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ber of sensors which can detect only localized fouling. Although
these temperatures can be useful for trending, there are many factors
that can affect this calculation, including variable process heat loads,
different temperature levels in different seasons, and even the accu-
racy of thermocouples used. Because this method involves sub-
traction of two large numbers, accurate measurement techniques
and equipment are also critical.
The aim of this paper is to alert the user before a significant deg-
radation of the heat exchanger occurs. This gives an indication when
the preventive maintenance can be carried out so that the life time
of the device can be increased efficiently. When fouling cannot be
avoided, it can be monitored. A good service program can monitor
several critical heat exchangers in a system to prove the performance
of a heat exchanger. Through proper monitoring, problems can be
identified and isolated long before the economics of the process are
threatened. This work introduces the statistical approach to develop
fouling growth models which can be used for optimal maintenance
schedule of the exchangers.MODELING OF FOULING PROCESS
Fouling can be determined by measuring the increase in overall
heat transfer resistance, which is the major concern in heat exchang-
ers. The overall heat transfer resistance is the sum of conductive
and convective heat transfer resistance. For a clean tube, at time
t=0, the conductive resistance of the deposit is zero so that the con-
vective resistance is equal to the overall heat transfer resistance. At
any time, t>0, the relative contribution of conductive and convec-
tive resistance to overall heat transfer resistance will depend on the
type of deposit accumulated on the heat transfer surface.
Regardless of the type of fouling process, the net fouling rate is
the difference between the foulant deposit rate md and the foulant
reentrainment rate mr . Hence the mass of foulant deposited on the
heat transfer surface over a given period of time can be expressed
as [15](1)
Eq. (1) can be reformulated in terms of mass per unit heat transfer
area for a uniform spatial distribution of deposit.
(2)
Furthermore, mass per unit heat transfer area considering uniform
distribution of fouling along the heat transfer surface can be expressed
The fouling resistance Rf
represents the thermal resistance of the
foulant layer deposited for a unit area of the heat transfer surface.
Consequently, fouling rate can be specified as
(4)
It is assumed that both the mass density and the thermal conductiv-
ity are invariant with time. Hence the Eq. (4) becomes
(5)
Where Rd=MA, d /ρf
kf
represents the fouling resistance rate for dep-
osition while Rr=MA, r /ρf
kf
represents the fouling resistance rate for
removal.
The relationship between overall heat transfer coefficient based
on tube outside surface area and thermal resistance for a clean heat
exchanger can be defined as
Similarly, for a fouled heat transfer surface the above relation is de-
fined as The model is idealized with the assumptions that ho, c=ho, f
and hi, c=hi, f
to calculate the overall thermal resistance due to fouling [15].
STATISTICAL ANALYSIS
Much of the research in engineering, basic science and industry
is empirical and makes extensive use of experimentation. Statisti-
cal analysis can greatly increase the efficiency of these experiments
and often strengthen the conclusion so obtained [16,17]. The objec-
tive of this work is to estimate the time required to reach a threshold
level of fouling in a heat exchanger. The threshold fouling [18] can