Pore Fluid Pressure Field Research Articles

Fully coupled thermo-hydro-mechanical modeling and simulation of a fluid-saturated porous medium under local thermal non-equilibrium condition

• Fully coupled THM model of porous media under LTNE condition is presented. • T s is always higher than T f due to the LTNE effect. • Dependences of multi-physical fields on the pertinent parameters are investigated. This paper presents a fully coupled thermo-hydro-mechanical (THM) model of a fluid-saturated and compressible porous medium under local thermal non-equilibrium (LTNE) condition and carries out the corresponding numerical simulation. First, the coupling among the temperature field, the pore fluid pressure field, and the solid stress/displacement field is fulfilled by means of strong explicit coupling of governing equations in this study. Then, the presented model is applied to the THM coupling problem in an infinite porous medium with a cylindrical borehole subjected to uniform fluid pressure and temperature at the borehole boundary. Subsequently, the partial differential equations (PDEs) module in COMSOL Multiphysics software is employed to numerically solve the studied problem. Consequently, the finite element solutions of the pore fluid pressure field, the strain/stress fields and the two temperature fields of pore fluid and skeleton solid are obtained, and the spatial-temporal distribution characteristics of the above multi-physical fields are investigated. Finally, the corresponding parametric studies are carried out. The numerical results show that the stress decreases with the increase of the bulk volumetric thermal expansion coefficient of porous media. And the pore pressure decreases when the pore fluid mobility increases. Meanwhile, it is found in this work that the solid temperature is always higher than that of pore fluid due to the LTNE effect. Besides, with increasing the specific solid–fluid interfacial heat transfer coefficient, the solid temperature decreases, while the temperature of pore fluid increases. Accordingly, the temperature difference between the solid and the pore fluid diminishes. In addition, the thermal conductivity of solid grains has a greater impact on the solid temperature but has a limited impact on the temperature of pore fluid, and vice versa. The findings in this work are of benefit to obtain in-depth understanding of THM fully coupling mechanism and LTNE effect in a fluid-saturated porous medium.

Stress and pore fluid pressure control of seismicity rate changes following the 2016 Kumamoto earthquake, Japan

We quantitatively examined the influence of pore fluid pressure and coseismic stress changes on the seismicity rate changes that followed the 2016 Kumamoto earthquake, on the basis of two approaches. One is a numerical calculation of the classic stress metric of ∆CFS, and the other is an inversion analysis of pore fluid pressure fields with earthquake focal mechanism data. The former calculation demonstrated that seismicity rate changes were consistent with the expectation from ∆CFS in 65% of the target region, whereas they were not in the remaining 35% of the region. The latter analysis indicates that seismicity rates increased in the regions where pore fluid pressure before the Kumamoto earthquake sequence was remarkably enhanced above hydrostatic, regardless of values of ΔCFS. This suggests that the increase in pore fluid pressure is one of the important physical mechanisms triggering aftershock generation. We obtained evidence that pore fluid pressure increased around the southern part of the main rupture zone after the mainshock, examining temporal changes in types of focal mechanism data. The average increases in pore fluid pressure were estimated to be 17, 20, and 17 MPa at depths of 5, 10, and 15 km, respectively. These large increases in pore fluid pressure cannot be explained under the undrained condition. The spatial derivative of the pore fluid pressure field in the depth direction implies that fluid supply from greater depths may have controlled increases in seismicity rates that followed the large earthquake.

Controls of hydrocarbon generation on the development of expulsion fractures in organic-rich shale: Based on the Paleogene Shahejie Formation in the Jiyang Depression, Bohai Bay Basin, East China

The development of expulsion fractures in organic-rich shale is closely related to hydrocarbon generation and expulsion from kerogen. Organic-rich shales from the upper part of the fourth member and the lower part of the third member of the Paleogene Shahejie Formation in the Jiyang Depression, Bohai Bay Basin, East China, are used as an example. Based on thin sections, SEM and thermal simulation experiments, the characteristics of hydrocarbon generation and the conditions supporting the development of expulsion fractures were explored. The key factors influencing these fractures include the presence of kerogens, their distribution along laminae and around particle boundaries, their exposure to heat and the build-up in pressure due to confinement by low permeability. The development of excess pore fluid pressures and intrinsic low rock fracture strength are the main influencing factors. Pressurization by rapid generation of hydrocarbon provides impetus for fracture initiation and cause bitumen to migrate quickly. The shale laminae results in distinctly lower fracture strength laminae-parallel than laminae-normal and this directs the formation of new fractures in the direction of weakness. When pore fluid pressure increases, maximum and minimum principal effective stresses decrease by different proportions with a larger reduction in the maximum principal effective stress. This increases the deviatoric stress and reduces the mean stress, thus driving the rock towards failure. Moreover, the tabular shape of the kerogen aids the generation of hydrocarbon and the initiation of expulsion fractures from the tip and edge. The resulting fractures extend along the laminae when the tensile strength is lower in the vertical direction than in the horizontal direction. Particle contact boundaries are weak and allow fractures to expand around particles and to curve as the stress/strength regime changes. When pore fluid pressure fields at different fracture tips overlap, fractures will propagate and interconnect, forming a network. This paper could provide us more detailed understanding of the forming processes of expulsion fractures and better comprehension about hydrocarbon expulsion (primary migration) in source rocks.

Overpressurized fluids drive microseismic swarm activity around Mt. Ontake volcano, Japan

Microseismic swarm activity has taken place since 1976 around Mt. Ontake, the second highest stratovolcano in Japan. This activity is thought to be linked to high pore-fluid pressure in the vicinity of the volcano. We analyzed well-constrained focal mechanism solutions of microseismicity to re-estimate the 3-D pore-fluid pressure field driving vigorous swarm activity around Mt. Ontake. Pore-fluid pressures were measured by mapping earthquake focal mechanisms on the 3-D Mohr diagram for the regional stress field with high resolutions of 2–5 km. The assumption of the reference stress pattern can cause modeling errors in measurements of pore-fluid pressure. To remove the effect, we statistically evaluated the estimation errors of the regional stress field and included these errors in the analysis. We detected an overpressurized fluid reservoir with a peak of about 10–30 MPa in the east flank of Mt. Ontake, where microseismic swarm activity has been vigorous for the last two decades. The level of pore-fluid pressure was maintained for at least 5 years after 2009. This finding indicates that there are some interactions between the intensive swarm activity and overpressurized fluids: the swarm activity has been driven by overpressurized fluids, whereas pore-fluid pressures have been suppressed by the swarm activity.Graphical abstract.

A stable Maximum-Entropy Meshless method for analysis of porous media

Consolidation analysis of saturated porous media demands the coupling of solid displacements with the pore fluid pressure via the equilibrium and the continuity of mass. In this paper, a stable numerical procedure is presented for coupled analysis of consolidation problems in geotechnical engineering. The numerical framework is based on the Element-Free Galerkin method and the principle of Maximum Entropy. Identical shape functions are employed for approximating the displacement field as well as the pore fluid pressure field. The proposed method is used for analysing several consolidation problems assuming elastic and elastoplastic soil behaviour. The numerical results indicate that the proposed Maximum-Entropy Meshless method based on the maximum entropy shape functions is able to provide stable and robust solutions for consolidation problems in porous media.

Evolution of pore fluid pressures in a stimulated geothermal reservoir inferred from earthquake focal mechanisms

AbstractThis paper proposes an inversion method to estimate the evolution of pore fluid pressure fields from earthquake focal mechanism solutions. Application of the method to induced seismicity in the Basel enhanced geothermal system in Switzerland shows the evolution of pore fluid pressure in response to fluid injection experiments. The pore fluid pressure in the reservoir was less than the minimum principal stress at each depth, indicating that hydraulic fracturing did not occur during the stimulation. This suggests that seismic events may play an important role in promoting the development of permeable channels, particularly southeast of the borehole where the largest seismic event (Mw 2.95) occurred. This is not directly related to a drastic decrease in fault strength at the hypocenter but rather to positive feedback between permeability enhancement and elastic/poroelastic stress loading from slipping interfaces.

Effects of pore fluid pressure and tectonic stress on diverse seismic activities around the Mt. Ontake volcano, central Japan

To understand the effects of pore fluid pressure and tectonic stress in generating diverse seismicity, we deployed 11 temporary seismic stations around an active volcano, Mt. Ontake, in central Japan during the summers of 2009–2011. We obtained well-constrained focal mechanism solutions from the seismic data recorded at the temporary stations and permanent stations located within 50 km around Mt. Ontake. We estimated the 3-D pore fluid pressure field, taking into consideration spatial changes in the tectonic stress pattern, by applying the method of focal mechanism tomography to the dataset. We found overpressurized fluid reservoirs with a peak of 100–150 MPa at depths between 5 and 12 km in the southeast and east flanks of Mt. Ontake. This region has experienced earthquake swarm activity since 1976. Many seismic events concentrated at the edge of the overpressurized fluid reservoirs, where pore fluid pressure gradients are steep. This indicates that a large amount of fluid flow would trigger seismic events by decreasing fault strength caused by an increase in pore fluid pressures. Many small events (M < 3) occurred on pre-existing faults that are unfavorably oriented or severely mis-oriented relative to the tectonic stress pattern, indicating that these events are driven by overpressurized fluids. However, the macroscopic rupture planes of microseismic clouds and larger events (M ≥ 3) appear to release tectonic stresses produced by steady plate subduction. The critical event magnitude (Mc = 3) at which seismic behavior changes would be characterized by a length scale of pore fluid pressure heterogeneity. This quantity might be an indicator of the maximum event magnitude in the region.

High fluid pressure and triggered earthquakes in the enhanced geothermal system in Basel, Switzerland

We analyzed 118 well‐constrained focal mechanisms to estimate the pore fluid pressure field of the stimulated region during the fluid injection experiment in Basel, Switzerland. This technique, termed focal mechanism tomography (FMT), uses the orientations of slip planes within the prevailing regional stress field as an indicator of the fluid pressure along the plane at the time of slip. The maximum value and temporal change of excess pore fluid pressures are consistent with the known history of the wellhead pressure applied at the borehole. Elevated pore fluid pressures were concentrated within 500 m of the open hole section, which are consistent with the spatiotemporal evolution of the induced microseismicity. Our results demonstrate that FMT is a robust approach, being validated at the meso‐scale of the Basel stimulation experiment. We found average earthquake triggering excess pore fluid pressures of about 10 MPa above hydrostatic. Overpressured fluids induced many small events (M &lt; 3) along faults unfavorably oriented relative to the tectonic stress pattern, while the larger events tended to occur along optimally oriented faults. This suggests that small‐scale hydraulic networks, developed from the high pressure stimulation, interact to load (hydraulically isolated) high strength bridges that produce the larger events. The triggering pore fluid pressures are substantially higher than that predicted from a linear pressure diffusion process from the source boundary, and shows that the system is highly permeable along flow paths that allow fast pressure diffusion to the boundaries of the stimulated region.

Evolution of the Pore-Pressure Field around a Moving Conical Penetrometer of Finite Size

A solution is developed for the evolution of buildup, steady, and postarrest dissipative pore-fluid pressure fields that develop around a finite-radius conical penetrometer advanced in a saturated linearly elastic porous medium. The analog with cone penetrometer testing is direct and is used to enable continuous distributions of permeability and diffusivity to be determined with depth. This analysis reveals the direct dependence of penetration rate on the induced fluid pressure field magnitudes, and predicts that a penetration rate threshold limit exists with respect to pore-pressure generation. This represents the essence of a partially drained system. The developed pore-pressure field is determined to be a function of the dissipation rate of the material, the penetration rate, and the storage effects of the advecting medium. Analysis of the pore-pressure field under start-up conditions reveals that the time required to reach steady state is strongly influenced by the penetration rate and the pressure-dissipation properties of the material. Analysis of the developed stable pressure fields illustrates the inversely proportional relationship that exists between penetration rate and pore-pressure magnitudes at the cone surface; representing the influence of storage in the medium on stable pore-pressure magnitudes. Stable pressure fields below the penetration threshold limit, UD10 1 , form a spherical response around the cone tip transitioning to an elongated radial response for penetration rates above this limit. Postarrest analysis indicates that the prearrest penetration rate strongly influences the dissipation rate and pattern of dissipation. The developed analysis can be correlated with CPTu-recovered data to independently evaluate permeability magnitudes during steady penetration.

Modeling Deformation-Induced Fluid Flow in Cortical Bone?s Canalicular?Lacunar System

To explore the potential role that load-induced fluid flow plays as a mechano-transduction mechanism in bone adaptation, a lacunar-canalicular scale bone poroelasticity model is developed and implemented. The model uses micromechanics to homogenize the pericanalicular bone matrix, a system of straight circular cylinders in the bone matrix through which bone fluids can flow, as a locally anisotropic poroelastic medium. In this work, a simplified two-dimensional model of a periodic array of lacunae and their surrounding systems of canaliculi is used to quantify local fluid flow characteristics in the vicinity of a single lacuna. When the cortical bone model is loaded, microscale stress, and strain concentrations occur in the vicinity of individual lacunae and give rise to microscale spatial variations in the pore fluid pressure field. Furthermore, loading of the bone matrix containing canaliculi generates fluid pressures in the contained fluids. Consequently, loading of cortical bone induces fluid flow in the canaliculi and exchange of fluid between canaliculi and lacunae. For realistic bone morphology parameters, and a range of loading frequencies, fluid pressures and fluid-solid drag forces in the canalicular bone are computed and the associated energy dissipation in the models compared to that measured in physical in vitro experiments on human cortical bone. The proposed model indicates that deformation-induced fluid pressures in the lacunar-canalicular system have relaxation times on the order of milliseconds as opposed to the much shorter times (hundredths of milliseconds) associated with deformation-induced pressures in the Haversian system.

Indentation of a Free-Falling Sharp Penetrometer into a Poroelastic Seabed

A solution is developed for the buildup, steady, and postarrest dissipative pore fluid pressure fields that develop around a conical penetrometer that self-embeds from free-fall into the seabed. Arrest from free-fall considers deceleration under undrained conditions in a purely cohesive soil, with constant shear strength with depth. The resulting decelerating velocity field is controlled by soil strength, bearing capacity factors, and inertial components. At low impact velocities the embedment process is controlled by soil strength, and at high velocities by inertia. With the deceleration defined, the solution for a point normal dislocation migrating in a poroelastic medium is extended to incorporate the influence of a tapered tip. Dynamic steady pressures, \IP\dD\N, develop relative to the penetrating tip geometry with their distribution conditioned by the nondimensional penetration rate, \IU\dD\N, incorporating impacting penetration rate, consolidation coefficient, and penetrometer radius, and the nondimensional strength, \IN\dD\N, additionally incorporating undrained shear strength of the sediment. Pore pressures may develop to a steady peak magnitude at the penetrometer tip, and drop as \IP\dD\N = 1/\Ix\dD\N with distance \Ix\dD\N behind the tip and along the shaft. Induced pore pressures are singular in the zone of tip taper for the assumed zero radius of the penetrometer, negating the direct evaluation of permeability magnitudes from pressures recorded on the cone face. However, peak induced pressure magnitudes may be correlated with sediment permeabilities, postarrest dissipation rates may be correlated with consolidation coefficients, and depths of penetration may be correlated with shear strengths. The magnitudes of fluid pressures evaluated on the shaft may be correlated with sharp penetrometer data (reported by Urgeles et al. in 2000) to independently evaluate magnitudes of strength and transport parameters.

Indentation of a free-falling lance penetrometer into a poroelastic seabed

A solution is developed for the buildup, steady, and postarrest dissipative pore fluid pressure fields that develop around a conical penetrometer that self-embeds from free-fall into the seabed. Arrest from free-fall considers deceleration under undrained condi- tions in a purely cohesive soil, with constant shear strength with depth. The resulting decelerating velocity field is controlled by soil strength, bearing capacity factors, and inertial components. At low impact velocities the embedment process is controlled by soil strength, and at high velocities by inertia. With the deceleration defined, the solution for a point normal dislocation migrating in a poroelastic medium is extended to incorporate the influence of a tapered tip. Dynamic steady pressures, PD , develop relative to the penetrating tip geometry with their distribution conditioned by the nondimensional penetration rate, UD , incorporating impacting penetration rate, consolidation coefficient, and penetrometer radius, and the nondimensional strength, ND , additionally incorporating undrained shear strength of the sediment. Pore pressures may develop to a steady peak magnitude at the penetrometer tip, and drop as PD51/x D with distance x D behind the tip and along the shaft. Induced pore pressures are singular in the zone of tip taper for the assumed zero radius of the penetrometer, negating the direct evaluation of permeability magnitudes from pressures recorded on the cone face. However, peak induced pressure magnitudes may be correlated with sediment permeabilities, postarrest dissipation rates may be correlated with consoli- dation coefficients, and depths of penetration may be correlated with shear strengths. The magnitudes of fluid pressures evaluated on the shaft may be correlated with sharp penetrometer data ~reported by Urgeles et al. in 2000! to independently evaluate magnitudes of strength and transport parameters.

Indentation of a sharp penetrometer in a poroelastic medium

Solution is developed for the build-up, steady and post-arrest dissipative pore fluid pressure fields that develop around a conical penetrometer advanced in a poroelastic medium. The analog with cone penetrometer testing is direct, and is used to enable continuous distributions of permeability and diffusivity to be determined, with depth. Solution for a point normal dislocation migrating in a poroelastic medium is extended to incorporate the influence of a tapered tip. Steady pressures develop relative to the migrating tip geometry with distribution conditioned by the non-dimensional penetration rate, U D , incorporating penetration rate, hydraulic diffusivity and penetrometer radius. The near-spherical pressure distribution, recovered for low penetration velocities, becomes radial as penetration rate increases. Along the penetrometer shaft, non-dimensional induced pore fluid pressures, P D , are independent of penetration rate, U D , and asymptote to an inverse radial distribution remote from the tip as P D = 1\\ x D . This importantly identifies the control on penetration induced pore fluid pressure as the magnitude of permeability, embodied in the non-dimensional pressure, P D , rather than a dependence on hydraulic diffusivity, as had previously been considered. Induced pore pressures are singular in the zone of tip taper for the assumed zero radius of the penetrometer, negating the direct evaluation of permeability magnitudes from pressures recorded on the cone face. However, the finite magnitudes of fluid pressures evaluated on the shaft may be correlated with field data to independently evaluate magnitudes of permeability during steady penetration.

THERMAL STRESSES IN A FLUID-SATURATED POROELASTIC HOLLOW SPHERE

By using the thermoporoelastic theory proposed previously, thermal stresses are analyzed that are induced in a fluid-saturated porous hollow sphere subjected to a sudden rise in temperature and pressure on its inner wall. Since the problem formulated is spherically symmetric, the displacement field is decoupled from the temperature and pore fluid pressure fields, which are still coupled with each other. Coupled diffusion equations for heat and fluid flows are solved by the Crank-Nicolson implicit method because they involve nonlinear and integral terms. The attention is focused on the effect of heat transfer by fluid flow through pores on the temperature and thermal stress distributions. This effect is very marked for the case where the fluid diffusivity is much larger than the thermal one. This suggests a possible control of thermal stresses by active fluid injection.

Kinematic models of dewatering accretionary prisms

Steady state two‐dimensional analytical solutions are derived for sediment velocity and rate of fluid expulsion in a thickening accretionary prism with smooth upper and lower surfaces. Two different kinematic assumptions lead to two similar sets of solutions. In one case, the sediment flow lines are assumed to diverge uniformly landward. In the other case, the horizontal velocity of any given sediment column is assumed uniform. By further assuming zero horizontal Darcy velocity in the prism, expressions can be obtained for the approximate vertical fluid velocity and pore fluid pressure fields. Results from applying these solutions to the Cascadia accretionary prism off Vancouver Island show the importance of modeling the effects of lateral as well as vertical porosity variation on the hydrogeology of the prism. These solutions provide a means to estimate fluid flow and pore pressure distribution for prisms with realistic geometry. The rate of fluid expulsion can also be incorporated into numerical models as the fluid source term.

Thermal Stresses of a Fluid-Saturated Poroelastic Hollow Cylinder

By use of the thermoporoelastic theory previously proposed by the author, analysis is made of the thermal stresses which are induced in d fluid-saturated porous hollow cylinder subjected to a sudden increase in temperature and pressure on its inner surface. Since the problem formulated is axisymmetric, the displacement field is decoupled from the temperature and pore fluid pressure fields, which are still coupled with each other. Coupled diffusion equations for heat and fluid flows are solved by the Crank- Nicolson implicit method, because they involve nonlinear and integral terms. The primary focus of this study is on the influence of heat transportation by fluid flow through pores on the temperature and thermal stress distributions. This influence is quite marked in the case where the fluid diffusivity is much larger than the thermal diffusivity, suggesting the possible control of thermal stresses by active fluid injection.