Condensation error

Unfortunately, the ideal-gas assumption can sometimes lead to serious error. While errors in the Lewis rule are often less, that rule has inherent in it the problem of evaluating the fugacity of a fictitious substance since at least one of the condensable components cannot, in general, exist as pure vapor at the temperature and pressure of the mixture. 

Thus D(r) is given by the slope of the V versus P plot. The same distribution function can be calculated from an analysis of vapor adsorption data showing hysteresis due to capillary condensation (see Section XVII-16). Joyner and co-woikers [38] found that the two methods gave very similar results in the case of charcoal, as illustrated in Fig. XVI-2. See Refs. 36 and 39 for more recent such comparisons. There can be some question as to what the local contact angle is [31,40] an error here would shift the distribution curve. 

Table 1 is condensed from Handbook 44. It Hsts the number of divisions allowed for each class, eg, a Class III scale must have between 100 and 1,200 divisions. Also, for each class it Hsts the acceptance tolerances appHcable to test load ranges expressed in divisions (d) for example, for test loads from 0 to 5,000 d, a Class II scale has an acceptance tolerance of 0.5 d. The least ambiguous way to specify the accuracy for an industrial or retail scale is to specify an accuracy class and the number of divisions, eg. Class III, 5,000 divisions. It must be noted that this is not the same as 1 part in 5,000, which is another method commonly used to specify accuracy eg, a Class III 5,000 d scale is allowed a tolerance which varies from 0.5 d at zero to 2.5 d at 5,000 divisions. CaHbration curves are typically plotted as in Figure 12, which shows a typical 5,000-division Class III scale. The error tunnel (stepped lines, top and bottom) is defined by the acceptance tolerances Hsted in Table 1. The three caHbration curves belong to the same scale tested at three different temperatures. Performance must remain within the error tunnel under the combined effect of nonlinearity, hysteresis, and temperature effect on span. Other specifications, including those for temperature effect on zero, nonrepeatabiHty, shift error, and creep may be found in Handbook 44 (5). The acceptance tolerances in Table 1 apply to new or reconditioned equipment tested within 30 days of being put into service. After that, maintenance tolerances apply they ate twice the values Hsted in Table 1.

Multiple-Effect Evaporators A number of approximate methods have been published for estimating performance and heating-surface requirements of a multiple-effect evaporator [Coates and Pressburg, Chem. Eng., 67(6), 157 (1960) Coates, Chem. Eng. Prog., 45, 25 (1949) and Ray and Carnahan, Trans. Am. Inst. Chem. Eng., 41, 253 (1945)]. However, because of the wide variety of methods of feeding and the added complication of feed heaters and condensate flash systems, the only certain way of determining performance is by detailed heat and material balances. Algebraic soluflons may be used, but if more than a few effects are involved, trial-and-error methods are usually quicker. These frequently involve trial-and-error within trial-and-error solutions. Usually, if condensate flash systems or feed heaters are involved, it is best to start at the first effect. The basic steps in the calculation are then as follows ... 

When one takes a sample at the rate of 0.3 liter min from a stack discharging 2000 m min to the atmosphere, the chances for error become quite large. If the sample is truly representative, it is said to be both accurate and unbiased. If it is not representative, it may be biased because of some consistent phenomenon (some of the hydrocarbons condense in the tubing ahead of the trap) or in error because of some uncontrolled variation (only 1.23 gm of sample was collected, and the analytical technique is accurate to 0.5 gm) (1). 

Assume that the system described below exists in a process unit recently purchased by your company. As the manager, the safety of this unit is now your responsibility. You are concerned because your process hazard analysis team identified the potential for an operator error to result in a rupture of the propane condenser. You have commissioned a human reliability analysis (HRA) to estimate the likelihood of the condenser rupturing as the result of such an error and to identify ways to reduce the expected frequency of such ruptures... 

Inspection of the HRA event tree reveals that the dominant human error is Error A the operator failing to isolate the propane valves first. The other potential human errors are factors only if a propane isolation valve sticks open. Based on these qualitative results alone, a manager rrught decide to periodically train operators on the proper procedure for isolating a failed condenser and to ensure that operators are aware of the potential hazards. The manager might... 

There is a written procedure for condenser isolation, but it is normally a simple step-by-step task that is second nature to the operator and is performed from memory. However, imder the threat of a potential vapor cloud explosion, the operator may forget to close the propane valves first (Error A). The HEP in Handbook Table 20-7 5 footnote (.01) is increased by a factor of 5 per Handbook Table 20-16 6a to account for stress. 

Note The value of hj, is not correct for the condensing coefficient as described in step 6 of this outline. In this case, the error is small, but that is not necessarily true for other situations. 

To calculate the outside film coefficient, you need to know the difference in temperature of the condensing vapor (T, ) and the pipe wall temperature (L). The pipe wall temperature is determined hy trial-and-error calculations using the following equation/ ... 

When steam pressures in the chest are near atmospheric, condensate can rise in the shell and drastically reduce avail-ahle surface—if the trap is too small to dump steam into the condensate return system or if the condensate return pressure is greater than the calculated chest pressure required. In these cases, the steam pressure will have to rise in the chest to overcome this error, if steam pressure is available. If not, the rehoiler will not deliver design flux. 

Proper condensate removal is important. An inverted split cup inside the shell, with the upper capped end above the nozzle and the lower open end -in. above the bottom tubesheet, should be used to cover the oudet nozzle. This can be made by splitting a pipe that is one size larger than the condensate oudet down the centerline. In this case, a 2-in. split is adequate. This cup must be fully seal welded (not tack welded) to force condensate down to the -in. clearance above the bottom tubesheet. A common error is to allow 6 in. or more above the tubesheet for the centerline of the condensate oudet. In this case, 6 in. of tube is 10% of the surface. If the cup is not used, add 10% more tubes to correct for the dead liquid space near the bottom. This is in addidon to the 10% safety factor. 

Again using trial and error, find the correct temperature for the bottom of the condenser, knowing... 

Fugacity, like other thermodynamics properties, is a defined quantity that does not need to have physical significance, but it is nice that it does relate to physical quantities. Under some conditions, it becomes (within experimental error) the equilibrium gas pressure (vapor pressure) above a condensed phase. It is this property that makes fugacity especially useful. We will now define fugacity, see how to calculate it, and see how it is related to vapor pressure. We will then define a related quantity known as the activity and describe the properties of fugacity and activity, especially in solution. 

In the design of a cooler-condenser for a mixture of vapour and a permanent gas, the method of Colburn and Hougen(66) is considered. This requires a point-to-point calculation of the condensate-vapour interface conditions T( and P . A trial and error solution is required of the equation ... 

To evaluate the required condenser area, point values of the group UAT as a function of qc must be determined by a trial and error solution of equation 9.181. Integration of a plot of qc against 1/17AT will then give the required condenser area. This method takes into account point variations in temperature difference, overall coefficient and mass velocities and consequently produces a reasonably accurate value for the surface area required. 

Id. Cyclic Condensation Polymers.—The foregoing discussion has proceeded under the assumption that the only products of bifunctional condensation are open chain polymer molecules—an assumption which obviously will not be exactly valid since cyclic polymers must always occur to some extent. The nature of the error introduced by this assumption will be examined in the course of the following discussion of cyclic polymer components. 

The preceding equations will, of course, be somewhat in error owing to the neglect of intramolecular condensations. Very large species will be suppressed relatively more on this account. All conceivable errors can do no more, however, than to effect a distortion of the quantitative features of the predictions, which will be small in comparison with the vast difference between the branched polymer distribution and that usually prevailing in linear polymers. From this point of view, the statistical theory given offers a useful description of the state of affairs. 

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