Poroelastic Stress Research Articles

Focal Mechanisms of Some Inferred Induced Earthquakes in Alberta, Canada

Although it has long been understood that injection of fluids into the subsurface can activate slip on a fault (e.g., Healy et al. , 1968), seismicity induced by fluid injection associated with oil and gas operations has recently come into sharper focus (Ellsworth, 2013; Keranen et al. , 2013; Schultz et al. , 2014). Since December 2013, anomalous seismicity of magnitude up to M L 4.4 has occurred episodically in parts of Alberta, Canada. In the Crooked Lake (CL) area of west‐central Alberta, induced seismicity appears to be spatially and temporally correlated with hydraulic fracturing, a process of injecting fracturing fluids into a rock formation at a force exceeding the fracture pressure of the rock, thus inducing a network of fractures through which oil or natural gas can flow to the wellbore (CCA, 2014). Farther south, an M w 3.8 earthquake on 9 August 2014 occurred within the Rocky Mountain House (RMH) cluster, an area where persistent seismic activity since the late 1970s has been interpreted to be triggered by poroelastic stress changes from the production of hydrocarbons (Baranova et al. , 1999). This recent earthquake is the largest event that has occurred to date within this cluster (Stern et al. , 2013), representing a significant departure from a trend of declining seismicity for the past three decades. In this article, we investigate focal mechanisms for some events that have occurred in Alberta since December 2013. These focal solutions were obtained using the polarity of P ‐wave first motions registered on regional seismograms. This investigation was facilitated by the installation of numerous seismograph stations in Alberta during the past few years (Schultz et al. , 2015), including the Regional Alberta Observatory for Earthquake Studies Network (RAVEN). For the purpose of this study, a crustal velocity model was developed based on sonic log data from …

Derivation of a Poroelastic Flexural Shell Model

In this paper we investigate the limit behavior of the solution to quasi-static Biot equations in thin poroelastic flexural shells as the thickness of the shell tends to zero and extend the results obtained for the poroelastic plate by Marciniak-Czochra and Mikelic in [Arch. Ration. Mech. Anal., 215 (2015), pp. 1035--1062]. We choose Terzaghi's time corresponding to the shell thickness and obtain the strong convergence of the three-dimensional solid displacement, fluid pressure, and total poroelastic stress to the solution of the new class of shell equations. The derived bending equation is coupled with the pressure equation, and it contains the bending moment due to the variation in pore pressure across the shell thickness. The effective pressure equation is parabolic only in the normal direction. As an additional term it contains the time derivative of the middle-surface flexural strain. Derivation of the model presents an extension of the results on the derivation of classical linear elastic shells by ...

A DYNAMIC DISCRETE FRACTURE APPROACH FOR MODELING MULTIPHASE FLOW AND TRANSPORT IN FRACTURED POROUS MEDIA

A numerical study was conducted to analyze multiphase fluid flow and transport processes in naturally fractured rocks during long-term waterflooding operations, particularly the dynamic discrete fracture models present for simulation of natural fracture, induced fracture, and fracture−matrix interactions. Different flow mechanisms for porous media, such as the non-Darcy model, fracture growth with respect to poroelastic stresses, and matrix−fracture transfer were considered. The method was solved by using the discrete fracture control-volume method. Results were obtained in terms of water cut, output, and pressure distribution for various fractured porous media. Comparisons for simulation results and purely analytical solutions show an excellent match. The new model allows us to better understand the flow behavior caused by multiscale fracture systems. The results from this investigation showed that the pressure drop across porous media increased with the length of dynamic fracture. In addition, water injection rate and injection-production ratio play an important role in determining the fracture growth. The proposed simulation method can be used to optimize injection pressures and rates, and water quality for maximizing oil recovery.

Spatiotemporal changes, faulting regimes, and source parameters of induced seismicity: A case study from The Geysers geothermal field

AbstractThe spatiotemporal, kinematic, and source characteristics of induced seismicity occurring at different fluid injection rates are investigated to determine the predominant physical mechanisms responsible for induced seismicity at the northwestern part of The Geysers geothermal field, California. We analyze a relocated hypocenter catalog from a seismicity cluster where significant variations of the stress tensor orientation were previously observed to correlate with injection rates. We find that these stress tensor orientation changes may be related to increased pore pressure and the corresponding changes in poroelastic stresses at reservoir depth. Seismic events during peak injections tend to occur at greater distances from the injection well, preferentially trending parallel to the maximum horizontal stress direction. In contrast, at lower injection rates the seismicity tends to align in a different direction which suggests the presence of a local fault. During peak injection intervals, the relative contribution of strike‐slip faulting mechanisms increases. Furthermore, increases in fluid injection rates also coincide with a decrease in b values. Our observations suggest that regardless of the injection stage, most of the induced seismicity results from thermal fracturing of the reservoir rock. However, during peak injection intervals, the increase in pore pressure may likewise be responsible for the induced seismicity. By estimating the thermal and hydraulic diffusivities of the reservoir, we confirm that the characteristic diffusion length for pore pressure is much greater than the corresponding length scale for temperature and also more consistent with the spatial extent of seismicity observed during different injection rates.

A Rigorous Derivation of the Equations for the Clamped Biot-Kirchhoff-Love Poroelastic Plate

In this paper we investigate the limit behavior of the solution to quasi-static Biot's equations in thin poroelastic plates as the thickness tends to zero. We choose Terzaghi's time corresponding to the plate thickness and obtain the strong convergence of the three-dimensional solid displacement, fluid pressure and total poroelastic stress to the solution of the new class of plate equations. In the new equations the in-plane stretching is described by the 2D Navier's linear elasticity equations, with elastic moduli depending on Gassmann's and Biot's coefficients. The bending equation is coupled with the pressure equation and it contains the bending moment due to the variation in pore pressure across the plate thickness. The pressure equation is parabolic only in the vertical direction. As additional terms it contains the time derivative of the in-plane Laplacean of the vertical deflection of the plate and of the the elastic in-plane compression term.

Pore pressure stress coupling in 3D and consequences for reservoir stress states and fault reactivation

The spatio-temporal changes of the stress state in a geothermal reservoir are of key importance for the understanding of induced seismicity and planning of injection and depletion strategies. In particular the poro-elastic effects on the stress state due to re-injection or depletion of water are of interest for both geothermal projects and hydrocarbon exploitation. In addition to the conventionally used effective stress concept, poro-elasticity affects the stress tensor components differently as a function of changes in pore pressure. Here, we provide an analytical base for the long-term changes of the 3D stress tensor components as a function of pore pressure changes. Results indicate that for a constant rate of injection or depletion the coupling between pore pressure and all stress tensor components depends on the location in the reservoir with respect to the re-injection/depletion point as well as the time since the beginning of pore pressure changes. Our systematic analysis suggests that poro-elastic stress changes can even locally modify the given tectonic stress regime. Furthermore, the results predict that localized changes of maximum shear stress can lead to different fracture orientations than those expected when poro-elastic effects are not considered. These results indicate a need for 3D geomechanical-numerical studies of more realistic reservoir settings in order to study the 3D effects of pore pressure/stress coupling. Our generic 3D geomechanical-numerical study shows that less than two years of production of a single well changes shear stresses by 0.2MPa. Thus, in reservoirs with decades of production shear stress change can reach sufficiently high values to re-activate pre-existing faults or even generate new fractures with unexpected orientations.

Analysis of Changes in Stress State and Fault Stability Related to Planned CO2 Injection at the Tomakomai Offshore Site

Abstract This paper presents results of analysis of changes in stress state and fault stability related to a planned geological CO 2 injection at the Tomakomai offshore site, Hokkaido, Japan. Predicted slip tendency in shallow Moebetsu formations is much lower than that in deep overpressured Takinoue formations, and estimated effects of the planned injection are relatively limited in both formations. Another point is that poro-elastic stress development leads to changes in fault stability compared to that calculated based on pressure buildup alone and the initial stress state. These poro-elastic effects on fault stability are comparable to those due to pressure buildup itself.

Micromechanics-based evaluation of the poroelastic effect and stress concentration in thermochemically-decomposed composites

The poroelastic effect and stress concentration of thermochemically decomposed composites are evaluated based on micromechanics. Considering the pore shapes and array patterns, representative volume elements (RVEs) of homogenized composites are modeled and analyzed using a finite element method. The effects of porosity and material anisotropy are carefully investigated. The poroelastic parameters are calculated based on the pore-pressure-induced strain and effective elastic moduli as well as on the differences between the elastic moduli of solid-skeleton composites and porous composites. The strain energy density is measured to evaluate the microstress concentration caused by pore pressure. Moreover, the effects of constituent phases on the poroelastic parameters and strain energy density are examined by improving the RVE models for heterogeneous composites. The usefulness of the calculation method for poroelastic parameters is investigated through numerical experiments.

A reactive thermo-poroelastic analysis of water injection into an enhanced geothermal reservoir

Coupled thermo-poro-chemo-mechanical processes in geothermal systems impact the reservoir response during injection and production procedures by affecting fracture permeability. A three-dimensional numerical model is presented to analyze these processes during fluid injection into geothermal reservoirs. The solid mechanics aspect of the problem is computed using the displacement discontinuity boundary element method (BEM) while transport processes within the facture are modeled using the finite element method (FEM). The FEM and BEM formulations are integrated to set up a system of equations for unknown temperature, pressure, concentration, and fracture aperture. The fluid diffusion, heat conduction and solute diffusion in the reservoir are treated using BEM so that the need of infinite reservoir domain discretization is eliminated. The numerical model is used to analyze the fracture response to non-isothermal reactive flow in EGS. Numerical examples of SiO2 undersaturated-cold water injection into the geothermal reservoir show that silica dissolves from the rock matrix, increasing the fracture aperture. The zone of silica dissolution spreads into the fracture with continuous fluid injection. At large injection times, thermoelastic stress has a greater impact on fracture aperture compared to poroelastic stress. Simulations that consider natural fracture stiffness heterogeneity show the development of a non-uniform flow path within the crack, with lower rock matrix cooling and thus enhanced silica reactivity in the high stiffness regions. As a result, areas of higher joint normal stiffness show lower aperture increases in response to the thermo-poroelastic processes, but a higher aperture expansion due to silica dissolution. Depending on the injectate saturation state with respect to quartz, silica is added or removed from the rock matrix. This process is likely to impact the rock matrix properties and its mechanical response to stress perturbations associated with fluid circulation.

Predicting Growth and Decay of Hydraulic-Fracture Width in Porous Media Subjected to Isothermal and Nonisothermal Flow

SummaryOn the basis of the continuum thermo-poroelastic theory, a new analytical formula of fracture width is developed to quickly predict its transient growth or decay. The effects of the poroelastic stress (also called back stress) and thermal stress are taken into account. The counterbalance between the effects of back stress and thermal stress (in case of injection of cold fluid) is shown to be a function of flow and thermal properties and can be easily demonstrated by the formula developed. The analytical formula of fracture width is not complicated and does not require complex calculations. Different phenomena affecting the magnitude of fracture width are easily examined, such as the presence or absence of leakoff, isothermal or nonisothermal fracturing, and initial effective stress in the formation. Results show that the fracture width continuously decays with time because of the effect of pore pressure when there is leakoff. On the other hand, the fracture width will grow with time by the influence of thermal stress when cold fluid is injected. Unlike cold fluid, when hot fluid is used, the crack may close completely and the speed of the process will depend on the temperature of the injected fluid. Formulae for penetration depths for pressure and temperature are also developed and applied to the crack-width equation so that time-dependent maximum width and crack profiles can be computed. The analytical solution has also been validated by the finite-element (FE) numerical method.

Role of Stress Reorientation in the Success of Refracture Treatments in Tight Gas Sands

Summary The redistribution of stresses around a fractured vertical well has two sources: opening of propped fracture (mechanical effects) and production or injection of fluids in the reservoir (poroelastic effects). In this paper, the coupling of both phenomena was numerically modeled to quantify the extent of stress reorientation around fractured production wells. The results have been compared to field data from the Codell tight gas formation and analyzed for their impact on refracturing operations. For previously fractured wells, a secondary fracture may be initiated perpendicular to the first fracture if a stress-reversal region is present. Altered-stress refracturing makes it possible to access zones of the reservoirs that are less depleted, thus increasing well production and reserves. The results of our model quantitatively agree with previous tiltmeter measurements, confirming the existence of refracture reorientation in the Codell formation. The performance of refracturing treatments has been observed to be highly variable in the Wattenberg field (Colorado), with some wells underperforming while others are restored to initial production rates. Historical production from neighboring wells and initial fracture performance were shown to impact the potential benefits from refracturing predicted by the numerical model. This paper introduces a 3D model, coupling mechanical and poroelastic stress reorientation used to interpret tiltmeter measurements and historical production in the Codell tight gas formation. Guidelines are drawn from the Wattenberg field case study that allow an operator to select candidate wells, choose the timing of the refracture operation in the life of the well, and evaluate the potential increase in well production after refracturing.

Estimates of Fracture Lengths in an Injection Well by History Matching Bottomhole Pressures and Injection Profile

Summary An injection-well model is presented and used to history match a field injector's bottomhole pressures (BHPs) and injection profile (injection rate into each layer), taking into account plugging of formation caused by suspended solids in the injection water, poro- and thermoelastic stresses, injector shut-ins/restarts, and changes in both the injection rates and the average reservoir pressure. Fracture lengths and injection profile are estimated for a field injector as a case study. The injection-well fracture model is very similar to the Perkins and Gonzalez (1985) model except that it has integrated a more comprehensive and experimentally tested internal filtration model (Rajagopalan and Tien 1976; Pang and Sharma 1997; Gadde and Sharma 2001; Suri 2000; Wennberg and Sharma 1997) for calculating permeability reduction. It has also added a pressure-transient model that makes the earlier reservoir flow models more accurate. The solids deposition is modeled using a filtration model (Rajagopalan and Tien 1976). The fluid flow in the reservoir is modeled using three approximated composite zones with uniform saturations and average mobilities, and the pressure for the fractured wellbore is calculated with the help of Gringarten's (1974) infinite-conductivity solution. The induced-fracture lengths are calculated on the basis of the Perkins and Gonzalez fracture-propagation model (1985) that accounts for the thermal and poroelastic stresses. The model is developed into a semianalytical numerical simulator that can predict and history match an injector's daily BHP, fracture lengths, and injection profile. Future estimates of pump pressures, BHP, injectivity, skin, front locations, fracture lengths, and injection profile can be obtained from this model. Both short-term pressure transients and long-term pseudosteady pressures observed over several years of injection can be history matched to capture effects that are important at both short and long time scales. Finally a field-case injection-well study is presented in which BHP and injectivity are history matched over a period of 3 years. We show that the model can be used to estimate the minimum horizontal stresses in the layers if they are not known. Estimates of fracture lengths, fraction of flow, permeability reduction, and skin and front locations are also obtained. There is significant uncertainty in the results because of uncertainty in the model inputs and in the completeness of the physics of the model of fracturing itself. Both the solids deposition and the opening/closing of the injection-induced fractures had to be accounted for to obtain the history match. The layer/sand stresses and the water quality are the most important parameters that determine the well's injectivity, fracture growth, and injection profile. Microseismic surveys and PLTs are needed to confirm fracture lengths in injection wells.

A model for seasonal changes in GPS positions and seismic wave speeds due to thermoelastic and hydrologic variations

It is known that GPS time series contain a seasonal variation that is not due to tectonic motions, and it has recently been shown that crustal seismic velocities may also vary seasonally. In order to explain these changes, a number of hypotheses have been given, among which thermoelastic and hydrology-induced stresses and strains are leading candidates. Unfortunately, though, since a general framework does not exist for understanding such seasonal variations, it is currently not possible to quickly evaluate the plausibility of these hypotheses. To fill this gap in the literature, I generalize a two-dimensional thermoelastic strain model to provide an analytic solution for the displacements and wave speed changes due to either thermoelastic stresses or hydrologic loading, which consists of poroelastic stresses and purely elastic stresses. The thermoelastic model assumes a periodic surface temperature, and the hydrologic models similarly assume a periodic near-surface water load. Since all three models are two-dimensional and periodic, they are expected to only approximate any realistic scenario; but the models nonetheless provide a quantitative framework for estimating the effects of thermoelastic and hydrologic variations. Quantitative comparison between the models and observations is further complicated by the large uncertainty in some of the relevant parameters. Despite this uncertainty, though, I find that maximum realistic thermoelastic effects are unlikely to explain a large fraction of the observed annual variation in a typical GPS displacement time series or of the observed annual variations in seismic wave speeds in southern California. Hydrologic loading, on the other hand, may be able to explain a larger fraction of both the annual variations in displacements and seismic wave speeds. Neither model is likely to explain all of the seismic wave speed variations inferred from observations. However, more definitive conclusions cannot be made until the model parameters are better constrained.

Dynamics and rapid migration of the energetic 2008–2009 Yellowstone Lake earthquake swarm

Yellowstone National Park experienced an unusual earthquake swarm in December–January, 2008–2009 that included rapid northward migration of the activity at 1 km per day and shallowing of the maximum focal depths from 12 to 2 km beneath northern Yellowstone Lake. The swarm consisted of 811 earthquakes, 0.5 < MW < 4.1, aligned on a N–S 12‐km‐long vertical plane of hypocenters. The largest earthquake of the swarm had a 50% tensile crack‐opening source determined by a full waveform inversion that we interpret as a magmatic expansion component. In addition, GPS data revealed E–W crustal extension coincident with the swarm. Modeling of GPS and seismic data is consistent with E–W opening of ∼10 cm on a N–S striking vertical dike. Our interpretation is that the swarm was induced by magmatic fluid migration or propagation of a poroelastic stress pulse along a pre‐existing fracture zone.

Natural fracture characterization in tight gas sandstones: Integrating mechanics and diagenesis

Accurate predictions of natural fracture flow attributes in sandstones require an understanding of the underlying mechanisms responsible for fracture growth and aperture preservation. Poroelastic stress calculations combined with fracture mechanics criteria show that it is possible to sustain opening-mode fracture growth with sublithostatic pore pressure without associated or preemptive shear failure. Crack-seal textures and fracture aperture to length ratios suggest that preserved fracture apertures reflect the loading state that caused propagation. This implies that, for quartz-rich sandstones, the synkinematic cement in the fractures and in the rock mass props fracture apertures open and reduces the possibility of aperture loss on unloading and relaxation. Fracture pattern development caused by subcritical fracture growth for a limited range of strain histories is demonstrated to result in widely disparate fracture pattern geometries. Substantial opening-mode growth can be generated by very small extensional strains (on the order of 104); consequently, fracture arrays are likely to form in the absence of larger scale structures. The effective permeabilities calculated for these low-strain fracture patterns are considerable. To replicate the lower permeabilities that typify tight gas sandstones requires the superimposition of systematic cement filling that preferentially plugs fracture tips and other narrower parts of the fracture pattern.

Effects of heat extraction on fracture aperture: A poro–thermoelastic analysis

Poroelastic and thermoelastic effects of cold-water injection in an enhanced (or engineered) geothermal system (EGS) are investigated by considering flow in a pre-existing fracture in a hot, rock matrix that could be permeable or impermeable. Assuming plane fracture geometry, expressions are derived for changes in fracture aperture caused by cooling and fluid leak-off into the matrix. The corresponding induced pressure profile is also calculated. The problem is analytically solved for the cases pertaining to a constant fluid injection rate with a constant leak-off rate. Results show that although fluid loss from the fracture into the matrix reduces the pressure in the crack, the poroelastic stress associated with fluid leak-off tends to reduce the aperture and increase the pressure in the fracture. High rock stiffness and low fluid diffusivity cause the poroelastic contraction of the fracture opening to slowly develop in time. The maximum reduction of aperture occurs at the injection point and become negligible near the extraction point. The solution also shows that thermally induced stress increases the fracture aperture near the injection point and, as a result, the fluid pressure at this point is greatly reduced. The thermoelastic effects are particularly dominant near the inlet compared to those of poroelasticity, but are pronounced everywhere along the fracture for large times. Although poroelasticity associated with leak-off does not change the fracture aperture significantly for low permeability rocks, it can lead to pore pressure increase and cause nearby fractures to slip.

Analysis of the induced seismicity of the Lacq gas field (Southwestern France) and model of deformation

SUMMARY The goal of this paper is to propose a model of deformation pattern for the Lacq gas field (southwest of France), considering the temporal and spatial evolution of the observed induced seismicity. This model of deformation has been determined from an updating of the earthquake locations and considering theoretical and analogue models usually accepted for hydrocarbon field deformation. The Lacq seismicity is clearly not linked to the natural seismicity of the Pyrenean range recorded 30 km farther to the south since the first event was felt in 1969, after the beginning of the hydrocarbon recovery. From 1974 to 1997, more than 2000 local events (M L < 4.2) have been recorded by two permanent local seismic networks. Unlike previously published results focusing on limited time lapse studies, our analysis relies on the data from 1974 to 1997. Greater accuracy of the absolute locations have been obtained using a well adapted algorithm of 3-D location, after improvement of the 3-D P-wave velocity model and determination of specific station corrections for different clusters of events. This updated catalogue of seismicity has been interpreted taking into account the structural context of the gas field. The Lacq gas field is an anticlinal reservoir where 3-D seismic and borehole data reveal a pattern of high density of fracturing, mainly oriented WNW‐ESE. Seismicity map and vertical cross-sections show that majority of the seismic events (70 per cent) occurred above the gas reservoir. Correlation is also observed between the orientation of the pre-existent faults and the location of the seismic activity. Strong and organized seismicity occurred where fault orientation is consistent with the poroelastic stress perturbation due to the gas recovery. On the contrary, the seismicity is quiescient where isobaths of the reservoir roof are closed to be perpendicular to the faults. These quiescient areas as well as the central seismic part are characterized by a surface subsidence determined by repeated levelling profiles. Moreover, the temporal evolution of the distribution of the seismicity clearly exhibits a spatial migration from the centre to the boundaries of the reservoir. We conclude that the entire field is strained but this deformation is seismically expressed only where faults are parallel to the isobaths of the reservoir roof and where these faults plunge towards outside the field according to one of the two theoretical deformation models considered in our study. Then we propose a temporal scenario of deformation along the principal axis of seismic deformation.

Poroelastic Model for Production- and Injection-Induced Stresses in Reservoirs with Elastic Properties Different from the Surrounding Rock

Closed-form and semianalytical solutions for induced poroelastic stresses and strains are extremely useful for the design of subsurface fluid storage in caverns because of their relative ease of implementation and their suitability for parameter sensitivity analyses. This paper describes the use of Eshelby’s inhomogeneity theory to derive equations that can be used to predict the induced stresses and strains for reservoirs that are elliptical in cross section, under plane strain conditions. Sensitivity analyses demonstrate that the induced stresses are relatively insensitive to the Poisson’s ratio of the surrounding rock, but they are strongly affected by the Poisson’s ratio of the reservoir, and the ratio of shear modulus of the reservoir to that of the surrounding rock. Results are presented in terms of dimensionless parameters, which facilitate their application to a broad range of reservoir dimensions and pressure-change magnitudes. These equations can also be used to predict the induced stresses arou...

Application of a three-dimensional poroelastic BEM to modeling the biphasic mechanics of cell–matrix interactions in articular cartilage

Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three-dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain.

Modeling Hydraulic Fractures in Unconsolidated Sands

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 96246, "A New Approach to Modeling Hydraulic Fractures in Unconsolidated Sands," by Z. Zhai, SPE, and M.M. Sharma, SPE, U. of Texas at Austin, prepared for the 2005 SPE Annual Technical Conference and Exhibition, Dallas, 9-12 October. Field data show that traditional models for brittle, linear-elastic rocks do not adequately represent fracturing in poorly consolidated rocks. A model was developed for describing the propagation of "fractures" in unconsolidated sands. The model departs radically from current models in that brittle-rock fracture mechanics is not used. Instead, the propagation of pore pressure is computed, and the porosity and permeability of the sand are specified as functions of the effective stress. This region of enhanced porosity defines a "fracture" in unconsolidated sands. The physics of creation and propagation of this oriented high-permeability zone is modeled. Introduction The application of frac packs in poorly consolidated reservoirs has been effective to prevent sanding problems. In conventional hydraulic-fracture simulations, to which linear-elastic fracture mechanics (LEFM) is applied, fracture initiation and propagation are governed by in-situ stresses, fracture toughness, tip dilatancy, and the process zone. Unlike competent formations, unconsolidated-sand beds have little or no tensile strength. LEFM is adequate for hard rocks, but the fracture-geometry predictions fall short when applied to fracturing soft rocks. For example, when using classical fracture models for simulating this process, it has been reported that millions of barrels of solid-waste slurry can be injected easily into soft formations over a period of several years. To accommodate such a large volume of solids, fracture lengths of several miles would be required, even with fractures that are several centimeters wide. Experimental and simulation studies identified mechanisms of fracture propagation and initiation in unconsolidated-sand formations. Many of those studies rely on classical brittle-rock fracture mechanics and in some cases do not account for shear failure. Permeability anisotropy induced by in-situ stresses is not considered. An approach to modeling the mechanical behavior of unconsolidated sands that are subjected to injection of water-based slurries is detailed in the full-length paper. Model for Stress Distribution Around an Injection Well To study fracture initiation and propagation, the effective-stress distribution around the well must be obtained and then the permeability and porosity updated in accordance with the appropriate constitutive relationships. The stresses around the wellbore can be divided into three parts.Stresses induced by far-field, in-situ stresses.Stresses induced by wellbore pressure.Flow-induced stresses (poroelastic stresses). On the basis of stress distribution, the anisotropic stress tensor can be determined as well as where and when tensile or shear failure occurs. This approach has been applied widely to wellbore-stability problems for homogeneous isotropic rocks. In this paper, the stress distribution is coupled with the pore pressure, and the model is applied to hydraulic-fracturing problems in unconsolidated sands. This iterative, coupled program was developed to calculate the pore pressure, stress/strain distribution, porosity, and permeability in the formation.