Modeling and simulation of two-phase two-component flow with disappearing nonwetting phase

Carbon capture and storage is a recently discussed new technology, aimed at allowing an ongoing use of fossil fuels while preventing the produced CO₂ to be released to the atmosphere. CCS can be modeled with two components (water and CO₂) in two phases (liquid and CO₂). To simulate the process, a multiphase flow equation with equilibrium phase exchange is used. One of the big problems arising in two-phase two-component flow simulations is the disappearance of the nonwetting phase, which leads to a degeneration of the equations satisfied by the saturation. A standard choice of primary variables, which is the pressure of one phase and the saturation of the other phase, cannot be applied here. We developed a new approach using the pressure of the nonwetting phase and the capillary pressure as primary variables. One important advantage of this approach is the fact that we have only one set of primary variables that can be used for the biphasic as well as the monophasic case. We implemented this new choice of primary variables in the DUNE simulation framework and present numerical results for some test cases.     

Thermo-hydro-mechanical modeling of fracturing porous media with two-phase fluid flow using X-FEM technique

In this paper, a fully coupled thermo-hydro-mechanical model is presented for two-phase fluid flow and heat transfer in fractured/fracturing porous media using the extended finite element method. In the fractured porous medium, the traction, heat, and mass transfer between the fracture space and the surrounding media are coupled. The wetting and nonwetting fluid phases are water and gas, which are assumed to be immiscible, and no phase-change is considered. The system of coupled equations consists of the linear momentum balance of solid phase, wetting and nonwetting fluid continuities, and thermal energy conservation. The main variables used to solve the system of equations are solid phase displacement, wetting fluid pressure, capillary pressure, and temperature. The fracture is assumed to impose the strong discontinuity in the displacement field and weak discontinuities in the fluid pressure, capillary pressure, and temperature fields. The mode I fracture propagation is employed using a cohesive fracture model. Finally, several numerical examples are solved to illustrate the capability of the proposed computational algorithm. It is shown that the effect of thermal expansion on the effective stress can influence the rate of fracture propagation and the injection pressure in hydraulic fracturing process. Moreover, the effect of thermal loading is investigated properly on fracture opening and fluids flow in unsaturated porous media, and the convective heat transfer within the fracture is captured successfully. It is shown how the proposed computational model is capable of modeling the fully coupled thermal fracture propagation in unsaturated porous media.     

Design of drainage blankets for leachate recirculation in bioreactor landfills using two-phase flow modeling

Drainage blankets (DB) are used for leachate recirculation in bioreactor landfills and consist of highly permeable material placed over a large area of the landfill with the leachate injection pipe embedded in the material at specified locations. DBs are generally installed at different depth levels during the waste filling operations. Very limited information is reported on performance of DBs, and that which exists is based on a small number of field monitoring and modeling studies. A rational method for the design of landfills using DBs has not been developed. This study performs a parametric analysis based on a validated two-phase flow model and presents design charts to guide the design of DBs for given hydraulic properties of MSW, the leachate injection rate and the dimensions and locations of the DB as measured from the leachate collection and recirculation system (LCRS) located at the bottom of the landfill cell. Numerical simulations were performed for the two established MSW conditions: homogeneous–isotropic and heterogeneous–anisotropic waste. The optimal levels of leachate saturation, wetted width, wetted area and developed pore water and pore gas pressures were determined, and design charts using the normalized parameters were developed. An example is presented on the use of design charts for typical field application.     

Numerical modeling of two-phase fluid flow and oil slick transport in estuarine water

Oil spills is one of the most important hazards in the estuarine and coastal water. In recent decades, engineers try to predict the status of oil slick to manage the pollution spreading. The prediction of oil slick transport is carried out mainly by means of numerical models. In the current study, the development and application of a two-phase fluid flow model to simulate oil transport in the marine environment are presented. Different transport and fate processes are included in the developed model. The model consists of the Lagrangian method for the advection process, the Random Walk technique for horizontal diffusion process and the empirical equations for the fate processes. The major forces for driving oil particles are fluid current, wind speed and turbulent flow. Therefore, the multi-component hydrocarbon method has been included to the developed model in order to predict fate processes. As prediction of particle velocity components is of major importance for oil slick advection, therefore the binomial interpolation procedure has been chosen for the particle velocity components computations. In addition, shoreline boundary condition is included in the developed model to simulate shore response to oil slick transport near the beaches. The results of the model applications are compared with the analytical solutions, experimental measurements and other numerical models cited in literature. Comparisons of different sets of results represent the capability of developed model to predict the oil slick transport. In addition, the developed model is tested for two oil spill cases in the Persian Gulf.     

Modeling compositional compressible two-phase flow in porous media by the concept of the global pressure

We derive a new formulation for the compositional compressible two-phase flow in porous media. We consider a liquid–gas system with two components: water and hydrogen. The formulation considers gravity, capillary effects, and diffusivity of each component. The main feature of this formulation is the introduction of the global pressure variable that partially decouples the system equations. To formulate the final system, and in order to avoid primary unknowns changing between one-phase and two-phase zones, a second persistent variable is introduced: the total hydrogen mass density. The derived system is written in terms of the global pressure and the total hydrogen mass density. The system is capable of modeling the flows in both one and two-phase zones with no changes of the primary unknowns. The mathematical structure is well defined: the system consists of two nonlinear parabolic equations, the global pressure equation, and the total hydrogen mass density equation. The derived formulation is fully equivalent to the original one. Numerical simulations show ability of this new formulation to model efficiently the phase appearance and disappearance.     

Uncertainty quantification of two-phase flow problems via measure theory and the generalized multiscale finite element method

The problem of multiphase phase flow in heterogeneous subsurface porous media is one involving many uncertainties. In particular, the permeability of the medium is an important aspect of the model that is inherently uncertain. Properly quantifying these uncertainties is essential in order to make reliable probabilistic-based predictions and future decisions. In this work, a measure-theoretic framework is employed to quantify uncertainties in a two-phase subsurface flow model in high-contrast media. Given uncertain saturation data from observation wells, the stochastic inverse problem is solved numerically in order to obtain a probability measure on the space of unknown permeability parameters characterizing the two-phase flow. As solving the stochastic inverse problem requires a number of forward model solves, we also incorporate the use of a conservative version of the generalized multiscale finite element method for added efficiency. The parameter-space probability measure is used in order to make predictions of saturation values where measurements are not available, and to validate the effectiveness of the proposed approach in the context of fine and coarse model solves. A number of numerical examples are offered to illustrate the measure-theoretic methodology for solving the stochastic inverse problem using both fine and coarse solution schemes.     

The significance of global snow and ice cover for global change studies

The spatial extent and volume of global snow and ice cover at present and during glacial conditions are reviewed for each of the principal components (snow cover, land ice, sea ice and permafrost). The state of global monitoring of snow and ice conditions is shown to be adequate for some variables, but unsatisfactory for others. Recent trends are reported and expected changes projected for increasing concentrations of greenhouse gases are examined.     

Numerical modeling of two-phase hysteresis combined with an interface condition for heterogeneous porous media

This paper presents a numerical implementation of two-phase capillary hysteresis and its combination with a capillary interface condition for the treatment of heterogeneities. The hysteresis concepts chosen in this work are first implemented in a node-centered FV discretization scheme and subsequently combined with the interface condition that predicts sharp saturation discontinuities at material interfaces, based on a pressure equilibrium concept. This approach allows for the approximation of history-dependent, and at the same time discontinuous, saturations at material interfaces. The resulting model provides a well-defined evolution of the hysteretic capillary pressure–saturation relationships at material interfaces that is independent of the grid spacing. As demonstrated with a simple 1-D example, this concept therefore offers the advantage that the solution of a two-phase flow problem involving hysteresis does not relate to the grid resolution at the material interfaces.     

An energy stable evolution method for simulating two-phase equilibria of multi-component fluids at constant moles,volume and temperature

In this paper, we propose an energy-stable evolution method for the calculation of the phase equilibria under given volume, temperature, and moles (VT-flash). An evolution model for describing the dynamics of two-phase fluid system is based on Fick’s law of diffusion for multi-component fluids and the Peng-Robinson equation of state. The mobility is obtained from diffusion coefficients by relating the gradient of chemical potential to the gradient of molar density. The evolution equation for moles of each component is derived using the discretization of diffusion equations, while the volume evolution equation is constructed based on the mechanical mechanism and the Peng-Robinson equation of state. It is proven that the proposed evolution system can well model the VT-flash problem, and moreover, it possesses the property of total energy decay. By using the Euler time scheme to discretize this evolution system, we develop an energy stable algorithm with an adaptive choice strategy of time steps, which allows us to calculate the suitable time step size to guarantee the physical properties of moles and volumes, including positivity, maximum limits, and correct definition of the Helmhotz free energy function. The proposed evolution method is also proven to be energy-stable under the proposed time step choice. Numerical examples are tested to demonstrate efficiency and robustness of the proposed method.     

Performance studies of the fixed stress split algorithm for immiscible two-phase flow coupled with linear poromechanics

In this work, we measure the performance of the fixed stress split algorithm for the immiscible water-oil flow coupled with linear poromechanics. The two-phase flow equations are solved on general hexahedral elements using the multipoint flux mixed finite element method whereas the poromechanics equations are discretized using the conforming Galerkin method. We introduce a rigorous calculation of the update in poroelastic properties during the iterative solution of the coupled system equations. The effects of the coupling parameter on the performance of the fixed stress algorithm is demonstrated in two field studies: the Frio oil reservoir and the Cranfield injection site.

     

A derivative-free methodology with local and global search for the constrained joint optimization of well locations and controls

In oil field development, the optimal location for a new well depends on how it is to be operated. Thus, it is generally suboptimal to treat the well location and well control optimization problems separately. Rather, they should be considered simultaneously as a joint problem. In this work, we present noninvasive, derivative-free, easily parallelizable procedures to solve this joint optimization problem. Specifically, we consider Particle Swarm Optimization (PSO), a global stochastic search algorithm; Mesh Adaptive Direct Search (MADS), a local search procedure; and a hybrid PSO–MADS technique that combines the advantages of both methods. Nonlinear constraints are handled through use of filter-based treatments that seek to minimize both the objective function and constraint violation. We also introduce a formulation to determine the optimal number of wells, in addition to their locations and controls, by associating a binary variable (drill/do not drill) with each well. Example cases of varying complexity, which include bound constraints, nonlinear constraints, and the determination of the number of wells, are presented. The PSO–MADS hybrid procedure is shown to consistently outperform both stand-alone PSO and MADS when solving the joint problem. The joint approach is also observed to provide superior performance relative to a sequential procedure.     

Population dynamics and global change: the need for new conceptual maps

Current approaches to population: 1) focus too much on humans and not on their interactions over time with populations of other species; 2) focus too much on the number of humans and not on their differential resource use and environmental impact; 3) accept uncritically the assumptions and concepts of industrial society regarding the nature of progress and the neutrality of technologies, markets, and trade. Broader and more integrated approaches are needed to address current international and global realities and trends.     

带相变瞬态温度场问题的扩展有限元解析

带相变瞬态传热问题是寒区工程多场耦合问题求解的关键.在剖析常规有限元法在求解带相变瞬态温度场问题的不足的基础上,结合冻土冻融温度变化的特点,提出采用扩展有限元法求解冻土工程带相变瞬态传热问题的新方法,以四边形单元为例推导了冻土工程温度场的求解格式,详细剖析了瞬态传热过程中移动界面水平集函数的构造、单元刚度矩阵的形成及高斯积分的求解.据此编写了相应的扩展有限元程序,通过经典Stefan问题全面验证了程序的正确性与合理性.     

非均质孔隙介质中两相流的光透法应用研究

地下水中非水相液体(Non-aqueous Phase Liquid,NAPL)的流动及其曝气修复技术是典型的两相流问题。基于实际地下水含水介质的普遍非均质性,本文应用光透法对非均质孔隙介质中两相流进行了定量试验研究,设计了两组砂箱实验,研究气体和重非水相液体(DNAPL)在非均质孔隙介质中的迁移规律,应用了水/气两相和水/NAPL两相饱和度计算模型。实验结果表明:气体主要由不规则通道向上运动,遇到低渗透性透镜体时在其下方堆积,并开始横向运动,绕过透镜体后继续向上运动,最终在砂箱顶部形成连续气体分布,注气速度越大,气体运移范围越宽;DNAPL在自身重力作用下克服毛管压力向下迁移至低渗透性透镜体,DNAPL无法克服该介质的毛管压力,停止垂向入渗,并在其表面堆积,开始横向运移,绕过透镜体后继续向下运动,最终在砂箱底部形成连续DNAPL污染池。均质介质中建立的计算流体饱和度的水/气模型及水/NAPL模型与实验结果较吻合,可用于非均质多孔介质中水/气相和水/NAPL相饱和度的计算。     

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part I: theory and formulation

Reservoir depletion results in rock failure, wellbore instability, hydrocarbon production loss, oil sand production, and ground surface subsidence. Specifically, the compaction of carbonate reservoirs with soft rocks often induces large plastic deformation due to rock pore collapse. On the other hand, following the compaction of reservoirs and failure of rock formations, the porosity and permeability of formations will, in general, decrease. These bring a challenge for reservoir simulations because of high nonlinearity of coupled geomechanics and fluid flow fields. In this work, we present a fully implicit, fully coupled, and fully consistent finite element formulation for coupled geomechanics and fluid flow problems with finite deformation and nonlinear flow models. The Pelessone smooth cap plasticity model, an important material model to capture rock compaction behavior and a challenging material model for implicit numerical formulations, is incorporated in the proposed formulation. Furthermore, a stress-dependent permeability model is taken into account in the formulation. A co-rotational framework is adopted for finite deformation, and an implicit material integrator for cap plasticity models is consistently derived. Furthermore, the coupled field equations are consistently linearized including nonlinear flow models. The physical theories, nonlinear material and flow models, and numerical formulations are the focus of part I of this work. In part II, we verify the proposed numerical framework and demonstrate the performance of our numerical formulation using several numerical examples including a field reservoir with soft rocks undergoing serious compaction.     

Using lithologic modeling techniques for aquifer characterization and groundwater flow modeling of the Sohag area, Egypt

Three dimensional lithologic modeling techniques have been used for detailed characterization and groundwater flow modeling of the Quaternary aquifer system of the Sohag area, Egypt. Well log data were used for building the lithologic model using RockWorks. A groundwater flow model, facilitated by MODFLOW 2000, was built using results of the lithologic model. The obtained lithologic model honored the well log data and revealed a complex sedimentary system, which is mainly composed of six lithologic categories: clay, clay and sand, fine sand, coarse sand, sand and gravel, and gravel. Inter-fingering and presence of lenses are the main characteristics of the sedimentary basin in the study area. A wide range of hydraulic conductivities is present, which vary spatially and control the groundwater flow. Heterogeneity of the aquifer system is spatially represented where different hydraulic conductivities are found in the different directions. Sandy layers tend to be connected. Hydraulic continuity is represented by inter-fingering and connection of sandy materials within the aquifer system.     

A virtual element method for the two-phase flow of immiscible fluids in porous media

A primal C⁰-conforming virtual element discretization for the approximation of the bidimensional two-phase flow of immiscible fluids in porous media using general polygonal meshes is discussed. This work investigates the potentialities of the Virtual Element Method (VEM) in solving this specific problem of immiscible fluids in porous media involving a time-dependent coupled system of non-linear partial differential equations. The performance of the fully discrete scheme is thoroughly analysed testing it on general meshes considering both a regular problem and more realistic benchmark problems that are of interest for physical and engineering applications.

     

A model for nonlinear flow behavior in two-dimensional fracture intersections and the estimation of flow model coefficients

Hydrogeology Journal - There are multiple flow paths with different flow directions in fracture intersections. A general flow model synthetically describing the nonlinear flow behavior of multiple...