# Browsing by Subject "Two-phase flow"

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Item A comprehensive numerical model for simulating two-phase flow in shale gas reservoirs with complex hydraulic and natural fractures(2017-09-15) AlTwaijri, Mohammad Hamad; Sepehrnoori, Kamy, 1951-Show more Increase in energy demand has played a significant role in the persistent exploitation and exploration of unconventional oil and gas resources. Shale gas reservoirs are one of the major unconventional resources. Advancements in horizontal drilling and hydraulic fracturing techniques have been the key to achieve economic rates of production from these shale gas reservoirs. In addition to their ultra-low permeability, shale gas reservoirs are characterized by their complex gas transport mechanisms and complex natural and induced (hydraulic) fracture geometries. Production from shale gas reservoirs is predominantly composed of two-phase flow of gas and water. However, proper modeling of the two-phase behavior as well as incorporating the complex fracture geometries have been a challenge within the industry. Due to the limitation of the local grid refinement (LGR) approach, hydraulic fractures are assumed to be planar (orthogonal), which is an unrealistic assumption. Although more flexible approaches are available, such as the use of unstructured grids, they require significantly high computational powers. In this research, an efficient embedded discrete fracture model (EDFM) is introduced to explicitly model complex fracture geometries. The EDFM approach is capable of explicitly modeling complex fracture geometries without increasing the computational demand. Utilizing EDFM alongside a commercial simulator, a 3D reservoir model is constructed to investigate the effect of complex fracture geometries on the two-phase flow of a shale gas well. In this investigation, varying degrees of hydraulic fracture complexity with 1-set and 2-set natural fractures were tested. The simulation results confirm the importance of properly modeling fracture complexity, highlighting that it plays an integral part in the estimation of gas and water recoveries. In addition, the simulation results hint to the pronounced effect of fracture interference as fracture complexity increases. Finally, variable fracture conductivities and initial water saturation values were analyzed to further assess their effect on the two-phase production behavior of the shale gas well. This study examines the effect of non-orthogonal complex fracture geometry on the two-phase flow of shale gas wells. The work can provide a significant insight toward understanding the extent to which fracture complexity can affect the performance of shale gas wells.Show more Item Development of a coupled wellbore-reservoir compositional simulator for horizontal wells(2010-12) Shirdel, Mahdy; Sepehrnoori, Kamy, 1951-; Ribeiro, Paulo R.Show more Two-phase flow occurs during the production of oil and gas in the wellbores. Modeling this phenomenon is important for monitoring well productivity and designing surface facilities. Since the transient time period in the wellbore is usually shorter than reservoir time steps, stabilized flow is assumed in the wellbore. As such, semi-steady state models are used for modeling wellbore flow dynamics. However, in the case that flow variations happen in a short period of time (i.e., a gas kick during drilling) the use of a transient two-phase model is crucial. Over the last few years, a number of numerical and analytical wellbore simulators have been developed to mimic wellbore-reservoir interaction. However, some issues still remain a concern in these studies. The main issues surrounding a comprehensive wellbore model consist of fluid property calculations, such as black-oil or compositional models, governing equations, such as mechanistic or correlation-based models, effect of temperature variation and non-isothermal assumption, and methods for coupling the wellbore to the reservoir. In most cases, only standalone wellbore models for blackoil have been used to simulate reservoir and wellbore dynamic interactions. Those models are based on simplified assumptions that lead to an unrealistic estimation of pressure and temperature distributions inside the well. In addition, most reservoir simulators use rough estimates for the perforation pressure as a coupling condition between the wellbore and the reservoir, neglecting pressure drops in the horizontal section. In this study, we present an implementation of a compositional, pseudo steady-state, non-isothermal, coupled wellbore-reservoir simulator for fluid flow in wellbores with a vertical section and a horizontal section embedded on the producing reservoir. In addition, we present the implementation of a pseudo-compositional, fully implicit, transient two-fluid model for two-phase flow in wellbores. In this model, we solve gas/liquid mass balance, gas/liquid momentum balance, and two-phase energy equations in order to obtain the five primary variables: liquid velocity, gas velocity, pressure, holdup and temperature. In our simulation, we compared stratified, bubbly, intermittent flow effects on pressure and temperature distributions in either a transient or steady-state condition. We found that flow geometry variation in different regimes can significantly affect the flow parameters. We also observed that there are significant differences in flow rate prediction between a coupled wellbore-reservoir simulator and a stand-alone reservoir simulator, at the early stages of production. The outcome of this research leads to a more accurate and reliable simulation of multiphase flow in the wellbore, which can be applied to surface facility design, well performance optimization, and wellbore damage estimation.Show more Item Discontinuous Galerkin finite element methods applied to two-phase, air-water flow problems(2005) Eslinger, Owen John; Wheeler, Mary F. (Mary Fanett)Show more A set of discontinuous Galerkin (DG) finite element methods are proposed to solve the air-water, two-phase equations arising in shallow subsurface flow problems. The different time-splitting approaches detailed incorporate primal formulations, such as Oden-Baumann-Babuska DG (OBB-DG), Symmetric Interior Penalty Galerkin (SIPG), Non-Symmetric Interior Penalty Galerkin (NIPG), and Incomplete Interior Penalty Galerkin (IIPG); as well as a local discontinuous Galerkin (LDG) method applied to the saturation equation. The two-phase flow equations presented are split into sequential and implicit pressure/explicit saturation (IMPES) formulations. The IMPES formulation introduced in this work uses one of the primal DG formulations to solve the pressure equation implicitly at every time step, and then uses an explicit LDG scheme for saturation equation. This LDG scheme advances in time via explicit Runge-Kutta time stepping, while employing a Kirchoff transformation for the local solution of the degenerate diffusion term. As fluid saturations may be discontinuous at the interface between two material types, DG methods are a natural fit for this problem. An algorithm is introduced to efficiently solve the system of equations arising from the primal DG discretization of the model Poisson’s Equation on conforming grids. The eigenstructure of the resulting stiffness matrix is examined and the reliance of this system on the penalty parameter is detailed. This analysis leads to an algorithm that is computationally optimal and guaranteed to converge for the order of approximation p = 1. The algorithm converges independently of h and of the penalty parameter σ. Computational experiments show that this algorithm also provides an excellent preconditioning step for higher orders of approximation and extensions are given to 2D and 3D problems. Computational results are also shown for a more general second order elliptic equation, for example, cases with heterogeneous and non-isotropic K. The numerical schemes presented are verified on a collection of standard benchmark problems and the two-phase flow formulations are validated using empirical results from the groundwater literature. These results include bounded column infiltration problems in which the soil air becomes compressed and entrapped, as well as other shallow subsurface infiltration problems. It is shown that the IMPES approach introduced holds promise for the future, especially for problems with very small, or even zero, capillary pressure. Such problems are commonly found in the SPE literature. Finally, initial computational results are shown which relate to a simplified model of the CO2 sequestration problem.Show more Item Mathematical modeling of the interaction between two-phase environmental flow and protective hydraulic structures(2016-12) Du, Wei, Ph. D.; Dawson, Clinton N.; Gamba, Irene; Ghattas, Omar; Demkowicz, Leszek; Bui-Thanh, TanShow more In August 2005, Hurricane Katrina struck the Gulf Coast of the United States. Over a thousand people lost their lives and the total damage was about 108 billion USD. It was the costliest United States hurricane. Two-thirds of the deaths and majority of economical loss were related to the protection system failure. This drives the study of fluid structure interaction to properly design the levees and floodwalls in the future for flooding vulnerable areas. Fluid-structure interaction is the interaction between a deformable structure and the surrounding flow. The fluid causes the deformation of the solid, and the solid reacts to the fluid. This thesis will focus on the interactions between two-phase environmental flow (air and water), and hydraulic structures (e.g. floodwalls, etc.) which are partially submerged in the water to disrupt the flow. Hydrodynamic and hydrostatic forces and impact loads from high water levels and velocities applied to the interface must be carefully monitored, as well as their impact on the structural stability. The main purpose of this work is to give a deeper understanding to the interaction processes and the coupling effects, and to determine the possible deformation or critical values of overturning moments for more robust future designs of floodwalls and levees. There are two main approaches to simulate fluid-solid interactions: the monolithic approach and the partitioned approach. In this work we use the partitioned approach by looking into the separate flow and structure models and simulating the interaction process. For the two-phase flow subproblem, the interface of air and water is treated as a material discontinuity in modeling, and is tracked by the level set method. The coupled system consists of Navier-Stokes Equation, level set method and the volume of fraction method, solved by the splitting method with residual-based variational multi-scale methods for stabilization. The structural mechanics is modeled by linear elasticity. Different types of floodwalls and two factors of safety against sliding and overturning are studied. In the Galveston area, the soil and floodwall properties determine the necessity to include soil as a part of the model. Hyperelastic and plastic models are discussed in simulating the soil behavior. The interaction process is modeled by imposing the matching conditions on the common fluid-structure boundary. Both one-way and two-way interaction models under synthetic waves are discussed and compared. One-way interaction is saving in computation and used widely in engineering design. Two-way interaction is formulated under the Arbitrary Lagrangian-Eulerian(ALE) framework. The operator splitting technique is developed for the coupled system to reduce computing cost while remain high accuracy.Show more Item Measuring void fraction in bubbly air-water mixtures with ultrasonic extinctions(1995-08) Maher, Thomas Francis, 1957-; Not availableShow more Item Mimetic finite differences for porous media applications(2014-05) Al-Hinai, Omar A.; Wheeler, Mary F. (Mary Fanett)Show more We connect the Mimetic Finite Difference method (MFD) with the finite-volume two-point flux scheme (TPFA) for Voronoi meshes. The main effect is reducing the saddle-point system to a much smaller symmetric-positive definite matrix. In addition, the generalization allows MFD to seamlessly integrate with existing porous media modeling technology. The generalization also imparts the monotonicity property of the TPFA method on MFD. The connection is achieved by altering the consistency condition of the velocity bilinear operator. First-order convergence theory is presented as well as numerical results that support the claims. We demonstrate a methodology for using MFD in modeling fluid flow in fractures coupled with a reservoir. The method can be used for nonplanar fractures. We use the method to demonstrate the effects of fracture curvature on single-phase and multi-phase flows. Standard benchmarks are used to demonstrate the accuracy of the method. The approach is coupled with existing reservoir simulation technology.Show more Item A multigrid preconditioner for two-phase flow in porous media(2001-12) Eaton, Frank Joseph; Wheeler, Mary F. (Mary Fanett)Show more Item Numerical analysis of multiphase flows in porous media on non-rectangular geometry(2017-12-06) Tao, Zhen; Arbogast, Todd James, 1957-; Wheeler, Mary F; Ghattas, Omar; Demkowicz, Leszek F; Hesse, Marc AShow more Fluid flow through porous media is a subject of common interest in many branches of engineering as well as applied natural science. In this work, we investigate the behavior and numerical treatment of multiphase flow in porous media. To be more specific, we take the sequestration of CO₂ in geological media as an example. Mathematical modeling and numerical study of carbon sequestration helps to predict both short and long-term behavior of CO₂ storage in geological media, which can be a benefit in many ways. This work aims at developing accurate and efficient numerical treatment for problems in porous media on non-rectangular geometries. Numerical treatment of Darcy flow and transport have been developed for many years on rectangular and simplical meshes. However, extra effort is required to extend them to general non-rectangular meshes. In this dissertation work, for flow simulation, we develop new H(div)- conforming mixed finite elements (AT and AT [superscript red] ) which are accurate on cuboidal hexahedra. We also develop the new direct serendipity finite element (DS [subscript r] ), which is H¹ -conforming and accurate on quadrilaterals and a special family of hexahedra called truncated cubes. The use of the direct serendipity finite element reduces the number of degrees of freedom significantly and therefore accelerates numerical simulations. For transport, we use the newly developed direct serendipity elements in an enriched Galerkin method (EG), which is locally conservative. The entropy viscosity stabilization is applied to eliminate spurious oscillations. We test the EG-DS [subscript r] method on problems with diffusion, transport, and coupled flow and transport. Finally, we study two-phase flow in heterogeneous porous media with capillary pressure. We work on a new formulation of the problem and force the continuity of the capillary flux with a modification to conquer the degeneracy. The numerical simulation of two-phase flow is conducted on non-rectangular grids and uses the new elements.Show more Item Numerical modeling of above-ground storage tank subject to multi-hazard event(2020-09-10) Lin, Yuxiang; Dawson, Clint N.; Landis, Chad Matthew; Ravi-Chandar, Krishnaswamy; Chen, YiShow more Above-ground storage tanks are typically thin-walled, cylindrical structures that can store large amounts of oil or chemicals. While this shape is efficient in sustaining large pressure from inside, it is susceptible from outside pressure such as loadings from hurricane storm surge and/or winds. For instance in the Houston Ship Channel there are over 4000 above-ground storage tanks, nearly 35 percent of these tanks lie within or in close proximity to the FEMA's 500 year return period surge estimates. Hurricane Katrina alone in 2006 caused over 7 millions gallon of oil leakage, causing significant economic and social consequences. Risk assessment of AST subject to storm event is of great importance considering its vulnerability to natural hazards. Before thoroughly assessing the failure risk of AST during hurricanes, understanding the possible failure mechanism and numerically predicting the tank response to multi-hazard event is inevitable. Existing literature primarily focuses on the post-event reconnaissance or one-way deterministic bucking analysis, the dynamic responses of AST subjected to surge flows is not well understood. Other knowledge gaps include the combined strong wind and wave effect and AST geometry imperfection etc, are also poorly characterized. In this dissertation, we are going to model the storm event using a two-phase air-water flow model and investigate the fluid-structure interaction(FSI) with the above-ground storage tank. Compared to one-way coupling, FSI considers the effect of structural response to fluid and vice-versa, thus making the predication more accurate and reliable. We use the FEniCS library to implement a two-phase Navier-Stokes solver, where the level-set method was utilized to distinguish the air and water. Incremental pressure correction scheme(IPCS) is used to decouple the two-phase Navier-Stokes equation, allowing the use of iterative solver for large scale computation. To recover the distance property during level set advection, a re-distance equation is solved to re-initialize the level set. For the tank part, we model it as cylindrical shell and use Calculix as a black box structure solver. Non-linear geometry and J2 flow plasticity can be included in the structural deformation. To reduce the computational time, semi-implicit coupling of two-phase flow and tank is proposed where only the pressure correction equation and structure solver are strongly coupled. To flexibly couple the fluid and structure solvers, or even more participant solvers, we use an open source coupling code called preCICE, which provides minimal invasive communication and coupling API for fluid and structure solvers. The numerical simulation of two-phase flow and cylindrical shell indicates that there are different time scales that need to be resolved in the FSI process. Constant time stepping is not optimal. Instead of complicated time adaptive method, we use the simple yet effective truncation error based method to adjust the time step size. To reduce the fluctuation of dt, I-control or PI-control, which is popular in control theory and explicit ODE problem, is used for the smooth change of time step. In the end, the dynamics of shell subject to dam break are analyzed and some parametric studies are carried out.Show more Item Simulation of rocket plume impingement and dust dispersal on the lunar surface(2012-12) Morris, Aaron Benjamin; Varghese, Philip L.; Goldstein, David Benjamin, doctor of aeronautics; Metzger, Philip; Trafton, Laurence M.; Raman, VenkatramananShow more When a lander approaches a dusty surface, the plume from the descent engine impinges on the ground and entrains loose regolith into a high velocity spray. This problem exhibits a wide variety of complex phenomena such as highly under-expanded plume impingement, transition from continuum to free molecular flow, erosion, coupled gas-dust motions, and granular collisions for a polydisperse distribution of aerosolized particles. The focus of this work is to identify and model the important physical phenomena and to characterize the dust motion that would result during typical lunar landings. A hybrid continuum-kinetic solver is used, but most of the complex physics are simulated using the direct simulation Monte Carlo method. A descent engine of comparable size and thrust to the Lunar Module Descent Engine is simulated because it allows for direct comparison to Apollo observations. Steady axisymmetric impingement was first studied for different thrust engines and different hovering altitudes. The erosion profiles are obtained from empirically derived scaling relationships and calibrated to closely match the net erosion observed during the Apollo missions. Once entrained, the dust motion is strongly influenced by particle-particle collisions and the collision elasticity. The effects of two-way coupling between the dust and gas motions are also studied. Small particles less than 1 µm in diameter are accelerated to speeds that exceed 1000 m/s. The larger particles have more inertia and are accelerated to slower speeds, approximately 350 m/s for 11 µm grains, but all particle sizes tend obtain their maximum speed within approximately 40 m from the lander. The maximum particle speeds and erosion rates tend to increase as the lander approaches the lunar surface. The erosion rates scale linearly with engine thrust and the maximum particle speed increases for higher thrust engines. Dust particles are able to travel very far from the lander because there is no background atmosphere on the moon to inhibit their motion. The far field deposition is obtained by using a staged calculation, where the first stages are in the near field where the flow is quasi-steady and the outer stages are unsteady. A realistic landing trajectory is approximated by a set of discrete hovering altitudes which range from 20 m to 3 m. Larger particles are accelerated to slower speeds and are deposited closer to the lander than smaller particles. Many of the gas molecules exceed lunar escape speed, but some gas molecules become trapped within the dust cloud and remain on the moon. The high velocity particulate sprays can be damaging to nearby structures, such as a lunar outpost. One way of mitigating this damage is to use a berm or fence to shield nearby structures from the dust spray. This work attempts to predict the effectiveness of such a fence. The effects of fence height, placement, and angle as well as the model sensitivity to the fence restitution coefficient are discussed. The expected forces exerted on fences placed at various locations are computed. The pressure forces were found to be relatively small at fences placed at practical distances from the landing site. The trajectories of particles that narrowly avoid the fence were not significantly altered by the fence, suggesting that the dust motion is weakly coupled to the gas in the near vicinity of the fence. Future landers may use multi-engine configurations that can form 3-dimensional gas and dust flows. There are multiple plume-plume and plume-surface interactions that affect the erosion rates and directionality of the dust sprays. A 4-engine configuration is simulated in this work for different hovering altitudes. The focusing of dust along certain trajectories depends on the lander hovering altitude, where at lower altitudes the dust particles focus along symmetry planes while at higher altitudes the sprays are more uniform. The surface erosion and trenching behavior for a 4-engine lander are also discussed.Show more Item A study of horizontal and down hill two-phase oil-water flow(1985) Cox, Alden Leroy; Hill, A. D. (A. Daniel); Podio, A. L.Show more Concurrent oil and water flow in inclined pipes is a common occurrence in deviated wells and production gathering systems. To predict properties associated with non-emulsified oil and water flow such as pressure gradient, two-phase flow correlations developed for gas-liquid flow or average flow properties of the oil and water must be used. The objective of this work was to study water holdup (water holdup defined as the in-situ fraction of the pipe occupied by water), and see what, if any, parameters have an effect on its magnitude. Flow pattern formation was also studied to determine its effect on holdup. The oil-water flow experiments were conducted with a flow loop constructed of 2 inch ID clean plastic pipe using a wide range of oil and water flow rates and involving inclination angles of 0, -15 and -30 degrees from horizontal. For each set of flowing conditions, the system was allowed to reach steady-state, then the flow regime was observed and the water holdup was measured. From the experiments, the flow regimes associated with oil-water flow differed greatly from flow regimes encountered with gas-liquid flow. It seems apparent that when comparing experimental flow regime data with modified and established gas-liquid dimensionless parameters there exists no meaningful correlation. Holdup data obtained indicates that it does vary according to certain parameters which include pipe inclination, flow patterns, and input fraction of waterShow more