Assessment of Reservoir Rock Properties from Rock Physics Modeling and Petrophysical Analysis of Borehole Logging Data to Lessen Uncertainty in Formation Characterization in Ratana Gas Field,Northern Potwar,Pakistan

Petrophysical evaluation and rock physics analysis are the important tools to relate the reservoir properties like porosity, permeability, pore fluids with seismic parameters. Nevertheless, the uncertainties always exist in the quantification of elastic and seismic parameters estimated through wireline logs and rock physics analysis. A workflow based on statistical relationships of rock physics and logs derived elastic and seismic parameters with porosity and the percentage error exist between them is given. The statistical linear regressions are developed for early Eocene Chorgali Formation between various petrophysically factors determined from borehole logging of well Ratana–03 drilled in tectonically disturbed zone and the seismic and elastic parameters estimated through rock physics modeling. The rock physics constraints such as seismic velocities, effective density and elastic moduli calculated from Gassmann fluid substation analysis are in harmony and close agreement to those estimated from borehole logs. The percentage errors between well logs and rock physics computed saturated bulk modulus (K _sat ), effective density (ρ _eff ), compressional and shear wave velocities (V _P and _V S) are 1.31%, 4.23 %, 5.25% and 4.01% respectively. The permeability of reservoir intervals show fairly strong linear relationship with the porosity, indicating that the reservoir interval of the Chorgali Formation is permeable and porous thus having large potential of hydrocarbon accumulation and production.     

Performance of flexible emergent vegetation in staggered configuration as a mitigation measure for extreme coastal disasters

The performance characteristics of emergent greenbelt vegetation has received considerable attention in the recent years, post-Great Indian Ocean Tsunami (26 December 2004). In the present work, a comprehensive laboratory study on the hydraulic resistance characteristics due to a group of slender cylindrical members representing flexible plantation has been carried out in a laboratory open channel. The model stem groups comprised of individual members of different sizes and concentrations in staggered configuration. The sizes and concentrations were chosen in such a way that they would fall into the practical ranges of vegetations in coastal forestry. The results indicate that the flow resistance varies with stem concentration, stem diameter and elastic properties of the individual members and the flow velocity. Based on the results, the Darcy friction factor, f, for various flow and vegetative parameters was derived. A new empirical equation is proposed for evaluating f for partially submerged vegetation in staggered configuration for a wide range of depths of flow in relation to un-deflected plant heights. It is expected that the f thus determined will be useful in modelling the shallow flows using shallow water equations.     

A simple geometric model of sedimentary rock to connect transfer and acoustic properties

A simple rock model is presented which reproduces the measured hydraulic and electric transport properties of sedimentary rocks and connects these properties with each other, as well as with the acoustic propagation velocities and elastic moduli. The model has four geometric parameters (average coordination number Z of the pores, average pore radius r, average distance between nearest pores d, and average throat radius δ) which can be directly determined from the measured porosity Φ, hydraulic permeability k, and cementation exponent m of the rock via simple analytic expressions. Inversion examples are presented for published sandstone data, and for cores taken from Saudi Arabian, Upper Jurassic and Permian carbonate reservoirs. For sandstone, the inversion works perfectly; for carbonates, the derived rock model shows order-of-magnitude agreement with the structure seen in thin sections. Inverting the equations, we express the transfer properties Φ, k, and m as functions of r, d, δ, and Z. Formulae are derived for the bulk density D _b, formation factor F, and P-wave velocity in terms of the proposed geometrical parameters.     

Activity–composition relations for phases in petrological calculations: an asymmetric multicomponent formulation

For petrological calculations, including geothermobarometry and the calculation of phase diagrams (for example, P–T petrogenetic grids and pseudosections), it is necessary to be able to express the activity–composition (a–x) relations of minerals, melt and fluid in multicomponent systems. Although the symmetric formalism—a macroscopic regular model approach to a–x relations—is an easy-to-formulate, general way of doing this, the energetic relationships are a symmetric function of composition. We allow asymmetric energetics to be accommodated via a simple extension to the symmetric formalism which turns it into a macroscopic van Laar formulation. We term this the asymmetric formalism (ASF). In the symmetric formalism, the a–x relations are specified by an interaction energy for each of the constituent binaries amongst the independent set of end members used to represent the phase. In the asymmetric formalism, there is additionally a "size parameter" for each of the end members in the independent set, with size parameter differences between end members accounting for asymmetry. In the case of fluid mixtures, for example, H₂O–CO₂, the volumes of the end members as a function of pressure and temperature serve as the size parameters, providing an excellent fit to the a–x relations. In the case of minerals and silicate liquid, the size parameters are empirical parameters to be determined along with the interaction energies as part of the calibration of the a–x relations. In this way, we determine the a–x relations for feldspars in the systems KAlSi₃O₈–NaAlSi₃O₈ and KAlSi₃O₈–NaAlSi₃O₈–CaAl₂Si₂O₈, for carbonates in the system CaCO₃–MgCO₃, for melt in the melting relationships involving forsterite, protoenstatite and cristobalite in the system Mg₂SiO₄–SiO₂, as well as for fluids in the system H₂O–CO₂. In each case the a–x relations allow the corresponding, experimentally determined phase diagrams to be reproduced faithfully. The asymmetric formalism provides a powerful and flexible way of handling a–x relations of complex phases in multicomponent systems for petrological calculations.     

The molar volume of FeO–MgO–Fe2O3–Cr2O3–Al2O3–TiO2 spinels

We define and calibrate a new model of molar volume as a function of pressure, temperature, ordering state, and composition for spinels in the supersystem (Mg, Fe²⁺)(Al, Cr, Fe³⁺)₂O₄ ? (Mg, Fe²⁺)₂TiO₄. We use 832 X-ray and neutron diffraction measurements performed on spinels at ambient and in situ high-P, T conditions to calibrate end-member equations of state and an excess volume model for this system. The effect on molar volume of cation ordering over the octahedral and tetrahedral sites is captured with linear dependence on Mg²⁺, Al³⁺, and Fe³⁺ site occupancy terms. We allow standard-state volumes and coefficients of thermal expansion of the end members to vary within their uncertainties during extraction of the mixing properties, in order to achieve the best fit. Published equations of state of the various spinel end members are analyzed to obtain optimal values of the bulk modulus and its pressure derivative, for each explicit end member. For any spinel composition in the supersystem, the model molar volume is obtained by adding excess volume and cation order-dependent terms to a linear combination of the five end-member volumes, estimated at pressure and temperature using the high-T Vinet equation of state. The preferred model has a total of 9 excess volume and order-dependent parameters and fits nearly all experiments to within 0.02 J/bar/mol, or better than 0.5 % in volume. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure.     

High-temperature thermal expansion and elasticity of calcium-rich garnets

We present new high temperature elasticity data on two grossular garnet specimens. One specimen is single-crystal, of nearly endmember grossular, the other is polycrystalline with about 22% molar andradite. Our data extend the high temperature regime for which any garnet elasticity data are available from 1000 to 1350 K and the compositional range of temperature data to near endmember grossular. We also present new data on the thermal expansivity of calcium-rich garnet. We find virtually no discernable differences in the temperatureT derivatives at ambient conditions of the isotropic bulkK _S and shearμ moduli when comparing our results between these two specimens. These calcium-rich garnets have the lowest values of ¦(?K _S /?T) _P ¦ = (1.47,1.49) x 10^-2GPa/K, and among the highest values of ¦(?μ/?T) _P ¦ = 1.25 x 10^-2GPa/K, when compared with other garnets. Small, but measurable, nonlinear temperature dependences of most of the elastic moduli are observed. Several dimensionless parameters are computed with the new data and used to illustrate the effects of different assumptions on elastic equations of state extra-polated to high temperatures. We discuss how dimensionless parameters and other systematic considerations can be useful in estimating the temperature dependence of some properties of garnet phases for which temperature data are not yet available. While we believe it is premature to quantitatively predict the temperature variation ofK _S andμ for majorite garnets, our results have bearing on the amount of diopside required to explain the shear velocity gradients in Earth's transition zone.     

High temperature elasticity of rutile-structure MgF2

The elastic moduli of single-crystal MgF₂ have been determined by the ultrasonic pulse superposition technique as a function of temperature from T=298?650° K. These new data are consistent with those obtained by other ultrasonic pulse techniques at and below room temperature and agree favourably with polycrystalline data above room temperature. The elastic moduli (c) are represented by quadratic functions in T over the experimental temperature range with the curvature in the same sense for all the moduli. For the rutile-structure fluorides and oxides, evaluation of the temperature derivatives of the elastic moduli at constant volume indicates that the dominant temperature effect is extrinsic for (?K _S /?T) _P and intrinsic for (?μ/?T) _P , where K _S and μ are the isotropic bulk and shear moduli, respectively. There appears to be no simple relationship between (?c/?T) _P and crystallographic parameters for the rutile structure, and |(?c/?T) _P | for the fluorides is in general very much lower than the corresponding |(?c/?T) _P | for the oxides. For the pair of compounds MgF₂-TiO₂, there is no evident analogue relationship for high-temperature elastic properties.     

Atomistic computer modeling of the local structure and mixing properties of a grossular-uvarovite solid solution

An original methodology for the atomistic computer modeling of solid solutions was applied for the study of the mixing properties and local structure of the grossular-uvarovite, i.e., Ca₃Al₂[SiO₄]₃ Ca₃Cr₂][SiO₄]₃, garnet series. The parameters of the interatomic potentials for end members of this series were optimized using experimental data on their structural, elastic, and thermodynamic characteristics. The optimized model of the potentials allowed us to describe the elastic, structural, and thermodynamic characteristics of grossular and uvarovite and estimate the energy of point defects in these crystal structures. Calculations of the mixing properties and local structure for seven different compositions of the solid solution were carried out on a “Chebyshev” supercomputer (Moscow State University) in a 2 × 2 × 4 supercell of the garnet-type structure containing 2560 atoms. Mixing properties, such as the enthalpy of mixing, parameters of interaction, excess mixing volume, deviation of bulk modulus from additivity, and the vibrational and configuration contribution to the entropy of mixing, were determined. This allowed us to estimate the stability field for the grossular-uvarovite solid solution. Histograms of the interatomic distances M-O (M = Ca, Al, Cr, Si) and O-O in supercells were plotted and the parameters of relaxation and changes of the CrO₆ and AlO₆ octahedron volumes were estimated. The data of the simulation are quite consistent with the experimental data on this system and supplement it significantly.     

An improved and extended internally consistent thermodynamic dataset for phases of petrological interest,involving a new equation of state for solids

The thermodynamic properties of 254 end‐members, including 210 mineral end‐members, 18 silicate liquid end‐members and 26 aqueous fluid species are presented in a revised and updated internally consistent thermodynamic data set. The PVT properties of the data set phases are now based on a modified Tait equation of state (EOS) for the solids and the Pitzer & Sterner (1995) equation for gaseous components. Thermal expansion and compressibility are linked within the modified Tait EOS (TEOS) by a thermal pressure formulation using an Einstein temperature to model the temperature dependence of both the thermal expansion and bulk modulus in a consistent way. The new EOS has led to improved fitting of the phase equilibrium experiments. Many new end‐members have been added, including several deep mantle phases and, for the first time, sulphur‐bearing minerals. Silicate liquid end‐members are in good agreement with both phase equilibrium experiments and measured heat of melting. The new dataset considerably enhances the capabilities for thermodynamic calculation on rocks, melts and aqueous fluids under crustal to deep mantle conditions. Implementations are already available in thermocalc to take advantage of the new data set and its methodologies, as illustrated by example calculations on sapphirine‐bearing equilibria, sulphur‐bearing equilibria and calculations to 300 kbar and 2000 °C to extend to lower mantle conditions.     

Monitoring in situ stress/strain behaviour during plastic yielding in polymineralic rocks using neutron diffraction

Attempts to use rock deformation experiments to examine the elastic and plastic behaviour of polymineralic rocks are hampered by the fact that usually only whole sample properties can be monitored as opposed to the separate contribution of each phase. To circumvent this difficulty, room-temperature, uniaxial compression experiments were performed in a neutron beam-line on a suite of calcite + halite samples with different phase volume proportions. By collecting diffraction data during loading, the elastic strain and hence stress in each phase was determined as a function of load to bulk strains of 1–2%. In all cases, the calcite behaved elastically while the halite underwent plastic yielding. During the fully elastic part of the deformation, the composite elastic properties and the within-phase stresses are well-described both by recent shear lag models and by analyses based on Eshelby's solution for the elastic field around an ellipsoidal inclusion in a homogeneous medium. After the onset of yielding, the halite in situ stress/total strain curve may be reconstructed using the rule of mixtures. At calcite contents of greater than 30%, the in situ halite response may be significantly weaker or stronger than that obtained at lesser calcite contents. The results highlight the potential that such techniques offer for developing an explicitly experimental approach for determining the influence of microstructural variables on the mechanical properties of polymineralic rocks.     

Lattice dynamics and Raman spectroscopy of protoenstatite Mg2Si2O6

Enstatites (Mg₂Si₂O₆) are important rock forming silicates of the pyroxene group whose structures are characterised by double MgO₆ octahedral bands and single silicate chains. Orthoenstatite transforms to protoenstatite above 1273 K with a doubling of the a axis and a rearrangement of the silicate chains with respect to the Mg₂₊ ions. Lattice dynamical calculations based on a rigid-ion model in the quasi-harmonic approximation provide theoretical estimates of elastic constants, long wavelength phonon modes, phonon dispersion relations, total and partial density of states and inelastic neutron scattering cross-sections of protoenstatite. The computed elastic constants are in good agreement with experimental data. The computed density of states of a chain silicate such as protoenstatite is distinct from that of olivines (forsterite, Mg₂SiO₄ and fayalite, Fe₂-SiO₄) with isolated silicate tetrahedra. The band gaps in the density of states in forsterite are largely due to the separation in the frequency ranges of the external and internal vibrations of the isolated silicate group, whereas in protoenstatite these gaps are filled by the vibrations of the bridging oxygens of the silicate chain. The computed density of states is used to calculate the specific heat, the mean square atomic displacements and temperature factors. Validity of these calculations are supported by Raman scattering measurements. Polarised and unpolarised Raman spectra are obtained from small single crystals of protoenstatite (Li,Sc)_0.6Mg_1.4Si₂O₆ stable at room temperature using the 488 nm or 514.5 nm lines of an Ar⁺ ion laser and a micro-Raman spectrometer with backscattering geometry. The Raman spectra were analysed and interpreted based on the lattice dynamical model. The experimental Raman frequencies and mode assignments (based on polarised single crystal spectra) are in good agreement with those obtained from lattice dynamical calculations.     

Elasticity of calcite: thermal evolution

The elastic properties of calcite have been determined by Brillouin spectroscopy for temperatures up to 600 °C. The results reveal that the variations of the aggregate bulk (K _VRH) and shear (G _VRH) moduli of calcite with respect to temperature can be approximately expressed as follows: $$\begin{aligned} K_{{{\text{VRH}}}} ({\text{GPa}}) & = 79.57-0.0230\;T\, (T\;{\text{in}}\;^{^\circ } {\text{C}}) \\G_{{{\text{VRH}}}} ({\text{GPa}}) & = 32.23 - 0.0097\;T. \\\end{aligned}$$ This indicates a nearly constant Poisson’s ratio (0.322) for calcite from 22 to 600 °C. A further analysis shows that the compressibility along the c axis (β _||) and that perpendicular to the c axis have comparable contributions to the volume compressibility of calcite, although the contribution of β _|| decreases with an increase in the temperature.     

Structural transformations of quartz and berlinite AlPO4 at high pressure and room temperature: a transmission electron microscopy study

Single crystals of α-quartz and α-berlinite AlPO₄ have been compressed at high pressure and room temperature in a diamond anvil cell (DAC). The pressure-induced microstructures have been studied on recovered specimens using transmission electron microscopy. As previously reported, quartz is shown to exhibit an amorphous transition at high pressure (≈30 GPa). Under the markedly non-hydrostatic conditions of the present study, a wide mixed-phase regime in which amorphous lamellae form within the crystalline matrix is encountered at lower values of the mean stress. The amorphous lamellae are interpreted as shear lamellae. The formation of these shear lamellae as well as their habit planes are described by the evolution with pressure of shear moduli μ as computed in anisotropic elasticity. Our calculations also show instabilities at higher pressure of the elastic moduli (i.e. of the α-quartz structure) which are related to the amorphous transition. Berlinite exhibits a more ductile behavior with simultaneous dislocation activity and shear on amorphous lamellae which become pervasive at high pressure (≈10 GPa). These amorphous lamellae of berlinite do not revert to crystal when pressure is released.     

A thermodynamic model for Ca–Na clinoamphiboles in Na2O–CaO–FeO–MgO–Al2O3–SiO2–H2O–O for petrological calculations

A calibration is presented for an activity–composition model for amphiboles in the system Na₂O–CaO–FeO–MgO–Al₂O₃–SiO₂–H₂O–O (NCFMASHO), formulated in terms of an independent set of six end‐members: tremolite, tschermakite, pargasite, glaucophane, ferroactinolite and ferritschermakite. The model uses mixing‐on‐sites for the ideal‐mixing activities, and for the activity coefficients, a macroscopic multicomponent van Laar model. This formulation involves 15 pairwise interaction energies and six asymmetry parameters. Calibration of the model is based on the geometrical constraints imposed by the size and shape of amphibole solvi inherent in a data set of 71 coexisting amphibole pairs from rocks, formed over 400–600 °C and 2–18 kbar. The model parameters are calibrated by combining these geometric constraints with qualitative consideration of parameter relationships, given that the data are insufficient to allow all the model parameters to be determined from a regression of the data. Use of coexisting amphiboles means that amphibole activity–composition relationships are calibrated independently of the thermodynamic properties of the end‐members. For practical applications, in geothermobarometry and the calculation of phase diagrams, the amphibole activity–composition relationships are placed in the context of the stability of other minerals by evaluating the properties of the end‐members in the independent set that are in internally consistent data sets. This has been performed using an extended natural data set for hornblende–garnet–plagioclase–quartz, giving the small adjustments necessary to the enthalpies of formation of tschermakite, pargasite and glaucophane for working with the Holland and Powell data set.     

Prediction of settlement trough induced by tunneling in cohesive ground

Surface settlements of soil due to tunneling are caused by stress relief and subsidence due to movement of support by excavation. There are significant discrepancies between empirical solutions to predict surface settlement trough because of different interpretations and database collection by different authors. In this paper, the shape of settlement trough caused by tunneling in cohesive ground is investigated by different approaches, namely analytical solutions, empirical solutions, and numerical solutions by the finite element method. The width of settlement trough was obtained by the finite element method through establishing the change in the slope of the computed settlement profile. The finite element elastic-plastic analysis gives better predictions than the linear elastic model with satisfactory estimate for the displacement magnitude and slightly overestimated width of the surface settlement trough. The finite element method overpredicted the settlement trough width i compared with the results of Peck for soft and stiff clay, but there is an excellent agreement with Rankin’s estimation. The results show that there is a good agreement between the complex variable analysis for Z/D = 1.5, while using Z/D = 2 and 3, the curve diverges in the region faraway from the center of the tunnel.     

Thermodynamic properties of CaCO3 calcite and aragonite: A quasi-harmonic calculation

A quasi-harmonic model has been used to simulate the thermodynamic behaviour of the CaCO₃ polymorphs, by equilibrating their crystal structures as a function of temperature so as to balance the sum of inner static and thermal pressures against the applied external pressure. The vibrational frequencies and elastic properties needed have been computed using interatomic potentials based on two-body Born-type functions, with O-C-O angular terms to account for covalency inside the CO₃ molecular ion. A good agreement with experimental data is generally shown by simulated heat capacity and entropy, while the thermal expansion coefficient seems to be more difficult to reproduce. The results obtained for aragonite are less satisfactory than those of calcite, but they are improved by using a potential specifically optimized on properties of that phase itself.     

Reappraisal of Fresnosaurus drescheri (Plesiosauria; Elasmosauridae) from the Maastrichtian Moreno Formation,California, USA

The elasmosaurid Fresnosaurus drescheri, Welles from the contact between the Tierra Loma/Marca members of the Moreno Formation (Maastrichtian), California, USA is reviewed. Most of the features included in Welles's original diagnosis are considered related only to the juvenile ontogenetic stage of the holotype and only specimen. The new diagnosis is based on diagnostic characters of the ilia, including long rectangular shaped sacral facets located in the dorsal part of the shaft, two gentle knobs in the shafts and unexpanded dorsal end. Additional material from the Moreno Formation (numbered under the same number as the F. drescheri holotype but not mentioned by Welles and therefore considered part of a different specimen) are described for the first time. The latter are referred to the aristonectine, being the first evidence of aristonectines from the North Hemisphere.     

X-ray powder data for Mg-Al-celadonite (leucophyllite) from Barcza,Poland

A natural 1 M-celadonite from Barcza, Poland, approximates closely the Mg-Al end member of the celadonite group. The lattice constants of this phase are $$a_0 = 5.208 \pm 0.005{\AA},b_0 = 9.006 \pm 0.003{\AA}, c_0 = 10.071 \pm 0.004{\AA}, \beta = 1$$ . A comparison with other end members indicates that within this group of minerals the substitution Mg+Si=2 Al diminishes c ₀, whereas the incorporation of Fe⁺³ instead of octahedral Al will increase both b ₀ and c ₀ sin β.