Volume Expansion space time

Albumin 5% and 25% concentrations are available. It takes approximately three to four times as much lactated Ringer s or normal saline solution to yield the same volume expansion as 5% albumin solution. However, albumin is much more costly than crystalloid solutions. The 5% albumin solution is relatively iso-oncotic, whereas 25% albumin is hyperoncotic and tends to pull fluid into the compartment containing the albumin molecules. In general, 5% albumin is used for hypovolemic states. The 25% solution should not be used for acute circulatory insufficiency unless diluted with other fluids or unless it is being used in patients with excess total body water but intravascular depletion, as a means of pulling fluid into the intravascular space. 

The situation is more complicated if expansion or contraction of a volume element does occur and the volumetric flowrate is not constant throughout the reactor. The ratio VJv, where v is the volume flow into the reactor, no longer gives the true residence time or contact time. However, the ratio VJv may still be quoted but is called the space time and its reciprocal v/V, the space velocity. The space velocity is not in fact a velocity at all it has dimensions of (time) 1 and is therefore really a reactor volume displacement frequency. When a space velocity is quoted in the literature, its definition needs to be examined carefully sometimes a ratio Vi/ V, is used, where V/ is a liquid volume rate of flow of a reactant which is metered as a liquid but subsequently vaporised before feeding to the reactor. 

Following the Morbidelli and Varma criterion, several other methods have been proposed in recent years in order to characterize the highly sensitive behavior of a batch reactor when it reaches the runaway boundaries. Among the most successful approaches, the evidence of a volume expansion in the phase space of the system has been widely exploited to characterize runaway conditions. For example, Strozzi and Zaldivar [9] defined the sensitivity as a function of the sum of the time-dependent Lyapunov exponents of the system and the runaway boundaries as the conditions that maximize or minimize this Lyapunov sensitivity. This has put the basis for the development of a new class of runaway criteria referred to as divergence-based approaches [5,10,18]. These methods usually identify runaway with the occurrence of a positive divergence of the vector field associated with the mathematical model of the reactor. 

The use of standard temperature and pressure (STP) conditions for the calculation of the space time means that all kinetic parameters are evaluated as if the residence time of the reactants was that appropriate to STP conditions, regardless of the actual experimental temperature and pressure. The actual residence time is corrected, indirectly, using the volume expansion formulas cited above to account for changes in the concentrations of the reactants in the PFR. The rates thus measured in a PFR operating at a given temperature and pressure correspond to those that would have been measured in a BR whose volume was that of the feed at STP and whose operating conditions were the same as in the PFR. 

Finally, a completely different approach to dealing with volume expansion is proposed. This procedure yields a value for 8 with each analysis, is much simpler to use, and avoids altogether the need to approximate expansion using the expansion coefficient e. With fractional conversions X computed, the next step is to compute rates dX/dt. This is a delicate procedure, because errors in measured X values can lead to large errors in the measured slopes. It turns out that simply fitting surfaces to the conversion-temperature-space-time data and then calculating slopes by numerical differences leads to unacceptably poor estimates of the rates. What is required instead is a... 

When the rate of reaction is given and a feed is to be converted to a value of, say x, Eq. 9.1-2 permits the required reactor volume V to be determined. This is one of the design problems that can be solved by means of Eq. 9.1 -2. Both aspects— kinetic analysis and design calculations—are illustrated further in this chapter. Note that Eq. 9.1-2 does not contain the residence time explicitly, in contrast with the corresponding equation for the batch reactor. E/f o> s expressed here in hr m /kmol 4—often called space time—is a true measure of the residence time only when there is no expansion or contraction due to a change in number of moles or other conditions. Using residence time as a variable offers no advantage since it is not directly measurable—in contrast with V/F q. 

For the case of HEC-metal complexes (Table 7.11), the relaxation times (r) were found to be less than that detected for different CMC-metal complexes. This view was realized to the presence of polyhydroxyethyl groups on the cellulose backbone, which result in inter-chain spaces and consequently reduce the effect of volume expansion due to the chelation of HEC with metal ions [18]. 

Tj. is the space time and Xr is the volume expansion coefficient due to the chemical reaction it is possible to calculate these values from the measured properties. 

In order to be able to use equation (71), the curves Cj.g(Xj.) and must first be plotted. The volume flow rate at the entrance is calculated using equation (50), the space time Xj. can then be calculated using equation (61) the volume expansion coefficient can then be calculated using equation (62), therefore ... 

The main parameters of the reaction rate are reaction order, initial concentrations (ratio M), and the factor of expansion or contraction (sa). The space time and consequently the reactor volume depend on these parameters. 

Given that the volume expansion is exs = 1, the space-time for the plug flow reactor (PFR) is given by ... 

If Sic particles are used to the healing agent, the volume expansion during its oxidation is 80 vol%. Thus, 1.8 times of the interlayer volume is equal to the volume that the formed oxide can be filled wiA the fi ee space between crack walls, XYZ(l-V ), where Ff is the volume fim tion of the fibers and corresponds to Z)fV4/ . Consequently, the minimum thickness of the interlayer can be expressed as,... 

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