Source rock-crude oil correlation by isotopic type-curves

An isotopic type-curve has been defined based on the ${}^{13}\text{C}{}^{12}\text{C}$ ratios of the saturated, aromatic, heterocomponent (NOSs), and asphaltene fractions of crude oils. These fractions show ¹³C enrichments with increasing polarity or polarizability. This systematic pattern can be used to estimate the ${}^{13}\text{C}{}^{12}\text{C}$ ratio of the kerogen from which the oil had been generated. Genetically associated source rock oil pairs have been used to show that the difference between the measured and the estimated δ-values of kerogen is about ?0.5%., and between the δ-values of the kerogen and the asphaltene fraction is approximately +0.6%.     

Light hydrocarbons in Red Sea brines and sediments

Light hydrocarbon (C₁-C₃) concentrations in the water from four Red Sea brine basins (Atlantis II, Suakin, Nereus and Valdivia Deeps) and in sediment pore waters from two of these areas (Atlantis II and Suakin Deeps) are reported. The hydrocarbon gases in the Suakin Deep brine (T = ~ 25°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 85‰}$, $\text{CH}{}_4\text{=}\text{~ 71}\text{1}$) are apparently of biogenic origin as evidenced by $\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3$) ratios of ~ 1000. Methane concentrations (6–8 μl/l) in Suakin Deep sediments are nearly equal to those in the brine, suggesting sedimentary interstitial waters may be the source of the brine and associated methane.The Atlantis II Deep has two brine layers with significantly different light hydrocarbon concentrations indicating separate sources. The upper brine (T = ~ 50°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 73‰}$, CH₄ = ~ 155 μl/l) gas seems to be of biogenic origin [$\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3\text{) = ~1100}$], whereas the lower brine (T = ~ 61°C, $\text{Cl}{}^{\mathrm{?}}\text{= ~ 155‰}$, CH₄ = ~ 120μl/l) gas is apparently of thermogenic origin [$\text{C}{}_1\text{(C}{}_2\text{+ C}{}_3\text{) = ~ 50}$]. The thermogenic gas resulting from thermal cracking of organic matter in the sedimentary column apparently migrates into the basin with the brine, whereas the biogenic gas is produced in situ or at the seawater-brine interface. Methane concentrations in Atlantis II interstitial waters underlying the lower brine are about one half brine concentrations; this difference possibly reflects the known temporal variations of hydrothermal activity in the basin.     

Growth pattern and 13C12C isotope fractionation of Cyanidium caldarium and hot spring algal mats

A study was undertaken with the thermophilic green alga Cyanidium caldarium which grows optimally at low pH and high concentrations of CO₂. Carbon-isotope fractionation was not found to be a simple linear function of temperature. Maximum enrichment of ¹²C in cellular material occurred under optimum growth conditions (at approximately pH 2 and at temperatures between 40–50°C in a CO₂ atmosphere). A maximum measured fractionation of ?24‰ may account for low values ($\text{δ}{}^{13}\text{C}\text{< ?30‰}{}_{\mathrm{<mtext>PDB</mtext>}}$) in Precambrian kerogen presumably derived from algal mats.     

Dissociation constants for alkali earth and sodium borate ion pairs from 10 to 50°C

Potentiometric measurements in dilute sodium borate solutions with added alkali earth chlordie salts yield the following expressions for the dissociation constants of alkali earth borate ion pairs from 10 to 50°C:

$\text{p}\text{K(}\text{MgH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.266+0.001204 T}$

$\text{p}\text{K(}\text{CaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.154+0.002170 T}$

$\text{p}\text{K(}\text{SrH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.033+0.001738 T}$

$\text{p}\text{K(}\text{BaH}{}_2\text{BO}{}_3{}^{\mathrm{+}}\text{=1.942+0.001850 T}$

where T is in °K. Enthalpies for the dissociation reactions at 25°C are less than 1 kcal./mole for all the alkali earth borate ion pairs.Values for pK(NaH₂BO₃°) from 5 to 55°C computed from the experimental data of Owen and King are in good agreement with those determined potentiometrically. The average value from both methods is 0.22 ± 0.1 at 25°C.Application to seawater of computed pK's for MgH₂BO₃⁺, CaH₂BO₃⁺ and NaH₂BO₃⁰ yields an apparent dissociation constant for boric acid of 8.73 vs. 8.70 measured by Lyman, 8.68 by Buch and 8.73 by Byrne and Kester.     

The solubilities of calcite,aragonite and vaterite in CO2-H2O solutions between 0 and 90°C,and an evaluation of the aqueous model for the system CaCO3-CO2-H2O

Calculations based on approximately 350 new measurements (Ca_T-PCO₂) of the solubilities of calcite, aragonite and vaterite in CO₂-H₂O solutions between 0 and 90°C indicate the following values for the log of the equilibrium constants K_C, K_A, and K_V respectively, for the reaction CaCO₃(s) = Ca²⁺ + CO^2?₃: $\text{Log K}{}_{\mathrm{C}}\text{= ?171.9065 ? 0.077993T +}\text{2839.319}\text{T}\text{+ 71.595 log T}$$\text{Log K}{}_{\mathrm{A}}\text{= ?171.9773 ? 0.077993T +}\text{2903.293}\text{T}\text{+71.595 log T}$$\text{Log K}{}_{\mathrm{V}}\text{= ?172.1295 ? 0.077993T +}\text{3074.688}\text{T}\text{+ 71.595 log T}$ where T is in ^oK. At 25°C the logarithms of the equilibrium constants are ?8.480 ± 0.020, ?8.336 ± 0.020 and ?7.913 ± 0.020 for calcite, aragonite and vaterite, respectively.The equilibrium constants are internally consistent with an aqueous model that includes the CaHCO⁺₃ and CaCO⁰₃ ion pairs, revised analytical expressions for CO₂-H₂O equilibria, and extended Debye-Hückel individual ion activity coefficients. Using this aqueous model, the equilibrium constant of aragonite shows no PCO₂-dependence if the CaHCO⁺₃ association constant is between 0 and 90°C, corresponding to the value logK_Cahco⁺3 = 1.11 ± 0.07 at 25°C. The CaCO⁰₃ association constant was measured potentiometrically to be between 5 and 80°C, yielding logK_CaCO⁰3 = 3.22 ± 0.14 at 25°C.The CO₂-H₂O equilibria have been critically evaluated and new empirical expressions for the temperature dependence of K_H, K₁ and K₂ are $\text{log K}{}_{\mathrm{H}}\text{= 108.3865 + 0.01985076T ?}\text{6919.53}\text{T}\text{? 40.45154 log T +}\text{669365.}\text{T}{}^2$, $\text{log K}{}_1\text{= ?356.3094 ? 0.06091964T +}\text{21834.37}\text{T}\text{+ 126.8339 log T —}\text{1684915.}\text{T}{}^2$ and logK₂ = ?107.8871 ? 0.03252849T + 5151.79/T + 38.92561 logT ? 563713.9/T² which may be used to at least 250°C. These expressions hold for 1 atm. total pressure between 0 and 100°C and follow the vapor pressure curve of water at higher temperatures.Extensive measurements of the pH of Ca-HCO₃ solutions at 25°C and 0.956 atm PCO₂ using different compositions of the reference electrode filling solution show that measured differences in pH are closely approximated by differences in liquid-junction potential as calculated by the Henderson equation. Liquid-junction corrected pH measurements agree with the calculated pH within 0.003-0.011 pH.Earlier arguments suggesting that the CaHCO⁺₃ ion pair should not be included in the CaCO₃-CO₂-H₂O aqueous model were based on less accurate calcite solubility data. The CaHCO⁺₃ ion pair must be included in the aqueous model to account for the observed PCO₂-dependence of aragonite solubility between 317 ppm CO₂ and 100% CO₂.Previous literature on the solubility of CaCO₃ polymorphs have been critically evaluated using the aqueous model and the results are compared.     

Polyunsaturated fatty acids in a lacustrine sediment as a possible indicator of paleoclimate

Polyunsaturated fatty acids (C_18:2 and C_18:3ω3 were analyzed in the upper 20m layer of a 200 m long sediment core taken from Lake Biwa. Concentration maxima occur in layers at depths of 0.2, 1–5, 11–12, and 16m. The vertical changes in the $\text{(C}{}_{\mathrm{18:2}}\text{C(C}{}_{\mathrm{18:0}}$ ratio appear to correlate with paleoclimatic condition suggested from palynological evidence. On the basis of $\text{C}{}_{\mathrm{18:2}}\text{C}{}_{\mathrm{18:0}}$ ratios, it was suggested that it has been colder at 200, 1000–4000, 15,000 and 20,000 yr BP than at other times.     

Trace element partitioning and melt structure: An experimental study at 1 atm pressure

Diopside-melt and forsterite-melt rare earth (REE) and Ni partition coefficients have been determined as a function of bulk compositions of the melt. Available Raman spectroscopic data have been used to determine the structures of the melts coexisting with diopside and forsterite. The compositional dependence of the partition coefficients is then related to the structural changes of the melt.The melts in all experiments have a ratio of nonbridging oxygens to tetrahedral cations ($\text{NBO}\text{T}$) between 1 and 0. The quenched melts consist of structural units that have, on the average, 2 (chain), 1 (sheet) and 0 (three-dimensional network) nonbridging oxygens per tetrahedral cation. The proportions of these structural units in the melts, as well as the overall $\text{NBO}\text{T}$, change as a function of the bulk composition of the melt.It has been found that Ce, Sm, Tm and Ni crystal-liquid partition coefficients ($\text{K}{}^{\mathrm{crystal?liq}}{}_{\mathrm{i}}\text{=}\text{C}{}^{\mathrm{crystal}}{}_{\mathrm{i}}\text{C}{}^{\mathrm{liq}}{}_{\mathrm{i}}$) decrease linearly with increasing $\text{NBO}\text{T}$. The values of the individual REE crystal-liquid trace element partition coefficients have different functional relations to $\text{NBO}\text{T}$, so that the degree of light REE enrichment of the melts would depend on their $\text{NBO}\text{T}$.The solution mechanisms of minor oxides such as CO₂, H₂O, TiO₂, P₂O₅ and Fe₂O₃ in silicate melts are known. These data have been recast as changes of $\text{NBO}\text{T}$ of the melts with regard to the type of oxide and its concentration in the melt. From such data the dependence of crystal-liquid partition coefficients on concentration and type of minor oxide in melt solution has been calculated.     

Prediction of Gibbs free energies of calcite-type carbonates and the equilibrium distribution of trace elements between carbonates and aqueous solutions

A linear correlation exists between the standard Gibbs free energies of formation of calcite-type carbonates (MCO3) and the corresponding conventional standard Gibbs free energies of formation of the aqueous divalent cations (M2+) at 25 °C and 1 bar ΔGMCO30 = m(ΔGf,M2+0) ? 141,200 cal · mole?1 where m is equal to 0.9715. This relationship enables prediction of the standard free energies of formation of numerous hypothetical carbonates with the calcite structure. Associated uncertainties typically range from about ± 250 to 600 cal · mole?1. An important consequence of the above correlation is that the thermodynamic equilibrium constant for the distribution of two trace elements M and N between carbonate mineral and aqueous solution at 25 °C and 1 bar is proportional to the free energy difference between the corresponding two aqueous ions: In Combination of predicted standard free energies, entropies and volumes of carbonate minerals at 25°C and 1 bar with standard free energies of aqueous ions and the equation of state in Helgesonet al. (1981) enables prediction of the thermodynamic equilibrium constant for trace element distribution between carbonates and aqueous solutions at elevated temperatures and pressures. Interpretation of the thermodynamic equilibrium constant in terms of concentration ratios in the aqueous phase is considerably simplified if pairs of divalent trace elements are considered that have very similar ionic radii (e.g., $\text{Sr}{}^{\mathrm{2+}}\text{Pb}{}^{\mathrm{2+}}$, $\text{Mg}{}^{\mathrm{2+}}\text{Zn}{}^{\mathrm{2+}}$). In combination with data for the stabilities of complex ions in aqueous solutions, the above calculations enable useful limits to be placed on the concentrations of trace elements in hydrothermal solutions.     

Rutile solubility and titanium coordination in silicate melts

The solubility of rutile has been determined in a series of compositions in the K₂O-Al₂O₃-SiO₂ system ($\text{K}{}^1\text{=}\text{K}{}_2\text{O}\text{(K}{}_2\text{O}$ + Al₂O₃) = 0.38–0.90), and the CaO-Al₂O₃-SiO₂ system ($\text{C}{}^1\text{=}\text{CaO}\text{(CaO + Al}{}_2\text{O}{}_3\text{)}\text{= 0.47–0.59}$). Isothermal results in the KAS system at 1325°C, 1400°C, and 1475°C show rutile solubility to be a strong function of the $\text{K}{}^1$ ratio. For example, at 1475°C the amount of TiO₂ required for rutile saturation varies from 9.5 wt% ($\text{K}{}^1\text{= 0.38}$) to 11.5 wt% ($\text{K}{}^1\text{= 0.48}$) to 41.2 wt% ($\text{K}{}^1\text{= 0.90}$). In the CAS system at 1475°C, rutile solubility is not a strong function of $\text{C}{}^1$. The amount of TiO₂ required for saturation varies from 14 wt% ($\text{C}{}^1\text{= 0.48}$) to 16.2 wt% ($\text{C}{}^1\text{= 0.59}$).The solubility changes in KAS melts are interpreted to be due to the formation of strong complexes between Ti and K⁺ in excess of that needed to charge balance Al³⁺. The suggested stoichiometry of this complex is K₂Ti₂O₅ or K₂Ti₃O₇. In CAS melts, the data suggest that Ca²⁺ in excess of A1³⁺ is not as effective at complexing with Ti as is K⁺. The greater solubility of rutile in CAS melts when $\text{C}{}^1$ is less than 0.54 compared to KAS melts of equal $\text{K}{}^1$ ratio results primarily from competition between Ti and Al for complexing cations (Ca vs. K).TiK_β x-ray emission spectra of KAS glasses ($\text{K}{}^1\text{= 0.43–0.60}$) with 7 mole% added TiO₂, rutile, and Ba₂TiO₄, demonstrate that the average Ti-O bond length in these glasses is equal to that of rutile rather than Ba₂TiO₄, implying that Ti in these compositions is 6-fold rather than 4-fold coordinated. Re-examination of published spectroscopic data in light of these results and the solubility data, suggests that the 6-fold coordination polyhedron of Ti is highly distorted, with at least one Ti-O bond grossly undersatisfied in terms of Pauling's rules.     

Carbon isotope geochemistry of the 3.7 × 109-yr-old Isua sediments,West Greenland: implications for the Archaean carbon and oxygen cycles

One hundred and twenty-four carbonate samples from the meta-sedimentary sequence of the 3.7 × 10⁹ yr old Isua supracrustal belt (W-Greenland) have yielded a δ¹³C_carb average of ?2.5 ± 1.7%. vs PDB and a δ¹⁸O_carb average of +13.0 ± 2.5%. vs SMOW. The oxygen mean comes fairly close to the averages of other early Precambrian carbonates. The carbon average, however, is some 2%. more negative than those of younger marine carbonates. In terms of a simple terrestrial ¹³C mass balance, if δ¹³C_carb values are original sedimentary values, this more negative δ¹³C average would imply a considerably smaller $\text{C}{}_{\mathrm{org}}\text{C}{}_{\mathrm{carb}}$ ratio in the sedimentary shell during Isua times, and would thus support the concept of a gradual buildup of a sedimentary reservoir of organic carbon during the early history of the Earth. Since, however, the Isua supracrustal rocks have experienced amphibolite-grade metamorphism, which in other areas has been shown to lower δ¹³C_carb values, it is most likely that the original values of these rocks were approx 0%.. This indicates that C_orx and C_carb were present in the ancient carbon reservoir in about ‘modern’ proportions. Unless this early stabilization of the terrestrial carbon cycle in terms of a constant partitioning of carbon between the reduced and oxidized species is shown to have been caused by some inorganic geochemical process, a considerably earlier start of chemical evolution and spontaneous generation of life must be considered than is presently accepted.     

Evaluation of ionic strength and salinity of groundwaters: effect of the ionic composition

An improved method has been used for rapid determination of the ionic strength (I) and the salinity of Apulian groundwaters. The parameters required are the electrolytic conductivity (EC) and the total solute concentration (C_T) of the solutions. A simple empirical relation between I, EC and C_T is presented. The relation holds over a wide concentration and composition range. The combined use of C_T and of the ratio $\text{I}\text{C}{}_{\mathrm{T}}$ is shown to be effective in defining the salinity of groundwaters.     

Sodium and potassium coprecipitation in aragonite

The coprecipitation of Na and K was experimentally investigated in aragonite. The distribution functions were determined at pH 6.8 and 8.8 over aqueous Na and K concentrations of between 5 × 10^?4and 2.0 M and temperatures of between 25 and 75°C.The mole fractions of Na and K in aragonite are related to the aqueous ratios of Na and Ca by a function of the form

$\text{log}\text{X}{}_{\mathrm{Na}}{}_2\text{CO}{}_3\text{,K}{}_2\text{CO}{}_3\text{= C}{}_0\text{+ C}{}_1\text{log}\text{a}{}^2{}_{\mathrm{Na}}\text{? ,K}{}^{\mathrm{?}}\text{a}{}_{\mathrm{Ca}}{}^{\mathrm{2+}}$

where C₀ and C₁ are constants at a given temperature. This equation was derived by a statistical model assuming a heterogeneous energy distribution for the sites of incorporation. The independence of the coprecipitation process from aqueous anion activities suggests that carbonate is the only anionic species in the solid solution.     

Distribution coefficients of Eu and Sr for plagioclase-liquid and clinopyroxene-liquid equilibria in oceanic ridge basalt: an experimental study

The distribution coefficients of Eu and Sr for plagioclase-liquid and clinopyroxene-liquid pairs as a function of temperature and oxygen fugacity were experimentally investigated using an oceanic ridge basalt enriched with Eu and Sr as the starting material. Experiments were conducted between 1190° and 1140°C over a range of oxygen fugacities between 10^?8 and 10^?14 atm.The molar distribution coefficients are given by the equations: log^PL_Sr = 7320/T ? 4.62logK^CPX_Sr = 18020/T ? 13.10. Similarly, the weight fraction distribution coefficients are given by the equations: logD^PL_Sr = 6570/T ? 4.30logD^CPX_Sr = 18434/T ? 13.62.Although the mole fraction distribution coefficients have a smaller dependence on bulk composition than do the weight fraction distribution coefficients, they are not independent of bulk composition, thereby restricting the application of these experimental results to rocks similar to oceanic ridge basalts in bulk composition.Because the Sr distribution coefficients are independent of oxygen fugacity, they may be used as geothermometers. If the temperature can be determined independently — for example, with the Sr distribution coefficients, the Eu distribution coefficients may be used as oxygen geobarometers. Throughout the range of oxygen fugacities ascribed to terrestrial and lunar basalts, plagioclase concentrates Eu but clinopyroxene rejects Eu.     

Revised values for the Gibbs free energy of formation of [Al(OH)4 aq−], diaspore,boehmite and bayerite at 298.15 K and 1 bar,the thermodynamic properties of kaolinite to 800 K and 1 bar,and the heats of solution of several gibbsite samples

Solution calorimetric measurements compared with solubility determinations from the literature for the same samples of gibbsite have provided a direct thermochemical cycle through which the Gibbs free energy of formation of [Al(OH)_{4 aq}^?] can be determined. The Gibbs free energy of formation of [Al(OH)_{4 aq}^?] at 298.15 K is ?1305 ± 1 kJ/mol. These heat-of-solution results show no significant difference in the thermodynamic properties of gibbsite particles in the range from 50 to 0.05 μm.The Gibbs free energies of formation at 298.15 K and 1 bar pressure of diaspore, boehmite and bayerite are ?9210 ± 5.0, ?918.4 ± 2.1 and ?1153 ± 2 kJ/mol based upon the Gibbs free energy of [A1(OH)_{4 aq}^?] calculated in this paper and the acceptance of ?1582.2 ± 1.3 and ?1154.9 ± 1.2 kJ/mol for the Gibbs free energy of formation of corundum and gibbsite, respectively.Values for the Gibbs free energy formation of [Al(OH)_{2 aq}⁺] and [AlO_{2 aq}^?] were also calculated as ?914.2 ± 2.1 and ?830.9 ± 2.1 kJ/mol, respectively. The use of [AlC_{2 aq}^?] as a chemical species is discouraged.A revised Gibbs free energy of formation for [H₄SiO_4aq⁰] was recalculated from calorimetric data yielding a value of ?1307.5 ± 1.7 kJ/mol which is in good agreement with the results obtained from several solubility studies.Smoothed values for the thermodynamic functions C_P⁰, ($\text{H}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, $\text{(}\text{G}{}_{\mathrm{T}}{}^0\text{- H}{}_{298}{}^0\text{)}\text{T}$, S_T⁰ - S₀⁰, $\text{ΔH}{}_{\mathrm{?,298}}{}^0$ kaolinite are listed at integral temperatures between 298.15 and 800 K. The heat capacity of kaolinite at temperatures between 250 and 800 K may be calculated from the following equation: C_P⁰ = 1430.26 ? 0.78850 T + 3.0340 × 10^?4T² ?1.85158 × 10^?4T²$\text{1}\text{2}\text{+ 8.3341 × 10}{}^6\text{T}{}^{\mathrm{?2}}$.The thermodynamic properties of most of the geologically important Al-bearing phases have been referenced to the same reference state for Al, namely gibbsite.     

Density calculations for silicate liquids. I. Revised method for aluminosilicate compositions

Equations are developed for calculating the density of aluminosilicate liquids as a function of composition and temperature. The mean molar volume at reference temperature T_r, is given by $\text{V}{}_{\mathrm{r}}\text{= ∑X}{}_{\mathrm{i}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{i}}\text{+ X}{}_{\mathrm{A}}\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$, where the summation is taken over all oxide components except A1₂O₃, X stands for mole fraction, terms are constants derived independently from an analysis of volume-composition relations in alumina-free silicate liquids, and $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is the composition-dependent apparent partial molar volume of Al₂O₃. The thermal expansion coefficient of aluminosilicate liquids is given by $\text{α = ∑X}{}_{\mathrm{i}}\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}\text{+ X}{}_{\mathrm{A}}\text{}\text{?}\text{ga}{}_{\mathrm{A}}{}^{\mathrm{o}}$, where $\text{}\text{?}\text{ga}{}_{\mathrm{i}}{}^{\mathrm{o}}$ terms are constants independent of temperature and composition, and $\text{}\text{?}\text{ga}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is a composition-dependent term representing the effect of Al₂O₃ on the thermal expansion. Parameters necessary to calculate the volume of silicate liquids at any temperature T according to V(T) = V_rexp[α(T-T_r)], where T_r = 1400°C have been evaluated by least-square analysis of selected density measurements in aluminosilicate melts. Mean molar volumes of aluminosilicate liquids calculated according to the model equation conform to experimentally measured volumes with a root mean square difference of 0.28 $\text{cc}\text{mole}$ and an average absolute difference of 0.90% for 248 experimental observations. The compositional dependence of $\text{V}\text{?}{}^{\mathrm{o}}{}_{\mathrm{A}}$ is discussed in terms of several possible interpretations of the structural role of Al³⁺ in aluminosilicate melts.     

Algal lipids as a possible contributor to the polymethylene chains in kerogen

Lipid fraction and cell-wall materials have been separated from three types of algae (blue green, Microcystis sp.; green, Scenedesmus sp. and diatomaceous Diatoma sp.) and their KMnO₄ oxidation products (aliphatic $\text{α,ω-C}{}_2\text{-C}{}_{12}$ dicarboxylic acids; aliphatic normal C₁₄–C₂₄ monocarboxylic acids; benzoic acid and C₁₈ isoprenoidal ketone) examined by gas chromatography and gas chromatographymass spectrometry. The results suggest that the lipid material could make a greater contribution to polymethylene chains in kerogen than the cell-wall material, when the kerogens are mainly derived from algal components.     

Settling velocities of particulate systems, 3. Power series expansion for the drag coefficient of a sphere and prediction of the settling velocity

The following equation has been previously developed for the drag coefficient of a sphere.

$\text{C}{}_{\mathrm{D}}\text{= C}{}_0\text{[1 + (σ}{}_0\text{/Re}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)]}{}^2$

In this work the authors propose a power series expansion for C₀ in terms of the Reynolds number:

$\text{C}{}_0\text{= 0 284153}\text{Σ}\text{α=0}\text{n}\text{B}{}_{\mathrm{\alpha }}\text{Re}{}^{\mathrm{\alpha }}$

A fifth-order polynomial permits obtaining the drag coefficient and the settling velocity of a sphere, up to a Reynolds number of 3 × 10⁵, with an average relative error of about 2%.     

The solubility of noble gases in water and in NaCl brine

A direct-sampling, mass-spectrometric technique has been used to measure simultaneously the solubilities of He, Ne, Ar, Kr, and Xe in fresh water and NaCl brine (0 to 5.2 molar) from 0° to 65 °C, and at 1 atm total pressure of moist air. The argon solubility in the most concentrated brines is 4 to 7 times less than in fresh water at 65 °C and 0°C, respectively. The salt effect is parameterized using the Setschenow equation.

$\text{ln}\text{[}\text{β}{}^{\mathrm{i}}{}_{\mathrm{o}}\text{(T)}\text{β}{}^{\mathrm{i}}\text{(T)}\text{= MK}{}^{\mathrm{i}}{}_{\mathrm{M}}\text{(T)}$

where M is NaCl moiarity, βⁱ_o(T) and βⁱ(T) the Bunsen solubility coefficients for gas i in fresh water and brine, and Kⁱ_M(T) the empirical salting coefficient. Values of Kⁱ_M(T) are calculated using volumetric concentration units for noble gas and NaCl content and are independent of NaCl molarity. Below about 40°C, temperature coefficients of all Kⁱ_M are negative. The value of K^He_M is a minimum at 40°C. K^Ar_M decreases from about 0.40 at 0°C to 0.28 at 65 °C. The absolute magnitudes of the differences in salting coefficients (relative to K^Ar_M) decrease from 0° to 65°C. Over the range of conditions studied, all noble gases are salted out, and K^He_M ? K^Ne_M < K^Ar_M < K^Kr_M < K^Xe_M.From the solubility data, we calculated $\text{Δ}\text{G}{}^0{}_{\mathrm{tr}}$, $\text{Δ}\text{S}{}^0{}_{\mathrm{tr}}$, $\text{Δ}\text{H}{}^0{}_{\mathrm{tr}}$ and $\text{Δ}\text{C}{}^{\mathrm{O}}{}_{\mathrm{p,tr}}$ for the transfer of noble gases from fresh water to 1 molar NaCl solutions. At low temperatures $\text{Δ}\text{S}{}^0{}_{\mathrm{tr}}$, is positive, but decreases and becomes negative at temperatures ranging from about 25°C for He to 45°C for Xe. At low temperatures, the dissolved electrolyte apparently interferes with the formation of a cage of solvent molecules about the noble gas atom. At higher temperatures, the local environment of the gas atom in the brine appears to be slightly more ordered than in pure water, possibly reflecting the longer effective range of the ionic fields at higher temperature.The measured solubilities can be used to model noble gas partitioning in two-phase geothermal systems at low temperatures. The data can also be used to estimate the temperature and concentration dependence of the salt effect for other alkali halides. Extrapolation of the measured data is not possible due to the incompletely-characterized minima in the temperature dependence of the salting coefficients. The regularities in the data observed at low temperatures suggest relatively few high-temperature data will be required to model the behavior of noble gases in high-temperature geothermal brines.