Chemical Product and Process Modeling
Volume 2, Issue 3 2007 Article 12

Nonlinear Modelling Application in Distillation Column
Zalizawati Abdullah, Universiti Sains Malaysia Norashid Aziz, Universiti Sains Malaysia Zainal Ahmad, Universiti Sains Malaysia

Recommended Citation: Abdullah, Zalizawati; Aziz, Norashid; and Ahmad, Zainal (2007) "Nonlinear Modelling Application in Distillation Column," Chemical Product and Process Modeling: Vol. 2 : Iss. 3, Article 12. Available at: http://www.bepress.com/cppm/vol2/iss3/12 DOI: 10.2202/1934-2659.1082 ©2007 Berkeley Electronic Press. All rights reserved.

Nonlinear Modelling Application in Distillation Column
Zalizawati Abdullah, Norashid Aziz, and Zainal Ahmad

Abstract
Distillation columns are widely used in chemical processes and exhibit nonlinear dynamic behavior. In order to gain optimum performance of the distillation column, an effective control strategy is needed. In recent years, model based control strategies such as internal model control (IMC) and model predictive control (MPC) have been revealed as better control systems compared to the conventional method. But one of the major challenges in developing this effective control strategy is to construct a model which is utilized to describe the process under consideration. The purpose of this paper is to provide a review of the models that have been implemented in continuous distillation columns. These models are categorized under three major groups: fundamental models, which are derived from mass, energy and momentum balances of the process, empirical models, which are derived from input-output data of the process, and hybrid models which combine both the fundamental and the empirical model. The advantages and limitations of each group are discussed and compared. The review reveals a remarkable prospect of developing a nonlinear model in this research area. It also shows the discovery of new advance methods in an attempt to gain a nonlinear model that is able to be used in industries. Neural network models have become the most popular framework in nonlinear model development over the last decade even though hybrid models are the most promising method to be applied for future nonlinear model development. KEYWORDS: nonlinear model, distillation column, empirical models, fundamental models, hybrid models Author Notes: This research was supported by Ministry of Science, Technology and Innovation (MOSTI), Malaysia through IRPA-8 project No: 03-02-4279EA019. N.Aziz, School of Chemical Engineering, Engineering Campus Universiti Sains Malaysia, Seri Ampangan, 14300 Nibong Tebal, Pulau Pinang, Malaysia. Phone: +604 -5996457, Fax: +604 -5941013

Abdullah et al.: Nonlinear Modelling Application in Distillation Column

1. Introduction Distillation is one of the most important unit operations in chemical engineering because it is the most frequently used separation technique in the chemical and petroleum industries. Distillation columns are fairly complex units and exhibit nonlinear dynamic behavior due to their nonlinear vapor liquid equilibrium relationships, the complexity processing configurations (e.g., prefractionators, sidestreams and multiple feeds) and high product purities (Luyben, 1987). Their dynamics are a mixture of very fast vapor flowrate changes, moderately fast liquid flowrate changes, slow temperature changes and very slow composition changes (Luyben, 2002). Effective control of distillation columns can improve product yield, reduce energy consumption, increase capacity, improve product quality and consistency, increase responsiveness and improve process safety. Therefore, an effective control system for the column is required but their nonlinear behavior and illcondition nature; hydraulic constraint, separation constraint, heat transfer constraint, pressure constraint and temperature constraint cause difficulties in control design of the distillation column. Model based control strategies that explicitly embed a process model in the control algorithm such as internal model control (IMC) and model predictive control (MPC) have been revealed as the better control systems compared to the conventional method because of their ability to satisfy strict performance required (Qin and Badgewell, 1997). Performance of model-based controller is mostly determined by its model. If the model is accurate, and if its inverse exists, then process dynamics can be cancelled by the inverse model. As a result, the output of the process will always be equal to the desired output which means model based control design has the potential to provide perfect control (Willis, 2007). In model-based controller, a model of the process is used in one of three ways (MACC, 2007): (i) explicit model in control algorithm; (ii) adaptive change to control algorithm based on model; (iii) combination of sensor data with models to provide improved estimates of process performance used by the control algorithm. One of the major challenges in developing the model based control strategy is to construct the model which is utilized to describe the process and this issue has been noted by several authors (Pearson, 2003; Qin and Badgewell, 1998). At present, most industrial controllers use a linear process model such as first-orderplus-dead-time or pure-integrator-plus-dead-time models. The linear model is applied to the estimation of the linearity and the dynamic range of the process. However, satisfactory performance of this linear model is generally achieved over a narrow operating range. They are only able to approximate the system around a given operating point but when a wide range of process operations with tight specifications on product composition is required, the nonlinearities become more

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critical and control performance is sacrificed (Mahfouf et al., 2002). Because most processes are nonlinear, together with higher product quality specifications, increasing productivity demands, tighter environmental regulations and demanding economical considerations in the process industry, consequently they require operating systems closer to the boundary of the admissible operating region. In these cases, linear models are inherently incapable of describing an enormous range of important dynamic phenomena (Findeisen and Allgower, 2002; Pearson, 2003). Therefore, good control of distillation column requires a nonlinear model based control. There are several models that can be used for distillation column and these models can be categorized under three major groups; fundamental models which are derived from mass, energy and momentum balances of the process, empirical models which are derived from input-output data of the process and hybrid models which combines both, the fundamental and empirical models. The aim of this paper is to provide a review of the models that have been implemented in continuous distillation column for both, binary and multicomponent systems. The details of the models are explained in the following section and the advantages and limitations of each group are highlighted and compared. 2. The Nonlinear Model The development of nonlinear process models is tremendously essential due to the unavoidable nonlinearity of the process and complexity of nonlinear system. The difficulty of the nonlinear model development arises from several sources and the following two are fundamental; the fact that model utility can be measured in general, in a conflicting way and the fact that the class of nonlinear models does not exhibit the unity. The four extremely important measures of model utility are (Pearson, 2003): 1. 2. 3. 4. approximation accuracy physical interpretation suitability for control ease of development

The fundamental models are the models which mathematical representation is based on an understanding of the physical processes that occur within the system. These models are derived by applying transient mass, energy and momentum balance to the process. These knowledge-based models which are also referred as the first principle models tend to involve on the order of 102–103 nonlinear differential equations and a comparable number of algebraic relations (Michelsen and Foss, 1996). Fundamental models are highly constrained with respect to their

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Abdullah et al.: Nonlinear Modelling Application in Distillation Column

structures and parameters. The model parameters can be estimated from laboratory experiments and routine operating data. As long as the underlying assumptions remain valid, fundamental models can be expected to extrapolate at operating regions which are not represented in the data set used for the model development (Henson, 1998). A major point of attraction is that a model obtained on the basis of fundamental principles would be globally valid and are usually more accurate and give more complete process understanding. However, the fundamental model is too complex for controller design and the process characteristics for fundamental models development are based on assumptions and these assumptions may be wrong (Pearson, 1995). The empirical models, also known as black-box models can be obtained in the absence of a priori physical knowledge and the most valuable information comes from the input-output data collected during the operation (i.e. the measurements). These models describe the functional relationships between system inputs and system outputs. The detailed process understanding is not required. Therefore, model complexity can be avoided and able to alleviate the computational burden on the controller. The empirical model can represent a nonlinear relationship accurately in the domain reflected by the data even if the unmeasured disturbances are present (Eikens et al., 2001). The results of the models depend not only on the accuracy of the measurements but also on the similarities between the situation to be analyzed and the situation where the measurements are carried out. The third group is the hybrid models which are developed by combining both, the empirical model and fundamental model. Most of the knowledge of the process can go to the fundamental model while the input output models can be developed for those parts of the process which are hardly formulated. Common method for developing the hybrid model is to use empirical models to estimate the unknown function in the fundamental model or to utilize a fundamental model to capture the basic process characteristic and then use a nonlinear empirical model to describe the residual between the plant and the model (Henson, 1998). 3. Fundamental Models Several works have been carried out to implement the fundamental models in the distillation column and they are summarized in Table 1. The fundamental dynamic model approach has been used by Can et al. (2002) for binary distillation column. The rigorous dynamic column model was developed under SPEEDUP which consists of mass, component and energy balances for each tray, Wilson equation has been used to calculate the activity coefficients for phase equilibrium, a Murphy tray efficiency of 0.7, Francis weir correlation for the liquid hydrodynamics and pressure loss correlation. Experiments were carried out in the

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pilot plant to validate this model. The mixed integer dynamic distillation model has been developed by Bansal et al. (2000) for separation of benzene and toluene. Their model consists of differential-algebraic equations for the trays, reboiler, condenser and reflux drum. Diehl et al. (2003) applied the differential algebraic first principles model to identify the high-purity separation of a binary mixture of methanol and npropanol. The model was described by means of material and energy balances, hydrodynamic effects, equilibrium relationships for each tray and for the reboiler and the condenser. The resulting model consists of 82 differential equations and 122 algebraic equations. They compared the experimental closed-loop trajectory from the pilot plant with the simulated optimal open-loop trajectory to observe the quality of the model. Olsen et al. (1997) developed the dynamic model for multicomponent distillation column in a different way. They proposed an algorithm which allows the critical parts of the model calculated by implicit, and effectively simultaneous, numerical methods. In the development of this dynamic model, rigorous equations were used for material and energy balances on each tray, together with hydraulic correlations describing internal liquid and vapor flows. Liquid flows along the column were determined by a single pass semiimplicit method where flow influences on liquid levels at the tray below are approximately taken into account. Internal vapor flows were calculated simultaneously with the solution of mass and energy balance equations. This column model has been developed and implemented in the commercial simulator package ProSim and has been used in the simulator for Statoil's methanol plant. Since the dynamic model is too complex to be applied in model based control system, the reduction technique becomes the alternative approach to derive a simplified model. This technique has been proposed by many researchers. Balasubramhanya and Doyle III (1995) applied the low order models based on the traveling waves of the composition profiles to identify high purity distillation column. They used the constant shape for the profile during the propagation of the wave. A nonlinear traveling wave is a spatial structure moving with a constant propagation velocity and constant shape along a spatial coordinate. The dynamic behavior of a distillation column can be characterized by the movement of the composition or the temperature profile up or down the column in response to the disturbances or manipulated variable changes. They compared their model with detailed model to observe the accuracy. Yang and Lee (1997) used the reduced order model to account for the detail dynamics of the multistage distillation column. This technique utilized the orthogonal collocation and cubic spline method. Then the extended Kalman filter was applied to identify the model parameters and the feed composition from the measurements of the column. They found out that only with few collocation points, the reduced-order model can represents the outputs of the full-order rigorous model.

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Nonlinear reduction model based on singular perturbation analysis has been proposed by Kumar and Daoutidis (1999). They focused on a simple distillation column to highlight the inherent time-scale separation which is the key to the model reduction. The singular perturbation analysis of the detailed tray-by-tray model allowed the derivation of a low-order nonlinear model of the slow dynamics that governs the overall input-output behavior of the column. They figured out that the low order model has an excellent performance and robustness characteristics compared to detailed tray-by-tray model. Hahn and Edgar (2002) proposed the improved method of reduction using balancing of empirical gramians. This method is optimal in some sense. It consists of two steps. First is to find a transformation that balances the observability and controllability gramians in order to determine which state has the greatest contribution to the input-output behavior. The second step is to perform a Galerkin projection onto the states corresponding to the largest singular values of the balanced gramians for the region of interest in state-space. Their reduced order model was compared with original full-order nonlinear model and a linear model and they found out that the reduced order model stays very close to the behavior of the full-order system. Kienle (2000) proposed the low order dynamic model for multicomponent distillation processes which made direct use of well-known spatio-temporal pattern formation phenomena which also termed as nonlinear wave propagation. It takes into account the coexistence of different constant pattern waves within a single section of a distillation column and the resulting wave interactions as well as the influence of the system boundaries. The reduced order model managed to achieve a good agreement with the reference model for the steady state and dynamic transient behavior. All simulations have been carried out with the dynamic flowsheet simulator DIVA. Bian and Henson (2006) proposed the nonlinear wave model for high purity distillation column in separation of benzene-toluene. In the nonlinear wave modeling, the high order column dynamics were reduced to a single differential equation for the traveling composition or temperature wave in each column section. The complete wave model consisted of two nonlinear differential equations for the wave positions and 11 nonlinear algebraic equations for steady-state feed stage, reboiler and condenser balances and the vapor–liquid equilibrium relations were considered. A dynamic simulation of the benzene–toluene column was constructed in Aspen dynamics. Nominal values of the two wave positions and the six wave profile parameters were regressed from the nominal Aspen composition profile. The model provided excellent agreement with the Aspen profiles and they found that the proposed method sufficiently flexible to address a wide range of practical measurement selection problems.

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The different advanced technique known as overall rate-based (ORB) models, which use multicomponent mass transfer rates rather than empirical efficiency factors, so as to incorporate non equilibrium effects have been proposed by Muller and Segura (2000). The aim of their work was to develop a rate-based stage model for industrial-scale distillation columns. The model developed considers the cross flow patterns on trays retaining the compact and mathematical attractive features of the nonequilibrium (NEQ) stage model. The ORB model provides a better approximation of concentration profiles, compared with the multicomponent efficiency and the NEQ stage model. A Fortran90 program was used to develop all the models described. Higler et al. (2004) applied the NEQ model for a complete three-phase distillation. The model consists of a set of mass and energy balances for each of the three possible phases present. Mass and heat transfer between these phases were modeled using the Maxwell–Stefan equations. Equilibrium was only assumed at the phase boundary between two phases. The method of solving the NEQ model equations described here consists of first, solving the equilibrium two phase model, using this solution to obtain a converged solution for the equilibrium three-phase problem by means of a differential arc length continuation method and subsequently using this as a starting guess for the nonequilibrium three-phase model with Newton’s method. They found out that results of the nonequilibrium model are in good match with the experimental data obtained from a small laboratory scale column for the water-ethanol-cyclohexane system. This review shows that the dynamic models which consist of a differential mass and energy balance equation becomes the most preferred method to develop the fundamental model. It also shows the growth of many reduction methods in order to allow the derivation of low order distillation column models directly from fundamental models. The reduction technique is still an active area of research based on the discovery of many advanced reduction methods such as the orthogonal collocation on finite elements approximation technique and the optimal Hankel norm approximation.

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No 1 2 3 4 5 6 7 8 9 10 11 12

Table 1: Summary – fundamental models applied in distillation column Model Distillation system Reference Dynamic model Methanol/water Can et al., 2002 Differential algebraic equation Benzene/toluene Bansal et al., 2000 model Differential algebraic first Methanol/n-propanol Diehl et al., 2003 principle model Dynamic distillation column Methanol/water/ impurities Olsen et al., 1997 model Low order modeling Not mentioned Balasubramhanya and Doyle III, 1995 Reduced order model Methanol/water Yang and Lee, 1997 Reduced-order nonlinear Not mentioned Kumar and Daotidis, models 1999 Reduction model Not mentioned Hahn and Edgar, 2002 Low order dynamic model Methanol/ethanol/1Kienle, 2000 propanol Nonlinear wave model Benzene/toluene Bian and Henson, 2006 Muller and Segura, Overall rate based stage model Acetone/methanol /2propanol /water 2000 Nonequilibrium model Ethanol/ water/cyclohexane Higler et al., 2004

4. Empirical Models This section reviews all models utilizing the empirical approach in developing the nonlinear distillation model. A summary of these models is given in Table 2. Block oriented models are one of the empirical models which combine the linear dynamic models with static or memoryless nonlinear function. These two model components can be combined by giving rise to three different model structures (Pearson and Pottmann, 2000): 1. Hammerstein model 2. Wiener model 3. Feed back block-oriented model The process identification of distillation column using Wiener model was studied by Zhu (1999). The nonlinear Wiener model considered consists of linear time-invariant transfer function vector followed by static nonlinear function. The idea of his work was to use the extended of parametric identification method for multi-input single-output Wiener models so called the asymptotic (ASYM) method. The cubic spline was used to model the nonlinear block and the linear part was approximated using Box-Jenkins structure by a high order autoregressive with exogenous input (ARX) model. He achieved the better model than linear model. Norquay et al. (1999) utilized the Wiener model for identification of highPublished by Berkeley Electronic Press, 2007 7

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purity distillation column. The Wiener model was constructed using cubic splines for the nonlinear elements and first order plus deadtime models for the linear elements. This model was identified using a steady-state AspenPlus™ model and the data collected from industrial C2-splitter at the Orica Olefines. Another Wiener model was developed by Bloemen et al. (2001). They proved that the Wiener model has the ability to approximate the nonlinearity of distillation column better than linear model and finite impulse response model. They used experimental data for identification of the Wiener model. The Wiener model developed enables one to identify both the low and high gain direction of the distillation column. The simple Hammerstein model for distillation column was developed by Nugroho et al. (2004). In their work, they developed the models to identify the ammonia stripper due to its nonlinear characteristic. Data for system identification have been obtained from a number of single-input multi-output experiments. The nonlinear model behaviors were described by Hammerstein model which consists of a static non linearity followed by a linear time-invariant block. The structure of the Hammerstein model is shown in Figure 1. For simplification, most models were considered only up to a quadratic form. The model obtained by structure identification and parameter estimation is validated using experimental data. u
Non linear

v Linear

y
1)

u

c 0  c1u(k )  c 2u 2 (k )

q v d B(q 1 ) Aq

y

Figure 1. Simple Hammerstein Model Another Hammerstein model was proposed by Bhandari and Rollins (2004). The proposed methodology was based on a closed-form exact solution to Hammerstein structure and hence referred to as the Hammerstein Block-oriented Exact Solution Technique or H-BEST. One major strength of H-BEST is its ability to vary its structure in the ultimate response over the input space and it does include a simple procedure for model identification with shorter test duration. The use of statistical design of experiment instead of pseudo-random sequence design allows one to estimate the behavior of the steady-state or ultimate response function as well as the dynamic function over the entire input space. They compare the EJL model (discrete-time Hammerstein model) to the HBEST model and they found out that the latter model is more accurate. Gomez and Baeyens (2004) used two different block-oriented nonlinear models; the multivariable Hammerstein model and the multivariable Wiener

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model in nonlinear identification of binary system. They proposed new noniterative algorithms for the identification of the model which are numerically robust, since they are based only on the least squares estimation and singular value decomposition. The Hammerstein model proposed was found to be consistent even in the presence of colored output noise, under weak assumptions on the persistency of excitation of the inputs. On the other hand, Wiener model only consistent in the noise free case. The use of rational orthonormal bases for the representation of the linear subsystem allows a priori information about the dominant dynamics, to be incorporated in the identification process and to improve the estimation accuracy. The different input-output modeling technique, the artificial neural network (NN) models have been used by many researchers to identify the distillation column. The majority of these models utilized the multilayer feedforward neural network to develop the nonlinear model. Brizuela et al. (1996) developed the feedforward neural network model for distillation column. Their neural network model consists of 50 neurons in one hidden layer, 14 network outputs and 31 input variables. The training data for the network was obtained from the simulation of column during startup, from initial state to a steady operating state. The performance of this neural network model for neural predictive control strategy was compared with PI controller. Savkovic–Stevanovic (1996) used the neural network approached for learning nonlinear dynamic model from distillation plant input-output data. The backpropagation algorithm of the Generalized Delta Rule adjust the weights in a feedforward NN consisting of several layers, and an output layer. Turner et al. (1996) proposed the filter-based neural network model. This model is quite similar to multilayer perceptron architecture. The dynamic modeling occurs at the output of the hidden layer via first order filters each with unit gain. One of the benefits of using this network architecture is that there is no initialization period since the system dynamics are completely defined by the fixed filter coefficients. The data for the model was gained from plant and 27 variables are taken from the real distillation plant. This neural network model was found to be a better model compared to linear model because it is able to predict a dynamic step response of the system accurately. Barrati et al. (1997) used the three layer feedforward neural network and trained through the backpropagation algorithm. The set of calibration data were produced making use of a dynamic simulator. The performance of the neural controller was assessed and compared with a conventional temperature control loop and a inferential control structure. Another neural network model for distillation column has been proposed by Ramchandran et al. (1997). They considered the separation of wastewater. The steady state model from rigorous first principles model which has been validated with operating data from the plant was used to generate all the process data for developing the neural network

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model. Karahan et al. (1997) used the neural network model for multicomponent high purity distillation column. In their study, the training data was obtained from the process and three layer neural networks was trained by backpropagation algorithm. Results of NN-MPC show high improvement in control of system over linear MPC algorithm. Yu (2003) used two hidden layers feedforward neural network approach to identify the behavior of binary distillation column. The input and output layer contains three and two nodes respectively. The modified back propagation was used to train the feedforward neural network. He found out that the neural network based controller performed better compared to nominal controller. Bo et al. (2003) applied the neural network model for industrial distillation operation. A three-layer Back Propagation Neural Network technology was adopted to build a soft-sensor model. An adaptive soft sensor was constructed as an alternative, for the physical sensors. A BP nerve network with 5 x 7 x 2 construction was applied to build the soft sensor model. For 300 sets of training data, 250 data obtained from the operation data that was arranged by the sample time and another 50 data was simulated data. Liau et al. (2004) used the feedforward neural network approach to build the operating model (knowledge database) of the crude oil distillation unit (CDU) operating model. The built artificial neural network (ANN) model can be applied on predicting the oil product qualities with respect to the system input variables. The neural network was trained using the experimental data collected from CDU operating system. Singh et al. (2005) proposed the modeling of multicomponent distillation column utilizing feedforward artificial neural network. The neural network model contains 17 inputs and 10 outputs. Data gained from the rigorous model was used for training and testing a neural network model. The results obtained from ANN based estimator found out to be in good agreement with the results of simulation as obtained using semi rigorous model. In their recent work, Singh et al. (2007) developed the NN estimator based on Levenberg–Marquardt (LM) algorithm and tested for binary as well as multi-component mixture case. The LM algorithm found to be more accurate and sensitive results as compared to the Steepest Descent Back Propagation algorithm for both cases binary and multicomponent. Wang and Rong (1999) proposed the neural network fuzzy system (NNFS) for propylene-propane distillation column. Associated with the NNFS was a twophase hybrid learning algorithm which utilizes the nearest-neighborhood clustering scheme and the gradient descent method which increases the learning speed much faster than the original back-propagation algorithm. They combined the low-level learning ability of neural networks and the high-level, human-like reasoning ability of the fuzzy logic systems into one framework. A typical format for a fuzzy rule base consists of a collection of fuzzy IF-THEN rules and the NNFS is a feedforward, four-layered network. History data were used as training

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data set. The performance of the NNFS was compared with the conventional three-layered back-propagation neural network. Different neural network approach has been proposed by Ou and Rhinehart (2003). They proposed the group neural network (GNN) model for methanolwater distillation column. The model comprises of a group of sub-models, each providing a prediction of one process output at one selected future point in time. The sub-models are mutually independent and therefore can run in parallel. They used neural networks for each sub-model. The advantage of the GNN model structure is its capability of direct long-range prediction. The multiple neural networks model for multicomponent distillation column has been proposed by Jazayeri-Rad (2004). A combination of multiple NNs was used to model an input-output nonlinear dynamic system. The proposed system consists of a two-dimensional array of NN blocks. Each block consists of a one step-ahead predictive neural model, which was identified to represent each output of the multiple-input multi-output (MIMO) system. Therefore, each block represents a multiple-input single-output (MISO) subsection of the whole MIMO system. The neural network models were a multilayer feed-forward NNs containing one hidden layer which contains 10 neurons. He found that this model has a better performance compared to the linear model of the plant. The Recurrent Dynamic Neuron Network (RDNN) model which was proposed by Shaw and Doyle III (1997) was used to identify a binary distillation column. The main idea of this RDNN was that a wide range of dynamics can be captured with the structure, due to its recursive nature and the fact that the neurons themselves are inherently dynamic. The RDNN structure contains two dynamic neurons and each neuron has an external input and feedback output as inputs and it is dynamic in nature. Open-loop simulations show that the RDNN was able to predict nonlinear output responses. Fortuna et al. (2005) used the three-step predictive dynamic neural models for debutanizer distillation column. Nonlinear autoregressive moving average models were used to fit real input/output data. The unknown function was implemented by a multilayer perceptron neural network with one hidden layer and a sigmoidal activation function. Levenberg–Marquardt algorithm was used to train the model. To avoid overlearning phenomena, learning data were organized into two sets and cross-validation with an early stopping approach was used. The training and validation data were obtained from debutanizer column. Yan et al. (2004) applied the soft sensing modeling based on the support vector machine (SVM) to estimate the freezing point of light diesel oil in distillation column. The soft sensing model based on SVM is shown in Figure 2. The soft sensing model generates a virtual measurement to replace a real sensor measurement. SVM is a powerful machine learning method based on statistical learning theory for the problems characterized by small samples, nonlinearity,

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high dimension and local minima. The SVM used the structural risk minimization principle, which seeks to minimize an upper bound of the generalization error rather than minimize the training error. Based on this principle, SVM achieves an optimum network structure by striking a right balance between the quality of the approximation of the given data and the complexity of the approximating function. Therefore, the overfitting phenomenon in general ANN can be avoided and excellent generalization performance can be obtained.
Secondary variables Secondary variables Secondary variables Secondary variables

u y
Xm(1) Estimation Yc (measurement) Ym

Xm(n

Support vector

Figure 2. Soft sensing model based on SVM Mahfouf et al. (2002) proposed the Takagi-Sugeno-Kang (TSK) piece wise linear fuzzy modeling approach for a binary distillation column. Fuzzy logic system provides a computing paradigm for modeling nonlinear processes when a sufficiently accurate model of the process to be controlled is unavailable. Piecewise linear fuzzy process model used fuzzy inference to combine the outputs of a number of auto regressive linear sub models to construct an overall nonlinear process model. This method provides a more compact model (hence requiring less computation) than fuzzy modeling methods which used relational arrays. It also provided an improvement in modeling accuracy and effectively overcoming the problem of model incompleteness which limits the usefulness of relational fuzzy models for control applications. TSK fuzzy modeling approach can provide an improvement in modeling accuracy over a single linear process model when used to represent the process dynamics of non-linear chemical processes over a wide range. The disadvantages of this approach are that it was posed within a strictly analytical framework and it was based on empirically acquired knowledge regarding the operation of the process. Identification of high purity distillation column using of the polynomial type nonlinear autoregressive models with exogenous inputs (NARX) was proposed by Sriniwas et al. (1995). This distillation column was used to separate binary methanol-ethanol system. A major advantage of polynomial NARX models is that their one-step ahead-prediction can be formulated as a linear regression. The main challenge is to determine which terms to include in the polynomial model. NARX models have been shown to perform quite well for predicting system outputs.

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Results show that the performance of the linear model was inferior to that of a nonlinear model. Kano et al. (2000; 2003) and Showchaiya et al. (2001) proposed the inferential models for estimating product compositions which were constructed using the dynamic Partial Least Squares (PLS) regression. PLS model is developed for multicomponent distillation. Inferential models are classified into three types, i.e. steady-state models, static models, and dynamic models. Steady-state models are defined as models that determined from steady-state data. When models were built using time-series data, they are called static or dynamic models. Models are only classified as dynamic models when measurements at different sampling times were used as input variables. Simulated data were used to build and validate the dynamic inferential models. They compared steady-state, static, and dynamic inferential models and found that the estimation accuracy could be greatly improved by using the dynamic models. Park and Han (2000) used the same model for industrial splitter columns. However their study was based on smoothness concept. The method has been directly motivated by the locally weighted regression that estimates a regression surface through multivariate smoothing so that the model can be used for cases with strong nonlinearities. This review shows that neural network is the most preferable approach among other empirical models because the ability of the neural network model to capture the nonlinearity behavior of distillation column and able to process large inputoutput information and it is a great approximator. Because of it great potential, many researches are on the move to improve the performance of neural network in order to make it functional in industrial plant.

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Table 2. Summary – empirical models applied in distillation column
No 1 2 3 4 5 6 7 8 9 10 11 12 Model Wiener model Wiener model Wiener model Simple Hammerstein model Continuous time Hammerstein model Block-oriented model Feedforward neural network model Feedforward neural network model Feedforward neural network model Feedforward neural network model Neural network model Neural network model Distillation system Not mentioned C2 splitter Not mentioned Ammonia/water Not mentioned methanol and ethanol Not mentioned buthylacetate-buthylalcohol water Not mentioned Propane/butane/n-pentane/ipentane/hexane Wastewater Ethyl Benzene (EB)/MethylEthyl-benzene (MEB)/di-ethylBenzene (DEB) Methanol/water C4 Crude oil 5 mixture Binary and multicomponent Propylene/propane Methanol/water Not mentioned Not mentioned Gasoline/butane Not mentioned Not mentioned Methanol/ ethanol Reference Zhu, 1999 Norquay et al., 1999 Bloemen et al., 2001 Nugroho et al., 2004 Bhandari and Rollins, 2004 Gomez and Baeyens, 2004 Brizuela et al., 1996 Savkovic – Stevanovic, 1996 Turner et al., 1996 Barrati and Corti, 1997 Ramchandran et al. 1997 Karahan et al., 1997

13 14 15 16 17 17 18 19 20 21 22 23 24

25 26 27 28

Feedforward neural network model Neural network model Feedforward neural network model Neural network model Neural network model Neural network fuzzy system model Group neural network model Multiple neural networks model Recurrent Neural network model NARMAX model Soft sensing model TSK piece wise linear fuzzy model Polynomial type nonlinear autoregressive models with exogenous inputs (NARX) PLS model PLS model PLS model PLS model

Yu, 2003 Bo et al., 2003 Liau et al., 2004 Singh et al., 2005 Singh et al., 2007 Wang and Rong, 1999 Ou and Rhinehart, 2003 Jazayeri-Rad, 2004 Shaw and Doyle III, 1997 Fortuna et al. 2005 Yan et al., 2004 Mahfouf et al., 2002 Sriniwas et al., 1995

Alcohol/water/ether Methanol/ethanol/propanol/nbutanol Methanol/ethanol/propanol/nbutanol C7

Kano et al., 2000 Kano et al., 2003 Showchaiya et al., 2001 Park and Han, 2000

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Abdullah et al.: Nonlinear Modelling Application in Distillation Column

5. Hybrid Models The hybrid wavelet-based neural networks model for distillation column which separates a binary mixture in continuous operation has been proposed by Safavi and Romagnoli (1997). Wave-nets were employed to simplify the mechanistic model of a distillation column. The hybrid model composed of a mechanistic part and a wave-net approximation part. The set of data points were obtained from pseudo-random variation of the input variables around a region of operation of the column. A wave-net is trained to learn part of an illustrative nonlinear and highdimensional chemical process. The wave-net model for the separation factor of the column was developed to reduce the size of the rigorous model of the column which leads to a hybrid model. The hybrid wave-net model was compared to a complex and fully mechanistic model of the column and the result shows the capability of wave-nets in the modeling and simplification of a typical multidimensional chemical process. Safavi et al. (1999) proposed the hybrid model to identify the binary distillation column which separates ethanol water mixture. The idea was to develop a simplified hybrid model for the column consisting of a wavelet-based neural network model part plus a mechanistic model part. A hybrid model may benefit from useful features of both the mechanistic and the neural network models while its compromise between the accuracy and the simplicity of the models. A trade-off between these approaches was to use a hybrid model consisting of a mechanistic model part and an input output model part. Most of the knowledge of the process can go to the mechanistic model to develop accurate models for the process while also provided sufficient access to internal variables of the process. Neural network models can be developed for those parts of the process which are hardly formulated or lead to the very complicated models. Gaussian wavelet which has a relatively high degree of smoothness is chosen to develop a wave-net model. The mass and energy balances are use to develop the mechanistic model part. The hybrid model is obtained by embedding the wave-net model within the mechanistic model. Pearson and Pottmann (2000) applied the three model structures of block oriented to develop the gray box model in identification of the high purity methanol-propanol column. They combined a single static nonlinearity with a linear dynamic model with specified steady-state gain constraint. They made a plausible working assumption that the steady-state behavior is known from an understanding of process fundamental and uses this knowledge to determine the static nonlinearity. This approach relies on both, measured process data and fundamental process understanding. Nonlinear balanced model has been developed by Hahn et al. (2000). They proposed a model reduction technique performed by the use of an artificial neural

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net. In this model, only those states that contribute little to the input-output behavior of the system are replaced by the neural net. The reduction scheme is an extension of balancing to nonlinear systems, using the concept of empirical gramians. These gramians are balanced by simple matrix computations, and a projection is used to map the nonlinear system to the reduced states. Balanced truncation and residualization have been used for the reduction step which lead to a reduced system of ordinary differential equations (ODE) and result in a differential–algebraic equation (DAE) system. They replace the algebraic equation in the DAE system with a neural network. This method allows the most important components of the system contained in the remaining states and the neural network only corrects the system for the reduced states. Sun and Hahn (2005) developed the dynamic model using reduction of stable differential–algebraic equation technique for cyclohexane and heptane separation. This method reduces the order of the differential equations as well as the number and complexity of the algebraic equations. The model is further reduced by replacing the algebraic equations with feedforward neural network. In these models, the method reduces the order of the model consisting of three major steps: (1) order reduction of the differential equations via balancing or proper orthogonal decomposition (POD) and reduction of algebraic equations via POD; (2) identification of the correlation in the variables that connect the differential equations to the algebraic ones; and (3) further reduction of the algebraic equations by retaining the “input–output” behavior via system identification. All the hybrid models applied to the continuous distillation column are summarized in table 3. Hybrid models that integrate first-principles models with empirical models are most promising for the future. Hybrid models have been implemented widely in various chemical processes such as batch distillation (van Lith et al., 2003), reactive distillation (Chen et al., 2004) and polymerization process (Cubillos et al., 2001; Chang, et al., 2007), but only a handful of works has been implemented in continuous distillation column. Table 3. Summary – hybrid models applied in distillation column
No 1 2 3 4 5 Model Hybrid wave-nets model Hybrid model Gray box model Nonlinear Balanced model Reduced DAE model Distillation system Water-ethanol Water - ethanol Methanol/propanol Not mentioned Cyclohexane/heptane Reference Safavi and Romagnoli, 1997 Safavi et al., 1999 Pearson and Pottmann, 2000 Hahn et al., 2000 Sun and Hahn, 2005

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Abdullah et al.: Nonlinear Modelling Application in Distillation Column

6. Conclusions Remarks According to the models review, the construction of models for control strategies are focus in particular on the nonlinear model because the distillation column is complex system and exhibit nonlinear dynamic behavior. These models can be categorized into several groups; fundamental model, empirical model and hybrid model. This review reveals that over the last decade empirical models are the most widely used in development of nonlinear models of distillation column. It also reveals that neural network models are the most popular framework for empirical model development. Even though fundamental models are generally far more accurate but these models tend to involve many equations. The models obtained may be too complex to be used for nonlinear model based control design and will increase the computational burden of the controller. Empirical models also suffered from some limitations. They are unable to predict the results beyond the conditions in which it is derived. Because of that, hybrid models become the most promising approaches based on their ability to allow exploitation of the advantages for both, fundamental and empirical models. From this review, the neural network approaches have become the most preferable framework to be combined with fundamental model. Many researches are still continuing to select the best framework to combine both models in order to develop a better hybrid model. Lately, many advanced approaches of fundamental, empirical and hybrid models have been discovered to overcome the weakness of each models and some are still in research. These models have been applied for another type of distillation column such as packed column, batch distillation column, reactive column and etc. This opens the scope for more application of those new approaches in development of nonlinear model for continuous distillation column. References Balasubramhanya, L.S. and Doyle III, F.J., Low Order Modeling for Nonlinear Process Control, Proceedings of the American Control Conference, Seattle, Washington, June 1995. Bansal, V., Perkins, J.D., Pistikopoulos, E.N., Ross, R. and van Schijndel, J.M.G., Simultaneous Design and Control Optimization under Uncertainty, Computers and Chemical Engineering, 2000, 24, 261-266. Baratti, R., Corti, S. and Servida, A., A Feedforward Control Strategy for Distillation Columns, Artificial Intelligence in Engineering, 1997, 11, 405-412.

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Bhandari, N. and Rollins, D., Continuous-time Hammerstein Nonlinear Modeling Applied to Distillation, AIChE Journal, 2004, 50, 530-532. Bian, S. and Henson M.A., Measurement Selection for On-line Estimation of Nonlinear Wave Models for High Purity Distillation Columns, Chemical Engineering Science, 2006, 61, 3210-3222. Bloemen, H.H.J., Chow, C.T., Van der Boom, T.T.J., Verdult, V., Verhaegen, M. and Backx, T.C., Wiener Model Identification and Predictive Control for Dual Composition Control of a Distillation Column, Journal of Process Control, 2001, 11, 601-620. Bo, C.M., Li, J., Zhang, S., Sun, C.Y. and Wang, Y.R., The Application of Neural Network Soft Sensor Technology to an Advanced Control System of Distillation Operation, Proceedings of the International Joint Conference on Neural Network, 2003, 2, 1054-1058. Brizuela, E., Uria, M. and Lamanna, R., Predictive Control of a Multi-Component Distillation Column Based on Neural Networks, Proceedings of the International Workshop on Neural Networks for Identification, Control, Robotics, and Signal/Image Processing (NICROSP '96), Venice, Italy, 1996. Can, U., Jimoh, M., Steinbach, J. and Wozny, G., Simulation and Experimental Analysis of Operational Failures in a Distillation Column, Separation and Purification Technology, 2002, 29, 163-170. Chang, J., Lu, S. and Chiu, Y., Dynamic Modeling of Batch Polymerization Reactors Via the Hybrid Neural-Network Rate-Function Approach, Chemical Engineering Journal, 2007, 130, 19-28. Chen, L., Hontoir, Y., Huang, D., Zhang, J. and Morris, A.J., Combining First Principles with Black-Box Techniques for Reaction Systems, Control Engineering Practice, 2004, 12, 819-826. Cubillos, F., Callejas, H., Lima E.L. and Vega, M.P., Adaptive Control Using a Hybrid-Neural Model: Application to a Polymerisation Reactor, Braz. J. Chem. Eng., 2001, 18, 113-120. Diehl, M., Findeisen, R., Schwarzkopf, S., Uslu, I., Allgöwer, F., Bock, H.G., Gilles, E.D. and Schlöder, J.P., An Efficient Algorithm for Nonlinear Model

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Kano, M., Showchaiya, N., Hasebe, S. and Hashimoto, I., Inferential Control of Distillation Compositions: Selection of Model and Control Configuration, Control Engineering Practice, 2003, 11, 927–933. Karahan, O., Ozgen, C., Hahci, U. and Leblebicioglu, K., Nonlinear Model Predictive Controller Using Neural Network, Neural Networks 1997 International Conference, 1997, 2, 690 – 693. Kienle, A., Low-Order Dynamic Models for Ideal Multicomponent Distillation Processes using Nonlinear Wave Propagation Theory, Chemical Engineering Science, 2000, 55, 1817-1828. Kumar, A. and Daoutidis, P., Nonlinear Model Reduction and Control of HighPurity Distillation Columns, Proceeding of the American Control Conference, San Diego, California, 1997. Liau, L.C.K., Yang, T.C.K. and Tsai, M.T., Expert System of A Crude Oil Distillation Unit for Process Optimization Using Neural Networks, Expert Systems with Applications, 2004, 26, 247–255. Luyben, W. L., Derivation of Transfer Functions for Highly Nonlinear Distillation Columns, Ind. Eng. Chem. Res., 1987, 26, 2490-2495. Luyben, W. L., Plantwide Dynamic Simulators in Chemical Processing and Control, 2002, Marcel Dekker, Inc., New York. MACC, McMaster Advanced Control Consortium, Retrieved June 27, 2007, from Chemical Engineering Department at McMaster University, Research center Web site: http://macc.mcmaster.ca/research/keywords.htm Mahfouf, M., Kandiah, S. and Linkens, D.A., Fuzzy Model-based Predictive Control Using an ARX Structure with Feedforward, Fuzzy Sets and Systems, 2002, 125, 39-59. Michelsen, F. and Foss, B., A Comprehensive Mechanistic Model of a Continuous Kamyr Digester, Applied Mathematical Modelling, 1996, 20, 523– 533. Muller, N.P. and Segura, H., An Overall Rate-Based Stage Model for Cross Flow Distillation Columns, Chemical Engineering Science, 2000, 55, 2515-2528.

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Safavi, A.A. and Romagnoli, J.A., Application of Wavelet-based Neural Networks to the Modelling and Optimisation of an Experimental Distillation Column. Engineering Applications of Artificial Intelligence, 1997, 10, 301-313. Safavi, A.A., Nooraii, A. and Romagnoli, J.A., A Hybrid Model Formulation for a Distillation Column and the On-Line Optimisation Study, Journal of Process Control, 1999, 9, 125-134. Savkovic–Stevanovic, J., Neural Net Controller by Inverse Modeling for a Distillation Plant, Computers Chem. Engineering, 1996, 20, 925-930. Shaw, A.M. and Doyle III, F.J., Multivariable Nonlinear Control Applications for a High Purity Distillation Column Using a Recurrent Dynamic Neuron Model, J. Proc. Cont., 1997, 7, 255-268. Showchaiya, N., Kano, M., Hasebe, S. and Hashimoto, I., Improvement of Distillation Composition Control by Using Predictive Inferential Control Technique, Journal of Chemical Engineering of Japan, 2001, 34, 1026-1032. Singh, V., Gupta, I. and Gupta, H.O., ANN Based Estimator for DistillationInferential Control, Chemical Engineering and Processing, 2005, 44, 785–795. Singh, V., Gupta, I. and Gupta, H.O., ANN-Based Estimator for Distillation Using Levenberg–Marquardt Approach, Engineering Applications of Artificial Intelligence, 2007, 20, 249-259. Sriniwas, G.R., Arkun, Y., Chien, I. and Ogunnaike, B.A., Nonlinear Identification and Control of a High Purity Distillation Column: A Case Study, J. Proc. Cont., 1995, 5, 149-162. Sun, C. and Hanh, J., Reduction of Stable Differential-Algebraic Equation Systems via Projections and System Identification, Journal of Process Control, 2005, 15, 639-650. Turner, P., Montague, A., Morris, A.J., Agammenoni, O., Pritchard, C., Barton, G. and Romagnoli, J., Application of a Model Based Predictive Control Scheme to a Distillation Column Using Neural Networks, Proceedings of the American Control, Conference Seattle, Washington, 1996.

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