Unsteady source flow in weakly heterogeneous porous media

Average nonuniform flows in heterogeneous formations are modeled with the aid of the nonlocal effective Darcy's law. The mean head for flow toward source of instantaneous discharge in a heterogeneous medium of given statistics represents the fundamental solution of the average flow equation and is called the Mean Green Function (MGF). The general representation of the MGF is obtained for weakly heterogeneous formations as a functional of the logconductivity correlation function. For Gaussian logconductivity correlation, the MGF is derived in terms of one quadrature in time t and it is analyzed for isotropic media of any dimensionality d and for 3D axisymmetric formations. The MGF is further applied to determining the mean head distribution for flow driven by a continuous source of constant discharge. The large time asymptotic of the mean head is analyzed in details.     

The influence of disordered,non-equilibrium dolomites on the Mg-solubility in calcite in the system CaCO3-MgCO3

The influence of different degrees of disorder of dolomites on the solubility of MgCO₃ in calcite has been studied under isothermal and isobaric conditions. At 900° C, 4kb and 1000° C, 5 and 7kb, varied smoothly as function of the particular structural and cationic disorder of coexisting dolomite. Higher degrees of disorder of dolomite, estimated by the d _00.6/d _11.0 values and the peak height ratio I _01.5/I_00.6, lead to greater solubility of MgCO₃ in calcite. The run time for all experiments was 96 h, much longer than in previous work. The influence of disorder of dolomite on appears to be larger than that of temperature, as shown by the large range of (0.12–0.30) in calcite at 900° C 4 kb, found in this study. The state of order of dolomite seems to control the solubility limits in this system, and may explain discrepancies found in previous experimental work.     

Efficiency of kriging estimation for square, triangular, and hexagonal grids

Although several researchers have pointed out some advantages and disadvantages of various soil sampling designs in the presence of spatial autocorrelation, a more detailed study is presented herein which examines the geometrical relationship of three sampling designs, namely the square, the equilateral triangle, and the regular hexagon. Both advantages and disadvantages exist in the use of these designs with respect to estimation of the semivariogram and their effect on the mean square error or variance of error. This research could be used to design optimal sampling strategies; it is based on the theory of regionalized variables, in which the intrinsic hypothesis is satisfied. Among alternative designs, an equilateral triangle design gives the most reliable estimate of the semivariogram. It also gives the minimum maximum mean square error of point estimation of the concentration over the other two designs for the same number of measurements when the nugget effect is small relative to the variance. If the nugget effect is large (.90 ² or more), and the linear sampling density is >0.85r where r is the range, the hexagonal design is best. This study computes and compares the maximum mean square error for each of these designs.     

Manganese olivine I: Electrical conductivity

To investigate the point defect chemistry and the kinetic properties of manganese olivine Mn₂SiO₄, electrical conductivity () of single crystals was measured along either the [100] or the [010] direction. The experiments were carried out at temperatures T=850–1200 °C and oxygen fugacities atm under both Mn oxide (MO) buffered and MnSiO₃ (MS) buffered conditions. Under the same thermodynamic conditions, charge transport along [100] is 2.5–3.0 times faster than along [010]. At high oxygen fugacities, the electrical conductivity of samples buffered against MS is 1.6 times larger than that of samples buffered against MO; while at low oxygen fugacities, the electrical conductivity is nearly identical for the two buffer cases. The dependencies of electrical conductivity on oxygen fugacity and temperature are essentially the same for conduction along the [100] and [010] directions, as well as for samples coexisting with a solid-state buffer of either MO or MS. Hence, it is proposed that the same conduction mechanisms operate for samples of either orientation in contact with either solid-state buffer.The electrical conductivity data lie on concave upward curves on a log-log plot of vs , giving rise to two regimes with different oxygen fugacity exponents. In the low- regime , the exponent, m, is 0, the MnSiO₃-activity exponent, q, is 0, and the activation energy, Q, is 45 kJ/mol. In the high regime 10^{ - 7} {\text{atm}}} \right)$$ " align="middle" border="0"> , m=1/6, q=1/4–1/3, and Q=45 and 200 kJ/mol for T<1100 °c=" and=">T>1100 °C, respectively.     

Spatial relationships of multivariate data

Spatial factor analysis (SFA) is a multivariate method that determines linear combinations of variables with maximum autocorrelation at a given lag. This is achieved by deriving estimates of auto-/cross-correlations of the variables and calculating the corresponding eigenvectors of the covariance quotient matrix. A two-point spatial factor analysis model derives factors by the formation of transition matrixU comparing auto-/cross-correlations at lag 0,R ₀, with those at a specified lag d,R _d, expressed asU _d=R ₀ ^–1 R_d. The matrixU _d can be decomposed into its spectral components which represent the spatial factors. The technique has been extended to include three points of reference. Spatial factors can be derived from the relationship:

Estimation of mean trace length of discontinuities

Summary Trace lengths of discontinuities observed on finite exposures are biased due to sampling errors. These errors should be corrected in estimating mean trace length. A technique, which takes into account the sampling errors, is proposed for estimating the mean trace length on infinite, vertical sections from the observations made on finite, rectangular, vertical exposures. The method is applicable to discontinuities whose orientation is described by a probability distribution function. The method requires that the numbers of discontinuities with both ends observed, one end observed, and both ends censored be known. The lengths of observed traces and the density function of trace length are not required. The derivation assumes that midpoints of traces are uniformly distributed in the vertical plane. Also independence between trace length and orientation is assumed. Data on a Pennsylvania shale in Ohio, U. S. A., were used as an example.Notations dip direction - direction of sampling plane - acute angle between dip direction and sampling plane - dip angle - _A apparent dip angle - mean density of trace mid-points per unit area - mean trace length - D diameter of discontinuity - f (.),g (.) probability density function - h height of rectangular window - estimator of mean trace length - m sample size, number of discontinuities intersecting window - m ₀ number of discontinuities intersecting window with both ends censored - m ₂ number of discontinuities intersecting window with both ends observed - n, N expected number of discontinuities intersecting the window - n ₀,N ₀ expected number of discontinuities intersecting the window with both ends censored - n ₂,N ₂ expected number of discontinuities intersecting the window with both ends observed - Pr (.) probability - w width of rectangular window - x trace length     

Palaeomagnetism of the Loch Doon Granite Complex, Southern Uplands of Scotland: The Late Caledonian palaeomagnetic record and an Early Devonian episode of True Polar Wander

The Southern Uplands terrane is an Ordovician–Silurian back-arc/foreland basin emplaced at the northern margin of the Iapetus Ocean and intruded by granite complexes including Loch Doon (408.3 ± 1.5 Ma) during Early Devonian times. Protracted cooling of this 130 km³ intrusion recorded magnetic remanence comprising a predominant (‘A’) magnetisation linked to initial cooling with dual polarity and mean direction D / I = 237 / 64° (α₉₅ = 4°, palaeopole at 316°E, 21°N). Subsidiary magnetisations include Mesozoic remanence correlating with extensional tectonism in the adjoining Irish Sea Basin (‘B’, D / I = 234/− 59°) and minority populations (‘C’, D / I = 106/− 2° and ‘D’, D / I = 199/1°) recording emplacement of younger ( 395 Ma) granites in adjoining terranes and the Variscan orogenic event. The ‘A’ directions have an arcuate distribution identifying anticlockwise rotation during cooling. A comparable rotation is identified in the Orthotectonic Caledonides to the north and the Paratectonic Caledonides to the south following closure of Iapetus. Continental motion from midsoutherly latitudes ( 40°S) at 408 Ma to equatorial palaeolatitudes by  395 Ma is identified and implies minimum rates of continental movement between 430 and 390 Ma of 30–70 cm/year, more than double maximum rates induced by plate forces and interpreted as a signature of true polar wander. Silurian–Devonian palaeomagnetic data from the British–Scandinavian Caledonides define a 430–385 Ma closed loop comparable to the distributed contemporaneous palaeomagnetic poles from Gondwana. They reconcile pre-430 Ma and post-380 Ma APW from this supercontinent and show that Laurentia–Baltica–Avalonia lay to the west of South America with a relict Rheic Ocean opening to the north which closed to produce Variscan orogeny by a combination of pivotal closure and right lateral transpression.     

On Preferential Flow, Channeling and Connectivity in Heterogeneous Porous Formations

This paper analyzes the emergence of channeling and preferential flow in heterogeneous porous media. Connectivity is studied through the statistical characterization of the length L of connected, high velocity patterns in both two-dimensional and three-dimensional media. A simple, physically based, fully analytic expression for the probability of L has been derived. It is found that the length L of connected, high velocity channels is flow-related and can be much larger than the conductivity integral scale I. Heterogeneity has a considerable impact on emergence of channeling patterns; connectivity is considerably enhanced in three-dimensional structures as compared to two-dimensional ones. The strong dependence on space dimensionality is a warning against the use of two-dimensional numerical models for assessing connectivity and preferential flow in heterogeneous media. The probability p(L) is employed in order to determine the early arrivals of the breakthrough curve at a given control plane; the simple model can be used for a preliminary assessment of preferential flow. Comparison with numerical simulations confirms that the main connectivity features were adequately captured by the model.     

A morphometric analysis of terrace gravels in Santa Ynez basin,Santa Barbara County,California

An analysis of 6,300 pebbles from eighteen river terraces within the five subareas of the Santa Ynez River basin has revealed significant differences in particle sphericity and roundness of the various terrace gravels.Using the Cailleux technique of pebble measurement, Krumbein's sphericity ratio formula (Y) and the author's own roundness ratio or the I/L¹ ratio (R) the computed values derived for $\text{Y}$ range from 0.92 to 1.11, and for $\text{R}$ from 0.66 to 0.79 on these benches.An analysis of variance, based on the F-test applied to samples has established that: (a) gravel sphericity and roundness increase significantly from upstream to the river mouth; (b) in the subareas themselves pebble sphericity and roundness vary significantly from bench to bench indicating varied energy conditions of deposition; (c) all terrace gravels measured show higher sphericity and roundness than the underlying Orcutt gravels. This suggests a reworking of the latter by the Santa Ynez River.     

Stochastic modeling of gold mineralization in the Champion lode system of Kolar gold fields (India)

Stochastic modeling of gold mineralization in the Champion lode of Kolar gold fields was carried out using assay data taken from developmental headings. After dividing the lode into 71 horizontal and 18 vertical strata, autoregressive (AR), moving average (MA), and autoregressive and moving average (ARMA) models were developed and applied. The model selection with the acf and pacf for the various strata showed that in most of the cases, ARMA modeling of first-order would forecast gold headings with a reasonable degree of confidence. This was substantiated by comparing the coefficients of variation. From a parsimony point of view, AR (1) model may also be considered valid. The best overall models are: ARMA (1, 1), ; AR (1), , where a_t is N (0, _a ² ), x is in logarithms of in-dwt, and t is in block units of 100 ft. The applications of these models to a specific stratum are given. These models would also be helpful to describe the characteristics of the gold mineralization process of this lode.     

Estimating relative bed-load contributions by lithology counts

In gravel-bedded streams where bed material of a tributary differs distinctly in lithology from that of the main stream, rock-type percentages can be used to estimate bed-load contributions of the two streams. The rock type that shows the greatest difference in abundance between the two streams is selected as the indicator lithology. Percentages of this lithology are estimated in both the main stream and tributary stream above their junction, and also in the main stream at a distance sufficiently downstream from the junction to allow complete mixing. The fraction of bed load contributed by the main stream, p,is estimated by ,where is an estimate of the proportion of indicator rock fragments in the bed of the main stream above the junction, is an estimate of the proportion in the bed of the tributary above the junction, and is an estimate of the proportion in the bed of the main stream below the junction. The variance of is obtained as var ( )= [p₁q₁(p_r – p₂)²/n(p₁ – p₂)⁴] + [p₂q₂(p_r – p₁)²/n(p₁ – p₂)⁴] + [p_rq_r/n(p₁ – p₂)²].Although no estimate of actual quantity of bed load is provided, the indicator rock technique supplies data that can serve as a check on data obtained by means of empirical formulas or actual transport measurements.     

Machatschkiit,ein neues Arsenatmineral aus der Grube Anton im Heubachtal bei Schiltach (Schwarzwald,Bundesrepublik Deutschland)

Zusammenfassung Machatschkiit ist ein neues wasserhaltiges Calciumarsenat, das in der Grube Anton bei Schiltach im mittleren Schwarzwald (BRD) 1960 gefunden wurde. Es kommt zusammen mit Gips, Pharmakolith, Pikropharmakolith und Sainfeldit als Sekundärbildung krustenförmig auf Granit vor.Als charakteristische Form tritt das Rhomboeder auf. Keine Spaltbarkeit, Bruch muschelig, Härte 2–3,G=2,5 bis 2,6 g·cm^–3,D _x =2,50 g·cm^–3, farblos, durchsichtig bis durchscheinend. Optische Daten:n =1,585±0,002,n =1,593±0,002, einachsig oder schwach zweiachsig, negativ.Gitterkonstanten:a ₀=15,10,c ₀=22,59 Å,a ₀c ₀=11,4960,Z=12;a _rh =11,52 Å, =81°52,Z=4. Mögliche Raumgruppen:R32,R3m, . Stärkste Linien des Pulverdiagramms: 8,59 (10) (110), 5,34 (8) (210), 3,59 (8) . Eine chemische Analyse ergab nach Umrechnung folgende Zusammensetzung: CaO 29,5%, As₂O₅ 40,8%, SO₃ 0,5%, H₂O 29,2%, Summe 100,0%. Dies kommt der Formel Ca₃(AsO₄)₂ · 9 H₂O sehr nahe. In verdünnter HCl und HNO₃ ist der Machatschkiit leicht löslich.

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Machatschkiite, a new arsenate mineral from the Anton Mine in the Heubach valley near Schiltach (Black Forest, Federal Republic of Germany)

Summary Machatschkiite is a new hydrous calcium arsenate which was found 1960 in the Anton Mine near Schiltach in the central Black Forest. It is a secondary mineral which occurs in crusts on granite in association with gypsum, pharmacolite, picropharmacolite and sainfeldite.The characteristic form is the rhombohedron . No cleavage, fracture conchoidal, hardness 2–3,G=2.5–2.6 g·cm^–3,D _x =2.50 g·cm^–3, colourless, transparent to translucent. Optical data:n =1.585±0.002,n =1.593±0.002, uniaxial or weakly biaxial, negative.Unit-cell dimensions:a ₀=15.10,c ₀=22.59 Å,a ₀c ₀=11.4960,Z=12;a _rh =11.52 Å, =81°52,Z=4. Possible space groups:R32,R3m, . Strongest lines of the powder pattern: 8.59 (10) (110), 5.34 (8) (210), 3.59 (8) . A chemical analysis gave the following composition after recalculation: CaO 29.5%, As₂O₅ 40.8%, SO₃ 0.5%, H₂O 29.2%, total 100.0%. This agrees well with the formula Ca₃(AsO₄)₂ · 9 H₂O. Machatschkiite is easily soluble in diluted HCl and HNO₃.

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Phase transitions in leucite,KAISi2O6

An order parameter treatment of the phase transitions in leucite, KAlSi₂O₆, at approximately 950 and 920 K: (cubic) I4₁ acd(tetragonal) I4₁ a(tetragonal) is presented in terms of Landau theory and induced representation theory. The Al-Si order with decreasing temperature is taken as the primary order parameter to which other distortions (K⁺ ion displacements, strain components, etc.) couple linearly. The expected Al-Si ordering behavior and the associated K⁺ ion displacements for both transitions are derived and the resulting twin domain orientations are listed. The sequence of phase transitions results from a coupling of ₃ ⁺ and ₄ ⁺ representations. The Landau free energy for the five-dimensional reducible representation has been simplified to two components resulting in a linearquadratic coupling of the components. Possible phase diagrams are derived by free energy minimization. The cubic tetragonal transition is first-order, whereas the tetragonal-tetragonal transition may be second order. A tricritical point exists at which the first-order transition changes to second-order.     

Estimation of statistical parameters for censored lognormal hydraulic conductivity measurements

Field tests of hydraulic conductivity (e.g., injection test, pumping test, etc.) in low permeability formations are subject to censoring due to the detection limit of the instruments used. An iterative method of estimating the mean and variance of hydraulic conductivity data with a presumed log-normal distribution function is presented. This method accounts for the data that are actually below the lower detection limit (called truncated data) and thus gives distribution parameters that are more representative for the underlying distribution. The proposed method is then tested on two simulated normally distributed random datasets having different variances. The results show that the means and variances estimated by the proposed method are very accurate. Finally, the method is used to estimate the mean and variance of hydraulic conductivity data from single hole water injection tests in a fractured geological formation.     

A dynamical model for the P1 — I1 phase transition in anorthite,CaAl2Si2O8

Electron diffraction and electron microscopic evidence is presented for a dynamical and reversible phase transition in anorthite at T _c=516 K. Antiphase boundaries with a displacement vector, R=1/2[111] become unstable at T _c, while other antiphase boundary loops with the same displacement vector are formed. These interfaces are very mobile and vibrate with a frequency which increases strongly with temperature. At temperatures considerably above T _c, a shimmering effect is observed on imaging in dark field using diffuse c reflections. These observations are in agreement with the interpretation of the high temperature body-centered phase as a statistical dynamical average of very small c type antiphase domains of primitive anorthite. We propose that the c type antiphase domains in primitive anorthite originate from ordered and anti-ordered configurations around Ca²⁺ ions at (ooo) and (oio) [likewise (zoo) and (zio)] positions. The dynamical model for the transition involves a two-stage mechanism: a softmode mechanism causing the aluminosilicate framework to approach body-centered symmetry, followed by an orderdisorder of the Ca²⁺ ion configurations. Close to T _c, statistical fluctuations set in and breathing motion type lattice vibrations of the aluminosilicate framework cause the configurations around Ca (ooo) and Ca(oio) [likewise Ca(zoo) and Ca(zio)] in the configuration to dynamically interchange through an intermediate configuration. The dynamical nature of the phase transition in anorthite is comparable to the — phase transition in quartz.     

Die Kristallstruktur des Ferrinatrits,Na3Fe[SO4]3 · 3H2O

Zusammenfassung Die Kristallstruktur des Ferrinatrits, Na₃Fe[SO₄]₃·3H₂O, Raumgruppe ,a _o=15,560 Å,c _o=8,666 Å,Z=6, wurde mittels der mit einem Zweikreis-Diffrak tometer gemessenen Röntgen-Intensitäten bestimmt und für 1591 symmetrieunabhängigeF _obs aufR=0,047 verfeinert. In Ferrinatrit sind FeO₆-Oktaeder und Sulfattetraeder über gemeinsame Ecken zu Ketten verknüpft. Diese Ketten verlaufen parallelz und sind untereinander über Natriumionen und Wassermoleküle verbunden. Die Mittelwerte der wichtigsten Bindun gslängen betrgen: Fe–O=1,997 Å, S–O=1,474 Å, Na–(4×O+2×Ow)=2,49 Å.

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The crystal structure of ferrinatrite, Na₃Fe[SO₄]₃ · 3H₂O

Summary The crystal structure of ferrinatrite, Na₃Fe[SO₄]₃·3H₂O, space group ,a ₀=15.560 Å,c ₀=8.666 Å,Z=6, was determined from X-ray intensities measured on a 2-circle diffractometer and was refined using 1591 independentF _obs toR=0.047. FeO₆ Octahedra and sulfate tetrahedra share common corners to from infinite chains which run parallel toz and are linked by sodium ions and water molecules. Important average bond lengths are: Fe–O=1.997 Å, S–O=1.474Å, Na-(4×0+2×Ow)=2.49 Å.

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Herrn Prof. DDr.H. Wieseneder zum 70. Geburtstag gewidmet.     

Johillerit,Na(Mg,Zn)3 Cu(AsO4)3, ein neues Mineral aus Tsumeb,Namibia

Zusammenfassung Die chemische Analyse des neuen Minerals Johillerit mit der Elektronenmikrosonde ergab: Na₂O 5,4, MgO 18,3, ZnO 5,4, CuO 15,8 und As₂O₅ 55,8, Summe 100.7%. Aus diesem Ergebnis wurde die idealisierte Formel Na(Mg, Zn)₃ Cu(AsO₄)₃ abgeleitet. Johillerit ist monoklin mit der RaumgruppeC2/c. Die Gitterkonstanten sind:a=11,870 (3),b=12,755 (3),c=6,770 (2) , =113,42 (2)°,Z=4. Die stärksten Linien des Pulverdiagramms sind: 4,06 (5) (22 ), 3,50 (4) (310), 3,25 (8) (11 ), 2,75 (10) (330, 240), 2,64 (5) (311, 13 , 40 ), 1,952 (4) (13 , 35 ), 1,682 (4) (20 , 460), 1,660 (5) (40 , 71 , 550, 64 ), 1,522 (4) (442, 153, 13 ). Es bestehen enge strukturelle Beziehungen zwischen Johillerit und O'Danielit, Na(Zn, Mg)₃H₂(AsO₄)₃, sowie einigen synthetischen. Verbindungen.Johillerit ist violett durchscheinend. Die Spaltbarkeit nach {010} ist ausgezeichnet und nach {100} und {001} gut.H (Mohs)3.D=4,15 undD _X =4,21 g·cm^–3. Das Mineral ist optisch zweiachsig positiv, 2V80 (5)°. Die Werte der Lichtbrechung sindn =1,715 (4),n =1,743 (4) undn =1,783 (4). Die Auslöschung istn b und auf (010)n c16°. Johillerit ist stark pleochroitisch mit den AchsenfarbenX=violett-rot,Y = blauviolett undZ = grünblau. Das neue Mineral kommt in radialstrahligen Massen gemeinsam mit kupferhaltigem Adamin und Konichalcit in zersetzem Kupfererz von Tsumeb, Namibia, vor. Die Benennung erfolgte nach Prof. Dr.J.-E. Hiller (1911–1972).

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Johillerite, Na(Mg, Zn) ₃ Cu(AsO ₄ ) ₃ , a new mineral from Tsumeb, Namibia

Summary Electron microprobe analysis of the new mineral johillerite gave Na₂O 5.4, MgO 18.3, ZnO 5.4, CuO 15.8, and As₂O₅ 55.8, total 100.7%. From this result, the ideal formula is given as Na(Mg, Zn)₃ Cu(AsO₄)₃. Johillerite crystallizes monoclinic,C2/c. The unit cell dimensions are:a=11.870(3),b=12.755 (3),c=6.770 (2) , =113.42 (2)°,Z=4. The strongest lines on the X-ray powder diffraction pattern are: 4,06 (5) (22 ), 3,50 (4) (310), 3,25 (8) (11 ), 2,75 (10) (330, 240), 2,64 (5) (311, 13 , 40 ), 1,952 (4) (13 , 35 ), 1,682 (4) (20 , 460), 1,660 (5) (40 , 71 , 550, 64 ), 1,522 (4) (442, 153, 13 ). There is a close relationship between johillerite, o'danielite, Na(Zn, Mg)₃H₂(AsO₄)₃, and some synthetic compounds. Johillerite is violet in colour, transparent. Cleavage is {010} perfect, {100} and {001} good.H (Mohs)3.D=4.15 andD _X =4.21 g·cm^–3. The mineral is optically biaxial positive, 2V80 (5)°. The refractive indices are:n =1.715 (4),n =1.743 (4),n =1.783 (4). The extinction isn b and on (010)n c16°. Strongly pleochroic with axial coloursX=violet-red,Y=bluish violet andZ=greenish blue. The new mineral was found in radiated masses together with cuprian adamite and conichalcite in an oxidized copper ore from Tsumeb, Namibia. It is named in honour of Prof. Dr.J.-E. Hiller (1911–1972).

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Die Kristallstruktur von Warikahnit,Zn3[(H2O)2|(AsO4)2]

Zusammenfassung Die Kristallstruktur des neuen Minerals Warikahnit, Zn₃[(H₂O)₂|(AsO₄)₂], wurde mit Diffraktometerdaten bestimmt und bis zuR=0,038 für 3428 unabhängige Reflexe verfeinert.Warikahnit ist triklin, , mita=6,710(1),b=8,989(2),c=14,533(2) Å, =105,59(1), =93,44(1), =108,68(1)°,Z=4.Die Kristallstruktur des Warikahnits enthält sechs unterschiedliche Koordinationspolyeder des Zinks mit den Koordinationszahlen 6, 5 und 4 und mit fünf verschiedenen Ligandenkombinationen. Die Wasserstoffbrückenbindungen werden mit Hilfe der Ladungsbilanz und des IR-Spektrums diskutiert.

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The crystal structure of warikahnite, Zn₃[(H₂O)₂|(AsO₄)₂]

Summary The crystal structure of the new mineral warikahnite, Zn₃[(H₂O)₂|(AsO₄)₂], was determined from diffractometer data and refined toR=0,038 for 3428 observed independent reflections.Warikahnit is triclinic, , witha=6.710(1),b=8.989(2),c=14.533(2) Å, =105.59(1), =93.44(1), =108.68(1)°,Z=4.The crystal structure of warikahnite contains 6 different coordination polyhedra of zinc with the coordination numbers 6,5 and 4 and with 5 different combinations of ligand. The hydrogen bonds are discussed on the basis of charge balance and IR spectra.

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Interpretation of reservoir rock mechanical properties by direct methods

Direct core analysis results of bulk density, porosity permeability, resistivity, transit time, and strength were correlated with logging data from an oil well. The interpretations were made in terms of index values between field and laboratory data obtained for the two reservoir units studied. An engineering classification scheme was suggested. Other rock engineering properties such as sonic velocity and dynamic modulus were calculated as well. An attempt was made to predict the fracture pressure gradient (FPG) of rock formation. This work has revealed the possibility of using the direct measured data to evaluate some of the in situ rock behavior.Notations K _L Liquid Permeability (m.d.) - K _g Gas permeability - a Constant dependent on rock type - poissons ratio - R _c Resistance of brine saturated core (ohm.m) - R _w Resistivity of Brine (Salt water) (ohm.m) - I _s Point Load Index value (Kg/cm²) - g accelaration constant of gravity - _ac Apparant acoustic log porosity - _D Apparent density log porosity - q Shaliness index - p Poisson ratio index - P _o Over burden pressure (Psi)