ROCK expression

Table 3.3 summarizes the radiation exposure doses due to the industrial exploitation of phosphate rock, expressed in terms of collective effective dose equivalent commitments resulting from the decision to use a unit mass of marketable ore to accomplish a defined purpose, as reported by UN Scientific Committee on Effects of Atomic Radiation (United Nations, 1982). 

Fig. S. Length and thickness of low-permeability lenses and nodules at Findel (Fig. 1) in a transect NE-SW parallel to the general transport direction. The maximum length measured in this outcrop (30 m) is limited by the tectonic dip and the internal foresets, both dipping towards the SW, and the height of the outcrop (2-5 m). Other outcrops (Aspelt) show cemented layers with a lateral extension of more than 300 m. The logarithmic relationship between the two variables in host rocks (expressed by the function T= 5.66 log(T)+ 17.95, with a correlation coefficient R =0.60 n = 344), is statistically significant.

We know that fluid velocities in geological processes are very slow and, by comparison, we will suppose that the chemical kinetics are rather fast (this is particularly true in the case of rocks formed at temperatures higher than 300°C, such as skarns [s], [s]). For those two reasons, we will consider that, at given x and t, there is a chemical equilibrium between the solid and fluid portions of the rock, expressed by a law c = f(c ) Eq.(l). This law is called isotherm and may be given by experimental data for mineral-fluid equilibria. The major point is that it is generally non linear. 

An analysis was done on a rock sample to determine its rubidium content. The rubidium content of a portion of rock weighing 0.350 g was extracted, and to the extracted sample was added an additional 29.45 ixg of Rb. The mass spectrum of this spiked sample showed a Rb peak that was 1.12 times as high as the peak for Rb. Assuming that the two isotopes react identically, what is the Rb content of the rock (expressed in parts per million by mass) The isotopic abundances and isotopic masses are shown in the table. 

A rather different method from the preceding is that based on the rate of dissolving of a soluble material. At any given temperature, one expects the initial dissolving rate to be proportional to the surface area, and an experimental verification of this expectation has been made in the case of rock salt (see Refs. 26,27). Here, both forward and reverse rates are important, and the rate expressions are... 

The lanthanides, distributed widely in low concentrations throughout the earth s cmst (2), are found as mixtures in many massive rock formations, eg, basalts, granites, gneisses, shales, and siUcate rocks, where they are present in quantities of 10—300 ppm. Lanthanides also occur in some 160 discrete minerals, most of them rare, but in which the rare-earth (RE) content, expressed as oxide, can be as high as 60% rare-earth oxide (REO). Lanthanides do not occur in nature in the elemental state and do not occur in minerals as individual elements, but as mixtures. 

There are many formulae to determine the above, all leading to almost the same results. The most adopted, assuming a layer of crushed rock (gravel) over the ground surface, is expressed by... 

One important measurement made by geochemists is the Total Organic Carbon (TOC) measurement. The results are expressed as a weight percentage. When the TOC is less than 0.5 percent, the rock is considered unlikely to have enough kerogen to produce oil or gas. 

Porosity is a measure of the void space within a rock, which is expressed as a fraction (or percentage) of the bulk volume of that rock [31]. 

Soil specific weight is the measure of the concentration of packing of particles in a soil mass. It is also an index of compressibility. Less dense, or loosely packed, soils are much more compressible under loads. Soil specific weight may be expressed numerically as soil ratio and ptorosity (porosity for soils being basically the same definition as that for rocks discussed earlier in this section). Soil porosity e is... 

The saturation of the pore space of a rock with gas, expressed in a percentage of the total pore space or as a fraction. The inverse of the gas saturation is called the water saturation. 

The porosity of a reservoir rock is the ratio of the pore volume to the total volume of the rock and is expressed either as a percentage or as a fraction. 

Furthermore, about 1920 the idea had become prevalent that many common crystals, such as rock salt, consisted of positive and negative ions in contact. It then became natural to suppose that, when this crystal dissolves in a liquid, the positive and negative ions go into solution separately. Previously it had been thought that, in each case when the crystal of an electrolyte dissolves in a solvent, neutral molecules first go into solution, and then a certain large fraction of the molecules are dissociated into ions. This equilibrium was expressed by means of a dissociation constant. Nowadays it is taken for granted that nearly all the common salts in aqueous solution are completely dissociated into ions. In those rare cases where a solute is not completely dissociated into ions, an equilibrium is sometimes expressed by means of an association constant that is to say, one may take as the starting point a completely dissociated electrolyte, and use this association constant to express the fact that a certain fraction of the ions are not free. This point of view leads directly to an emphasis on the existence of molecular ions in solution. When, for example, a solution contains Pb++ ions and Cl- ions, association would lead directly to the formation of molecular ions, with the equilibrium... 

Madelung constant (A) A number that appears in the expression for the lattice energy and depends on the type of crystal lattice. Example A = 1.748 for the rock-salt structure. 

What are the relative contributions of these two sources Two approaches have been taken. One is to establish the geology and hydrology of a basin in great detail. This has been carried out for the Amazon (Stallard and Edmond, 1981) with the result that evaporites contribute about twice as much sulfate as sulfide oxidation. The other approach is to apply sulfur isotope geochemistry. As mentioned earlier, there are two relatively abundant stable isotopes of S, and The mean 34/32 ratio is 0.0442. However, different source rocks have different ratios, which arise from slight differences in the reactivities of the isotopes. These deviations are expressed as a difference from a standard, in the case of sulfur the standard being a meteorite found at Canyon Diablo, Arizona. 

Horiguchi, T., Nishikawa, T., and Ohta, Y. et al. (2007). Retinoid X receptor gene expression and protein content in tissues of the rock sheU Thais clavigera. Aquatic Toxicology 84, 379-388. 

Figure 21. ( Ra/ Ra)-K/( Ra) diagram proposed by Voltaggio et al. (1995). In this diagram, equivalent to a ( Ra/ °Th)-K/( °Th) diagram, are reported the data resulting from successive leachings of K-rich volcanic rocks from Vulcano (Eolian Islands). For each rock, the data define a straight line, whose intercept on the y-axis gives the ( Ra/ h) ratio of the Th-emiched accessory phase and thus the age of the rock (UCS 2.9 0.4 ka DS 2.1 0.3 ka PLZ 1.5 0.2 ka). K/( Ra) ratios are expressed in weight % K/dpm.g (results from Voltaggio et al. 1995 see text for a detailed explanation).

The relaxation time for each pore will still be expressed by Eq. (3.6.3) where each pore has a different surface/volume ratio. Calibration to estimate the surface relaxivity is more challenging because now a measurement is needed for a rock sample with a distribution of pore sizes or a distribution of surface/volume ratios. The mercury-air or water-air capillary pressure curve is usually used as an estimator of the cumulative pore size distribution. Assuming that all pores have the same surface relaxivity and ratio of pore body/pore throat radius, the surface relaxivity is estimated by overlaying the normalized cumulative relaxation time distribution on the capillary pressure curve [18, 25], An example of this process is illustrated in Figure 3.6.5. The relationship between the capillary pressure curve and the relaxation time distribution with the pore radii, assuming cylindrical pores is expressed by Eq. (3.6.5). 

If the NMR response is capable of estimating the pore size distribution, then it also has the potential to estimate the fraction of the pore space that is capable of being occupied by the hydrocarbon and the remaining fraction that will only be occupied by water. The Free Fluid Index (FFI) is an estimate of the amount of potential hydrocarbons in the rock when saturated to a given capillary pressure. It is expressed as a fraction of the rock bulk volume. The Bulk Volume Irreducible (BVI) is the fraction of the rock bulk volume that will be occupied by water at the same capillary pressure. The fraction of the rock pore volume that will only be occupied by water is called the irreducible water saturation (Siwr = BVI/cj>). The amount of water that is irreducible is a function of the driving force to displace water, i.e., the capillary pressure. Usually the specified driving force is an air-water capillary pressure of 0.69 MPa (100 psi). 

The four isotopes, as those of any element, have the same chemical properties. The four are not, however, uniformly distributed in the earth s crust the occurrence of three of them, in minerals and rocks, is associated with the radioactive decay of isotopes of thorium and uranium. In most minerals and rocks the relative amounts (or the isotopic ratios) of the isotopes of lead (often expressed relative to the amount of stable lead-204) are generally within well-known ranges, which are independent of the composition of the mineral or rock they are, however, directly related to the amounts of radioactive thorium and uranium isotope impurities in them. 

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