Head-based isogeometric analysis of transient flow in unsaturated soils

Surfactant effects on unsaturated flow in porous media with hysteresis: horizontal column experiments and numerical modeling

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

A simplified model of nitrate ion transport (and other nonadsorbing solutes) in unsteady, unsaturated flow in porous media has been developed. The model represents nitrate flow in infiltration and drainage in sand quite well and can be applied to unsaturated flow in other homogeneous media with only minimum extra experimental data needed to describe the medium.

SummaryNumerical modeling of large deformations in fluid‐infiltrated porous media must accurately describe not only geometrically nonlinear kinematics but also fluid flow in heterogeneously deforming pore structure. Accurate simulation of fluid flow in heterogeneous porous media often requires a numerical method that features the local (elementwise) conservation property. Here, we introduce a new finite element framework for locally mass conservative solution of coupled poromechanical problems at large strains. At the core of our approach is the enriched Galerkin discretization of the fluid mass balance equation, whereby elementwise constant functions are augmented to the standard continuous Galerkin discretization. The resulting numerical method provides local mass conservation by construction with a usually affordable cost added to the continuous Galerkin counterpart. Two equivalent formulations are developed using total Lagrangian and updated Lagrangian approaches. The local mass conservation property of the proposed method is verified through numerical examples involving saturated and unsaturated flow in porous media at finite strains. The numerical examples also demonstrate that local mass conservation can be a critical element of accurate simulation of both fluid flow and large deformation in porous media.

In this research study, we conducted a coupled thermalstress-fluid flow numerical modeling on the UTF Phase A SAGD project in order to investigate the fundamental geomechanical behavior 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 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 processes in the heavy oil or oil sand reservoirs. Numerical modeling of the coupled processes is historically carried out in the areas of geomechanics modeling and the reservoir simulation. The former is to compute the stress-strain behavior, 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 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 the FDM reservoir simulators cannot be used. Settari and Mourits(3) present an approach to couple the stress-strain behavior 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 finite difference method (FDM), cannot accommodate the full permeability tensor, since they adopt the standard discretization scheme such as 5-spot for 2-D problems and 7-spot for 3-D problems. In this paper, the development of a coupled geomechanicsmultiphase flow-heat transfer simulator using finite element method (FEM) is described with the use of the Galerkin's least squares (GLS) technique(4) to stabilized the saturation equation.

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 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 isogeometric analysis (IGA), which employs non-uniform rational B-splines (NURBS) basis as shape functions for both representation of geometry and approximation of the field variables, owns several inherent advantages to become an effective numerical method such as an exact geometry description with fewer control points, high-order continuity, and high accuracy. Unlike the C0-continuity shape functions in the conventional finite element method (FEM), the high-order basis functions in IGA are not confined to one element, but span on several elements instead. This property makes the programming task difficult, and more importantly they cannot be straightforwardly embedded into the existing FEM framework. In this paper, we provide an effective numerical scheme by further extending the IGA based on the Bezier extraction of NURBS to study mechanical behavior of elasto-plastic problems in three-dimension (3D). The Bezier extraction operator decomposes NURBS functions into a set of Bernstein polynomials and provides C0-continuity Bezier elements for the IGA, which are similar to Lagrange elements structure. Consequently, the implementation of IGA is now similar to that of conventional FEM, and can easily be embedded in most existing FEM codes. The merits of the proposed formulation are also demonstrated by its convergence and validation studies against reference solutions considering both simple and complicated configurations.

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.

Mobil plots normalized rates of penetration in real-time using its Drilling Data Center. Field results indicate that this technique reveals changes in lithology and pore pressure. It illustrates one way that the Drilling Data Center integrates computer based drilling technology into field operations. This technique differs from those previously reported in that: (1) A departmental computer collects, calculates, and displays real-time drilling information; (2) Normalized rate of penetration is correlated with conductivity for pore pressure prediction. Prudent use of this tool directly reduces cost per foot. Confidence that pore pressure changes will be quickly noticed encourges the operator to drill near-balance, which yields faster rates of penetration. This tool also provides the geologist with an excellent correlation tool when wireline logs are not run. This paper: (1) reviews normalized rate of penetration theory and its application with field results; (2) illustrates how the plot is obtained; (3) discusses predictions of lithology and pore pressure; and (4) discusses development plans.

Hydraulic conductivity is of central importance in modelling both saturated and unsaturated flow in porous media. This is because it is central to Darcy's Law governing flow velocity and Richards' equation that is often used as the governing partial differential equation (PDE) for unsaturated flow. When doing numerical modelling of groundwater flow, two dominant challenges regarding hydraulic conductivity are heterogeneous media and unsaturated flow.

Pore pressures in the sediment were measured at two locations in the East Bay area of the Mississippi delta. These measurements showed the sediment to be highly under-consolidated with the effective stress approaching zero even at significant depths below the mudline. During storms the pore pressures exhibited cyclic response to the wave-induced bottom pressures. In at least two instances the pore pressures increased significantly during storms, which is probably indicative of major sub-bottom movements. Several different piezometers systems were utilized to make the pore pressure measurements. Each system is described in detail and the advantages and shortcomings of the systems with respect to measurements of pore pressures in the marine environment are presented. Analysis of the data leads to the conclusion that pore gas, rather than pore water, pressure was measured in most instances even though in one set of experiments high air entry stones were utilized to exclude gas from-the measuring system. Introduction The two projects known as SEASWAB I and SEASWAB II were aimed at studying sediment behavior in the Mississippi delta under the action of storm waves. Details of the projects have been discussed elsewhere1,2 and will not be repeated here. During both SEASWAB projects, pore pressures in the sediment were measured. These measurements were made to help determine the degree of consolidation in the sediments, and to detect gross subsurface movements. The rationale for the latter was that any significant subsurface slides or sediment collapse would be accompanied by a marked change in pore pressures. Further, it was anticipated that the pore pressures would exhibit a cyclic response to the wave-induced bottom pressures which have been hypothesized as a cause for sub-bottom movements in soft sediments3,4. The primary purpose of this paper is to describe the pore pressure measuring systems that have been used to accomplish these functions, to discuss the suitability of the various systems, and to present a preliminary analysis of the pore pressure results. Detailed analysis of the pore pressure data is still underway. Seaswab I SEASWAB I was initiated in September 1975 when several sensors were implanted in South Pass Block 28 in East Bay. Among the sensors installed were an accelerometer to measure mudline motions, a wave staff, and a bottom pressure transducer. However, the two systems of primary interest to this paper were probes for measuring pore pressures which were developed at Lehigh University and at the Atlantic Oceanographic and Marine Laboratory of NOAA in Miami, Florida. Devices used to measure pore pressures in soils are termed piezometers. They may range from a simple open stand pipe with a well point at the tip to the more sophisticated closed system utilizing an electronic pressure transducer. Closed system piezometers can be remotely read and if a hard system is utilized the response times to changes in pore pressures are very rapid.

<p><b>Increases in rainfall-induced landsliding following large earthquake are well documented but the time frames over which this heightened hazard persists in the land scape remains poorly understood. Whilst it is well known that the presence of failed and partially slopes after earthquakes significantly reduces the rainfall thresholds required to activate slope movement, their failure susceptibility during specific storms and how this changes through time remains poorly studied. To improve knowledge in this field requires well documented slope failures following earthquakes and a detailed understanding of their potential failure mechanisms when pore pressures are elevated in the slope. The 2016 Mw 7.8 Kaikōura earthquake provides a unique opportunity to study how rainfall events following the earthquake may impact the timing and mechanisms of landslide reactivation. </b></p><p>This study conducted a suite of specialist triaxial cell experiments, designed to replicate varying rainfall scenarios on remoulded samples collected from two sites where numerous earthquake-induced landslides were recorded in similar Late Cretaceous to Neogene sediments with similar physical properties (the Leader Dam Landslides (LDL) and the Limestone Hill landslide (LHL)). In each experiment rainfall events were simulated using a series of different pore pressure scenarios (increases and decreases in mean effective stress) at representative field stress conditions whilst monitoring material deformation behaviour. </p><p>The results demonstrate that both the deformation behaviour and pore pressure required to generate failure were influenced by the previous changes in pore pressure. Samples subjected to stepped increases in pore pressure were subject to greater pre-failure deformation (dilation) and subsequently failed at lower pore pressures (higher mean effective stress) when compared to samples subjected to linear increases in pore pressure. In addition, increases in the rate of pore pressure also increased the amount of pre-failure deformation allowing failure to occur when pore pressures were lower. In contrast a sample subjected to both increases and decreases in pore pressure underwent pre-failure densification and subsequently required a larger increase in pore pressure to fail. The results demonstrate that landslide reactivation is influenced by a number of factors including the amount and rate of previous changes in pore pressure and the slope drainage history. </p><p>The results provide new insights into why landslide susceptibility may remain elevated for prolonged periods of time (e.g. decades) in the landscape as well as why the rainfall thresholds for site specific failures during storms may be difficult to predict. </p>

The water penetration in soil is investigated numerically using the finite element method (FEM) in a novel way. In the suggested method, new spherical Hankel shape functions are used and the finite element method is reformulated based on them. These new functions are obtained from the first and second kind of Bessel functions. The properties of Hankel shape functions lead to having more accuracy and robustness for the proposed method with low number of elements. To validate the suggested approach, at first, a boundary value problem is solved and the results are compared with the available analytical solution. Then, in order to prove the efficiency and applicability of the present model in the seepage problems, five examples including saturated and unsaturated flow in porous media are studied and the hydraulic head is calculated. Afterward, the results obtained from the classical and new method are compared together. The comparisons indicate that the suggested method with the low number of elements is more precise than the classic FEM with the same mesh.

In this paper, an isogeometric analysis (IGA) framework based on the high-order sandwich plate theory is developed for the first time to deal with both buckling and wrinkling problems of variable-stiffness sandwich plates under compression. The present sandwich plate model is formulated based on the extended high-order sandwich plate theory (EHSAPT). The weak-form governing equations are firstly derived from the principle of virtual work, and afterward the IGA formulations based on the Non-Uniform Rational B-Splines (NURBS) are applied to predict the instability loads and the corresponding instability modes. Both the membrane and non-membrane conditions are integrated into the linear buckling analysis. The novelty of this work lies in that the employment of high-order continuous NURBS basis functions can directly fulfill the [Formula: see text] continuity requirement inherent in the EHSAPT theory, which enables the EHSAPT-based IGA model to be formulated with fewer degrees of freedom. Besides, the developed EHSAPT-based IGA model has also the ability to capture the overall buckling or wrinkling modes of the sandwich plates. The accuracy and effectiveness of the proposed EHSAPT-based IGA model are verified by comparison with previously published results and those obtained using ABAQUS. Effects of the core thickness and fiber angle on the buckling behaviors of the sandwich plates are also studied in numerical examples. It is observed that the non-uniform in-plane pre-stress over the skin layers is the main reason for the non-periodic wrinkling of constant-stiffness sandwich constructions, whereas the non-uniformity of both the in-plane pre-stress and out-of-plane bending stiffness is responsible for the non-periodic wrinkling of variable-stiffness sandwich constructions. The results presented herein may be beneficial for the design of variable-stiffness sandwich constructions under compression.