METHOD TO DETECT FOULING IN HEAT EXCHANGERS

Oddgeir Gudmundsson1, Olafur Petur Palsson1, Halldor Palsson1, Sylvain Lalot21Faculty of Industrial Engineering, Mechanical Engineering and Computer Science, University of Iceland

2LME, University of Valenciennes and Hainaut Cambrsis, Le Maont Houy, France

ABSTRACT

Heat exchangers are frequently used in district heatingsystems, at power plants and public homes. Detectingfouling in district heating heat exchangers is of greatimportance. There are currently many different waysto detect fouling in heat exchangers that either rely onphysical examination of the heat exchanger or modelingthe heat exchanger and use measurements of the heatexchanger to predict fouling. The method describe inthe paper can be used to detect fouling by using the inletand outlet temperatures and either the hot or cold massflow. Results of the method described on a simulateddata are given.

INTRODUCTION

Heat exchangers are important devices that are widelyused in industrial and domestic applications. Their pur-pose is to transport heat from one fluid to another byconduction through solid walls. Typical applications in-clude chemical processes, air heating and cooling as wellas use in district heating systems. Many different typesand sizes of heat exchangers exist, but they are similarin principle and their classification is well defined (20).One side effect of using heat exchangers is the possibilitythat internal fouling will occur. Fouling typically occurswhen the solid that is placed between the two fluids ac-cumulates deposits from the fluids, builds up biofilm orcorrodes. When fouling increases, the heat transfer be-tween fluids decreases, which will increase the energycost of the heat exchanger. It is therefore importantto minimize or at least to monitor fouling in heat ex-changers when possible, which is particularly importantin district heating systems, where the amount of heattransfer is large.Studies have shown that the total cost of fouling inheat exchangers in highly industrialized countries canbe up to 0.25% of gross national production, (11) and(3). Fouling also has an effect on the environment sincethe increased resistance from fouling will increase powerconsumption of pumps. For instance in a 550 MW coal-fired power plant a fouling biofilm of 200µm lead toincrease of about 12 tons of CO2 per day, (9). Due tothe cost and the environmental issues introduced withfouling, it is preferred to take steps to detect or reducefouling if possible. Effective fouling mitigation tech-niques include, (4),

• Reduction of the rate of fouling by adding chemicalmaterials into the flow.

• Increasing the heat transfer area of the heat ex-changer.

• Cleaning of the heat exchangers when they getfouled.

Research of fouling, both causes and detection, has beenextensively studied. Studies that involve causes of foul-ing include (10) and (11) where modifications of theheat transfer surface was studied and ion implantationof fluorine and silicon ion into the heater alloys werealso studied respectively. Other studies with a focuson detection of fouling include (12) and (13) where thethermal efficiency and temperature drop in the outletswere studied respectively.The effect of fouling is often represented by a foulingfactor, which measures the relative thermal resistanceintroduced by fouling. For a new heat exchanger thefouling factor is zero and it increases with time withincreased fouling. The development of fouling dependson a number of things, (5) and (16). Major groups offouling dependents are:

• Composition of the fluids.

• Operating conditions in the heat exchanger.

• Type and characteristics of the heat exchanger.

• Location of fouling.

• Presence of micro-organisms.

According to (5), (6) and (8) there is usually an induc-tion time before a noticeable amount of mineral depositshas formed, which will change the overall heat transfernoticeably. Furthermore, research on fouling shows thatthe fouling may enhance the heat transfer for a shorttime in the beginning of fouling due to enhanced rough-ness on the heat transfer surface. It has also been shownthat the fouling will grow with increased rate during thefouling period, (7).Detection of fouling in heat exchangers have been stud-ied extensively and the following list summarizes justfew of the methods for fouling detection.

• In (17), a good overview of the use of ultrasonics,acoustic and optical techniques to detect foulingon-line is presented.

• In (18), heat exchangers are modeled with neuralnetworks and in (1) the neural networks are usedto detect fouling on-line.

The 11th International symposium on District Heating and Cooling,

August 31 to September 02, 2008, Reykjavik, ICELAND

• In (19), a measurements of electric resistance isused to detect fouling build up in the heat ex-changer.

• In (2), an extended Kalman filter is used to detectfouling in counter-flow heat exchangers.

In this paper, changes in the overall heat transfer coeffi-cient in heat exchangers is monitored by assuming thatthe heat exchanger is operating in a steady state condi-tion over periods of time. Based on the model results,the Cumulative Sum control chart is used to detect iffouling occurs and estimate the starting time of fouling.The method is tested by using a dynamic finite volumemodel to generate data by simulation. This methodo-logy results in a very controlled environment for gener-ating data, where stochastic changes can be added tothe data in order to generate realistic series.

FOULING DETECTION

The slope method

The following method is specially designed to monitorheat exchangers that operates in a condition close toa steady state. For instance the heat exchangers usedin the district heating industry. According to the en-ergy company Hitaveita Suurnesja the heat exchangersused there are usually close to a steady state operationtheir whole operating time. The heat exchangers gethot steam with almost constant pressure and flow. Thecold side usually has almost constant temperature, butthe cold mass flow can have some variations.The method uses the following assumptions:

• Steady operating conditions exist.

• Changes in the kinetic and potential energies offluid streams are negligible.

• Fluid properties are constant.

The heat transfer rate for a parallel-flow and counter-flow heat exchanger in a steady state is

Q = UA∆TLMTD = mkcp∆Tk (1)

where the subscript k indicates either the hot or thecold side.For a cross-flow heat exchanger it is necessary to adda correction factor F for the log mean temperature dif-ference, ∆TLMTD. The value of F can be found intables in (16). By looking at Eq. (1) the followingrelation can be derived for cross-flow heat exchangersm∆T ∝ UAF∆TLMTD.This method finds the fouling by calculating the slopeAUF over a sliding window of size N from the plotm∆T against ∆TLMTD. A typical plot can be seenin Figure 1. By viewing the figure it can clearly beseen that there are strong correlations between obser-vations. By monitoring the slope for changes from theslope of a reference operation it is possible to find out

83 84 85 86 87 8840

50

60

70

80

90The slope of the line is equal to UAF

∆TLMTD

m∆c

pTh

Equation of the line:

UAF = 5.08

y = 5.08*x − 366

Fig. 1: The figure shows a typical plot of mcp∆T against∆TLMTD for one window.

when the heat exchanger starts to build up fouling. Asthe slope decreases the more fouled the heat exchangeris. Because of the correlations it is necessary to haverelatively long windows when estimating the slopes tominimize the effect of the correlations, especially whenestimating the reference slope because the detection isdone by comparing how the slope is changing with timeto the reference slope.

Cumulative sum control chart

According to (15) the Cumulative sum control chart(CuSum) is very efficient when detecting small shift inmean of a process. Thus is the CuSum chart is used inthis study.A result of fouling in heat exchangers is a decrease inthe overall heat transfer coefficient, U . Since the slope,AUF that is calculated in the method include the over-all heat transfer coefficient, U , and that the heat trans-fer area, A, and the correction factor, F , should changerelatively small comparing to the changes in U whenfouling occurs it is possible to monitor the changes inthe slope to detect fouling. The detection is made byusing the CuSum chart.When analyzing the parameters the average value ofthe parameters is calculated over a window of a specificlength, which is chosen in accordance with the processbeing studied, and the CuSum chart is used to monitorthe average value of the parameters for a shift from theirreference value. If the average is not changing in timeit is said to be under control, if on the other hand thereis a shift in the average it is said to be out of control.If the process remains in control the cumulative sumshould fluctuate around zero. If there is a shift in thevalue of the parameters, either upwards or downwards,the CuSum chart should pick it up quickly. If there isan upward shifting it is said to be a positive shift andconversely if there is a downward shift in the parame-ters, it is said to be a negative shift in the parameter.The CuSum control chart is calculated with Eq. (2) andEq. (3), (15).

The 11th International symposium on District Heating and Cooling,

August 31 to September 02, 2008, Reykjavik, ICELAND

SH(i) = max[0, xi − (µ0 + K) + SH(i − 1)] (2)

SL(i) = max[0, (µ0 − K) − xi + SL(i − 1)] (3)

Where the starting values are SH(0) = 0 and SL(0) = 0.SH(i) and SL(i) accumulate deviations from the targetvalue that is greater than the reference value K, withboth quantities reset to zero upon becoming negative.Care needs to be taken when choosing the value of K tominimize the chance of detecting fouling when none is,error of type 1, and not detecting fouling when foulinghas occurred, error of type 2. If either sH(i) or sL(i)exceeds a constant H , the process is out of control. Thisconstant H is the decision interval.There are many possible ways of choosing K and it isusually chosen to be about halfway between the targetmean and the mean corresponding to an out of controlstate.

THE SIMULATED DATA

Since it was difficult to get access to data during thisstudy from a cross-flow heat exchanger where foulingoccurs the data used in the analysis was simulatedwith a Matlab program developed by Halldor Pals-son. The program simulates time series from an un-mixed/unmixed cross-flow heat exchanger. A cross-flowheat exchanger test rig is now under construction at theUniversity of Valenciennes where fouling can be inducedin a controlled environment. In the following sections anintroduction will be given to the model used for simula-tion, the fouling factor and the data used in the analysis.

Dynamic simulation model

The mathematical model of a general heat exchangerspecifies the fluid temperature as position dependentfields inside the heat exchanger, where energy travel intwo ways:

• By pure convection from the hot fluid to the metalsheet.

• By conduction through the metal sheet. It is as-sumed that the conduction within each fluid is neg-ligible.

In the program it is possible to model the heat ex-changer either with a thin metal sheet between the flu-ids or without the metal sheet, that is, assume that themetal sheet has negligible heat capacity and infinit ther-mal conductivity. To compare the effect of the metalthe output temperatures where calculated for with andwithout the metal sheet with the same input tempera-ture and mass flow.It is assumed that the cold and hot fluid flow only inx and y direction respectively. The width of the ex-changer is W , the height is H and the thickness of thehot and cold passages are dh and dc respectively. Theenergy balance for this system is described by two cou-pled partial differential equations where the field vari-ables are the temperatures Tc and Th for the cold and

0 0.2 0.4 0.6 0.8 10.4

0.5

0.6

0.7

0.8

0.9

1

Changes in the overall heat transfercoefficient, U, because of fouling

Dimensionless time

Ufo

uled

/Ucl

ean

Continuously fouling heat exchanger

Fig. 2: Evolution of the overall heat transfer coefficient,U , because of fouling

hot side respectively. The equations are

∂Tc

∂t+

mc

ρcHdc

∂

∂x(cTc) =

U

ρcdc

(Th − Tc) (4)

∂Th

∂t+

mh

ρcHdh

∂

∂y(cTh) =

U

ρcdh

(Tc − Th) (5)

In this formulation ρ and c are dependent on the flowtemperature and U is dependent on both Th and Tc aswell as position x and y. Also the mass flow of thecold stream, mc, can depend on y. The mass flow ofthe hot stream, mh, can depend on x. Mass flow, heattransfer coefficient as well as the inflow temperaturescan be time dependent.

Simulation of fouling

Resistance to heat transfer is the inverse of U . Theresistance to heat transfer corresponding to fouling, Rf ,is the increased resistance to heat transfer from the timethat the heat exchanger is new.

Rf (t) =1

U(t)A−

1

U(0)A(6)

When the data used in this study was simulated theeffect of fouling was introduced to the extent that theoverall heat transfer coefficient, U , dropped to half ofwhat U would be for a clean heat exchanger. In Figure

2 the ratioUfouled

Ucleanis shown. In (7) it is shown that foul-

ing increases with time, to simulate this effect the foul-ing used in this study was started slowly but increasedwith time. In Figure 2 it can clearly be seen that theaccumulation of fouling starts slowly but increases withtime.The effect of fouling on U is calculated in the simulationwith Eq. (7)

Ufouling = Uclean cos(at + b) (7)

The 11th International symposium on District Heating and Cooling,

August 31 to September 02, 2008, Reykjavik, ICELAND

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5x 10

−3Evolution of the resistance

to heat transfer because of fouling

Dimensionless time

Fou

ling

fact

or, R

f [m2 °C

/(W

)]

Continuously fouling heat exchanger

Rf = 0.0001

0.89

6

Rf = 0.0007

0.39

5

Fig. 3: Evolution of the fouling factor Rf through thesimulated time series

where

a =arccos(cf1)

m − floor(mcf2) + 1

b = −a(floor(mcf2) + 1)

(8)

The constant cf1 indicates the value of Ufouling as apercent of Uclean from a clean heat exchanger at theend of the time series. The constant cf2 indicates whenthe fouling will start. The values of cf1 and cf2 can bebetween [0, 1].When a heat exchanger is designed a fouling factor ischosen, the fouling factor indicates how much foulingthe heat exchanger can sustain before it needs to becleaned. According to (1) a fouling factor for water istypically in the range [0.0001, 0.0007]. Typical valuesfor the fouling factor can be found at (14). For thedata used in this study the fouling factor on the pre-viously mentioned interval corresponds to the interval[0.395, 0.876] in dimensionless time. In Figure 3 thecorresponding fouling factor is shown.

Simulation data

The simulated heat exchanger was 0.5 meters wide andheight and had a depth of 0.002 meters for both thehot and the cold side. The reason for these dimensionswas to insure turbulent flow in the simulated heat ex-changer.The inlet temperatures and the mass flows where chosenby randomly choosing base points over certain interval.The temperatures and the mass flows where then al-lowed to vary between the base points by interpolatingrandomly between the base points.In all the data simulations the same fouling effect wasused, in order to be able to compare the results for themethods and to do sensitivity analysis on their results.The fouling was allowed to decrease U to half of U froma clean heat exchanger, see Figure 2. To represent aheat exchanger in a district heating system only smallvariations in the inlets were allowed. Figure 4 showsone of the used data sets.

0 2 4 6 8 10

x 104

0

50

100

150

Sample no.

°C

Example of a typical data set

thintcinthouttcout

0 2 4 6 8 10

x 104

0

2

4

6

Sample no.

l/s

mhmc

1000 1100 1200 1300 1400 15000

50

100

150

Sample no.

°C

Closer look on the data set above

thintcinthouttcout

1000 1100 1200 1300 1400 15000

2

4

6

Sample no.

l/s

mhmc

Fig. 4: Data set used in the slope method

RESULTS - SLOPE METHOD

The slope method, described above, is derived to de-tect fouling in heat exchangers which usually have smallvariation in their inlets, as is the case for district heat-ing heat exchangers. In district heating systems all theinlets have small variations except the cold mass flow.The cold mass flow varies with water demand. To simu-late a case similar to a district heating system the inlettemperatures and the hot mass flow were only allowedsmall variations while the cold mass flow were allowedto vary considerably comparing to the hot mass flow.The effect of fouling was allowed to decrease the overallheat transfer coefficient, U , to half of the value of U fora clean heat exchanger, see Figure 2.As has been mentioned previously, the method monitorschanges in the slope AUF by comparing it to a referenceslope, the reference slope is calculated with part of thedata. In Figure 5 typical estimation of the referenceslope is shown.In Figure 6 the changes in the slope, AUF , is moni-tored. The straight black line is the reference slope andthe green line shows how the slope is changing in time.The above figure shows all the data points from all thewindows the slope AUF is estimated from, in the lowerfigure the data points have been removed and the valueof the x-axis have been changed to a dimensionless timeto show how the slope is changing in time. If the slopeis decreasing it may mean that the heat exchanger isaccumulating fouling or that the inputs have changed.

The 11th International symposium on District Heating and Cooling,

August 31 to September 02, 2008, Reykjavik, ICELAND

82 83 84 85 86 87 882

2.5

3

3.5

4x 10

5 The slope, UAF, calculated with window size=400

∆TLMTD

mc p∆T

h

Reference slopeEquation of the line:

UAF = 1.96e+4

y = 1.96e+004*x − 1.4e+006

Fig. 5: Estimation of a reference slope.

82 84 86 88 90 92 941

2

3

4x 10

5

Fouled slope

The slope, UAF, calculated with window size=400

∆TLMTD

mc p∆T

h

Reference slope

0.2 0.4 0.6 0.8 12

2.5

3

3.5

4x 10

5

Fouled slope

The slope, UAF, calculated with window size=400

Dimensionless time

mc p∆T

h

Clean Gradually foulingReference slope

Fig. 6: Figure a) shows all the data points from all thewindows that the slope AUF is estimated from. Figureb) shows only the slopes, that is the data points havebeen removed, and the values of the x-axis represent adimensionless time.

0 0.2 0.4 0.6 0.8 1−4000

−3000

−2000

−1000

0

CuSum chart for the slope method

Dimensionless time

CuS

um v

alue

s

Fouled heat exchanger1471 CuSum values

Shi

ft de

tect

ed in

∆U

A: 0

.42

Fig. 7: Detection of shift in the slope.

To check statistically where the shift in the slope beginsthe CuSum chart was used. That is if there is a shiftin ∆UAF = UAFreference − UAFfouling. Figure 7 showsonly the CuSum values for the fouled part of the data.The CuSum charts detects shifts in the slope at 0.42 indimensionless time.If the detection is compared to the fouling factors inFigure 3 it can be seen that the detection correspondsto Rf = 0.00016 which can be considered a good resultif compared to typical fouling factor values, which arein the range [0.0001, 0.0007].

Sensitivity analysis on detection

It can be shown that the mass flow has considerable ef-fect on the heat transfer. This effect can influence thedetection of fouling. The influence was studied by simu-lating 50 different time series and by going through theprocess of detection of fouling with the slope method.The result of this analysis is that the fouling is detectedwith 95% certainty between 0.33 and 0.92 in dimen-sionless time for the fouling factor used. This intervalcorresponds to a fouling factor on the interval [0.00007,0.0008], see Figure 3.It should be mentioned that in some cases the refer-ence slope was either over- or underestimated, whichresulted in the slope either overshooting, or undershoot-ing the clean slope almost from the beginning. In thecase where the slope was underestimated the fouling de-tection was made relatively late. In the case where theslope was overestimated the fouling detection was maderelatively soon. These two cases explain the wide rangeof the detection interval. Solution to this problem mightbe to have a longer reference interval.

CONCLUSIONS

The aim of the present study was to detect foulingin cross-flow heat exchangers that are operating in asteady state condition. As mentioned above heat ex-changers are designed to account for the effects of foul-ing by incorporating a fouling factor. The fouling factorindicates the maximum fouling the heat exchanger cansustain and still fulfill it operational requirements. Thefouling factor is usually on the interval [0.0001, 0.0007].It has been shown that the method derived can be used

The 11th International symposium on District Heating and Cooling,

August 31 to September 02, 2008, Reykjavik, ICELAND

to detect fouling in cross-flow heat exchangers.The detection analysis was only used on the fouled partof the data, that is the fouling begins in 0 in dimension-less time. The main results were the following:

• The slope method can detect fouling in a heat ex-changer with a small variation of the inlet variables.

• The 95% detection interval for the slope methodis [0.33, 0.92] in dimensionless time, which cor-responds to the fouling factor interval [0.00007,0.0008].

The slope method can be used to detect fouling inheat exchangers which have small variations in theirinlet variables. The sensitivity analysis shows that thefouling detection is made when the fouling factor is inthe interval [0.00007, 0.0008]. The wide range of thedetection interval is due to the difficulties in estimatingthe reference slope. Typical fouling factor values are inthe range [0.0001, 0.0007], as previously mentioned.

ACKNOWLEDGEMENTS

The study was sponsored by the University of IcelandResearch fund and the France-Icelandic Jules Vernefund.

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