Coupled Geomechanics-Reservoir Simulation of UTF Phase A Project Using a Full Permeability Tensor

In this research study, we conducted a coupled thermal-stress-fluid flow numerical model on the UTF Phase A SAGD project in order to investigate the fundamental geomechanical behaviour involved in the SAGD process, and to gain insight into the reservoir response to temperature and pore pressure changes. The numerical simulation is carried out by using a self-developed coupled finite element model which incorporates our proposed strain-induced permeability model. The obtained simulation results were compared with the measured data. Introduction Thermal recovery processes involve coupling between heat transfer, multiphase flow and stress/deformation, which has become an increasingly important subject in the petroleum field(1). Particularly, the coupling is crucial in problems such as borehole stability, hydraulic fracturing and injection/production induced deformation of the ground surface during the thermal recovery process in heavy oil or oil sand reservoirs. Numerical modelling of the coupled processes is historically carried out in the areas of geomechanics modelling and reservoir simulation. The former is to compute the stress-strain behaviour; therefore, the deformation. The latter is to essentially model the multiphase flow and heat transfer in porous media. Each of these disciplines simplifies the part of the problem that is not of primary interest. These approaches are unacceptable in situations where the coupling is strong and the changes of porosity and permeability cannot be accounted for by rock compressibility alone. Gutierrez and Lewis(2) extend Biot's theory to multiphase fluid flow in deformable porous media. Based on their formulation, they conclude that the coupling between the geomechanics and the multiphase flow occurs simultaneously. Thus, fully coupled system equations of deformations, multiphase flow and heat transfer should be solved simultaneously. Development of such kinds of fully coupled geomechanics-multiphase flow-heat transfer simulators needs tremendous effort, since the existing FEM geomechanics codes and FDM reservoir simulators cannot be used. Settari and Mourits(3) present an approach to couple the stress-strain behaviour to multiphase flow-heat transfer using porosity as a coupling parameter. The geomechanics module and the thermal reservoir simulator are used in a staggered manner. Pore pressure and temperature changes are calculated from the thermal reservoir simulator and transferred to the geomechanics module. The stress and the displacement changes are then calculated in the geomechanics simulation. An iterative algorithm is used to ensure that the porosity calculated from the geomechanics module is the same as that from the thermal reservoir simulator. The staggered technique employed to solve the coupled system equations allows for the use of the existing geomechanics codes in conjunction with a standard reservoir simulator. Currently, most of the commercial coupled geomechanics-multiphase flow-heat transfer simulators are developed in this way. The disadvantage of these kinds of coupled simulators is that the thermal reservoir module, usually developed using the finite difference method (FDM), cannot accommodate the full permeability tensor, since they adopt the standard discretization scheme, such as 5-spot for 2D problems and 7-spot for 3D problems. In this paper, the development of a coupled geomechanics-multiphase flow-heat transfer simulator using the finite element method (FEM) is described with the use of Galerkin's least squares (GLS) technique(4) to stabilize the saturation equation.

The paper presents a discussion on the issues related to the interaction between geomechanics and reservoir simulation in deformable hydrocarbon reservoirs. Geomechanics is important in order to account for rock deformations due to pore pressure and temperature changes resulting from production and fluid injection. Rock deformation can affect the permeability and pore compressibility of the rock. In turn, the pore pressures will be vary due to changes in the pore volume. Geomechanics is also required in order to account for the effect of the non-pay rock surrounding the reservoir on the overall reservoir compressibility and the loads transmitted to the reservoir by the weight of the overburden rock. The paper gives the formulation and finite element discretization of Biot's equations for multi-phase fluid flow in deformable porous media. Based on this formulation, it is argued that geomechanical response and multi-phase fluid flow are fully-coupled processes in that pore pressure changes affect rock mechanical response and vice-versa, and that the two processes occur simultaneously. By contrasting Biot's equations and its discretization to the corresponding multiphase fluid flow equations used in reservoir simulations, it is shown that reservoir simulators neglect or simplify important geomechanical aspects that can have impact on reservoir productivity. This is attributed to the fact that the only rock mechanical parameter involved in reservoir simulations is pore compressibility. This parameter is not sufficient in representing aspects of rock behaviour such as stress path dependency and dilatancy, which require a full constitutive relation. Furthermore, the pore pressure changes due to the applied loads from the non-pay rock cannot be accounted for by simply adjusting the pore compressibility. Example problems are shown in order to illustrate the value of coupling geomechanics to reservoir simulators. Finally, the practical benefits of using coupled geomechanics and reservoir simulations are discussed. P. 439

The paper presents a discussion on the issues related to the interaction between rock deformation and multiphase fluid flow behaviour in hydrocarbon reservoir simulations. Pore pressure and temperature changes resulting from production and fluid injection induce rock deformations which should be accounted for in reservoir modelling. Reservoir rock deformation can affect the permeability and pore compressibility of the rock. In turn, the pore pressures will vary due to changes in the pore volume. The deformation of the surrounding non-reservoir rocks (under-, side- and over- burdens) should also be taken into account in order to assess their effects on the overall reservoir compressibility as well as the loads transmitted to the reservoir by the weight of the overburden. The paper presents the formulation of Biot's equations for multi-phase fluid flow in deformable porous media. Based on this formulation, it is argued that rock deformation and multi- phase fluid flow are fully-coupled processes which should be accounted for simultaneously. However, the coupled equations can be decoupled to a classical hydraulic diffusivity equation for pre-defined simple stress paths. In the general case, by contrasting Biot's equations and its finite element discretization to the corresponding multiphase fluid flow equations used in classical reservoir simulations, it is shown that reservoir simulators neglect or simplify important geomechanical aspects that can have impact on reservoir productivity. This is attributed to the fact that the only rock mechanical parameter involved in reservoir simulations is the pore compressibility. This parameter is not sufficient in representing aspects of rock behaviour such as stress path dependency and dilatancy, which require a full constitutive relation. Furthermore, the pore pressure changes due to the applied loads from the non-pay rock cannot be accounted for by simply adjusting the pore compressibility. Example problems are shown in order to illustrate the importance of coupling flow and deformation in reservoir simulators. P. 63

The focus of the underlying research work is on the macroscopic modeling of unstable multiphase fluid flow in deformable porous media, where a lower‐viscous fluid is displaced by a more viscous fluid. This process leads to the formation of channel‐like networks, called viscous fingering. The instability effect is involved in a wide range of different fields in engineering. Some of the most common applications include carbon sequestration to store carbon dioxide (CO2) in underground reservoirs, contaminant transport in geostructures, in industrial processes, such as filtration, catalytic reactions, and in the operation of polymer electrolyte membrane fuel cells with multiphase flow in the gas diffusion layers. In this work, ideal miscible water–glycerin fluids are considered. It is assumed that the interacting fluids in the deformable porous media are incompressible. In addition, a dispersion–diffusion law is applied to capture the fluid–fluid interactions. The presence of a deformable porous material adds additional effects to the problem of the multiphase flow in porous media. The stresses in the porous solid matrix lead to changes in the porosity and influence the flow velocity of the fluids. To couple the deformable porous media with the multiphase flow, a macroscopic approach is used that relies on the theory of porous media. For the porous solid matrix, a linear elastic material model within small strains assumption is applied. The influence of the deformation‐dependent porosity on the instability is studied for 2D simulations, such as a multilayered geometry with different elastic parameters. The presented coupled nonlinear system of differential equations is simulated with the finite element method. Furthermore, a stabilization technique based on the quasi‐compressibility method is used.

Permeable porous media are widely occurring in nature and are frequently used in various apparatuses in the metallurgical, chemical, and electric-power industries. The heating and processing of bulk materials, the heating of charge in shaft furnaces, the processes of heat transfer in recuperators and heating furnaces, and modern high-intensity cooling systems employed in aviation-and-space engineering and in radio electronics make rather an incomplete list of applications associated with heat and mass transfer in permeable porous media. The theoretical description of these processes or the generalization of experimental data are usually based on a number of assumptions, of which the most important one is the introduction of one or several linear scales describing adequately the structure of a porous medium. It is the objective of this paper to critically analyze the problem of the choice of linear scale and assess the possibility of constructing a generalized model of hydrodynamics and heat transfer in permeable porous media within a deterministic approach.

The multiphase fluid flow in porous media is one of the most fundamental phenomena in various physical processes, such as oil/gas flow in reservoir, subsurface contamination dispersion, chemical separation, etc. Due to its importance, the efficient and accurate solution and prediction of multiphase flow in porous media is highly required in engineering applications and mechanism studies, which has been a research hot spot with increasing interest in recent years. However, the strong nonlinearity implicated in the multiphase flow model has brought great challenges for the computation and analysis. In addition, the permeability in Darcy-type pressure equation is always represented as a high contrast coefficient, which further complicates the simulation difficulty especially for high fidelity prediction and decision-making process. In this study, we attempt to apply one popular global model reduction method, namely Proper Orthogonal Decomposition (POD), to accelerate the simulation of incompressible multiphase flow in porous media. The cornerstone of POD is processing information from a sequence of snapshots (or instantaneous solutions) to identify a set of basis functions to construct a low-dimensional space, the most energetic part of these basis functions is then selected to represent the solution of the original system. In our work, one key point is how to establish the accurate POD reduced order model (ROM) for incompressible mul-tiphase porous flow problems. According to Li et al. [1], the traditional Galerkin projection method (directly project the original governing equation into the low-dimensional space spanned by basis functions) is incapable of introducing the fluid saturation and permeability located on the cell face in POD-ROM for incompressible multiphase flow whether in homogeneous or heterogeneous porous media, thus we adopt the matrix operation method (project the discrete governing equation instead of the original governing equation into the low-dimensional space spanned by basis functions) to build the POD-ROM in this study. Based on the proposed POD-ROM framework, we use the implicit method to solve the (non-) wetting-phase pressure and saturation equations. However, in the implicit solution of the pressure and saturation equations, the standard POD-ROM alone sometimes cannot yield an expected acceleration owing to two main reasons: (1) the nonlinearity between pressure and saturation is sensitive, thus the saturation would change largely even with slight pressure change. And the small error of pressure results would lead to a large deviation of saturation, which in turn exerts negative impacts on the computation of pressure; (2) the complexity for computing a projected nonlinear term in POD-ROM still depends on the dimension of the original full-order system, it is unavoidable in conventional POD-ROM. Therefore, more POD modes are needed to be used in order to achieve the prescribed numerical accuracy, which could worsen the speed up efficiency of proposed POD-ROM. To further reduce the computational complexity of POD-ROM to speed up the implicit solution of pressure and saturation equations, another model reduction method called Discrete Empirical Interpolation Method (DEIM) [2] is applied to treat the projected nonlinear term in the proposed incompressible multiphase porous flow POD-ROM. Different from previous studies, we develop an adaptive DEIM (ADEIM) in this work to achieve a more flexible selection of the interpolation points. Combined the POD-ROM with ADEIM, a POD-ADEIM-ROM for incompressible multiphase flow in porous media is established. The computational efficiency and numerical accuracy of the proposed model is validated through several representative numerical examples. Numerical results indicate that an outstanding acceleration (2~3 orders of magnitude faster) without sacrificing numerical accuracy significantly is obtained from the proposed model when comparing to the traditional solution method that without any acceleration technique. In addition, the effects of POD mode number, the distribution of permeability field, and the mesh density on the overall performances of the proposed model are investigated in detail.

Multiphase Flow and Heat Transfer in Porous Media

Instantaneous heat transfer between different phases, known as local thermal equilibrium (LTE), is commonly assumed for modeling heat transfer in porous media. This assumption may not hold in certain technical and environmental applications, particularly with large temperature gradients, large differences in thermal properties, or high velocities. Local thermal non-equilibrium (LTNE) models aim to describe heat transfer processes when the LTE assumption may fail. We compare three continuum-scale models from the pore to the representative elementary volume (REV) scale. Specifically, dual-network and REV-scale models are evaluated against a pore-resolved model used as a reference in the absence of experimental results. Different effective models are used to obtain upscaled properties on the REV scale and to compare resulting temperature profiles. The systems investigated are fully saturated, consisting of one fluid and one solid phase. This study focuses on purely conductive systems without significant differences in thermal properties. Results show that LTE holds for low interfacial resistances. However, for large interfacial resistances, solid and fluid temperatures differ. The REV-scale model with effective parameters obtained by homogenization leads to similar results as the pore-resolved model, whereas the dual-network model deviates more due to fixed spatial resolution. Among the evaluated REV-scale formulations, only the homogenization-based approach captures the LTNE behavior, as it incorporates the interfacial heat transfer coefficient. Our results provide a basis for conduction-dominated heat transfer in saturated porous media and for further systematic comparisons that incorporate convection relevant to a broader range of applications.

Heat transfer in porous media considering phase change and capillarity—the heat pipe effect

Analysis of field synergy on natural convective heat transfer in porous media

The capability to monitor the enhanced oil recovery processes in heavy oil reservoirs by active or passive seismic methods provides valuable tools for the reservoir engineer to manage the recovery process. The seismic wave velocities (compressional and shear wave) in reservoir formations are strongly dependent on the formation's mechanical and thermal characteristics which are influenced by changes in temperature, pore pressure and stress slate. In order to analyze and understand lhe field seismic data, the influence of temperature, pore pressure and compressional and shear deformations on the seismic wave velocities must be known. A state-of-the-art laboratory testing system to determine these influences on seismic wave velocities has been developed and is described in this paper. The calibration oi the equipment and typical calibration results determined during the development of the apparatus are presented. Introduction Enhanced oil recovery (EOR) processes are used to extract bitumen and heavy oil from deeply buried heavy oil reservoirs by water or steam flooding, cyclic steam stimulation or fire flooding. The capability to monitor EOR processes by active or passive seismic methods provides new tools for the reservoir engineer to monitor the recovery development. Such monitoring allows the reservoir engineer to know when the recovery process should be altered and to modify the processes promptly. The strong dependence of seismic wave velocities in oil sand and heavy oil reservoir formations on the formation's mechanical and thermal characteristics make it possible to apply in situ seismic methods to track the progress of temperature fronts, flooded zones and fractures; and to assess the effectiveness of the thermally enhanced oil recovery processes. However, to allow these seismic monitoring methods to be used in situ, the influence of temperature, pore pressure, effective stress, compressional and shear deformations on the seismic wave velocities must be known. A comprehensive laboratory study is underway at the University of Alberta in geomechanics engineering to identify the effects of temperature, pore pressure, effective stress, porosity, volumetric changes, shearing, gas and liquid saturation on the seismic velocities. This research will provided important data to assist in the interpretation of field seismic survey results. The objective of this paper is to describe the development of laboratory equipment for the measurement of seismic velocities under controlled conditions of confining stress, shear stress and temperature. The calibration of the equipment and typical calibration results determined during the development of the apparatus are presented. Material Changes Affecting Seismic Wave Velocities Research by Tosaya et al. (1988); Wang (1989); Wang and Nur (1987, 1988, 1989, 1990) show that seismic wave velocities in oil sand and heavy oil bearing materials decrease significantly as the temperature increases. Other research by Agar (1984); Agar, Morgenstern and Scott (1989); Kosar (1989); Scott, Adhikary and Proskin (1991) show that during the recovery processes, stresses and deformations occur in the reservoir and adjacent strata which are caused by changes in pore pressures and temperature. These changes cause shearing and compressive deformations which can affect formation permeability and hydraulic fracturing.

Purpose – The purpose of this paper is to analyze two different approaches (Models A and B) for an adiabatic boundary condition at the wall of a channel filled with a porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived and compared with numerical solutions. The phenomenon of heat flux bifurcation for Model A is demonstrated. The effects of pertinent parameter C on the applicability of the Models A and B are discussed. Analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived and the influence of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution is discussed. Design/methodology/approach – Two approaches (Models A and B) for an adiabatic boundary condition in porous media under local thermal non-equilibrium (LTNE) conditions are analyzed in this work. The analysis is applied to a microchannel which is modeled as a porous medium. Findings – The phenomenon of heat flux bifurcation at the wall for Model A is demonstrated. The effect of pertinent parameter C on the applicability of each model is discussed. Model A is applicable when C is relatively large and Model B is applicable when C is small. The heat flux distribution is obtained and the influence of Da and k is discussed. For Model A, ϕAfin increases and ϕAsub, ϕAcover decrease as Da decreases and k is held constant, ϕAsub increases and ϕAfin, ϕAcover decrease as k increases while Da is held constant; for Model B, ϕBfin increases and ϕBsub decreases either as Da decreases or k decreases. The overall Nusselt number is also obtained and the effect of Da and k is discussed: Nu increases as either Da or k decrease for both models. The overall Nusselt number for Model A is larger than that for Model B when Da is large, the overall Nusselt numbers for Models A and B are equivalent when Da is small. Research limitations/implications – Proper representation of the energy equation and the boundary conditions for heat transfer in porous media is very important. There are two different models for representing energy transfer in porous media: local thermal equilibrium (LTE) and LTNE. Although LTE model is more convenient to use, the LTE assumption is not valid when a substantial temperature difference exists between the solid and fluid phases. Practical implications – Fluid flow and convective heat transfer in porous media have many important applications such as thermal energy storage, nuclear waste repository, electronic cooling, geothermal energy extraction, petroleum processing and heat transfer enhancement. Social implications – This work has important fundamental implications. Originality/value – In this work the microchannel is modeled as an equivalent porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are obtained and compared with numerical solutions. The first type of heat flux bifurcation phenomenon, which indicates that the direction of the temperature gradient for the fluid and solid phases is different at the channel wall, occurs when Model A is utilized. The effect of pertinent parameter C on the applicability of the models is also discussed. The analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived, and the effects of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution are discussed.

ABSTRACTThis article deals with natural convection heat and moisture transfer with thermal radiation in a cavity partially filled with hygroscopic porous medium. The governing equations for the momentum and heat transfer in both free fluid and hygroscopic porous medium and moisture content transfer in hygroscopic porous medium were solved by the finite element method. The radiative heat transfer is calculated by making use of the radiosity of the surfaces that are assumed to be grey. Comparisons with experimental and numerical results in the literature have been carried out. Effects of thermal radiation and Rayleigh number on natural convection and heat transfer in both free fluid and porous medium and moisture content transfer in porous medium were analyzed. It was found that surface thermal radiation can significantly change the temperature and moisture content fields in the regions of free flow and porous medium. The mean temperature at the interface decreases, the temperature and moisture content gradients are created on the upper two corners of the porous medium region, and the moisture content in the porous medium decreases in the porous medium as Ra increases.

Massive steam injection during SAGD operation may result in significant changes in pore pressure, temperature, stress and strain in the overlying caprock as well as the injected formations. These changes lead to containment breach of the caprock as reported in the steam release incident at the Joslyn Creek field in 2006. To avoid such a catastrophic event, the integrity of the caprock and risks of steam release must be properly evaluated during planning and operating SAGD wells. In this study, a thermo-poro-mechanical model is developed to evaluate the integrity of the caprock due to temperature and pressure changes observed during SAGD operations. A commercial reservoir simulator is used to calculate changes of pore pressure and temperature during steam injection. These results are used as a part of input data for the geomechanical model that considers poro-elasto-plastic stress-strain relations of the formations. The shear failure of the rocks is determined by the Drucker-Prager criterion while the tensile failure is judged by the tensile strength of the rocks, which are used to assess the integrity of the caprock. Our simulation results indicate that the temperature change can be extended deep into the overlying formations while the steam chamber is developed in the reservoir interval. Because the caprock is expected to have low permeability, these temperature changes lead to notable pore pressure changes in the caprock interval, which plays an important role in the stability of the caprock in the geomechancial analysis. The simulation results also suggest the importance of considering free surface, underburden, and sideburdens as well as assigning appropriate boundary conditions in the model. Using the model developed in this work, the Joslyn field case is investigated showing the existence of failure region in the caprock layer during the steam circulation phase. These findings may explain the mechanism of the caprock failure and the resultant steam release at the surface experienced in the field. It should be noted that the analysis results indicate, not only possible shear failure events but also a possibility of tensile failure developed in the caprock interval above the steam chamber. It is also found that the geological complexity including the existence of a mudstone layer between the reservoir and the caprock affects the likelihood of the steam release event. The caprock integrity analysis method presented in this work can help engineers evaluate risks of the containment breach during a planning phase of SAGD project. Also, using the simulation model developed in this work as a forward model, the integrity of the caprock and the development of steam chamber during SAGD operation can be monitored by surface displacement measurements by In-SAR or tiltmeters. These study results can enable effective and safe operation for future SAGD production.

Understanding heat transfer mechanisms in subsurface environments is crucial for deep geothermal energy exploitation. Despite multiple studies on heat transfer in porous media, the combination of different heat transfer mechanisms with fracture networks leads to uncertainty in the temperature distribution in geothermal sites. More specifically, heat convection and conduction are two major mechanisms responsible for heat transfer in porous media. Conduction occurs through rock matrix and is more dominant than convection in intact rocks due to their low porosity. However, fracture networks in rocks increase fluid transfer in certain directions, making convection more important in heat transfer. At a certain point, it becomes difficult to identify which mechanism is more prevalent. Besides this difficulty, achieving a balance between these two key mechanisms and determining the optimal Peclet number is very crucial for the geothermal energy industry to extract adequate volume of water at the desired temperature, which is essential for smooth operation of geothermal systems. In this study, a two dimensional coupled thermo-hydraulic model in COMSOL is developed to simulate heat transfer mechanisms in enhanced geothermal systems on field scale. Characteristic time variables based on hydraulic and thermal diffusivities are defined to monitor heat distribution through the domain caused by each mechanism. Finally, a sensitivity analysis is performed to identify how the temperature is affected by rock (thermal and hydraulic) parameters and fracture patterns. The simulation results indicate that the Peclet number is highly dependent on fracture network.