Centrifugal Pump-Based Predictive Models for Kraft Black Liquor

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Centrifugal Pump-Based Predictive Models for Kraft Black Liquor Viscosity: An Artificial Neural Network Approach Sunday B. Alabi*,† and Chris J. Williamson† †

Department of Chemical and Process Engineering, University of Canterbury, PB 4800, Christchurch 8140, New Zealand ABSTRACT: Previous investigators have shown that the Newtonian viscosity of black liquor (BL), a byproduct of kraft pulping process, can be estimated online from the performance parameters of an installed centrifugal pump (CP). Unfortunately, the existing models from which such estimates can be obtained lack the necessary robustness for process control applications and/or would require a substantial amount of data for periodic updates. This study developed a generalized artificial neural network (ANN)-based model which directly accounts for the effect of aging on the pump performance (hence the model). Simulation results show that ANN predicts BL viscosity better than the existing linear models as the former gives accurate and robust predictions at all practical operating points of the pump. Moreover, the ANN model requires just a single data point for its periodic recalibration as the pump ages significantly. The methodologies presented here can easily be adapted for use in any process industry where Newtonian process fluids are transferred by a CP.

1. INTRODUCTION Viscosity is one of the most important quality parameters in many industrial products and processes.1 Systems and applications such as fluid flow in pipes and the lubrication of engine parts are controlled to some degree by fluid viscosity.2 It is a dominant variable which affects the performance of steam and chemical recovery facilities in a kraft pulp mill. It affects the rate of heat transfer in the evaporation units, the capacity of the pumps, and the spray and combustion characteristics of black liquor (BL) in a recovery boiler (RB).3,4 This paper is concerned with the online prediction of heavy black liquor viscosity and its potential use for the control and optimization of the RB operation in a kraft pulp mill. However, the methodologies presented in this work would generally be applicable to Newtonian fluids in any process industry where centrifugal pumps are widely used. Despite the significance of viscosity on the performance of BL processing equipment, its online measurement, monitoring, and control have not received much attention (see refs 5 and 6). Recently, some investigators showed that BL viscosity can be estimated online from the performance parameters of an installed centrifugal pump (CP). The CP-based online viscosity estimation capitalizes on the changes which occur in the performance of a centrifugal pump as the viscosity of the fluid being pumped changes due to the changes in its influential factors. For BL, such factors include its solids concentration (SC), temperature, and the liquor composition. The liquor composition in turn depends on the type of wood pulped, pulping conditions, and post pulping factors/processes (see refs 7 and 8). Rather than focusing on the effects of wood type, pulping conditions, or post pulping operations on BL composition and its direct influence on the BL viscosity, the CP-based method utilizes the concept of cause-effect relationships. For a given pump model with a known impeller size, at any definite operating point of the pump and unique shaft speed, changes (due to changes in SC, temperature, and/or liquor composition) in the viscosity of a fluid being pumped will lead to a change in the flow rate through the pump and a corresponding change in the torque required to maintain r 2011 American Chemical Society

the speed of the pump’s impeller shaft.9 McCabe et al.8 showed that using the amperage of a strong black liquor recirculation pump as an online measure of BL viscosity and its subsequent control resulted in a significant improvement in the recovery boiler performance at the Irvin Pulp and Paper mill, Canada. Porter et al.10 reported that another unnamed mill collected actual viscosity data from an online viscometer and obtained an unpublished relationship between the liquor viscosity and the recirculation pump’s current thereby directly making available the viscosity estimates to the recovery boiler operators to effect control actions. They claimed that this approach resulted in a significant improvement in the recovery boiler performance in the unnamed mill. Alabi et al.9 proposed a short-cut modeling approach for possible use in the online prediction of fluid viscosity from the centrifugal pump performance parameters. Taking BL as the process fluid, they showed that for a given centrifugal pump model, their performance characteristics at a predefined range of viscosities can be estimated from the generalized performance database of a variety of rotodynamic pumps by using the Hydraulic Institute (HI) viscosity correction method.11 This approach was shown to be capable of minimizing the amount of or eliminating the need for actual experimental data required for a predictive model development. There are a number of advantages associated with the use of centrifugal pump performance parameters as a basis for an online indication or a direct prediction of black liquor viscosity: (i) There was no need to install any hardware-based viscometer as the centrifugal pumps are a part of an installed mill.9 This eliminates the concern for a capital investment or space for the installation of new equipment (e.g., large and expensive analyzers). Received: April 2, 2011 Accepted: July 27, 2011 Revised: June 30, 2011 Published: July 27, 2011 10320

dx.doi.org/10.1021/ie200684n | Ind. Eng. Chem. Res. 2011, 50, 10320–10328

Industrial & Engineering Chemistry Research (ii) Hitherto, the available composition-independent predictive models for kraft black liquor viscosity are inadequate for online application as they are limited to a narrow range of process conditions (see refs 1214). Conversely, the pump’s amperage value depends on the overall liquor property at the pumping conditions and hence it is robust to changes in the liquor type or composition which has a significant effect on BL viscosity.9 Although the above methods show good promise, they did not address a number of issues pertinent to centrifugal pump performance characteristics, the quality of a good predictive model and the ultimate use of the viscosity estimates obtained from the model. McCabe et al.8 method does not provide actual viscosity estimates and, therefore, cannot be used for flow and spray calculations where actual viscosity value is required. Porter et al.10 and Alabi et al.9 models provide actual viscosity estimates; unfortunately, the model discussed by Porter and co-workers is unknown and would require the use of a substantial amount of actual experimental data for its development and possibly for regular updates. Conversely, the linear models reported by Alabi et al.9 were developed based on the estimated data obtained from the HI’s generalized performance database for a variety of rotodynamic pumps using a vendor-supplied water-based pump curve as a reference. The approach was shown to be capable of minimizing the amount of or eliminating the need for actual experimental data, but the reported linear models lack necessary robustness for process control applications. A major setback common to all the reported centrifugal pump-based BL viscosity modeling/measurement methods is that there is no clear indication that the mechanical status of the pump is taken into consideration either during the predictive model development or after its online installation. As the pump ages, its efficiency would deteriorate due to wear and tear of its mechanical components and as such more motor power will be required to deliver the same flow even when other parameters including the process fluid viscosity remain the same. This implies that the fluid viscosities will be inaccurately predicted and wrong control actions will be taken. In addition, whenever there is a significant deterioration in the pump efficiency and hence significant change in the operating point of the pump, the installed model may have to be redeveloped and this may require a substantial amount of new data. This may be cumbersome and sometimes economically prohibitive. The efficiency of a centrifugal pump (CP) and hence its operating condition depends on a number of factors including the pump model and geometry, piping system, fluid properties, degree of wear and tear of the pump’s mechanical components, etc. (see refs 15 and 16). Since the CP-based modeling/measurement methods are based on power (hence torque) requirements of the motor connected to the pump, as the pump ages, higher power (hence torque) requirement will give an erroneous indication of higher viscosity, and any modeling/measurement methods developed based on new pump data will fail under such circumstances. This would mean that from time to time, a substantial amount of data may be required to rebuild the predictive model which has been installed as an online viscosity sensor. Figure 1 shows a typical trend in the efficiency deterioration of a centrifugal pump due to wear and tear in its mechanical components. It is observed that over a period of about 25 years, the efficiency deterioration follows a minimum or average or maximum trend. Intermediate or nonuniform trends are likely.

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Figure 1. Typical trends in the efficiency deterioration of an aging pump.15

In this paper, the CP-based BL viscosity modeling approach developed around HI viscosity correction method by Alabi et al.9 is modified. First a new input variable, pump age (PA), is introduced to account for the effect of aging on the performance of the CP under consideration. Second, a new CP-based nonlinear model for predicting BL viscosity is developed using an artificial neural network (ANN) paradigm. This is opposed to linear modeling approaches reported in Alabi et al.9 The robustness and generalization capabilities of the resulting ANN-based models are discussed.

2. DATA ESTIMATION Centrifugal pumps are usually a part of an installed kraft pulp mill where the typical byproduct from the pulping unit is black liquor (BL).17 The origin and the nature of BL and its subsequent processing in a pulp mill have been discussed elsewhere.18,19 The CP-based BL viscosity models described in this paper are developed from the performance data of an Ahlstrom-made THP-10 centrifugal pump (CP) having an outer impeller diameter of 360 mm. The pumping fluid was taken as a Newtonian BL of varying viscosities. The method presented here can be applied to any other CP model and size and other Newtonian fluids in any process industry. Using the manufacturer’s (Ahlstrom) reference pump curve at a shaft speed N = 960 rpm in combination with the HI viscosity correction method,11 two batches of viscous performance data (head (m), Hvis; flow or capacity (m3/s), Qvis, and efficiency (%), ηvis) for a constant-density heavy BL were obtained. Based on these data, brake horsepower data, BHPvis (W) were obtained from eq 1. By making use of the affinity laws,15,16 the first batch of the data was extended to other shaft speeds ranging from 300 to 1800 rpm, while the second batch was extended to other shaft speeds between 500 and 1600 rpm. Equations 2 and 3 were then used to estimate TQvis (Nm) and TQp (%) from the two batches of data. The first batch was obtained over a range of viscosities, V = 5552 cP and across 7 operating points or flow conditions (FC1-FC7) of the pump, while the second batch of data was obtained at V = 6.9345 cP; and across four FCs, FC3-FC6. FC1-FC7 is a vector of dimensionless ratios, [0.2:0.2:1.4], where FC1 = 0.2 and FC7 = 1.4 as discussed in Alabi et al.;9 Fvis is the viscous liquor density (kg/m3) and was

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BHPvis ðWÞ ¼ Fvis gQ vis Hvis =ηvis

ð1Þ

TQ vis ðNmÞ ¼ 9:5481BHPvis ðWÞ=N ðrpmÞ

ð2Þ

TQ p ð%Þ ¼ 100TQ m =TQ nom

ð3Þ

dx.doi.org/10.1021/ie200684n |Ind. Eng. Chem. Res. 2011, 50, 10320–10328

Industrial & Engineering Chemistry Research

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Table 1. Statistics for the New Pump Performance Data

Table 2. Statistics for the Combined New and Aging Pump Performance Data

variables statistics

Q/N (L/min/rpm)

105 TQp/N3 (%/rpm2)

variables

V (cP)

5

a

minimum

0.3030

1.938

5.000

maximum

2.625

4.658

552.0

mean

1.394

3.181

STDa

0.7069

0.6S94

range

2.322

2.720

547.0

10 TQP/N2 statistics

Q/N (Umin/rpm)

(%/rpm2)

PA

V (cP)

172.7

minimum

0.3030

1.938

1.000

5.000

186.4

maximum mean

2.625 1.394

5.6804 3.515

4.000 2.500

552.0 172.7

STDa

0.7062

0.8063

1.118

186.2

range

2.322

3.742

3.000

547.0

Standard deviation.

assumed as 1380 kg/m3 for heavy BL9; g is the acceleration due to gravity = 9.8 m/s2; TQm (Nm) is the torque developed by the installed electric motor connected to the pump; and TQnom (Nm) is the motor’s nominal torque (based on the given motor power and shaft speed ratings). It was assumed that the torque (TQm) developed at the motor/drive unit is completely transmitted to the pump shaft as TQvis in eq 2 so that TQm in eq 3 is ∼TQvis for estimation purposes. Note that the two batches of data described above were based on the performance of a new pump and all the analyses, modeling, and validation done in Alabi et al.9 were based on them. The operating point or FC of the pump was defined in light of the new pump status. In order to incorporate aging effects on the pump’s overall performance, four hypothetical pump ages (PAs) based in Figure 1 are defined as PA = 1 (new pump condition at 0% efficiency deterioration), PA = 2 (at 6% efficiency deterioration), PA = 3 (at 12% efficiency deterioration), and PA = 4 (at 18% efficiency deterioration). It was assumed that any major shifts in the pump performance characteristics are due mainly to the significant change in its efficiency. Therefore, the 2 batches of the new pump (PA = 1) performance data described in the preceding paragraph were modified for the aging pump (at PAs = 24) using eqs 1-3. The earlier performance data at PA = 1 were then combined with the aging pump performance data at PAs = 24 to obtain complete performance data for the analysis of the pump throughout its entire lifespan (PAs = 14). The first batch of the data was designated modeling data, while the second independent batch was designated validation data. The statistics of the new pump modeling data (378 cases) and the combined new and aging pump modeling data (1512 cases) are as summarized in Table 1 and Table 2, respectively. The inclusion of PA would allow the new pump performance characteristics at any FCs to be shifted uniformly to new trajectories as the pump ages.

3. ANN-BASED BL VISCOSITY MODELING 3.1. Motivation for the Choice of an ANN. Alabi et al.9 had

demonstrated (see Figure 2) that a consistent relationship exists among TQNN (normalized TQp/N2), QN (normalized Q/N), and Vn (normalized V) across a range of pump’s operating points or FCs. They therefore proposed two forms of linear models to describe the relationships between the CP performance parameters (input variables) TQNN and QN and the output variable Vn across the entire pump’s operating points or FCs jointly. Note that subscript “vis” has been omitted from variable Q for convenience. Variables normalization was done using zscore function in the MATLAB

a

Standard deviation.

statistics toolbox or eq 4 z ¼ ðy ym Þ=ystd

ð4Þ

where y is the variable (e.g., TQp/N2, Q/N, V, etc.) to be normalized; ym is the mean of y; ystd is the standard deviation of y; and z is the normalized y. The models reported in the work of Alabi et al.9 are found to be sensitive to the changes in the pump’s FCs, and this sensitivity increases with the liquor viscosity. Although the lack of robustness of these models to changes in FC was attributed to the presence of underlying nonlinear relationships between the variables, the nature of this relationship has yet to be investigated. A closer look at Figure 2 shows that across the lower flow conditions FC1-FC3, the relationship between QN and TQNN is linear at constant Vn. Across higher FCs, FC4-FC7, a similar linear relationship between QN and TQNN was observed at constant Vn. However, there is a sharp curvature (nonlinear behavior) between F3 and F4. Within each flow region (lower and higher), two main viscosity regions are identified. A closer look across FC1-FC7 shows that there are two roughly linear regions at each FC. Regions of low-to-moderate Vn (0.8996 to 0.7413) and that of moderate-to-high Vn (0.6488 to 2.035) are observed. Between 0.8996 and 0.7413, at each FC there is a curvature (nonlinearity) which increases or becomes sharper as FC increases. On a casual look, it seems the relationship between QN and TQNN across all FCs at each Vn can be described by a quadratic model whose parameters can be related to Vn. Unfortunately, as discussed above, there are roughly four unique discontinuous linear sections with sharp curvatures (one demarcating the region of low-to-moderate Vn and moderate-to-high Vn and the other demarcating the regions of low and high FCs). While linear models may be able to describe the linear sections reasonably, it is clear that they will suffer grossly around the identified curvatures. This may be the reason why the linear models proposed by Alabi et al.9 could not give good robust predictions at moderate-to-high viscosities. ANN is regarded as a universal approximator because of its ability to model any function even in the presence of discontinuities20 such as those observed in Figure 2. Therefore it is deemed suitable to model the nonlinear relationship between BL viscosity and the centrifugal pump performance parameters across all the practical operating points of the pump. 3.2. Multilayer Feed-Forward ANN Architecture. ANN is the generalization of the mathematical model of a biological nervous system.21 It is a highly parallel system that processes information through modifiable weights, thresholds/biases, and mathematical transfer functions.22 Different architectures for, 10322



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Figure 2. Relationship between QN and TQNN at different viscosities and FCs.9

Figure 4. Transfer functions used in this paper. Figure 3. A simplified model of a typical 2-layer FF ANN.

and training algorithms associated with, ANNs are well discussed in the literature (e.g., refs 2325). This paper describes only the application of a multilayer (ML) feed-forward (FF) ANN to the CP-based modeling of BL viscosity. In FF networks, the signal flow is from the input to the output units, strictly in a feedforward direction. The data processing can extend over one or several layers (ML) of neurons, but no feedback connections are present.21 A simplified model of a typical 2-layer FF ANN used in this paper is given in Figure 3. The hyperbolic tangent sigmoid transfer function and a linear transfer function as shown in Figure 4 are used in the hidden and output neurons, respectively, throughout this paper. 3.3. ANN Training and the Problem of Overfitting. An ANN needs to be properly configured so that a set of inputs produces a desired set of outputs.21 The process of configuring the network involves the selection of a network structure, number of hidden and output layers, choice of activation or transfer functions, selecting the number of neurons in each layer, and the subsequent setting of the network weights and biases.

The totality of these steps is called training26 and is usually done in an iterative manner. 3.3.1. Determination of the Number of Hidden Units. Although the number of output neurons may easily be decided for a specific task, it is rarely a straightforward task to select the number of hidden neural units27 The numbers of hidden layers, their associated neurons and weights used by a given network are dependent on the complexity of the problem considered. They depend on the numbers of the input and output units, the number of training cases, the network’s architecture, types of hidden transfer functions, training algorithm, and whether the network’s training involves any form of regularization. Although rules of thumb exist, there is no way to determine in advance the best number of hidden units in a neural network without training several networks and estimating their generalization errors (see ref 28 and the references therein). Normally, these have to be determined by trial and error; there is no universal criterion for determining them.27 Although approaches to dynamically change the number of hidden units during the training process exist (see ref 27), they were not used in this work. The software utilized for this work requires the user to specify these in a trial and error manner. 10323



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3.3.2. Problem of Overfitting. One of the major problems associated with the training of ANN is that of overfitting. During training, the network prediction error can be driven to a very small value as the inputs and outputs data are presented to the network. However, when the networks are exposed to new inputs, they perform poorly. Regularization is one of the most effective methods reported in the literature for addressing overfitting problem in ANNs. One regularization approach is to use early stopping, where the algorithm which minimizes the error function is prevented from doing so by stopping the algorithm at some point.26 In early stopping, the available data are divided into three sets: training, validation, and test. The training set is used for the networks training and for updating the network weights. The validation set is not used in the training, but the validation error is monitored during training process. Generally, both the training and the validation errors will decrease in the initial stage of the training. However, when the network begins to overfit, the error on the validation set will typically increase. When the validation error increases over a specified number of iterations, the training is stopped. The test set error is not used during training but used to compare different models. If the test set error reaches a minimum at a significantly different iteration number than the validation set error, this might be an indication that the data sets are poorly divided, and new divisions of data may be required to continue the training process. One major weakness with early stopping approach is the difficulty to tell when the validation error actually starts to increase.28 It may increase and decrease many times during training, and, therefore, there is no guarantee that the point at which the training is stopped is a global minimum. A more sophisticated regularization approach is to modify the network performance function by adding a penalty term to the error function. The usual penalty is the sum of squared weights times a decay constant. The penalty term in the weight decay penalizes large weights.28 This approach is called weight decay regularization. In this method, instead of minimizing the usual network prediction error such as mean squared error (MSE), a modified performance function defined as regularized mean squared error (MSEREG) is minimized. MSEREG is given by eq 520 MSEREG ¼ RMSE þ ð1 RÞMSW

ð5Þ

where ‘R’ is the performance ratio, “MSE” is the usual mean squared error of the network predictions, and “MSW” is the additional objective, mean squared weights and biases. The algorithm minimizes MSEREG (eq 5) to produce a network that generalizes well. The idea behind this approach is that using the modified performance function causes the network to have smaller weights and biases. This forces the network response to be smoother and less likely to overfit.20 Though this approach seems promising to produce a network that generalizes well, it is difficult to determine the optimum performance ratio parameter, R. If it is too large, the network might overfit the data; if it is too small, the network may underfit the data. Demuth and co-workers20 suggests the use of Bayesian framework of David McKay to overcome this problem. In this framework, neural network learning is approached from a probability point of view.26 The weights and the biases of the network are assumed to be random variables with specified distributions. The regularization parameters are related to the unknown variances associated with these distributions.20 With this framework, the

optimal regularization parameters can then be obtained in an automated fashion.26 Unlike the early stopping method, Bayesian approach does not require division of data into training, validation, and/or test sets. All the available data are used in model fitting and model comparison.26 In other words, Bayesian framework provides a platform to simultaneously train, validate, and select an optimal neural network model using all the available data. Bayesian framework was used in this work. The fundamental principles and various applications of Bayesian regularization as well as other methods which can be used to improve ANN generalization capability are well discussed in the literature (e.g., refs 29 and 30). 3.3.3. Input-Output Data Processing. ANN works well when the input and output data are all scaled to identical ranges. In this study, the input and output variables were scaled to between 1 and +1 prior to the networks training. The scaling of the relevant variables to [1, 1] range was done using the “mapminmax” function in the MATLAB NN toolbox or eq 6 B ¼ 1 þ 2ðA A min Þ=A range

ð6Þ

where B is the new variable in the range [1, 1]; and A, Amin, and Arange are the original variable, minimum of A, and range of A, respectively. 3.3.4. Parameter Search Using MATLAB-Based Bayesian Regularization Algorithm. The optimal weights and the biases of the feed forward neural network described in this paper were obtained using the automated Bayesian regularization algorithm in the MATLAB NN toolbox. The algorithm requires the user to specify the numbers of hidden layers and neurons, and the types of transfer functions required in the hidden and output layers, before the automated search commenced. Linear transfer function is a default for the output neuron, and the number of output neurons correspond to the number of the output variables (one, for viscosity in this work). Therefore, first, the training began with a network having 1 hidden layer and 1 hidden neuron. These were then increased gradually until the most acceptable network was obtained. Second, each complete optimization process was carried out at least 10 times starting from different initial weights and biases. This was to minimize the chances of the network converging to a local optimum. The initial values were chosen at random (automatically done via initialization tools available in the MATLAB NN toolbox). If the network’s performance indices are not satisfactory after different optimization attempts and starting from different initial parameter values, the number of hidden neurons would be increased and the process repeated until satisfactory performance criteria were obtained. The typical criteria for the evaluation of the performance of a Bayesian trained network include Marquardt adjustment parameter (MU), the effective number of parameters per total number of tunable parameters (#), sum of squared weights (SSW), and the network prediction error. It is important to train the network until the network parameters converge. Given a sufficient training epochs (depending on the complexity of the problem) e.g. 5000, a true convergence is attained when maximum MU is reached. Convergence is also attained when #, SSW, and the network prediction error remains fairly constant over a significant number of iterations.20 In addition to monitoring the above-stated indices, the R-squared statistic, R2 (based on the scaled viscosity data), and maximum absolute relative error (MARE) between unscaled actual prediction 10324



Figure 5. Robust performance of the new pump ANN model.

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Figure 6. Robust performance of the linear quartic model.9

and actual viscosity (given by eq 7) were checked at the end of each complete optimization stage. A network with R2 = ∼1 and MARE e 5% is considered accurate. Once a network which satisfies all these conditions is found, the training can be terminated. In this paper, the #, SSW, R2, and MARE obtained when the network converged are reported. Note, a network with 1 hidden layer having L neurons and 1 output layer having M neurons is denoted as an [L, M] network 0 ! μ μ p a ð7Þ MAREð%Þ ¼ 100maximum@ μa

)

where μp = predicted viscosity (mPa.s) in an untransformed state; μa = actual viscosity (mPa.s) in an untransformed state; and = modulus (absolute value) of the terms in the bracket.

4. RESULTS AND DISCUSSION 4.1. New Pump ANN Model Training and Selection. A 2-input 1-output [L, M] network was used to describe the relationship between the new pump parameters and the liquor viscosity. The two inputs are TQp/N2 and Q/N, and the only output is viscosity (V). Before the network’s training according to the procedures outlined in section 3.3, eq 4 was used to normalize all the variables (with prior logarithmic transformation of V). A [7, 1] network having 25 effective out of 29 tunable parameters, SSW = 889, and acceptable performance indices R2 = 1 and MARE = 2.72% was obtained. 4.1.1. Comparison of the New Pump ANN Model and the Linear Quartic Model. The main motivation for utilizing ANN, a nonlinear data-driven model in this paper was to be able to accurately describe the underlying nonlinear relationship between the CP parameters and BL viscosity across the varying pump’s operating points. The ability of this network to predict BL viscosity from its input variables in the presence of changing pump operating points was therefore investigated and compared with the predictions from the linear quartic model reported in Alabi et al.9 under similar conditions. Their simulation results are as shown in Figures 5 and 6. It is observed from Figure 5 that the new pump ANN (nonlinear) model gives more robust predictions than the linear quartic model (in Figure 6) at all viscosities and FCs. This indicates that the underlying nonlinear

Figure 7. Effect of PA on the new pump ANN model.

relationships among the variables across all the FCs which could not be captured by the linear model have been adequately captured by ANN model. The results justify ANN model as a better descriptor of the relationship between BL viscosity and the CP parameters across a wide range of pump’s operating points than the reported linear model. Further investigation on the suitability of the ANN model using an independent batch of a new pump performance data shows that the network has a strong generalization capability. 4.1.2. Sensitivity of the New Pump ANN Model to the Pump Age (PA). Although the new pump ANN model reported in subsection 4.1.1 gives robust predictions in the presence of changing pump’s operating points when exposed to new pump data (modeling data at PA = 1) from which it was built, there is no guarantee that the model will continue to perform reliably as the pump ages significantly. The effect of PA on the performance of the new pump model was investigated by exposing it to the entire modeling input data (at PAs = 14) whose statistics are summarized in Table 2. Figure 7 shows the network’s predictions based on the training inputs as a three-dimensional (3D) surface, while the actual performance outputs at different inputs and each 10325



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Figure 8. Robust performance of the aging pump ANN model.

PA are shown as 3D scatter points. As expected, at PA = 1 which corresponds to the new pump data (training data domain), the model predicts the viscosity accurately at all inputs. Conversely, at PAs = 24 which indicates aging pump conditions, some of the outputs fall outside the prediction surface of the new pump model. The number of outputs which the network fails to predict accurately increases as the PA increases. This should be expected since the pump’s efficiency reduces as the degree of wear and tear increases thereby leading to an increase in TQ (and BHP) requirement of the motor, while other process conditions remain the same. As can be seen, the ANN which was obtained based on new pump data overpredicts or underpredicts the liquor viscosity from the pump parameters as the pump ages. This demonstrates that although the new pump ANN model is able to accurately capture the nonlinear relationship between BL viscosity and the CP parameters when the pump is newly installed, it will fail to perform reliably as the pump ages significantly. Since the effect of aging on the pump performance is not directly modeled by this network (having 29 tunable parameters), the model would have to be modified periodically, requiring at least 29 carefully (being a nonlinear empirical model) obtained data. This process may be cumbersome and sometimes economically prohibitive. 4.2. Aging Pump ANN Model Training and Selection. Over the entire life span (PAs = 14) of the pump, a 3-input 1-output [L, M] network was used to describe the relationship between the aging pump parameters and the liquor viscosity. The three inputs to the network are Q/N, TQp/N2, and PA (the mechanical status of the pump), and the only output is viscosity, V (cP). Based on the entire modeling data whose statistics are summarized in Table 2, and following similar procedures used for training and selection of the new pump ANN model, different aging pump ANN models were searched. A [9, 1] network having 42 effective out of 46 tunable parameters, SSW = 787, and acceptable performance indices R2 = 1 and MARE = 4.48% was obtained. 4.2.1. Robust Performance of the Aging Pump ANN. The aging pump ANN model was exposed to the original entire

training (modeling) data used to build the ANN at all FCs of the pump and all PAs. The normalized predicted and actual viscosities are as shown in Figure 8. It is observed that across all the FCs and all the PAs, the model gives robust predictions. The results demonstrate that if an appropriate PA of the pump can be determined, the model can perform excellently if used for the online predictions of BL viscosity. It has an added advantage over the new pump ANN model or other existing models in that its mechanical status can be defined in advance to capture the current degree of wear and tear in the mechanical components of the pump. It is clear that an ANN model which explicitly accounts for the degree of wear and tear in the mechanical components of the pump is a better descriptor of the relationship between BL viscosity and the pump parameters across all the FCs and the entire life of the pump. 4.2.2. Aging Pump ANN Generalization. A robust model may not eventually generalize to new inputs. However, normally, a carefully Bayesian trained network would generalize to new inputs since both model fitting and model comparison phases were simultaneously incorporated into the training process. There should be no concern regarding the generalization capability of the aging pump network reported in this paper. First, it was trained to convergence with the reported indices. Second, the 1512 training cases used for the simultaneous model training and selection span the practical operating points of the pump. So the data are considered a good representation of the system. Third, the size of the training cases is approximately 33 times the effective number of the network parameters. Even if no regularization scheme was used, a network obtained from such a large and a representative sample could not have been overfitted. However, in order to gain further insight into the performance of the aging pump [9, 1] network, its generalization capability was investigated by exposing it to the entire independent validation input data obtained in section 2. The model’s predictions based on the domain of the entire training input data (at all PAs and FCs) are shown as the 3D surface in Figure 9, while the 3D scatter points of the entire training data and the entire 10326



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liquor processing equipment such as evaporators and the recovery boilers, whose performances are known to be viscositydependent. The methodologies presented in this paper should easily be adaptable for the online prediction of the viscosity of any Newtonian fluid in an industry where centrifugal pumps are widely used to transport process fluids.

’ AUTHOR INFORMATION Corresponding Author

*Phone: + 64 3 364 2543. Fax: + 64 3 364 2063. E-mail: [email protected] or [email protected].

Figure 9. The aging pump ANN model generalization.

intermediate validation data sets are also shown in the same Figure 9. Unlike the off-prediction scatter points observed in Figure 7 for the new pump [7, 1] ANN at PAs = 24, it is seen in Figure 9 that all the modeling and the validation scatter points fall smoothly on the prediction surface of aging pump [9,1] ANN at all FCs as well as all PAs. Validation output scatter points fall at intermediate positions of the training output scatter points as expected indicating the model’s strong generalization capability. It is noteworthy that the aging pump ANN model though has 46 tunable parameters is potentially able to minimize the amount of data required for its periodic modifications when there is a significant drift in the pump’s performance due to aging. For instance, the new pump ANN model would require at least 29 new data points which must be carefully obtained for recalibration whenever the mechanical condition of the pump changes significantly. Conversely, the aging pump ANN model would theoretically require just a single new data point to shift the entire prediction trajectory of the network without changing any of its parameters. Only PA will be reset depending on the current mechanical condition of the pump.

5. CONCLUSIONS In this work, two generalized artificial neural network (ANN) based black liquor viscosity models were developed from the performance data of a new centrifugal pump (CP) and an aging CP, respectively. For the new pump, simulation results indicate that an ANN model is a better descriptor of the underlying relationship between black liquor viscosity and its CP based inputs than the existing linear quartic model, as the former was able to give robust predictions over a practical range of pump operating points where the latter failed. It was however shown that pump age has a significant impact on the performance of the new pump ANN model. Therefore, the incorporation of the aging factor in the ANN model development stage has a unique advantage of minimizing the efforts required in model recalibration as the aging pump ANN model would theoretically require just a single data point for its periodic modifications. It is concluded that the aging pump ANN model can be used with minimal maintenance to provide online estimates of black liquor viscosity for the purposes of control and optimization of black

’ ACKNOWLEDGMENT This work was financially supported by the Foundation for Research, Science and Technology (Grant: CHHP0601), Carter Holt Harvey Pulp and Paper (CHHP&P) (at Kinleith), and Department of Chemical and Process Engineering, University of Canterbury, New Zealand. The study leave granted the first author by his employer, University of Uyo, Nigeria enabled him to focus on this study. This project exists because of the vision of Mr. John Lee while he was an employee of CHHP&P. ’ REFERENCES (1) Chang, V.; Zambrano, A.; Mena, M.; Millan, A. A sensor for online measurement of the viscosity of non-Newtonian fluids using a neural network approach. Sens. Actuators, A 1995, 47 (13), 332–336. (2) Leblanc, G. E.; Secco, R. A.; Kostic, M. Viscosity measurement. In The measurement, instrumentation and sensors handbook on CD-ROM; CRC Press: 1999; 24pp. (3) Venkatesh, V.; Nguyen, X. N. Evaporation and concentration of black liquor. In Chemical recovery in the alkaline pulping processes, 3rd ed.; Green, R. P., Hough, G., Eds.; TAPPI Press: Atlanta, GA, 1992; pp 533. (4) Moosavifar, A.; Sedin, M.; Theliander, H. Correlations for the viscosity of lignin lean black liquor. Nord. Pulp Pap. Res. J. 2010, 25 (1), 15–20. (5) Barrall, G. A. Viscosity of black liquor project; DOE/ID/12726--4Pt.3; USDOE: USA, 01/06/98, 1998; 8pp. (6) Fricke, A. K.; Crisalle, O. D. Development of viscometers for kraft black liquor. Final report - phases I, II, IIA, and III; DOE/GO/10564-F; USDOE: USA, 1999; 173pp. (7) Frederick, J. W. Black liquor properties. In Kraft recovery boilers; Adams, T. N., Ed.; TAPPI Press: Atlanta, GA, 1997; pp 59100. (8) McCabe, F. D.; Mott, D.; Savoy, D.; Tran, H. Controlling black liquor “viscosity” to improve recovery boiler performance. In International chemical recovery conference; TAPPI/PAPTAC: Quebec, Canada, 2007; pp 427432. (9) Alabi, S. B.; Lee, J.; Williamson, C. J. A novel quartic model for predicting black liquor viscosity using centrifugal pump parameters. Chem. Prod. Process Model. 2010Submitted for publication. (10) Porter, J.; Sands, T.; Trung, T. Improving recovery boiler performance by controlling variability (new tools for an old problem). In International chemical recovery conference; TAPPI/PAPTAC: Virginia, USA, 2010; 16pp. (11) ANSI/HI. Effects of liquid viscosity on rotodynamic (centrifugal and vertical) pump performance. 9.6.7., 2004. (12) Moosavifar, A.; Sedin, P.; Theliander, H. Viscosity and boiling point elevation of black liquor: Consequences when lignin is extracted from the black liquor. Nord. Pulp Paper Res. J. 2006, 21 (2), 180–187. (13) Zaman, A. A.; Fricke, A. L. Effects of pulping conditions and black liquor on viscosity of softwood kraft black liquors: predictive models. Tappi J. 1995, 78 (10), 107–119. 10327



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Centrifugal Pump-Based Predictive Models for Kraft Black Liquor

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