Flow of CO<Subscript>2</Subscript>–ethanol and of CO<Subscript>2</Subscript>–methanol in a non-adiabatic microfluidic T-junction at high pressures

In this work, an experimental investigation of the single- and multiphase flows of two sets of fluids, CO₂–ethanol and CO₂–methanol, in a non-adiabatic microfluidic T-junction is presented. The operating conditions ranged from 7 to 18 MPa, and from 294 to 474 K. The feed mass fraction of CO₂ in the mixtures was 0.95 and 0.87, respectively. Under these operating conditions, CO₂ was either in liquid, gas or supercritical state; and the mixtures experienced a miscible single phase or a vapour–liquid equilibrium (VLE), with two separated phases. Taylor, annular and wavy were the two-phase flow regimes obtained in the VLE region. In the single phase region, the observed flows were classified into standard single-phase flows, “pseudo” two-phase flows and local phenomena in the T-junction. Flow regime maps were generated, based on temperature and pressure conditions. Two-phase flow void fractions and several parameters of Taylor flow were analysed. They showed a clear dependency on temperature, but were mostly insensitive to pressure. A continuous accumulation of liquid, either in the CO₂ channel or at the CO₂-side wall after the T-junction, disturbed most of the experiments in VLE conditions by randomly generating liquid plugs. This phenomenon is analysed, and capillary and wetting effects due to local Marangoni stresses are suggested as possible causes.     

TOUGHREACT—A simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media: Applications to geothermal injectivity and CO2 geological sequestration

TOUGHREACT is a numerical simulation program for chemically reactive non-isothermal flows of multiphase fluids in porous and fractured media. The program was written in Fortran 77 and developed by introducing reactive geochemistry into the multiphase fluid and heat flow simulator TOUGH2. A variety of subsurface thermo-physical–chemical processes are considered under a wide range of conditions of pressure, temperature, water saturation, ionic strength, and pH and Eh. Interactions between mineral assemblages and fluids can occur under local equilibrium or kinetic rates. The gas phase can be chemically active. Precipitation and dissolution reactions can change formation porosity and permeability. The program can be applied to many geologic systems and environmental problems, including geothermal systems, diagenetic, and weathering processes, subsurface waste disposal, acid mine drainage remediation, contaminant transport, and groundwater quality. Here we present two examples to illustrate applicability of the program. The first example deals with injectivity effects of mineral scaling in a fractured geothermal reservoir. A major concern in the development of hot dry rock and hot fractured rock reservoirs is achieving and maintaining adequate injectivity, while avoiding the development of preferential short-circuiting flow paths. Rock–fluid interactions and associated mineral dissolution and precipitation effects could have a major impact on the long-term performance of these reservoirs. We used recent European studies as a starting point to explore chemically induced effects of fluid circulation in the geothermal systems. We examine ways in which the chemical composition of reinjected waters can be modified to improve reservoir performance by maintaining or even enhancing injectivity. The second TOUGHREACT application example is related to CO₂ geologic sequestration in a saline aquifer. We performed numerical simulations for a commonly encountered Gulf Coast sediment under CO₂ injection conditions in order to analyze the impact of CO₂ immobilization through carbonate precipitation. Using the data presented in this paper, the CO₂ mineral-trapping capability after 10,000 years can reach 60 kg/m³ of sandstone by secondary carbonate mineral precipitation such as siderite, ankerite, and dawsonite. Most of the simulated mineral alteration pattern is consistent with the field observations of natural CO₂ reservoirs.     

All-angle removal of CO2 bubbles from the anode microchannels of a micro fuel cell by lattice-Boltzmann simulation

The removal of carbon dioxide (CO₂) at the anode of a micro direct methanol fuel cell (μDMFC) is critical. The bubbles are generated at the anode and may block part of the catalyst/diffusion layer, causing the μDMFC to malfunction. This work discusses the CO₂ bubble dynamics of microfluidics in a μDMFC from a microscopic perspective. A two-dimensional, nine-velocity lattice-Boltzmann model was adopted in this work to simulate the two- component (CO₂ bubble plus methanol solution) two-phase (gaseous and liquid) micro flow in a microchannel. The liquid–gas surface tension, the buoyancy force and the fluid–solid wall interaction force play the major roles in the bubble dynamics. They are treated as source terms in the lattice momentum equation. Simulation results indicate that the methanol stream flow rate, the pore size and the channel incline angle significantly affect the removal of CO₂ bubbles. The effect of the incline angle is substantial at low stream flow rates. The critical pore size in the microchannel for removing bubbles at all angles under various flow conditions has been predicted quantitatively.     

Fast and inexpensive method for the fabrication of transparent pressure-resistant microfluidic chips

The recent rise of high-pressure applications in microfluidics has led to the development of different types of pressure-resistant microfluidic chips. For the most part, however, the fabrication methods require clean room facilities, as well as specific equipment and expertise. Furthermore, the resulting microfluidic chips are not always well suited to flow visualization and optical measurements. Herein, we present a method that allows rapid and inexpensive prototyping of optically transparent microfluidic chips that resist pressures of at least 200 bar. The fabrication method is based on UV-curable off-stoichiometry thiol-ene epoxy (OSTE+) polymer, which is chemically bonded to glass. The reliability of the device was verified by pressure tests using CO₂, showing resistance without failure up to at least 200 bar at ambient temperature. The microchips also resisted operation at high pressure for several hours at a temperature of 40 °C. These results show that the polymer structure and the chemical bond with the glass are not affected by high-pressure CO₂. Opportunities for flow visualization are illustrated by high-pressure two-phase flow shadowgraphy experiments. These microfluidic chips are of specific interest for use with supercritical CO₂ and for optical characterization of phase transitions and multiphase flow under near-critical and critical CO₂ conditions.     

Simulating flows with moving rigid boundary using immersed-boundary method

The present study is to apply the immersed-boundary method to simulate 2- and 3-D viscous incompressible flows interacting with moving solid boundaries. Previous studies indicated that for stationary-boundary problems, different treatments inside the solid body did not affect the external flow. However, the relationship between internal treatment of the solid body and external flow for moving-boundary problems was not studied extensively and is investigated here. This is achieved via direct-momentum forcing on a Cartesian grid by combining “solid-body forcing” at solid nodes and interpolation on neighboring fluid nodes. The influence of the solid body forcing within the solid nodes is first examined by computing flow induced by an oscillating cylinder in a stationary square domain, where significantly lower amplitude oscillations in computed lift and drag coefficients are obtained compared with those without solid-body-forcing strategy. Grid-function convergence tests also indicate second-order accuracy of this implementation with respect to the L¹ norm in time and the L² norm in space. Further test problems are simulated to examine the validity of the present technique: 2-D flows over an asymmetrically-placed cylinder in a channel, in-line oscillating cylinder in a fluid at rest, in-line oscillating cylinder in a free stream, two cylinders moving with respect to one another, and 3-D simulation of a sphere settling under gravity in a static fluid. All computed results are in generally good agreement with various experimental measurements and with previous numerical simulations. This indicates the capability of the present simple implementation in solving complex-geometry flow problems and the importance of solid body forcing in computing flows with moving solid objects.     

Status of the TOUGH-FLAC simulator and recent applications related to coupled fluid flow and crustal deformations

This paper presents recent advancement in and applications of TOUGH-FLAC, a simulator for multiphase fluid flow and geomechanics. The TOUGH-FLAC simulator links the TOUGH family multiphase fluid and heat transport codes with the commercial FLAC^3D geomechanical simulator. The most significant new TOUGH-FLAC development in the past few years is a revised architecture, enabling a more rigorous and tight coupling procedure with improved computational efficiency. The applications presented in this paper are related to modeling of crustal deformations caused by deep underground fluid movements and pressure changes as a result of both industrial activities (the In Salah CO₂ Storage Project and the Geysers Geothermal Field) and natural events (the 1960s Matsushiro Earthquake Swarm). Finally, the paper provides some perspectives on the future of TOUGH-FLAC in light of its applicability to practical problems and the need for high-performance computing capabilities for field-scale problems, such as industrial-scale CO₂ storage and enhanced geothermal systems. It is concluded that despite some limitations to fully adapting a commercial code such as FLAC^3D for some specialized research and computational needs, TOUGH-FLAC is likely to remain a pragmatic simulation approach, with an increasing number of users in both academia and industry.     

TOUGH+CO2: A multiphase fluid-flow simulator for CO2 geologic sequestration in saline aquifers

TOUGH+CO₂ is a new simulator for modeling of CO₂ geologic sequestration in saline aquifers. It is a member of TOUGH+, the successor to the TOUGH2 family of codes for multicomponent, multiphase fluid and heat flow simulation. The code accounts for heat and up to 3 mass components, which are partitioned into three possible phases. In the code, the thermodynamics and thermophysical properties of H₂O-NaCl-CO₂ mixtures are determined based on system status and subdivided into six different phase combinations. By solving coupled mass and heat balance equations, TOUGH+CO₂ can model non-isothermal or isothermal CO₂ injection, phase behavior and flow of fluids and heat under typical conditions of temperature, pressure and salinity in CO₂ geologic storage projects. The code takes into account effects of salt precipitation on porosity and permeability changes, and the wettability phenomena. The new simulator inherits all capabilities of TOUGH2 in handling fractured media and using unstructured meshes for complex simulation domains. The code adds additional relative permeability and capillary pressure functions. The FORTRAN 95 OOP architecture and other new language features have been extensively used to enhance memory use and computing efficiency. In addition, a domain decomposition approach has been implemented for parallel simulation. All these features lead to increased computational efficiency, and allow applicability of the code to multi-core/processor parallel computing platforms with excellent scalability.     

Numerical investigation of formation and dissolution of CO<Subscript>2</Subscript> bubbles within silicone oil in a cross-junction microchannel

In this paper, a numerical investigation is conducted to study the formation and dissolution process of CO₂ bubbles within silicone oil in a cross-junction microchannel. A coupled multiphase–multicomponent computational fluid dynamics model based on the volume-of-fluid method is used, which is able to capture the physics of the multiphase bubble formation, dissolution mass transfer, and the tracking of the dissolved CO₂ species. The computational model is firstly validated with experimental results where good agreement is attained. Next, the model is used to investigate the bubble formation process at the cross-junction in the presence of dissolution and also the bubble evolution as it is transported along the downstream channel. It is revealed that during bubble formation, there is a high concentration of CO₂ solute around the cross-junction walls, as silicone oil flow to this region is minimal. As the CO₂ bubble travels downstream, the transport of the CO₂ solute is largely driven by the local flow currents of the silicone oil within the vicinity of the bubble. An extensive parametric study is also conducted, looking at the effects of varying the surface tension, diffusion coefficient and flow rates. The results demonstrate that the initial CO₂ bubble length and period of bubble formation are most affected by the flow rate, while the mass transfer is most strongly governed by the diffusion coefficient.     

Hysteretic upscaled constitutive relationships for vertically integrated porous media flow

Subsurface two-phase flow in porous media often takes place in reservoirs with a high ratio between the associated lateral and vertical extent and the lateral and vertical flow time scales. This allows for a two-scale approach with effective quantities for two-dimensional horizontal flow equations obtained from reconstructed hydrostatic vertical pressure and saturation distributions. Here, we derive explicit expressions for the two dimensional constitutive relationships for a play-type hysteretic Brooks–Corey capillary pressure function with a pore-size distribution index of 2 and quadratic relative permeabilities. We obtain an explicit hysteretic parametrization for the upscaled capillary pressure function and the upscaled relative permeabilities. The size of the hysteresis loop depends on the ratio between buoyancy and the entry pressure, i.e. it scales with the reservoir height and the ratio between drainage and imbibition capillary pressure. We find that the scaling for the relative permeability is non-monotonic and hysteresis vanishes for both small and large reservoirs.     

Nonlinear model identification and adaptive control of CO2 sequestration process in saline aquifers using artificial neural networks

In recent years, storage of carbon dioxide (CO₂) in saline aquifers has gained intensive research interest. The implementation, however, requires further research studies to ensure it is safe and secure operation. The primary objective is to secure the CO₂ which relies on a leak-proof formation. Reservoir pressure is a key aspect for assessment of the cap rock integrity. This work presents a new pressure control methodology based on a nonlinear model predictive control (NMPC) scheme to diminishing risk of carbon dioxide (CO₂) back leakage to the atmosphere due to a fail in the integrity of the formation cap rock. The CO₂ sequestration process in saline aquifers is simulated using ECLIPSE-100 as black oil reservoir simulator while the proposed control scheme is realized in MATLAB software package to prevent over-pressurization. A modified form of growing and pruning radial basis function (MGAP-RBF) neural network model is identified online for prediction of reservoir pressure behaviors. MGAP-RBF is recursively trained via extended Kalman filter (EKF) and unscented Kalman filter (UKF) algorithms. A set of miscellaneous test scenarios has been conducted using an interface program to exchange ECLIPSE and MATLAB in order to demonstrate the capabilities of the proposed methodology in guiding saline aquifer to follow some desired time-dependent pressure profiles during the CO₂ injection process.     

Consolidation of concentrated suspensions – shear and irreversible floc structure rearrangement

A mathematical model for a consolidation process of a highly concentrated, flocculated suspension is developed. The suspension is treated as a mixture of a fluid and solid particles by an Eulerian two-phase fluid model. We characterize the suspension by constitutive relations correlating the stresses, interaction forces, and inter-particle forces to concentration and velocity gradients. Irreversibility of the permeability and yield stress is modeled by a memory function. A simulation program using finite difference methods in time and space is applied to a two dimensional test case. Numerical experiments are carried out on consolidation under shear and gravity in a 2D box with moving bottom. Received: 30 January 2001 / Accepted: 30 May 2001     

Generating gas/liquid/liquid three-phase microdispersed systems in double T-junctions microfluidic device

This article describes the generation of microdispersed bubbles and droplets in a double T-junctions microfluidic device to form immiscible gas/liquid/liquid three-phase flowing systems. Segmented gas plugs are controllably prepared in water at the first T-junction to form gas/liquid two-phase fluid with the perpendicular flow cutting method. Then using this two-phase fluid as the cross-shearing fluid for the oil phase at the second T-junction, the gas/liquid/liquid three-phase flowing systems are prepared. Interestingly, it is found that the break-up of the oil droplets is mainly dominated by the cutting effect of the gas/liquid interface or the pressure drop across the emerging droplet, but independent with the viscous shearing effect of the continuous phase, even at the capillary number (Ca = u _wμ_w/γ_ow) higher than 0.01. The size laws and the distributions of the bubbles and droplets are investigated carefully, and a mathematical model has been developed to relating the operating conditions with the dispersed sizes.     

Numerical investigation of erosion threshold velocity in a pipe with sudden contraction

This paper deals with erosion prediction in a pipe with sudden contraction for the special case of two-phase (liquid and solid) turbulent flow with low particle concentration. The pipe axis was considered vertical and the flow was either in direction of gravity (downflow) or against it (upflow). The mathematical models for the calculations of the fluid velocity field and the motion of the solid particles have been established and an erosion model was used to predict the erosion rate. The fluid velocity (continuous phase) model was based on the time-averaged governing equations of 3-D turbulent flow and the particle-tracking model (discrete phase) was based on the solution of the governing equation of each particle motion taking into consideration the effect of particle rebound behavior. The effects of flow velocity and particle size were investigated for one contraction geometry considering water flow in a steel pipe. The results showed the strong dependence of erosion on both particle size and flow velocity but with little dependence on the direction of flow. The effect of flow direction was found to be significant only for large particle size and moderate flow velocity. The erosion critical area was found to be the inner surface of the tube sheet (connecting the two pipes) in the region close to the small pipe. The results also indicated the presence of a threshold velocity below which erosion is insignificant for all particle sizes.     

Experimental study of drying effects during supercritical CO<Subscript>2</Subscript> displacement in a pore network

Underground storage in geological aquifers is one of the most important options for large-scale mitigation of CO₂. During the supercritical CO₂ (scCO₂) injection process, water dissolved in scCO₂ may have significant impact on the displacement process. In this study, a series of wet scCO₂ (WscCO₂, 100% water saturation) and dry scCO₂ (DscCO₂, 0% water saturation) displacement experiments were conducted in micromodels for a large range of flow rates. The displacement was visualized using fluorescence microscopy. Results showed that DscCO₂ saturations were up to 3.3 times larger than WscCO₂ saturations when the capillary fingering dominated the displacement. The specific interfacial areas and mobile fractions for the DscCO₂ displacements were also much larger than those for WscCO₂. The capillary forces combined with drying effects are identified as the leading causes for the considerably higher DscCO₂ sweep efficiency. Results from this study showed the important impact of mutual solubility of scCO₂ and water on the displacement process and saturation of scCO₂ (S_scCO2), suggesting that the conventional model describing the relationship between capillary pressure and S_scCO2 needs to be modified for the effect of the mutual dissolution of multiple phases to more adequately describe the scCO₂ displacement process in saline aquifer formation.     

Numerical simulation of a compressible turbulent boundary layer over a conductive wall with line heat source

A conjugated problem of supersonic turbulent flow over a conductive solid wall with an embedded line heat source has been investigated as a model of a separation detector and skin friction gage. The 2-D Navier-Stokes equations for compressible fluid, including a two layer eddy viscosity model, are solved simultaneously with the heat transfer equation for the solid, written in general coordinates. The effect of the interface boundary condition on the stability of the implicit scheme of the flow field has been checked. A careful investigation of the effect of heat source strength, solid and fluid conductivity and Mach and Reynolds numbers on flow and temperature fields has been performed. The results of this investigation may be used to design an optimal gage with a minimum influence on the flow field.     

Chebyshev pseudospectral solution of the incompressible Navier-Stokes equations in curvilinear domains

A pseudospectral method for the calculation of 2-D flows of a viscous incompressible fluid in curvilinear domains is presented. The incompressible Navier-Stokes equations, expressed in terms of the primitive variables velocity and pressure, are solved in a non-orthogonal coordinate system. All the variables are expanded in double truncated series of Chebyshev polynomials. Time integration is performed by an implicit finite differences scheme for both the advective and diffusive terms. The pressure is calculated by the use of a truncated influence matrix involving all the collocation points in the field. A preconditioned iterative method is used to solve the system of linear equations resulting from the pseudospectral Chebyshev approximation. The algorithm is applied to the classical problem of the Green-Taylor vortices in order to check its accuracy; then 2 examples of viscous flow calculation are given in the case of a driven polar cavity and of a 2-D channel.     

基于RBF网络的固相质量流量检测

气固两相流流动的复杂性和多样性直接影响了固相质量流量的测量精度,严重限制了其在工业生产中的应用。在双弯管法检测固相质量流量原理的基础上,利用人工神经网络优良的非线性映射能力,以两弯管处的压力差为输入,建立了一种基于径向基(RBF)网络的软测量模型,实现了对固相质量流量的在线测量。实验结果表明:该模型测量误差在3%以内,能够有效解决固相质量流量在线检测的问题,并且具有测量快速、精度高的优点。