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Air Quality Research Program TCEQ Grant No. 582-10-94300

Additional Tests Days for TCEQ 2010 Flare Study Project 10-009 (Task 2)

Modeling of Flare Performance Using Multivariate Image Analysis and Computational Fluid Dynamics

Draft Final Report

Prepared by

B.C. Rawlings, O.A. Ezekoye, and T. F. Edgar

The University of Texas at Austin

The Center for Energy and Environmental Resources

December 20, 2011

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Executive Summary The goal of the modeling project (Task 2) is to be able to assess the relative impact on flare combustion efficiency by operating variables such as vent gas flow, steam or air assist, flame temperature, and the presence of certain volatile organic compounds. Two types of models were used to better understand the performance data obtained in Task 1 and the effect of such parameters as wind, vent gas flow rate and composition, and air and steam assist at operating points that were not run in Task 1. One modeling approach (Multivariate Image Analysis or MIA) uses feature variables extracted from the spectral information of the flare images on the video recordings from the tests. This complements the predictive capability of the second modeling approach, computational fluid dynamics (CFD), which uses first principles to model the full-scale flares used in the Task 1 tests and compare the model predictions with the test data. The CFD model will predict flare performance, i.e., combustion efficiency and destruction and removal efficiency, while at the same time predicting emissions produced at different operating conditions. In the MIA approach (Task 2.1) for the steam-assisted flare, 8 tests were usable (the flame was visible), while there were 13 usable tests for the air-assisted flare. Different training/validation approaches were examined: 1) Use half the images from each test as a training set, and the other half to validate the model. 2) Leave-one-test-out cross-validation, wherein for each set, all of the other sets are used to

train the model, which is then tested on the remaining point. This process is repeated for each of the sets.

Other variables recorded for each test included lower heating value of fuel stream, assist gas flow rate, air to fuel ratio in combined assist/fuel stream, and crosswind velocity. These variables were used along with the feature variables in the regression. The best results were obtained when odd-numbered images were used to train the model and even-numbered images were used as the validation set. Leave-one-out validation also provided accurate results when a large number of training sets were available. When building a model with the goal of making predictions about previously unseen flares, a wide range of training data is required. In this case, combustion efficiency from analytical equipment such as FTIR will be needed to train the image analysis model. Then the MIA model could be used for real-time adjustment of steam flow to a flare. In Task 2.2, a CFD model was used to model a flare and calculate the combustion efficiency for use in MIA. However, It takes a long time (hours) to obtain a result from CFD, so this approach could not be used to analyze on-line measurements. Fitting of the CFD model to the data was needed due to the uncertainty of the reaction kinetics mechanism for propylene combustion, so one parameter is adjusted to match the field data, which provides a reasonably accurate fit for both steam and air-assisted flare tests. In Task 2.3, the Combustion Zone Heating Value (CZHV), or the heating value of the combined assist gas and fuel stream, is related to the combustion efficiency. We have concluded that the correlation is not strong enough to make accurate predictions (± 20% variation in some cases).

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1. Introduction Air quality measurements taken in field studies in the Houston-Galveston area (HGA) have found evidence of localized regions with elevated concentration of highly reactive volatile organic compounds (HRVOCs). The elevated HRVOCs appear to result from daily variability in emissions (or episodic emissions) from refineries and petrochemical plants. Major sources of episodic emissions are flare combustion systems. The standard EPA emission factor indicates that combustible hydrocarbons (including HRVOCs) are burned with a 98% efficiency. This assumes that combustion flares operate under a consistent set of operating conditions, which probably does not apply for upsets or episodic conditions. Recent field studies by UT-Austin under TX AQRP funding found that combustion efficiencies depend on parameters that influence flame size such as stack velocities, flare gas composition, wind speed, and steam feed rates. These factors greatly influence the ability of flares to destroy pollutants sent through vapor streams. Development of a predictive model for flare emissions is important. Such a model can be based on a first principles approach using simplified flare configurations, mass and energy balances, fluid flow and heat transfer, chemical kinetics, and thermodynamics. In previous work UT-Austin has developed a first principles flare performance model using Fluent, a software package for computational fluid dynamics. In 2006 the Edgar research group performed initial two-dimensional modeling using flame and wind tunnel data available in the literature. We proposed to build on our modeling experience and apply models to full-sized flares in order to assess the relative impact on combustion efficiency by operating variables such as gas flow, waste gas heating value, amount of steam assist, flame temperature, and presence of certain HRVOCs (ethylene, propylene). Parametric sensitivity of the model can be evaluated. Data from the 2010 pilot scale flare tests at John Zink in Tulsa, OK, will be used to validate the model. In addition, UT-Austin has previously developed a flare image analysis method that can be used to correlate video images to combustion efficiency. That methodology is also applied to the John Zink test data.

2. Task Descriptions

Task 2.1. Multivariate Image Analysis of Flares Previous work by T.F. Edgar and his group at UT-Austin developed a new approach for flare monitoring based on multivariate image analysis using principal component analysis (PCA) of computational fluid dynamics (CFD) simulations of flare performance variables. In those studies, several feature variables were extracted from the spectral information of the flame images that could be used for real-time feedback control of flare efficiency. In an analogous fashion, image data from the TCEQ-John Zink pilot scale testing was correlated with flare

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efficiencies, using spectral data from video recordings of the flare image. The data were then analyzed for new feature variables to be used in the resulting regression model, in order to obtain satisfactory prediction of the combustion efficiency. We also studied effects of the fuel flow rate, the fuel type, and the crosswind velocity as additional parameters to improve the partial least squares regression. An accurate predictive model would enable formulation of flare control strategies to minimize air quality impacts. Such strategies could include changes in operational practices as well as active feedback and feedforward control strategies based on actual measurements. CFD simulation models developed in Task 2 below could be very useful in developing these control strategies.

Multivariate Image Analysis

Approach The purpose of applying MIA to flare combustion is to provide a fast, inexpensive, on-line method for monitoring the combustion efficiency of the flare. From an image of the flare, a set of feature variables can be extracted which are based on the appearance of the flame. These variables include the size, shape, and brightness of the flame, the variability of the flame’s color, and the brightness of the image background. Assuming that the appearance of a flare is related to its combustion efficiency, these values can then be used to generate a model to predict the combustion efficiency. See Appendix A for more details on the MIA method. The regression results are recorded both as the predicted combustion efficiency from each input image, and also as the average predicted combustion efficiency for the entire duration over which the flare was recorded. The recording length for each flare varied from 10 to 20 minutes. The rationale behind using the average combustion efficiency over the entire recording is that flares are not steady processes, instead they continually change shape and appearance. Therefore, a single image cannot be used to accurately represent the state of the flare, and an average over a reasonable time-scale (on the order of minutes) must be used.

Flare Descriptions The John Zink-UT tests that resulted in a visible flame are described below. The other tests either did not produce visible flames (so image analysis in the visible spectrum was not possible), or did not differ appreciably in appearance from those flames described. The descriptions are provided to indicate how much the appearance of the flare varied between tests, as image analysis relies on variations in the appearance of the flare in order to accurately predict the combustion efficiency. The operating conditions which were used in the regression are shown in Table 1.

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S1.5 Bright, small flame. Roughly 45◦ angle. S3.7 Longer, dark orange flame. 45◦ angle. Slow movement in the wind. S4.1 Very faint flame. S5.6 Weak flame, almost horizontal. S6.1 Similar shape to S1.5, but not as bright. In some frames, parts of the flame are cut

off by the camera. A2.1, A2.3, A2.4, A2.5

Bright, small flame. Flame does not extend much past the flare tip, and is not long enough to be significantly bent over by the wind

A3.1 Bigger, darker orange, less vigorous flame. Bent over nearly horizontal in the wind. A3.6 Weaker flame than A3.1, otherwise similar. A6.1 Bright, small flame, bent nearly horizontal in the wind. A6.4, A6.5

Vary between almost invisible and a flame similar to A2.1

Test CE (%) Crosswind (mph) Wind direction (degrees) LHV (btu/scf) Assist rate (lb/h) S1.5 99.9 8.0 176 2,145 3,794 S3.7 99.2 7.1 133 346 228 S4.1 95.0 5.6 146 350 536 S5.6 92.6 9.6 180 590 463 S6.1 99.2 8.8 180 609 1,003 A2.1 95.5 12.8 174 2125 83,818 A2.3 94.0 10.1 180 2108 88,791 A2.4 87.6 10.0 185 2113 148,799 A2.5 91.8 13.3 174 2124 119,580 A3.1 99.1 10.3 178 339 19,387 A3.6 88.9 11.9 170 338 60,121 A6.1 99.3 15.9 180 584 11,404 A6.4 86.3 14.1 180 585 40,584 A6.5 81.6 15.5 185 584 56,594

Table 1. Combustion efficiency and operating conditions of the different tests. CE stands for combustion efficiency, LHV for lower heating value. A wind direction of 180 degrees is sideways, from the perspective of the camera used to record the flares. Assist rate refers to the flow rate of the assist gas in the steam-assisted and air-assisted flares.

Results The image analysis code was applied to the usable tests (those with a visible flame) for both the air-assisted and steam-assisted flares. Five minutes of video data, with frames selected at one second intervals (total of 300 data points) were used in image analysis for each test. Two separate training/validation schemes were examined. In scheme “A”, half of all the images were used as a training set to train the model. This means that half of the images from every flare test (such as A1.1) were used for training. The other images were used to validate the model. In scheme “B”, for each test, all the other cases were used to train the model, which was then

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applied to the remaining case; this is known as leave-one-out cross-validation. This scheme simulates the real-world application, wherein a series of different tests would be used to train the model, which would then be applied to an unknown case. The results are shown in Figures 1 through 4. When training/validation scheme “A” is used, the model accurately predicts the combustion efficiency for both the steam-assisted and air-assisted flare. What this means is that while the appearance of the flame varies over time, if the model is trained using some images from a given test, the other images will be similar enough (and distinct from the other tests) that the model will function properly. The different results when using scheme “B” (with respect to the accuracy of the model’s predictions) indicate that a wide range of conditions must be used to train the model in order for it to make accurate predictions about similar (but previously unseen) flares. In the case of the steam-assisted flare, there were not enough usable tests (8) to train the model such that it could make accurate predictions. For the air-assisted flare, there were 13 usable tests, which proved to be enough for the model to accurately predict the combustion efficiency of a flare that was not in the training set.

Figure 1: Predictions using the image analysis model on the air-assisted flare, with testing/validation scheme “A”.

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Figure 2: Predictions using the image analysis model on the air-assisted flare, with testing/validation scheme “B”.

Figure 3: Predictions using the image analysis model on the steam-assisted flare, with testing/validation scheme “A”.

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Figure 4: Predictions using the image analysis model on the steam-assisted flare, with testing/validation scheme “B”. There were not enough usable tests for this approach to work with the steam-assisted flare.

Task 2.2. Computational Fluid Dynamics Modeling of Flare Data Initial computations were carried out using FLUENT 13.0 after making the mesh in auxiliary software. The basic model assumptions are listed below: • The simulation is a 3-D steady state system. • The FLUENT prediction of the turbulent reacting flow is concerned with prediction of the

time-averaged values of these fluctuation scalars. Hence only time-averaged results are computed.

• Pressure operation is 1atm (101325 Pa.). • The flow has a very low Mach number and is essentially incompressible. • Because the jet is round, and therefore axisymmetric, only one half of the domain is modeled

with CFD code. This saves computational time (typical runs on computer clusters take one hour).

• Turbulence is modeled by using the classical k-ε turbulence model. • Radiation is modeled by using the P1 radiation model. • 7 species, CH4, C3H6, N2, O2, CO, CO2, and H2O are considered in order to describe the

flame chemistry. FLUENT uses finite volume methods to numerically solve the problem. The flow domain was meshed and packed towards the symmetry axis and near the jet exit because greater gradients were expected in these zones, based on the previous work of Castiñeira (2006).

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An important issue is what parameters must be tuned in FLUENT in trying to match the experimental data. A well-known advantage of FLUENT is it has many thermochemistry models to choose from. The most difficult task is to decide which of these models are more representative of the real system. For example, the user must choose the best flow geometry for the system, and appropriate mesh for the flow domain, the most realistic boundary conditions, the species model, the chemistry model, the flow viscous model, the radiation model, the numerical discretization parameters, the PDF function, etc. Engineering knowledge is necessary to understand how the characteristics of each model fit the real flare. The real “tuning” process is basically reduced to a) solution initialization, b) number if iterations, c) convergence criteria, d) under-relaxation factors, and e) grid adaptation. As an extension, the work with FLUENT (proprietary software) could be followed in the future by use of an open source software package called Fire Dynamics Simulator developed under the auspices of NIST. The goal is to generate a CFD model that can accurately predict the combustion efficiency of a flare, over the range of operating conditions present in the flare test. Because propylene is not included in the reaction set available in FLUENT, it was necessary to propose a reaction mechanism that accurately describes propylene combustion. The simulations depend on this mechanism because propylene made up either 100% or 80% of the fuel gas in all of the test cases. The propane combustion model was selected as a starting point due to the similarity in flame speed between propene and propane (Davis, et.al., 1999: Saeed and Stone, 2007). The pre-exponential factor in the combustion model was then varied, and the results were compared to the measured combustion efficiency. Interpolation led to the pre-exponential factor in the combustion model which would lead to the most accurate prediction. The downside of this approach is that a limited set of tests were used to estimate the combustion mechanism for propylene. With a validated CFD model, it is possible to compute the combustion efficiency of a flare, given the operating conditions, and then either use that information to design the flare, to evaluate its operation under a range of variable parameters, or to train an image analysis model to enable fast on-line monitoring.

Results The results, seen in Figures 5 and 6, indicate that while the resulting mechanism yields accurate predictions for some tests, in other cases it yields inaccurate predictions. Figures 5 and 6 show that the model does accurately predict the combustion efficiency for some of the cases, while providing an inaccurate prediction for other cases. In general, however, the predicted values do follow the same trend as the measured combustion efficiencies. Further examination of the CFD model would be necessary to determine how the model needs to be adjusted in order to provide accurate predictions over the entire range of operating conditions.

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Figure 5: The combustion efficiency predicted by the CFD model for the air-assisted flare, compared to the measured value.

Task 2.3. Evaluation of CRZ (Combustion Reaction Zone) Benchmark Using John Zink Tulsa Flare Data and CFD Models The performance test data can yield insights into variables that could potentially be used as parametric monitoring points (“macroobservables”) to ensure high efficiency during high turndown operation. As applied in previous tests, the Combustion Zone Gas Net Heating Value (CZG NHV) is a calculated term representing the net heating value of all components in the combustion zone. The combustion zone is directly above the flare tip and is the point at which all materials combine for combustion. The CZG NHV is the resultant heat content from the mixture of the vent gas from the flare header, the pilot gas, and the total steam. In previous tests by Marathon, the CZG NHV showed a rough correlation to combustion efficiency, with efficiency rapidly declining below about 250 BTU/scf for the base load and refinery fuel gas test series and below about 425 BTU/scf for the propylene Test Series. The combustion efficiency results for the Detroit 2010 Marathon test are similar to the results from the 2009 Texas City flare performance test. The trends for the base load, refinery fuel gas, and propylene test series show approximately the same inflection points in both Detroit and Texas City tests. Unlike Texas City, which did not have favorable wind conditions for the hydrogen and nitrogen test series, Detroit wind conditions were much more favorable for the hydrogen and nitrogen test series.

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. Figure 6: The combustion efficiency predicted by the CFD model for the steam-assisted flare, compared to the measured value.

Results The John Zink Tulsa tests were analyzed for similar correlations, but the efficiency in this test did not show a satisfactory correlation with CZG NHV, as shown in Figures 7 and 8. Figure 7 in particular clearly shows that for the air-assisted flare, the combustion efficiency can vary by up to 30% for a given value of the combustion zone heating value. For the steam-assisted flare, the combustion efficiency can also vary due to factors other than the CZG NHV for a given heating value. This is most prominent in the range from approximately 150 Btu/scf to 200 Btu/scf, which is the region of greatest interest, as that is where the combustion efficiency declines the fastest. Therefore, we did not use the CZGNHV model to explore this idea further.

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Figure 7: The combustion efficiency of the air-assisted flare versus the combustion zone heating value. The combustion efficiency varies greatly for a given CZG NHV.

Figure 8: The combustion efficiency of the steam-assisted flare versus the combustion zone heating value. The correlation is not strong enough to make accurate predictions about the combustion efficiency using only the CZG NHV.

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Recommendations for Further Research

1) Run MIA software on other flare data if available (e.g., Marathon tests with video), followed by tests at other plants where field data will be collected using a remote sensor such as FTIR. This project would require about a two year effort.

2) The image analyzer should be utilized in a test with closed-loop control of combustion efficiency by changing steam assist rates or air rates. Control strategies should be postulated and tested. This should be done at the same plant chosen in (1) above.

3) The MIA model is not a predictive model in that it must be calculated with data from an operating flare and independent sensor for combustion efficiency. The CFD model is a predictive model so it is a very powerful approach, although some parameters would need to be fitted to operating data. The propylene combustion mechanism will need to be refined in a software tool like Fluent. However, more extensive study on evaluating the sensitivity of assumptions used in the CFD model should be conducted. Also the development and validation of an open source CFD model such as NIST Flare Dynamics Simulator would make it more readily available to industry, due to its lower cost.

References Castiñeira, D.A. A Computational Fluid Dynamics Simulation Model for Flare Analysis and Control. PhD thesis, The University of Texas, 2006. Davis, S. G., Law, C. K., and Wang, H., "Propene pyrolysis and oxidation kinetics in flow reactor and in laminar premixed flames." Combustion and Flame Vol. 119: 375-399 (1999). Marathon Petroleum Company, “Detroit Performance Test of Steam-Assisted Elevated Flare,” Detroit, MI, 2010. Marathon Petroleum Company, “Performance Test of Steam-Assisted Elevated Flare with Passive FTIR,” Texas City, TX, May 2010. Saeed, K.and Stone, R., “Laminar burning velocities of propene–air mixtures at elevated temperatures and pressures”, Journal of the Energy Institute, Vol. 80, Number 2 , pp. 73- 82 (2007).

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APPENDIX A

MULTIVARIATE IMAGE ANALYSIS

1. Multivariate Image Analysis (MIA) Fundamentals In order to manage an image for scientific purposes, a mathematical description of this image is necessary. Consider a simple 2D black-and-white image. This image has a horizontal dimension and a vertical dimension which can be discretized, transforming the continuous image into a digital image. The latter is basically a chessboard-type structure, where each square is assigned with a certain intensity-gray-value. Each of these squares is called a pixel. The intensity-gray-value assigned to each pixel allows to mathematically representing the image in matrix form. For color images, the analysis of the properties of black-and-white images may simply be repeated three times. In fact, the tristimulus theory claims that any visual color can be simulated by the mixture of three color information channels (Giorgianni and Madden, 1997). Traditionally these three colors have been chosen as red, green and blue (RGB system). According to this, any color scene can be approximated by combining three intensity-gray-value images that are given by the numerical values (normally integers from 0 to 255) of its R, G, and B channels. Color images also represent a class of multivariate image (Geladi and Grahan, 1996). A multivariate image is a stack of “congruent” images, that is, images where pixel positions match for all images in the stack. Multivariate imaging has been introduced in different scientific fields, where congruent images of the same object or scene have been traditionally obtained by using different radiation energies or wavelengths. Multivariate images can also be obtained by combining images resulting from different instruments or even by combining a univariate image with copies of it that are derived from filtering operations. The fact of the matter is that an RGB color image is a multivariate image with three variables (e.g., the horizontal dimension, the vertical dimension, and a third dimension which is the variable way given by the R, G and B channels).

2. Procedure for implementing MIA The practical implementation of multivariate image analysis (MIA) carries out several steps. The procedure is shown below, which allows to create a regression model that can be used to predict the flare combustion efficiency from an image of the flare.

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2.1.- Converting color images into three-way arrays ( X ) of data. The first step in any multivariate image analysis is to convert the actual color images into three-way arrays of data. As commented earlier, in this particular work, images are obtained directly from computer simulation of the flares. Hence, the commercial software MATLAB 7.0 can be used to read these color images and transform them into a three-way array of data according to its RGB intensity values.

→MATLAB)( KJIX ××

Flare Image where I and J are the horizontal and vertical dimensions of the image respectively and K=3 for RGB color images It should be noted that analysis of real flare images would be more complex due to the presence of the flare stack and a potential interfering background (for example, a highly luminous sky may affect the color analysis of the flare image). Under these circumstances, some sort of processing and transformation operations should be performed in the image to remove all these background features. 2.2.- Isolating the flame The next step in analyzing a flare based on its visual appearance is to isolate the region of the image that corresponds to the flame. This task is made easier by the fact that flames are “red-colored,” while the background is generally a different color; for example, elevated flare stacks would have the sky as the background. When the flame is the only red-colored region in the image, it can be isolated by comparing the red, green, and blue intensity of each pixel. A simple test for “red” colors is if the red intensity is greater than the green intensity, which is in turn greater than the blue intensity, the pixel will appear red. A masking matrix M can be generated as follows:

Mij = �1, if Xi,j,1 > Xi,j,2 > Xi,j,3

0, all other (i, j)

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The result of applying this test is shown in Figure A-1:

Figure A-1: The original flare image is shown on the left, with the masked image on the right. For the image set from the flare tests at the John Zink facility, no further processing was necessary to identify the region of the image occupied by the flame. 2.3. Extracting features from the flare images Once pixels corresponding to the flame’s luminous region have been delineated, the user is in position to extract useful information from the image. In fact, certain features or “image measurements” can be easily extracted which have physical meaning. Those measurements will then be regressed against the experimental combustion efficiencies of the flares so that a predictive model is obtained. Using the masking matrix M, the following “feature variables” can be extracted from each image: 2.3.1 Luminous region area (A). The area of the flame image that corresponds to the luminous region can be easily computed by counting the number of pixels falling into the flame mask. Mathematically,

A = �Mi,ji,j

2.3.2 Flame brightness (B). Flame brightness can be obtained by integrating the luminous intensity level contributed from all pixels falling inside the luminous region. The luminous intensity level for any pixel can be

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calculated by converting the color image to grayscale. The total brightness of the flame is the sum of the brightness of each pixel in the flame region,

B = ��0.299 Xi,j,1 + 0.587 Xi,j,2 + 0.114 Xi,j,3�Mi,ji,j

where the coefficients 0.299, 0.587, and 0.114 are the contributions of the red, green, and blue values to the brightness of a pixel. 2.3.3 Average brightness of the non-luminous area (W). While the brightness of the flame region is dominated by the combustion process, it is important to keep in mind that flames are semi-transparent. Therefore, the brightness of the background can contribute to the appearance of the flame. The brightness of the background can be calculated similarly to the brightness of the flame region, but using the inverse of the masking matrix:

W = ��0.299 Xi,j,1 + 0.587 Xi,j,2 + 0.114 Xi,j,3�(1− Mi,ji,j

)

2.3.4 Direction of the flame (P) The effect of crosswind can be seen as the “bending” of the flame. A simple way to quantify this is to perform a linear regression using the x- and y-coordinates of each pixel in the NxM masking matrix, M. The matrix indices can be converted to coordinates

(x, y) = (j, N − i) ∀ i, j | Mi,j = 1 2.4. – Regression of the feature variables Once the feature variables have been extracted from the images, the regression model can be trained using the measured combustion efficiency values. Partial least squares is used to generate the model (Abdi, 2010).

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References (Appendix A) Abdi, H. “Partial least squares regression and projection on latent structure regression (PLS regression).” Computational Statistics, 2(1):97–106, (January/February 2010). Esbensen K. and Geladi, P., “Strategy of Multivariate Image Analysis (MIA)”, Chemometr. Intell. Lab. Syst., Vol. 7, pp. 67-86 (1989). Geladi, P. and Grahan, H., Multivariate Image Analysis, Wiley, Chichester, UK (1996). Geladi, P., Isaksson, H., Lindqvist, L., Wold, S. and Esbensen, K., “Principal Component Analysis of Multivariate Images”, Chem. Int. Lab. Sy., Vol. 5, pp. 209-220 (1989). Giorgianni, E.J. and Madden, T.E., Digital Color Managment: Encoding Solutions, Addison-Wesley (1997). Golub, G.H. and Van Loan, C.F., Matrix Computations, The John Hopkins University Press, Baltimore, MD (1983). Liu, J.J., Bharati, M.H., Dunn, K.G., and MacGregor J.F., “Automatic Masking in Multivariate Image Analysis Using Support Vector Machines”, Chemometrics and Intelligent Laboratory Systems, Vol. 79, pp. 42-54 (2005). Petrou, M., and Bosdogianni, P., Image Processing: The Fundamentals, Wiley, New York (1999). Smilde A. “Three-way Analysis: Problems and Prospects”, Chemometr. and Intell. Lab Syst., Vol. 15, pp. 143-57 (1992). Wold, H. “Path Models with Latent Variables: the NIPALS Approach”, In H.M. Blalock et al. (editor), Quantitative Sociology: International Perspectives on Mathematical and Statistical Modeling, Academic Press, New York (1975). Yu, H., and MacGregor, J.F., “Monitoring Flames in an Industrial Boiler Using Multivariate Image Analysis”, AIChE Journal, Vol.50, No 7, pp. 1474-83 (2004).