Excess Multiplication Factor

Another function, the osmotic coefficient, has been used in place of the excess chemical potential or the activity coefficient. It is a multiplicative factor rather than additive, and is defined in terms of the chemical potential of the solvent. Two such functions are used, one based on molalities and the other on molarities. The first is defined, except for its absolute value, by... 

This isothermal bulk modulus (Kj) measured by static compression differs slightly from the aforementioned adiabatic bulk modulus (X5) defining seismic velocities in that the former (Kj) describes resistance to compression at constant temperature, such as is the case in a laboratory device in which a sample is slowly compressed in contact with a large thermal reservoir such as the atmosphere. The latter (X5), alternatively describes resistance to compression under adiabatic conditions, such as those pertaining when passage of a seismic wave causes compression (and relaxation) on a time-scale that is short compared to that of thermal conduction. Thus, the adiabatic bulk modulus generally exceeds the isothermal value (usually by a few percent), because it is more difihcult to compress a material whose temperature rises upon compression than one which is allowed to conduct away any such excess heat, as described by a simple multiplicative factor Kg = Kp(l + Tay), where a is the volumetric coefficient of thermal expansion and y is the thermodynamic Griineisen parameter. 

Two similar methods for phosphate ion which involve an amplification reaction, solvent extraction, and reverse solvent extraction were described at about the same time by Umland and Wiinsch (29) and Djurkin, Kirkbright and West (10, 30). An acidic solution containing the phosphate ion is treated with an excess of molybdate ion to form the phosphomolybdic acid, which is extracted into a water-immiscible solvent to free it of excess molybdate ion. The phosphomolybdic acid is then broken down and re-extracted by an aqueous basic solution and the molybdate ion determined colorimetrically through the use of 2-amino-4-chlorobenzenethiol or thiocyanate ion. The effective molar absorptiv-ities of the reagents are 359,000 at 710 m/x. for 2-amino-4-chlorobenzene-thiol and 150,600 at 470 m/x. for thiocyanate, which represent multiplication factors of 10 and 12, respectively, caused by phosphate molybdate ratio in the extracted phosphomolybdic acid. 

This section will cover some simple calculations related to the reactor. The reactor had a cold, beginning of life, neutron multiplication factor of 1.037 0.001, which corresponds to an excess positive reactivity of 5.7 based on a delayed neutron fraction of 0.0065. The burnup for the reactor was determined using a fairly simple set of equations. The consumption over 10 years at a power level of 200 kWth was 0.8 kgs of and at 400 kWth, 1.6 kgs of would be consumed. Given that the fuel loading is 186 kgs of the burnup is -0.86% for the upper end of the uranium consumed. This burnup results in a loss of 1 reactivity. 

The primary goal of this study was to ensure that there was sufficient excess reactivity in the neutron multiplication factor to keep the reactor critical for the 10 year lifespan while ensuring that the reactor would be subcritical during major accident scenarios. The position of the reflector can be used to set the multiplication factor of the reactor. Burnup in the reactor causes a proliferation of additional materials to absorb neutrons and reduces the density of fissile materials, lowering the neutron multiplication of the reactor. This can be offset by closing the reflector, which decreases the neutron leakage of the system. This is shown in Figure 5-1. 

The scope of this subject is here limited to a comparison of the values of the ckling B and the excess infinite multiplication factor kx,- , which are variously derived from critical and subcritical experiments. These two Integral parameters can be measured more or less directly. They are about equally Important to the reactor physics design of low-enrichment graphite reactors, since the real question is the size of the assembly which gives a sufficient margin of excess effective k to allow the reactor to reach the planned operating conditions. 

Performance criteria established by regulatory statutes to ensure that the shipment is safely subcritical must also be met. Nuclear criticality in Irradiated fUel shipments can be successfully controlled through the use of l-in. boral plates to reduce the excess reactivity of the fuel element array such that kw, the infinite-medium neutron multiplication factor, is less than unity. This is a requisite for Fissile Class I shipments. 

Nearly constant fissile fuel content and neutron multiplication factor hence, very small excess reactivity built-in and very simple reactor control system that requires adjustment for burn-up only once every few years ... 

Further modifications of the ELR-base protein purification approach have been made in order to circumvent some problems related to protein purification when the protein is expressed at ultra-low levels. One of the multiple factors that influence thermosensitive behavior is polymer concentration. Some proteins, and their respective fusion proteins, have the drawback of being expressed at low levels, which have repercussions on inverse transition cycling efficiency. To overcome this problem, the addition of free ELR to the soluble lysate containing the fusion protein has been proposed [126, 132, 133]. Free ELR acts as a co-aggregant that leads not only to a decrease in T, due to the increase in ELR concentration but also to an easier recovery of aggregates thanks to their large size. This ITC variant focused on the addition of excess ELR has allowed the purification of ultra-low concentration ELR fusion constructs, with several such examples having been reported [126, 132, 133]. 

Using codeine as an example of the effects of a metabolizer state, patients who lack enzymatic activity (PM) will not be able to convert codeine to its most active metabolite, morphine, and thus patients will get little if any analgesic benefit from the drug. In contrast, it has been reported that ultrarapid metabolizers (UM) may convert codeine to morphine too quickly, resulting in an excessive dose of morphine even when giving only a standard dose of codeine. A true codeine overdose is probably due to multiple factors since it is not commonly reported and the CYP2D6 UM can be as high as approximately 30% in some populations. 

For optimization of the spike addition, it is necessary to know the approximate element concentration in the sample. As the precision of results is not significantly influenced over a wide range of analyte to spike mixing ratios, preanalysis via a semiquantitative method is typically sufficient. If the expected amount of analyte is very low, it can also be advantageous to work with a distinct excess of spike to make chemical isolation of the isotope-diluted sample easier. This means that conditions to the left of the minimum in Figures 8.5 and 8.6 are used. Under extreme conditions of analyte to spike ratio, not only the enhanced error multiplication factor has to be taken into account, but also the deteriorating... 

Answer Ihe amount by which the multiplication factor exceeds one is called the excess multiplication factor, or excess k, and is usually expressed in terms of per cent of the multiplication factor. For example, a multiplication factor of 1.01 corresponds to an excess k of 0.01, or 1. ... 

What effect does excess k have on the multiplication factor ... 

Answer Since one neutron per generation Is required to maintain the chain reaction, the relative number of neutrons will increase by k excess in one generation. Therefore, if the multiplication factor k" is greater than one (actually, k kexcess the number of neutrons... 

Answer If the multiplication factor is greater than one (excess k), the Increase in the number of neutrons will mean an increase in the fission rate and a... 

Answer Zero per cent excess k a pile operating steadily at 100 MW has a multiplication factor of exactly one, or k 1.0000,... 

What is the effective multiplication factor for a reactor having a k excess. of 0.0002 ... 

Answer Controlling the multiplication factor by absorption Is the more preictlcal method In a Hanford pile control rods containing cadmium boron or other high neutron cross section materials are used to absorb excess neutrons from the reaction. In o Uier words, It Isn t practical to chahge the size of the pile for fine control (leakage). 

Answer If the delayed neutron effect sets the effective neutron lifetime as 0.1 seconds, it follows that for a reaction that is just barely critical (keff = l.OOO), the rate of neutron population increase or decrease will be determined by the average neutron emission time of 0.1 second. Since the delayed neutron effect is 0.75 per cent, or a fraction 0.0075 of the total, prompt critical can be avoided provided the multiplication factor is kept between 1.0000 and.1.0075-In other words, the control rods should be withdrawn in steps so that at criticality, the keff is less than 1.0075i but greater than 1.0000. If criticality can be attained with keff sli tly in excess of 1.0000, the neutron population can increase only throu the additional contribution from the delayed neutrons. 

Excess Reactivity - (Sometimes called ih-ln-rcds) - The excess reactivity that the pile would have above the poison, I lattening, xenon, etc., if the HCR s were withdrawn. The inhours in horizontal control rods that are necessary to keep the effective multiplication factor at unity during pile operation. 

Multiplication Factor - The ratio of the number of neutrons present in a reactor at a given time to the number present one finite lifetime earlier. Sometimes called the effective multiplication constant (Xeff) For a homogeneous medium the infinite multiplication constant ( qq) refers to the multiplication constants in an infinite mecium. The multiplication constant minus one is called the excess multiplication constant (kex) ... 

In this paper the applications of CANDLE burnup strategy to fast reactors are discussed. The infinite neutron multiplication factor of natural uranium in fast neutron spectrum satisfies the required condition mentioned above. However, the excess reactivity is marginal. Though a hard spectrum large fast reactor can realize CANDLE burnup strategy, most small fast reactors cannot realize it with only natural uranium because of the large neutron leakage from their cores. 

Consider a reactor in which the multiplication factor is where is greater than unity. The excess multiplication factor of the reactor is defined as... 

The radial dependence of the net charge density (due to the excess of counterions and depletion of coions) from the wall of the pore into the solution is similar to the results of Figure 3.13b, except for the multiplicative factor of k. ... 

For the neutronic design of the fuel assembly, the monotonous decrease of the infinite multiplication factor of the fuel (Fig. 2.39 [9]) is suitable for reducing fluctuations in the radial core power distribution during the operation cycle. However, in order to reduce the excess reactivity at the BOC, highly concentrated burnable poison, which still remains at the EOC, needs to be introduced. This design restriction can be removed by cooling the outer core region by the downward flow. Hence, the concentration of the burnable poison can be reduced so that it does not remain at the end of the first cycle of exposure as shown in Fig. 2.72. 

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