Large-eddy simulation of turbulent collision of heavy particles in isotropic turbulence

The small-scale motions relevant to the collision of heavy particles represent a general challenge to the conventional large-eddy simulation (LES) of turbulent particle-laden flows. As a first step toward addressing this challenge, we examine the capability of the LES method with an eddy viscosity subgrid scale (SGS) model to predict the collision-related statistics such as the particle radial distribution function at contact, the radial relative velocity at contact, and the collision rate for a wide range of particle Stokes numbers. Data from direct numerical simulation (DNS) are used as a benchmark to evaluate the LES using both a priori and a posteriori tests. It is shown that, without the SGS motions, LES cannot accurately predict the particle-pair statistics for heavy particles with small and intermediate Stokes numbers, and a large relative error in collision rate up to 60% may arise when the particle Stokes number is near St_K=0.5. The errors from the filtering operation and the SGS model are evaluated separately using the filtered-DNS (FDNS) and LES flow fields. The errors increase with the filter width and have nonmonotonic variations with the particle Stokes numbers. It is concluded that the error due to filtering dominates the overall error in LES for most particle Stokes numbers. It is found that the overall collision rate can be reasonably predicted by both FDNS and LES for St_K>3. Our analysis suggests that, for St_K<3, a particle SGS model must include the effects of SGS motions on the turbulent collision of heavy particles. The spectral analysis of the concentration fields of the particles with different Stokes numbers further demonstrates the important effects of the small-scale motions on the preferential concentration of the particles with small Stokes numbers.

Subgrid scale fluid velocity timescales seen by inertial particles in large-eddy simulation of particle-laden turbulence

Large-eddy simulation (LES) has emerged as a promising tool for simulating turbulent flows in general and, in recent years,has also been applied to the particle-laden turbulence with some success (Kassinos et al., 2007). The motion of inertial particles is much more complicated than fluid elements, and therefore, LES of turbulent flow laden with inertial particles encounters new challenges. In the conventional LES, only large-scale eddies are explicitly resolved and the effects of unresolved, small or subgrid scale (SGS) eddies on the large-scale eddies are modeled. The SGS turbulent flow field is not available. The effects of SGS turbulent velocity field on particle motion have been studied by Wang and Squires (1996), Armenio et al. (1999), Yamamoto et al. (2001), Shotorban and Mashayek (2006a,b), Fede and Simonin (2006), Berrouk et al. (2007), Bini and Jones (2008), and Pozorski and Apte (2009), amongst others. One contemporary method to include the effects of SGS eddies on inertial particle motions is to introduce a stochastic differential equation (SDE), that is, a Langevin stochastic equation to model the SGS fluid velocity seen by inertial particles (Fede et al., 2006; Shotorban and Mashayek, 2006a; Shotorban and Mashayek, 2006b; Berrouk et al., 2007; Bini and Jones, 2008; Pozorski and Apte, 2009).However, the accuracy of such a Langevin equation model depends primarily on the prescription of the SGS fluid velocity autocorrelation time seen by an inertial particle or the inertial particle–SGS eddy interaction timescale (denoted by $\delt T_{Lp}$ and a second model constant in the diffusion term which controls the intensity of the random force received by an inertial particle (denoted by C_0, see Eq. (7)). From the theoretical point of view, dTLp differs significantly from the Lagrangian fluid velocity correlation time (Reeks, 1977; Wang and Stock, 1993), and this carries the essential nonlinearity in the statistical modeling of particle motion. dTLp and C0 may depend on the filter width and particle Stokes number even for a given turbulent flow. In previous studies, dTLp is modeled either by the fluid SGS Lagrangian timescale (Fede et al., 2006; Shotorban and Mashayek, 2006b; Pozorski and Apte, 2009; Bini and Jones, 2008) or by a simple extension of the timescale obtained from the full flow field (Berrouk et al., 2007). In this work, we shall study the subtle and on-monotonic dependence of $\delt T_{Lp}$ on the filter width and particle Stokes number using a flow field obtained from Direct Numerical Simulation (DNS). We then propose an empirical closure model for $\delta T_{Lp}$. Finally, the model is validated against LES of particle-laden turbulence in predicting single-particle statistics such as particle kinetic energy. As a first step, we consider the particle motion under the one-way coupling assumption in isotropic turbulent flow and neglect the gravitational settling effect. The one-way coupling assumption is only valid for low particle mass loading.

A Simple Model For Predicting The Void Fraction Of Gas/Non-Newtonian Fluid Intermittent Flows In Upward Inclined Pipes

In this work, a simple correlation, which incorporates the mixture velocity, drift velocity, and the correction factor of Farooqi and Richardson, was proposed to predict the void fraction of gas/non-Newtonian intermittent flow in upward inclined pipes. The correlation was based on 352 data points covering a wide range of flow rates for different CMC solutions at diverse angles. A good agreement was obtained between the predicted and experimental results. These results substantiated the general validity of the model presented for gas/non-Newtonian two-phase intermittent flows.

Simulations of thermal upgrading methods for oil shale reservoirs

This paper analyzes reaction and thermal front development in porous reservoirs with reacting flows, such as those encountered in shale oil extraction. A set of dimensionless parameters and a 3D code are developed in order to investigate the important physical and chemical variables of such reservoirs when heated by in situ methods. This contribution builds on a 1D model developed for the precursor study to this work. Theory necessary for this study is presented, namely shale decomposition chemical mechanisms, governing equations for multiphase flow in porous media and necessary closure models. Plotting the ratio of the thermal wave speed to the fluid speed allows one to infer that the reaction wave front ends where this ratio is at a minimum. The reaction front follows the thermal front closely, thus allowing assumptions to be made about the extent of decomposition solely by looking at thermal wave progression. Furthermore, this sensitivity analysis showed that a certain minimum permeability is required in order to ensure the formation of a traveling thermal wave. It was found that by studying the non-dimensional governing parameters of the system one can ascribe characteristic values for these parameters for given initial and boundary conditions. This allows one to roughly predict the performance of a particular method on a particular reservoir given approximate values for initial and boundary conditions. Channelling and flow blockage due to carbon residue buildup impeded each method's performance. Blockage was found to be a result of imbalanced heating. Copyright 2012, Society of Petroleum Engineers.

海底沉积层中水合物成藏过程模拟

水合物成藏是一种动态演变过程，从生成和分解速度相对大小角度提出了天然气水合物的动态成藏理论；分析指出天然气水合物储层状态主要存在三种类型：成长型（包括渗透型与扩散型）、成熟型和消退型，必须结合经济型指标对这三种类型水合物藏进行开采可行性研究。 通过在自制的透明鼓泡反应釜内模拟气体迁移与水合物形成实验，解释了气体迁移对体系内传热与传质、溶解性质、过压等的影响因，进一步指出需要研究新的水合物相图。 从传热角度建立了水合物生长模型，计算并比较了南海北部陆坡琼东南盆地里甲烷水合物在渗漏系统和扩散系统下的生长速度，指出前者比后者快约20-40倍。 建立了水-气（游离气）-水合物-盐反应的多相流模型，演绎了在四个不同时刻随着水合物的形成，溶解度、渗透率、毛细压力、饱和度及盐度等的联动演变关系，并分析和比较了在沉积层水合物稳定区域内不同游离气饱和度和甲烷渗漏通量情况下水合物的形成过程和三种成藏类别。 反演了神狐海域水合物的形成，指出该区很可能是属于发育阶段的成长型渗漏系统水合物储藏，按照甲烷渗漏通量为0.5kg/m2·a计算，该地区已演化了约4800a，还需要约2700ka孔隙中水合物可到最大体积饱和度，达约75%，并在此后游离气将溢出沉积层进入海水中；计算得最终的甲烷水合物储量约为1.47×109m3，即该区最终将储存着约2200亿立方米甲烷气，是现在预测的约13倍！

The methane hydrate formation and the resource estimate resulting from free gas migration in seeping seafloor hydrate stability zone

It is a typical multiphase flow process for hydrate formation in seeping seafloor sediments. Free gas can not only be present but also take part in formation of hydrate. The volume fraction of free gas in local pore of hydrate stable zone (HSZ) influences the formation of hydrate in seeping seafloor area, and methane flux determines the abundance and resource of hydrate-bearing reservoirs. In this paper, a multiphase flow model including water (dissolved methane and salt)-free gas hydrate has been established to describe this kind of flow-transfer-reaction process where there exists a large scale of free gas migration and transform in seafloor pore. In the order of three different scenarios, the conversions among permeability, capillary pressure, phase saturations and salinity along with the formation of hydrate have been deducted. Furthermore, the influence of four sorts of free gas saturations and three classes of methane fluxes on hydrate formation and the resource has also been analyzed and compared. Based on the rules drawn from the simulation, and combined information gotten from drills in field, the methane hydrate(MH) formation in Shenhu area of South China Sea has been forecasted. It has been speculated that there may breed a moderate methane flux below this seafloor HSZ. If the flux is about 0.5 kg m-2 a-1, then it will go on to evolve about 2700 ka until the hydrate saturation in pore will arrive its peak (about 75%). Approximately 1.47 109 m3 MH has been reckoned in this marine basin finally, is about 13 times over preliminary estimate.

Pool boiling heat transfer of ultra-light copper foam with open cells

High speed visualizations and thermal performance studies of pool boiling heat transfer on copper foam covers were performed at atmospheric pressure, with the heating surface area of 12.0 mm by 12.0 mm, using acetone as the working fluid. The foam covers have ppi (pores per inch) from 30 to 90, cover thickness from 2.0 to 5.0 mm, and porosity of 0.88 and 0.95. The surface superheats are from -20 to 190 K, and the heat fluxes reach 140 W/cm(2). The 30 and 60 ppi foam covers show the periodic single bubble generation and departure pattern at low surface superheats. With continuous increases in surface superheats, they show the periodic bubble coalescence and/or re-coalescence pattern. Cage bubbles were observed to be those with liquid filled inside and vented to the pool liquid. For the 90 ppi foam covers, the bubble coalescence takes place at low surface superheats. At moderate or large surface superheats, vapor fragments continuously escape to the pool liquid. Boiling curves of copper foams show three distinct regions. Region I and II are those of natural convection heat transfer, and nucleate boiling heat transfer for all the foam covers. Region III is that of either a resistance to vapor release for the 30 and 60 ppi foam covers, or a capillary-assist liquid flow towards foam cells for the 90 ppi foam covers. The value of ppi has an important effect on the thermal performance. Boiling curves are crossed between the high and low ppi foam covers. Low ppi foams have better thermal performance at low surface superheats, but high ppi foams have better one at moderate or large surface superheats and extend the operation range of surface superheats. The effects of other factors such as pool liquid temperature, foam cover thickness on the thermal performance are also discussed.

Pool Boiling on Wire in Microgravity - What Have We Learned

In the past years, steady pool boiling of degassed R113 on thin platinum wires has been studied systematically in our lab, including experiments in long-term microgravity aboard RS-22, in short-term microgravity in the Drop Tower Beijing / NMLC, and in normal gravity on the ground. Slight enhancement of nucleate boiling heat transfer is observed in microgravity, while dramatic changes of bubble behaviors are much evident. The value of CHF in microgravity is lower than that in normal gravity, but it can be predicted well by the Lienhard-Dhir correlation, although the dimensionless radius in the present case is far beyond its initial application range. The scaling of CHF with gravity is thus much different from the traditional viewpoint. Considering the influence of the Marangoni effects, the different characteristics of bubble behaviors in microgravity have been explained. A new bubble departure model has also been proposed, which can predict the whole observation both in microgravity and in normal gravity.

二氧化碳在孔隙咸水层中多相流动数值模拟研究

There has been a growing concern about the use of fossil fuels and its adverse effects on the atmospheric greenhouse and ecological environment. A reduction in the release rate of CO2 into the atmosphere poses a major challenge to the land ecology of China. The most promising way of achieving CO2 reduction is to dispose of CO2 in deep saline aquifers. Deep aquifers have a large potential for CO2 sequestration in geological medium in terms of volume and duration. Through the numerical simulation of multiphase flow in a porous media, the transformation and motion of CO2 in saline aquifers has been implemented under various temperature and hydrostatic pressure conditions, which plays an important role to the assessment of the reliability and safety of CO2 geological storage. As expected, the calculated results can provide meaningful and scientific information for management purposes. The key problem to the numerical simulation of multiphase flow in a porous media is to accurately capture the mass interface and to deal with the geological heterogeneity. In this study, the updated CE/SE (Space and time conservation element and solution element) method has been proposed, and the Hybrid Particle Level Set method (HPLS) has extended for multiphase flows in porous medium, which can accurately trace the transformation of the mass interface. The benchmark problems have been applied to evaluate and validate the proposed method. In this study, the reliability of CO2 storage in saline aquifers in Daqingzi oil field in Sunlong basin has been discussed. The simulation code developed in this study takes into account the state for CO2 covering the triple point temperature and pressure to the supercritical region. The geological heterogeneity has been implemented, using the well known geostatistical model (GSLIB) on the base of the hard data. The 2D and 3D model have been set up to simulate the CO2 multiphase flow in the porous saline aquifer, applying the CE/SE method and the HPLS method .The main contents and results are summarized as followings. (1) The 2D CE/SE method with first and second –order accuracy has been extended to simulate the multiphase flow in porous medium, which takes into account the contribution of source and sink in the momentum equation. The 3D CE/SE method with the first accuracy has been deduced. The accuracy and efficiency of the proposed CE/SE method have been investigated, using the benchmark problems. (2) The hybrid particle level set method has been made appropriate and extended for capturing the mass interface of multiphase flows in porous media, and the numerical method for level set function calculated has been formulated. (3) The closed equations for multiphase flow in porous medium has been developed, adept to both the Darcy flow and non-Darcy flow, getting over the limitation of Reynolds number to the calculation. It is found that Darcy number has a decisive influence on pressure as well as velocity given the Darcy number. (4) The new Euler scheme for numerical simulations of multiphase flows in porous medium has been proposed, which is efficient and can accurately capture the mass interface. The artificial compressibility method has been used to couple the velocities and pressure. It is found that the Darcy number has determinant effects on the numerical convergence and stability. In terms of the different Darcy numbers, the coefficient of artificial compressibility and the time step have been obtained. (5) The time scale of the critical instability for critical CO2 in the saline aquifer has been found, which is comparable with that of completely CO2 dissolved saline aquifer. (6) The concept model for CO2 multiphase flows in the saline aquifer has been configured, based on the temperature, pressure, porosity as well as permeability of the field site .Numerical simulation of CO2 hydrodynamic trapping in saline aquifers has been performed, applying the proposed CE/SE method. The state for CO2 has been employed to take into account realistic reservoir conditions for CO2 geological sequestration. The geological heterogeneity has been sufficiently treated , using the geostatistical model. (7) It is found that the Rayleigh-Taylor instability phenomenon, which is associated with the penetration of saline fluid into CO2 fluid in the direction of gravity, has been observed in CO2 multiphase flows in the saline aquifer. Development of a mushroom-type spike is a strong indication of the formation of Kelvin-Helmholtz instability due to the developed short wavelength perturbations present along the interface and parallel to the bulk flow. Additional key findings: the geological heterogeneity can distort the flow convection. The ascending of CO2 can induce the persistent flow cycling effects. The results show that boundary conditions of the field site have determinant effects on the transformation and motion of CO2 in saline aquifers. It is confirmed that the proposed method and numerical model has the reliability to simulate the process of the hydrodynamic trapping, which is the controlling mechanism for the initial period of CO2 storage at time scale of 100 years.

Simulador de escoamento multifásico em poços de petróleo (SEMPP)

The multiphase flow occurrence in the oil and gas industry is common throughout fluid path, production, transportation and refining. The multiphase flow is defined as flow simultaneously composed of two or more phases with different properties and immiscible. An important computational tool for the design, planning and optimization production systems is multiphase flow simulation in pipelines and porous media, usually made by multiphase flow commercial simulators. The main purpose of the multiphase flow simulators is predicting pressure and temperature at any point at the production system. This work proposes the development of a multiphase flow simulator able to predict the dynamic pressure and temperature gradient in vertical, directional and horizontal wells. The prediction of pressure and temperature profiles was made by numerical integration using marching algorithm with empirical correlations and mechanistic model to predict pressure gradient. The development of this tool involved set of routines implemented through software programming Embarcadero C++ Builder® 2010 version, which allowed the creation of executable file compatible with Microsoft Windows® operating systems. The simulator validation was conduct by computational experiments and comparison the results with the PIPESIM®. In general, the developed simulator achieved excellent results compared with those obtained by PIPESIM and can be used as a tool to assist production systems development