Pressure rise analysis

The pressure rise analysis method (PRA method), recently proposed by Chouvenc et al. (2004a), derived from the MTM method originally developed by Milton et al. (1997) and next modified by Obert (2001), appears to be a very promising noninvasive control method. It is a rapid, simple to implement and averaging tool that requires a freeze-dryer equipped with an external condenser and a very fast closing separating valve. The values of the main freeze-drying parameters, such as the temperature of the sublimation front, T , the resistance to water vapor mass transfer of the dried layer, J p, and the overall heat transfer coefficient, could be... 

MDSC modulated scanning microscopy MTM manometric temperature measurement NMR nuclear magnetic resonance PAR pressure rise analysis US ultrasound... 

Chouvenc, P., Vessot, S., Andrieu, J., Vacus, P., 2004a. Optimization of the freeze-drying cycle A new model for pressure rise analysis. Drying Technol. 22(7) 1577—1601. 

Vacus, P., 2005. Optimization of the freezedrying cycle adaptation of the Pressure Rise Analysis to non-instantaneous isolation valves. PDA J. Pharm. Sci. Technol. 5 ... 

If a simple pump is considered, it is possible to state that there must be a working relation between the power input, and the flow rate, pressure rise, fluid properties, and size of the machine. If a dimensional analysis is performed, it can be shown that a working relation may exist... 

Subsequently, the problem was investigated by Karpov and Severin [6]. They used closed vessels with a diameter of 10cm and 10, 5, and 2.5cm width, initially at atmospheric pressure. The vessels were filled with different lean hydrogen and methane/air mixtures and rotational speeds in the range of 130-4201/s were employed. They also included data from the study of Babkin et al. [3] in their analysis. Unfortunately, they did not observe the flame itself and measured only the pressure rise in the vessel, which was compared with pressure development in the vessel without rotahon, to draw a conclusion with respect to flame speeds and quenching. 

A mathematical analysis of the process is extremely difficult and requires to solve the Reynolds equation of lubrication theory and apply the solution to the cavitation boundary conditions. A two-dimensional analysis of the pressure distribution in the plane of the roll nip showed that the liquid pressure rises sharply to a large value near the nip, and drops equally sharply to a minimum justbeyond the nip. Before large negative pressures are reached, the liquid may cavitate as a result of the expansion of entrained gases within the liquid. 

Partial pressure analysis using a mass spectrometer or the pressure rise method may be used to differentiate between these two causes. Since the pressure rise method will only prove the presence of a leak without Indicating Its location In the apparatus. It Is advisable to use a helium leak detector with which leaks can, in general, also be located much more quickly. 

The development of the reaction was followed by measuring pressure change (Ap), light emission (7), reaction rate (dAp/dt), and by chemical analysis. Pressure rise was recorded by a pressure transducer (A.C.B. 504H). Reaction rate (dAp/dt = W) was obtained by using a resistance-capacity circuit of suitable time constant, 6 = RC (76, 78), appropriate to the branching factor of the reaction, < . It was possible to record simultaneously pressure rise vs. time and rate vs. time or rate vs. pressure rise. 

Thus the pressure of any shock wave generated in a pipeline would continue to rise if it were not for the fact that at a time 2Lie a return unloading pressure wave reaches the valve and stops the pressure rise at a value of about 53 ft, as contrasted with about three times that value if this were not the case. Subsequent pressure changes as elastic waves travel back and forth are very complex and require a detailed step-by-step analysis that is beyond the scope of this text. In brief, the method consists of assuming that the valve movement takes place in a series of steps each of which produces a pressure p proportional to each V. Other texts contain details of computing successive pressures for slow valve closure and further explanation of much of this condensed treatment [47-49]. 

There are two approaches to ERS design. One is system modeling, which identifies the cause of a pressure rise from a hazard analysis. It uses approximate models—allvapor flow, all-liquid flow, or two-phase flow—to simulate the pressure increase of the reacting system vs. time and to determine vent size. The method is complex since it must identify the stoichiometry, the mechanism, and the kinetics of the decomposition causing the pressure rise. Two pressure models are used for vent sizing ... 

Residual moisture is the low level of water, usually in the range of less than 1-3% (wt/wt), remaining in a freeze-dried product after the freeze-drying (vacuum sublimation) process [1-5] is complete. Nail [6] has described in-process methods to monitor the endpoint of freeze-drying using residual gas analysis, pressure rise, comparative pressure measurement, and product temperature measurement. Roy and Pikal [7] used an electronic moisture sensor inside the lyophilization chamber. Residual moisture [8] content is important in the final freeze-dried product because it affects the potency of the product, its long-term stability, and the official shelf life of the product. 

A small hold-up volume can be provided between main reservoir and the condenser, allowing small liquid samples to be taken, an analysis of which will yield independent reaction rates. The recycling of even small concentration percentages of liquid products can be eliminated by interposing several reservoirs containing about two or three times the amount of liquid circulated in an individual experiment. The gas evolution rates are measured by determining the rate of pressure rise with a manometer when the system is temporarily closed off from the atmosphere. 

It should be noted that the specific volume does not enter into this equation, implying that the head produced for a given flow will be the same whatever the liquid being pumped-hence the preference of working in terms of head rather than pressure rise. It is possible to estimate the form of the function, 1, from a detailed analysis of the velocities of the impeller and liquid, making due allowance for losses, but an accurate determination requires experiment. 

A more rigorous, quantitative analysis of the pressure time curve for ft nitrogen proceeds as follows (6). The nature of the processes involved is revealed by the family of curves in Fig. 16 taken at different heating rates. It is apparent that fixing the temperature does not fix the population of adsorbed entities or the number already evolved. The smaller the rate of heating (that is, the smaller the heating current) the greater the number of adsorbed entities evolved at lower temperatures. Clearly the steady state approximation does not apply to these systems The pressure rise is dictated by the rate of desorption. 

Isothermal arrhenius analysis were performed as follows. Measurements were started after several hydriding/dehydriding cycles with samples in the fully hydrided condition and cooled to room temperature. The pressure rise from desorption into a known volume at a given temperature was measured and the temperature was then increased. Desorption rates were determined at each temperature from the slope of the essentially linear increase in pressure with time. This procedure was continued up to 150°C. The sample was held at this temperature until the NaAlH4 decomposition step was finished. The rate data are presented as moles of desorbed hydrogen per mole active sodium per hour as shown in Figure 2. 

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