Pore Pressure Field Research Articles

Prediction of water inflow into a tunnel based on three-district zoning of faults

Water inflow into a tunnel subject to fault zones and fault effective zones is interpreted in this study using a three-district zoning method. An improved Brinkman model is proposed to investigate the seepage law of the geological defects of a fault. A coupled calculation model of typical Darcy seepage and Brinkman rapid seepage is constructed to establish a mathematical model of nonlinear seepage flow based on three-district zoning and the corresponding numerical implementation. In addition, the influence of the angle between the fault dip and tunneling directions on the water inrush in a tunnel is also studied. The variation characteristics of the pore pressure and velocity fields under various construction stages are analyzed, as is the seepage velocity of pore water at the tunnel heading. Moreover, the effects of the fault dip direction on the seepage field and water inflow are discussed. The following results were obtained. (1) Before excavation to the fault effective zone, the pore pressure at the same depth remained essentially unchanged in front of the tunnel heading. After excavation to the fault effective zone, the pore pressure at the same depth increases linearly with distance in front of the tunnel heading. (2) The seepage velocity changed gently before excavation to the fault effective zone but showed wavy fluctuating after excavation to the fault effective zone. The velocity reached its maximum value in the fault zone before decreasing rapidly and remaining close to zero in the general surrounding rock zones. (3) As the excavation length increased, the water inflow increased gradually, reaching its maximum value in the fault zone. (4) In the fault zone, the seepage velocity decreased with an increase in the fault dip. The water inflow reached maximum and minimum values at angles of 90° and 150°, respectively.

Dynamic Stress Field Evolution of the Shale Oil Reservoirs: Development and Optimization of Well Patterns

Research on shale oil has gained considerable attention with regard to global unconventional oil exploration, which is of the strategic significance in the field of energy. Considering the characteristics of continental shale reservoirs, a three-dimensional fluid–solid coupling model of a multistage fracturing horizontal well was established based on the poroelasticity theory. The difference in stress sensitivity among different layers was also considered in this model. The evolution of pore pressure and stress field during the production process was analyzed through numerical simulation. A comparison of the planar well pattern and stereo well pattern revealed that the latter has less interwell-flow interference and smaller alteration angle of the minimum principal stress; thus, in the latter pattern, intersection with existing hydrofractures during refracturing can be avoided. It is more advantageous to refracturing in the middle of the outside horizontal section, but with increase in production time, the optimal fracturing section shrinks. Considering the maximum recovery factor and interwell interference, well-spacing optimization is recommended from 200 m to 300 m.

A Crack Propagation Control Study of Directional Hydraulic Fracturing Based on Hydraulic Slotting and a Nonuniform Pore Pressure Field

Hydraulic fracturing techniques for developing deeply buried coal reservoirs face routine problems related to high initial pressures and limited control over the fracture propagation direction. A novel method of directional hydraulic fracturing (DHF) based on hydraulic slotting in a nonuniform pore pressure field is proposed. A mechanical model is used to address crack initiation and propagation in a nonuniform pore pressure field, where cracks tend to rupture and propagate towards zones of high pore pressure for reducing the effective rock stress more. The crack initiation pressure and propagation morphology are analyzed by rock failure process analysis software. The numerical results show that the directional propagation of hydraulic fracturing cracks is possible when the horizontal stress difference coefficient is less than or equal to 0.5 or the slotting deviation angle is less than or equal to 30°. These findings are in good agreement with experimental results, which support the accuracy and reliability of the proposed method and theory.

Seismoelectric effect in Lamb’s problem

Seismoelectric effect is studied in the framework of classical Lamb’s problem with impulse or time- variable mechanical action on an elastic porous half-space. Radiation of elastic waves gives rise to pressure variation of groundwater fluid contained in pores and cracks. This causes the generation of telluric electric fields and currents due to the seismoelectric effect. A diffusion type equation is applied to describe the variations of the pore pressure and telluric electric field. Particular emphasis has been placed on the properties of seismoelectric signals caused by Rayleigh wave propagation since this wave has maximal amplitude at a considerable distance from the seismic source. For practical purposes and geophysical application, the co-seismic phenomena related to seismoelectric effect are examined in more detail.

A poroelastic model for laboratory hydraulic fracturing of weak permeable rock

Water injection laboratory experiments in weak, poorly consolidated sandstones show evidence that the peak injection pressure is much larger than the one predicted by the Haimson-Fairhurst breakdown criterion. A model based on poroelasticity, fracture mechanics, and lubrication theory is constructed to simulate the laboratory experiments. It aims at computing the propagation of a bi-wing hydraulic fracture from a borehole with increasing injection rate, until the crack reaches the boundary of the sample. The model is applicable to situations for which the pore pressure field reaches a steady state quasi-instantaneously when changing the injection rate, on account of the large permeability of these rocks. Taking advantage of the linearity of the poroelasticity equations, the model is formulated in terms of singular integral equations. Combined with the nonlinear lubrication equation, the convolution integrals, resulting from the application of the boundary conditions, are approximated by discretizing the unknown distribution of singularities. Finally, the injection rate corresponding to a given crack length is obtained by solving a nonlinear system of equations involving only unknowns along the crack. Two asymptotic regimes of solution are found: (i) a rock-flow regime where the induced fracture is hydraulically invisible, and (ii) a fracture-flow regime where the fluid penetrates the rock via the crack. In the rock-flow regime, fracture propagation is stable, i.e., the borehole pressure increases with the injection rate; while in the fracture-flow regime, the reverse is true. It is concluded that the peak injection pressure reflects a transition between two flow regimes, rather than breakdown. A parametric analysis also indicates that poroelasticity significantly affects the magnitude of the injection pressure.

Excavation induced over pore pressure around drifts in the Callovo-Oxfordian claystone

Continuous field monitoring during drifts excavation at the Meuse/Haute-Marne Underground Research Laboratory showed anisotropic hydromechanical responses, which are mainly evidenced in: (1) pore pressure field around the drifts with zones of marked overpressure; (2) the development of a dissymmetrical fractured zone induced by the excavation. These observations suggest that in addition to the initial stress state, the inherent anisotropy of the Callovo-Oxfordian claystone plays a key role in the response of rock formation. Numerical modelling show that inherent elastic anisotropy is not adequate to fully explain the pore pressure evolution during excavation. This paper aims to show and explain qualitatively and quantitatively the main trends of the excavation induced pore pressure evolution around drifts. First, a qualitative analysis is performed, based on a closed-form solution of elastic fields around an elliptical opening (in order to simulate fractured zone shape), embedded in a transversely isotropic rock. Then, a coupled poro-elasto-plastic analysis is performed, by taking into account a perfect poro-elasto-plastic behavior for both the intact rock and the induced fractured zones with different plastic parameters. It is shown that upon the determination of extension and shape of fractured zone, overpressures induced by the excavation can be well reproduced.

Analysis of Chemo-Poro-Thermo-Mechanical Effects on Wellbore Strengthening

Abstract The application of wellbore strengthening treatment has less effect on shale formations. Several numerical studies were developed to describe the mechanism, which promoted the development of wellbore strengthening theory. Previous studies explored the mechanism mainly by considering the seepage flow. Therefore, multi-field coupled models were established to analyze the solute transmission, thermal convection, and heat conduction on wellbore strengthening by introducing the theory of multi-field coupling into physical model. First, the fracture width distribution and wellbore tangential stress were investigated to research the interaction of thermal and chemical effects with different gradients. Then, the concrete mechanism of temperature and solute concentration gradient was analyzed based on the distribution of pore pressure and stress field. Results show that the prediction of hoop stress and fracture aperture may not be accurate without considering the influence of solute transfer, thermal convection, and heat conduction, because stress state is mainly affected by temperature field and the pore pressure varies greatly under different chemical gradients. Additionally, the lower temperature and larger solute concentration improve the wellbore strengthening effect of drilling fluid.

Faults as Volumetric Weak Zones in Reservoir-Scale Hydro-Mechanical Finite Element Models—A Comparison Based on Grid Geometry, Mesh Resolution and Fault Dip

An appropriate representation of faults is fundamental for hydro-mechanical reservoir models to obtain robust quantitative insights into the spatial distribution of stress, strain and pore pressure. Using a generic model containing a reservoir layer displaced by a fault, we examine three issues which are typically encountered if faults have to be incorporated in reservoir-scale finite element simulations. These are (1) mesh resolution aspects honoring the scale difference between the typical cell size of the finite element (FE) reservoir model and the heterogeneity of a fault zone, (2) grid geometry relative to the fault geometry and (3) fault dip. Different fault representations were implemented and compared regarding those on the modeling results. Remarkable differences in the calculated stress and strain patterns as well as the pore pressure field are observed. The modeling results are used to infer some general recommendations concerning the implementation of faults in hydro-mechanical reservoir models regarding mesh resolution and grid geometry, taking into account model-scale and scope of interest. The goal is to gain more realistic simulations and, hence, more reliable results regarding fault representation in reservoir models to improve production, lower cost and reduce risk during subsurface operations.

3D thermo-hydro-mechanical coupled discrete beam lattice model of saturated poro-plastic medium

In this paper, we present a 3D thermo-hydro-mechanical coupled discrete beam lattice model of structure built of the nonisothermal saturated poro-plastic medium subjected to mechanical loads and nonstationary heat transfer conditions. The proposed model is based on Voronoi cell representation of the domain with cohesive links represented as inelastic Timoshenko beam finite elements enhanced with additional kinematics in terms of embedded strong discontinuities in axial and both transverse directions. The enhanced Timoshenko beam finite element is capable of modeling crack formation in mode I, mode II and mode III. Mode I relates to crack opening, mode II relates to in-plane crack sliding, and mode III relates to the out-of-plane shear sliding. The pore fluid flow and heat flow in the proposed model are governed by Darcy\'s law and Fourier\'s law for heat conduction, respectively. The pore pressure field and temperature field are approximated with linear tetrahedral finite elements. By exploiting nodal point quadrature rule for numerical integration on tetrahedral finite elements and duality property between Voronoi diagram and Delaunay tetrahedralization, the numerical implementation of the coupling results with additional pore pressure and temperature degrees of freedom placed at each node of a Timoshenko beam finite element. The results of several numerical simulations are presented and discussed.

Experimental and numerical investigation on influence of pore-pressure distribution on multi-fractures propagation in tight sandstone

During the process of reservoir stimulation, how to create more fractures has become a key issue for the tight sandstone reservoir development. From the experimental investigation and numerical simulation, the effect of pore pressure distribution on fracture propagation was analyzed. The experiment consisted of 300 × 300 × 600 mm3 sandstone specimens was divided into two laboratory tests to investigate the fracture propagation of simultaneous fracturing and sequence fracturing subjected to true tri-axial confinement stresses. The experimental results showed that the fracture distribution was asymmetric due to the influence of pore pressure and stress field. Meanwhile, the numerical simulation results discovered that the increase of pore pressure can not only cause the deflection of fracture, but also increase the breakdown pressure and extension pressure of rock. When the pore pressure increment was over 4 MPa, the fracture deflected obviously in the process of extension, and the breakdown pressure and extension pressure can increase by 22.8% and 23.05%.

In Situ Investigation of the THM Behavior of the Callovo-Oxfordian Claystone

The thermo-hydro-mechanical behavior of the host rock is essential while designing an underground radioactive waste disposal repository, and in particular, while considering the long-term safety of the facility. In 2000, the French National Radioactive Waste Management Agency (Andra) started constructing an underground research laboratory located in the Meuse Haute Marne to carry out a research program aiming to demonstrate the feasibility of constructing and operating a radioactive waste disposal facility in the Callovo-Oxfordian claystone, and to optimize its implementation. To study the thermo-hydro-mechanical effects of the early thermal phase on the clay host rock of a deep repository, Andra has performed various in situ heating tests; one of them is called the TED experiment. The aim of the TED experiment was to measure the evolution of the temperature and pore pressure fields around several heaters and to back-analyze the thermo-hydro-mechanical properties of the Callovo-Oxfordian claystone. Thermal conductivity and heat capacity values were determined based on the back-analysis of the in situ measurements and compared to those measured on samples. The in situ experimental data and numerical model confirm the anisotropic behavior of the claystone. The TED experiment results demonstrate the ability of current models to predict the evolution of temperature and pore pressure in the far field of disposal cells.

An elastoplastic damage constitutive model of concrete considering the effects of dehydration and pore pressure at high temperatures

Pore pressure and thermal dehydration of concrete are two major factors which affect the spalling of concrete at high temperatures. Thermal dehydration can cause deterioration of concrete properties and promote the development of micro cracks in the skeleton of concrete. Pore pressure will also be influenced by dehydration when the hydrated water enters the micro pores. In the current study, a framework of elastoplastic damage constitutive model is developed to described the mechanical behaviour of concrete and pore pressure at high temperatures. Both load induced damage and thermal dehydrated damage are considered. The thermal dehydrated damage is temperature related, which reflects the impact of temperature on concrete properties. A model of pore pressure is developed by considering the influence of thermal dehydration and damage related permeability. The pore pressure field associated with vapor, liquid water and dry air is predicted and compared with experimental results.

Induced fault reactivation by thermal perturbation in enhanced geothermal systems

Heat extraction by circulating cold water through a geothermal reservoir could potentially induce earthquakes of large magnitudes. In this work, we explore the role of water injection inside a normal fault in triggering seismic slip, under different temperature and rate scenarios of fluid injection into fault damage zones. The resulted non-uniformity of thermal drawdown along the fault damage zones significantly affects the magnitude and timing of induced earthquakes. A non-dimensional expression integrating fault configuration (e.g. length and thickness) and injection condition (e.g. rate and temperature) is used to describe the relationship between the injection schedule and the resulting fault seismic slip event. As the dimensionless parameter QD increases, suggesting a transition from heat conduction to convection, the dimensionless event timing also grows nonlinearly. The perturbation of fault stress field induced from localized thermal cooling process is pronounced, compared to decoupled hydro-mechanical scenarios. The stress field perturbation in the system due to thermal cooling is characterized through a Coulomb friction ratio analysis for evaluating the stress changes along the fault plane and a tensor-based stress perturbation analysis for quantifying the stress changes in the damage zones and host rocks. The thermal influence acting on local patches along the fault strike not only advances the timing of seismic slip, but also increases the magnitude of induced seismic events, by unloading the fault to prompt seismic rupture. The injection temperature has a significant impact on facilitating the onset of seismic slip, i.e. attempting to accelerate the timing and increase the magnitude of fault reactivation. The injection rate variation will affect the timing by changing the pore pressure field and heat transfer manner. Prior to the onset of fault reactivation, the thermal unloading response increases fault permeability by decreasing normal stress, such that more permeable channels in the fault allow fluid to diffuse. Produced plastic shear strain due to fault slip provide extra positive contributions to increased normal aperture through shear dilation, thereby the fault permeability increases significantly by around two orders of magnitude.

Stabilized material point methods for coupled large deformation and fluid flow in porous materials

The material point method (MPM) has been increasingly used for the simulation of large-deformation processes in fluid-infiltrated porous materials. For undrained poromechanical problems, however, standard MPMs are numerically unstable because they use low-order interpolation functions that violate the inf–sup stability condition. In this work, we develop stabilized MPM formulations for dynamic and quasi-static poromechanics that permit the use of standard low-order interpolation functions notwithstanding the drainage condition. For the stabilization of both dynamic and quasi-static formulations, we utilize the polynomial pressure projection method whereby a stabilization term is augmented to the balance of mass. The stabilization term can be implemented with both the original and generalized interpolation material point (GIMP) methods, and it is compatible with existing time-integration methods. Here we use fully-implicit methods for both dynamic and quasi-static poromechanical problems, aided by a block-preconditioned Newton–Krylov solver. The stabilized MPMs are verified and investigated through several numerical examples under dynamic and quasi-static conditions. Results show that the proposed MPM formulations allow standard low-order interpolation functions to be used for both the solid displacement and pore pressure fields of poromechanical formulations, from undrained to drained conditions, and from dynamic to quasi-static conditions.

A poro-viscoelastic substitute model of fine-scale poroelasticity obtained from homogenization and numerical model reduction

Numerical model reduction is exploited for computational homogenization of the model problem of a poroelastic medium under transient conditions. It is assumed that the displacement and pore pressure fields possess macro-scale and sub-scale (fluctuation) parts. A linearly independent reduced basis is constructed for the sub-scale pressure field using POD. The corresponding reduced basis for the displacement field is constructed in the spirit of the NTFA strategy. Evolution equations that define an apparent poro-viscoelastic macro-scale model are obtained from the continuity equation pertinent to the RVE. The present model represents an extension of models available in literature in the sense that the pressure gradient is allowed to have a non-zero macro-scale component in the nested hbox {FE}^2 setting. The numerical results show excellent agreement between the results from numerical model reduction and direct numerical simulation. It was also shown that even 3D RVEs give tractable solution times for full-fledged hbox {FE}^2 computations.

A computationally efficient system for assessing near-real-time instability of regional unsaturated soil slopes under rainfall

The objective of this paper is to obtain an applicable assessment method and a Web-GIS-based prediction system for regional landslides. The traditional Richards function is reconstructed using the soil-water characteristic curve (SWCC) and the coordinate transformation technique. The analytical pore pressure for a slope model is derived by solving the modified Richard equation via the Green function and Fourier transformation. The obtained transient pore pressure field is then incorporated with Brakensiek’s matric suction theory, to build a conceptual model for rainfall-induced shallow landslides. The safety factor is obtained by solving the limit equilibrium equation of the conceptual model. The method is then implemented in a Web-GIS system, considering influence of slope geometry features, geology parent material, and near-real-time rainfall intensity of the study area. It is verified that this method is computationally efficient and reliable for gentle slopes and short rainfall durations. Moreover, an extensive parameter study shows that the two commonly used coefficients in the intensity-duration equation are both correlated to rainfall inter-event time via exponential functions, and rainfall event time via power functions. The primary influential factor for regional landslides is the initial water content, followed by the rainfall duration and intensity, and least by soil thickness.

Analysis of the penetration mechanism of CPTU based on large deformation finite element

The Piezocone Penetration Test (CPTU) is a new in-situ testing technology developed in the 1980s. Compared with the traditional Cone Penetration Test (CPT), it has the advantages of high precision, large amount of data, good stability and wide application. Because of the short history of pore pressure static penetration (CPTU) technology, the CPTU develops slowly in China. By the large deformation, finite element simulation method is used to numerically simulate the CPTU penetration process in ABAQUS software; and the distribution and variation characteristics of soil stress, strain and pore pressure field at different penetration depths are studied. The results show that during the penetration of the cone, there is a stress concentration zone around the cone. The resistance of the cone is mainly the resistance below the cone tip. When the penetration is shallow, the soil is disturbed with the penetration. As the depth increases, the disturbance becomes smaller; according to the variation of the pore water pressure, the water permeable element can be placed at the junction of the conical head and the conical body.

Overburden characterization with formation pore pressure and anisotropic stress field estimation in the Athabasca Basin, Canada

One of the challenges encountered during the life cycle of an oil-sand thermal-production reservoir is the prediction of the formation pore pressure and in situ stress regime during the assessment phase of the reservoir development and, more importantly, during the development phase. We have investigated the state of formation pore pressure and stress in the overburden — represented by the Clearwater Formation, Grand Rapids Formation, and Colorado Group — of a preproduction oil-sands reservoir situated in the Athabasca Basin of Alberta, Canada. Our methodology integrates pressure data from piezometers, stress data from mini-frac (MF), dipole sonic logs, and elastic properties obtained from multicomponent 3D seismic inversion data. It combines the Terzaghi effective stresses with the Schoenberg and Sayers elastic stiffness matrix for horizontal transversely isotropic fractured materials. The total principal stresses (vertical, minimum, and maximum horizontal stresses) are expressed as functions of the normal fracture weakness (anisotropic correction factor), formation pore pressure, seismic data (Lamé constants), and the Biot-Willis coefficient. The effective principal stresses are estimated from the equivalent total principal stresses and the formation pore pressure multiplied by the Biot-Willis coefficient. On all three overburden intervals analysed, the relations between principal stresses indicate a normal stress regime. The estimated total minimum horizontal stress matches the MF values within 10%. The formation pore pressure, along with the 3D seismically derived estimates of the total and effective principal stresses, allows for better assessment of the caprock integrity and for operational savings based on a reduced number of MF tests. It can also be used for stress estimation within the formations hosting aquifers, which is so important for thermal production. Understanding the subsurface on the reservoir area is important for efficient production, but knowing the subsurface of the overburden is equally important for reducing potential issues due to production.

A porothermoelastic wellbore stability model for riserless drilling through gas hydrate-bearing sediments in the Shenhu area of the South China Sea

Wellbore instability during the gas hydrate drilling process frequently occurs due to the metastable character of sediment-hosted hydrates and weakly consolidated sediments. An accurate prediction of wellbore stability in gas hydrate drilling is very important. In this paper, a transient heat transfer model between the wellbore and sediment in a gas hydrate reservoir is proposed to simulate temperature profiles inside the drilling string and annulus. Using these temperature profiles, a porothermoelastic model is proposed to compute the temperature and pore pressure field in the entire formation during riserless drilling. Then, the thermodynamic stability of the gas hydrate and wellbore stability are analysed. The findings indicate that it is not necessary to use low-temperature drilling mud during riserless drilling. The risk of in situ hydrate dissociation is very low with a drilling mud density of 1.1 g/cm3. Then, a safe mud density window is obtained for future riserless drilling in the gas hydrate reservoirs in the Shenhu area.

Effects of non-uniform pore pressure field on hydraulic fracture propagation behaviors

Hydraulic fracturing is one of the key technologies to stimulate oil and gas production in low-porosity and low-permeability reservoirs. Thus, understanding the hydraulic fracture (HF) propagation behaviors is of great significance for optimizing the fracturing design. It is usually assumed that HF tends to take a straight path in a symmetric stress and uniform pore pressure field. However, much more complex stress and pore pressure distribution could be encountered during the fracturing treatment as a result of long-time fluid injection and production in the reservoir. In this paper, considering the arrangement of five-spot well pattern, the effects of unsymmetric stress and non-uniform pore pressure distribution on HF growth is investigated using the cohesive zone method (CZM) and extended finite element method (XFEM). The interesting results indicate that in-situ stress and pore pressure distribution are gradually altered due to fluid injection and production, which affects subsequent HF growth. And in the reservoir developed by five-spot well pattern, HF tends to initially propagate along a straight line with fracture growth rate gradually decreasing and then prefers to extend towards the nearby injection well with fracture growth rate gradually increasing when there exists an intersection angle (0°<θ<45°) between the direction of well arrays and minimum horizontal stress orientation. When θ equals 0° or 45°, HF will extend along a straight line without curving. The results also show that a larger water injection pressure leads to a greater fracture deviation angle, but a larger fracturing fluid injection rate and a larger water injection well distance results in a smaller fracture deviation angle. Moreover, the influence of fracturing fluid viscosity on fracture deviation angle can be ignored.