F-EX-1-1 A Theoretical Study of Fouling and the Factors Which Influence It

J. G. Knudsen
1964; revised 1979

A theoretical study is made of fouling of heat transfer surfaces in order to provide a sounder basis of analyzing experimental data to be obtained on fouling test apparatus now under construction for HTRI. The experimental data obtained will give t/kf (scale thickness/scale conductivity) as a function of time. Therefore, the present analysis is directed towards deriving equations (based upon assumed mechanism) which relate t/kf to time as well as to the other parameters (heat flux, diameter, flow rate, concentration) of the test system.

In the analysis, scale deposition and removal are considered and the resulting exponential equation has the form

t/kf = c1/c2 [1 - e-c2q]

where c1 is determined by the mechanism of deposition and c2 by the mechanism of removal. Eight postulated mechanisms of deposition and one mechanism of removal are analyzed. The eight exponential equations obtained are expressed in terms of the several variables of the system.

For six of the mechanisms considered, the initial rate of fouling is independent of diameter or flow rate. The important parameters for a salt with inverse solubility are slope of solubility curve, heat flux, diameter, and flow rate. If chemical reaction takes place, surface temperature becomes important. There also may be situations where bulk temperature and concentration are significant variables.

For scaling of calcium sulfate, an experimental program of 27 individual tests is outlined in which each of three values of heat flux, tube diameter, and mass flow rate are specified. Inlet bulk temperatures in the neighborhood of 160 °F are recommended for all tests.

It appears reasonable to fit experimental data into an equation of the form shown above. Means of analyzing data to obtain values of c1 and c2 by a least square analysis are described.