A fully coupled numerical modeling to investigate the role of rock thermo-mechanical properties on reservoir uplifting in steam assisted gravity drainage

One of the crucial consequences of steam assisted gravity drainage (SAGD) process is abnormal reservoir uplifting under thermal steam injection, which can significantly influence the reservoir rock deformation, specifically thin bed reservoirs and causes intensive failures and fractures into the cap rock formations. A thorough understanding of the influences of rock thermo-mechanical properties on reservoir uplifting plays an important role in preventing those aforementioned failures within design and optimization process in SAGD. In addition, coupling of reservoir porous medium and flowing of specific fluid with temperature as an additional degree of freedom with initial pore pressure and in-situ stress condition, are also very challenging parts of geomechanical coupled simulation which would be clearly explained. Thus, a fully coupled thermo-poro-elastic geomechanical model with finite element codes was performed in ABAQUS to investigate the role of rock thermo-mechanical parameters on reservoir vertical uplift during steam injection. It is clearly observed that, any increase in rock thermo-mechanical properties specifically rock’s thermal properties such as specific heat, thermal expansion, and formation’s thermal conductivity, have significant influences on reservoir uplift. So by coupling the temperature as an additional degree of freedom with the coupled pore-fluid stress and diffusion finite element model of SAGD process, the more realistic simulation will be conducted; hence, the errors related to not having heat as an additional degree of freedom will be diminished. In addition, Young’s modulus and specific heat are the rock thermo-mechanical parameters which have the maximum and minimum effects on the reservoir uplift, respectively.     

用流固耦合方法研究油藏压裂后应力应变和孔渗特性变化

油藏压裂后将引起地应力场发生变化，使岩石变形，导致孔隙度和渗透率变化，进而影响产量，为研究这一问题，作者建立了油藏压裂后流－固耦合渗流模型，考虑了以下因素：油藏岩石变形，地应力，孔隙度和渗透率变化，人工裂缝，流体渗流与岩石应变耦合，储藏渗流与裂缝渗流耦合，非达西效应等。较详细地给出了耦合方程及推导过程，控制方程包括的未知变量有压力，饱和度及位移，11个变量，和11个方程，用有限差分方法将流体渗流和岩石应变方程离散成主对角占优的七对角矩阵，可在修改已有三维二相渗流和三维固体力学程序的基础上，采用隐式迭代方法求解，示例分析表明，用此模型可以研究储层应力变变，孔隙度和渗透率随时间和空间变化规律，为开发方案制定，整体压裂设计，压后生产管理等方面提供定量分析技术。     

Large‐scale poroelastic fractured reservoirs modeling using the fast multipole displacement discontinuity method

An effective approach to modeling the geomechanical behavior of the network and its permeability variation is to use a poroelastic displacement discontinuity method (DDM). However, the approach becomes rather computationally intensive for an extensive system of cracks, particularly when considering coupled diffusion/deformation processes. This is because of additional unknowns and the need for time‐marching schemes for the numerical integration. The Fast Multipole Method (FMM) is a technique that can accelerate the solution of large fracture problems with linear complexity with the number of unknowns both in memory and CPU time. Previous works combining DDM and FMM for large‐scale problems have accounted only for elastic rocks, neglecting the fluid leak‐off from the fractures into the matrix and its influence on pore pressure and stress field. In this work we develop an efficient geomechanical model for large‐scale natural fracture networks in poroelastic reservoirs with fracture flow in response to injection and production operations. Accuracy and computational performance of the proposed method with those of conventional poroelastic DDM are compared through several case studies involving up to several tens of thousands of boundary elements. The results show the effectiveness of the FMM approach to successfully evaluate field‐scale problems for the design of exploitation strategies in unconventional geothermal and petroleum reservoirs. An example considering faults reveals the impact of reservoir compartmentalization because of sealing faults for both geomechanical and flow variables under elastic and poroelastic rocks. Copyright © 2015 John Wiley & Sons, Ltd.     

Cell to node projections: An assessment of error

Reservoir simulators typically use cell‐centered finite volume schemes and do not model directly the coupling of the flow processes with the geomechanics. Coupling of geomechanics with fluid flow can be important in many cases, but introducing fully coupled geomechanical effects in those simulators is not a trivial issue, because the geomechanics is better done by using the Galerkin vertex‐centered finite element methods by which the solid displacements are computed at the vertices of the cells. This creates difficulties in interfacing cell variables with nodal variables. Uncoupled or loosely coupled models are used by many researchers/practitioners by which a reservoir model is coupled to a geomechanical model by staggering in‐time flow and deformation via a sophisticated interface that repeatedly calls first flow and then mechanics. The method therefore requires projection of the reservoir cell variables onto the nodes of the geomechanics Galerkin finite element mesh. In this note, we attempt to quantify the errors associated with cell to node projection operations. For that purpose, we use a simple model of the pressure equation for a heterogeneous medium in one dimension. We are able to derive the exact analytical solution for this problem for both nodal and cell pressures. This allows us to compute the errors due to projection analytically, function of meshing refinement and permeability field variations. We compute upper and lower bounds for the errors, and analyze their magnitude for a variety of cases. We conclude that, in general, cell to node projection operations lead to substantial errors. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical modelling of regional faults in land subsidence prediction above gas/oil reservoirs

The stress variation induced by gas/oil production may activate pre‐existing regional faults. This may enhance the expected land subsidence due to the generation of mechanically weak points close to the producing field. A class of elasto‐plastic interface elements (IE), specifically designed to address the mechanical behaviour of faults over a regional scale, is integrated into a finite element (FE) geomechanical model and used to investigate the role exerted by active faults in anthropogenic land subsidence. The importance of regional faults depends on a variety of factors including depth of the depleted reservoir, fault number, orientation and size, geomechanical properties of porous medium, pore pressure drawdown induced by fluid production, etc. With the aid of some representative examples, a useful indication is provided as to where and how fault activation may influence both magnitude and extent of the land subsidence bowl above producing gas/oil reservoirs, pointing to a generally limited impact on the ground surface. The simulation of a real faulted gas reservoir in a complex 3‐D setting shows that the proposed IE can be simply and efficiently incorporated into a FE geomechanical model, thus improving the quality of the stress and displacement prediction. Copyright © 2007 John Wiley & Sons, Ltd.     

Coupled flow and geomechanical processes during enhanced coal seam methane recovery through CO2 sequestration

The sensitivity of coal permeability to the effective stress means that changes in stress as well as pore pressure within a coal seam lead to changes in permeability. In addition coal swells with gas adsorption and shrinks with desorption; these sorption strains impact on the coal stress state and thus the permeability. Therefore the consideration of gas migration in coal requires an appreciation of the coupled geomechanical behaviour. A number of approaches to representing coal permeability incorporate the geomechanical response and have found widespread use in reservoir simulation. However these approaches are based on two simplifying assumptions; uniaxial strain (i.e. zero strain in the horizontal plane) and constant vertical stress. This paper investigates the accuracy of these assumptions for reservoir simulation of enhanced coalbed methane through CO₂ sequestration. A coupled simulation approach is used where the coalbed methane simulator SIMED II is coupled with the geomechanical model FLAC3D. This model is applied to three simulation case studies assembled from information presented in the literature. Two of these are for 100% CO₂ injection, while the final example is where a flue gas (12.5% CO₂ and 87.5% N₂) is injected. It was found that the horizontal contrast in sorption strain within the coal seam caused by spatial differences in the total gas content leads to vertical stress variation. Thus the permeability calculated from the coupled simulation and that using an existing coal permeability model, the Shi–Durucan model, are significantly different; for the region in the vicinity of the production well the coupled permeability is greater than the Shi–Durucan model. In the vicinity of the injection well the permeability is less than that calculated using the Shi–Durucan model. This response is a function of the magnitude of the strain contrast within the seam and dissipates as these contrasts diminish.     

3D geomechanical modeling and estimating the compaction and subsidence of Fahlian reservoir formation (X-field in SW of Iran)

A geomechanical model can reveal the mechanical behavior of rocks and be used to manage the reservoir programs in a better mode. Fluid pressure will be reduced during hydrocarbon production from a reservoir. This reduction of pressure will increase the effective stress due to overburden sediments and will cause porous media compaction and surface subsidence. In some oil fields, the compacting reservoir can support oil and gas production. However, the phenomena can also cause the loss of wells and reduced production and also cause irreparable damage to the surface structures and affect the surrounding environment. For a detailed study of the geomechanical behavior of a hydrocarbon field, a 3D numerical model to describe the reservoir geomechanical characteristics is essential. During this study, using available data and information, a coupled fluid flow-geomechanic model of Fahlian reservoir formation in X-field in SW of Iran was constructed to estimate the amount of land subsidence. According to the prepared model, in this field, the maximum amount of the vertical stress is 110 MPa and the maximum amount of the horizontal stress is 94 MPa. At last, this model is used for the prediction of reservoir compaction and subsidence of the surface. The maximum value of estimated ground subsidence in the study equals to 29 mm. It is considered that according to the obtained values of horizontal and vertical movement in the wall of different wells, those movements are not problematic for casing and well production and also the surrounding environment.     

Thermal reservoir modeling in petroleum geomechanics

Thermal oil recovery processes involve high pressures and temperatures, leading to large volume changes and induced stresses. These cannot be handled by traditional reservoir simulation because it does not consider coupled geomechanics effects. In this paper we present a fully coupled, thermal half‐space model using a hybrid DDFEM method. A finite element method (FEM) solution is adopted for the reservoir and the surrounding thermally affected zone, and a displacement discontinuity method is used for the surrounding elastic, non‐thermal zone. This approach analyzes stress, pressure, temperature and volume change in the reservoir; it also provides stresses and displacements around the reservoir (including transient ground surface movements) in a natural manner without introducing extra spatial discretization outside the FEM zone. To overcome spurious spatial temperature oscillations in the convection‐dominated thermal advection–diffusion problem, we place the transient problem into an advection–diffusion–reaction problem framework, which is then efficiently addressed by a stabilized finite element approach, the subgrid‐scale/gradient subgrid‐scale method. Copyright © 2008 John Wiley & Sons, Ltd.     

Upscaling of elastic properties for large scale geomechanical simulations

Large scale geomechanical simulations are being increasingly used to model the compaction of stress dependent reservoirs, predict the long term integrity of under‐ground radioactive waste disposals, and analyse the viability of hot‐dry rock geothermal sites. These large scale simulations require the definition of homogenous mechanical properties for each geomechanical cell whereas the rock properties are expected to vary at a smaller scale. Therefore, this paper proposes a new methodology that makes possible to define the equivalent mechanical properties of the geomechanical cells using the fine scale information given in the geological model. This methodology is implemented on a synthetic reservoir case and two upscaling procedures providing the effective elastic properties of the Hooke's law are tested. The first upscaling procedure is an analytical method for perfectly stratified rock mass, whereas the second procedure computes lower and upper bounds of the equivalent properties with no assumption on the small scale heterogeneity distribution. Both procedures are applied to one geomechanical cell extracted from the reservoir structure. The results show that the analytical and numerical upscaling procedures provide accurate estimations of the effective parameters. Furthermore, a large scale simulation using the homogenized properties of each geomechanical cell calculated with the analytical method demonstrates that the overall behaviour of the reservoir structure is well reproduced for two different loading cases. Copyright © 2004 John Wiley & Sons, Ltd.     

Coupled Numerical Evaluations of the Geomechanical Interactions Between a Hydraulic Fracture Stimulation and a Natural Fracture System in Shale Formations

Due to the low permeability of many shale reservoirs, multi-stage hydraulic fracturing in horizontal wells is used to increase the productive, stimulated reservoir volume. However, each created hydraulic fracture alters the stress field around it, and subsequent fractures are affected by the stress field from previous fractures. The results of a numerical evaluation of the effect of stress field changes (stress shadowing), as a function of natural fracture and geomechanical properties, are presented, including a detailed evaluation of natural fracture shear failure (and, by analogy, the generated microseismicity) due to a created hydraulic fracture. The numerical simulations were performed using continuum and discrete element modeling approaches in both mechanical-only and fully coupled, hydro-mechanical modes. The results show the critical impacts that the stress field changes from a created hydraulic fracture have on the shear of the natural fracture system, which in-turn, significantly affects the success of the hydraulic fracture stimulation. Furthermore, the results provide important insight into: the role of completion design (stage spacing) and operational parameters (rate, viscosity, etc.) on the possibility of enhancing the stimulation of the natural fracture network (‘complexity’); the mechanisms that generate the microseismicity that occurs during a hydraulic fracture stimulation; and the interpretation of the generated microseismicity in relation to the volume of stimulated reservoir formation.     

Role of Geomechanics in Assessing the Feasibility of CO2 Sequestration in Depleted Hydrocarbon Sandstone Reservoirs

Carbon dioxide (CO₂) sequestration in depleted sandstone hydrocarbon reservoirs could be complicated by a number of geomechanical problems associated with well drilling, completions, and CO₂ injection. The initial production of hydrocarbons (gas or oil) and the resulting pressure depletion as well as associated reduction in horizontal stresses (e.g., fracture gradient) narrow the operational drilling mud weight window, which could exacerbate wellbore instabilities while infill drilling. Well completions (casing, liners, etc.) may experience solids flowback to the injector wells when injection is interrupted due to CO₂ supply or during required system maintenance. CO₂ injection alters the pressure and temperature in the near wellbore region, which could cause fault reactivation or thermal fracturing. In addition, the injection pressure may exceed the maximum sustainable storage pressure, and cause fracturing and fault reactivation within the reservoirs or bounding formations. A systematic approach has been developed for geomechanical assessments for CO₂ storage in depleted reservoirs. The approach requires a robust field geomechanical model with its components derived from drilling and production data as well as from wireline logs of historical wells. This approach is described in detail in this paper together with a recent study on a depleted gas field in the North Sea considered for CO₂ sequestration. The particular case study shows that there is a limitation on maximum allowable well inclinations, 45° if aligning with the maximum horizontal stress direction and 65° if aligning with the minimum horizontal stress direction, beyond which wellbore failure would become critical while drilling. Evaluation of sanding risks indicates no sand control installations would be needed for injector wells. Fracturing and faulting assessments confirm that the fracturing pressure of caprock is significantly higher than the planned CO₂ injection and storage pressures for an ideal case, in which the total field horizontal stresses increase with the reservoir re-pressurization in a manner opposite to their reduction with the reservoir depletion. However, as the most pessimistic case of assuming the total horizontal stresses staying the same over the CO₂ injection, faulting could be reactivated on a fault with the least favorable geometry once the reservoir pressure reaches approximately 7.7 MPa. In addition, the initial CO₂ injection could lead to a high risk that a fault with a cohesion of less than 5.1 MPa could be activated due to the significant effect of reduced temperature on the field stresses around the injection site.     

Iteratively coupled solution strategies for a four‐field mixed finite element method for poroelasticity

In this paper, we consider numerical algorithms for modeling of the time‐dependent coupling between the fluid flow and deformation in elastic porous media. Here, we employ a four‐field formulation which uses the total stress, displacement, flux, and pressure as its primary variables and satisfies Darcy's law and linear elasticity in mixed weak form. We present four different iteratively coupled methods, known as drained, undrained, fixed‐strain, and fixed‐stress splits, in which the diffusion operator is separated from the elasticity operator and the two subproblems are solved in a staggered way while ensuring convergence of the solution at each time step. A‐priori convergence results for each iterative coupling which differs from those found when using a traditional two‐field or three‐field formulation are presented. We also present some numerical results to support the convergence estimates and to show the accuracy and efficiency of the algorithms. Copyright © 2016 John Wiley & Sons, Ltd.     

Coupled finite‐element simulation of injection well testing in unconsolidated oil sands reservoir

This paper presents a finite‐element (FE) model for simulating injection well testing in unconsolidated oil sands reservoir. In injection well testing, the bottom‐hole pressure (BHP) is monitored during the injection and shut‐in period. The flow characteristics of a reservoir can be determined from transient BHP data using conventional reservoir or well‐testing analysis. However, conventional reservoir or well‐testing analysis does not consider geomechanics coupling effects. This simplified assumption has limitations when applied to unconsolidated (uncemented) oil sands reservoirs because oil sands deform and dilate subjected to pressure variation. In addition, hydraulic fracturing may occur in unconsolidated oil sands when high water injection rate is used. This research is motivated in numerical modeling of injection well testing in unconsolidated oil sands reservoir considering the geomechanics coupling effects including hydraulic fracturing. To simulate the strong anisotropy in mechanical and hydraulic behaviour of unconsolidated oil sands induced by fluid injection in injection well testing, a nonlinear stress‐dependent poro‐elasto‐plastic constitutive model together with a strain‐induced anisotropic permeability model are formulated and implemented into a 3D FE simulator. The 3D FE model is used to history match the BHP response measured from an injection well in an oil sands reservoir. Copyright © 2013 John Wiley & Sons, Ltd.     

A Review of Some Rock Mechanics Issues in Geothermal Reservoir Development

Rock mechanics and geomechanical studies can provide crucial information for economic geothermal reservoir development. Although significant progress has been made in reservoir geomechanics, technical challenges specific to the geothermal area (high temps, data collection, experimentation issues) have prevented widespread use of geomechanics in geothermal reservoir development. However, as the geothermal industry moves to develop more challenging resources using the concept of enhanced geothermal systems (EGS), and to maximize productivity from conventional resources, the need for improved understanding of geomechanical issues and developing specific technologies for geothermal reservoirs has become critical. Rock mechanics research and improved technologies can impact areas related to in-situ stress characterization, initiation and propagation of artificial and natural fractures, and the effects of coupled hydro-thermo-chemo-mechanical processes on fracture permeability and induced seismicity. Rock mechanics/geomechanics research, including experimental and theoretical investigations as well as numerical and analytical solutions, has an important role in optimizing reservoir design and heat extraction strategies for sustainable geothermal energy development. A number of major areas where rock mechanics research can facilitate geothermal systems development are reviewed in this paper with particular emphasis on EGS design and management.     

准噶尔盆地阜康凹陷侏罗系超压成因、垂向传导及油气成藏

沉积盆地中超压广受关注,但对超压传导规律认识的不足制约了高压领域的油气勘探.以准噶尔盆地阜康凹陷侏罗系为例,通过超压类型地质综合判识、关键超压表征参数的理论计算及流体包裹体压力恢复,首次认识到了垂向传导对于储集层超压的重要贡献,结合压力垂向传导机制及过程,探讨了油气藏的运聚及泄露意义.研究结果表明,侏罗系超压由4类超压环境中7种致压因素引起,经历2期大规模压力跨层垂向传导,储集层段发育以垂向传导为主因的复合超压,形成3类不同动力特征的油气藏.压力垂向传导是储集层超压的主要成因机制,断-盖的力学性质、差应力及流体压力等3类因素控制压力垂向传导,传导背景下,形成3类与传导作用有关的油气藏:受断层垂向传导控制的超压油藏、受连通砂体侧向传导控制的超压油藏以及超压界面上的常压油藏,上述3类油气藏的运聚及泄露特征差异较大.      

流固耦合问题及研究进展

传统的渗流理论一般假设流体流动的多孔介质骨架是完全刚性的,即在孔隙流体压力变化过程中,固体骨架不产生任何弹性或塑性变形,这时可将渗流作为非耦合问题来研究。这种简化虽然可以得到问题的近似解,但存在许多缺陷,而且也不切合生产实际。比如:在油田开采过程中,孔隙流体压力会逐渐降低,将导致储层内有效应力的变化,使储层产生变形。近年来,流固耦合问题越来越受到人们的重视,这方面的研究涉及许多领域。该文介绍了有关工程涉及到的流固耦合问题,重点针对油、气开采问题,介绍了储层流固耦合渗流的特点及研究方法和理论进展,包括单相、多相流体渗流的流固耦合数学模型及有限元数值模型。      

Probabilistic Analysis of Fracture Reactivation Associated with Deep Underground CO2 Injection

In the context of carbon capture and storage, deep underground injection of CO₂ induces the geomechanical changes within and around the injection zone and their impact on CO₂ storage security should be evaluated. In this study, we conduct coupled multiphase fluid flow and geomechanical modeling to investigate such geomechanical changes, focusing on probabilistic analysis of injection-induced fracture reactivation (such as shear slip) that could lead to enhanced permeability and CO₂ migration across otherwise low-permeability caprock formations. Fracture reactivation in terms of shear slip was analyzed by implicitly considering the fracture orientations generated using the Latin hypercube sampling method, in one case using published fracture statistics from a CO₂ storage site. The analysis was conducted by a coupled multiphase fluid flow and geomechanical simulation to first calculate the three-dimensional stress evolution during a hypothetical CO₂ injection operation and then evaluate the probability of shear slip considering the statistical fracture distribution and a Coulomb failure analysis. We evaluate the probability of shear slip at different points within the injection zone and in the caprock just above the injection zone and relate this to the potential for opening of new flow paths through the caprock. Our analysis showed that a reverse faulting stress field would be most favorable for avoiding fracture shear reactivation, but site-specific analyses will be required because of strong dependency of the local stress field and fracture orientations.     

Geomechanical modelling to assess fault integrity at the CO2CRC Otway Project,Australia

This paper presents the first published 3D geomechanical modelling study of the CO2CRC Otway Project, located in the state of Victoria, Australia. The results of this work contribute to one of the main objectives of the CO2CRC, which is to demonstrate the feasibility of CO₂ storage in a depleted gas reservoir. With this aim in mind, a one-way coupled flow and geomechanics model is presented, with the capability of predicting changes to the in situ stress field caused by changes in reservoir pressure owing to CO₂ production and injection. A parametric study investigating the pore pressures required to reactivate key, reservoir-bounding faults has been conducted, and the results from the numerical simulation and analytical analysis are compared. The numerical simulation indicates that the critical pore fluid pressure to cause fault reactivation is 1.15 times the original pressure as opposed to 1.5 times for the comparable analytical model. Possible reasons for the differences between the numerical and analytical models can be ascribed to the higher degree of complexity incorporated in the numerical model. Heterogeneity in terms of lateral variations of hydrological and mechanical parameters, effect of topography, presence of faults and interaction between cells are considered to be the main sources for the different estimation of critical pore pressure. The numerical model, which incorporates this greater complexity, is able then to better describe the state of stress that acts in the subsurface compared with a simple 1D analytical model. Moreover, the reactivation pressures depend mainly on the state of stress described; therefore we suggest that numerical models be performed when possible.     

地下储气库地应力模拟研究与地质完整性评估——以相国寺为例

为保障国家调峰保供需求,目前相国寺地下储气库(以下简称储气库)提出并正在进行扩压增量工程,为有效指导储气库运行上限压力优化,同时确保储气库长期安全运行,亟需对相国寺储气库开展地质体完整性评估。综合地质、地震、测井、动态监测资料以及各类室内岩芯实验数据,建立相国寺储气库三维静态及四维地质力学模型,分析了储气库地质体地质力学特征,分别对不同气藏孔隙压力特征下的盖层、底托层、断层稳定性进行应力应变模拟及评估。结果表明：梁山组盖层以及韩家店组底托层在储气库运行过程中产生的地层形变量小;5条控藏断层在储气库前期运行及现今注采条件下没有断层活化风险;模拟储气库注入压力高于原始气藏压力6 MPa时,储气库地质体完整性存在失稳风险。研究成果精细定量化评估了储气库在动态应力场影响下的运行安全,对优化储气库运行方案具有重要的指导意义。