Estimation and Control of Fouling in Heat Exchangers

Copyright © IFAC Algorithms and Architectures for Real-Time Control, Ostend, Belgium, 1995

ESTIMATION AND CONTROL OF FOULING IN HEAT EXCHANGERS

Peel, D., Wbeeldon, P., Virdee. G.S. School o/Science and Technology University o.fTeesside Middlesbrough Cleveland UK TS13EA

Abstract: The development of non-invasive sensors to indicate the presence and the degree of fouling is described. This application relates primarily to fouling in the crude oil refining industry although the approaches are generally applicable. Data driven models derived using the standard linear least squares technique and artificial feed-forward neural networks are used to predict the degree of fouling either directly or indirectly. Keywords: Least-squares estimation; neural network models; chemical industry: modelling; efficiency enhancement. 1.0 IN1RODUCTION availability of such a sensor can be useful in providing evidence for fault diagnosis Heat exchangers are designed, like most unit operations of a chemical plant, to run continuously 2. THE PROCESS at steady state. Like all unit operations. they do not. A small scale rig has been constructed to investigate In the case of heat exchangers. one of the more fouling of crude oil at conditions which are related common problems is that of fouling. Fouling is a to the operating flows and temperatures experienced tenn which is given to the deposition of inert by the full scale industrial process. The rig which material on the heat exchange surfaces. The fouling has been used to produce the experimental results material depends on the application to which the demonstrated throughout this paper is shown below: heat exchanger is put, however, the consequences are generally consistent: with significantly reduced Temp-4 heat transfer efficiency: reduced effectiveness of the associated control systems: and increased down time and difficulty in cleaning and maintenance. The industrial interest in the development of a fonling estimator (<;ensor) is the rl~re to monitor the perfonnance of the system as it fouls and thereby judge when. where and how much anti-fouling agent needs to be added to the process stream to maintain a satisfactory le"el of perfonnance. The development of a non-intrusi\'c fouling scnsor is a fundamental requircmcnt for pcrfonnance monitoring.

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This paper describes the de\'e!cpment and comparison of a number of on-line fouling sensors using methods based on linear least-squares parameter estimation and 'standard' artificial feedforward neural networks. Additionally, the

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Items indicated Temp-l through to Temp-J are temperatures which are recorded every thirty seconds. as is the flowrate. HTX-I to HTX-3 represent the heat exchanger units as shown in greater detail in figure 2. Inlet temperature

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a heat transfer efficiency which proportioned the sensible energy used in raising steam to the total energy entering the system. Unfortunately this approach does not have a simple comparison in this work due to the constant power input in the system under consideration.

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Equation (I) introduces a fouling factor, (faborek et al 1972) which is used in this study to describe the amount of fouling. (1)

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where h is the film coefficient between the fouled surface and the oil, "i arc the thicknesses of thc layers in the composite wall between the heater and the fouling surface in contact with the oil. le; are the thermal conductivities of each of the layers. The only \-ariabks in this expression are the thickness of fouling. "f. and kr- the thermal conductivity of the fouling. Both of which are time, temperature and operating condition dependent leading to a complex time dependent, non-linear relationship.

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Fig 2. Schematic of a Heat Exchanger clement

During normal operation of this rig the effects of fouling can be demonstrated over a period of 6-8 hours whereas on the real process the equivalent time can vary from weeks to months. This 'acceleration' was a design requirement of the rig as was the low volume of oil neceSS,1ry to operate it. The operating conditions of the experimental rig are recognised as being significant by the collaborating company.

A typical set of data collected over a 12 hour period will result in a fouling factor vs Time graph as shown below.

2. 1 Process Operation

Tn the experimental rig each of the three heat exchange units has a solid heater in the central core with oil flowing in the annular space. The heaters provide a power input of between 2-3 kW which is then transferred to the oil through the inner tube wall of the annulus and the fouling deposited on the outer surface of this wall. The oil temperature therefore rises as it passes through each of the heat exchange units. In order to maintain the input oil temperature constant (as measured at Temp-I), the oil is cooled in the reservoir prior to its recycling through the system. Once these models have been established. their use will be directed towards the situation where anti-foulants are introduced to the system. The estimators which are developed must therefore take this proposed use into account.

Fig. 3. A Typical Variation of Fouling Factor It is possible to take 2 distinct approaches to this problem. the first being to provide an estimate of the 'normal' Ran-fouled situation and to regard fouling as a process fault and commence with a 'fault detection' approach. or secondly. to attempt to predict the effects of fouling directly. Additionally. it is important that the model also provides evidence with regard to the fouling mechanism. i.e. does increased fouling occur with prolonged operation at high temperatures and low flowrates. This is a more constrained requirement in comparison with the development of a fouling sensor.

3.0 MODELLING APPROACHES A simple and related study on the fouling of the stream raising pipes in a coal-fired boiler. (McMichael. 1988) based the measure of fouling on

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4.0 RESULTS

3. I Fouling Estimation

Due to the relatively narrow range of temperatures which were used, the non-linearities of the system were not as pronounced as they would be on the industrial units. Consequently, the linear methods resulted in similar performance as the non-linear results. However, as the operating ranges increase. the non-linear estimators outperform the linear estimators.

The estimation of the fouling in the system has been undertaken by anal~'sis of the data collected during operation. From this data. a range of linear and nonlinear techniques have been used to produce fouling estimators. The overall heat transfer coefficient U. and the thermal conductivity, k. are dependent on time, flowrate and temperature(s). Consequently, "f. the thickness of fouling is also a similarly dependent variable. Although the system has been described as time varying. the use of time as an input has obvious problems as it is not clear how time itself can be scaled in such a way as to be easily generalised.

A range of fouling estimates using ANNs are sho\\n below:

Linear [,east Squares. Least squares methods for the estimation of coefficients of linear equations is a well understood practice. In this case equation (1) describing the fouling factor is non-linear thereby reducing the general applicability of this approach to this problem.

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Non-linear E...timation. The particular non-linear approach which was used was that of the Feed forward Artificial Neural Network. Although many structures of 'Neural Network' have been suggested, the F ANN has been chosen due to its relative simplicity in providing a non-linear structure relating inputs to outputs. As the aim of the investigation was to provide an estimation of degree of fouling the increased burden of a 'relatively slow' training method or a non exhaustive approach to achieving the optimal architecture are issues which are not discussed further in this paper.

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The mechanism which was used was to fix the number of inputs and outputs to the network; vary the number of hidden neurons in the one hidden layer which was implemented and to look for a minimum in the performance measure which would then indicate a satisfactory architecture. This approach was supplemented by repeatedly trying the (apparently) converged network on unseen data. The final strucnlre which was used di!iplayed a minimum in the performance measure for both the training data and the unseen data . This added weight to the argument for deciding upon this stnlctl.1fC.

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Perfnrmance .\fe(lslIres. As both least square and Rackpropagation embody thc principle of minimising the sum of the squares of the prediction errors then their performances can be directly compared given that the error scales are equivalent (ic. eithcr both scaled or both unsealed).

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displayed in fig . 7 can also be used to train a network. F o

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The results shown in fig. 4-6 highlight the extent to which the fouling of the system can be estimated. These results form the basis for further analysis relating to the sensitivity of the operating condition to produce fouling . For example, the oil flowrate was approximately constant for the above results with a slight variation due to the inherent system noise. However, a second series of experiments were carried out where the flowrate was varied considerably. A representative result is shown in figure 7.

Eliminating the tlowrate allows a similar estimation to be produced but these estimates present a better average trend than that shown in figure 8.

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Figure 7. Variation in Oil Flowrate.

Figures 8 and 9 require one further question to be answered. That is what is the effect of flowrate itself on the fouling factor. The result shown in figure 10 indicates that the answer is that the effect is negligible.

/\5 an example of how the models C'.m be used to :ield information regarding the underlying process mechanisms. the ci.'lta which has been generated :md

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... Bhid ... taJej Figure 10. Estimator Based on Oil Flowrate. Further model generation is also underway using physical measures of the amount of fouling in place of the fouling factor. However the proposed use is the same, that is to use these models to investigate and quantify the effect of anti-foulants on the operation of the process.

5.0 CONCLUSION The results shown in this paper demonstrate the usefulness of non-linear estimation techniques in the development of an on-line estimator for heat exchanger fouling. This approach has been developed for use in evaluating the contribution of anti-fouling agents during operation. The models which have been produced are currently being used as part of an ongoing study into crude oil fouling alongside the development of a mechanistic model.

6.0 REFERENCES McMichael. D.W.. (1988), "On-Line Fault Detection: a system nonspecific approach" . OeEL J 729/'88. Oxford University. Taborek. 1.. Knudscn. Fouling Progress.

Aoki. T.. Ritter. RB. . Palen, 1.W .. 1. G.. (1972) "Predictive Methods for Behaviour". Chemical En.~ineering 68. 7.

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