Multi-fluid Flows Research Articles

Numerical Simulation of Carbon Dioxide Injection in the Western Section of the Farnsworth Unit

Abstract Numerical simulation is an invaluable analytical tool for scientists and engineers in making predictions about of the fate of carbon dioxide injected into deep geologic formations for long-term storage. Current numerical simulators for assessing storage in deep saline formations have capabilities for modeling strongly coupled processes involving multifluid flow, heat transfer, chemistry, and rock mechanics in geologic media. Except for moderate pressure conditions, numerical simulators for deep saline formations only require the tracking of two immiscible phases and a limited number of phase components, beyond those comprising the geochemical reactive system. The requirements for numerically simulating the utilization and storage of carbon dioxide in partially depleted petroleum reservoirs are more numerous than those for deep saline formations. The minimum number of immiscible phases increases to three, the number of phase components may easily increase fourfold, and the coupled processes of heat transfer, geochemistry, and geomechanics remain. Public and scientific confidence in the ability of numerical simulators used for carbon dioxide sequestration in deep saline formations has advanced via a natural progression of the simulators being proven against benchmark problems, code comparisons, laboratory-scale experiments, pilot-scale injections, and commercial-scale injections. This paper describes a new numerical simulator for the scientific investigation of carbon dioxide utilization and storage in partially depleted petroleum reservoirs, with an emphasis on its unique features for scientific investigations. The mathematical foundations of this new simulator for enhanced oil recovery are those of the simulators developed for carbon sequestration in deep saline reservoirs, altered to consider the increased number of potential phases and compositional aspects by considering the oil in the system. As a demonstration of the simulator, a numerical simulation of carbon dioxide utilization for enhanced oil recovery in the western section of the Farnsworth Unit, representing an early stage in the progression of numerical simulators for carbon utilization and storage in depleted oil reservoirs.

P1/P0+ elements for incompressible flows with discontinuous material properties

We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown constant pressure field and a prescribed linear field that satisfies the steady state momentum equations for a constant body force. The elements are termed P1/P0+ as the “effective” pressure field is linear, although the unknown pressure field is piecewise constant within each element. The elements have an excellent behavior for incompressible viscous flow problems with discontinuous material properties formulated in either Eulerian or Lagrangian descriptions. The necessary numerical stabilization for dealing with the inf–sup condition imposed by the incompressibility constraint and high convective effects (in Eulerian flows) is introduced via the Finite Calculus (FIC) approach. For the sake of clarity, the element derivation is presented first for the simpler Stokes equations written in the standard Eulerian frame. The extension of the formulation to the Navier–Stokes equations written in the Eulerian and Lagrangian frameworks is straightforward and is presented in the second part of the paper.The efficiency and accuracy of the new P1/P0+ triangle is verified by solving a set of incompressible multifluid flow problems using a Lagrangian approach and a classical Eulerian description. The excellent performance of the new triangular element in terms of mass conservation and general accuracy for analysis of fluids with discontinuous material properties is highlighted.

A volume of fluid method based ghost fluid method for compressible multi-fluid flows

A ghost fluid method for compressible multi-fluid flows is presented in an adaptive mesh refinement (AMR) environment, where the volume of fluid method is used to track the interface. Various numerical examples are presented to compare the proposed method with interface capturing methods using pressure–temperature equilibrium and non-equilibrium temperature mixed cell approaches. It is found both mixing models are unable to generate accurate results for strong shock refractions through high acoustic impedance mismatch interfaces. The proposed method is found to be quite robust and can provide relatively reasonable results across a wide variety of flow regimes. The ghost fluid coupling between the fluid solver and the volume of fluid method is designed to be simple and consistent in any spatial dimension on AMR grid.

Taxila LBM: a parallel, modular lattice Boltzmann framework for simulating pore-scale flow in porous media

The lattice Boltzmann method is a popular tool for pore-scale simulation of flow. This is likely due to the ease of including complex geometries such as porous media and representing multiphase and multifluid flows. Many advancements, including multiple relaxation times, increased isotropy, and others have improved the accuracy and physical fidelity of the method. Additionally, the lattice Bolzmann method is computationally very efficient, thanks to the explicit nature of the algorithm and relatively large amount of local work. The combination of many algorithmic options and efficiency means that a software framework enabling the usage and comparison of these advancements on computers from laptops to large clusters has much to offer. In this paper, we introduce Taxila LBM, an open-source software framework for lattice Boltzmann simulations. We discuss the design of the framework and lay out the features available, including both methods in the literature and a few new enhancements which generalize methods to complex geometries. We discuss the trade-off of accuracy and performance in various methods, noting how the Taxila LBM makes it easy to perform these comparisons for real problems. And finally, we demonstrate a few common applications in pore-scale simulation, including the characterization of permeability of a Berea sandstone and analysis of multifluid flow in heterogenous micromodels.

A 3D Numerical Model for Free Interfacial Flows and Applications to Offshore Waves with Submerged Obstacles

A 3D numerical model for incompressible multi-fluid flows has been developed by using a multi-moment finite volume method and an accurate and efficient VOF type scheme for capturing moving interfaces of multi-fluids. The numerical model is validated with the theoretical and experimental results of the benchmark tests of solitary wave and dam break flow, which indicates the adequate numerical accuracy of the model as a practical tool to assess and predict offshore waves and their impacts on coastal structures. Numerical experiments have been systematically conducted to investigate wave breaking phenomena and the impacts on seawalls.

A 3D Numerical Model for Free Interfacial Flows and Applications to Offshore Waves with Submerged Obstacles

A 3D numerical model for incompressible multi-fluid flows has been developed by using a multi-moment finite volume method and an accurate and efficient VOF type scheme for capturing moving interfaces of multi-fluids. The numerical model is validated with the theoretical and experimental results of the benchmark tests of solitary wave and dam break flow, which indicates the adequate numerical accuracy of the model as a practical tool to assess and predict offshore waves and their impacts on coastal structures. Numerical experiments have been systematically conducted to investigate wave breaking phenomena and the impacts on seawalls.

Fluid flow and heat transfer investigation of pebble bed reactors using mesh-adaptive LES

The very high temperature reactor is one of the designs currently being considered for nuclear power generation. One its variants is the pebble bed reactor in which the coolant passes through complex geometries (pores) at high Reynolds numbers. A computational fluid dynamics model with anisotropic mesh adaptivity is used to investigate coolant flow and heat transfer in such reactors. A novel method for implicitly incorporating solid boundaries based on multi-fluid flow modelling is adopted. The resulting model is able to resolve and simulate flow and heat transfer in randomly packed beds, regardless of the actual geometry, starting off with arbitrarily coarse meshes. The model is initially evaluated using an orderly stacked square channel of channel-height-to-particle diameter ratio of unity for a range of Reynolds numbers. The model is then applied to the face-centred cubical geometry. coolant flow and heat transfer patterns are investigated.

Development of a coupled thermo-hydro-mechanical model in discontinuous media for carbon sequestration

Geomechanical alteration of porous media is generally ignored for most shallow subsurface applications, whereas carbon dioxide (CO2) injection, migration, and trapping in deep saline aquifers will be controlled by coupled multifluid flow, energy transfer, and geomechanical processes. The accurate assessment of the risks associated with potential leakage of injected CO2 and the design of effective injection systems require that we represent these coupled processes within numerical simulators. The objectives of this study were to develop a coupled thermo-hydro-mechanical model into a single software and to examine the coupling of thermal, hydrological, and geomechanical processes for simulation of CO2 injection into the subsurface for carbon sequestration. A numerical model was developed to couple nonisothermal multiphase hydrological and geomechanical processes for prediction of multiple interconnected processes for carbon sequestration in deep saline aquifers. The geomechanics model was based on the Rigid Body-Spring Model (RBSM), a discrete method for modeling discontinuous rock systems. Poisson’s effect that was often ignored by RBSM was considered in the model. The simulation of large-scale and long-term coupled processes in carbon capture and storage projects requires large memory and computational performance. The Global Array Toolkit was used to build the model to permit high-performance simulations of coupled processes. The model was used to simulate a case study with several scenarios to demonstrate the impacts of considering coupled processes and Poisson’s effect for the prediction of CO2 sequestration. As a demonstration of the coupled model, a conceptual 3D model was used to explain the double-lobe uplift pattern observed in the Krechba gas field at In Salah (Algeria), a site that demonstrated the success of a CO2 sequestration effort into a deep saline formation.

Progress in computational microfluidics using TransAT

The paper reports on the progress made in predicting single- and multi-phase microfluidics flows using the computational multi-fluid flow dynamics (CMFD) code TransAT. In the multi-phase context, the code uses either the level-set approach or the phase-field variant as the “Interface Tracking Methods”. The solver incorporates phase-change capabilities, triple-line dynamics models, Marangoni effects, electro-wetting and a micro-film sub-grid scale model for lubrication. Subtle microfluidics problems like droplet generation or surface tension-driven flows are shown to be within reach of modern CMFD techniques using interface tracking, with relatively fast CPU response times. In most of the cases presented here, the comparison between CMFD and experiments is rather satisfactory.

Smoothed particle simulation of gravity waves in a multi-fluid system

The generation and propagation of gravity waves in a multi-fluid system have significant environmental impacts. This paper presents an incompressible smoothed particle hydrodynamics model to simulate this process. The method is a mesh-free particle modelling approach that can treat the free surfaces and multi-interfaces in a straightforward manner. The proposed model is based on the general multi-fluid flow equations and uses a unified pressure formulation to address the interactions among the different components of the fluids. The model will be used to investigate the gravity currents generated from one fluid intruding into other fluids with different densities. The general features of the gravity current have been disclosed and the computed gravity wave height and wave propagation speed agree well with the theoretical analysis. The error analysis proved the convergence of the numerical scheme and it was found that the multi-fluid model is close to first-order accurate.

Towards front-tracking based on conservation in two space dimensions III, tracking interfaces

This is the third paper in the series of our conservative front-tracking method. In this paper, we describe how our method tracks fluid interfaces in multi-fluid flows. Two important ingredients in our conservative front-tracking method in tracking fluid interfaces are: (1) the velocities and pressures of the left and right cell-averages in a discontinuity cell are respectively maintained to be equal to each other, and in doing so the physics that the normal velocity and pressure are continuous cross the interface is simulated but that the tangential velocity may be discontinuous is ignored, and (2) a so-called numerical surface dissipation is designed on the tracked interface to eliminate possible numerical instability there, and we believe that this numerical surface dissipation is a good substitute for the missing physical dissipation acting on the interface. We then present numerical simulation of Haas–Sturtevant’s two shock–bubble interaction experiments [J.F. Haas, B. Sturtevant, Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech. 181 (1987) 41–76] using this method. Our numerical results are in good agreement with the experimental and other numerical results in the early times of the flow. Moreover, our numerical results are also in good agreement with the experimental results in the later times of the flow and give clear pictures of the bubble deformation then, which show that the right boundaries of the bubble behave just as Rychtmyer–Meshkov instabilities with the shock coming from either heavy or light gases.

Convective transport of nanoparticles in multi-layer fluid flow

Technologically, multi-layer fluid models are important in understanding fluid-fluid or fluid-nanoparticle interactions and their effects on flow and heat transfer characteristics. However, to the best of the authors’ knowledge, little attention has been paid to the study of three-layer fluid models with nanofluids. Therefore, a three-layer fluid flow model with nanofluids is formulated in this paper. The governing coupled nonlinear differential equations of the problem are non-dimensionalized by using appropriate fundamental quantities. The resulting multi-point boundary value problem is solved numerically by quasi-linearization and Richardson’s extrapolation with modified boundary conditions. The effects of the model parameters on the flow and heat transfer are obtained and analyzed. The results show that an increase in the nanoparticle concentration in the base fluid can modify the fluid-velocity at the interface of the two fluids and reduce the shear not only at the surface of the clear fluid but also at the interface between them. That is, nanofluids play a vital role in modifying the flow phenomena. Therefore, one can use nanofluids to obtain the desired qualities for the multi-fluid flow and heat transfer characteristics.

A novel hierarchical crystalline structure of injection-molded bars of linear polymer: co-existence of bending and normal shish–kebab structure

The hierarchy structures and orientation behavior of high-density polyethylene (HDPE) molded by conventional injection molding (CIM) and gas-assisted injection molding (GAIM) were intensively examined by using scanning electronic microscopy (SEM) and 2D wide-angle X-ray diffraction (2D-WAXD). Results show that the spatial variation of crystals across the thickness of sample molded by CIM was characterized by a typical skin–core structure as a result of general shear-induced crystallization. Unusually, the crystalline morphologies of the parts prepared by GAIM, primarily due to the penetration of secondary high-compressed gas that was exerted on the polymer melt during gas injection, featured a richer and fascinating supermolecular structure. Besides, the oriented lamellar structure, general shish–kebab structure, and common spherulites existed in the skin, sub-skin, and gas channel region, respectively; a novel morphology of shish–kebab structure was seen in the sub-skin layer of the GAIM parts of HDPE. This special shish–kebab structure (recognized as “bending shish–kebab”) was neither parallel nor perpendicular to the flow direction but at an angle. Furthermore, there was a clear interface between the bending and the normal shish–kebab structures, which may be very significant for our understanding of the melt flow or polymer rheology under the coupling effect of multi-fluid flow and complex temperature profiles in the GAIM process. Based on experimental observations, a schematic illustration was proposed to interpret the formation mechanism of the bending shish–kebab structure during GAIM process.

Parallelization Strategy for the Volume-of-fluid Method on Unstructured Meshes

The Volume-of-Fluid (VOF) is one of the most widely used methods for interface tracking in the simulation of multi-fluid flows. The interface between different fluids is generated from the volume fraction scalar fields, which account for the ratio of volume of each fluid in each control volume. Then, an advection equation is solved to obtain the new distribution of the fluids after momentum is applied. Since this is a time-consuming process, parallelization techniques play an essential role. In the VOF approaches most of computing cost of the algorithm is concentrated in operations with the cells that form the interface, i.e. the cells in which coexist different fluids. When the interface is not homogeneously distributed throughout the domain, the standard domain decomposition strategy results in an unbalanced partition. A possible strategy to overcome this limitation is to adapt the domain decomposition to the interface distribution, however, this approach presents a number of drawbacks mainly related to the dynamic location of the interface. In this paper a new strategy, based in a load balancing process complementary to the domain decomposition, is presented with the aim to overcome the limitations of standard domain decomposition based approaches

Fully Coupled Well Models for Fluid Injection and Production

Wells are the primary engineered component of geologic sequestration systems with deep subsurface reservoirs. Wells provide a conduit for injecting greenhouse gases and producing reservoirs fluids, such as brines, natural gas, and crude oil, depending on the target reservoir. Well trajectories, well pressures, and fluid flow rates are parameters over which well engineers and operators have control during the geologic sequestration process. Current drilling practices provide well engineers flexibility in designing well trajectories and controlling screened intervals. Injection pressures and fluids can be used to purposely fracture the reservoir formation or to purposely prevent fracturing. Numerical simulation of geologic sequestration processes involves the solution of multifluid transport equations within heterogeneous geologic media. These equations that mathematically describe the flow of fluid through the reservoir formation are nonlinear in form, requiring linearization techniques to resolve. In actual geologic settings, fluid exchange between a well and reservoir is a function of local pressure gradients, fluid saturations, and formation characteristics. In numerical simulators, fluid exchange between a well and reservoir can be specified using a spectrum of approaches that vary from totally ignoring the reservoir conditions to fully considering reservoir conditions and well processes. Well models are a numerical simulation approach that account for local conditions and gradients in the exchange of fluids between the well and reservoir. As with the mathematical equations that describe fluid flow in the reservoir, variation in fluid properties with temperature and pressure yield nonlinearities in the mathematical equations that describe fluid flow within the well. To numerically simulate the fluid exchange between a well and reservoir the two systems of nonlinear multifluid flow equations must be resolved. The spectrum of numerical approaches for resolving these equations varies from zero coupling to full coupling. In this paper we describe a fully coupled solution approach for a well model that allows for a flexible well trajectory and screened interval within a structured hexahedral computational grid. In this scheme, the nonlinear well equations have been fully integrated into the Jacobian matrix for the reservoir conservation equations, minimizing the matrix bandwidth.

Selection Principle of Optimal Profiles for Immiscible Multi-Fluid Hele-Shaw Flows and Stabilization

In this paper, we discuss a previously unknown selection principle of optimal viscous configurations for immiscible multi-fluid Hele-Shaw flows that have emerged from numerical experiments on three- and four-layer flows. Moreover, numerical investigation on four-layer flows shows evidence of four-layer systems which are almost completely stabilizing. Simple physical mechanisms that explain both of these findings are discussed.

Turbulent concentration diffusion in multiphase flow

In multifluid multiphase flow models, the velocity of each phase is determined by its own momentum equation, which is coupled to the other phases by pairwise interphase drag forces proportional to velocity differences. When the drag coefficients are large, the phase velocities become nearly equal and the relative motion of the phases becomes diffusional rather than inertial. The multifluid momentum equations then reduce to a single momentum equation for the mixture and a system of linear relations that determine the small residual velocity differences between the phases. We derive such diffusional relations in a very general form that applies to nearly all multiphase flow models of this type. The simplest such models then reduce to “drift flux” models that exhibit pressure diffusion but not ordinary (Fick's law) diffusion driven by concentration gradients. The question then arises of how to consistently account for turbulent concentration diffusion in models of this type. This question is resolved by specializing the general diffusional relations to a rather typical single-pressure multiphase flow model which includes turbulent momentum transport due to Reynolds stresses. This special case serves as a paradigm which illustrates that (a) turbulent concentration diffusion in multiphase flow is a direct consequence of the isotropic (turbulent pressure) part of the Reynolds stresses, provided the latter are expressed in their proper divergence form; and (b) the order of magnitude of the resulting turbulent diffusivities is just what one would anticipate on dimensional grounds. Properly formulated models of this type therefore automatically include turbulent concentration diffusion, and consequently require no further additions or modifications to introduce it.

INTERACTION OF SHOCK WAVE WITH MULTI-FLUIDS INTERFACE USING QUADRILATERAL-BASED ADAPTIVE MESH

In this paper, the interaction of shock waves with multi-fluids interfaces is investigated by numerical simulations using unstructured quadrilateral adaptive meshes. In order to obtain a detailed structure of the interface, a solution adaptive method for compressible multi-fluid flows developed by Zheng et al. is employed. Firstly, the method is verified by a planar shock and interface interaction problem, which is compared with the front tracking method for the Richtmyer–Meshkov instability problem. Following the verification, the interaction between a circular shock and a sinusoidally perturbed circular interface in cylinder vessel is firstly investigated in our paper. The results show that the solution adaptive method can be employed to study the compressible multi-fluid cases with relatively complex geometry as well as capturing the fine details of interfacial structures of the interaction.

Systems of conservation laws with rotation and Galilean symmetry

We show that the structure of multidimensional systems of conservation laws, equipped with a single, convex entropy, and with both rotation and Galilean symmetries, is perhaps surprisingly limited. The following are established.The simplest examples of such systems, with only one vector field, are at most simple extensions of the familiar Euler systems.In such models of magnetohydrodynamic flow, including a solenoidal, Galilean invariant magnetic field, the property of finite signal propagation speeds is often lost.The only such system describing adiabatic multi-fluid flow, with the mass of each species conserved separately, corresponds to independent flow of each species. Whatever interaction between the different species occurs in an energy equation or through some other dependent variable, and not simply through expressions for the pressures in terms of the speciesʼ densities. A similar conclusion holds for incompressible flow.

Sensor and Numerical Simulator Evaluation for Porous Medium Desiccation and Rewetting at the Intermediate Laboratory Scale

Soil desiccation, in conjunction with surface infiltration control, is considered at the Hanford Site as a potential technology to limit the flux of technetium and other contaminants in the vadose zone to the groundwater. An intermediate‐scale experiment was conducted to test the response of a series of instruments to desiccation and subsequent rewetting of porous media. The instruments include thermistors, thermocouple psychrometers, dual‐probe heat pulse sensors, heat dissipation units, and humidity probes. The experiment was simulated with the multifluid flow simulator STOMP, using independently obtained hydraulic and thermal porous medium properties. All instrument types used for this experiment were able to indicate when the desiccation front passed a certain location. In most cases the changes were sharp, indicating rapid changes in moisture content, water potential, or humidity. However, a response to the changing conditions was recorded only when the drying front was very close to a sensor. Of the tested instruments, only the heat dissipation unit and humidity probes were able to detect rewetting. The numerical simulation results reasonably match the experimental data, indicating that the simulator captures the pertinent gas flow and transport processes related to desiccation and rewetting and may be useful in the design and analysis of field tests.