Saturation index limitations

Figure 8-5 plots the carbonate parameters in the steady state as a function of depth between 0 and 400 centimeters. The figure shows that the saturation index, dissolution rate, and respiration rate all are very close to zero at 400 centimeters. The results for this simulation therefore do not depend on the total thickness of the sedimentary column, provided that this total thickness exceeds 400 centimeters, a limit that depends on the rate at which respiration decreases with increasing depth. 

Supersaturation of up to nearly 4 orders of magnitude is indicated relative to a log K= 4.9 which reflects freshly precipitated HFO. When elimination of all data points which are below the detection limits for Fe(lll) and for electrode measurements, values of Eh measured agree with Eh calculated from Fe(ll/lll) determinations and speciation calculations and the revised ferrihydrite saturation index diagram looks like fig. 3. 

Biliary cholesterol saturation index (CSI) in nonacromegalic patients with cholesterol GBS (CH-GBS), acromegalic patients with Octreotide-associated GBS (OT-GBS), and stone-free patients before Octreotide treatment (No OT-GBS). "Hie value of CSI = 1.0 indicates the limit of cholesterol solubility points above the line are supersaturated, whereas those below the line are unsaturated with cholesterol. (All graphs show mean values SEMs.) Data taken from reference 18. 

When the number of concentrations of the circulating water is in the order of 3-7, some of the salts dissolved can exceed their solubility limits and precipitate, causing scale formation in pipes and coolers. The purpose of the treatment of the cooling water is to avoid scale formation. This is achieved by the injection of sulfuric acid to convert Ca and Mg carbonates (carbonate hardness) into more soluble sulfates. The amount of acid used must be limited to maintain some residual alkalinity in the system. If the system pH is reduced to far below 7.0, it would result in an accelerated corrosion within the system. As stated earlier, scale formation and/or corrosion tendency is defined by the Saturation Index (Langelier Index) and Stability Index (Ryznar equation). 

Other indices proposed that have tried to overcome the basic limitations of LSI include the Stiff and Davies Saturation Index, Larson and Buswell Index, Puckorius (Practical) Scale Index, Oddo-Tomson Index, and Larson-Skold Corrosivity Index, some of which are discussed briefly here. 

The existing input file is extended by setting up equilibrium not only with pyrite but also with calcite. 2.621 mmol of calcite dissolve. The amount of pyrite dissolved is the same as in the absence of calcite (1.347 mmol). The pH value of 7.58 is in the neutral range. Thus, to neutralize the pH approximately 2 moles of calcite must be added for every mol of pyrite. The saturation index of gypsum is still clearly undersaturated (SI = -1.09), i.e. that gypsum is not a limiting mineral phase and hence the sulfate contents stay more or less invariable. 

Fig. 66 shows the undersaturation of some mineral phases of interest. If the saturation index is attained, the respective mineral is precipitated by the model and acts as a limiting phase (kinetics are not considered). The possible limitation by coffinite, uraninite, and pyrite from 500 days onwards (not distinguishable in the figure coffinite is not a limiting mineral phase any more from 2000 days on furthermore it is questionable that coeffinite forms under this conditions) is remarkable. Kaolinite is supersaturated after 2000, calcite after 7000, and Al(OH)3... 

According to Eqs. 3.10 and 3.13, the inlet of a confluent stream promotes a decrease in the recorded peak height, h, and an increase in sample width, a (Fig. 5.15), but these effects are only evident for systems with limited sample dispersion. In this situation, larger sample volumes are used, the saturation index approaches unity, and sample dispersion occurring after the confluence site is very low [84]. Consequently, modifications in h and a caused by confluence addition cannot be compensated downstream, and manifest themselves in the shape of the recorded peaks (see also Fig. 5.16, right). 

Simple Natural saturation/% Liquid limit/% Plastic limit/% Plasticity index/Vo Liquidity index/Vo... 

Aqueous species do not occur in pure form, because their solubility in water is limited [2]. The solubility is the maximum amount of a substance that can be dissolved in a solution [6]. The saturation index indicates the saturation state of a solution with respect to a mineral phase, which is given by... 

The solubility of elements in freshwater is limited and the solubility of calcium and magnesium carbonates are of particular importance in freshwaters. The solubility of carbonates is inversely proportional to the temperature of the water. In other words, as the water temperature increases, calcium and magnesium carbonates become less soluble. If the solubility decreases sufficiently, carbonates will precipitate and form a scale on the surfaces of the system. This scale can provide a protective barrier to prevent corrosion of the metallic elements in a system. Excessive scale deposits can interfere with water flow and heat transfer. The quality of the scale is dependent on the quantity of calcium that can precipitate as well as water flow and the chloride and sulfate content of the water. The tendency of water to precipitate a carbonate scale is estimated from corrosion indices such as the Langelier Saturation Index (LSI) and Caldwell-Lawrence calculations [6-8] which use calcium, alkalinity, total dissolved solids, temperature and pH properties of the water. Other indices, such as the Ryznar Index... 

The reactivity index is the conventional theoretical quantity which is used as a measure of the relative rate of reactions of similar sort occurring in different positions in a molecule or in different molecules. As has already been mentioned in Chap. 2, most reactivity indices have been derived from LCAO MO calculations for unicentric reactions of planar n electron systems as). The theoretical indices for saturated molecules have also been put to use B0>. In the present section the discussion is limited to the indices derived from the theory developed in the preceding sections, since the other reactivity indices are presented in more detail than the frontier-electron theory in the usual textbooks 65,86) jn this field. 

For the AJL8/APC polymer, saturation was not achieved until 250 h of exposure to the DNT vapor. However, the sensing polymer produces a detectable amount of refractive index change within a few minutes of exposure to DNT vapor of 100 ppb concentration. The response rate is thought to be limited by the diffusion of DNT molecules into the polymer. In the initial experiments reported here PMMA and polycarbonate were used as the host polymers. These polymers are relatively less permeable to DNT. The response rate is expected to improve if a more permeable polymer host is used. 

Fig. 2. Hill plot for oxygenation of human hemoglobin A as a function of the partial pressure (PO2) of molecular oxygen. The diagram at the right shows that the Hill coefficient will reach a limiting value of one at both extremes of ligand concentration. For this reason this cooperativity index is best measured at ligand concentrations near half-maximal saturation.

For transporters, relatively low protein expression level and limited transport capacity makes for nonlinear, enzyme-like transport kinetics that is, the transport rate saturates with increasing substrate concentration. This phenomenon is the basis for the competitive interactions generally found for chemicals that are handled by one or more common transporters this is usually manifest as inhibition of the transport of one chemical by a structural analog. The extent to which these competitive interactions are important depends on the concentrations of the chemicals involved, their relative affinities for the common transporter, and their phar-macological/toxicological profiles (effects, effective concentrations, therapeutic index). Competition for transport is discussed below in the context of drug-drug interactions. 

Several drugs, including salicylate (in overdose), alcohol, and possibly some hydrazines and other drugs which are metabolised by acetylation, have saturable elimination kinetics, but the only significant clinical example is phenytoin. With this drug, capacity-limited elimination is complicated further by its low therapeutic index. A 50% increase in the dose of phenytoin can result in a 600% increase in the steady-state blood concentration, and thus expose the patient to potential toxicity. Capacity-limited pathways of elimination lead to plasma concentrations of drugs which can be described by a form of the Michaelis-Menten equation. In such cases, the plasma concentration at steady state is given by... 

Surfactant surface activity is most completely presented in the form of the Gibbs adsorption isotherm, the plot of solution surface tension versus the logarithm of surfactant concentration. For many pure surfactants, the critical micelle concentration (CMC) defines the limit above which surface tension does not change with concentration, because at this stage, the surface is saturated with surfactant molecules. The CMC is a measure of surfactant efficiency, and the surface tension at or above the CMC (the low-surface-tension plateau) is an index of surfactant effectiveness (Table XIII). A surfactant concentration of 1% was chosen where possible from these various dissimilar studies to ensure a surface tension value above the CMC. Surfactants with hydrophobes based on methylsiloxanes can achieve a low surface tension plateau for aqueous solutions of —21-22 mN/m. There is ample confirmation of this fact in the literature (86, 87). 

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