Modeling Gas Transport in the Shallow Subsurface During the ZERT CO<Subscript>2</Subscript> Release Test

We used the multiphase and multicomponent TOUGH2/EOS7CA model to carry out predictive simulations of CO₂ injection into the shallow subsurface of an agricultural field in Bozeman, Montana. The purpose of the simulations was to inform the choice of CO₂ injection rate and design of monitoring and detection activities for a CO₂ release experiment. The release experiment configuration consists of a long horizontal well (70 m) installed at a depth of approximately 2.5 m into which CO₂ is injected to mimic leakage from a geologic carbon sequestration site through a linear feature such as a fault. We estimated the permeability of the soil and cobble layers present at the site by manual inversion of measurements of soil CO₂ flux from a vertical-well CO₂ release. Based on these estimated permeability values, predictive simulations for the horizontal well showed that CO₂ injection just below the water table creates an effective gas-flow pathway through the saturated zone up to the unsaturated zone. Once in the unsaturated zone, CO₂ spreads out laterally within the cobble layer, where liquid saturation is relatively low. CO₂ also migrates upward into the soil layer through the capillary barrier and seeps out at the ground surface. The simulations predicted a breakthrough time of approximately two days for the 100kg d⁻¹ injection rate, which also produced a flux within the range desired for testing detection and monitoring approaches. The seepage area produced by the model was approximately five meters wide above the horizontal well, compatible with the detection and monitoring methods tested. For a given flow rate, gas-phase diffusion of CO₂ tends to dominate over advection near the ground surface, where the CO₂ concentration gradient is large, while advection dominates deeper in the system.     

Non-isobaric Marangoni boundary layer flow for Cu,Al<Subscript>2</Subscript>O<Subscript>3</Subscript> and TiO<Subscript>2</Subscript> nanoparticles in a water based fluid

In this paper, a non-isobaric Marangoni boundary layer flow that can be formed along the interface of immiscible nanofluids in surface driven flows due to an imposed temperature gradient, is considered. The solution is determined using a similarity solution for both the momentum and energy equations and assuming developing boundary layer flow along the interface of the immiscible nanofluids. The resulting system of nonlinear ordinary differential equations is solved numerically using the shooting method along with the Runge-Kutta-Fehlberg method. Numerical results are obtained for the interface velocity, the surface temperature gradient as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ (0≤φ≤0.2) and the constant exponent β. Three different types of nanoparticles, namely Cu, Al₂O₃ and TiO₂ are considered by using water-based fluid with Prandtl number Pr =6.2. It was found that nanoparticles with low thermal conductivity, TiO₂, have better enhancement on heat transfer compared to Al₂O₃ and Cu. The results also indicate that dual solutions exist when β<0.5. The paper complements also the work by Golia and Viviani (Meccanica 21:200–204, 1986) concerning the dual solutions in the case of adverse pressure gradient.     

ℒ<Subscript>2</Subscript>–ℒ<Subscript>∞</Subscript> nonlinear system identification via recurrent neural networks

This paper proposes a new neural network ℋ_∞ synchronization (NNHS) scheme for unknown chaotic systems. In the proposed framework, a dynamic neural network is constructed as an alternative to approximate the chaotic system. Based on this neural network and linear matrix inequality (LMI) formulation, the NNHS controller and the learning law are presented to reduce the effect of disturbance to an ℋ_∞ norm constraint. It is shown that finding the NNHS controller and the learning law can be transformed into the LMI problem and solved using the convex optimization method. A numerical example is presented to demonstrate the validity of the proposed NNHS scheme.     

Numerical investigation of natural convection of Al<Subscript>2</Subscript>O<Subscript>3</Subscript> nanofluid in vertical annuli

This paper presents the numerical study of internal free convection of Al₂O₃ water nanofluid in vertical annuli. Vertical walls are maintained at constant temperatures and horizontal walls are adiabatic. Results are validated by experimental data. Effect of nanofluids on natural convection is investigated as a function of geometrical and physical parameters and particle fractions for aspect ratio of 1 ≤ H/L ≤ 5, Grashof number of 10³ ≤ Gr ≤ 10⁵ and concentration of 0 ≤ ϕ ≤ 0.06. More than 330 different numerical cases are investigated to develop a new correlation for the Nusselt number. This correlation is presented as a function of Nusselt number of base fluid and particle fraction which is a linear decreasing function of particle fraction. The developed correlation for annuli is also valid for the natural convection of Al₂O₃ water nanofluid in a square cavity. Furthermore, the effect of the viscosity and conductivity models on the Nusselt number of nanofluids in cylindrical cavities are discussed.     

Numerical study of conjugate heat transfer in rectangular microchannel heat sink with Al<Subscript>2</Subscript>O<Subscript>3</Subscript>/H<Subscript>2</Subscript>O nanofluid

In the present paper, conjugate heat transfer approach has been used to numerically study laminar forced convective heat transfer characteristics of Al₂O₃/H₂O nanofluid flowing in a silicon microchannel heat sink (MCHS) of rectangular cross-section using thermal dispersion model. Results are presented in terms of thermal resistance that characterizes MCHS performance. It is observed that use of nanofluid improves MCHS performance by reducing fin (conductive) thermal resistance.     

Properties of an Al/(Al<Subscript>2</Subscript>O<Subscript>3</Subscript>+TiB<Subscript>2</Subscript>+ZrB<Subscript>2</Subscript>) hybrid composite manufactured by powder metallurgy and hot pressing

The properties and microstructure of an Al/(Al₂O₃ + TiB₂ + ZrB₂) hybrid composite made by using hot pressing of aluminum combined with different amounts of TiB₂, ZrB₂, and Al₂O₃ powders are studied. The mechanical properties of the composites are investigated on the basis of microhardness and compression tests. The results show that the microstructure of the composites is uniform and the particles are well distributed in the matrix.     

Electrorheological response of SnO<Subscript>2</Subscript> and Y<Subscript>2</Subscript>O<Subscript>3</Subscript> nanoparticles in silicon oil

The electrorheological properties (ER) of some fluids containing particles change extensively under the external electrical field. This phenomenon is applicable in many industries and equipments, such as clutches and motor driven rotor, which would transfer the spin to a drive shaft through a thin layer of electrorheological fluid. In this investigation, the effects of external electrical field on ER properties of non-Newtonian fluids (silicon oil) with the addition of SnO₂ and Y₂O₃ nanoparticles were studied. The ER properties were measured for a wide range of SnO₂ and Y₂O₃ nanoparticle concentrations and DC electrical voltages using concentric cylinder rotary rheometer. Based on the results, ER properties of nanofluids, e.g., apparent viscosity, shear stress, and yield stress, were enhanced by applying electrical field and increasing SnO₂ and Y₂O₃ concentrations.

Injection and Storage of CO<Subscript>2</Subscript> in Deep Saline Aquifers: Analytical Solution for CO<Subscript>2</Subscript> Plume Evolution During Injection

Injection of fluids into deep saline aquifers is practiced in several industrial activities, and is being considered as part of a possible mitigation strategy to reduce anthropogenic emissions of carbon dioxide into the atmosphere. Injection of CO₂ into deep saline aquifers involves CO₂ as a supercritical fluid that is less dense and less viscous than the resident formation water. These fluid properties lead to gravity override and possible viscous fingering. With relatively mild assumptions regarding fluid properties and displacement patterns, an analytical solution may be derived to describe the space–time evolution of the CO₂ plume. The solution uses arguments of energy minimization, and reduces to a simple radial form of the Buckley–Leverett solution for conditions of viscous domination. In order to test the applicability of the analytical solution to the CO₂ injection problem, we consider a wide range of subsurface conditions, characteristic of sedimentary basins around the world, that are expected to apply to possible CO₂ injection scenarios. For comparison, we run numerical simulations with an industry standard simulator, and show that the new analytical solution matches a full numerical solution for the entire range of CO₂ injection scenarios considered. The analytical solution provides a tool to estimate practical quantities associated with CO₂ injection, including maximum spatial extent of a plume and the shape of the overriding less-dense CO₂ front.     

STREAMLINE-BASED MATHEMATICAL MODEL FOR CO2 MISCIBLE FLOODING

According to the research theory of improved black oil simulator, a practical mathematical model for C02 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance fast, streamline method is employed to solve this model as an alternative to traditional finite difference methods. Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method (BEM), an explicit total variation diminishing (TVD) method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less information need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an effective tool for early stage screening andmiscible oil field.reservoir dynamic management of the CO2 miscible oil field.     

<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> invariant relative orbits via differential correction algorithm

This paper describes a practical method for finding the invariant orbits in J ₂ relative dynamics. Working with the Hamiltonian model of the relative motion including the J ₂ perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth’s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J ₂ invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte–Carlo simulation. The project supported by the Innovation Foundation of Beihang University for Ph.D. Graduates, and the National Natural Science Foundation of China (60535010).     

Pore Scale Modeling of Reactive Transport Involved in Geologic CO<Subscript>2</Subscript> Sequestration

We apply a multi-component reactive transport lattice Boltzmann model developed in previous studies for modeling the injection of a CO₂-saturated brine into various porous media structures at temperatures T = 25 and 80°C. In the various cases considered the porous medium consists initially of calcite with varying grain size and shape. A chemical system consisting of Na⁺, Ca²⁺, Mg²⁺, H⁺, CO₂^°(aq){{\rm CO}_2^{\circ}{\rm (aq)}}, and Cl⁻ is considered. Flow and transport by advection and diffusion of aqueous species, combined with homogeneous reactions occurring in the bulk fluid, as well as the dissolution of calcite and precipitation of dolomite are simulated at the pore scale. The effects of the structure of the porous media on reactive transport are investigated. The results are compared with a continuum-scale model and the discrepancies between the pore- and continuum-scale models are discussed. This study sheds some light on the fundamental physics occurring at the pore scale for reactive transport involved in geologic CO₂ sequestration.     

Effects of CO<Subscript>2</Subscript> Compressibility on CO<Subscript>2</Subscript> Storage in Deep Saline Aquifers

The injection of supercritical CO₂ in deep saline aquifers leads to the formation of a CO₂ plume that tends to float above the formation brine. As pressure builds up, CO₂ properties, i.e. density and viscosity, can vary significantly. Current analytical solutions do not account for CO₂ compressibility. In this article, we investigate numerically and analytically the effect of this variability on the position of the interface between the CO₂-rich phase and the formation brine. We introduce a correction to account for CO₂ compressibility (density variations) and viscosity variations in current analytical solutions. We find that the error in the interface position caused by neglecting CO₂ compressibility is relatively small when viscous forces dominate. However, it can become significant when gravity forces dominate, which is likely to occur at late times of injection.     

Sensitivity Study of Simulation Parameters Controlling CO<Subscript>2</Subscript> Trapping Mechanisms in Saline Formations

The primary purpose of this study is to understand quantitative characteristics of mobile, residual, and dissolved CO₂ trapping mechanisms within ranges of systematic variations in different geologic and hydrologic parameters. For this purpose, we conducted an extensive suite of numerical simulations to evaluate the sensitivities included in these parameters. We generated two-dimensional numerical models representing subsurface porous media with various permutations of vertical and horizontal permeability (k _v and k _h), porosity (f{\phi}), maximum residual CO₂ saturation (S_gr^max{S_{\rm gr}^{\max}}), and brine density (ρ _br). Simulation results indicate that residual CO₂ trapping increases proportionally to k_v, k_h, S_gr^max{k_{\rm v}, k_{\rm h}, S_{\rm gr}^{\max}} and ρ _br but is inversely proportional to f.{\phi.} In addition, the amount of dissolution-trapped CO₂ increases with k _v and k _h, but does not vary with f{\phi } , and decreases with S_gr^max{S_{\rm gr}^{\max}} and ρ _br. Additionally, the distance of buoyancy-driven CO₂ migration increases proportionally to k _v and ρ _br only and is inversely proportional to k_h, f{k_{\rm h}, \phi } , and S_gr^max{S_{\rm gr}^{\max}} . These complex behaviors occur because the chosen sensitivity parameters perturb the distances of vertical and horizontal CO₂ plume migration, pore volume size, and fraction of trapped CO₂ in both pores and formation fluids. Finally, in an effort to characterize complex relationships among residual CO₂ trapping and buoyancy-driven CO₂ migration, we quantified three characteristic zones. Zone I, expressing the variations of S_gr^max{S_{\rm gr}^{\max}} and k _h, represents the optimized conditions for geologic CO₂ sequestration. Zone II, showing the variation of f{\phi} , would be preferred for secure CO₂ sequestration since CO₂ has less potential to escape from the target formation. In zone III, both residual CO₂ trapping and buoyancy-driven migration distance increase with k _v and ρ _br.     

Production of nanomaterials by vaporizing ceramic targets irradiated by a moderate-power continuous-wave CO<Subscript>2</Subscript> laser

The efficiency of utilization of CO ₂ laser energy for vaporization of Al ₂ O ₃ ceramics is evaluated using a mathematical model for the interaction of laser radiation with materials. It is shown that the calculated efficiency of radiation-energy utilization is not higher than 15% at a radiation power density of 10⁵ W/cm ² on the target. On the experimental facility designed for the synthesis of nanopowders, a vaporization rate of 1 g/h was achieved for Al ₂ O ₃, which corresponds to a 3% efficiency of radiation-energy utilization. The dependence of the characteristic particle size of a zirconium oxide nanopowder on helium pressure in the range of 0.01–1.00 atm was studied. Results of experiments on vaporization of multicomponent materials (LaNiO ₃ and the Tsarev meteorite) are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 172–184, March–April, 2007.     

An Experimental Study of CO<Subscript>2</Subscript> Exsolution and Relative Permeability Measurements During CO<Subscript>2</Subscript> Saturated Water Depressurization

Dissolution of CO₂ into brine is an important and favorable trapping mechanism for geologic storage of CO₂. There are scenarios, however, where dissolved CO₂ may migrate out of the storage reservoir. Under these conditions, CO₂ will exsolve from solution during depressurization of the brine, leading to the formation of separate phase CO₂. For example, a CO₂ sequestration system with a brine-permeable caprock may be favored to allow for pressure relief in the sequestration reservoir. In this case, CO₂-rich brine may be transported upwards along a pressure gradient caused by CO₂ injection. Here we conduct an experimental study of CO₂ exsolution to observe the behavior of exsolved gas under a wide range of depressurization. Exsolution experiments in highly permeable Berea sandstones and low permeability Mount Simon sandstones are presented. Using X-ray CT scanning, the evolution of gas phase CO₂ and its spatial distribution is observed. In addition, we measure relative permeability for exsolved CO₂ and water in sandstone rocks based on mass balances and continuous observation of the pressure drop across the core from 12.41 to 2.76 MPa. The results show that the minimum CO₂ saturation at which the exsolved CO₂ phase mobilization occurs is from 11.7 to 15.5%. Exsolved CO₂ is distributed uniformly in homogeneous rock samples with no statistical correlation between porosity and CO₂ saturation observed. No gravitational redistribution of exsolved CO₂ was observed after depressurization, even in the high permeability core. Significant differences exist between the exsolved CO₂ and water relative permeabilities, compared to relative permeabilities derived from steady-state drainage relative permeability measurements in the same cores. Specifically, very low CO₂ and water relative permeabilities are measured in the exsolution experiments, even when the CO₂ saturation is as high as 40%. The large relative permeability reduction in both the water and CO₂ phases is hypothesized to result from the presence of disconnected gas bubbles in this two-phase flow system. This feature is also thought to be favorable for storage security after CO₂ injection.     

An experimental—Numerical evaluation of the<Emphasis Type="Italic">T</Emphasis><Stack><Subscript>ε</Subscript><Superscript>*</Superscript></Stack> integral for a three-dimensional crack front

TheT _ε ^* integral was calculated on the surface of single edge notched, three-point bend (SE(B)) specimens using experimentally obtained displacements. Comparison was made withT _ε ^* calculated with the measured surface displacements andT _ε ^* calculated at several points through the thickness of a finite element (FE) model of the SE(B) specimen. Good comparison was found between the surfaceT _ε ^* calculated from displacements extracted from the FE model and the surfaceT _ε ^* calculated from experimentally obtained displacements. The computedT _ε ^* integral was also observed to decrease as the crack front was traversed from the surface to the mid-plane of the specimen. Mid-planeT _ε ^* values tend to be approximately 10% of the surface values.     

Inequalities relating to Lp-version of Petty＇s conjectured projection inequality

Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty＇s conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.     

Three-Dimensional Simulation of Turbulent Hot-Jet Ignition for Air-CH<Subscript>4</Subscript>-H<Subscript>2</Subscript> Deflagration in a Confined Volume

This work describes essential aspects of the ignition and deflagration process initiated by the injection of a hot transient gas jet into a narrowly confined volume containing air-CH₄-H₂ mixture. Driven by the pressure difference between a prechamber and a long narrow constant-volume-combustion (CVC) chamber, the developing jet or puff involves complex processes of turbulent jet penetration and evolution of multi-scale vortices in the shear layer, jet tip, and adjacent confined spaces. The CVC chamber contains stoichiometric mixtures of air with gaseous fuel initially at atmospheric conditions. Fuel reactivity is varied using two different CH₄/H₂ blends. Jet momentum is varied using different pre-chamber pressures at jet initiation. The jet initiation and the subsequent ignition events generate pressure waves that interact with the mixing region and the propagating flame, depositing baroclinic vorticity. Transient three-dimensional flow simulations with detailed chemical kinetics are used to model CVC mixture ignition. Pre-ignition gas properties are then examined to develop and verify criteria to predict ignition delay time using lower-cost non-reacting flow simulations for this particular case of study.     

CFD studies on natural convection heat transfer of Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-water nanofluids

This work is focused on numerical simulations of natural convection heat transfer in Al₂O₃-water nanofluids using computational fluid dynamics approach. Fluent v6.3 is used to simulate water based nanofluid considering it as a single phase. Thermo-physical properties of the nanofluids are considered in terms of volume fraction and size of nanoparticles, size of base fluid molecule and temperature. The numerical values of effective thermal conductivity have also been compared with the experimental values available in the literature. The numerical result simulated shows decrease in heat transfer with increase in particle volume fraction. Computed result shows similar trend in increase of Nusselt number with Relayigh number as depicted by experimental results. Streamlines and temperature profiles are plotted to demonstrate the effect.     

Effect of Vertical Heterogeneity on Long-Term Migration of CO<Subscript>2</Subscript> in Saline Formations

For deep injection of CO₂ in thick saline formations, the movements of both the free gas phase and dissolved CO₂ are sensitive to variations in vertical permeability. A simple model for vertical heterogeneity was studied, consisting of a random distribution of horizontal impermeable barriers with a given overall volume fraction and distribution of lengths. Analytical results were obtained for the distribution of values for the permeability, and compared to numerical simulations of deep CO₂ injection and convection in heterogeneous formations, using multiple realizations for the permeability distribution. It is shown that for a formation of thickness H, the breakthrough times in two dimensions for deep injection scale as H ² for moderate injection rates. In comparison to heterogeneous shale distributions, a homogeneous medium with equivalent effective vertical permeability has a longer breakthrough time for deep injection, and a longer onset time for convection.