Asymptotic fouling

The rate of fouling decreases with time but does not appear to approach an asymptotic maximum during the time of operation. This is the most common type of folding in the process industry and is usually the result of a combination of different fouling mechanisms occurring together. 

Figure 10-41. For many cooling waters, the fouling resistance increases rapidly, then decreases, and finally approaches an asymptotic value. (Used by permission Knudsen, J. G., Chemical Engineering Progress. V. 87, No. 4, 1991. American Institute of Chemical Engineers. All rights reserved.)...

And, finally, it can answer after how much time will the fouling resistance achieve a desired percentage of the asymptotic fouling value, R ... 

The Nomograph Part 3 may also be used to predict when the fouling resistance will reach an appropriate percentage of the asymptotic R value, or any desired R value. 

There is a high degree of turbulence, which increases the rate of foulant removal and results in a lower asymptotic value of fouling resistance. 

R0 = Asymptotic value of fouling resistance, hr-ft2-°F/Btu t = Time corresponding to the fouling resistance R,... 

An alternative insert for tubes is the spiral insert produced by Cal Gavin. The device consists of a matrix of wire loops on a twisted wire core. The diameter of the coils is such that it is a push fit. Laboratory studies using these wire matrix inserts with an Arabian crude oil demonstrate that the steady asymptotic value of the fouling resistance is reached in only 10 hr from start up and only of the order of 2-7% of the recommended TEMA value. The presence of the wires, particularly those in contact with the heat-transfer surface, creates turbulence that is largely responsible for the beneficial effects on the fouling. The benefits are not without the potential penalty of increased pressure drop and hence increased pumping costs. By suitable design for the same duty, this penalty can be substantially reduced. 

Fig. 1.2 shows an idealised asymptotic graph of the rate of growth of a deposit on a surface. In region A the process of adhesion is initiated. In some fouling situations the conditioning (or induction) period can take a long time, perhaps of the order of several weeks. In other examples of fouling the initiation period may be only of the order of minutes or even seconds. 

The initial rate of deposition and the asymptotic fouling resistance can be... 

FIGURE 7.12. The effect of velocity, friction velocity and Reynolds number on the asymptotic fouling resistance... 

Williamson [1990] has presented data that show the dependence of the haematite deposition (i.e. 0.2 pm particles) on velocity. Fig. 7.12 illustrates the rapid fall in asymptotic deposit mass mg/m ) as velocity is increased. Fig. 7.12 also records the corresponding values of friction velocity u and Reynolds number. The data suggest that employing velocities > 2 m/s would minimise the fouling due to particle deposition. 

Normalised data for a particular test are given in Fig. 7.16 and the friction factor / shows a steady increase with time although it would appear that the curve is asymptotic in character. The shape is consistent with the asymptotic fouling curve discussed in Chapter 1, i.e. the friction factor change mirrors the change in fouling resistance. On Fig. 7.16 also the change in heat transfer efficiency with time shows... 

Non-boiling conditions represent the simplest crystallisation fouling process and may be based on the Kern and Seaton [1959] model. Hasson [1981] presents an expression for asymptotic fouling resistance... 

For very large values of t and constant operating conditions of water quality, flow velocity and surface temperature. Equation 8.21 can be used to calculate the asymptotic fouling resistance, i.e. 

The work by Bott and Gudmundsson [1977] with wax dissolved in kerosene demonstrates that the attainment of the equilibrium condition is likely to be a rapid process. It would appear from Fig. 8.19 that the asymptotic fouling resistance is reached after only 2 hours. Rapid deposition occurs in the first few minutes of exposure of the metal surface to the flowing waxy hydrocarbon. 

FIGURE 8.20. Asymptotic fouling resistance for deposition fiom waxy hydrocarbon versus the inverse of Reynolds number squared... 

Average asymptotic fouling resistance at different Reynolds number for two wax... 

Watkinson and Epstein [1969] Liquid phase fouling from gas oil Mass transfer and adhesion of suspended particles First order Kem and Seaton shear removal term (1) Correct prediction of initial rate dependence on velocity (2) Incorrect prediction of asymptotic resistance on velocity... 

At higher temperatures deposition may be controlled by diffusion, i.e. k (because the reaction rate is higher at higher temperatures). Inspection of the equation suggests that the fouling resistance cannot tend towards asymptotic. 

These authors demonstrate the effectiveness of a threshold agent (aceto diphosphonic acid) and a crystal modifying additive (polymaleic acid) Fig. 14.4 shows the plot of fouling resistance with time and it will be evident that the asymptotic fouling resistance has been reached in each example. The fouling resistance in the presence of both these additives is significantly less than that obtained with no inhibitor present. 

Laboratory studies using wire matrix inserts have been made by Crittenden et al [1993] using a light Arabian crude oil containing 10% waxy residue. The experimental data show that with inserts in place, asymptotes on the fouling resistance - time curves are reached within 10 hours of start up. Furthermore the values of the fouling resistance at the asymptote are only between about 2 and 7% of the recommended TEMA values recently revised [Chenoweth 1990]. 

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