Non-uniform Pore Pressure Research Articles

Numerical analysis on mechanical difference of sandstone under in-situ stress, pore pressure preserved environment at depth

Deep in-situ rock mechanics considers the influence of the in-situ environment on mechanical properties, differentiating it from traditional rock mechanics. To investigate the effect of in-situ stress, pore pressure preserved environment on the mechanical difference of sandstone, four tests are numerically modeled by COMSOL: conventional triaxial test, conventional pore pressure test, in-situ stress restoration and reconstruction test, and in-situ pore pressure-preserved test (not yet realized in the laboratory). The in-situ stress restoration parameter is introduced to characterize the recovery effect of in-situ stress on elastic modulus and heterogeneous distribution of sandstone at different depths. A random function and non-uniform pore pressure coefficient are employed to describe the non-uniform distribution of pore pressure in the in-situ environment. Numerical results are compared with existing experimental data to validate the models and calibrate the numerical parameters. By extracting mechanical parameters from numerical cores, the stress-strain curves of the four tests under different depths, in-situ stress and pore pressure are compared. The influence of non-uniform pore pressure coefficient and depth on the peak strength of sandstone is analyzed. The results show a strong linear relationship between the in-situ stress restoration parameter and depth, effectively characterizing the enhanced effect of stress restoration and reconstruction methods on the elastic modulus of conventional cores at different depths. The in-situ pore pressure-preserved test exhibits lower peak stress and peak strain compared to the other three tests, and sandstone subjected to non-uniform pore pressure is more prone to plastic damage and failure. Moreover, the influence of non-uniform pore pressure on peak strength gradually diminished with increasing depth.

Numerical simulation of hydraulic fracturing with consideration of the pore pressure distribution based on the unified pipe-interface element model

Understanding hydraulic fracture propagation behaviours is vital for optimizing fracturing design in oil and gas production. It has been observed that the stress and pore pressure distribution are much more complex during fracturing treatment as a result of long-term fluid injection and production in the reservoir. When rock is subjected to internal hydraulic pressure and external mechanical loading, the closing, opening, or other interactions of pre-existing weaknesses or induced new fractures will be altered. In this paper, a number of hydraulic simulation scenarios are performed to investigate the effect of pore pressure distribution on fracture initiation and propagation using the unified pipe-interface element method (UP-IEM). The proposed method for predicting the hydraulic fracture path in the permeable porous medium with non-uniform pore pressure field is validated with experimental results. Considering the arrangement of well patterns and natural fractures in the rock, the problems of hydraulic fracture propagation behaviours with wellbore interaction and pore pressure induced natural fracture activation are simulated. The influence of pore pressure saturation and the injection sequence of wellbores on hydraulic fracturing are researched. A sensitivity analysis is carried out to investigate the parameter effects on pre-existing fracture tortuosity, opening width and breakdown pressure under pore pressure. These numerical examples provide guidance to engineers to estimate the probability of danger or possibilities to improve the injection and production of wells.

Numerical evaluation of refracturing fracture deflection behavior under non-uniform pore pressure using XFEM

Refracturing has become an important technique for tapping old wells to stabilize and improve well performance. However, due to inaccurate well selection and formation selection for refracturing and inadequate prediction of refracturing fracture propagation, refracturing effectiveness sometimes may be diminished. Hence, the objective of this paper is to establish a numerical model to efficiently simulate the processes of first fracturing, injection and production, and hydraulic refracturing. The extended finite element method (XFEM) is first applied. Then, a five-spot well pattern is considered, which couples the angle of the well array to the maximum horizontal principal stress with the angle of the perforation orientation. Afterward, we optimize the refracturing orientation under non-uniform pore pressure conditions. Fracture length and fracture deflection angle are utilized as evaluation indicators. Results indicate that the orientation of refracturing is not recommended to follow the injection well and the optimal perforation area exists when the direction is along the middle of the two injection wells. Long fractures with large deflection angles can be obtained along the mid-line of the well array in a clockwise as well as a counter-clockwise direction of 15°, leading to a higher reservoir modification area. In addition, fractures tend to propagate into areas of high pore pressure. This work provides a useful model including the dynamic propagation of fractures during refracturing after initial fracturing and production operations, which can assist operators optimize the fracturing process.

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.

Analytical study of the thermo-osmosis effect in porothermoelastic responses of saturated porous media under axisymmetric thermal loadings

Thermo-osmosis effect is defined as the additional fluid flux caused by the thermal gradient in the porous medium and has recently received much attention in thermally coupled processes of soils and rocks, such as the geological disposal of nuclear waste. However, majority of research studies on thermo-osmosis flow have considered plane-strain conditions which disregard the local thermal expansion and contraction due to finite-dimension loadings. In this paper, we have extended the three-dimensional porothermoelastic model with the thermo-osmosis effect under axisymmetric thermal loadings. With the Laplace-Hankel transform, we obtain the explicit expressions of the temperature, pore pressure, stresses and displacements in the transformed domain. After the verification of this model against analytical and experimental results, we carry out the case study of a disk thermal loading placed at the surface of half space. The thermo-osmosis effect can increase the maximum value of the non-uniform pore pressure caused by the finite-dimension thermal loading. After the dissipation of pore pressure, the driving force from the thermo-osmosis effect can maintain the osmotic flux near the thermal loading. These results show that the thermo-osmosis effect is important to the porothermoelastic behaviors of porous media but is mainly limited to the vicinity of the finite-dimension loading.

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.

Numerical modeling of hydraulic fracture propagation behaviors influenced by pre-existing injection and production wells

Hydraulic fracturing treatments are capable of enhancing the well production performance in low-porosity and low-permeability reservoirs because of the resulted improvement in communication between the formation and wellbore through created hydraulic fractures (HFs). In fact, not only the in-situ stress underground but also the pre-existing offset wells induced non-uniform pore pressure field will influence the HF propagation process. In this work, to investigate the HF propagation behaviors under the effects of adjacent production and injection wells, a new numerical model is developed within the framework of extended finite element method (XFEM) and cohesive zone method (CZM). The model can simultaneously simulate the HF initiation, propagation and reorientation, fracturing fluid flow and leakoff, formation fluid flow and rock deformation. Reliability of the new model is validated by comparing the numerically calculated fracture geometry with the experimental observation in the literature. The interesting and new results show that pore pressure field, stress field and fracture propagation speed can be altered around the pre-existing offset wells. Also, HF prefers to propagate toward injection wells when production and injection wells co-exist, and the fracture propagation trajectory will not be affected in the cases that only production or injection wells exist. The fracture will be shorter and wider when only injection wells exist or production and injection wells co-exist, while the pre-existence of only production wells leads to a longer and thinner HF. Moreover, a smaller pumping pressure can be applied to generate the HF when only production wells locate nearby, while a greater injection pressure is required to drive the HF forward when only injection wells pre-exist or injection and production wells co-exist. The obtained results provide new insights for understanding the fracture propagation behaviors in the field scale.

Effect of non-uniform pore pressure fields on hydraulic fracture propagation

In elastic materials, it is evident that the path of a propagating fracture is deflected from its normal course in presence of imperfections of the material or loading conditions. This paper aims at investigating hydraulic fracture deviation induced by non-uniformity of pore pressure fields with the use of a fully coupled poroelastic model based on the finite element method. The model includes a poroelastic domain in which pressurized hydraulic fractures are explicitly embedded, thus allowing to realistically model the fluid flow inside the fracture and to intrinsically consider the fracturing fluid load on the fracture walls as well as fluid leak-off into the formation. The latter process (fluid leak-off into the formation) controls both the length and the orientation of the fracture by changing the local pore pressure which in turn leads to a change in magnitude and direction of local principal stresses around the fracture tip. An innovative method, Mean Rotation Angle (MRA) is utilised for post-processing of evolving stress data at the vicinity of the fracture tip. The MRA predicts the potential growth path of pressurized fractures. In this paper pore pressure induced fracture reorientation is studied for a single fracture as well as closely spaced fractures. Results of this study indicate that presence of a pore pressure anomaly changes the growth path of a hydraulic fracture, towards or away from the anomaly. A higher than average pore pressure zone attracts the fracture while a lower pressure anomaly zone repulses the growing fracture. The fracture growth direction depends on the differential pressure and the distance between the anomaly and the fracture tip. Also in case of two simultaneously growing transverse fractures pressurized by injected fluid, it has been observed that the fluid leak-off controls the potential deviation angle of the fractures through changing the local pore pressure distribution pattern. It is shown that there are three distinct trends for the change of potential deviation angle due to fluid leak-off and that these three trends are linked to three corresponding stages of hydraulic communication between the two fractures. Furthermore, this study shows that change in matrix permeability, stress anisotropy, fracture half-length, spacing and the rate of leak-off influence the timing of each of the stages to the extent to which the corresponding stage of hydraulic communication of the two fractures are affected. This new understanding gives a better insight into the mechanism by which closely spaced hydraulic fractures interact and help optimize the design of multi-stage hydraulic fracture treatments.

Efficient Three Dimensional Nonlinear Thermo-Mechanical Analysis of Structures Subjected to Fire

Abstract In this paper, a computationally efficient integrated frame-work is developed for coupled thermo-mechanical analysis of 3D frames. It can account for physical phenomena like large deformations, temperature dependent material degradation, permanent plastic deformations and fire induced spalling which are prevalent at elevated temperatures. The developed frame-work utilizes three way sequential coupling between thermal, mass transport and structural analysis. A two level discretization scheme is incorporated where 1D beam column elements are utilized for structural analysis, the cross-section of these beam-column elements are further discretized into matrix of segments. Aforementioned strategy entails sequential coupling of effects of non-uniform temperature and pore pressure across the cross-section into structural analysis. Subsequently structural analysis is performed with an updated Lagrangean based formulation with force deformation relationships deduced form classical Euler-Bernoulli beam column theory. Critical physical phenomena like cracking, crushing, spalling and transient states of strain in case of concrete and yielding in case of steel are duly accounted. Cross-sectional reduction due to spalling are accounted for by replacing the spalled segments with void segments in the subsequent time steps. Numerical examples of steel and concrete structures subjected to various fire scenarios are presented to demonstrate the accuracy of developed framework. Furthermore, progressive collapse analysis is carried out for concrete and steel 3D subjected to fire.

Clay squirt: Local flow dispersion in shale-bearing sandstones

Dispersion of elastic-wave velocity is common in sandstone and larger in shaly sandstone than in clean sandstone. Dispersion in fluid-saturated shaly sandstone often exceeds the level expected from the stress-dependent elastic moduli of dry sandstone. The large dispersion has been coined clay squirt and is proposed to originate from a pressure gradient between the clay microporosity and the effective porosity. We have formulated a simple model that quantifies the clay-squirt effect on bulk moduli of sandstone with homogeneously distributed shale laminae or dispersed shale. The model predictions were compared with the literature data. For sandstones with dispersed shale, agreement was found, whereas other sandstones have larger fluid-saturated bulk modulus, possibly due to partially load-bearing shales or heterogeneous shale distribution. The data that agree with the clay-squirt model indicated nonuniform pore pressure in the high-frequency regime and uniform pore pressure in the low-frequency regime. Therefore, our model showed that clay-squirt dispersion can attain a sufficient magnitude to explain much of the large dispersion observed in shaly sandstone.

Mechanism of Hydrofracture Propagation Control by Non-uniform Pore Pressure Field

Mechanism of Hydrofracture Propagation Control by Non-uniform Pore Pressure Field

A method for hydrofracture propagation control based on non-uniform pore pressure field

Hydraulic fracturing technology, a technique for increasing productivity applicable in low-permeability oil-gas reservoir, has been used in the extraction of coal seam methane in underground coal mines. However, because of the more complex structure of coal seam compared with that of oil-gas reservoir, the hydrofracture propagation can easily extend to roof-floor rocks, limiting the range of permeability and making damages of roof-floor rocks in subsequent coal mining and support difficulty. How to control the hydrofracture propagation well-aligned in a large area of coal seam has become the key to long-time highly effective extraction of coal seam methane. Firstly, it starts with the perspective of stress field of crack tip, by means of thermal elasticity fracture mechanics theory, to get the stress intensity factor of hydrofracture tip while taking pore pressure into consideration. Next, a laboratory fracturing experiment using sandstone specimens was conducted to study the impact of non-uniform pore pressure on the direction of hydrofracture propagation. Lastly, a numerical simulation software RFPA2D-Flow is adopted to further verify the theoretical and experimental results. The study shows that pore pressure can effectively increase the stress intensity factor of the crack tip, the more pressure of pore, the smaller the needed fluid pressure for hydrofracture propagation. In a large area, affected by the direction and distribution of pore pressure gradient, the hydrofracture will propagate along higher pore pressure area. A method is put forward for controlling hydrofracture propagation in underground coal mines accordingly. Meanwhile, the matching relationship between the space between boreholes and the water injection maintaining pressure and maintaining time are studied together, with methods and steps for calculating key fracture parameters established.

A micromechanical analysis of the fracture properties of saturated porous media

A two-dimensional single edge crack problem is employed to investigate the fracture behavior of saturated poroelastic media. The media are mimicked by a micromechanical model consisting of elastic matrix and square arrays of voids with prescribed uniform pore pressure. Finite element method is used to simulate the fracture responses of the model subject to remote stress and pore pressure loading. The stress extrapolation method is extended for the porous media to calculate the nominal stress intensity factor (SIF) from the crack tip stress field. By adopting the tensile strength criterion and assuming either brittle or ductile failure of the constituent solid skeleton of the porous media, lower and upper bounds of the fracture toughness are obtained. Theoretical expressions for the stress intensity factor and the toughness are derived, agreeing well with numerical results. The effects of the arrangement of pores and the non-uniform pore pressure on the cracking of porous media are discussed and are found to only have moderate effects on the obtained results.

Calculating cv based on non-uniform initial excess pore pressure

The coefficient of consolidation (cv) is often determined by comparing the characteristics of the experimental and theoretical consolidation using empirical curve-fitting procedures which are based on the theoretical U−T curve generated by a layer subjected to a uniform initial excess pore water pressure distribution. However, in cases where settlement–time data are a result of a non-uniform initial pore pressure distribution, these curve-fitting procedures are no longer valid. In this technical note, a generalised procedure for Taylor and Casagrande's popular curve-fitting procedures is proposed, where the user is directed to select appropriate adjustment factors, depending on the type of non-uniform initial excess pore pressure distribution encountered. These factors were determined by approximating separate regions of the U−T curves using simple power and exponential functions. In non-uniform cases where the power approximation only captures a small portion of the U−T curve it may be difficult to use the corresponding modified curve-fitting procedure objectively.

Simulation of Multiple Hydraulic Fracturing in Non-Uniform Pore Pressure Field

A series of numerical simulations of hydraulic fracturing were performed to study the initiation, propagation and breakdown of fluid driven fractures. The simulations are conducted with a flow-coupled Rock Failure Process Analysis code (RFPA2D). Both heterogeneity and permeability of the rocks are taken into account in the studies. The simulated results reflect macroscopic failure evolution process induced by microscopic fracture subjected to porosity pressure, which are well agreeable to the character of multiple hydraulic fracturing experiments. Based on the modeling results, it is pointed out that fracture is influenced not only by pore pressure magnitude on a local scale around the fracture tip but also by the orientation and the distribution of pore pressure gradients on a global scale. The fracture initiation, the orientation of crack path, the breakdown pressure and the stress field evolution around the fracture tip are influenced considerably by the orientation of the pore pressure. The research provides valuable guidance to the designers of hydraulic fracturing engineering.

Undrained Cyclic Loading of Anisotropically Consolidated Clayey Silts

Data are presented from cyclic triaxial tests on anisotropically consolidated kaolin clay and silica silt mixtures prepared in the laboratory. The soil type ranged from a pure silt to a silty clay with 40% clay content. The undrained behavior of clay-silt soils subjected to anisotropic cyclic loads without shear stress reversal can be adequately described by the average resultant cyclic strain rate provided that the test conditions account for strain rate effects and cross-sectional area changes during straining. Strain rate effects in cyclic triaxial tests may induce nonuniform pore pressure distribution within the specimen. Nonuniform pore pressure effects are related to the average resultant cyclic strain rate, while the dynamic strength parameters are related to the maximum cyclic strain rate. It has been established that the average resultant cyclic strain rate depends upon the imposed static shear stress, the cyclic stress ratio, and clay content. Cyclic frequency, however, did not significantly affect the 20% clay/80% silt mixtures.

Pore pressure influence on tensile fracture propagation in sedimentary rock

Theoretical analysis and experimental results are presented to describe the influence of pore pressure on tensile fracture initiation and propagation direction. Fracture is influenced by both pore pressure magnitude on a local scale around the crack tip and by the orientation and distribution of pore pressure gradients on a global scale. Simple fracture initiation tests conducted on cylindrical limestone and sandstone rock samples are first described which support an effective stress law for tensile fracture initiation in very porous rocks. In other experiments, controlled fractures are propagated both mechanically and hydraulically across sandstone slabs subjected to non-uniform pore pressure fields. The fractures are shown to propagate towards regions of higher local pore pressure. Finallt, the influence of pressure gradient induced body forces is demonstrated by generating fractures connecting two pore pressure source points. The experimental results are supported by poroelasticity and fracture mechanics analysis of the process, and may be applied to influence hydrailic fracture orientation in the field.

Effects of Arching on Response Time of Miniature Pore Pressure Transducer in Clay

Abstract A study of the response time of miniature pore pressure transducers embedded in clay soils is presented. The highly nonuniform pore pressure distributions around the transducers due to arching and stress concentration can have a significant effect on transducer response especially when the surrounding soil is loaded anisotropically. This is caused by the difference in compressibility of the soil and the transducer housing. Finite-element analysis and experimental results confirm the importance of these effects. A spherical porous stone or a cylindrical stone with top and side drainage results in significant reduction in response time and in overshoot due to arching effects.

A Quick Method To Determine Subsidence, Reservoir Compaction, and In-Situ Stress Induced by Reservoir Depletion

This paper provides a quick method to determine subsidence, compaction, and in-situ stress induced by pore-pressure change. The method is useful for a reservoir whose Young's modulus is less than 20% or greater than 150% of the Young's modulus of the surrounding formation (where the conventional uniaxial strain assumption may not hold). In this work, a parameter study was conducted to find groups of parameters controlling the in-situ stress, subsidence, and compaction. These parameter groups were used to analyze the numerical calculation results generated by a three-dimensional (3D), general, nonlinear, finite-element model (FEM). The procedure and a set of figures showing how to calculate the in-situ stress, subsidence, and compaction induced by pore-pressure changes are provided. Example problems are also included to prevent confusion on sign convention and units. This work showed that Geertsma's results, which are based on no modulus contrast between cap and reservoir rocks, should be extended to simulate more closely real reservoirs, which generally have distinct property differences between the cap and reservoir rocks.