We propose and investigate formulation and numerical simulation for largely deformable anisotropic reservoirs in this study. We employ the total Lagrangian method (TL) for coupled flow and geomechanics, which does not need to update the coordinate system each time step. The use of the deformation gradient as well as the first and second Piola stresses reflects the change of reservoir configuration, being mathematically equivalent to the updated Lagrangian method. To accurately model full-tensor permeability derived from the Piola transformation in permeability, we use the multi-point flux approximation (MPFA). The total Lagrangian method with MPFA can provide high accurate and rigorous modeling. We thus consider the total Lagrangian method with MPFA as the reference method in this study. Then, we compare it with two other methods: Total Lagrangian method with the two-point flux approximation (TPFA) and infinitesimal transformation assumption with TPFA. From numerical simulation, we find differences between the reference method and the other two methods. Displacement based on the assumption of the infinitesimal transformation is different from that of the total Lagrangian method. Also, we find that volumetric strain and pressure of TL-MPFA are different from those of TL-TPFA. As the anisotropy ratio of permeability increases, the errors between MPFA and TPFA increases.
Small deformation (i.e., infinitesimal transformation) is typically assumed in reservoir geomechanics [1, 2, 3, 4]. This assumption is usually valid in reservoir engineering problems associated with rock, which induce small deformation. However, the assumption might be invalid in largely deformable reservoirs, such as oceanic gas hydrate deposits and fractured/crashed salt domes [5, 6]. Anisotropic reservoirs are profoundly sensitive to substantial changes in reservoir configuration, having full-tensor permeability and elastic moduli during deformation. This causes non-orthogonal grids in flow. However, the modeling of largely deformable anisotropic reservoirs has little been investigated.
In this study, we employ the total Lagrangian method for coupled flow and geomechanics. The coordinate system remained fixed both for flow and geomechanics. Instead, the deformation gradient reflects the change of reservoir configuration, which yields mathematical equivalence to the updated Lagrangian method [7, 8, 9]. The total Lagrangian method also induces full-tensor permeability from the Piola transformation, even if the initial permeability tensor is diagonal . To accurately model full-tensor permeability, we use the multi-point flux approximation (MPFA) . Then, the total Lagrangian method with MPFA can provide high accurate and rigorous modeling, honoring the objective stress rates (i.e., Lie derivatives). We thus consider the total Lagrangian method with MPFA as the reference model in this study.
Full nonlinear elasticity theory of a two-velocity continuum describing the propagation of elastic deformations in microfractured porous media is based on general physical principles: the first law of thermodynamics, the conservation laws, the kinematic relationships in the metric tensor and the Galilean principle of relativity. As theory verification, the theory of the Stoneley waves in microfractured porous media is developed. The simulation results are compared with the results of physical measurement of the Stoneley wave parameters in boreholes. It is shown that an additional fluid transport through fractures makes it possible to satisfactorily correlate the experimental and theoretical data. In general, the developed theory is a nonlinear physical model of fluid dynamics in a fractured porous deformable media. The Stoneley wave attenuation under borehole conditions has been studied. It is shown that the discrepancy observed between results of two-velocity filtration theory and direct permeability measurements in cores may be eliminated within the framework of the theory of microfractured porous medium developed here.
Modeling fluid flow in the microfractured porous medium is especially relevant for the problems of applied geophysics. By using physically and mathematically correct equations that would serve as the basis for describing these processes; we can develop the acoustic theory. The acoustic theory of the microfractured porous medium enables a method of implicit measurement of formation permeability when the formation is saturated with the water-oil mixture under borehole conditions. The general ideas behind this measurement method may be found in (Dorovsky et al. 2010b). In addition, creating models of the microfractured porous media is relevant for the general description of condensed media with different sorting patterns (Landau and Lifshitz, 1987; Dorovsky, 1989, 1995). Models of the microfractured porous media taking into account the finite deformations of the elastic skeleton and the multi-velocity character of the motion of the microfractured porous media are of a special interest. Accurate descriptions of these processes must be based on fundamental physical principles to yield reliable results. These principles include conservation laws (whose general structure flows from the kinetic theory of condensed media), principles of the equations' invariance with respect to the Galileo transform, and the First and Second Principles of Thermodynamics (for equilibrium and non-equilibrium processes). There are publications devoted to developments of the acoustic theory of the microfractured porous media. The models developed there tend to introduce frequency-dependent coefficients in the Biot acoustic equations (Dvorkin and Nur, 1993; Parra, 1997; Diallo and Appel, 2000; Chen et al., 2002; Yang and Zhang, 2002; Adelinet et al., 2011; Tang, 2011; Tang et al., 2012), while the Biot equations are considered within the frequency domain. Many papers do not consider satisfying the First and Second Principles of Thermodynamics as important. Furthermore, these problems are often neglected, even though these theories appear to be continual. It should be noted that conservation laws, principles of the equations' invariance with respect to the Galileo transform, and the First and Second Principles of Thermodynamics are the cornerstones of any continual physical theory that aspires to be accurate. Moreover, at the moment there seems to be little reported in regards to the comparison of the theoretically and experimentally obtained parameters of Stoneley waves for the microfractured porous media.
Swyer, M. W. (AltaRock Energy Inc.) | Cladouhos, T. T. (AltaRock Energy Inc.) | Forson, C. (Washington Department of Geology and Earth Resources) | Czajkowski, J. L. (Washington Department of Geology and Earth Resources) | Davatzes, N. C. (Temple University Department of Earth and Environmental Science) | Schmalzle, G. M. (BOS Technologies LLC)
This study seeks to better understand geothermal energy development risk in Washington State. In this region, crustal stress is dominated by the complex tectonics of the Cascade volcanic arc, and active faulting promotes and sustains geothermal reservoir permeability and provides connection to the postulated heat source. Three prospect-scale sites were selected for Phase 1 of a geothermal play-fairway analysis (PFA); Mount St. Helens seismic zone (MSHSZ), Wind River valley (WRV), and Mount Baker (MB). In Phase 1 of the PFA, heat and permeability potential was modeled from existing and publicly available data which are integrated into a map for each site of geothermal development potential using weighting derived from a multiple experts-opinion approach using an analytical hierarchy process. A heat potential model was created based on the locations of Quaternary volcanic vents, hot springs, Quaternary intrusive rocks, geothermometry, and temperature gradient data. Permeability potential was estimated using three dimensional modeled fault geometries in an elastic half space that slips in response to tectonic crustal stresses estimated from regional strain rates modeled from publicly available Global Positioning System (GPS) velocities. Volcanic deformation at MSHSZ and MB are modeled as Mogi sources of deformation. The resulting permeability potential analysis reveals 1) if faults are acting as fluid conduits or barriers, 2) the portions of faults likely to host fluid flow where slip is promoted and large slip gradients imply damage, and 3) the geometry of adjacent rock volumes that have dense fracture networks due to locally concentrated stresses that provide the porosity and permeability to host a commercially viable reservoir. Geometric fault location uncertainty is explored to determine where improved constraints would significantly alter predicted geothermal potential and thus target new data acquisition planned in Phase 2 of the project.
Geothermal resources require heat, fluid, and permeability. Active faulting and accompanying fractures can supply this permeability, allowing sustained deep circulation of hot water to shallow reservoirs accessible to wells and the high flowrates necessary for commercial electricity production.
Predicting drilling conditions in advance is of prime importance in oil and gas exploration. A close estimate of predrill pore pressure profiles helps reducing drilling operational risks (e.g. kicks) as well as optimizing drilling operations (e.g. mud weight window, casing design). In addition to undercompaction and other overpressure generation mechanisms, chemical compaction effects can produce overpressure in lithologies subject to high temperature conditions. This work presents a pore pressure model for an exploratory well that reproduces the depositional history of the well including chemical and mechanical compaction. The model has been calibrated and verified by comparison to drilling experience and available logs. Advantages and limitations of the model are presented, as well as its capabilities for pore pressure prognosis for new offset exploratory wells in the region. For such a purpose, the calibrated lithology models have been verified by reproducing the depositional and overpressure generation in two offset wells, obtaining results that compare well with their drilling experience. Finally, the model is used to predict the pore pressure conditions along a proposed new well trajectory. The models also provide estimates of overpressure timing in all the trajectories as valuable information for geologists studying the basin evolution.
Exploratory operations can have major uncertainty in predicting drilling conditions, especially in areas that lack drilling experience or in areas that due to some specific depositional history and conditions depart from the general trend observed in nearby wells. One of such special cases is related to overpressure mechanisms due to chemical diagenesis and compaction related processes, which can play a big role in specific rock fabrics exposed to high-temperature conditions [1, 2].
Predicting pore pressure in advance helps reducing wells operational risks and costs by optimizing drilling operations (e.g. mud weight windows, trajectory analysis and casing design amongst others). Traditional methodologies for pore pressure prediction are based on quasi-empirical estimations of the mechanical compaction disequilibrium that can appear in low permeability rocks (e.g. equivalent depth or Eaton's methods). These methods identify deviations from normal compaction trends using logs like neutron density, compressional velocities (sonic) or/and resistivity, to quantify the amount of overpressure that remains in the formation (e.g. ). Finite element modeling can be also used to reproduce the depositional sequence of sediments and study the evolution of overpressure and thermal maturation in sedimentary basins . Other aspects like buoyancy and centroid effect, increase in compressive stress or chemical compaction amongst others can produce overpressure conditions too . In the particular case of overpressure due to chemical processes, this can be triggered by temperature increases and the chemical composition of the rock, which can induce changes in the porosity and pore-pressure generation mechanisms [6, 7]. Overpressure related to chemical compaction might not correlate well with sonic velocities. In order to account for the combination of mechanical and chemical compaction processes, alternative methods to the classical approach based on normal compaction trends can be used, one of them being numerical modeling.
Bedayat, H. (Louisiana State University) | Hosseini, S. A. (Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas) | Moghadam, M. (Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas)
The mechanical response of the target formations during Carbon geological storage strongly depends to the fluid pore pressure alterations in the formation. The storage formations must have sufficient capacity and could avoid migration of CO2 to the surface. When the highly pressurized CO2 is injected into the geological repository the fluid pressure increases in the formation, which results in changes in stresses and deformation of the medium. From geomechanics point of view, the pressure caused by CO2o injection, should not exceed the formation strength and should not cause activation of existing faults. Therefore, finding a realistic estimation of alteration of stresses during the CO2 injection job, has been subject of several studies in the literature. Most of the analytical methods available in the literature to calculate the stress distribution are well established for single-phase flows, but it requires extension when a second fluid, in this case CO2, is also flowing. In the current work, an approximate analytical model is developed for calculating different stresses caused by injection of CO2 in a saline formation, assuming two phase flow pressure regime. Here, we investigated the stress regime under induced fluid pressure and temperature alterations during the injection time.
Carbon dioxide storage or carbon dioxide sequestration refers to the processes by which captured CO2 is securely stored in deep geologic formations. Carbon dioxide storage in geologic formations includes oil and gas reservoirs, unmineable coal seams, and deep saline reservoirs. It has been reported by The Intergovernmental Panel on Climate Change (IPCC) that the global capacity of deep saline storage sites is more than thousands of gigatons of CO2, which is hundreds of times greater than the annual CO2 emissions from industrial sources [1–3]. Therefore studying the behavior of CO2 when stored in these sites are crucial for the industry.
This study presents a numerical approach to account for the non-linear clay plasticity on wellbore stability analysis for deep water drilling. The numerical model considers the stress path dependent (anisotropic) strain-hardening/post peak softening behavior, which is typically observed during undrained laboratory testing of clay materials, using the NGI-ADP soil model. A linear-elastic assumption estimated almost no drilling window that did not fit with the field drilling experience. The analysis including the hardening behavior results in a smaller failure zone around the wellbore wall than the linear-elastic perfectly plastic model. When the collapse criterion is defined as an extension of the failure zone that does not trigger a drastic reduction in the shear strength around the well, the proposed approach estimates a possible drilling window for a horizontal well, which was originally estimated as having no drilling window. This study indicates that proper modelling of clay plasticity can provide an efficient solution for deep water drilling of shallow reservoirs.
Shallow clay sections in deep water settings are a complex challenge regarding wellbore stability analysis. Often, clay strength is low compared to pore pressures and the drilled formation behaves under an undrained condition due to relatively low permeability compared to typical drilling times. Consequently, collapse gradients, estimated using an idealized linear elastic or linear elastic perfectly plastic behavior, are commonly estimated as too high .
As illustrated in Figure 1, clay materials show significant non-linear plastic ductility, more than mudstones or stiff shales. When the idealized elastic model is used for the clay material, importance of nonlinear plasticity is ignored. Neglecting plasticity may result in inaccurate wellbore analyses. It is common in the field to observe that drilling through clays or soft shale formations are possible even beyond their elastic limit or the peak failure strain due to non-linear plasticity [2, 3]. Therefore, for an optimum well design in deep-water drilling scenarios, the non-linear plastic behavior of clay around the drilled wellbore should be properly taken into account.
This study investigates the effect of non-linear clay plasticity on wellbore stability by a numerical approach.
The numerical model considers anisotropic strain-hardening and softening behavior of clay, which is typically observed during undrained laboratory testing of clay material, using NGI-ADP soil model . First, a typical plastic behavior of clay while drilling is discussed and compared to laboratory tests. The model is then applied to a deep water drilling design, which initially estimated almost no drilling window using a linear-elastic assumption; a mismatch with a field drilling experience. In the end, applicability of calculated plasticity on the collapse gradient is discussed.
Authors analyzed four geomechanical hypotheses used in rock mass classifications (RMC): hypothesis No.1: the loads on rigid support for the equal criteria of the RMC are equal; hypothesis No.2: scale factor and rock mass mechanical characteristics are the same for different sizes of underground constructions; hypothesis No.3: load on the support is independent from opening size for the same geomechanical condition; hypothesis No.4: support capacity is determined by value of the maximum load on the support. Authors ascertained that the hypotheses are verisimilar but not one of them was proved. They are introduced in empirical approach in order to compensate insufficient statistics data. Approach for estimation rock mass mechanical characteristics and Theoretical-Experimental method for estimation rock pressure manifestation in underground openings are proposed.
In spite of rapid development of the comprehensive geomechanical theoretical models and powerful computer programs, empirical methods are predominantly used in the design practice. The main reason for this is the simplicity of these methods, certainty of baseline data and relative proximity of the predicted results to the data of field measurements.
Modern analytical and numerical solutions for 2D/3D nonlinear problems helped engineers to better understand the mechanism interaction between support structure and rock mass. However, imperfection of the theoretical models and lack of reliable initial characteristics of the rock mass have shown that the results of calculation are not reliable.
The rock mass classifications and support selection provided engineers with a standardized approach for the characterization of rock quality (Proceedings of the International workshop, 2007). The most widely used in current design practice are the following Rock Mass Classifications (RMC): RMR - Rock Mass Rating system (Bieniawski, 1973); Q - Tunneling Quality Method (Barton et al., 1974); U - Quantitative Ground Classification, based on contour displacement criterion (Regulation Guide, 1983). In order to compensate the limited statistical data gathered in field observations, engineers introduced plausible hypotheses and assumptions in these classifications. The ideal method for the design of underground constructions shall take into account not only Geological and Geomechanical conditions (in situ stress state and mechanical properties of the rock mass; dip angle of seams and discontinues; opening direction with respect to strike direction), but also Technological parameters of the system “support – rock mass interaction” (dimensions of the opening cross section; rate of opening driving; distance and time of support installation from the face; type of construction: drill-and-blast (D&B) or tunnel boring machine (TBM); type of support: concrete, shotcrete, anchors or yielding support; contact conditions: full contact or backfilling between opening contour and support or grouting of backfilling; type of opening: separate opening, chamber, parallel or intersection of the openings).
Cao, Wenke (China University of Petroleum) | Deng, Jingen (China University of Petroleum) | Yu, Baohua (China University of Petroleum) | Tan, Qiang (China University of Petroleum) | Liu, Wei (China University of Petroleum) | Li, Yang (China University of Petroleum) | Gao, Jiajia (China University of Petroleum)
Wellbore breakouts and drilling-induced fractures(DIFs) which are usually used to determine in-situ stress magnitude and orientation can be recognized by formation microscanner image plot. An exploration well was drilled in a high temperature and low permeability formation, DIFs showed below 4240m depth and there were no breakouts nearly, Zoback's stress polygon model base on Anderson's faulting theory and Coulomb faulting theory cannot explain the failure phenomenon and determine in-situ stress states. In order to revise the method of stress determination, a thermo-poroelastic model was set up which took into consideration wellbore temperature variation because of drilling fluid circulation, the maximum principle stress magnitude had an upper and lower bound according to wellbore failure, meanwhile DIFs occurrence time was also a factor for stress calculation, so a series of charts including minimum effective tangential stress and damage coefficient were built to determine in-situ stress. It is stated that thermo-poroelastic model can explain wellbore failure and determine in-situ stress states comparing to elastic theory more properly. The research provides a theoretical method for determining in-situ stress by FMI plot especially for high temperature and low permeability wells.
In-situ stresses are primary parameters for analyzing wellbore stability, sand controlling and hydraulic fracture, but it is not easy to determine in-situ stresses underground until now. Mini-frac and leak off tests can measure field stress directly, but this measurement has to be conducted at a specific depth and only the minimum horizontal principal stress (σh) can be determined by this way. The continuous stress magnitude along the well has to be accessed by means of wireline logging and Formation MicroScanner Imager (FMI) logging. Wellbore breakouts and drilling induced tensile fractures (DIFs) are two kinds of typical wall failure which can be identified by FMI, wellbore breakouts direction is aligned with σh direction while DIFs direction is aligned with σH for vertical well, these two kinds of failure have been used widely to estimate in-situ stress orientation and magnitude. Zoback built a polygon model to estimate stress states base on Coulomb faulting theory and Anderson's stress and faulting classification system (Zoback et al. 2003). Analytical solutions(Zoback et al. 1985) were set up to calculate maximum horizontal stress magnitude depending on wellbore breakout depth and opening angel. In order to increase stress calculation accuracy, rock anisotropy was taken into consideration further(Lee et al. 2013), Walton set up a two-dimensional numerical stress model for hard rock (Walton et al. 2015), on the other hand, drilling induced tensile wall fractures were used to be implication to determine the lower bound of σH (Brudy and Zoback 1999; Bérard and Cornet 2003). These models are nearly base on pure elastic theory while determining stress upper and lower bounds.
Low-permeability sand rock is porous material and formation temperature variety can change pore pressure and near wellbore stresses distribution which are important for analyzing wellbore stability. Pore pressure, temperature and stresses couple each other, so several control equations are set up to solve the thermo-poroelastic problem, then in-situ stresses can be back calculated on the basis of wellbore instability condition by comparing effective stresses to strength and tensile failure criteria.
The Mount Messenger Formation in Taranaki New Zealand provides both reservoir and seal units for hydrocarbon accumulations. This paper presents the results of geomechanics testing of samples from the formation at the GNS Science Rock and Soil Mechanics Laboratory, in combination with mercury injection testing. Strength testing, which was on blocks from outcrop exposures or shallow (<60 m) depth cores, included unconfined and triaxial compression at effective confining pressures up to 20 MPa that gave Mohr Coulomb strength parameters of cohesion (c') between 1.5 and 2.5 MPa and friction angles (Φ') between 15° and 26°. Other testing, which included consolidation, ultrasonic (p and s wave) velocities, air permeability gave results typical of New Zealand sedimentary soft rocks with unconfined compressive strength <5 MPa. The mercury injection testing gave a mercury-air threshold entry pressure of ~80 psia. The low to moderate strengths and a low threshold entry pressure together indicate a borderline hydrocarbon reservoir seal quality for the samples.
The Taranaki region of New Zealand is known for both onshore and offshore hydrocarbon production. The Mount Messenger Formation , which has a widespread onshore distribution in North Taranaki (Fig. 1), is associated with both reservoir and seal units for hydrocarbon accumulations (e.g., ).
This paper presents the results of a range of laboratory geomechanics testing, in particular for strength and compressibility properties. The main intention of the paper is to demonstrate the capability of the GNS Science Rock and Soil Mechanics Laboratory in Lower Hutt to obtain mechanical properties at pressures associated with New Zealand hydrocarbon reservoirs.
GNS Science has well-established capabilities in engineering geology and petroleum geoscience. In engineering geology these are largely associated with infrastructure foundations, landslides and geological hazards and for hydrocarbon geology the assessment of hydrocarbon systems, including the development of reservoir traps and associated seals.
The Rock and Soil Mechanics Laboratory was originally established to complement engineering geology programmes (e.g., ), while a recent expansion of capabilities has targeted an ability to perform testing at higher loads and pressures including use of a stiff loading frame and associated triaxial cells.
This paper studies the apparent relation between the ultimate strength and the elastic properties, anisotropy, and composition of shale rock. The study uses a series of Finite Element Models created in the numerical analysis software ABAQUS. The model considers a representative volume of shale rock adopting a binary mixture of a soft phase (clay and kerogen), and a stiff phase (quartz, feldspar, pyrite, and carbonates). The geometry of the finite element model is similar to the theoretical representation of the clay and kerogen shale constituent as an ellipsoidal inclusion in a stiff matrix. This method describes how the far field stress which is the average stress acting on the total volume of rock is partitioned among its stiff and soft constituents. The volume fraction of the ellipsoidal inclusion controls the clay and kerogen volume, while the aspect ratio of this inclusion controls the anisotropy of the rock. The Young's Modulus predicted by the FE models match very well with those predicted from the semi-analytical Differential Effective Medium (DEM) model when the same elastic properties are adopted for the inclusion and matrix. The DEM investigates the correlation between the internal stresses acting on each rock constituent and the mechanical properties of the composite rock. Two groups of analysis are performed to investigate failure anisotropy. The first group used MC model for both stiff and soft component and the second group used MCC for the soft component. Results explain the mechanical anisotropy by depicting the failure mechanisms in both horizontal and vertical samples.
The strength and deformability of shales are fundamental properties relevant to shale gas production. Understanding how different factors affect these mechanical properties is of great importance to successful exploration and production from unconventional reservoirs. Sone and Zoback (2013a, 2013b) showed a clear correlation between ultimate strength and stiffness of the shale gas and the percentage of clay and kerogen content. Another factor crucial to the characterization of shales is its mechanical anisotropy and how it is related to the orientation of bedding planes in the fabric.
Although it is not easy to accurately predict rock strength from petrophysical parameters (Chang et al., 2006); Sone and Zoback (2013b) showed that the elastic modulus seems to be a reasonable indicator of rock strength and ductility. An explanation for that is not readily available because of the fundamental differences in time scale and strain magnitude between elastic deformation and rock failure. In addition, both elastic modulus and ultimate rock strength are found to be consistently higher in horizontal samples (compression direction is parallel to bedding) than in vertical samples (compression direction is perpendicular to bedding).