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Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004
Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004

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Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004

Paper Number: ARMA-04-502

... drilling fluid chemistry hydraulic fracturing drilling fluid selection and formulation Upstream Oil & Gas concentration pressure drop drilling fluids and materials drilling fluid property drilling fluid formulation fracture growth

**Fluid****Dynamics**coefficient slurry particle...
Abstract

ABSTRACT: In order to evaluate the growth of fractures for cuttings re-injection, a solid transport model is included in a solidfluid coupled hydraulic fracturing simulator. The fracture geometry is a critical factor affecting the safety of the re-injection operation, and solid particle flow in the fractures is known to have a dominant effect on the fracture propagation. To improve the accuracy of the simulation, the finite element method (FEM) is introduced for modeling the particle motion in the fracture fluid. In the model, opening of the fracture, interaction between multiple particles, and change in viscosity by the solid concentration are taken into account. Numerical examples shown here reveal that the fracture geometry is highly dependent on the concentration of the solid due to the change of gravity and slurry viscosity. The injected solid concentration is one of the few controllable parameters, thus the results suggest the feasibility of geometry control. INTRODUCTION Hydraulic fracturing technique is widely used in the petroleum industry for stimulating wells. Another application of the technology is drill cuttings reinjection, in which huge fractures are created in formations around wellbores to contain the slurrified solid waste produced by the drillings [1]. The major concern of cuttings re-injection is a breakthrough of fracture into adjacent formations and surfaces. If a fracture propagates into usable aquifers, petroleum reservoirs, or the surface or seabed, it can cause the grave environmental pollution and operational risk. Although this operation requires careful design of the fracture growth, there are few controllable factors, and those that are controllable are also restricted by operation margins. A numerical study using a solid transport model in the fracture shows that the solid concentration of the injected cuttings slurry influences the fracture growth significantly through the leak-off character of the formation [2]. The authors have developed another numerical simulator of hydraulic fracturing, in which the true three-dimensional geometry and interaction of multiple fractures are considered [3]. The solid transport model is added to the fully coupled model of fluid flow in the fracture and opening of the fracture in an elastic medium. For the cuttings slurry problem, we need an accurate solution for the case of a high concentration of solid particles. In this paper, we demonstrate a solid transport model that considers the effect of the fracture wall and in the interaction of multiple particles. Furthermore, some numerical results for different concentrations of injected solids are shown to exhibit the effect of this parameter on the final geometry of the fracture. The slurry viscosity and vertical pressure gradient can be manipulated by varying the solid concentration in the slurry, so the fracture growth is controllable by this parameter. NUMERICAL MODELING A fully coupled model of a hydraulic fracturing simulator is developed for the design of well stimulation in complicated stress state and well and fracture geometries [3]. The coupled solution of the fluid pressure and fracture opening is computed using the displacement discontinuity (DD) methodfor solid, and the finite element method (FEM) for Newtonian or non-Newtonian fluid.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004

Paper Number: ARMA-04-490

... viscosity Reservoir Characterization Upstream Oil & Gas constitutive equation

**Fluid****Dynamics**platen experiment application strain rate deformation migration Geophy power law localization Redistribution matrix rheology steel platen liquid pressure equation 1. INTRODUCTION There is...
Abstract

ABSTRACT: A simple approximation of the rheological constitutive equations for isotropic poro-viscoelastic material is proposed. The model is developed by modifying Biot's theory in the transient viscoelsatic regime. This is achieved by considering a liquid-filled spherical shell consisting of Maxwell viscoelastic material as the simplest representation of the poro-viscoelastic materials subjected to large volumetric strains. It is shown that in transition to viscous asymptotic, the stress-strain relations deviates from the canonic poroelastic form and Biot's constants become time-dependent. The proposed model is tested using the published experimental data on the deformation of partially melted rocks at elevated PT conditions. Experimental results are usually interpreted in terms of the power law viscous materials. However, in this work we consider the effect of strain damage on viscosity by treating the latter as a dynamic time-dependent parameter; with the variation rate proportional to the second invariant of strain rate. By taking healing into account, the dynamic power law viscosity has constant asymptotic at a given strain rate. The proposed rheological model is implemented in a 2D FEM code and used to study the formation of partial melt in biaxial tests. It is found that the numerically calculated stress-strain curves demonstrate maxima similar to those found in experiments. Also, the computed pattern of melt redistribution and strain localization at the contact with a stiff spacer is qualitatively similar to the experimental observations. The results also indicate that the matrix sensitivity to damage affects the scale of strain localization and liquid re-distribution. Additionally, the problem of the liquid migration in a folding of poro-viscoelastic layer was considered. 1. INTRODUCTION There is increasing interest in using damage theory in the formulation of geomechanics problems [1-3]. This is in response to the need to model the onset and accumulation of micro-cracks in the process of mechanical rapture of elastic materials. Healing of micro-scale damage is also possible. This occurs in the form of recrystallization when a fluid phase is present or due to thermally activated processes of grain boundary migration and dislocation motion. This approach can potentially provide an alternative to the traditional method of tracking crack propagation using the stress intensity analysis or classic theory of the plastic deformations. The concept of evolution of distributed damage has been used by Lyakhovsky et al. (2001) [2] to describe the non-stationary nature of the effective elastic moduli of porous and nonporous elastic geomaterials undergoing deformation. Such models produce a very realistic portrait of spatial strain localization in the elastic crust underlain by a flowing viscoelastic mantle. Spatial dynamics of the rheological parameters of viscous and viscoelastic materials lead to strain localization and formation of localized rapture zones similar to the cracks in elastic solids. Description of the compliance (viscosity) tensor as a dynamic parameter exposed to strain-weakening and thermally activated healing was suggested by Sleep (2001) [4]. At a constant strain rate, the conventional power law strain-rate dependent viscosity becomes the asymptote of the dynamic power law (for isotropic deformation). For geomechanical applications of the dynamic power law formalism, we use a simplified variant of the poro-viscoelasticity theory.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the Gulf Rocks 2004, the 6th North America Rock Mechanics Symposium (NARMS), June 5–9, 2004

Paper Number: ARMA-04-467

... by comparing stresses with rock strength using various failure criteria. Reservoir Characterization

**Fluid****Dynamics**radial stress Wellbore Design pore pressure stability high-permeability rock Upstream Oil & Gas boundary condition hoop stress diffusivity flow in porous media...
Abstract

ABSTRACT: In the fully-coupled thermoporoelastic wellbore stress modeling, pore pressure and temperature can be decoupled for a low-permeability shale and the decoupled equations can be solved analytically in the Laplace domain. For a high-permeability rock, such as sandstone or carbonate, the fully-coupled pore pressure and temperature can also be decoupled by assuming the pore fluid flow reaches steady-state. This assumption of steady-state fluid flow in a high-permeability rock is validated by solving the fully-coupled pore pressure equations. It is found that the assumption is valid as long as the dimensionless time exceeds a certain time. Under this assumption, the temperature equation can be decoupled and can be solved analytically in the Laplace domain for both injection and production conditions. Closed-form solutions for thermally-induced stresses are also presented in the Laplace domain. The undrained loading effect, which usually occurs at short time and small distances in a low-permeability formation, may be negligible for a high-permeability non-shale formation. Results show that the undrained loading effect can be ignored for a high-permeability non-shale formation when the pore fluid flow reaches steady state. Modeling results of near-wellbore temperature and stresses can be applied to injection well design (pressure and temperature of the injection fluid), wellbore stability analysis, and sanding prediction analysis. 1. INTRODUCTION It has been demonstrated that thermal effects can be very important to both wellbore stability and injection design (Guenot and Santarelli, 1989 [1]; Paige and Murray, 1994 [2]; Charlez, 1997 [3]). Formation temperature and formation pore pressure are fully-coupled for fluid flow in porous media, such as in oil and gas drilling, injection, and production operations. The fully coupled thermoporoelastic equations and solutions for some initial and boundary conditions, and their applications in the petroleum industry, can be found in the literature (Kurashige, 1989 [4]; Wang and Papamichos, 1994 [5]). Theoretically, for any initial and boundary conditions, the fully coupled thermoporoelastic equations can be solved using the finite-difference method, but sometimes at the expense of computation time (Chen, 2001) [6]. In the meantime, the fully-coupled temperature and pore pressure can be partially or completely decoupled for various ranges of rock permeabilities. The decoupled equations might be solved analytically in the Laplace domain as well as in the real time domain under certain initial and boundary conditions (Kurashige, 1989) [4]. For low-permeability (~nanodarcy, or ~1e-21 m 2 ) shale formations, pore pressure, temperature and thermally-induced stresses can be determined analytically for a permeable wellbore boundary (Wang and Papamichos, 1994 [5]; Li et al., 1998 [7]; Chen et al., 2003 [8]) as well as for an impermeable wellbore boundary condition (Chen and Ewy, 2003) [9]. For intermediate and high permeability rocks, Wang and Dussault (2003) [10] presented temperature and pore pressure solutions for a permeable wellbore. Once pore pressure and temperature solutions are determined, the pressure-induced and thermally-induced stresses around the wellbore can then be solved. Rock failure can also be determined by comparing stresses with rock strength using various failure criteria.

Proceedings Papers

H. Arns, H. Averdunk, F. Bauget, A. Sakellariou, T.J. Senden, A.P. Sheppard, R.M. Sok, W.V. Pinczewski, M.A. Knackstedt

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-498

... laboratory NMR response petrophysical property sandstone pore size distribution permeability capillary pressure resolution pore porosity permeability correlation

**Fluid****Dynamics**agreement calculation prediction plug subset ARMA/NARMS 04-498 Digital Core Laboratory: Reservoir core analysis...
Abstract

Abstract: Fragments of a number of core plugs have been analysed using a high resolution X-ray micro-computed tomography (micro-CT) facility at resolutions down to 2 µm . The samples analysed include a range of sandstone samples and one reservoir carbonate core. We show that data over a range of porosity can be computed from a single plug. Computational results made directly on the digitized tomographic images are presented for the permeability and drainage capillary pressure and are compared to conventional laboratory measurements on the same core material. The results are in good agreement and demonstrate the potential to predict petrophysical properties from core material not suited for laboratory testing (e.g., sidewall or damaged core and drill cuttings). Pore size information, NMR response and Formation factor are also calculated on the images. Empirical correlations linking fluid permeability to Formation factor and to a number of pore size parameters based on 3D digitized images of sedimentary rock are compared. 1. INTRODUCTION The petroleum industry is increasingly reliant on more effective reservoir characterization to reduce the risks associated with new field development, better delineate producing fields and identify new reserves. The primary tools for reservoir characterization are wellbore logging and limited core derived laboratory measurements for calibrating field logs and establishing relationships between log responses and the petrophysical properties of interest. These relationships are necessarily empirical and introduce considerable uncertainty in the interpretation of logging measurements and in the resulting reservoir description. A major source of the uncertainty is related to the present inability to effectively characterize complex rock microstructure at the pore scale. A significant reduction in the level of uncertainty requires the development of techniques to accurately characterize rock microstructure and to relate this information to measured petrophysical properties. This paper describes the development of a capacity to characterize and predict petrophysical properties from experimental 3D images of rock microstructures. A micro-CT ( µ - CT ) facility for imaging, visualizing and calculating sedimentary rock properties in three dimensions (3D) is described. We image and characterise small plugs obtained from a range of cores including homogeneous sandstones, reservoir sandstone and carbonate core. Computations made directly on the digitized tomographic images are presented for permeability and drainage capillary pressure. Comparisons with conventional laboratory measurements show good agreement. A number of pore length scale parameters are derived; these include pore volume-to-surface-area ratio, channel diameters associated with mercury porosimetry measurements and length scales associated with the NMR relaxation time. The differences in length scales are discussed. Numerical predictions of Formation factor are also given. This allows one to directly compare common permeability correlations in a controlled fashion. Overall the results show the feasibility of combining digitized images with numerical calculations to predict petrophysical properties. We discuss the challenge to extend the methodology to a wider range of petrophysical properties. 2. EXPERIMENTAL METHOLOGY This section describes the methodology of image acquisition and phase identification methods for the samples studied.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-505

... water saturation Upstream Oil & Gas pore pressure flow in porous media sand production particle capillary strength capillary force coefficient permeability proceedings water breakthrough chemical reaction Reservoir Characterization sandstone saturation

**Fluid****Dynamics**calculation...
Abstract

ABSTRACT: Based on research and model development, including a new rock strength model that considers the effects of both chemical reactions and capillarity changes, a new pressure model that calculates fluid pressure variations with water saturation, an improved nonlinearity model for rock deformation modulus, and a coupled analytical elastoplastic model for stress estimation, the mechanisms for sand instability have been identified, quantified, and compared to address the question of why sand often fails after water breakthrough in an oil well. Model calculations indicate that, with increase of water saturation, sands tend to become weaker (strength reduction) and softer (stiffness reduction) while the loading stresses are elevated and the maximum shear stress moves outward into the reservoir (i.e. a larger zone is affected). For the case discussed, losses of both rock strength and modulus can be up to 80%, while the shear stresses can double because of fluid relative permeability changes and strength loss. Furthermore, after shear failure the sands are more easily detached from the rock matrix because of a decrease in tensile capillary strength with an increase of water saturation. Since the capillary strength is shown to depend only on water saturation, the sanding rate for each value of saturation is constant until destabilizing forces are changed, which leads to so-called episodic sand production after an oil well starts to produce water. These analytical tools can serve as a basis to develop more useful sand stability tools for multiphase fluid flow environments. 1. INTRODUCTION Sands become unstable and start to flow after water intrusion even though no preceding sand production was observed [3,4], and massive sand production occurs when S w reaches a particular value [6]; For sanding wells, the average sanding rate during water breakthrough is higher than before breakthrough [2]; The critical global pressure gradient that activates sanding drops when S w increases [5]; and, Sanding appears as an episodic phenomenon: at a given S w , a sand cavity starts to grow and then becomes stabilized; additional cavity growth episodes require either an increase of pressure gradient or a change in the water saturation value [5,6]. It is estimated that, on average, companies produce three barrels of water for each barrel of oil [1], seventy percent of which comes from weakly consolidated or unconsolidated sandstone. The intrusion of formation water into water-wetted but oil-saturated sand, which is the usual case in oil fields, may trigger or worsen the sand instability that has been frequently observed both in the field [2, 3] and in the laboratory [4-6]. Some characteristics of water-related sand production are: Chemical reactions between water and solids and the dissolution of cementitious materials may weaken the rock; Changes in the surface tension and capillary force may lower the cohesive strength; Extensive experiments have been carried out to study the effect of changes in S w (or moisture content, humidity, etc.) on different rock samples, such as shale [7, 8], chalk [9-11], and sandstone [2, 5, 12-15]. The various possible mechanisms may be generalized as follows [16]:

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-567

... transition

**Fluid****Dynamics**Reservoir Characterization clay model Upstream Oil & Gas viscoplastic deformation unconsolidated sand hydrostatic compression test unconsolidated reservoir sand volumetric strain rate critical state line strain rate end cap model constitutive law...
Abstract

ABSTRACT : Laboratory studies of deforming unconsolidated reservoir sands from the Wilmington Field, CA and the Gulf of Mexico indicate that a significant portion of the deformation is both time-dependent and permanent. Furthermore, a threshold viscous compaction pressure has been identified in these sands, marking the transition from elastic to viscoplastic behavior, and which in general can be approximated by the maximum in situ effective pressure experienced by the sand at depth. Because the viscous component of deformation is significant, a standard elastic-plastic end cap model is not sufficient, and a model that includes viscoplasticity must be used. An appropriate model for unconsolidated sands can be developed by incorporating Perzyna viscoplasticity theory into the modified Cambridge clay cap model. Perzyna viscoplasticity theory simply states that pressure (and the location of the end cap) should follow a power law function of strain rate when a material is deforming viscoplastically. Hydrostatic compression tests were conducted at volumetric strain rates of 10 -6 , 10 -5 , and 10 -4 per second in order to find values for the required model parameters, namely the threshold viscous compaction pressure as a function of strain rate. As a result, by using an end cap model and Perzyna viscoplasticity theory, changes in porosity in both the elastic and viscoplastic regimes can be predicted as a function of both stress path and strain rate. 1. INTRODUCTION Inelastic porosity loss and its associated compaction and subsidence is commonly observed in unconsolidated sand and shale and weakly consolidated chalk reservoirs during production. A classic example of this is the Ekofisk field, where both field evidence and laboratory studies showed that production-induced compaction was permanent, and that the observations could be modeled with an elastic-plastic cap-type constitutive equation [1]. More recently, Chan and Zoback [2] used the modified Cambridge clay cap model to describe the deformation of unconsolidated sands from the Gulf of Mexico, and developed the DARS (Deformation of Reservoir Space) method of transferring model parameters from laboratory boundary conditions to reservoir boundary conditions in order to predict changes in porosity associated with production. Fossum and Fredrich [3] derived a unique and continuous end cap model by analyzing laboratory data from a variety of unconsolidated earth materials, and built the resulting constitutive equations into a large 3-D finite element code capable of meter-scale deformation analysis of reservoirs and aquifers. Incorporating cap-type constitutive laws into finite element models is not unique to reservoir analysis; such models are commonly used in civil engineering and soil mechanics at both the field scale [4,5] and the laboratory scale [6]. End cap elastic-plastic constitutive laws have proven to be robust and reliable predictors of the deformation of a variety of unconsolidated materials over several orders of magnitude in scale. There are several advantages to choosing an end cap constitutive law for describing elasticplastic materials. The main advantage for geomechanical applications is that the model provides a means of quantitatively predicting changes in porosity as a function of stress under both shearing and compaction. In addition, most end cap models require solving for only a few parameters in order to be fully defined.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-523

... Upstream Oil & Gas material property

**Fluid****Dynamics**Simulation flow in porous media displacement rock joint specimen shear process joint surface roughness shear behavior dilation Reservoir Characterization aperture mechanical model direct shear test shear mechanical model...
Abstract

ABSTRACT: In this paper, we have carried out the permeability tests for rock joints under the shear process and have discussed the influence of the joint surface roughness and the material properties on the permeable character of rock joints. Based on the experimental results, it has been found that the permeability of rock joints is strongly affected by both the aperture and the joint surface roughness. In particular, it is thought that the flow path along the rock joint is determined by the contact condition of the joint surface roughness. Based on the shear mechanical model for rock joints [1], [2], we have carried out simulations for the permeability of rock joints. In this paper, we have applied two kinds of simulation methods, namely, the discrete cubic law model and the two-dimensional flow model. The channeling flow can be expressed in consideration of the various types of joint surface roughness. 1. INTRODUCTION In order to estimate the stability and the performance of underground structures, nuclear waste disposal facilities in particular, and CO 2 geosequestrations, etc., we must grasp not only the mechanical behavior, but also the hydro-mechanical behavior in the subsurface. In jointed rock masses, both the mechanical behavior and hydro-mechanical behavior are strongly controlled by rock fractures and/or rock joints [3]. In order to grasp the permeability of single rock joints under the shear process, in consideration of the geometrical properties, permeability tests on rock joints have been carried out under the direct shear process. Moreover, by applying the shear mechanical model [1], [2] to rock joints, the shear behavior and the variation shapes of joint surface roughness on rock joints have been clarified. Using the geometry of the joint surface roughness and the aperture distributions through the shear mechanical model, two kinds of flow simulations, that is the discrete cubic law model and the two-dimensional flow model, have been applied. Comparing the experimental results with the numerical simulations, the hydro-mechanical behavior of rock joints has been discussed. 2. EXPERIMENTS In this study, direct shear tests and permeability tests are simultaneously conducted in consideration of the joint surface roughness and the material properties under constant normal confining conditions. The shear behavior and the permeable properties of rock joints are then discussed. 2.1. Specimens In order to investigate the influence of the joint surface roughness and the material properties, artificial specimens are employed in this research work. After choosing three kinds of natural joint surface roughness, impressions are made of them. Using the impressions, reproduced plaster specimens are then created. The artificial specimens used in this research are rectangular, and each has a length of 80 mm along the shear direction at the cross section, a width of 120 mm , and a height of 120 mm . Every specimen contains a single joint, located at the center (lengthwise) of the specimen, and is approximately aligned on the horizontal plane. Before and after performing the tests, measurements of the joint surface roughness are taken with a roughness profiler [4]. Each kind of joint surface roughness is measured at intervals of 0.25 mm .

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-526

...

**Fluid****Dynamics**thin plate mass evolution hollow cylinder Reservoir Characterization equilibrium gallery Upstream Oil & Gas transfer process moisture transfer evolution equation flow in porous media thin plate diffusivity experimental data relative humidity saline solution...
Abstract

ABSTRACT: Hydromechanical and mass transfer phenomena in argillaceous rocks mass are currently studied in order to predict the perturbations around ventilated galleries of a nuclear waste storage. This paper presents the results of drying experiments performed on argillite samples bored at 500 m depth at Bure (France) where an underground research laboratory will be built. Relative humidity and mass evolution of thin plates and hollow cylinders samples are continuously measured in tight box in which relative humidity is imposed by saline solutions. The mass transfer phenomenon is characterized by the moisture diffusivity coefficient computed by comparing the measured mass evolution and the linearized analytical solutions for each drying step. The linearized water moisture diffusivity increases exponentially according to the relative humidity from about 0.5x10 -10 m 2/ s -1/ for the 44 % to 32% relative humidity step to 1.2x10 -10/ m 2/ s -1/ for the 97% to 90% relative humidity step. A theoretical moisture transfer model, accounting for the vapour water transfer and liquid water transfer is then proposed. The confrontation with the experimental data leads to the identification of permeability of the unsaturated rock. The model assumes an intrinsic permeability value of 10 -22/ m 2/ , which is a lower bound of measured permeability in the saturated state for this argillite. 1. INTRODUCTION The French Radioactive Waste Management Agency (ANDRA) has selected an argillaceous site in the east of France (Bure, Haute-Marne) as potential nuclear waste storage host. An underground research laboratory at a 500 m depth is currently under construction. The digging of the galleries is expected to create a damaged zone around the galleries, increasing the permeability by several orders of magnitude. Additional damage could be induced by the desaturation due to the ventilation of the galleries. Such hydric induced cracks have already been observed in the argillaceous Tournemire tunnel [1]. A complete experimental investigation is currently conducted at the LMS (Laboratoire de Mécanique des Solides) in order to characterize, on one hand, the unsaturated hydromechanical behaviour of the rock at moisture equilibrium and on the other hand, the mass transfer process during desaturation steps. The argillite under investigation belongs to the Callovo-Oxfordian layer at a depth of 400-500 m. The tested samples are bored from cores at a depth of about 480 m. The mineral content is: 40% of clay materials, 25 to 30% of quartz and 20 to 30% of carbonates. Microscopic observations have shown that the argillaceous phase is continuous whereas the quartz and carbonates phases are discontinuous [2]. The observed quasi-linear relationship between the water content and the logarithm of suction is typical of clay materials. Water permeability in saturated state has been measured by transient method and ranges from 10 -22 m 2 to 10 -20 m 2 [3], [4] for the undamaged material. The hydromechanical behaviour of Bure argillite has been extensively studied in the saturated state; however in the unsaturated state, few data are available, especially when the mass transfer process is concerned. We present in this paper the results of drying experiments leading to the experimental characterisation of the mass transfer process in term of moisture diffusivity coefficient as a function of air relative humidity.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-568

... flow in porous media Upstream Oil & Gas reservoir geomechanics reservoir space kozeny-carman relationship depletion Reservoir Characterization

**Fluid****Dynamics**experiment reduction laboratory experiment deformation unconsolidated reservoir sand permeability loss stress path...
Abstract

ABSTRACT: Utilizing a modified Cam clay cap model, we have transformed laboratory measurements of the stress-dependency of unconsolidated deformation to reservoir space (i.e., in terms of in-situ stress and pore pressure) such that changes in both stress and strain can be assessed as a function of depletion. In previous studies, this transformation, which we term Deformation Analysis in Reservoir Space (DARS), has been performed based on static laboratory experiments. Although this static approach yields a reasonable first order approximation of total deformation, it fails to capture the effects of the change in production rate and the time-dependency of inelastic deformation associated with depletion in unconsolidated reservoirs. To address time-dependent deformation (e.g., creep strain), we have incorporated Perzyna viscoplasticity theory to the modified Cam clay cap model. Following the procedure described by Hagin and Zoback in the accompanying paper, the threshold compaction pressure as a function of strain rate is determined from basic hydrostatic compression tests. As strain rate can also be expressed as a function of production rate, the static DARS can now be extended into a dynamic formalism that predicts the change in physical properties such as porosity reduction, permeability reduction and changes in rock properties associated with production. 1. INTRODUCTION In a depleting reservoir, the reduction in pore pressure can induce marked reductions in porosity leading to compaction (and possibly subsidence), and potentially significant reductions in permeability. Thus, understanding the relationship between production, compaction and permeability loss is an important factor in reservoir management. For most weak sand reservoirs, both elastic and inelastic deformations occur during production. While most reservoir deformation models are based on poroelasticity theory, the impact of viscoplasticity on reservoir deformation cannot be ignored [e.g., 1,2]. In this paper, we will first review standard formalism we termed as Deformation Analysis in Reservoir Space (DARS) in previous studies [3]. Incorporating the viscoplastic theory, we will then extend the standard DARS from a static analysis to a dynamic analysis that characterizes both instantaneous and time-delayed deformations in terms of reservoir compaction and the associated permeability changes. We will also present a plausible relationship between porosity reduction and permeability change during reservoir depletion based on laboratory experiments. This relationship will then be applied to our case studies to demonstrate how permeability can be estimated in a producing reservoir. A number of laboratory studies of the dependency of permeability on porosity, stress and deformation mechanism have been published. Zhu and Wong [4] suggested that permeability and porosity changes for most low-porosity sandstones closely track one another in the cataclastic flow regime. However, a drastic change in permeability was triggered by the onset of shear-enhanced compaction once the sample is loaded beyond the elastic domain into the plastic deformation domain in the reservoir stress space. The effects of plastic deformation and permeability alteration can be extremely significance in reservoir simulations of a highly compressible reservoir [5]. another in the cataclastic flow regime. However, a drastic change in permeability was triggered by the onset of shear-enhanced compaction once the sample is loaded beyond the elastic domain into the plastic deformation domain in the reservoir stress space.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-546

... US government Reservoir Characterization reservoir geomechanics

**Fluid****Dynamics**GeoModel microcrack porosity application Upstream Oil & Gas strength triaxial compression compression test invariant compaction pore collapse Wellbore Design limit surface elasticity stress state...
Abstract

ABSTRACT: Sandia's GeoModel is a generalized plasticity model that was developed primarily for geological materials, but is also applicable to a much broader class of materials such as concretes, ceramics, and even some metals. Nonlinear elasticity has been incorporated through empirically fitted functions found to be well suited for a wide variety of materials. The yield surface has been generalized to include any form of inelastic material response including pore collapse and growth. Deformation-induced anisotropy is supported in a limited sense through kinematic hardening. Applications involving high strain rates are supported through an overstress model. Inelastic deformation can be associated or non-associated, and the GeoModel can employ up to 40 material input parameters in the rare case when all features are needed, but simpler idealizations (such as linear elasticity, or Von Mises yield, or Mohr-Coulomb failure) can be replicated by simply using fewer parameters. 1. INTRODUCTION Simulating deformation and failure of natural geological materials (such as limestone, granite, and frozen soil) as well as rock-like engineered materials (such as concrete [1] and ceramics [2]) is at the core of a broad range of applications, including exploration and production activities for the petroleum industry, structural integrity assessment for civil engineering problems, and penetration resistance and debris field predictions for the defense community. For these materials, the common feature is the presence of microscale flaws such as porosity (which permits inelasticity even in purely hydrostatic loading) and networks of microcracks (leading to low strength in the absence of confining pressure and to noticeable nonlinear elasticity, rate-sensitivity, and differences in material behavior under triaxial extension compared with triaxial compression). For computational tractability and to allow relatively straightforward model parameterization using standard laboratory tests, the Sandia GeoModel strikes a balance between first-principals micro-mechanics and phenomenological, homo-genized, and semi-empirical modeling strategies. The over-arching goal is to provide a unified general-purpose constitutive model that can be used for any geological or rock-like material that is predictive over a wide range of porosities and strain rates. Being a unified theory, the GeoModel can simultaneously model multiple failure mechanisms, or (by using only a small subset of the available parameters) it can duplicate simpler idealized yield models such as classic Von Mises plasticity and Mohr-Coulomb failure. Thus, running this model can require as many as 40 parameters for extremely complicated materials to only two or three parameters for idealized simplistic materials. 2. GEOMODEL OVERVIEW The GeoModel shares some features with earlier work by Schwer and Murry [3] in that a Pelessone function [4] permits dilatation and compaction strains to occur simultaneously. For stress paths that result in brittle deformation, failure is associated ultimately with the attainment of a peak stress and subsequently work-softening deformation. Tensile or extensile microcrack growth dominates the micromechanical processes that result in macroscopically dilatant (volume increasing) strains even when all principal stresses are compressive. At higher pressures, these processes can undergo strain-hardening deformation associated with macroscopically compactive volumetric strain (i.e., pore collapse).

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-534

... Upstream Oil & Gas porosity Reservoir Characterization

**Fluid****Dynamics**fluid pressure MPa specific storage effective stress law rock sample flow in porous media effective pressure sandstone Tennessee Sandstone Artificial Intelligence pore pressure deformation permeability...
Abstract

ABSTRACT: Laboratory measurements under hydrostatic pressure demonstrate both permeability and specific storage are dependent upon effective confining pressure, where both properties decrease as effective hydrostatic pressure is increased. Within the limits of experimental reproducibility, values of permeability in a single effective pressure loading cycle agree with the effective stress concept, i.e. that permeability is approximately constant for a given P eff irrespective of the particular combination of P con and P flu used to achieve the given effective pressure. However, permeability and specific storage are found to be non-linearly related to effective pressure over the effective pressure range experienced by the sample (20 MPa - 80 MPa), and Biot's a parameter for permeability and specific storage varies as a function of effective pressure. For a given sample of Tennessee sandstone values of a for permeability range from 1.1 at low effective pressures (relatively high permeability) to 0.5 at relatively high effective pressures (relatively low permeability). Therefore, the simple effective stress law, where P eff = P con - aP flu and where a = 1 does not hold for permeability and specific storage over the whole range of test effective pressures, inferring that the stress dependence of the a parameter for permeability and specific storage should be characterized for individual materials. 1. INTRODUCTION A wide range of rock properties and processes, including permeability and fluid specific storage, depend on effective pressure. Effective pressure can be defined as P eff = P con - a P flu where P eff is the effective confining pressure, P con the external confining pressure, P flu the internal pore pressure, and a a poro-elastic multiplier termed the Biot effective stress parameter. The 'simple' effective pressure law, taken to be the difference between P con and P flu with a = 1, applies for some rock properties but does not hold universally. Not only is a specific to a particular property, but it is also markedly sensitive to the magnitude of applied effective pressure. Hydrostatic compression experiments have been conducted to investigate the effective pressure sensitivity of both permeability and specific storage in a low porosity tight reservoir sandstone analogue (Tennessee sandstone). The effective stress a parameter for both permeability and specific storage has been determined. A novel, single-ended transient pulse permeability measurement technique was implemented to enable synchronous measurement of fluid flow and specific storage. Derivation of the a parameter for specific storage is unique to this study. Laboratory measurements under hydrostatic pressure demonstrate both permeability and specific storage are dependent upon effective confining pressure, where both properties decrease as effective hydrostatic pressure is increased. Within the limits of experimental reproducibility, values of permeability in a single effective pressure loading cycle agree with the effective stress concept, i.e. that permeability is approximately constant for a given P eff irrespective of the particular combination of P con and P flu used to achieve the given effective pressure. However, permeability and specific storage are found to be non-linearly related to effective pressure over the effective pressure range experienced by the sample (20 MPa - 80 MPa), ie Biot's a parameter for permeability and specific storage varies as a function of effective pressure. For a given sample of Tennessee sandstone value

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-613

... Science. reservoir simulation volumetric strain strain-induced permeability model Reservoir Characterization

**Fluid****Dynamics**pore pressure flow in porous media displacement viscosity Upstream Oil & Gas injection pressure injection test equation permeability model porosity...
Abstract

ABSTRACT: The paper presents a discussion on the strain-induced anisotropy in permeability for deformable granular media. A coupled deformation-flow-heat transfer simulator, which has incorporated the strain-induced permeability model, was developed using finite element method (FEM). It was used to conduct a coupling analysis of two-dimensional non-isothermal single-phase fluid flow in elastic porous media. As well, two fluid injection tests were carried out to investigate the effects of the permeability anisotropy. It is shown that the strain-induced permeability anisotropy does have significant impacts on the pressure response. It is also found that the proposed permeability model can accurately reflect the directional increase in permeability during fluid injection. 1. INTRODUCTION The dependence of permeability on direction or permeability anisotropy in porous media has been confirmed by many field studies. The existing reservoir simulators usually deal with permeability anisotropy in such a way that the permeability in the principal directions may vary in magnitude at different locations; however, the orientations of the principal permeability remain the same throughout the reservoir. In reality, both the magnitude and the orientation of the principal permeability may vary from region to region in the reservoir due to the variation of effective stress in the reservoir formation. The permeability anisotropy mentioned in the following context is referred to the latter case. Deformations in a reservoir are induced by the changes of pore pressure and temperature due to fluid injection and production in thermal recovery processes, thereby affecting permeability. However, in the geomechanics and petroleum literature, the permeability change of reservoir formation subjected to deformation changes is usually assumed as a function of porosity or volumetric strain, which is a scalar variable. Thus, the changes in permeability are equal in all directions even though the changes in strains are different in each direction. Wong [1] analyzed the grain fabric of intact and sheared oil sand specimens using the thin section imaging method. He observed that even in intact natural oil sand specimens, the hydraulic radius and tortuosity factors vary in vertical and horizontal directions resulting in an intrinsic anisotropy in permeability. Based on theoretical and laboratory works, he developed a new permeability model for deformable porous media. This model assumes the tensor permeability is governed by induced principal strains. It can quantify the changes in permeability when the material experiences shear deformation and the changes in permeability can be anisotropic. Coupled geomechanics-reservoir simulation is necessary in order to account for deformations due to pore pressure and temperature changes resulting from production and fluid injection. Conventional reservoir simulators usually use finite difference method (FDM) and assume permeability either isotropic or diagonal tensor. It is impractical to develop coupled geomechanics-reservoir simulators based on FDM numerical schemes due to its complexity. A coupled deformation-fluid flow-heat transfer simulator using finite element method (FEM) was developed. The full tensor permeability and the strain-induced permeability model were implemented into the simulator. It was then used to conduct a coupling analysis of two-dimensional non-isothermal single-phase fluid flow in elastic porous media. As well, two fluid injection tests were carried out to investigate the effects of the permeability anisotropy.

Proceedings Papers

M.M. Molenaar, P.J. Hatchell, A.C. van den Beukel, N.J. Jenvey, J.G.F. Stammeijer, J.J. van der Velde, W.O. de Haas

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-639

... analyses. Oil & Gas Science and Technology (Rev. IPF). 57: 5, 443- 458. reservoir geomechanics Modeling & Simulation sand production rock property Reservoir Characterization overburden calibration

**Fluid****Dynamics**depletion Upstream Oil & Gas displacement compaction strain molenaar...
Abstract

ABSTRACT: Here we present the results of a geo-mechanical study combined with a new way of 4D interpretation, applied to a depleting offshore gas condensate field. The 4D interpretation uses the predicted stress changes from the geo-mechanical study, by bringing them to the seismic domain in the form of 'synthetic' time-shifts. It is demonstrated that, by comparing measured time-shifts with these 'synthetic' time-shifts, discrepancies in geomechanics (e.g. in the rock properties and formation stiffness contrasts) and reservoir dynamics modeling (e.g. undepleted pockets and activity of waterdrive) become much better traceable. The rock properties and the pressure distributions were then iteratively calibrated and harmonized with the measured 4D and other field observations (GPS and compaction-log). The applied workflow reduced uncertainties in forward predictions of stress changes from the geo-mechanical model in and around the compacting reservoir, and enabled the design of a new strategy for sand management in the field. 1. INTRODUCTION In petroleum engineering, a geo-mechanical field evaluation focuses on understanding the subsurface mechanical in-situ conditions and the changes in the subsurface induced by pressure depletion or pressure maintenance. Given the structural complexity of certain fields, numerical modeling techniques are nowadays a preferred tool to predict the induced changes in stresses, strains, properties and failure condition of the rock formations. Top-seal integrity. Subsidence or uplift of the seabed. Fault slip. Borehole instability. Risk of sand or fines production. Completion failure. Undepleted reservoir pockets. Sealing or non-sealing faults. Depending on the problem(s) , anticipated the geo-mechanical forward model predictions are used to address specific aspects that impact the economy of the field at different stages. In the e a geo-mechanical evaluation focuses on e.g.: At the e a geo-mechanical assessment looks at e.g.:However, the use of geo-mechanical modeling also provides a new opportunity [1, 2], by incorporating geo-mechanical results of the whole earth [3] in the time-lapse seismic (4D) monitoring of producing oil and gas fields. It can enhance the current reservoir technologies to better detect e.g.: Here we present the workflow of a geo-mechanical study combined with this new way of 4D interpretation, applied to an offshore gas condensate field [4]. 2. GEO-MECHANICS AND 4D The structural geometry of the field, the initial stress state, the formation rock properties and the pressure depletion (or injection) scenario from the dynamic reservoir simulator, are the primary unknowns in the geo-mechanical field equations for calculating production induced stress changes (¿ s ). 2.1. Compaction and Subsidence The subsurface is subjected to the total stress ( s ) of the overburden and the horizontal tectonic stresses, which are carried in the rocks by effective stress ( s eff ) on the grain-to-grain contacts and the fluid pressure ( p ) in the pores: s eff = s - ap I (1) where, a and I , denote the coefficient of Biot and the unit tensor, respectively.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-599

... unconventional resource economics back analysis Testing Methodology Rio de Janeiro wellbore integrity interaction reflectivity saline solution drilling fluid property oil shale

**Fluid****Dynamics**water content pontifical catholic university diffusion phase permeability pressure test ARMA/NARMS 04...
Abstract

ABSTRACT: The drilling of oil wells through shales, which constitute the majority of rocks in the stratigraphic column, may present instability problems due to physico-chemicals interactions between the drilling fluids and these rocks. The costs to solve these problems are very high and, depending upon the intensity of these problems, wells can be lost. This paper presents new equipment designed to apply hydraulic and chemical gradients through shale samples in order to evaluate the shale interaction with a given fluid. The proposed test allows the determination of rock permeability, the coefficient of reflectivity (membrane efficiency) and the ionic diffusion coefficient. These parameters are essential to carry out proper wellbore stability analysis when taking into account the shale-drilling fluid interaction. Tests carried out on Brazilian offshore shale using different saline solutions confirmed the good performance of the equipment. Details of the equipment and test results are described. 1. INTRODUCTION Drilling through shales has presented serious problems of instability and most of them have been attributed to interactions between this rock and the drilling fluid. Normally, long periods of time are necessary to solve some of these problems and that contributes to raise drilling costs. 10-years old data, [1], indicate that nearly 30% of the additional costs during drilling operations are caused by wellbore instabilities and from these, almost 90% occur during drilling through shales. These problems used to consume more than US$ 500 million per year considering the technology available then. Much has been learned since then, and that allowed the successful drilling of highly inclined wells with the use of a new generation of drilling fluids. However, on average, the losses are still quite high and there is much to be done to transform the research results into daily practice. The proper selection of the drilling fluid for a given situation is still an issue to be dealt with in drilling operations. The ideal drilling fluid concerning stability of wells must keep the confining effective stresses around the well high enough to preclude rock failure. This can be achieved by at least three distinct manners. Firstly, by avoiding pore pressure increase due to fluid penetration, through the use high-entry pressure fluids, i.e., oil-based-like type of fluid. Secondly, by playing with the osmotic effects caused by water-based, saline fluids. Thirdly, by the use of invert-emulsion fluids, [2], that combine the two previous mechanisms. The pore pressure control, achieved through osmotic effects, can be exercised through the concepts of mass transport due to hydraulic and chemical gradients. In low permeability rocks such as shales, these gradients induce changes in pore pressures due to effects of hydraulic and ionic diffusion and osmotic effects that can change with rock capability to restrict the ion flux through the formation. This is the most studied topic related to shale-drilling fluid interaction. In order to evaluate the shale-drilling fluid interactions, new equipment capable to simulate in situ pressure conditions was developed. In this equipment, hydraulic and ionic gradients can be imposed in order to estimate the rock permeability, the coefficient of reflectivity (membrane efficiency) and the ionic diffusion coefficient. These parameters are used as input in borehole stability programs that consider the physical-chemical interactions.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-548

... metals & mining optical triangulation distance measurement device depth ratio subsidence phenomenon Interferometry

**Fluid****Dynamics**laser optical triangulation distance measurement Modeling & Simulation displacement subsidence model sensor model material subsidence profile...
Abstract

ABSTRACT: Surface subsidence causes damage such as the failure and deterioration of buildings, infrastructures, dams, underground utility lines, ground water regimes, etc., resulting in severe economic loss and environmental hazards. The major cause of subsidence is underground mining activities. In order to minimize or prevent subsidence damage, it is necessary to understand subsidence phenomena. It is difficult to simulate or predict subsidence development because of the complexity in physical characteristics such as rock failure and yield behavior, dimensional variations and time dependent behavior. In this paper a new physical subsidence modeling technique is introduced. The method utilizes laser optical triangulation distance measurement devices, which can scan the surface of any material, including granular or viscous materials, and digitally measure vertical distances with an extremely high accuracy and resolution. With this new technique, the effect of cavity shape and size, depth, and material parameters can be analyzed. Using this unique technology and method of analysis, significant results were produced. Subsidence profiles, subsidence factors, and angles of draw were analyzed. Further research is being continued using the same technique for simulating subsidence with different model materials for various underground cavity dimensions, tunneling, and time dependent subsidence phenomena. 1. INTRODUCTION When underground excavation is performed over a significant area, the overlying rock mass subsides into underground cavities.. The majority of subsidence results from underground coal mining that employs longwall and room-and-pillar mining methods. Subsidence may also be caused by failures of tunnels and underground cavities naturally created in limestone rich formations. Subsidence is also caused by withdrawal of fluid, such as ground water or oil. However, the most significant subsidence problems result from underground mining. Surface subsidence damages surface structures such as foundations, utility lines, infrastructures, ground water regimes, etc. In order to avoid or reduce subsidence damages, it is imperative to know the subsidence characteristics of the particular site, and proper design work has to be performed to prevent or minimize subsidence hazards. There are two types of subsidence: (1) pit, also called sinkhole or pot hole, and (2) trough or sag. 1]. Pit subsidence is characterized by an abrupt sinking of the surface, resulting in circular steepsided, crater-like features. Trough subsidence is a gentle, gradual depression of the surface. Subsidence is controlled by many factors, including width of unsupported cavity, height of cavity, thickness of overburden, strength and fracture system of rock, hydrology, and time. For the last several decades, various methods of analysis have been utilized for interpreting and predicting subsidence phenomena. The principal methods of interpreting and predicting subsidence can be grouped as follows [2,3]. Empirically derived relationships Profile functions Influence functions Analytical models Physical models The empirically derived relationships are determined based on large numbers of observations and case studies. The profile functions method and the influence functions methods use equations derived from field measurement data. Analytical modeling consists of theoretical and numerical models that treat subsidence as a problem involving the laws of elasticity, plasticity, and visco-elasticity [4]. Finite element methods are the most commonly used in this group [3-6].

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-537

... Reservoir Characterization aperture crack density

**Fluid****Dynamics**intensifier flow in porous media quartz Westerly granite permeability evolution porosity granite permeability connectivity grain boundary Upstream Oil & Gas pore pressure basalt Heat Treatment Temperature...
Abstract

ABSTRACT: To investigate the relationship between crack damage evolution and permeability changes we conducted a series of experiments where different amounts of isotropic crack damage were introduced into rock samples through heat treatment. Three different materials were used; Westerly granite, Ailsa Craig microgranite and a basalt from Iceland. Microcracking was monitored by means of acoustic emission measurements, and characterized by acoustic wave velocity measurements on the heat treated samples. Subsequent to heat treatment the fluid permeability of the rocks was measured under hydrostatic stress conditions using the steady state flow method. Increasing crack damage results in permeability enhancement although no simple relationship between permeability and crack density or permeability and porosity exists over the whole range of heat treatment temperatures. In all three rock types, three phases exist between permeability evolution and amount of crack damage. Two levels of critical changes in pore network connectivity, or percolation thresholds, are identified in permeability as heat treatment temperature is increased. Comparison of the three rock samples shows that either large changes in crack density leading to increased crack linkage, or small changes in crack density leading to increased crack linkage, is responsible for critical changes in pore connectivity. These results emphasize that changes in crack interconnectivity, and not crack density or porosity alone, is the critical factor in controlling permeability evolution. 1. INTRODUCTION Permeability in rock is critically dependent upon interconnectivity of the pore network. Thus a high porosity material may exhibit negligible permeability until a critical threshold of pore interconnectivity, the percolation threshold, is achieved. Such critical changes in crack network connectivity need not necessarily result from large changes in crack density. This has important implications for modeling of fluid flow in which damage parameters derived from more easily measurable rock properties (velocities, porosity, quantitative microstructural analysis) are used to calculate permeability. To investigate the relationship between crack damage evolution and permeability changes we conducted a series of experiments where isotropic crack damage was introduced into rock samples through heat treatment. Samples were heated at a rate of 1°C/min to various peak heat treatment temperatures up to 900°C at ambient pressure. A low rate of heating was established to ensure that cracking events were the result of temperature alone and not due to thermal gradients across the sample. Once the selected peak temperature was reached the samples were held at peak temperature for an hour before being cooled at 1°C /min to room temperature. Thermally-induced microcracking was monitored through recording the acoustic emissions (AE) during heat treatment. Data from acoustic emission (AE) monitoring was used to relate the main periods of thermal cracking to heat treatment temperature. Before and after heat treatment, ultrasonic compressional and shear wave velocities were measured on the Westerly granite and the Iceland basalt. The changes in velocities were interpreted in terms of a crack density parameter using the method of [1]. Subsequent to heat treatment the fluid permeability was measured under hydrostatic stress conditions using the steady state flow method.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-594

... wellbore integrity

**Fluid****Dynamics**Reservoir Characterization reservoir geomechanics Wellbore Design Upstream Oil & Gas displacement subsidence cylindrical surface Reservoir Compaction compressibility compaction shear stress element analysis reservoir simulation Modeling...
Abstract

ABSTRACT: This paper outlines a solution approach for evaluating the stability of casing and faults due to reservoir compaction. Firstly, a geomechanics model is presented for the evaluation of casing failure due to reservoir compaction. Secondly, a threedimensional finite element analysis is coupled with the developed geomechanics compaction model for the detailed casing failure analysis. Deformations and stresses are determined on a cylindrical surface surrounding the length of the newly drilled or completed wellbore in the regions of interest. This cylindrical surface is sufficiently remote from the wellbore so that the wellbore has no or little influence on the stresses and displacements due to the reservoir compaction on this surface. The calculated displacements on the cylindrical surface are then used as boundary conditions for a focused near-wellbore stress and strain analysis using finite element technology. This hybrid analysis affords evaluating the near wellbore details that are often glossed over with a fastly compacted solution not requiring multimillion FEA cells. Yet, it preserves the fine details around the wellbore and allows for incorporating fault loading and macro influences of geologic structures and reservoir extent. It preserves the material balance and does not alter the pressure volume relationship in the reservoir void space. Interface elements can account for the slippage between the casing and the cement and between the formation rock and the cement. Field cases are presented for both the geomechanics model and hybrid finite element model. 1. INTRODUCTION Depletion can generate large vertical deformation in the vicinity of reservoirs, especially in the Gulf of Mexico, where reservoirs are typically deep, multilayered, over-pressured and weakly cemented sands and silt sequences. Rock geomechanics plays a major role in both the recovery mechanisms and the integrity of the reserve delivery via well survivability. Hence it becomes necessary for the operators in these fields to carry out geomechanics assurance of reserve delivery by assessing the risk of well and casing failure, evaluating fault seal integrity during production, and by analyzing the impact of reservoir compaction on the integrity and recovery of the reservoir's resources. The results of these evaluations would assist the operators in devising appropriate strategies for more optimal recovery of the hydrocarbon from deepwater reservoirs. The studies must be aimed at a careful evaluation of the reservoir's pore volume compressibility, the impact of pressure depletion on reservoir recovery, production rates, fault movements, and well casing integrity [1-7]. Issues related to the impact of compaction on pressure maintenance, total recovery, and the survivability of well casing and completions have been well documented in various reservoirs worldwide such as in the North America fields in California, Western Canada and in the Gulf of Mexico. Many fields have experienced well failures (as illustrated in Figure 1) and loss of productivity following pressure depletion and reservoir compaction. This risk adds to the economic and technical challenges of developing deepwater reservoirs. While the industry has access to large coupled finite elements (FE) software that can model rock and casing deformations caused by pressure changes, widespread use of these packages is severely hampered by several vital factors, such as, lack of long-term reservoir performance forecasts and strategy studies needed by the reservoir engineers, unnecessarily large number (several million) of model cells required for the FE analysis, and lack of sufficiently detailed description of the rock properties for these cells.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-634

..., S.D. 1988. Augmentation of Well Productivity With Slant and Horizontal Wells. JPT. June: 729-739. Upstream Oil & Gas well pi reduction procedure orientation well productivity index reduction pi reduction area 5000

**Fluid****Dynamics**flow in porous media productivity index productivity...
Abstract

ABSTRACT: This paper quantifies the relationship between rock compaction and well flow by including an anisotropic, stressdependent permeability tensor. When producing oil from a weak reservoir, rock compaction induced by pressure drawdown may occur, often with adverse consequences. For weak reservoirs such as unconsolidated sands, rock compaction often causes permeability reduction that may significantly influence the well productivity to the extent that production becomes uneconomic. A 3D finite element model was developed in order to simulate fluid production through a well in a deforming reservoir. Constitutive models for weak reservoir rock and deformation-dependent permeability tensor are also supplemented in the finite element model. The developed model was used to evaluate the influence of rock compaction on well productivity for compaction-sensitive formations. Results show that the model provides an effective tool to identify possible mechanisms associated with rock compaction that cause permeability reduction. The improved understanding of the permeability reduction mechanisms achieved by the model provides a guide to mitigate well productivity impairment resulting from the compaction of these deformable reservoirs. Numerical simulations for different reservoir characteristics, operating conditions, and well configurations were performed in order to establish quantitative relationships between well productivity declines and key field operational control variables. Modeling results for representative cases and the description and formulation of the finite element model are also presented. 1.INTRODUCTION Fluid production of a hydrocarbon reservoir results in decreasing fluid pressure and increasing effective overburden load on reservoir rock. The increase in effective overburden load will in turn compact the reservoir rock and change the stress state in the reservoir. Significant permeability reduction associated with rock compaction around the wellbore region is a well-known phenomenon in oil and gas production in weak reservoirs. As a consequence, rock compaction has adverse effects on well productivity. To quantify well productivity reduction caused by rock compaction, a coupled analysis is required because the physical process involves both geomechanics and fluid flow. Also, in a geologically and geometrically complex setting, it is very difficult, if not possible, to analyze the coupled problem analytically or semi-analytically. On the other hand, advances in numerical computing technology have made the numerical modeling of the coupled geomechanics and fluid flow problem rigorous, robust and efficient in a general fashion. Thus, the objective of this paper is to develop a general 3D finite element model that couples geomechanics and fluid flow, to quantify well productivity reduction induced by rock compaction for practical production operations. In the following sections, first, we present the details of the numerical model that include coupled field equations, initial and boundary conditions, constitutive relations, and numerical procedures. Second, the model was verified for its accuracy and its ability of retaining primary physics by test problems. Third, to demonstrate the capabilities of the model for practical field applications, we conducted modeling studies to examine and discuss how well productivity loss is influenced by operating variables such as production rate, well configurations, and reservoir characteristics including permeability anisotropy and layered heterogeneity in a compacting reservoir. Lastly, conclusions are drawn from this work.

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper Number: ARMA-04-611

... Reservoir Characterization wellbore integrity Upstream Oil & Gas plasticity compaction lochaline sand axial stress unconsolidated sand reservoir geomechanics

**Fluid****Dynamics**strength porosity Wellbore Design compressibility pore collapse stress path effective stress onset...
Abstract

ABSTRACT: Drained and undrained triaxial stress path testing has been conducted on three clean unconsolidated quartz sands in order to investigate the influence of textural parameters on elastoplastic behavior. For all sands tested, pore collapse and porosity reduction were observed to be strong functions of the applied stress path, due to shear enhanced compaction. At elevated pressures pertinent to petroleum engineering practices, grain-crushing can be a significant mechanism of plastic strain accommodation, depending on both sand texture and applied stress path. Yield caps with an additional shape parameter allowing flattening of the ellipse accurately capture the observed onset of plastic yielding. For unconsolidated sands it is important to ascertain whether preconsolidation pressure or grain-crushing pressure controls the onset of plasticity under isotropic loading conditions. 1. INTRODUCTION Approximately 90% of the world's oil and gas wells are drilled in siliciclastic reservoirs [1] with most new discoveries being made in either unconsolidated sands or weakly cemented sandstones [2]. Pressure depletion associated with hydrocarbon production can rapidly induce largestrain plastic deformational behavior in these weak "problem" geomaterials, resulting in well failures, solids production and general reservoir impairment. Plastic strains are accommodated either through brittle shear failure or compactive pore collapse mechanisms depending on the exact stress path followed. For more deviatoric stress paths (relatively low mean effective stress, P', and high stress difference, Q) dilational microcracking occurs prior to shear localization into failure planes orientated at a given angle to the principal stress state [3]. However for more isotropic stress paths (relatively high P' and low Q) continuous plastic compaction occurs with no localization, leading to pore collapse and subsequent strain hardening on further loading. Weak geomaterials with generally high porosity and low cohesive strength can deform plastically to large strain even under hydrostatic stress conditions. High porosity enables the material to deform irreversibly due to a purely contractant volumetric collapse mechanism. The locus of such compactive yield points associated with different stress paths defines a yield function or "plastic cap" which delineates the onset of unrecoverable porosity loss due to material implosion [4]. Classical elastoplastic constitutive laws that integrate both compactive pore collapse and dilational shear failure were originally derived by the soil mechanics community. Elastoplastic material properties are generated from experimental testing, however traditionally soil mechanics laboratory applied pressures have been in the kPa range whereas effective pressures relevant to the etroleum industry can be in the 10'sMPa range. Accordingly, we have tested a suite of unconsolidated sands at elevated pressures up to 130MPa in order to assess: (i) the performance of various cap models at elevated pressure; (ii) sand textural controls on elastoplastic material properties. Rock strength prediction is fundamental to deformation-related problems in which no core is available for direct measurement, or for real-time numerical analyses such as wellbore stability assessment. Thus much effort has been expended in developing correlations between rock fracture strength parameters (cohesion, friction angle) and other physical properties such as rock composition/texture [5] and wireline-derived data [6]. With the upsurge in recent years of geomechanics modeling to answer reservoir engineering problems, the industry is increasingly applying strength correlations to populate dataspars

Proceedings Papers

Publisher: American Rock Mechanics Association

Paper presented at the 4th North American Rock Mechanics Symposium, July 31–August 3, 2000

Paper Number: ARMA-2000-0169

... under uniaxial strain conditions. Finally, the influence of pore pressure on lateral stresses, under uniaxial strain conditions, is discussed. Upstream Oil & Gas reservoir geomechanics pore pressure sandstone Reservoir Characterization compressibility addis

**Fluid****Dynamics**pore...
Abstract

ABSTRACT ABSTRACT: Some implications of the static theory of linear poroelasticity for reservoir compaction are discussed. First, the relationship between the bulk compressibility and the uniaxial compaction coefficient is reviewed. Then, an expression is derived for the pore compressibility under uniaxial strain conditions. Finally, the influence of pore pressure on lateral stresses, under uniaxial strain conditions, is discussed.