Fluid-saturated Porous Medium Research Articles

Inferring rock strength and fault activation from high-resolution in situ Vp/Vs estimates surrounding induced earthquake clusters

Fluid injection/extraction activity related to hydraulic fracturing can induce earthquakes. Common mechanisms attributed to induced earthquakes include elevated pore pressure, poroelastic stress change, and fault loading through aseismic slip. However, their relative influence is still an open question. Estimating subsurface rock properties, such as pore pressure distribution, crack density, and fracture geometry can help quantify the causal relationship between fluid-rock interaction and fault activation. Inferring rock properties by means of indirect measurement may be a viable strategy to help identify weak structures susceptible to failure in regions where increased seismicity correlates with industrial activity, such as the Western Canada Sedimentary Basin. Here we present in situ estimates of Vp/Vs for 34 induced earthquake clusters in the Kiskatinaw area in northeast British Columbia. We estimate significant changes of up to ±4.5% for nine clusters generally associated with areas of high injection volume. Predominantly small spatiotemporal Vp/Vs variations suggest pore pressure increase plays a secondary role in initiating earthquakes. In contrast, computational rock mechanical models that invoke a decreasing fracture aspect ratio and increasing fluid content in a fluid-saturated porous medium that are consistent with the treatment pressure history better explain the observations.

The Elder Problem with Reactive Infiltration Effects

The occurrence of buoyancy-driven flow and reactive solute transport in a fluid-saturated porous medium can be induced by either natural processes or human activities. Typical examples include the groundwater salinization in carbonate-rock aquifers and the acid treatment of oil wells in petroleum drilling industry. In this paper, the classical Elder problem of buoyancy-driven convection in two-dimensional porous media is extended to include the local chemical interactions between the solute in the pore liquid (e.g. salt such as NaCl or acids such as HCl and HCl/HF mixtures) and the solid space of the porous medium (e.g. minerals such as calcite and dolomite). Effects of the geochemical processes on the flow and mass transport are investigated. For the reactive, strongly solute-driven case in the regime dominated by the diffusive mass transport, a decrease in the net solute concentration is found as compared to the non-reactive case. This decrease is pronounced at higher values of the Damköhler number when the solute reaction rate becomes larger than the solute diffusion rate. Furthermore, the flow structure is affected by products generated by the chemical reaction when the Rayleigh number for the products is sufficiently high. In that case, numerical simulations show the formation of diluted fluid tongues exhibiting damped periodic oscillations about a nonzero mean. The results are obtained using the pseudospectral numerical method, verified against the analytical solution for the non-reactive, purely diffusive case.

Effect models for the stationary Navier–Stokes fluid in a porous medium with different scales

In this paper, we investigate an incompressible flow through a thin corrugated domain fill with fluid saturated porous medium. The porous medium flow is governed by Navier–Stokes model. The thickness of the domain is assumed to be aɛ and the solid part is supposed to be periodical cylinders of size ɛ. We rigorously derive different asymptotic models by comparing the relation between ɛ and aɛ. To prove the main results, we employ the homogenization technique based on the generalized Poincaré inequality.

Biot's theory-based dynamic equation modeling using a machine learning auxiliary approach

Abstract Characterizing seismic wave propagation in a fluid-saturated porous media well enhances the precision of interpreting seismic data, bringing benefits to understanding reservoir properties better. Some important indicators, including wave dispersion and attenuation, along with the wavefield, are widely used for interpreting the reservoir, and they can be obtained from a rock physics model. In existing models, some of them are limited in scope due to their complexity, for example, numerical solutions are difficult or costly. In view of this, this study proposes an approach of establishing equivalent dynamic equations of existing models. First, the framework of the equivalent model is derived based on Biot's theory, while the elastic coefficients are set as unknown factors. The next step is to use deep neural networks (DNNs) to predict these coefficients, and surrogate models of unknowns are established after training DNNs. The training data is naturally generated from the original model. The simplicity of the equation forms, compared to the original complex model and some other equivalents such as the viscoelastic model, enables the framework to perform wavefield simulation easier. Numerical examples show that the established equivalent model can not only predict similar dispersion and attenuation, but also obtain wavefields with small differences. This also indicates that it may be sufficient to establish an equivalent model only according to dispersion and attenuation, and the cost of generating such data is very small compared to simulating the wavefield. Therefore, the proposed approach is expected to effectively improve the computational difficulty of some existing models.

Effects of confining pressure and pore pressure on multipole borehole acoustic field in fluid-saturated porous media

In-situ stress is a common stress in the exploration and development of oil reservoirs. Therefore, it is of great significance to study the propagation characteristics of borehole acoustic waves in fluid-saturated porous media under stress. Based on the acoustoelastic theory of fluid-saturated porous media, the field equation of fluid-saturated porous media under the conditions of confining pressure and pore pressure and the acoustic field formula of multipole source excitation in open hole are given. The influences of pore pressure and confining pressure on guided waves of multipole borehole acoustic field in fluid-saturated porous media are investigated. The numerical results show that the phase velocity and excitation intensity of guided wave increase significantly under the confining pressure. For a given confining pressure, the phase velocity of the guided wave decreases with pore pressure increasing. The excitation intensity of guided wave increases at low frequency and then decreases at high frequency with pore pressure increasing, except for that of Stoneley wave which decreases in the whole frequency range. These results will help us get an insight into the influences of confining pressure and pore pressure on the acoustic field of multipole source in borehole around fluid-saturated porous media.

Near-field seismoacoustic wave scattering due to an irregular interface: a unified framework

SUMMARY Near-field seismoacoustic scattering must be considered across various domains, including marine seismic exploration, ocean acoustics and marine seismic engineering. This is a complex process due to the fluid–solid interaction between seawater and the seabed, particularly when the seabed is saturated with fluid. The interaction between sea fluid, saturated porous seabed and solid bedrock must also be considered. In this study, seawater and dry bedrock are treated as generalized saturated porous media with porosity of one and zero, respectively. The coupling between seawater, saturated seabed and dry bedrock can be analysed within a unified framework of generalized saturated porous media. Therefore, we proposed an efficient, unified method to address the challenges posed by near-field seismoacoustic scattering. This method comprises free field wave motion computation, which is used to provide input for scattering analysis. It also introduces a unified computational framework for modelling the wave propagation in the water-saturated seabed-bedrock system, and local transmitting boundary are used to account for the effect of an infinite domain. First, the differential equation of the generalized saturated porous media is discretized using lumped mass-based FEM, and the ordinary differential equation is integrated in time using an explicit scheme. Then, the equations for the motion of the nodes on the interface between two generalized saturated porous media with various porosity are derived. These equations are suitable for special cases such as fluid–solid interface, fluid-saturated porous media interface and saturated porous media-solid interface. To demonstrate the validity and feasibility of the proposed approach, a 1-D problem is considered, and the obtained response is verified using an analytical solution. Then, we compute the cases of a vertically incident plane P wave onto a 2-D basin-like fluid–solid structure, and compared the synthetic seismograms with results reported by other researchers. In this study, the findings of our proposed approach satisfy the continuity requirements at the interface and are consistent with those obtained using the reflection/transmission matrix method. Additionally, a 3-D site with basin-like terrain was analysed. The proposed approach treats the fluid, saturated porous media and solid in a unified framework, and has high efficiency due to lumped mass matrix-based explicit finite element and local transmitting artificial boundary. Furthermore, our approach can be easily implemented in parallel, making it suitable for solving large-scale seismoacoustic scattering problems.

A sequential global programming approach for two-scale optimization of homogenized multiphysics problems with application to Biot porous media

We present a new approach and an algorithm for solving two-scale material optimization problems to optimize the behaviour of a fluid-saturated porous medium in a given domain. While the state problem is governed by the Biot model describing the fluid–structure interaction in homogenized poroelastic structures, the approach is widely applicable to multiphysics problems involving several macroscopic fields in which homogenization provides the relationship between the microconfigurations and the macroscopic mathematical model. The optimization variables describe the local microstructure design by virtue of the pore shape which determines the effective medium properties, namely the material coefficients, computed by the homogenization method. The numerical optimization strategy involves (a) precomputing a database of the material coefficients associated with the geometric parameters and (b) applying the sequential global programming (SGP) method for solving the problem of macroscopically optimized distribution of material coefficients. Although there are similarities to the free material optimization (FMO) approach, only effective material coefficients are considered admissible, for which a well-defined set of corresponding configurable microstructures exists. Due to the flexibility of the SGP approach, different types of microstructures with fully independent parametrizations can easily be handled. The efficiency of the concept is demonstrated by a series of numerical experiments that show that the SGP method can simultaneously handle multiple types of microstructures with nontrivial parametrizations using a considerably low and stable number of state problems to be solved.

Throughflow effect on bi-disperse convection

The aim of this paper is to investigate the effect of a vertical constant throughflow on convective instabilities in a horizontal layer of fluid-saturated bi-disperse porous medium heated from below. Via linear instability and nonlinear stability analyses of the throughflow solution, the linear and nonlinear critical Rayleigh numbers for convective instabilities have been determined and studied as functions of the strength of the throughflow.

Surface Motion for P-Wave Scattering by an Arbitrary-Shaped Canyon in Saturated Half-Space

This paper obtained a semianalytical solution for the P-wave scattering problem by an arbitrary-shaped canyon in a saturated half-space by using Biot’s theory, the wave function expansion method, and the moments method. Firstly, based on the Biot fluid-saturated porous media theory and the wave function expansion method, the wave potentials which automatically satisfy the zero-stress boundary condition on the surface of the half-space are obtained. Then, the boundary value problem is transformed into an algebraic problem by the method of moments according to the boundary conditions, and then solved numerically by truncation. By adjusting the parameters, the saturated medium in the original model approximately degenerates into a single-phase elastic medium, and the correctness of the proposed method is verified by comparing it with published results. Finally, the effects of the canyon shape, the porosity of the soil, and the incidence angle and frequency of the incident wave on the amplitude of ground surface motion are investigated. The results show that the incidence angle has a significant effect on the ground surface motion, while the porosity of the soil has little influence on the amplitude of surface motion. The influence of canyon shape on surface motion is mainly reflected in the shielding effect on the incident wave. Although P-wave scattering by a canyon is a traditional problem, most of the analytical solutions are limited to solving the scattering of seismic waves in geometric regular canyons. However, the actual shape of the canyon is not regular, which limits the application of closed analytical solutions in practical engineering. In this paper, the scattering of P-waves in arbitrary-shaped canyons is successfully solved by using a semianalytical method combined with a numerical method-moments method, which provides a possibility for engineering application.

The onset of penetrative convection in an inclined porous layer

In the present article, a model for penetrative convection in a fluid-saturated inclined porous medium is analyzed. Penetrative convection occurs when an unstably stratified fluid moves into a stably stratified region. In this study, it will be shown that the inclination of the layer plays a relevant role for the penetrative thermal convection of a fluid-saturated porous medium. The results reported in the literature for the limiting case of horizontal layer are recovered and the numerical results for the linear instability, obtained via the Chebyshev-τ method, show that the most destabilizing perturbations are the longitudinal and, as expected, the transverse ones destabilize only up to a certain critical inclination angle of the layer. Moreover, in the numerical analysis of the three-dimensional perturbations, we show that the longitudinal perturbations are the most destabilizing not only with respect to the transverse but also with respect to any general perturbation. We also give nonlinear stability results for the longitudinal perturbations via the weighted energy method.

Complexity measurements for the thermal convection in a viscoelastic fluid saturated porous medium

Measuring complexity statistical indicators is a key method to analyze and characterize dynamical systems. In this work, we perform a comparative analysis among the López-Ruiz, Mancini & Calbet complexity indicator and the largest Lyapunov exponent for the convection problem of a viscoelastic fluid in a porous medium with feedback control based in an Oldroyd carrier liquid through a four-dimensional generalized Lorenz system. With both indicators can be distinguished from chaotic to periodic states. We perform intensive numerical simulations with 4×106 in the space parameters, finding good agreement between them, such that difference is close to 2%. We have also detected that the computing time is much faster in the case of complexity indicator than for Lyapunov exponents. Finally, we have also studied the effect of the initial conditions in the coexistence states, encountering multistability.

An improved semi-implicit material point method for simulating large deformation problems in saturated geomaterials

This study presents an improved semi-implicit MPM formulation for coupled large deformation problems in geotechnics based on the fractional step method. The main objective of this study is to make the choice of the time step size independent of the permeability and to reduce the pressure oscillations by applying the special splitting procedure and the stabilized technique. The proposed coupled MPM is validated by comparing numerical results with analytical solutions of the one-dimensional consolidation problem in both small and large deformation regimes. Three numerical tests are performed to further evaluate the performance of the proposed method, including a self-weight slumping block, 2D consolidation test, and the stability of a saturated elasto-plastic slope. The numerical results indicate that the proposed method is suitable for simulating fluid-saturated porous media involving large deformation.

Identification of the seismoelectric field induced by a slow compressional wave at an ultrasonic frequency

Theoretical studies predict that a slow compressional wave propagating in a fluid-saturated porous medium can produce a coseismic electric field due to the electrokinetic effect, but the experimental proof is still lacking. Laboratory experiments are conducted to measure such a seismoelectric conversion inside a synthetic rock. Fluid pressure signals are recorded by using mini hydrophones 1.6 mm in diameter, and then electric field signals generated at the liquid-solid interface and inside the rock sample based on the seismoelectric effect are recorded by electrode arrays, respectively. The seismoelectric waves induced by fast and slow compressional waves can be clearly identified in the recorded electric signals and their attenuation properties are analyzed at an ultrasonic frequency, which confirms that the seismoelectric signals induced by fast/slow compressional waves are measurable in the experiments. To support our explanation of the experimental observation, theoretical simulations are conducted according to the experimental model and then compared with the recorded experimental data. The results find that the simulated wavefields are in excellent agreement with those signals measured in the measurements, which proves the theoretical prediction of the seismoelectric signal accompanying the slow compressional wave and suggests a feasible way for detecting the slow compressional wave property with seismoelectric conversions in field measurements.

Near-field performance of chemical dissolution-front instability around a circular acid-injection-well in fluid-saturated porous media

Near-field performance of chemical dissolution-front instability around a circular acid-injection-well in fluid-saturated porous media

Characteristics of Elastic Wave Propagation in Fluid-Saturated Porous Media Based on the Model of Soil Mechanics

Characteristics of Elastic Wave Propagation in Fluid-Saturated Porous Media Based on the Model of Soil Mechanics

Functional group resolved NMR relaxation of 3-carbon adsorbates in mesoporous alumina

NMR relaxation analysis provides a unique and non-invasive probe of fluid dynamics within porous materials, and may be applied to the interpretation of a wide variety of material and interfacial characteristics. Here, we report two-dimensional 1H T1−T2 relaxation correlation measurements of a range of three-carbon adsorbates (1-propanol, 2-propanol and propanoic acid) imbibed within the mesoporous metal oxide gamma-alumina. Our data, acquired across field strengths of 2 MHz, 12.7 MHz and 43 MHz, clearly reveal two populations in each measurement, identified as the alkyl and hydroxyl moieties of each adsorbate. These results expand the range of materials in which such functional group resolved relaxation is known to occur, and demonstrate the clear persistence of such phenomena using a range of typical benchtop NMR systems employed to study fluid-saturated porous media.

Computational Simulation of Chemical Dissolution-Front Instability Problems Associated with Radially Divergent Flow in Fluid-Saturated Porous Media

Computational Simulation of Chemical Dissolution-Front Instability Problems Associated with Radially Divergent Flow in Fluid-Saturated Porous Media

Compressibility Effect on Darcy Porous Convection

Perfectly incompressible materials do not exist in nature but are a useful approximation of several media which can be deformed in non-isothermal processes but undergo very small volume variations. In this paper, the linear analysis of the Darcy-Bénard problem is performed in the class of extended-quasi-thermal-incompressible fluids, introducing a factor beta which describes the compressibility of the fluid and plays an essential role in the instability results. In particular, in the Oberbeck-Boussinesq approximation, a more realistic constitutive equation for the fluid density is employed in order to obtain more thermodynamically consistent instability results. The critical Rayleigh-Darcy number for the onset of convection is determined, via linear instability analysis of the conduction solution, as a function of a dimensionless parameter widehat{beta } proportional to the compressibility factor beta, proving that widehat{beta } enhances the onset of convective motions.Article HighlightsThe onset of convection in fluid-saturated porous media is analyzed, taking into account fluid compressibility effect.The critical Rayleigh-Darcy number is determined in a closed algebraic form via linear instability analysis.The critical Rayleigh-Darcy number is shown to be a decreasing function of the dimensionless compressibility factor.

An analytical study on transient thermal behavior of a packed-bed molten salt thermocline thermal storage

A volume averaged set of the governing equations for local thermal non-equilibrium fluid saturated porous media was applied to study transient thermal behavior of convection and conduction within a packed-bed thermocline thermal storage tank. General analytical expressions, which agree well with numerical results, were derived for the prediction of transient temperature fields of molten salt and granulated material. Three important dimensionless parameters, namely, the solid fluid heat capacity ratio, interstitial Stanton number and Peclet number based on the effective thermal diffusivity, are identified to investigate their effects on the thermal response of the packed-bed thermocline thermal storage tank. An explicit analytical expression for the effective discharging efficiency has been derived as a function of the three important dimensionless parameters. The expression may serve as a powerful tool to design a packed-bed thermocline thermal storage tank according to required operational conditions.

Mathematical Theory of Nonlinear Single-Phase Poroelasticity

In this paper, we study the equations of nonlinear poroelasticity derived from mixture theory. They describe the quasi-static mechanical behavior of a fluid saturated porous medium. The nonlinearity arises from the compressibility of the fluid and from the dependence of porosity and permeability on the divergence of the displacement. We point some limitations of the model. In our approach, we discretize the quasi-static formulation in time and first consider the corresponding incremental problem. For this, we prove existence of a solution using Brézis’ theory of pseudo-monotone operators. Generalizing Biot’s free energy to the nonlinear setting, we construct a Lyapunov functional, yielding global stability. This allows us to construct bounds that are uniform with respect to the time step. In the case when dissipative interface effects between the fluid and the solid are taken into account, we consider the continuous time case in the limit when the time step tends to zero. This yields existence of a weak free energy solution.