Fouling calculations

Clearly, the number of CSFs included in the CI calculation can be far in excess of the number considered in typical MCSCF calculations CI wavefunctions including 5,000 to 50,000 CSFs are routinely used, and functions with one to several million CSFs are within the realm of practicality (see, for example, J. Olsen, B. Roos, Foul Jorgensen, and H. J. Aa. Jensen, J. Chem. Phys. 89, 2185 (1988) and J. Olsen, P. Jorgensen, and J. Simons, Chem. Phys. Letters 169, 463 (1990)). 

The rate of heat-transfer q through the jacket or cod heat-transfer areaM is estimated from log mean temperature difference AT by = UAAT The overall heat-transfer coefficient U depends on thermal conductivity of metal, fouling factors, and heat-transfer coefficients on service and process sides. The process side heat-transfer coefficient depends on the mixing system design (17) and can be calculated from the correlations for turbines in Figure 35a. 

The values of h, and AP, calculated by this procedure are for clean exchangers and are intended to be as accurate as possible, not conservative. A fouled exchanger will generally give lower heat-transfer rates, as reflected by the dirt resistances incorporated into Eq. (11-2), and higher pressure drops. Some estimate of fouling effects on pres-... 

The compressor of a gas turbine is one of the most important components of the gas turbine. It consumes between 50-65% of the energy produced in a gas turbine. Thus fouling of the compressor can cause large losses in power and efficiency for the gas turbine. Furthermore, the fouling of the compressor also creates surge problems, which not only affects the performance of the compressor but also creates bearing problems and flame-outs. The following are some of the major characteristics that need to be calculated ... 

Using a cooled bypass around the compressor, or by any means possible, try to establish spread between the points. It is amazing how data points can look different and still come back to the same point on the curve when the calculations are complete. If the compressor is tied to a reactor, the points may have to be taken over quite a period of time which can be done if the instruments are maintained. Be careful of fouling when using this method. 

Figure 10-43A. Predict fouling by nomograph, Part 1. Calculation of R value for fouling factor use in conjunction with Figures 10-43B and 10-43C. (Used by permission Zanker, A., Hydrocarbon Processing. March 1978, p. 146. Gulf Publishing Company, Houston, Texas. All rights reserved.)...

The Nomograph Part 3 (Figure I0-43C) may be used in a number of ways. For example, what will the fouling resistance, R(, be after an arbitrarily chosen time, t, or it can calculate the thickness of a fouling deposit after an arbitrarily chosen time t, providing the thermal conductivity of the deposited material is known. It can calculate thermal conductivity of a deposit, providing thickness is known, or estimated. 

The simplest calculation is to find the unknown fouling resistance after a time t. For this purpose, the nomograph is used as follows ... 

Calculate the overall fouling coefficient, adding the appropriate fouled factors to clean, U. ... 

Calculate the required area, based on the film coefficient of steps 4 and 5 together with fouling and tube wall resistances A = Q/U At. 

Now, the hb coefficient can be used with the overall U equation, including shell-side fouling, to calculate a final overall coefficient for boiling. 

Assume fouling resistances for shell side and tube side. Calculate the overall resistance, less shell-side film resistance ... 

The double-pipe longitudinal finned exchanger is designed by adding the fouling factor to each respective film coefficient before calculating the overall... 

Since no serious problems exist with corrosion, the materials of constmction can be cheaper and the thicknesses reduced. Fouling coefficients do not need to be incorporated into the design calculations, as the surfaces remain clean indefinitely. This in itself provides a secondary benefit in that the pitching of fins may be reduced without the risk of reducing flow. 

The values of /"fh and ffc (the film resistances for the hot and cold fluids, respectively) can be calculated from the Dittus-Boelter equations previously described and the wall metal resistance / from the average metal thickness and thermal conductivity. The fouling resistances of the hot and cold fluids /"dh and are often based on experience, but a more detailed discussion of this will be presented later in this chapter. 

From these correlations it is possible to calculate the film heat transfer coefficient and the pressure loss for laminar flow. This coefficient, combined with that of the metal and the calculated coefficient for the service fluid together with the fouling resistance, is then used to produce the overall coefficient. As with turbulent flow, an... 

The added capability of calculating unknown values based on measured inputs will greatly enhance the system capabilities. For example, the neither fouling factor nor efficiency of a heat exchanger can be directly measured. A predictive maintenance system that can automatically calculate these values based on the measured flow, pressure and temperature data would enable the program to automatically trend, log and alarm deviations in these unknown, critical parameters. 

By substituting the appropriate values for viscosity and diffusion at various temperatures, they found that corrosion rates could be calculated which were confirmed by experiment. The corrosion rates represent maxima, and in real systems, corrosion products, scale and fouling would reduce these values often by 50%. The equation was useful in predicting the worst effects of changing the flow and temperature. The method assumes that the corrosion rate is the same as the limiting diffusion of oxygen at least initially this seems correct. 

Equation (20-80) requires a mass transfer coefficient k to calculate Cu, and a relation between protein concentration and osmotic pressure. Pure water flux obtained from a plot of flux versus pressure is used to calculate membrane resistance (t ically small). The LMH/psi slope is referred to as the NWP (normal water permeability). The membrane plus fouling resistances are determined after removing the reversible polarization layer through a buffer flush. To illustrate the components of the osmotic flux model. Fig. 20-63 shows flux versus TMP curves corresponding to just the membrane in buffer (Rfouimg = 0, = 0),... 

Fig. 5.1.10 (a) MR measured propagators and (b) corresponding calculated RTDs for flow in a model packed bed reactor composed of 241 -pm monodisperse beads in a 5-mm id circular column for a fixed observation time of 300 ms and as a function of biofilm fouling. As the porous media becomes biofouled, a high veloc-... 

Calculate the overall coefficient, allowing for fouling factors. 

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