Influence of the sedimentation regime and compaction of sediments under subaqueous conditions on the accumulation of gas hydrates in the zone of their stability

Formation of gas hydrate that form in a porous medium of sediments from gas dissolved in a gassaturated fluid is analyzed for different regimes of fluid movement determined by the permeability of sediments, their physical properties, and their accumulation rate. In the framework of the presented general mathematical model of viscoelastic compaction of accumulated sediments, characteristic porosity decrease patterns, fluid movement, and gas hydrate accumulation are described by a nonlinear system of eight partial differential equations. The regime of compaction and fluid movement is determined by the values of dimensionaless similarity numbers defined as nonlinear combinations of physical and dynamic parameters of the process studied. The results of model calculations with the use of representative physical and hydrodynamic parameters of the system provided constraints on the dependence of the hydrate formation rate on the similarity numbers of the problem. It is shown that the rate and volume of hydrate accumulation are determined by the similarity numbers and dimensionless time.     

Numerical simulation of accumulation of gas hydrates during sedimentation and compaction of sediments under subaqueous conditions

The mutual influence of compaction of depositing sediments and formation of gas hydrates in a porous medium is examined. Within the framework of the general mathematical model developed in this study, these interrelated processes are described by a nonlinear system of eight partial differential equations and are analyzed using numerical simulation in terms of the model including compaction of depositing sediments, movement of pore fluids, and formation of gas hydrates from dissolved methane accumulated during sedimentation. On the basis of model examples calculated with the use of representative parameters of the system, it is shown that the hydrate formation rate depends on the sedimentation rate and thermal conditions. Gas hydrate formation is shown to influence the pore fluid velocity in the near-surface zone of sediments.     

The blanketing effect of sediments in basins formed by extension: a numerical model. Application to the Gulf of Lion and Viking graben

A numerical finite difference model is employed to reconstruct the time/temperature history of sediments in basins formed by extension, in which crustal thinning by stretching as well as the effects associated with sedimentation and compaction are taken into account. Two extreme cases of basins were investigated to identify the scale of this mechanism: the Gulf of Lion illustrates a case of a young basin, in which the average sedimentation rate is high (620 m/Ma), and the Viking graben in the North Sea offers a case of a basin formed in the Triassic, but where average sedimentation rate is much less (37 m/Ma). In the former, the sediments absorb 30% of the surface heat flow, while in the latter the effect is only 10%.     

对波达波夫和Pride震电波方程组的对比分析

用Biot介质参数说明了波达波夫震电波方程组中弹性动力学 参数的含义，解释了第一类和第二类震电效应的意义，在忽略第一类震电效应条件下将该方 程组与Pride方程组进行比较，说明了二者在描述第二类震电效应方面的异同点. 同时指出 ：波达波夫方程组忽略了流体与固体的耦合质量；方程中的黏性耗散项丢掉了一个孔隙度因 子，依据该方程组计算出的弹性波和转换电场的幅度将偏大；边界条件之一存在错误，会影 响对波在界面上的反射透射规律的描述.     

Scattering and refracting of plane strain wave by a cylindrical inclusion in fluid-saturated soils

The problems involving scattering and refracting of plane strain wave by a cylinder in fluid-saturated soils are studied in this paper. The theoretical solutions for the amplitudes of scattering and refracting are derived on the basis of modified Biot’s theory for two-phase medium in engineering, in which the compressibility of soil grains and the viscous coupling effect between the skeletal frame and the pore fluid are taken into account. Moreover, the amplitude equations of potential function are presented when the fluid-saturated soil cylindrical inclusion is degenerated into cylindrical cavity, rigid cylinder, single phase elastic cylinder and single phase fluid cylinder.     

粘性可压缩流体中的波

本文在小扰动条件下,从粘性可压缩流体的运动方程、状态方程以及连续性方程导出了它的波动方程,从而表明粘性可压缩流体中能够存在有耗损的纵波与横波。文中还针对自由界面、刚性界面、粘性流体内部分界面、粘性流体与弹性固体分界面等,求出了平面波的反射系数和透射系数。     

Low-frequency dilatational wave propagation through fully-saturated poroelastic media

The strong coupling of applied stress and pore fluid pressure, known as poroelasticity, is relevant to a number of applied problems arising in hydrogeology and reservoir engineering. The standard theory of poroelastic behavior in a homogeneous, isotropic, elastic porous medium saturated by a viscous, compressible fluid is due to Biot, who derived a pair of coupled partial differential equations that accurately predict the existence of two independent dilatational (compressional) wave motions, corresponding to in-phase and out-of-phase displacements of the solid and fluid phases, respectively. The Biot equations can be decoupled exactly after Fourier transformation to the frequency domain, but the resulting pair of Helmholtz equations cannot be converted to partial differential equations in the time domain and, therefore, closed-form analytical solutions of these equations in space and time variables cannot be obtained. In this paper we show that the decoupled Helmholtz equations can in fact be transformed to two independent partial differential equations in the time domain if the wave excitation frequency is very small as compared to a critical frequency equal to the kinematic viscosity of the pore fluid divided by the permeability of the porous medium. The partial differential equations found are a propagating wave equation and a dissipative wave equation, for which closed-form solutions are known under a variety of initial and boundary conditions. Numerical calculations indicate that the magnitude of the critical frequency for representative sedimentary materials containing either water or a nonaqueous phase liquid is in the kHz–MHz range, which is generally above the seismic band of frequencies. Therefore, the two partial differential equations obtained should be accurate for modeling elastic wave phenomena in fluid-saturated porous media under typical low-frequency conditions applicable to hydrogeological problems.     

Non-equilibrium compaction and abnormal pore-fluid pressures: effects on rock properties1

Knowledge of pore pressure using seismic data will help in planning the drilling process to control potentially dangerous abnormal pressures. Various physical processes cause anomalous pressures on an underground fluid. Non-equilibrium compaction is a significant process of overpressure generation. This occurs when the sedimentation rate is so rapid that the pore fluids do not have a chance to 'escape' from the pore space.
The model assumes a closed system and that the pore space is filled with water and hydrocarbon in a liquid state. Balancing mass and volume fractions yields the fluid pressure versus time of deposition and depth of burial. Thermal effects are taken into account. The pore pressure, together with the confining pressure, determines the effective pressure which, in turn, determines the bulk moduli of the rock matrix.
We assume a sandstone saturated with hydrocarbons and water, for which calibration of the model with experimental data is possible. The seismic velocities and attenuation factors are computed by using Biot's theory of dynamic poroelasticity and the generalized linear solid. The example shows that the formation can be overpressured or underpressured depending on the properties of the saturating fluid. Wave velocities and quality factors decrease with decreasing differential pressure. The effect is important below approximately 20 MPa. The model is in good agreement with experimental data for Berea sandstone and provides a tool for predicting pore pressure from seismic attributes.     

Magnetostratigraphy of the lower member of the hadar formation (Ethiopia): Evidence for a short normal event in the mammoth subchron

Summary Rock magnetism and magnetostratigraphy of the lower part of the Hadar Formation (Afar, Ethiopia) is presented after analysis of multiple new collection of samples from over 84 horizons. The Hadar Formation is composed of lacustrine, lake margin, fluvial and flood plain sediments and known for important Pliocene vertebrate faunas including Australopithecus afarensis. Hysteresis measurements, thermomagnetic analysis, growth and decay of isothermal remanent magnetisation are used to unravel the complex magnetic mineralogy of the different representative lithologies. Ferrimagnetic minerals of magnetite or titanomagnetite in composition, in the stable pseudo-single domain (PSD) size range are found to be the main carriers of the remanence. In most sites the characteristic remanence was isolated using stepwise thermal demagnetisation. The overall mean direction for about 72 horizons (434 samples) is D=358·6°, I=7° (k=17·9, α₉₅=4°) implying some 14° of inclination shallowing, related to sediment compaction due to the very rapid sedimentation history of the site. Five successive polarity zones (N1-R1-N2-R2-N3) are identified and correlation with the lower Gauss chron of the astronomically calibrated geomagnetic polarity time scale (GPTS) is proposed using the existing⁴⁰Ar/³⁹Ar ages. This implies the existence of a short normal polarity event (N2), identified on six different sites, within the reversed Mammoth subchron, called the Kada-Hadar event. The age calculated for the Kada-Hadar event, using linear interpolation of the dated horizons, assuming a constant rate of sedimentation is 3.246 Ma and its duration is about 8 kyr.     

Taylor columns in horizontally sheared flow

Abstract

Solutions of the steady, inviscid, non-linear equations for the conservation of potential vorticity are presented for linearly sheared geostrophic flow over a right circular cylinder. The indeterminancy introduced by the presence of closed streamline regions is removed by requiring that the steady flow retains above topography a given fraction of that fluid initially present there, assuming the flow to have been started from rest. Those solutions which retain the largest fraction in uniform and negatively sheared streams satisfy the Ingersoll (1969) criterion (that, in the limit of vanishingly small viscosity, closed streamline regions are stagnant) and so are unaffected by Ekman pumping. These flows are set up on the advection time scale. In positively sheared flows the maximum retention solutions do not satisfy the Ingersoll criterion and thus would be slowly spun down on the far longer viscous spin-up time.

For arbitrary isolated topography, both the partial retention and Ingersoll problems are reduced to a one-dimensional non-linear integral equation and the solution of the Ingersoll problem obtained in the limit of strong positive shear. The stagnant region is symmetric about the zero velocity line and extends to infinity in the streamwise direction. Its cross-stream width is proportional to the rotation rate and fractional height occupied by the obstacle and inversely proportional to the strength of the shear, decreasing inversely as the square of distance upstream and downstream.     

吉林向海沼泽湿地典型剖面沉积及年代序列重建

沼泽湿地发育过程中堆积的各类沉积物真实地记录下区域环境演变与沼泽湿地发育过程。本文以无尾河下游漫流区——向海沼泽湿地为研究对象,对其典型沉积剖面结构、沉积物容重、年龄指标、沉积速率等多项沉积记录进行了综合剖析。结果表明：沼泽沉积物的层序关系可以揭示沼泽的形成途径及环境变化;溪边沼泽接受更多的矿质沉积物;1880-1885年该区域出现河道变迁的痕迹;向海沼泽湿地沉积速率与典型的河口三角洲类似,体现了河口尾端湿地的特点;近50年来,向海沼泽湿地沉积速率急剧上升,其原因可能与解放后该流域人类活动增强、植被破坏、水土流失严重有关,在时间上,与流域上游大型露天煤矿开采时段有较好的耦合性。     

Variations in sediment thickness and type along the northern Philippine Sea Plate at the Nankai Trough

Abstract   We documented regional and local variations in basement relief, sediment thickness, and sediment type in the Shikoku Basin, northern Philippine Sea Plate, which is subducting at the Nankai Trough. Seismic reflection data, tied with ocean drilling program drill cores, reveal that variations in the incoming sediment sequences are correlated with basement topography. We mapped the three-dimensional seismic facies distribution and measured representative seismic sequences and units. Trench-parallel seismic profiles show three regional provinces in the Shikoku Basin that are distinguished by the magnitude of basement relief and sediment thickness: Western (<200–400 m basement relief, >600 m sediment thickness), Central (>1500 m relief, ∼2000 m sediments), and Eastern (<600 m relief, ∼1200 m sediments) provinces. The total thickness of sediment in basement lows is as much as six times greater than that over basement highs. Turbidite sedimentation in the Shikoku Basin reflects basement control on deposition, leading to the local presence or absence of turbidite units deposited during the middle Oligocene to the middle Miocene. During the first phase of sedimentation, most basement lows were filled with turbidites, resulting in smooth seafloor morphology that does not reflect basement relief. A second phase of turbidite deposition in the Eastern Province was accompanied by significant amounts of hemipelagic sediments interbedded with turbidite layers compared to the other provinces because of its close proximity to the Izu–Bonin Island Arc. Both regional and local variations in basement topography and sediment thickness/type have caused lateral heterogeneities on the underthrusting plate that will, in turn, influence lateral fluid flow along the Nankai accretionary prism.     

Determining the dilation factor in 4D monitoring of compacting reservoirs by rock-physics models

Hydrocarbon depletion and fluid injection cause compaction and stretching of the reservoir and overburden layers. 4D prestack seismic data can be used to detect these changes because compaction/stretching causes changes in traveltimes and seismic velocities. We show that, by using two different petro‐elastic models at varying effective pressures, a good approximation is to assume that the fractional changes in layer thickness, ΔL/L, and seismic velocity, Δv/v, are related by a linear function of ΔL/L. The slope of this function (the dilation factor, α= (Δv/v)/(ΔL/L) ) is negative and its absolute value generally decreases (shale, low porosity) or increases (sandstone, high porosity) with increasing layer thickness and decreasing effective pressure. The analysis is mainly performed for isotropic deformations. The dilation factor for uniaxial deformations is smaller in absolute value. The dilation factor, which can be calculated from time‐lapse data, can be used to predict reservoir compaction/stretching as a function of depth and surface subsidence.     

Permeability Evolution During Non-linear Viscous Creep of Calcite Rocks

Permeability, storage capacity and volumetric strain were measured in situ during deformation of hot-pressed calcite aggregates containing 10, 20, and 30 wt% quartz. Both isostatic and conventional triaxial loading conditions were used. The tests were performed at confining pressure of 300 MPa, pore pressures between 50 to 290 MPa, temperatures from 673 to 873 K and strain rates of 3 × 10⁻⁵ s⁻¹. Argon gas was used as the pore fluid. The initial porosities of the starting samples varied from 5% to 9%, with higher porosity correlated to higher quartz content. Microstructural observations after the experiment indicate two kinds of pores are present: 1) Angular, crack-like pores along boundaries between quartz grains or between quartz and calcite grains and 2) equant and tubular voids within the calcite matrix. Under isostatic loading conditions, the compaction rate covaries with porosity and increases with increasing effective pressure. Most of the permeability reduction induced during compaction is irreversible and probably owes to plastic processes. As has been found in previous studies on hot-pressed calcite aggregates, permeability, k, is nonlinearly related to porosity, ϕ. Over small changes in porosity, the two parameters are approximately related as k ∝ ϕⁿ. The exponent n strongly increases as porosity decreases to a finite value (from about 4 to 6% depending on quartz content), suggesting a porosity percolation threshold. When subjected to triaxial deformation, the calcite-quartz aggregates exhibit shear-enhanced compaction, but permeability does not decrease as rapidly as it does under isostatic conditions. During triaxial compaction the exponent n only varies between 2 and 3. Non-isostatic deformation seems to reduce the percolation threshold, and, in fact, enhances the permeability relative to that at the same porosity during isostatic compaction. Our data provide constraints on the governing parameters of the compaction theory which describes fluid flow through a viscous matrix, and may have important implications for expulsion of sedimentary fluids, for fluid flow during deformation and metamorphism, and melt extraction from partially molten rocks.     

The role of magma chamber-fault interaction in caldera forming eruptions

This paper examines the role of the position and orientation of a regional fault in the roof of a magma chamber on stress distribution, mechanical failure, and dyking using 2D finite element numerical simulations. The study pertains to the magma chamber behavior in the relatively short time intervals of several hundreds to thousand of years. The magma chamber is represented as an elliptical inclusion (eccentricity, a/b = 0.12) at a relative depth, H/a, of 0.9. The fault has a 45° dip and is represented by a frictionless fracture. The temperature field in the host rock is calculated assuming a quasisteady-state thermal regime that develops through periodic episodes of magma supply. The rheology of the surrounding rocks is treated using viscoelasticity with temperature activated strain-rate dependent viscosity. Strain weakening of the rocks in the ductile zone is described within the frame of the Dynamic Power Law model . The magma pressure is coupled with the deformation of the rock mass hosting the chamber, including the fault. The variation of magma pressure in response to magma supply and chamber deformation is calculated in the elastic and viscoelastic regimes. The latter corresponds to slow filling, while the former represents a filling time much less than the viscous relaxation time scale. The resulting “equation of state” for the magma chamber couples the magma pressure with the chamber volume in the elastic regime, and with the filling rate for the viscoelastic regime. Analysis of stresses is used to predict dyke propagation conditions, and the mechanical failure of the chamber roof for different fault positions and magma overpressures. Results show that an outward dipping fault located on the periphery of the chamber roof hinders the propagation of dykes to the surface, causing magma to accumulate under the footwall of the fault. At high to moderate overpressures (30–40 MPa), the fault causes localized shear failure and chamber roof collapse that might lead to the first stage of a caldera-forming eruption.     

Statistical models for the estimation of net phosphorus sedimentation in lakes

The empirical adequacy of four phosphorus mass-balance models is evaluated with respect to how the prediction error variance of the corresponding net sedimentation parameters is propagated in the steadystate equations. Using the criterion of minimum propagation error variance (PEV), different groups of lakes can be distinguished for which different empirical equations are used to predict net phosphorus sedimentation. The classification reduced prediction error significantly and also reflected different patterns of sedimentation. Application of this criterion to time-series of individual lakes shows that it is possible to determine a priori whether net annual sedimentation will be better correlated to the annual loading or to the lake content. The correlations depended also on the load/lake content ratio, suggesting that net sedimentation is best viewed as the sum of the partial sedimentation of the load and of the partial sedimentation of the lake content. On average, 25% of the load and 18% of the lake content are sedimented annually. Viewing net phosphorus sedimentation as a function of both the load and the lake content can also explain and predict the well-known cross-sectional correlation between phosphorus retention and water residence time.     

Modeling seismic reflections from thin-bed dolomite layers in diatomite formation

Abstract The origin of dolomite and its diagenesis are still not fully understood. The timing and occurrence of dolomite beds remain key problems. Many thin‐bed layers of dolomite in marine sediments were discovered at drill sites in the forearc basin west of the Japan Trench during the Ocean Drilling Program Leg 186. The thickness of the dolomite layers ranges from 0.5 to 2 m, estimated from the well log. These thin‐bed dolomite layers were able to be identified on seismic data, through quantitative analysis and comparison of the data with synthetic seismograms. Amplitude‐preserved seismic data processing with broadband high‐resolution enhancement helps to estimate the reflectivity series dominated by the large impedance contrast between the dolomite layers and the host sediments. In this report, the first geophysical evidence of large‐scale dolomitization is provided. The occurrence of thin dolomitic layers embedded in diatomaceous sediments is on a basin scale rather than being an isolated event, which constrains the type of dolomitization and the timing of layered dolomitization. It was found that thin‐bed dolomite layers occur where there is an abrupt change in sedimentation rate. Layered dolomitization starts when sedimentation rate changes (from high to low or vice versa). Two dolomite layers coincide with the Miocene–Pliocene and Pliocene–Pleistocene age boundaries. Formation of dolomite beds could be a timing signal of a dramatic change in paleoceanographic and paleoclimatic environments.     

The interaction of ash flows with ridges

 Using both laboratory experiments and theoretical models, we examine the different flow regimes that may develop when an ash flow encounters a ridge. For very small ridges, all the flow may pass over the ridge. For intermediate-size ridges, the flow may be partially blocked, with a fraction of the flow reflected upstream as a travelling bore. In this case, the remainder of the flow, which does pass over the ridge, is hydraulically controlled at the ridge crest. Finally, if the ridge is sufficiently high, then the flow will be totally blocked. New laboratory experiments show that the sedimentation patterns associated with these flow regimes may be very different. Most importantly, flows that involve partial blocking and the formation of upstream propagating bores display enhanced sedimentation upstream of the ridge, analogous to valley-ponded and caldera-fill deposits. In contrast, under some circumstances, if the flow is able to scale a ridge, the deposit may be relatively unaffected by the presence of the ridge. The minimum ridge height that leads to total blocking of the flow increases with mass eruption rate and has a complex variation with distance from the source. In a one-dimensional channel, the minimum ridge height that causes blocking increases with distance downstream. This is because the flow becomes less dense through sedimentation of particles and entrainment of air and so requires less energy to scale a ridge of a particular height. In axisymmetric flow, the minimum ridge height initially decreases with distance downstream as the flow spreads radially, but subsequently increases as the flow becomes less dense through sedimentation and entrainment. A new quantitative model of dilute ash flows propagating over ridges indicates that flows with mass fluxes in excess of 10⁸–10⁹ kg/s can partially scale barriers as high as 1000 m at distances of tens of kilometres from the source, whereas smaller flows are likely to be totally blocked by such an obstacle. Our results shed new insight on the possible long-range transport mechanism of several large flows including the Ata, Fisher and Aniakchak pyroclastic flows. Received: 20 December 1996 / Accepted: 15 March 1998     

Numerically quantifying energy loss caused by squirt flow

In interconnected microcracks, or in microcracks connected to spherical pores, the deformation associated with the passage of mechanical waves can induce fluid flow parallel to the crack walls, which is known as squirt flow. This phenomenon can also occur at larger scales in hydraulically interconnected mesoscopic cracks or fractures. The associated viscous friction causes the waves to experience attenuation and velocity dispersion. We present a simple hydromechanical numerical scheme, based on the interface-coupled Lamé–Navier and Navier–Stokes equations, to simulate squirt flow in the frequency domain. The linearized, quasi-static Navier–Stokes equations describe the laminar flow of a compressible viscous fluid in conduits embedded in a linear elastic solid background described by the quasi-static Lamé–Navier equations. Assuming that the heterogeneous model behaves effectively like a homogeneous viscoelastic medium at a larger spatial scale, the resulting attenuation and stiffness modulus dispersion are computed from spatial averages of the complex-valued, frequency-dependent stress and strain fields. An energy-based approach is implemented to calculate the local contributions to attenuation that, when integrated over the entire model, yield results that are identical to those based on the viscoelastic assumption. In addition to thus validating this assumption, the energy-based approach allows for analyses of the spatial dissipation patterns in squirt flow models. We perform simulations for a series of numerical models to illustrate the viability and versatility of the proposed method. For a 3D model consisting of a spherical crack embedded in a solid background, the characteristic frequency of the resulting P-wave attenuation agrees with that of a corresponding analytical solution, indicating that the dissipative viscous flow problem is appropriately handled in our numerical solution of the linearized, quasi-static Navier–Stokes equations. For 2D models containing either interconnected cracks or cracks connected to a circular pore, the results are compared with those based on Biot's poroelastic equations of consolidation, which are solved through an equivalent approach. Overall, our numerical simulations and the associated analyses demonstrate the suitability of the coupled Lamé–Navier and Navier–Stokes equations and of Biot's equations for quantifying attenuation and dispersion for a range of squirt flow scenarios. These analyses also allow for delineating numerical and physical limitations associated with each set of equations.     

Effects of petrophysical parameters on attenuation and dispersion of seismic waves in the simplified poroelastic theory: Comparison between the Biot's theory and viscosity‐extended theory

The simplified macro‐equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro‐equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine‐saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine‐saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid–fluid combination behaviour properly.