Extended Roof snap-off for a continuous nonwetting fluid and an example case for supercritical CO2

A dominant mechanism for residual trapping of a nonwetting fluid in porous media during imbibition is snap-off or the disconnection of a continuous stream of the nonwetting fluid when it passes through pore constrictions and when a criterion based on capillary pressure imbalance is met. While quasi-static criteria for Roof snap-off have been defined for pores based on the imbalance between capillary pressure across the front/tail meniscus and local capillary pressure at the pore throat, and expressed in terms of pore body to pore throat ratio for simplification, we extended the previous quasi-static snap-off criterion by considering the local capillary pressure imbalance between the pore body and the pore throat for both circular and noncircular pores when the wetting film exists. We then used the criterion to analyze results from computational fluid dynamics (CFD) simulations of multi-phase flow with supercritical CO₂ as the nonwetting fluid and water as the wetting fluid. The extended criterion successfully described most situations we modeled. Furthermore, we compared fluid interface shape for a noncircular 3D pore predicted by the minimum surface energy (MSE) theory against 3D CFD simulations. While the fluid interface shape at the pore throat for 3D simulation was consistent with the shape predicted by MSE theory, the shape could not be successfully predicted by the MSE theory at the upstream and downstream pore body. Moreover, film flow existed for the noncircular pore at the downstream pore body.     

Reflection and transmission of attenuated waves at the boundary between two dissimilar poroelastic solids saturated with two immiscible viscous fluids

The phenomenon of reflection and transmission of plane harmonic waves at the plane interface between two dissimilar poroelastic solids saturated with two immiscible viscous fluids is investigated. Both porous media are considered dissipative due to the presence of viscosity in pore‐fluids. Four attenuated (three dilatational and one shear) waves propagate in such a dissipative porous medium. A finite non‐dimensional parameter is used to define the effective connections between the surface‐pores of two media at their common interface. Another finite parameter represents the gas‐share in the saturation of pores. An attenuated wave in a dissipative medium is described through the specification of directions of propagation and maximum attenuation. A general representation of an attenuated wave is defined through its inhomogeneous propagation, i.e., different directions for propagation and attenuation. Incidence of an inhomogeneous wave is considered at the interface between two dissipative porous solids. This results in four reflected and four transmitted inhomogeneous waves. Expressions are derived for the partition of incident energy among the reflected and transmitted waves. Numerical examples are studied to determine the effects of saturating pore fluid, frequency, surface‐pore connections and wave inhomogeneity on the strengths of reflected and transmitted waves. Interaction energy due to the interference of different (inhomogeneous) waves is calculated in both the dissipative porous media to verify the conservation of incident energy.     

A three-dimensional model study of near-inertial motion: generation and influence of an along-shelf flow

A three-dimensional baroclinic model of the Balearic Sea region is used to examine the processes influencing the distribution of near-inertial currents and waves in the region. Motion is induced by a spatially uniform wind impulse. By using a uniform wind, Ekman pumping due to spatial variability in the wind is removed with the associated generation of internal waves. However, internal waves can still be produced where stratification intersects topography. The generation and propagation of these waves, together with the spatial distribution of wind-forced inertial oscillations, are examined in detail. Diagnostic calculations show that in the near-coastal region inertial oscillations are inhibited by the coastal boundary. Away from this boundary the magnitude of the inertial oscillations increases, with currents showing a 180° phase shift in the vertical. The inclusion of an along-shelf flow modifies the inertial currents due to non-linear interaction between vorticity in the flow and the inertial oscillations. Prognostic calculations show that besides inertial oscillations internal waves are generated. In a linear model the addition of an along-shelf flow produces a slight reduction in the energy at the near-inertial frequency due to enhanced viscosity associated with the flow and changes in density field. The inclusion of non-linear effects modifies the currents due to inertial oscillations in a manner similar to that found in the diagnostic model. A change in the effective inertial frequency also influences the propagation of the internal waves. However, this does not appear to be the main reason for the enhanced damping of inertial energy, which is due to the along-shelf advection of water of a different density into a region and increased viscosity and mixing associated with the along-shelf flow.Responsible Editor: Phil Dyke     

裂缝-孔隙介质储层渗透率表征及其影响因素分析

含裂缝多孔介质渗透率预测是非常规油气资源勘探开发的一个紧迫问题.现有多孔介质岩石物理模型通常利用圆形孔管模拟宏观岩石孔隙空间,难以定量描述软孔隙/裂缝在压力作用下的闭合情况,缺乏裂缝/孔隙间流量交换的连通机制.本文提出含三维裂缝/软孔隙网络多孔介质模型,将储层岩石裂缝/软孔隙表示为椭圆截面微管,建立了周期性压力作用下微...     

Effect of fracture fill on frequency‐dependent anisotropy of fractured porous rocks

In fractured reservoirs, seismic wave velocity and amplitude depend on frequency and incidence angle. Frequency dependence is believed to be principally caused by the wave‐induced flow of pore fluid at the mesoscopic scale. In recent years, two particular phenomena, i.e., patchy saturation and flow between fractures and pores, have been identified as significant mechanisms of wave‐induced flow. However, these two phenomena are studied separately. Recently, a unified model has been proposed for a porous rock with a set of aligned fractures, with pores and fractures filled with two different fluids. Existing models treat waves propagating perpendicular to the fractures. In this paper, we extend the model to all propagation angles by assuming that the flow direction is perpendicular to the layering plane and is independent of the loading direction. We first consider the limiting cases through poroelastic Backus averaging, and then we obtain the five complex and frequency‐dependent stiffness values of the equivalent transversely isotropic medium as a function of the frequency. The numerical results show that, when the bulk modulus of the fracture‐filling fluid is relatively large, the dispersion and attenuation of P‐waves are mainly caused by fractures, and the values decrease as angles increase, almost vanishing when the incidence angle is 90° (propagation parallel to the fracture plane). While the bulk modulus of fluid in fractures is much smaller than that of matrix pores, the attenuation due to the “partial saturation” mechanism makes the fluid flow from pores into fractures, which is almost independent of the incidence angle.     

Computer simulation of flow through a lattice flow-cell model

For single-phase flow through a network model of a porous medium, we report (1) solutions of the Navier–Stokes equation for the flow, (2) micro-particle imaging velocimetry (PIV) measurements of local flow velocity vectors in the “pores throats” and “pore bodies,” and (3) comparisons of the computed and measured velocity vectors. A “two-dimensional” network of cylindrical pores and parallelepiped connecting throats was constructed and used for the measurements. All pore bodies had the same dimensions, but three-different (square cross-section) pore-throat sizes were randomly distributed throughout the network. An unstructured computational grid for flow through an identical network was developed and used to compute the local pressure gradients and flow vectors for several different (macroscopic) flow rates. Numerical solution results were compared with the experimental data, and good agreement was found. Cross-over from Darcy flow to inertial flow was observed in the computational results, and the permeability and inertia coefficients of the network were estimated. The development of inertial flow was seen as a “two-step” process: (1) recirculation zones appeared in more and more pore bodies as the flow rate was increased, and (2) the strengths of individual recirculation zones increased with flow rate. Because each pore-throat and pore-body dimension is known, in this approach an experimental (and/or computed) local Reynolds number is known for every location in the porous medium at which the velocity has been measured (and/or computed).     

The Frequency (or Time) -Temperature Equivalence of Relaxation in Saturated Rocks

Laboratory data on dry and saturated rocks show that pore fluid has the most important effect on rock attenuation. It is known that viscous and inertial coupling between the frame of a porous rock and its pore fluid dissipates seismic energy by conversion to heat and hence cause attenuation. We show that attenuation peaks, in saturated rock have the same property as that of typical thermally activated relaxations. In the frequency domain, a plot of attenuation versus frequency shows an obvious systematic shift to higher frequencies with increasing temperatures. Similarly, the attenuation versus temperature curve moves to higher temperature with increasing frequencies. The attenuation peaks are somewhat broader than that for a Zener relaxation. A Cole-Cole distribution of relaxation times closely matches the attenuations. This behavior can be explained theoretically by local flow mechanisms.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 4. Species transport fundamentals

This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems.     

Gas exsolution and flow during supersaturated water injection in porous media: I. Pore network modeling

Degassing and in situ development of a mobile gas saturation take place when an aqueous phase saturated with gas at a pressure higher than the subsurface pressure is injected in water-saturated porous media. In the first part of this work, a pore network model is used to study the key physical aspects of this novel and hitherto unexplored way of introducing a gas phase in the subsurface. Following heterogeneous nucleation, growth of gas phase clusters driven by convective diffusion of solute from the bulk aqueous phase, is shown to result in a ramified pattern of gas-occupied pores, which is controlled by capillary and buoyancy forces. The interplay between mass transfer and immiscible displacement processes, namely gas cluster coalescence, mobilization under the action of buoyancy forces and fragmentation resulting from capillary instabilities, is seen to favour the propagation of a stable gas saturation front. Pore network model predictions of the macroscopic mass transfer rate coefficient are in fair agreement with a recently published empirical correlation.     

Velocity variations in carbonate rocks due to dual porosity and wave-induced fluid flow

Stiffness variations in carbonates may be described as resulting from different concentrations of flat compliant pores or cracks, which can have a significant effect on the effective stiffness and acoustic properties (e.g., velocities and attenuations) of dry as well as saturated carbonates, although they carry extremely little porosity. As shown in this paper, the effects of dual porosity and wave-induced fluid flow or pore pressure communication may also play a significant role. On the basis of a previously published T-matrix approach to model the effective viscoelastic properties of cracked porous media, we illustrate the (frequency-dependent) effects of wave-induced fluid flow (mainly squirt flow) or pore pressure communication for a model structure consisting of a mixture of fluid-saturated porous grains and fluid-saturated cavities (vugs, etc.) that are embedded in a solid matrix associated with carbonates. We assume that the pores within the porous grains are decoupled from the pores in the solid matrix (and possibly saturated with different fluids) but that each pore system at the micro and/or mesoscale may or may not be connected. For each of four different connectivity models, we present numerical results for four different cases of microstructure (that emphasize the importance of cracks and flat compliant pores). Our numerical results indicate that the velocity and attenuation spectra of carbonates vary significantly, even when the crack density and all other volume concentrations are constant.     

Dispersion relation for ballooning modes and condition of their stability in the near-earth plasma

The ballooning disturbances in a finite-pressure plasma in a curvilinear magnetic field are described by a system of coupled equations for Alfvén and slow magnetosonic modes. The local dispersion relation obtained in a WKB approximation is the simplest and most evident method that can be used to characterize the properties of these disturbances. This dispersion relation is widely used to predict the possible instabilities and spectral properties of LF oscillations in the nightside magnetosphere. The formal derivation of the dispersion relation from the initial system of coupled MHD modes and the transition to different limiting cases have been traced. The behavior of dispersion curves in different oscillation branches and the possible development of instabilities and formation of regions where waves cannot propagate have been studied in detail. This made it possible to specify the results of previous works and even indicate the incorrectness in some works. In particular, it has been indicated that a fast Alfvén branch of oscillations is always stable and an aperiodic instability can originate on a slow magnetosonic oscillation branch.     

球管孔隙模型的核磁共振(NMR)弛豫特征及应用

将岩石孔隙归结为由毛细管和球形孔组成的孔隙系统,提出孔隙球管孔隙模型. 岩石孔隙按大小分组后,每一组孔隙的氢核弛豫时间可以用球管孔隙模型计算. 将此弛豫时间作为反演T2分布的时间控制点,反演岩芯的核磁共振弛豫信号. 研究表明, T2分布与特定的孔隙结构相联系. 使用不同结构的球管孔隙模型,可以使反演T2分布最大限度地拟合弛豫信号,此时的球管模型以最近似的方式模拟了岩芯的孔隙结构. 使用球管模型对实验室核磁共振资料进行了处理,对比压汞分析得到毛管力分布数据,结果证明球管孔隙模型描述了岩石孔隙的弛豫特征,而且,岩石特定孔隙结构的弛豫特征与孔隙流体有关.     

POROSITY AND PORE STRUCTURE FROM ACOUSTIC WELL LOGGING DATA1

Wyllie's time-average equation and subsequent refinements have been used for over 20 years to estimate the porosity of reservoir rocks from compressional (P)-wave velocity (or its reciprocal, transit time) recorded on a sonic log. This model, while simple, needs to be more convincingly explained in theory and improved in practice, particularly by making use of shear (S)-wave velocity. One of the most important, although often ignored, factors affecting elastic velocities in a rock is pore structure, which is also a controlling factor for transport properties of a rock. Now that S-wave information can be obtained from the sonic log, it may be used with P-waves to provide a better understanding of pore structure. A new acoustic velocities-to-porosity transform based on an elastic velocity model developed by Kuster and Toksöz is proposed. Employing an approximation to an equivalent pore aspect ratio spectrum, pore structure for reservoir rocks is taken into account, in addition to total pore volume. Equidimensional pores are approximated by spheres and rounded spheroids, while grain boundary pores and flat pores are approximated by low aspect ratio cracks. An equivalent pore aspect ratio spectrum is characterized by a power function which is determined by compressional-and shear-wave velocities, as well as by matrix and inclusion properties. As a result of this more sophisticated elastic model of porous rocks and a stricter theory of elastic wave propagation, the new method leads to a more satisfactory interpretation and fuller use of seismic and sonic log data. Calculations using the new transform on data for sedimentary rocks, obtained from published literature and laboratory measurements, are presented and compared at atmospheric pressure with those estimated from the time-average equation. Results demonstrate that, to compensate for additional complexity, the new method provides more detailed information on pore volume and pore structure of reservoir rocks. Examples are presented using a realistic self-consistent averaging scheme to consider interactions between pores, and the possibility of extending the method to complex lithologies and shaly rocks is discussed.     

含两项不混合/单项黏性流体孔隙介质分界面上反透射系数特征研究

弹性孔隙介质分界面上的反透射系数特征,在岩性划分、流体识别、储层边界判识等方面有重要的应用.本文研究上层为含两项不混合黏性流体孔隙介质、下层为含单项黏性流体孔隙介质分界面上的反透射理论.首先根据两种孔隙介质分界面上的能量守恒得到边界条件,再将波函数、位移、应力与应变关系代入边界条件,推导出完全连通孔隙情况下,第一类纵波入射到孔隙介质分界面上的反透射系数方程.通过建立砂岩孔隙介质模型,分别分析不同孔隙流体类型、不同含油饱和度及不同入射角情况下,各类波的反透射系数特征.研究表明,第二、三类纵波反透射系数数值比第一类纵波小多个数量级,且两者对入射角的变化不敏感,但对孔隙流体性质、含油饱和度的变化较敏感,而横波反透射系数特征恰好与此相反;第一类纵波反透射系数特征比较复杂,入射角、孔隙流体的性质及含油饱和度的变化都对其产生影响.不同孔隙流体弹性物性的差异、孔隙介质中含油饱和度的变化及不同入射角引起垂向和切向应力分量的变化都会影响各类波的反透射系数特征,分析这些特征可以为研究储层含油气性提供理论基础.     

Formation of systems of incompact bands parallel to the compression axis in the unconsolidated sedimentary rocks: A model

Uniaxial compression of poorly lithified rocks leads to the formation of thin incompact layers (or bands, in the two-dimensional case) parallel to the compression axis, which are characterized by increased porosity. The standard model of the formation of such bands, as well as deformation bands of other types, associates them with the narrow zones of localization of plastic deformations. In the case of decompaction, it is assumed that transverse tensile deformations are localized within the band, which cause the band to dilate. Here, the formation of a band of localized deformations is treated as a loss-of-stability phenomenon. Based on observations, we propose a fundamentally different model of incompact bands formation, according to which the microdefects in sediment packing (pores) rather than the deformations are localized in the narrow zones. The localization of pores, which are initially randomly distributed in the medium, occurs as a result of their migration through the geomaterial. The migration and subsequent localization of pores are driven by a common mechanism, namely, a trend of a system to lower its total energy (small variations in total energy are equal to the increment of free energy minus the work of external forces). Migration of a single pore in a granular sedimentary rock is caused by the force f driving the defect. This force was introduced by J. Eshelby (1951; 1970). An important feature of our model is that the formation of an incompact band here does not have a sense of a loss of stability. Quite the contrary, the formation of incompact bands is treated as a gradual process spread over time. In this context, the origination of incompact band systems directly follows from our model itself, without any a priori assumptions postulating the existence of such systems and without any special tuning of the model parameters. Moreover, based on the proposed model, we can predict the incompact bands to always occur in the form of systems rather than as individual structures. A single incompact band may only be formed when the force resisting the pore motion, f _c , is absent.     

Effects of beach slope breaks on nearshore groundwater dynamics

Interactions between fresh groundwater and seawater affect significantly the nearshore pore water flow, which in turn influences the fate of nutrients and contaminants in coastal aquifers prior to discharge to the marine environment. Field investigations and numerical simulations were carried out to examine the groundwater dynamics in the intertidal zone of a carbonate sandy aquifer on the tropical island of Rarotonga, Cook Islands. The study site was featured by distinct cross‐shore slope breaks on the beach surface. Measured pore water salinities revealed different distributions under the influences of different beach profiles, inland heads, and tidal oscillations. Fresh groundwater was found to discharge around a beach slope break located in the middle area of the intertidal zone. The results indicate a strong interplay between the slope break beach morphology and tidal force in controlling the nearshore groundwater flow and solute transport. The fresh groundwater discharge location was largely determined by the beach morphology in combination with the tidal force. The nearshore groundwater flow can be very sensitive to beach slope breaks, which induce local circulation and flow instabilities. As slope breaks are a common feature of beaches around the world, these results have important, general implications for future studies of nutrients transport and transformations in nearshore aquifers and associated fluxes via submarine groundwater discharge.     

Transformation of spatial and perturbation derivatives of travel time at a curved interface between two arbitrary media

We consider the partial derivatives of travel time with respect to both spatial coordinates and perturbation parameters. These derivatives are very important in studying wave propagation and have already found various applications in smooth media without interfaces. In order to extend the applications to media composed of layers and blocks, we derive the explicit equations for transforming these travel–time derivatives of arbitrary orders at a general smooth curved interface between two arbitrary media. The equations are applicable to both real–valued and complex–valued travel time. The equations are expressed in terms of a general Hamiltonian function and are applicable to the transformation of travel–time derivatives in both isotropic and anisotropic media. The interface is specified by an implicit equation. No local coordinates are needed for the transformation.     

Oscillations of frontal currents

The problem of interpreting Eulerian current measurements in sharp fronts with current shears much larger than the planetary vorticity is discussed for the case when there are tidal and/or inertial oscillations present. For a situation taken from the Norwegian Coastal Current, long-frontal oscillations in speed exceeded cross-frontal oscillations by a factor of about 4 as a result of the frontal shear field moving back and forth past the moored current meter. It is shown how these large amplifications can be used to estimate the cross-frontal shear. The example highlights the problem of computing energy density spectra in frontal regions.     

Clear evidence for the sign-reversal of the pressure admittance to gravity near 3 mHz

The influence of the atmosphere on gravity measurements by Newtonian attraction and vertical displacements due to surface loading is well known and studied especially at frequencies below 1 mHz. Less work has been done at the higher seismic frequencies where inertial effects come into play. The sensor mass of a vertical accelerometer responds to several forces caused by the atmosphere, on global, regional and local scales. For the seismic frequencies the atmosphere above the observation site has the largest influence. A simple “Gedankenexperiment” demonstrates that the gravitational effect on one hand and the free air and inertial effects due to deformation on the other have opposite sign. Since the inertial effect is strongly frequency-dependent there should be a crossover-frequency where the pressure admittance to gravity changes sign. Simple analytical models clearly show this property near frequencies of a few mHz and are used here to amplify the variance reduction of the gravity residuals. The crossover-frequency depends on the properties of the models of the atmospheric phenomena and the elasticity of the Earth’s crust. Therefore in reality it must be expected to vary in time and space.We show one extremely clear example of this sign-reversal detected in the gravity data from the superconducting gravimeter GWR-C025 in Vienna among other examples which demonstrate the reality of this effect.