Homogeneous Poroelastic Medium Research Articles

Sensitivity limits for strain detection of hypothetical remote fluid-induced earthquakes (Mw ≥ 4): a case study in Taiwan

Capturing and quantifying the timing of remotely triggered earthquakes and understanding the physical processes responsible for this delay represent major challenges in earthquake forecasting. In this study, we propose a physical framework for the integration of borehole strainmeter observations for the investigation of remote triggering of moderate to large earthquakes (Mw ≥ 4) in Taiwan. Based on the time-delay computation between regional events and global earthquakes, we establish a selection of earthquakes showing fault zone properties (hydraulic diffusivity and nucleation length) that may be compatible with a magnitude-dependent fluid-induced nucleation process. Using theoretical fault zones parameters, we calculate the evolution of fluid pressure transiting along the nucleation region under the assumption of a one-dimensional, homogeneous poroelastic medium. Pore pressure levels reached before earthquake rupture are ranging from about 0.02 kPa to 3 kPa in the case of teleseismic wave-induced elastic pressure ranging from 0.15 kPa to 27.3 kPa. To compute the time-dependent evolution of deformation generated by a remote diffusing pressure front, we model the nucleation region using the analogue volcano source represented by a horizontal circular crack, and calculate synthetic dilatation at the strainmeter location from displacements using a finite-difference approach. In general, predictions are about two to four orders of magnitude smaller than observations (∼ 10–5 to 10–3 nϵ). Therefore, this suggests that detection of pore pressure-related deformation would have required change of volume in the nucleation region that is at least one order of magnitude larger than for the hypothetical cases considered here. The study represents the first attempt to analyze strain time-series for detecting pre-earthquake strain anomalies related to fluid-induced earthquakes and illustrates the challenge for detecting and characterizing intermediate-to far-field earthquake precursors caused by fluid flow in active regions.

Permeability simulation in an elastic deformable sandstone under stress changes

Fluid flow and rock mechanics become coupled in various important phenomena in Geosciences. In order to study this coupling, laboratory work has been carried out in triaxial cells along the years for various rock and fluid types at different confinement stress and pore pressure conditions. In a similar way, poromechanic models have been developed to simulate them, in which constitutive porosity and permeability correlation models in terms of strain, stress and fluid pressure have to be provided. However, to date, the applicability of the available correlation models to describe this phenomenon in different types of rock remains to be analyzed. In this work, a single-phase poroelastic model is applied to simulate a published geomechanical test performed in sandstones to examine the capacity of commonly used constitutive porosity and permeability correlations to describe the behavior of a homogeneous poroelastic medium. After discussing the results, we conclude that for this sandstone, the best permeability constitutive correlation model is Walder and Nur.

Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media

Recently, an accurate coupling between subsurface flow and reservoir geomechanics has received more attention in both academia and industry. This stems from the fact that incorporating a geomechanics model into upstream flow simulation is critical for accurately predicting wellbore instabilities and hydraulic fracturing processes. One of the recently introduced iterative coupling algorithms to couple flow with geomechanics is the undrained split iterative coupling algorithm as reported by Kumar et al. (2016) and Mikelic and Wheeler (Comput. Geosci. 17: 455–461 2013). The convergence of this scheme is established in Mikelic and Wheeler (Comput. Geosci. 17:455–461 2013) for the single rate iterative coupling algorithm and in Kumar et al. (2016) for the multirate iterative coupling algorithm, in which the flow takes multiple finer time steps within one coarse mechanics time step. All previously established results study the convergence of the scheme in homogeneous poroelastic media. In this work, following the approach in Almani et al. (2017), we extend these results to the case of heterogeneous poroelastic media, in which each grid cell is associated with its own set of flow and mechanics parameters for both the single rate and multirate schemes. Second, following the approach in Almani et al. (Comput. Geosci. 21:1157–1172 2017), we establish a priori error estimates for the single rate case of the scheme in homogeneous poroelastic media. To the best of our knowledge, this is the first rigorous and complete mathematical analysis of the undrained split iterative coupling scheme in heterogeneous poroelastic media.

Effects of gas generation on stress states during burial and implications for natural fracture development

The complexity of fracture networks in shale gas reservoirs may result from the superimposition of several fracture sets forming in temporally modified stress states during burial. In addition to tectonic evolution, this modification can also be caused by the overpressure generated by gas generation. Compared with undercompaction, gas generation shows a different overpressuring process and may cause different effects on stress states. This paper addresses these effects during burial in terms of pore pressure stress coupling. A series of finite element simulations for this investigation are designed with different tectonic stress regimes using a simplified model with a homogeneous poroelastic medium. The results show that during burial, gas generation not only significantly decreases effective stresses but also changes differential stress by decreasing it in the normal faulting regime and increasing it in the thrust faulting regime compared with undercompaction. Furthermore, gas generation during burial may locally transform the given tectonic stress regime from normal faulting to strike slip or even thrust faulting regimes. The investigation implies that gas generation rather than undercompaction in burial history can significantly diversify the patterns of natural fractures by affecting the differential stress and even the local stress regime in addition to influencing their spatial distribution due to its spatial heterogeneity and its different effects on stress states in different stress regimes. As a result, the contribution of gas generation to overpressures should be differentiated from that of undercompaction before analysing the effects of overpressures on natural fracture development.

Poroelastic contribution to the reservoir stress path

Pore pressure/stress coupling is the change in the smaller horizontal stress σ h associated with changes in pore pressure P, and has been measured in numerous reservoirs worldwide. These measurements suggest that the change in minimum horizontal stress Δ σ h is on average ca. 64% of the change in the reservoir pore pressure Δ P, but can be as low as 34% and as high as 118%. Conventionally it is assumed that the total vertical stress σ v , given by the overburden, is not affected by changes in pore pressure, in contrast to the horizontal stresses σ H and σ h . We investigate analytically and numerically the spatio-temporal pore pressure and stress evolution in poroelastic media for continuous fluid injection at a point source, and calculate from the numerical modelling results the ratio Δ σ/Δ P. Analytically, we show that the measured average of Δ σ h /Δ P can mathematically be deduced from the long-term limit of the spatio-temporal evolution of pore pressure and horizontal stress caused by fluid injection at a point source. We compare our numerical results to the analytical solution for continuous point injection into homogeneous poroelastic media as well as to Δ σ h /Δ P values measured in the field, and show that all stress components change with a variation in P. We use the concept of poroelasticity to explain the observed coupling between pore pressure and stress in reservoirs, and we consider different measurement locations and measurement times as one possible reason for the measured variation in Δ σ h /Δ P in different oil fields worldwide.

Dynamic torsional response of an end bearing pile in saturated poroelastic medium

A comprehensive analytical solution is developed in this paper to investigate the torsional vibration of an end bearing pile embedded in a homogeneous poroelastic medium and subjected to a time-harmonic torsional loading. The poroelastic medium is modeled using Biot’s two-phased linear theory and the pile using one-dimensional elastic theory. By using the separation of variables technique, the torsional response of the soil layer is solved first. Then based on perfect contact between the pile and soil, the dynamic response of the pile is obtained in a closed form. Numerical results for torsional impedance of the soil layer are presented first to portray the influence of wave modes, slenderness ratio, pile–soil modulus ratio and poroelastic properties. A comparison with the plane strain theory is performed. The selected numerical results are obtained to analyze the influence of the major parameters on the torsional impedance at the level of the pile head. Finally, the dynamic torsional impedance of this study is compared with that for floating pile in elastic soil.

Torsional response of pile embedded in a poroelastic medium

The response of a cylindrical elastic pile embedded in a homogeneous poroelastic medium and subjected to torsional loading is studied for the first time. Based on the Muki's model, the pile-porous medium system is decomposed into a fictitious pile system and an extended porous medium system. The one-dimensional, vertical, elastic pile and the three-dimensional poroelastic medium are solved, respectively. Considering the mixed boundary-value conditions at the interface of pile and soil, a Fredholm's integral equation of the second kind for the bar-force is established. The force and the displacement of the pile are calculated by applying numerical quadrature.

Effects of Stress and Pore Pressure on Deformation of a Thin Crack-Like Inhomogeneity in a Poroelastic Medium

The influence of applied stresses and internal fluid pressure on deformation of a flat ellipsoidal inhomogeneity in a homogeneous poroelastic medium is studied. The inhomogeneity is filled with a porous material having a skeleton much softer than the corresponding to the surrounding medium (crack-like inclusion). The result of the calculation of stress and strain fields inside such inclusion is presented. Explicit formulas for the inclusion aspect ratio changing are obtained. They are relevant for velocities of seismic waves in porous rocks (Toksoz et al, 1976) their permeability (Gibson & Toksoz, 1990) as functions of confining and pore pressures. Results are compared with the ones available in literature.

Dynamic response of pile groups embedded in a poroelastic medium

The dynamic response of pile groups embedded in a homogeneous poroelastic medium and subjected to vertical loading is considered. The piles are represented by compressible beam-column elements and the porous medium uses Biot's three-dimensional elastodynamic theory. The dynamic impedance of pile groups can be computed directly by using pile–soil–pile dynamic interaction factors. The axial forces and pore pressures along the length of pile groups are computed by superposition method, which greatly reduces the computational time for the direct analysis of pile groups. Parametric studies are conducted for various conditions of pile groups. The superposition method is proposed for the dynamic response analysis of pile groups that is computationally feasible for practical applications.

Dynamic Axial Load Transfer from Elastic Bar to Poroelastic Medium

The time-harmonic response of a cylindrical elastic bar (pile) partially embedded in a homogeneous poroelastic medium and subjected to a vertical load is considered. The bar is modeled using 1D elastic theory valid for long bars in the low-frequency range, and the porous medium using Biot's 3D elastodynamic theory. The bar is bonded to the surrounding medium along the contact surface. The problem is formulated by decomposing the bar/porous medium system into a fictitious bar and an extended porous medium. A Fredholm's integral equation of the second kind governs the distribution of axial force in the fictitious bar. The integral equation involves kernels that are displacement and strain influence functions of a poroelastic half-space subjected to a buried, uniform vertical patch load. The governing integral equation is solved by applying numerical quadrature. The solutions for axial displacement and axial force of the bar, and the pore pressure are also derived. Selected numerical results for vertical impedance, axial force, and pore pressure profiles are presented to portray the influence of bar stiffness and length/radius ratio, frequency of excitation, and poroelastic properties.

Dynamic streaming currents from seismic point sources in homogeneous poroelastic media

SUMMARY In a porous medium saturated with a £uid electrolyte, mechanical and electromagnetic disturbances are coupled. The coupling is electrokinetic in nature. The seismic waves generate relative £uid^solid motion that induces an electrical streaming current. Mechanically induced streaming currents generated by point sources in homogeneous, isotropic porous media are presented. The electrically induced streaming current is shown to be second order in electrokinetic coupling coe⁄cient and is neglected. This decouples the mechanical behaviour from the electromagnetic behaviour withrespect to the induced £uxes.We have used Biot theory to calculate the amount of induced relative £ow by Green’s function solution. The transport coe⁄cients, conductivity, dynamic permeability and electrokinetic coupling coe⁄cient, and their sensitivities with respect to porosity, DC permeability and frequency changes are evaluated. The conductivity decreases with increasing DC permeability. It has a k {1=2 0 dependence when grainsurface conductances dominate over the bulk-£uid-phase conductivity. Stationaryphase relative-£ow and streaming current solutions are calculated for point sources acting on both phases of the porous medium. The streaming currents are induced by both P and S waves.The streaming current decreases with increasing £uid conductivity. This is consistent with the decrease of the diiuse double-layer thickness and f-potential. The porosity aiects the bulk moduli of the solid. Its eiect combined with the frame bulk modulus and compressibility of the saturating £uid determines the streaming current amplitude induced by a P wave.The increase in streaming current amplitude induced by S waves with increasing porosity is due to the decrease of the shear frame modulus with increasing porosity.The streaming current behaviour with respect to DC permeability is found to diier for sources applied to the elastic frame and volume-injection sources.