Measurements of thermal conductivity and specific heat in volcanogenic rocks

A laboratory installation has been developed together with a technique for determining thermo-physical properties (thermal conductivity and specific heat) in cylindrical rock specimens. The technique is based on iTOUGH2-EOS3 inversion modeling using temperature measurements inside specimens as a result of their short-term heating and subsequent return to the initial temperature. We estimated the thermal conductivity and specific heat for a collection of volcanogenic petrotypes that reflect the rocks that compose the Rogozhnikovskii volcanogenic oil reservoir (29 specimens). The average thermal conductivity of the dry rocks is 1.47 W/m °C and the average specific heat is 754 kJ/kg °C; the reproducibility of this estimation is 2.2% for thermal conductivity and 0.7% for specific heat.     

Inverse magnetic fabric in carbonate-bearing rocks

The observation of a magnetic susceptibility ellipsoid whose maximum axis corresponds to the minimum axis of petrofabric (pole of bedding or schistosity) is referred to as an inverse magnetic fabric. The investigation of the magnetic properties of some ferroan carbonate monocrystals and paramagnetic limestones demonstrates thatc-axis preferred orientation of paramagnetic carbonates results in a maximum susceptibility parallel to the flattening direction.Inverse magnetic fabrics due to magnetite are also encountered in weakly deformed limestones. A mineralogical model based on the property of single-domain grains to have a zero susceptibility parallel to their long axis is proposed. However, more complex cases are also encountered.     

Dielectric anisotropy and fabric of rocks

Summary Measurements have been made of the dieletric anisotropies of a number of rocks for which magnetic anisotropy data have been obtained previously. The purpose was to examine the possible usefulness of dielectric anisotropy as a physical property indicative of rock fabrics. Its advantage over the magnetic method is that it measures an average alignment of crystals of the dominant minerals, whereas magnetic anisotropy is due only to the ferromagnetic grains. Disadvantages are an extreme sensitivity to specimen shape and difficulty in distinguishing the several types of alignment which can give rise to dielectric anisotropy. In a number of strongly foliated rocks the axes of dielectric anisotropy were found to coincide with the axes of magnetic anisotropy. Specimens from a magnesian-pyroxene rich layer in a Tasmanian dolerite sill and from the olivine rich layer of the Palisades dolerite sill, New York, were found to have no systematic anisotropy. The pyroxenes in the Tasmanian dolerite are elongated crystals (about 2: 1) so that the dielectric measurements show that they do not have a preferred horizontal alignment and therefore have probably not settled as individual crystals. Most of the olivines in the Palisades dolerite are more nearly equidimensional so that the absence of measurable anisotropy in this rock is less conclusive evidence against crystal settling.     

Surface conductivity in rocks: a review

Electrical properties of rocks depend on composition (i.e. bulk properties of the constituents), micro structure (i.e. geometrical arrangement of the constituents) and interfacial effects. We consider here a rock as a three component system — grains, pores, and interfaces — in order to account for the observed behaviour. We review first the main results relative to DC. conductivity. Surface conductivity effects show up clearly in the case of shaly formations or at low salinities. Although Archies' law (1942) and Waxman and Smits model (1968) are widely used, a more physically based model is that of Johnson and Sen (1988). We review also the variable frequency conductivity (complex conductivity) data and models. The important effect in that case is the enhancement of the dielectric constant at low frequencies (Knight and Nur, 1987) which can be interpreted as a geometrical effect although electrochemical interactions may also play an important role at low frequencies, depending on the rock type.     

Relation of fracture resistance to fabric for granitic rocks

Double-torsion specimens of two granitic rocks were prepared in several directions with reference to microcracks fabric. Even for the same rock and at the same stress levels, the observed crack velocities in two granitic rocks were dependent on both the propagation direction and the opening direction. The maximum difference by several orders of magnitude was found for both rocks. The highest crack velocity was observed when the subcritical crack was parallel to most of the preexisting cracks. The maximum critical stress intensity factor was about twice as high as the minimum one in different directions. An analysis for a thin plate having anisotropic elasticity under torsional load showed that the observed difference in the crack velocity and the critical stress intensity factor was not an error due to conventional equations derived on the assumption of isotropic elasticity but the true material's property. As the preferred orientation of microcracks has been pointed out for many granitic rocks, we can conclude that the anisotropic nature of the fracture resistance of the two granitic rocks used in this study was not exceptional. A region of a transport-limited velocity was not found for rocks, even at the velocity of 10^–2 m/s, that is almost equal to the theoretical limit of the stress corrosion cracking.     

Modelling the stress-strain behaviour of saturated rocks undergoing triaxial deformation using complex electrical conductivity measurements

Measurement of complex electrical conductivity as a function of frequency is an extremely sensitive probe for changes in pore and crack volume, crack connectivity, and crack surface topography. Such measurements have been made as a function of pore fluid chemistry, hydrostatic confining pressure, as well as uniaxial and triaxial deformation. This paper will; (1) describe the effects of triaxial deformation on the complex electrical conductivity of saturated porous rocks, (2) use the electrical data to model the mechanical stress-strain behaviour, and (3) compare the modelled behaviour with the stress-strain behaviour measured during the deformation. Experimental conductivity data tracks how the rock undergoes compaction with progressive loss of crack volume, followed by dilatation due to new crack formation, growth of existing cracks, crack interlinkage, and finally failure, as axial strain is increased. We have used the complex electrical data to produce a direction-sensitive (anisotropic) crack damage parameter, and used it to calculate the effective Young's modulus by employing the models of Walsh and Bruner. Comparison of the synthetic stress-strain curves so produced, with the experimentally derived stress-strain curves shows good agreement, particularly for undrained tests. This modelling is an improvement on similar curves produced using isotropic crack damage parameters derived from acoustic emission data. The improvement is likely to be due to the directional sensitivity of the electrical conductivity measurement, and its ability to discriminate between the formation of isolated cracks, and those cracks that contribute to the inter-connected crack space i.e. those cracks upon which transport properties of the rock such as electrical conductivity, and mechanical properties depend most critically during triaxial deformation.     

Electrical conductivity of ultramafic rocks to 1820 kelvin

Electrical conductivity, σ, of six ultramafic rocks (garnet-bearing peridotites and an eclogite) has been investigated in the temperature range 670–1820 K under known environment. Between 670 and ～1320 K σ increases with 1/T monotonically, first slowly, by 1–1.5 orders of magnitude. Above 1320 K σ increases sharply; an increase of 3–4 orders of magnitude is observed between 1320 and 1670 K. In the same temperature range the σ values for all the six rocks fall within 1.5 orders of magnitude, the lowest conductivity being for a spinel lherzolite. The range of σ values is narrowed at higher temperatures. The differences in σ values above 1470 K may be explained on the basis of varying degrees of partial melting in the rocks. Over the entire range of temperature, the σ values for the ultramafic rocks are lower than those reported for basalts but higher (by 1–2 orders of magnitude) than those for single-crystal olivines.     

Electrical conductivity of rocks in the heating and cooling cycle

Summary The values of the electrical conductivity, recorded during the heating and cooling cycle, of eclogites and basalts are compared. The observed difference in the values is explained by reversible and irreversible changes which take place in the samples.     

Acoustic and petrophysical relationships in low-shale sandstone reservoir rocks

This paper describes the measurements of the acoustic and petrophysical properties of two suites of low‐shale sandstone samples from North Sea hydrocarbon reservoirs, under simulated reservoir conditions. The acoustic velocities and quality factors of the samples, saturated with different pore fluids (brine, dead oil and kerosene), were measured at a frequency of about 0.8 MHz and over a range of pressures from 5 MPa to 40 MPa. The compressional‐wave velocity is strongly correlated with the shear‐wave velocity in this suite of rocks. The ratio V_P/V_S varies significantly with change of both pore‐fluid type and differential pressure, confirming the usefulness of this parameter for seismic monitoring of producing reservoirs. The results of quality factor measurements were compared with predictions from Biot‐flow and squirt‐flow loss mechanisms. The results suggested that the dominating loss in these samples is due to squirt‐flow of fluid between the pores of various geometries. The contribution of the Biot‐flow loss mechanism to the total loss is negligible. The compressional‐wave quality factor was shown to be inversely correlated with rock permeability, suggesting the possibility of using attenuation as a permeability indicator tool in low‐shale, high‐porosity sandstone reservoirs.     

Modelling the relationship between magnetic fabric and strain in polymineralic rocks

We present a model that is applicable to the relatively frequent case of rocks in which the magnetic fabric is dominated by uniaxial paramagnetic minerals, and in which the deformation (pure shear) corresponds to the March-Fernandez model. Borradaile et al.'s procedure for the isolation of the magnetic fabric of monocrystals of anisotropic components allows us to obtain the magnetic properties equivalent to those of all the component minerals if they should be artificially aligned. In the case of real component minerals with similar shape parameters, χ (dependent on dimension ratio), these properties will correspond to those of a theoretical equivalent mineral. Therefore, finite strain and orientation tensors may be determined from magnetic fabric measurements of such polymineralic rocks.     

Diagrammatic theory of effective hydraulic conductivity

This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit.     

Diagrammatic theory of effective hydraulic conductivity

This work presents a stochastic diagrammatic theory for the calculation of the effective hydraulic conductivity of heterogeneous media. The theory is based on the mean-flux series expansion of a log-normal hydraulic conductivity medium in terms of diagrammatic representations and leads to certain general results for the effective hydraulic conductivity of three-dimensional media. A selective summation technique is used to improve low-order perturbation analysis by evaluating an infinite set of diagrammatic terms with a specific topological structure that dominates the perturbation series. For stochastically isotropic media the selective summation yeilds the anticipated exponential expression for the effective hydraulic conductivity. This expression is extended to stochastically anisotropic media. It is also shown that in the case of non homogeneous media the uniform effective hydraulic conductivity is replaced by a non-local tensor kernel, for which general diagrammatic expressions are obtained. The non-local kernel leads to the standard exponential behavior for the effective hydraulic conductivity at the homogeneous limit.     

Interpretation of magnetic resonance soundings in rocks with high electrical conductivity

Magnetic resonance sounding (MRS) is an electromagnetic method designed for groundwater investigations. MRS can be applied not only for studying fresh-water aquifers, but also in areas where intrusion of saline water is rendering the subsurface electrically conductive. In the presence of rocks with a high electrical-conductivity attenuation and a phase shift of the MRS signal may influence the efficiency of the MRS method. We investigated the performance of MRS for allowing us to propose a procedure for interpreting MRS data under these conditions. For numerical modeling, we considered a subsurface with a resistivity between 0.5 and 10 Ω m. The results show that the depth of investigation with MRS depends upon the electrical conductivity of groundwater and surrounding rocks, on the depth of the saline water layer, and on the amount of fresh water above the saline water. For interpreting MRS measurements, the electrical conductivity of the subsurface is routinely measured with an electrical or electromagnetic method. However, due to the equivalence problem, the result obtained with these methods may be not unique. Hence, we investigated the influence of the uncertainty in conductivity distribution provided by transient electromagnetic measurements (TEM) on MRS results. It was found that the uncertainty in TEM results has an insignificant effect on MRS.     

Electrical conductivity of some rocks from the Indian subcontinent

Summary Results on electrical conductivity, chemical analysis and age of the rock samples from the Indian Subcontinent are presented. The old Precambrian Indian rocks tend to be less conductive than characteristic rocks of crustal and upper mantle structures.

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Automation of measuring the temperature dependence of electrical conductivity of rocks using a PMD-85-1 microcomputer

Summary The new for measuring the electrical conductivity of rocks and minerals developed in the Geophysical Institute is briefly discussed. Unlike the earlier method it uses a PMD-85-1 microcomputer and related equipment (all of CMEA production), which enable the automatic control of the experiment, collection, evaluation, graphic display and storage of the results. This method is verified by measuring the electrical conductivities of granitoids.

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Numerical simulation of divided-bar thermal conductivity measurements

Summary A three-dimensional numerical model of the divided-bar thermal conductivity measuring device that can include both solid and fluid sample portions has been developed. The model has been employed to investigate the effects of porosity in divided-bar measurements and the effects of the distribution of solid sample and contained fluids in porous material on the thermal conductivity calculated from the bar temperature measurements. The results show that the positions of the temperature sensors and thus the nature of the vertical column between the temperature measuring points is of prime importance, and that the sizes of the solid and fluid portions of the sample affect the sample conductivity estimates. The divided bar measures the thermal conductivity parallel to the axis of the bar. Thermal conductivity variations in the radial direction have little effect on the calculated conductivity. Whether or not the sides of the bar are insulated strongly affects the calculated conductivity.Presented at the International Meeting on Terrestrial Heat Flow and the Structure of Lithosphere, Bechyn Castle, Czech Republic, September 2 – 7, 1991.     

Some aspects of stochastic reservoir theory

This paper examines the problem of the reservoir size-reliability-draft relationship. It compares the mathematicians' analytical efforts with the simulation techniques of the engineers and hydrologists, and suggests that the two methods should complement each other. It examines the various models for generating gamma Markov sequences and suggests a new one which is analytically more suitable to the problem in question. An alternative to the traditional formulation of the problem in terms of probability of failure is suggested, and a method based on random-walk techniques is employed to give close approximations. Finally, the effects of various parameters of the inflow distribution on the reservoir size to give the same reliability for a constant draft ratio are discussed.     

Electrical conductivity of igneous rocks: Composition and temperature relations

The conductivity of four igneous rocks with, 49, 65, 77, and 84% SiO₂ was measured as a function of temperature in the interval from 20° to 1280°C; measurements were made in a vacuum of 10^?3 torr. No simple relationships were found between conductivity and SiO₂ content or versus major element groupings such as Na₂O=K₂O=CaO and TiO₂=Cr₂O₃=Al₂O₃=Fe₂O₃=FeO. An analytical expression was obtained between conductivity and the albite-quartz ratio, valid for temperatures between 300° and 1200°C. It was necessary to compute the CIPW norm in order to obtain the albite and quartz percentages. The onset of melting apparently occurred between 600° and 700°C. Petrography performed on two samples after cooling showed 70 and 85% partial melting. Three conduction regions were identified: 1) below 300°C, 2) between 300°C and 600°C, and 3) above 600°C. Different activation energies obtained for the heating and cooling intervals confirm that the sample undergoes textural changes in the heating-cooling cycle. Activation energy increments of 0.1 and 0.2 eV per decade of albite-quartz ratio were obtained.     

Anisotropic effective conductivity in fractured rocks by explicit effective medium methods

In this work, we assess the use of explicit methods for estimating the effective conductivity of anisotropic fractured media. Explicit methods are faster and simpler to use than implicit methods but may have a more limited range of validity. Five explicit methods are considered: the Maxwell approximation, the T‐matrix method, the symmetric and asymmetric weakly self‐consistent methods, and the weakly differential method, where the two latter methods are novelly constructed in this paper. For each method, we develop simplified expressions applicable to flat spheroidal “penny‐shaped” inclusions. The simplified expressions are accurate to the first order in the ratio of fracture thickness to fracture diameter. Our analysis shows that the conductivity predictions of the methods fall within known upper and lower bounds, except for the T‐matrix method at high fracture densities and the symmetric weakly self‐consistent method when applied to very thin fractures. Comparisons with numerical results show that all the methods give reliable estimates for small fracture densities. For high fracture densities, the weakly differential method is the most accurate if the fracture geometry is non‐percolating or the fracture/matrix conductivity contrast is small. For percolating conductive fracture networks, we have developed a scaling relation that can be applied to the weakly self‐consistent methods to give conductivity estimates that are close to the results from numerical simulations.     

Propagation of drought through groundwater—a new approach using linear reservoir theory

The effect of drought on groundwater heads and discharge is often complex and poorly understood. Therefore the propagation of a drought from groundwater recharge to discharge and the influence of aquifer characteristics on the propagation was analysed by tracking a drought in recharge through a linear reservoir. The recharge was defined as a sinusoid function with a period of 1 year. The decrease in recharge owing to drought was simulated by multiplying the recharge during 1 year with a drought fraction between 0 and 1, which represents a decrease in the recharge of 100 to 0%, respectively. The droughts were identified using the threshold level approach, with a threshold that is constant in time. For this case analytical formulations were derived, which express the drought duration and deficit in the groundwater discharge in terms of the decrease in recharge, the reservoir coefficient that characterizes aquifer properties and the height of the threshold level. The results showed that the delay in the groundwater system caused a shift of the main part of the decrease in recharge from the high‐flow to the low‐flow period. This resulted in an increase in drought deficit for discharge compared with the drought deficit for recharge. Also the development of multiyear droughts caused an increase in drought deficit. The attenuation in the groundwater system caused a decrease in drought deficit. In most cases the net effect of these processes was an increase of drought deficit as a result of the propagation through groundwater. Only for small droughts the deficit decreased from recharge to discharge. The amount of increase or decrease depends on the reservoir coefficient and the severity of the drought. Under most conditions a maximum in the drought deficit occurred for a reservoir coefficient of around 200 days. Copyright © 2003 John Wiley & Sons, Ltd.