Operating limit curves

Section 5.3.1.6.1) and to formulate the initial heatup and cooldown limit curves for plant operation. Once actual post-irradiation surveillance data become available for each reactor vessel, these data will be used to adjust plant operating limit curves. 

FIG. 28-1 Operating limits for steels in hydrogen service, Each steel is suitable for use under hydrogen-partial-pressure-temperature conditions below and to the left of its respective curve, (Coutiesy of National Association of Conosion Engineers)... 

A qualitative and somewhat quantitative indication of the case with which the two (or more) fans will parallel is represented by their limit curve of Figure 12-145. This curve is constructed by starting at pressure P corresponding to the system intersection A, and plotting the increments of Volume X, y, etc., to define the limit of available volume that the duct can accept and which the second fan must pick up as it comes on the line. For good parallel operation, the limit curve must intersect the combined static pressure curve, SP, at only one point. 

Another operational limit in the CFB system involves gas suppliers. Three types of gas suppliers, i.e., a reciprocating compressor, a blower with throttle valve, and a compressor, are commonly used in the CFB system. For blower operation, as the gas flow rate decreases, the pressure head of the blower increases. For compressor operation, the pressure head of the compressor can be maintained constant with variable gas flow rates. The interactive behavior between a CFB system and a blower can be illustrated in Fig. 10.9, where dashed curves refer to the blower characteristics and solid curves refer to the riser pressure drop. At point A, the pressure drop across the riser matches the pressure head provided by a blower thus, a stable operation can be established. Since the pressure drop across the riser in fast fluidization increases with a decrease in the gas flow rate at a given solids circulation rate, a reduction in the gas flow rate causes the pressure drop to move upward on the curve in the figure to point B with an increase in the pressure drop of Spr. In the case shown in Fig. 10.9(a), with the same reduction in the gas flow rate, i.e., SQ, the increase in the pressure drop, Spr, from point A to point B is greater than that which can be provided by... 

The Nelson curves in API 941 (published by the American Petroleum Institute) list the operating limits that should be followed to avoid de-... 

LLD, lower limit of detection 99th, 99th percentile reference limit ROC, receiver operator characteristic curve optimized cutoff 10% Cy lowest concentration to provide a total imprecision of 10%. 

Discrimination can be summarized by various single statistics, such as the area under the receiver operating characteristic curve (or the equivalent C statistic), measures, or the d statistic, although all of these measures have limitations (Royston and Sauerbrei 2004 Altman and Royston 2007 Lewis 2007). 

Figure 44-16 Receiver operating characteristic curves to establish the best discriminator limit for cardiac troponin T (cTnT) for predicting AMI.The number of true positives (/-axis) and false positives (x-axis) are reported in relation to time (h) after the onset of symptoms.The best discriminating point for cTnT is 0.20 Xg/L at 9 hours after the onset of chest pain. (Reprinted by permission of Elsevier Science from Burlina A, Zaninotto M, Seccfiiero S, Rubin D.Accorsi F. Troponin T as a morfcer of ischemic myocardial injury. Clin 6/ocbem I994 27 t 13-21. Copyright 1993 by Canadian Society of Clinical Chemists.)...

The SPARG (Sulfur Passivated Reforming) principle (ref. 3) allows operation below the carbon limit curve. It was demonstrated (ref. 4) that carbon-free operation could be obtained above a certain sulfur coverage at conditions which would otherwise result in carbon formation. Sulfur passivated reforming as practiced in the Topsoe SPARG process (ref. 5) solves the problem of carbon formation by "ensemble control" which means that the sites for carbon formation are blocked while sufficient sites for the reforming reactions are maintained. This effect is obtained by adding sulfur to the process feed. 

It is obvious that operation on the left side of the carbon limit curve in Fig. 2 results in more economic conditions (lower steam and C02-addition for a given H,/C0 ratio). Operation on mixtures of C02 and methane without steam is also possible. The conventional processes are limited by the carbon limit curve. Conditions for the SPARG process which have been demonstrated in a full size monotube process demonstration unit are listed in Table 1. 

This demonstrates the advantage of the graphical over the pure calculation method, which compares the values of two thermal reaction number values only. If the graphical presentation shows no operating point in the relevant range to be enveloped by the limiting curve of dynamic instability, it may also be concluded that all these points are statically stable. 

This very special operating point has an additional mathematical property. The gradient of the curve for possible steady state solutions in this point is equal to the gradient of the dynamic stability limit curve this way, both gradients are equal to the sensitivity in this point of operation. The best way to make use of this characteristic is by setting equal the steady state mass balance and the dynamic stability relationship in a suitable parameter presentation (c.f. Equ. 4-120). In a second step the term in the middle and the very right hand term are partially differentiated with respect to the steady state conversion Xs (c.f. Equ. 4-121). This represents the equality of both gradients, as the term dXs/dTo, which would have to be calculated to form the total derivative, cancels out. 

The safety assessment now follows a procedure which starts with the calculation of the steady state values for ln(Da ) based on the production requirements for Xs and Ts and the kinetic parameters E/R and n, which must be known. The plausibility of this value may be checked by using the scheduled residence time, the frequency factor and the feed concentration Cgj for an alternative determination, which must result in an identical value. This step is followed by the determination of P using Equ. (4-122) and the known process and plant data. If the point defined by P and ln(Daco) is above the limit curve in the nomogram for the corresponding Stanton munber, the operating point is safe under normal operating conditions. 

With the help of Equ.(4-160) and (4-162), a limit value diagram can now be developed which allows the determination of the maximum sensitivity in its dependence on the thermal reaction number at the point. This is shown in Fig. 4-43. All operating conditions with B values which form an intersection with a desired sensitivity below or right of the limit curve can only be conducted safely if the overheating is limited to less than 4/9 of the adiabatic temperature increase. By inserting the value for Smt into the condition for an ignition... 

To compare isothermal and isoperibolic operation the limit curve for S = 2 under isoperibolic conditions has been assumed. It becomes obvious that isothermal processes can only be performed safely and uncritically if the thermal reaction number has a very small value, or, in other words, if the reaction proceeds at low rates and only with moderate exothermicity. If reaction rate and thermal reaction number have higher... 

For all operating conditions below the limit curve the MSTR rises monotonously with the process temperature above the curve the MSTR passes through a minimiun. An example of a second-order reaction with optimization potential regarding the MSTR is shown in Figure 4-80. 

The course of this limit curve separating processes with and without the possibility to optimize the MTSR is shown graphically in Figure 4-82. All operating points with an optimization potential are above the limit curve. The minimum value is B = 2. 

For clarity, one should note that in the limit as approaches 100, the probability of a type II error approaches f3 = - a. Ai the exaet point ixq = 100, the null hypothesis is true and a type II error does not exist hence, /3 = 0 at that single point. Figure 4 graphically depicts the behavior of the j8 error as a function of the true (unknown) population mean, under the original rejection criterion specified by the null hypothesis and the chosen a. error. This curve is called an operating characteristic curve, or simply an OC curve ... 

Comparison of conventional and risk-informed P-7 limit curves, and typical operational and operational constraint curves. 

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