding. With properly selected filter and indicator functions, this method may be able to detect 10745

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2. ASSESSMENT OF THE DEGREE OF STEADINESS In statistics there are two common ways to estimate the sample variance of a data series. The most widely adopted formula for variance estimation is

deviating from the NOC data and possessing statistical significance will trigger an alarm. Such a scheme is not suited for flooding prognosis, because deviations from NOC do not necessarily imply flooding. In industrial applications, the NOC of packing columns is often far from the flooding point. Flooding happens only when a very high value of the gas or liquid flow rate is set. Therefore, even though the system may be operated below the flooding point, the operating data may lie outside the statistical control set. This will then be identified as a fault by the control limits, which are defined by the NOC. Let us consider a scenario in which the heat load on the reboiler at the bottom of the column is increased, to improve the output concentration at the column bottom. In this scenario, the gas flow rate is increased from its normal condition to a higher level, while the liquid flow rate is retained at approximately the same level. Although the flooding point may not be reached, the conventional SPC may, upon beginning the adjustments, trigger an alarm, because such an operation leads to a deviation from the NOC. The trajectory of the pressure drop in a packed column operated in the above-mentioned scenario is shown in Figure 1. In this experiment, the liquid flow rate was maintained at 0.89 × 10−4 m3/s, while the gas flow rate was increased continuously until flooding was observed. From the figure, it is apparent that the slope of the variable trajectory changes sharply when the column is approaching the flooding point, thereby indicating that the pressure drop is a parameter indicative of flooding. However, the SPC technique cannot be applied to monitoring this process variable for flooding prognosis. To illustrate this, another experiment was conducted, where the gas flow rate was changed in a ladder-shaped manner. The corresponding pressure drop is depicted in Figure 2. It is observed that, even though the flooding point has not been reached, the mean and the variance of the pressure drop change with fluctuations in the gas flow rate. A similar phenomenon can be seen if the liquid flow rate is manipulated. Such data characteristics violate the statistical assumption of implementing SPC. Hence, it is impossible to calculate a statistical control limit using a direct method for monitoring this variable and predict flooding. Appropriate feature extraction is a necessary step before conducting SPC. To design a proper statistical control chart for dealing with a chemical engineering problem, relevant domain knowledge is helpful. For flooding prognosis in packed columns, the key question is what is the key difference between the trajectories of pressure drop before and after the occurrence of flooding? The answer is the pronounced shift in the degree of steadiness (DOS). As per this finding, a DOS-based statistical process monitoring strategy is proposed, which extracts useful process information for flooding prognosis and can be implemented in a simple and an efficient manner. In this paper, a DOS assessment method is proposed in Section 2, which quantifies the DOS of the process variable trajectory with a numerical value in each time window. Section 3 introduces a nonparametric charting method for conducting SPC on the DOS. In Section 4, the feasibility of implementation of the proposed method for flooding prognosis in a packed column is demonstrated. Finally, Section 5 summarizes the work and concludes the paper.

n

s2 =

∑i = 1 (xi − x ̅ )2 n−1

(1)

where n is the sample size, xi the ith observation in the sample, and x̅ the sample mean. This estimate does not consider the sequence of the observations. As a result, it is negatively affected by the unsteady trend contained in the data series. To solve this problem, another estimate of sample variance can be utilized, which is derived from the mean square successive difference (δ2):15 n−1

2

δ =

∑i = 1 (xi + 1 − xi)2 (2)

n−1 2

The sample variance estimate (δ /2) minimizes the trend effect, which is more robust than s2. Williams16 studied the moments of the variance ratio, η=

δ2 s2

(3) 17

Based on this parameter, Von Neumann suggested that such a ratio can be used to judge whether a trend exists. If there is no such trend in the data series, the value of R, R=

η δ2 = 2 2 2s

(4)

is expected to be near 1; otherwise, R is statistically greater than 1. In the situation that the observations are from a population that can be described using a Gaussian distribution function, the confidence bound for trend detection can be found in the textbook.18 In recent years, such variance ratio test has been adopted for automated steady-state identification in both continuous and batch chemical processes.19−21 In these applications, the data series xi (i = 1, ..., n) is sampled from process variable trajectories within a moving time window, where the window length is n. Cao and Rhinehart22,23 modified the above method by adopting exponentially weighted moving (EWM) filters. In their method, the following values are calculated: xf , i = λ1xi + (1 − λ1)xf , i − 1

(5)

s f , i 2 = λ 2(xi − xf , i − 1)2 + (1 − λ 2)s f , i − 12

(6)

δf , i 2 = λ3(xi − xi − 1)2 + (1 − λ3)δf , i − 12

(7)

where xf,i is the filtered value of is the sample variance, δf,i2 is the mean square successive difference, and λ1, λ2, and λ3 are the filter parameters. Accordingly, the variance ratio can be calculated as xi, sf,i2

R̃ =

(2 − λ1)s f , i 2 δf , i 2

(8)

Without using a moving window, Cao and Rhinehart’s method avoids the requirements of storing past data and selecting the window length. Instead, the parameters λ1, λ2, and λ3 should be specified. 10746

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Industrial & Engineering Chemistry Research It is clear that both R and R̃ can indicate the DOS of a data series. The more unsteady the data series is, the larger the value of R (or R̃ ). In other words, these indices quantify the degree of steadiness of a data series. In the following sections, R is utilized for DOS assessment of the process variable trajectory, because the calculation of R involves fewer parameters to be selected. For an investigated process variable x, the steps of real-time calculation of the DOS index R are summarized as follows: Step 1: Define the window length as n observations and the moving step size as l observations. Set the initial window index j = 1. Step 2: In the current window, i.e., the jth window, calculate both sj2 and δj2, using eqs 1 and 2. Step 3: Calculate Rj using eq 4. Step 4: Move the window according to the step size l and set j = j + 1. Return to Step 2. The above procedure is conducted iteratively for online implementation. A tradeoff should be made in the determination of the window length n. On one hand, if the window length is too large, the monitoring may be not efficient enough. On the other hand, if the window length is too small, the estimation of the variance may be inaccurate. For flooding prognosis, the target variable x is the pressure drop in the packed column. When the flooding phenomenon tends to occur, a shift in R values is expected to be observed. The remaining problem is to draw a control chart to detect this shift efficiently. Note that the confidence bounds listed in the textbook,18 which are useful in steady-state identification, cannot be adopted directly for flooding prognosis. The main reason for this is that the pressure drop in packed columns often behaves unsteadily, even though the system may be in normal operation. However, the R values derived from the incontrol data are relatively smaller than those calculated in the situation of flooding. Therefore, flooding can be detected by monitoring the R values.

Figure 3. Normal probability plot of R values.

3. NONPARAMETRIC CONTROL CHART FOR DOS MONITORING In this section, a nonparametric SPC technique is introduced for DOS monitoring. Before constructing a control chart for the DOS index R, the normality test is conducted to determine if the R values can be interpreted by a Gaussian distribution. Figures 3 and 4 show the normal probability plot and the histogram of the R values calculated, respectively, based on the pressure drop data in a packed column. These data were collected under the same gas flow and liquid flow rates. It is observed that, in this case, the distribution of R is nonGaussian, even under the same normal operating conditions. Different types of non-Gaussian charting strategies have been utilized in the previous research of chemical engineering process monitoring, most of which are distribution-based.24−31 These strategies may be implemented in DOS monitoring. Alternatively, nonparametric or distribution-free charting techniques,32−34 which are useful when there is limited or lack of knowledge about the underlying process distribution, can also be adopted here. In comparison with traditional control charts, the distribution-free charts do not require estimating the distribution parameters, so that the influence of the estimation errors can be avoided. In this paper, the nonparametric control chart based on the Mann−Whitney (MW) test34 is adopted.

Figure 4. Histogram of R values.

The main idea of the MW control chart is as follows. Suppose that a training sample set of size m1, X = {X1,···,Xm1}, is collected from an in-control process and that the test sample of size m2 is denoted as Yh = {Yh1,···,Yhm2}. Here, h denotes the hth test sample. In the case of flooding prognosis, X contains m1 number of R values calculated during a normal operation without flooding, while Yh consists of m2 number of R values calculated online. The MW statistic (MhX,Y summarizes the total number of (X, Y) pairs where the value of Yhj is larger than that of Xi, i.e., MXh , Y

m1

=

m2

∑ ∑ I(Xi < Y jh) i=1 j=1

(9)

where I(Xi < Yhj ) is the indicator function for the event {Xi < Yhj }. It is clear that the value of MhX,Y is between 0 and m1m2. Large values of MhX,Y indicate the occurrence of a positive shift, whereas small values correspond to a negative shift. In the case discussed in this paper, only positive shifts in R are considered, which indicate a decrease in DOS of the pressure drop trajectory. Therefore, the upper control limit Um1m2, which can be found in an available table provided in the reference,34 10747

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maintained at ∼1.45 × 10−4 m3/s. To change the gas velocity, the operating frequency of the blower was increased incrementally until the flooding phenomenon was observed by the process engineers. During each grade, the gas flow rate was kept constant for ∼10 min. The effects of grade switches can be observed in the trajectory of the pressure drop, as shown in Figure 2, which were measured and recorded in real time. The sample interval is 2.5 s. According to the experience of process engineers, incipient and obvious flooding phenomena can be observed. For real-time flooding prognosis, the R values were calculated using the moving-window technique by analyzing process data, where the window length n was set to be 20 sampling intervals and the step size l was selected as 1. The obtained R values are depicted in Figure 6. Note that the R values are small and

should be utilized to construct a one-side control chart. The chart triggers an alarm if eq 10 is satisfied:

MXh , Y > Um1m2

(10)

To develop an MW control chart, there are two parameters, m1 and m2, that should be specified in advance. The guidelines to be followed are the size of the training set (m1) should be large enough to adequately reflect the systematic variations during normal operation. At the same time, a tradeoff should be made in the determination of the size of each test sample (m2), because a value that is too large may delay the prognosis, whereas a value that is too small may lead to inefficient detections.

4. APPLICATION RESULTS In order to illustrate the proposed method, experiments were conducted on a laboratory-scale packed column shown in Figure 5. The apparatus consisted of an acrylic column with a

Figure 6. R values calculated in the first scenario (with a stepwise adjusted gas flow rate).

relatively consistent before the onset of flooding and increase pronouncedly when the process status is close to flooding. If such a change can be detected with a statistical control chart, early prognosis of flooding can then be achieved. However, because of the non-Gaussian distribution of the pressure drop data, the distribution of R is unknown. Therefore, it is difficult to conduct process monitoring by directly setting a feasible control limit for R. As such, the distribution-free MW control chart has been used. For constructing the MW chart, the first 500 R values in Figure 6 were chosen as the training data. The parameters selected were m1 = 500 and m2 = 5, and the MW statistic was calculated accordingly. The control limit was determined by choosing the average run length (ARL) in control as 500 (i.e., ARL0 = 500, which means that probability of a false alarm is 0.002 when the process status is normal. A reference to the table34 shows the control limit Um1m2 to be 2172. The plot of the control chart corresponding to Figure 6 is depicted in Figure 7. In Figure 7, the monitoring statistic remained below the control limit Um1m2 = 2172 (the red line in Figure 7) when the gas flow rate was low, and the process conditions were far from resulting in flooding, while the MW values calculated during flooding were significantly out of statistical control. It is worth

Figure 5. Photograph of the experimental system: a laboratory-scale packed column.

diameter of 0.22 m and a height of 2.20 m. The heights of both the upper and the lower packing layers are both 0.46 m. In the experiments, air is introduced from the bottom of the column, while water is fed from the top. The structured packing is CY1700 and the spray density ranges from 7 m3/(m2 h) to 24 m3/(m2 h). Because the body of the column is transparent, the process engineers/operators can observe the process status, providing a cross reference to the prognosis results. Two scenarios are considered here, with the variable trajectory of pressure drop shown in Figures 2 and 1, respectively. As mentioned in the Introduction, in each scenario, the liquid flow rate was maintained at an approximate constant, while the gas velocity was increased in a stepwise (or continuous) manner. The flooding phenomenon occurred after the gas velocity reached a certain value. It is important to prognosticate the flooding before it disturbs the process. In the first experiment, the packed column was operated at different grades of gas flow rate, while the liquid flow rate was 10748

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prevent any process abnormalities that could be caused by flooding. The experimental results obtained show that the proposed DOS-based monitoring method can be simply and efficiently implemented for handling the flooding prognosis problem in packed columns.

5. CONCLUSIONS In this work, a DOS-based statistical process monitoring method has been proposed, in order to achieve real-time flooding prognosis in packed columns. In this method, the DOS information is extracted from the original variable trajectory of the pressure drop in the column with an R index. As a type of feature extraction, the useful process characteristics summarized by DOS can facilitate the subsequent monitoring steps. Then, an MW statistic-based nonparametric control chart is adopted to detect the shift in the R values. In doing this, it is neither necessary to know the distribution function of R nor estimate the distribution parameters. Such a control chart, also called a distributionfree control chart, is easy to use. Experimental results show the feasibility and simplicity of the proposed method.

Figure 7. MW control chart developed in the first scenario (with a stepwise adjusted gas flow rate).

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noting that the control chart can trigger alarms before the onset of flooding. This is because of the significant increase in the DOS of the variable trajectory of pressure drop. This characteristic of the control chart makes early prognosis of flooding possible. As a result, efficient and effective process adjustments can be executed before the flooding phenomenon disturbs the process. In the second scenario to be investigated, the gas flow rate was adjusted to increase continuously, while the liquid flow rate was set to 0.89 × 10−4 m3/s. Comparing to the first experiment, this scenario is more realistic. It simulates the efforts to improve the output concentration at the column bottom by increasing the heat load on the reboiler. The trajectory of the pressure drop in the column is depicted in Figure 1. Following a similar procedure as presented in previous paragraphs, the MW control chart was developed, as shown in Figure 8. Although a small number of false alarms are observed near the 100th sample, this control chart successfully raises warnings before the onset of flooding, facilitating early adjustments of the process settings to

AUTHOR INFORMATION

Corresponding Author

*Tel.: +886-3-5713690. Fax: +886-3-5715408. E-mail: yyao@ mx.nthu.edu.tw. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported in part by Ministry of Science and Technology, ROC (under Grant No. MOST 105-2622-8-007009) and Jiangsu Key Laboratory of Process Enhancement & New Energy Equipment Technology (Nanjing University of Technology).

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Figure 8. MW control chart developed in the second scenario (with a continuously increasing gas flow rate). 10749

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