Onset of instability in CO2 sequestration into saline aquifer: scaling relationship and the effect of perturbed boundary

Storage and disposal of greenhouse gases in saline aquifers is an important solution for reduction of these gases from atmosphere. Understanding the concepts and mechanisms involved in the storage process, especially natural convection and their impact on long-term fate of injected CO₂ are essential. Natural convection is an effective mechanism which increases solubility of carbon dioxide in the storage process. In this work, injection of carbon dioxide into aquifer is numerically simulated. First, numerical criteria are developed to provide numerical accuracy and stability by mesh resolution. Then, changes in input wave number in surface perturbation and order of element used in finite element method were analyzed. It was found that depending on Rayleigh number, there is a wave number at which instability occurs earlier and grows faster. Also, onset of CO₂ convective mixing in saline aquifers was obtained and correlated for a number of field cases. Results show that onset of convection can be approximated by a scaling relationship for dimensionless time as a function of inverse square of Rayleigh number, Ra ^?2, for Rayleigh range used in this work. This scaling relationship provides a predictive tool for onset of convection and also long-term fate of disposed CO₂ in large scale geological sequestration.     

Effect of flow conditions on the amplification and generation of pulsed gasdynamic lasers in N2O and CO2

The weak signal amplification is studied in jets involving N₂O-N₂He, N₂O-N₂ and CO₂-CO-N₂-He mixtures with installations combining a shock-tube and slit-throat (1.5×40 and 2.5×70 mm²) or two-dimensional wedge (=15°, A/A _* = 15) nozzles. The relationships between amplification and gasdynamic characteristics are elucidated.     

Numerical investigation of the spray-mesh-turbulence interactions for high-pressure, evaporating sprays at engine conditions

This work presents a numerical methodology to simulate evaporating, high pressure Diesel sprays using the Eulerian-Lagrangian approach. Specific sub-models were developed to describe the liquid spray injection and breakup, and the influence of the liquid jet on the turbulence viscosity in the vicinity of the nozzle. To reduce the computational time and easily solve the problem of the grid dependency, the possibility to dynamically refine the grid where the fuel-air mixing process takes place was also included.The validity of the proposed approach was firstly verified simulating an evaporating spray in a constant-volume vessel at non-reacting conditions. The availability of a large quantity of experimental data allowed us to investigate in detail the effects of grid size, ambient diffusivity and used spray sub-models. In this way, different guidelines were derived for a successful simulation of the fuel-air mixture formation process. Finally, fuel injection and evaporation were simulated in an optical engine geometry and computed mixture fraction distributions were compared with experimental data.     

Measurement of the turbulent diffusivity in the near field of variable density jets using conditional velocimetry

Pulsed laser Mie scattering and laser Doppler velocimetry (LDV), both conditioned on the origin of the seed particles, have been successively performed in turbulent jets with variable density. In the early stages of the jet developments, significant differences are measured between the ensemble average LDV data obtained by jet seeding and those obtained by seeding the ambient air. Careful analysis of the marker statistics shows that this difference is a quantitative measure of the turbulent mixing. The good agreement with gradient–diffusion modelling suggests the validity of a general diffusion equation where the velocities involved are expressed in terms of ensemble conditional Favre averages. This operator accounts for all events (including intermittent ones) and for variations in the density of the marked fluid whose velocity is still specified by the binary origin of the marker.List of symbols D_L laminar diffusivity, m²/s - D_T turbulent diffusivity, m²/s - d diameter of the jet nozzle, m - F_r Froude number - J diffusion vector, m/s - k global sensitivity of the detection system for one particle (signal level) - N_P number of seed particles in the probe volume - N_P,i number of seed particles in sample i - N_P⁽ⁱ⁾ value of N_P in channel i - N_B number of Doppler bursts - count rate of bursts, s^–1 - N_v number of validated Doppler bursts - count rate of validated bursts, s^–1 - N_id number of ideal particles - N_id* number of marked ideal particles - P* probability that an ideal particle be marked by a seed particle - P(z) probability density function for z, m³/kg - probability to have k seed particles in the probe volume - probability of having k seed particle conditioned on a given value of z - r radial coordinate, m - R =⁽¹⁾/⁽²⁾, density ratio - S₁ local signal level with jet seeding - S₁⁽¹⁾ reference signal level in pure stream 1 with jet seeding - s₁ = S_1/S₁⁽¹⁾, normalized signal - v_c volumic capacity of the probe volume, m³ - V velocity vector, m/s - V_x axial velocity component, m/s - V_r radial velocity component, m/s - V_P particulate velocity vector, m/s - V_Pj velocity vector of particle j, m/s - V_Pij velocity vector of the jth particle in sample i, m/s - V_i velocity vector of the marked flow for realization i, m/s - V_1,i velocity vector of the flow such it is marked in realization i by particles issuing only from stream 1, m/s - x axial coordinate, m - Y_i local mass fraction of species i - Z mixture fraction:local mass fraction of jet fluid - Z_i mixture fraction for realization iGreek local density, kg/m³ - _i local density for realization i, kg/m³ - ⁽¹⁾ density in stream 1 (density of the jet fluid), kg/m³ - ₁ time of flight of jet seed particles to reach the probe volume, s - _B duration of a Doppler burst, sAverages <A> ensemble average of A - Ā time average of A - Favre average, , ( ) the present notation is only due to printing problems - A Favre fluctuation,      

Necessary conditions for the existence of positive solutions of second-order linear difference equations and sufficient conditions for the oscillation of solutions

We consider the difference equation

Dependence of particle size on the effective thermal diffusivity and conductivity of nanofluids: role of base fluid properties

Effect of nanoparticle size on effective thermal diffusivity and conductivity of polymeric and water based nanofluids are investigated following thermal wave interference technique. Two sets of nanofluids, prepared by dispersing TiO₂ nanoparticles, with average sizes in the range 5–100?nm, in polyvinyl alcohol and water show opposing particle size dependences. Variations are explained invoking effective medium theory, including size of nanoparticles, molecular weight of base fluid and effects associated with it.     

Measurement of the probability of the transition P20 (00 °1–10 °0) in CO2 and impact broadening in collisions with CO2, N2, and He

We measured the dependence of the absorption, coefficient on the pressure for the vibrational-rotational transition P20 (00 °1–10 °0) in CO₂ using a CO₂ laser as a light source. We consider the question of the systematic error due to the contribution of impact broadening, when finding the probability from the experimental absorption. The refined value of the transition probability A _{10 °0.20} ^{00 °1.19} =0.169 sec^–1. We obtain the values of the impact half-widths for collisions of the type CO₂-CO₂, CO₂-N₂, CO₂-He, the values of which at J=300 °K are respectively 3.28, 2.74, and 2.27 MHz/torr.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 24–28, November–December, 1972.The authors thank A. K. Konyukhov for interest in the work and for valuable discussions.     

CH4/N2、CH4/CO2二元和CH4/N2/CO2三元混合气体爆炸极限的实验与估算

为了获取甲烷与不可燃组分组成的混合物的爆炸极限,采用一种基于绝热火焰温度的混合物爆炸极限估算方法,对CH₄/N₂和CH₄/CO₂这2种二元混合气体及3种不同阻燃剂体积分数的CH₄/N₂/CO₂三元混合气体的爆炸极限进行实验研究,并将实验结果与估算值进行比较。CH₄/N₂与CH₄/CO₂二元混合物实验值与估算值在爆炸上限处的平均绝对偏差为0.34%,在爆炸下限处的平均绝对偏差为0.15%。3种不同比例的三元混合物实验值与估算值在爆炸上限处的平均绝对偏差为0.43%,在爆炸下限处的平均绝对偏差为0.20%。结果表明,估算方法对甲烷与不可燃组分的二元混合物与三元混合物爆炸极限的估算均具有较高的准确度。     

Viscosity enhancement in the flow of hydrolysed poly(acrylamide) saline solutions around spheres: implications for enhanced oil recovery

We have studied dilute aqueous solutions of hydrolysed poly(acrylamide), in various ionic environments, in flow around single spheres and around two spheres aligned on the axis of flow. The spheres are held on flexible cantilevers, while the polymer solutions, or solvent, are drawn past at controlled flow rates. We estimate the specific viscosities of the various solutions as a function of the strain rate over strain rates encompassing both the shear thinning and extension thickening regimes. For flow of solutions without added salts around a single sphere, we observe shear thinning followed by a significant increase in the non-Newtonian viscosity with increasing strain rate. The shear thinning reduces the maximal extensional viscosities of the solutions, which has important implications regarding the effectiveness of hydrolysed poly(acrylamide) in oil field applications. For flow of polymer solutions around two axially aligned spheres, we observe a significant reduction in the non-Newtonian forces experienced by the downstream sphere in comparison to the upstream sphere. We consider that this is salient to the understanding of non-Newtonian viscosification in porous media flow.     

The role of particle interactions in the rheology of dispersed systems

Summary Certain aspects of the rheological behaviour of dispersions cannot be understood unless attractive forces between the particles are assumed, resulting in the building-up of a network structure.A network model is postulated in which the particles are arranged in chains. During deformation these chains are stretched resulting in breakage of bonds between the particles. In this process and especially in what happens after that, an important question is whether the relative motion of a single particle with respect to the surrounding network is noticeable to only a few particles in the immediate vicinity or to a large number of particles over relatively large distances. The necessary information about the changing network structure during a large deformation at constant shear rate was derived from dielectric measurements in the case of water in oil emulsions and from super-imposed oscillatory shear experiments in the case of fat crystal dispersions.It is shown that the rheologieal behaviour of the water in oil emulsions may be characterized by motion of single particles, whereas in the fat-dispersions in oil collective displacements of large numbers of particles (aggregates) have to be taken into account.In the fat dispersions the magnitude of the forces acting in the network chains is explained in terms ofvan der Waals interaction. In the emulsions such forces determine the behaviour only at sufficiently low rates of shear. At higher shear rates the hydrodynamic interaction between single particles has to be taken into account.Among the quantities, which emerge from these network considerations is the characteristic time related with the motions of the particles or agglomerates. Therefore, time effects in dispersed systems are discussed more extensively.

---

Zusammenfassung Bestimmte Aspekte des rheologischen Verhaltens von Dispersionen lassen sich nur unter der Voraussetzung von Anziehungskräften zwischen den Teilchen, die zur Bildung einer Netzwerkstruktur führen, erklären.Es wird ein Netzwerkmodell postuliert, in welchem die Teilchen kettenförmig angeordnet sind. Während der Deformation werden diese Ketten gedehnt, was zum Bruch der Bindungen zwischen den Teilchen führt. In bezug auf diesen Vorgang und besonders auf das, was nachher geschieht, erhebt sich die wichtige Frage, ob die relative Bewegung eines einzelnen Teilchens sich hinsichtlich des umgebenden Netzwerks nur auf einige benachbarte Teilchen auswirkt oder sich auf eine größere Anzahl weiter entfernter Teilchen erstreckt. Die benötigte Information über die Änderungen der Netzwerkstruktur während größerer Deformationen bei konstanter Schergeschwindigkeit wurde an Hand von dielektrischen Messungen für Wasser-in-Öl-Emulsionen und im Falle von Fettkristalldispersionen mit Hilfe von Versuchen mit überlagerter oszillierender Scherung ermittelt. Es zeigt sich, daß das rheologische Verhalten von Wasser-in-Öl-Emulsionen sich durch die Bewegung einzelner Teilchen charakterisieren läßt, während bei Dispersionen in Öl kollektive Bewegungen einer größeren Zahl von Teilchen (Aggregaten) berücksichtigt werden müssen. In den Fettdispersionen wird die Größe der in den Ketten des Netzwerkes ausgeübten Kräfte durchvan derWaalssche Wechselwirkungen erklärt. In den Emulsionen bestimmen derartige Kräfte das Verhalten nur bei genügend niedrigen Schergeschwindigkeiten. Bei höheren Schergeschwindigkeiten ist mit einer hydrodynamischen Wechselwirkung zwischen den einzelnen Teilchen zu rechnen.Unter den Größen, die sich aus diesen Betrachtungen der Netzwerkstruktur ableiten lassen, ist die mit den Bewegungen der Teilchen oder Agglomerate verbundene charakteristische Zeit. Aus diesem Grunde werden die Zeiteffekte in dispersen Systemen ausführlich besprochen.

---

     

The role of resonant interactions in the dynamic stability of elastic systems

A resonance phenomenon which can occur in elastic systems supporting wave motion is discussed. An analytical and numerical study of the dynamic stability of a cylindrical shell under axial compression illustrates the potential importance of this resonance phenomenon for imperfection-sensitive structures.     

Measurement of pressure loss in the flow of polymer solutions through wavy channels

In order to examine the flow behavior of polymer solutions through porous media, the measurement of pressure loss and the experiment for flow visualization were carried out with wavy channels as one of the model channels of porous media. The test fluids used are aqueous solutions of polyacrylamide (PAA) with two different concentrations. The occurrence of the excess pressure loss, which was not due to the effect of the centrifugal force, was found for the PAA solutions. The relations between the friction factor ratio and the Deborah number were similar to that obtained for the flow through porous media. Furthermore, the results of the flow visualization suggest that the elongational property of the PAA solutions is connected with the occurrence of the excess pressure loss.     

The role of boundary conditions in the instability of one-dimensional systems

We investigate the instability properties of one-dimensional systems of finite length that can be described by a local wave equation and a set of boundary conditions. A method to quantify the respective contributions of the local instability and of wave reflections in the global instability is proposed. This allows to differentiate instabilities that emanate from wave propagation from instabilities due to wave reflections. This is illustrated on three different systems, that exhibit three different behaviors. The first one is a model system in fluid mechanics (Ginzburg–Landau equation), the second one is the fluid-conveying pipe (Bourrières equation), the third one is the fluid-conveying pipe resting on an elastic foundation (Roth equation).     

Singularity solutions for ellipsoids in low-Reynolds-number flows: With applications to the calculation of hydrodynamic interactions in suspensions of ellipsoids

The disturbance velocity fields due to translational and rotational motions of an ellipsoid in a uniform stream. constant vorticity and constant rate-of-strain. required in fundamental studies of behavior of suspensions. have been obtained by the singularity method. These solutions extend earlier solutions for prolate spheroids. Although equivalent solutions problems were obtained by Oberbeck. Edwardes and Jeffery by separation of variables in ellipsoidal coordinates. the singularity solutions are far more simple in form. Other significant results obtained by the singularity method include the exposition of the unified structure shared by the three boundary value problems and the construction of new forms of the Faxen laws for ellipsoids through application of the reciprocal theorem. The disturbance solutions and Faxen laws. the basis for Smoluchowski's method-of-reflections technique. are used to calculate hydrodynamic interactions between two or more arbitrarily oriented ellipsoids. In particular. mobility problems are solved directly to orderR⁻⁵. whereR is the centroid-to-centroid separation between the ellipsoids.     

Examples of the simplest boundary conditions for electron and ion concentrations and electron and heavy-particle temperatures

Examples of boundary conditions in certain particular cases are considered. The conditions proposed in [1, 2] can be used for any plasma component The boundary conditions for the same wall will generally be distinct for each of the components.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 169–172, November–December, 1976.