Leak model

FIGURE 5.5 Comparison of measured stack test data to that predicted by Ceramatec s Leak Model. 

For a barrier consisting of two sizes of straight circular holes, with Cmoi fraction occupied by small holes of radius through which pure molecular flow takes place and eyjs fraction occupied by larger holes of radius Zyis througjt which viscous flow takes place, the molar velocity for this viscous leak model would be... 

Here F is known as the permeability, Fo is interpreted as the permeability for molecular flow, and S is sometimes called the slope factor. Comparison of Eq. (14.10) with (14.8) and (14.9) shows that a physical interpretation can be given to the parameters Fo and S in terms of pore radius and void fraction for the mixed flow and viscous leak models ... 

Effect of nonseparating flow. The effect of nonseparating viscous flow on the barrier separation efficiency depends on the detailed structure of the barrier. Because the theoretical derivation of this effect for the viscous leak model can be worked out simply and completely, this model will be dealt with first. Then results for the mixed flow model derived by Present and de Bethune [P3] will be summarized and both models will be compared with empirical correlations of separation performance suggested by experimental investigators of barrier performance. 

Barrier separation efficiency, viscous leak model. In the viscous leak model, flow through the small holes of radius is of the separating, molecular type dealt with in deriving Eqs. 

Comparison with Eq. (14.42) shows that evaluated from the slope factor with the mixed flow model is only 9.17 percent the value of Pc evaluated from Are slope factor with the viscous leak model. Equation (14.56) comes closer to representing the characteristics of actual barriers. 

From these experiments a pump-leak model for the vesicular transport system with a (K -H H )-ATPase pump and passive conductances for K, Cl and H ions has been postulated (Fig. 5). 

Some recently obtained results appear to be pertinent to this discussion. We have perfused proximal and distal tubules with 0.1 M phosphate solutions at an initial pH of 5.5, and recorded the alkalinization of these columns toward the steady state level. This is also an exponential process, and linear graphs relating the log of the difference between acid concentration at time t and steady state concentration with time are obtained. According to the previously given pump-leak model, the slopes of these lines should not be different from acidification lines, since they both depend essentially on the permeability of the epithelium to outflow of H ions from the tubular lumen. In our series, the difference between the mean values of the rate constants obtained in the proximal tubule during alkaline and acid perfusions was small, and of borderline significance, in view of the inherent uncertainties of the method, and we believe still compatible with the pump-leak model. In the distal tubule, however, these differences are quite considerable. 

This depends on the model you use. According to the pump-leak model, one assumes a constant pump and assumes pH changes are due to H ion backflow. However, in distal tubules the shown data may be interpreted in terms of low passive permeability and a pump dependent on the electrochemical potential gradient. 

The leak model can be determined by applying a criterion, the ratio of the corrected activity concentrations ( Icorr) of and where the actual concentrations of the... 

In many cases faults will only restrict fluid flow, or they may be open i.e. non-sealing. Despite considerable efforts to predict the probability of fault sealing potential, a reliable method to do so has not yet emerged. Fault seal modelling is further complicated by the fact that some faults may leak fluids or pressures at a very small rate, thus effectively acting as seal on a production time scale of only a couple of years. As a result, the simulation of reservoir behaviour in densely faulted fields is difficult and predictions should be regarded as crude approximations only. 

Systematic Operating Errors Fifth, systematic operating errors may be unknown at the time of measurements. Wriile not intended as part of daily operations, leaky or open valves frequently result in bypasses, leaks, and alternative feeds that will add hidden bias. Consequently, constraints assumed to hold and used to reconcile the data, identify systematic errors, estimate parameters, and build models are in error. The constraint bias propagates to the resultant models. 

However, given that reconciliation will not always adjust measurements, even when they contain large random and gross error, the adjustments will not necessarily indicate that gross error is present. Further, the constraints may also be incorrect due to simphfications, leaks, and so on. Therefore, for specific model development, scrutiny of the individual measurement adjustments coupled with reconciliation and model building should be used to isolate gross errors. 

Considered leak proof (although some models use gaskets and o-rings as secondary seals). 

Belore, R. and J. Buist, 1986, A Computer Model for Predictin Leak Rates of Chemicals from Damaj 1 Storage and Transportation Tanks, Report EE-75, Environmental Canada. 

Do not assume that such things could not happen in your company (unless you have spent some time in the relief-valve workshop). All relief valves should be tested and inspected regularly. Reference 3 describes model equipment and procedures. When a large petroleum company introduced a test program, it was shocked by the results out of 187 valves sent for testing, 23 could not be tested because they were leaking or because the springs were broken, and 74 failed to open within 10% of the set pressure—that is, more than half of them could not operate as required [4]. 

Figure 4.4 gives an example of an OAET for events that might follow release of gas from a furnace. In this example a gas leak is the initiating event and an explosion is the final hazard. Each task in the sequence is represented by a node in the tree structure. The possible outcomes of the task are depicted as "success" or "failure" paths leading out of the node. This method of task representation does not consider how alternative actions (errors of commission) could give rise to other critical situations. To overcome such problems, separate OAETs must be constructed to model each particular error of commission. 

To estimate tlie potential iiupaet on tlie publie or tlie environment of aeeidents of different types, the likely emergeney zone must be studied. For example, a liazardous gas leak, fire, or explosion may eause a toxie cloud to spread over a great distance. The minimum atmospheric dispersion model. Vtirious models can be used tlie more difficult models produce more realistic results, but tlie simpler and faster models may provide adequate data for planning purposes. A more tliorough discussion of atmospheric dispersion is presented in Part 111 - Healtli Risk Assessment. 

R. Yang, S.V. Parker, J.A. Leake, R.W. Cahn, New metastable phases in nickel -rich Ni-Al-Ti alloys, in Alloy Modelling and Design, ed.G.M.Stocks and P.A. Turchi, The Minerals, Metals Materials Society (1994), p.303. 

Many office equipment models consume some electricity when nominally off. This results in leaking or standby energy use. Usually this amounts to... 

Otherwise it has been shown that the accumulation of electrolytes by many cells runs at the expense of cellular energy and is in no sense an equilibrium condition 113) and that the use of equilibrium thermodynamic equations (e.g., the Nemst-equation) is not allowed in systems with appreciable leaks which indicate a kinetic steady-state 114). In addition, a superposition of partial current-voltage curves was used to explain the excitability of biological membranes112 . In interdisciplinary research the adaptation of a successful theory developed in a neighboring discipline may be beneficial, thus an attempt will be made here, to use the mixed potential model for ion-selective membranes also in the context of biomembrane surfaces. 

The fluid leak-off during hydraulic fracturing can be modeled, calculated, and measured experimentally. Procedures for converting laboratory data to an estimate of the leak-off under field conditions have been given in the literature [1426]. 

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