Porosity measurements in natural porous rocks using magnetic resonance imaging

A magnetic resonance imaging (MRI) method is presented to measure localized porosity values inside natural porous rocks for the purpose of obtaining frequency distributions of the porosity (porosity distributions). The method is applied to study six different cores, including three Berea sandstone samples, Casper sandstone, Indiana limestone, and San Andres dolomite. An image of the porosity is shown for a transverse and a longitudinal slice in order to show qualitative variations of the porosity within each core sample. The porosity distribution for the entire core has been acquired, and it is shown with a Gaussian fit to the data. In addition, for cores known to have a layered structure, a bimodal distribution is fit to the data, and the fit is used to estimate the value of the porosity for two characteristic types of layers within the core sample.     

Delayed fracture in porous media

The fracture of porous media subjected to a constant load is studied. Contrary to homogeneous solids in which fracture usually happens instantaneously at a well-defined breaking strength, the fracture of a porous medium can occur with a delay, allowing us to quantify the average lifetime of the unbroken material. We show that the average fracture probability, a key property for risk analysis in civil engineering, is given by the probability of crack nucleation. The nucleation process can be understood qualitatively by calculating the activation energy for crack nucleation, taking into account the porosity of the medium.     

A rapid measurement of flow propagators in porous rocks

NMR flow propagators have been obtained for brine flowing through Bentheimer sandstone using the rapid DiffTrain pulse sequence. In this way, 8 flow propagators at different observation times Delta were acquired in 67 mins, compared to 7 h for the same measurements implemented with conventional pulsed field gradient (PFG) sequences. DiffTrain allows this time saving to be achieved through the acquisition of multiple displacement probability distributions over a range of Delta in a single measurement. If only the propagator moments are required, this experiment time can be further reduced to 9 mins through appropriate sparse sampling at low q values. The propagator moments obtained from DiffTrain measurements with dense and sparse q-space sampling are shown to be equivalent to those obtained from conventional PFG measurements.     

Application of the semivariogram to MRI data: a useful approach for the characterization of natural porous rocks

Geostatistics is used to study the heterogeneities of reservoir cores, as well as to observe the orientation of layers inside the cores. This information obtained from geostatistics could be very useful for coreflood simulation programs. In this paper, it has been shown how semivariograms can be drawn using local porosities obtained from magnetic resonance imaging (MRI). These semivariograms are then used to determine the correlation lengths of the porosity in the cores and to qualitatively estimate the degree of heterogeneity in the core samples.     

Thermally activated fracture of porous media

The lifetime of a porous media, submitted to a constant subcritical stress, is studied by means of a numerical model. This model is based on a spring network where the porosity is represented by missing springs. The dynamics is produced adding thermal fluctuations in spring forces. The lifetime predicted by the models are compared to experimental data of delayed fracture of porous media submitted to three-point flexion fracture experiments.     

A numerical analytic method for electromagnetic radiation accompanying with fracture of rocks

This paper studies Rabinovitch’s compression experiments on granite and chalk and proposes an oscillating dipole model to analyse and simulate the electromagnetic radiation phenomenon caused by fracture of rocks. Our model assumes that the electromagnetic radiation pulses are initiated by vibrations of the charged rock grains on the tips of the crack. The vibrations of the rock grains are stimulated by the pulses of the cracks. Our simulations show comparable results with Rabinovitch’s compression experiments. From the simulation results, it verifies an assumption that the crack width is inversely proportional to the circular frequency electromagnetic radiation, which is presented by Rabinovitch et al. The simulation results also imply that, by using our oscillating dipole model together with Rabinovitch’s two equations about the crack length and crack width, we can quantitatively analyse and simulate the electromagnetic radiation phenomenon, which is induced from the fracture of the rocks.     

Electric field driven flow in natural porous media

Electric fields were applied to fluid-saturated packed sand beds (0.23+/-0.03 mm average pore diameter), and the effects on the mobility of the water molecules were monitored using stimulated echo (STE) and pulsed field gradient (PFG) experiments. The mean flow velocity, averaged over the entire sample, is expected to vanish in closed systems, but the PFG and time dependent signal decay was enhanced beyond the effects of thermal diffusion, due to velocity dispersion. The internal flow generated by the electric field was shown to be fully time-reversible upon inverting the electric field polarity (for total flow times of up to 0.4s), a strong indication that the NMR detected displacements were mainly due to electro-osmotic flow (EOF). However, a comparison of the velocity dispersion for different electrolyte concentrations showed that the measured effect scaled with the applied power VI (V = voltage, I = electric current), rather than with the voltage alone, contrary to the prediction of the basic model for EOF in a single capillary channel.     

各向异性粘弹性孔隙介质地震波场伪谱法正演模拟

地球介质各向异性、粘弹性以及孔隙特征是地震资料描述油气储层时应综合考虑的. 建立了各向异性粘弹性孔隙介质模型，导出了各向异性粘弹性孔隙介质的弹性波波动方程，采用伪谱法正演模拟了各向异性粘弹性孔隙介质地震波，进行了其波场特征分析. 该研究有益于加深对地震波在实际地球介质中传播规律的认识.     

Direct pore-level modeling of incompressible fluid flow in porous media

We present a dynamic particle-based model for direct pore-level modeling of incompressible viscous fluid flow in disordered porous media. The model is capable of simulating flow directly in three-dimensional high-resolution micro-CT images of rock samples. It is based on moving particle semi-implicit (MPS) method. We modify this technique in order to improve its stability for flow in porous media problems. Using the micro-CT image of a rock sample, the entire medium, i.e., solid and fluid, is discretized into particles. The incompressible Navier–Stokes equations are then solved for each particle using the MPS summations. The model handles highly irregular fluid–solid boundaries effectively. An algorithm to split and merge fluid particles is also introduced. To handle the computational load, we present a parallel version of the model that runs on distributed memory computer clusters. The accuracy of the model is validated against the analytical, numerical, and experimental data available in the literature. The validated model is then used to simulate both unsteady- and steady-state flow of an incompressible fluid directly in a representative elementary volume (REV) size micro-CT image of a naturally-occurring sandstone with 3.398 μm resolution. We analyze the quality and consistency of the predicted flow behavior and calculate absolute permeability using the steady-state flow rate.     

Determining NMR flow propagator moments in porous rocks without the influence of relaxation

Flow propagators, used for the study of advective motion of brine solution in porous carbonate and sandstone rocks, have been obtained without the influence of Nuclear Magnetic Resonance (NMR) relaxation times, T₁ and T₂. These spin relaxation mechanisms normally result in a loss of signal that varies depending on the displacement ζ of the flowing spins, thereby preventing the acquisition of quantitative propagator data. The full relaxation behaviour of the system under flow needs to be characterised to enable the implementation of a true quantitative measurement. Two-dimensional NMR correlations of ζ − T₂ and T₁ − T₂ are used in combination to provide the flow propagators without relaxation weighting. T₁ − ζ correlations cannot be used due to the loss of T₁ information during the displacement observation time Δ. Here the moments of the propagators are extracted by statistical analysis of the full propagator shape. The measured displacements (first moments) are seen to correlate with the expected mean displacements for long observation times Δ. The higher order moments of the propagators determined by this method indicate those obtained previously using a correction were overestimated.     

Symbolic regression modeling of noise generation at porous airfoils

Based on data sets from previous experimental studies, the tool of symbolic regression is applied to find empirical models that describe the noise generation at porous airfoils. Both the self noise from the interaction of a turbulent boundary layer with the trailing edge of an porous airfoil and the noise generated at the leading edge due to turbulent inflow are considered. Following a dimensional analysis, models are built for trailing edge noise and leading edge noise in terms of four and six dimensionless quantities, respectively. Models of different accuracy and complexity are proposed and discussed. For the trailing edge noise case, a general dependency of the sound power on the fifth power of the flow velocity was found and the frequency spectrum is controlled by the flow resistivity of the porous material. Leading edge noise power is proportional to the square of the turbulence intensity and shows a dependency on the fifth to sixth power of the flow velocity, while the spectrum is governed by the flow resistivity and the integral length scale of the incoming turbulence.     

Influence of natural aging on photoluminescence from porous silicon

The influence of natural aging on the photoluminescence intensity and the position of a photolu-minescence peak in n-type por-Si (por-Si) is studied. The variation of the phase composition and the relative content of the amorphous and oxide phases of silicon in por-Si during aging is determined by fitting simulated spectra to experimental ultrasoft Si L _2,3 X-ray emission spectra using reference spectra.     

多孔脆性介质冲击波压缩破坏的细观机理和图像

本文采用一种具有良好定量性质的离散元模型研究了带孔洞的各向同性脆性介质在细观尺度上的压缩破坏特征. 通过对孤立孔洞、三种简单的孔洞排布方式和大量孔洞随机排布等几种情况的模拟, 认识到了剪切破坏和局域拉伸破坏是冲击波压缩下多孔介质的基本破坏模式; 孔洞之间的损伤贯通会促进孔洞在较低应力下发生塌缩, 但损伤区的应力松弛过程却会对一定范围内的介质起到损伤屏蔽作用; 不同区域中损伤促进和损伤屏蔽的综合效果是在多孔脆性介质中形成一种高损伤区与低损伤区间错排布的奇特损伤分布. 本文的研究结果为深入理解脆性材料冲击波压缩破坏的演化过程和机理提供了细观尺度上的初步物理图像.     

Comparison of two modeling approaches for highly heterogeneous porous media

The purpose of this paper is to study the acoustic behavior of highly heterogeneous, low density porous structures having a complex pore size distribution using two distinct theoretical approaches. The first approach requires the direct numerical integration of the Biot viscosity correction function. The main requirement here is a knowledge of the probability density function of the pore size, which can be achieved by an optical pore-counting technique. The fact that the observed pore size distribution in these materials could be distinctively split into two parts suggested the use of the second approach based upon the double-porosity theory by Olny and Boutin [J. Acoust. Soc. Am. 114(1), 73-89 (2003)]. The latter approach assumes a low permeability contrast between the two porous scales so that the acoustic properties could be estimated using the semi-phenomenological models of Johnson and Lafarge for the viscous and thermal dynamic permeabilities. Numerical results predicted by the two models are then compared with impedance tube experimental data showing good accuracy of the selected prediction methods.     

Radiative effects on magnetohydrodynamic natural convection flows saturated in porous media

A boundary layer solution is presented to study the effects of joule heating on magnetohydrodynamic natural convection flow. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. Four different cases of flows have been studied namely an isothermal surface, a uniform heat flux surface, a plane plume and flow generated from—a horizontal line energy source a vertical adiabatic surface. Numerical results presented for the perturbation analysis four boundary conditions with various parameters are tabulated.     

Poroelastic modeling of seismic boundary conditions across a fracture

Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.     

Nonlinear effects of non-Newtonian fluids on natural convection in a porous medium

This paper investigates the rheological effects of non-Newtonian fluids on the natural convection mechanism in a porous medium. A non-Newtonian behavior of power law fluid with a yield stress, saturating a porous medium, in which yield stress is temperature dependent, is considered. The cases of constant temperature boundary and constant heat flux boundary, along the heated vertical cylinder, are analyzed. The approximate similarity solutions in a closed form are shown, from which the velocity and temperature profiles are determined. The numerical solutions for a constant temperature boundary are also shown and discussed.