Growing Plants in Space: Manipulating Medium Wettability to Create Different Saturation Conditions

Growing plants under microgravity conditions in a space ship is essential for future long-term missions to supply needs for food and oxygen. Although plant growth modules for microgravity have been developed and tested for more than 40 years, creating optimal saturation conditions for plant growth in the absence of gravity still remains a challenge. In this study, we present results from a series of spontaneous imbibition experiments designed to approximate microgravity conditions by using density-matched fluid pairs. Porous media with patterned wettability characteristics are used to manipulate macroscopic fluid saturation and microscopic fluid interfacial configurations. These are compared to an additional experiment under Earth gravity, wherein we observe spontaneous imbibition of water into common potting soil. Patterning grains of different wettabilities under microgravity conditions proves to be an effective method to manipulate spatial distributions and saturations of fluids. These wettability patterns can be optimised to fine-tune residual fluid characteristics, e.g. non-wetting phase saturation, connectivity and interfacial area. Furthermore, we present tomographic evidence supporting previous work which was suggesting enhanced snap-off and disconnection of the gas phase in porous media under microgravity.

     

Saturated Elastic Porous Solids: Incompressible,Compressible and Hybrid Binary Models

Constitutive models for a general binary elastic-porous media are investigated by two complementary approaches. These models include both constituents treated as compressible/incompressible, a compressible solid phase with an incompressible fluid phase (hybrid model of first type), and an incompressible solid phase with a compressible fluid phase (hybrid model of second type). The macroscopic continuum mechanical approach uses evaluation of entropy inequality with the saturation condition always considered as a constraint. This constraint leads to an interface pressure acting in both constituents. Two constitutive equations for the interface pressure, one for each phase, are identified, thus closing the set of field equations. The micromechanical approach shows that the results of Didwania and de Boer can be easily extended to general binary porous media.     

Smoothed Particle Hydrodynamics Model of Non-Aqueous Phase Liquid Flow and Dissolution

A smoothed particle hydrodynamics model was developed to simulate the flow of mixtures of aqueous and non-aqueous phase liquids in porous media and the dissolution of the non-aqueous phase in the aqueous phase. The model was used to study the effects of pore-scale heterogeneity and anisotropy on the steady state dense non-aqueous phase liquid (DNAPL) saturation when gravity driven DNAPL displaces water from initially water saturated porous media. Pore-scale anisotropy was created by using co-oriented non-overlapping elliptically shaped grains to represent the porous media. After a steady state DNAPL saturation was reached, water was injected until a new steady state DNAPL saturation was reached. The amount of trapped DNAPL was found to be greater when DNAPL is displaced in the direction of the major axes of the soil grains than when it is displaced in the direction of the minor axes of the soil grains. The amount of trapped DNAPL was also found to increase with decreasing initial saturation of the continuous DNAPL phase. For the conditions used in our simulations, the saturation of the trapped DNAPL with a smaller initial DNAPL saturation was more than 3 times larger than the amount of trapped DNAPL with a larger initial saturation. These simulations were carried out assuming that the DNAPL did not dissolve in water. Simulations including the effect of dissolution of DNAPL in the aqueous phase were also performed, and effective (macroscopic) mass transfer coefficients were determined. The U.S. Government’s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

About macroscopic models of instability pattern formation

Various macroscopic models to describe instability pattern formation are discussed in this paper. They are similar to the Ginzburg–Landau envelope equation, but they can remain valid away from the bifurcation and are based on the technique of Fourier series with slowly varying coefficients. We focus on two questions: the need to take phase changes into account and the boundary conditions to be associated with macroscopic models. The analysis is carried out on the basis of numerical simulations for the problem of a compressed beam on a nonlinear foundation that is quite similar to the well known Swift–Hohenberg equation. The first macroscopic model involves a real envelope so that the phase is assumed to be constant. The second model is also macroscopic and it is a sort of Ginzburg–Landau equation with a complex envelope. The third one follows from a multi-scaled approach with a numerical bridging between the full model near the boundary and a macroscopic model in the bulk.     

三维编织复合材料模量的双尺度有限元计算

针对三维编织复合材料的力学性能进行了双尺度有限元(TSA)数值计算,给出了计算模型和算法过程,并将数值结果与文献中的实验数据进行了比较,验证了算法的物理准确性。编织复合材料的力学性能不仅依赖于材料的基本组份,也与细观构造相关。双尺度有限元计算可以数值模拟出三维编织复合材料的整体力学性能,从而为材料的研发提供指导。本文的双尺度有限元三维数值计算方法可以推广到其他增强／孔隙等多相复合材料的数值模拟。     

On consistent micromechanical estimation of macroscopic elastic energy,coherence energy and phase transformation strains for SMA materials

An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.     

Modeling Geometric State for Fluids in Porous Media: Evolution of the Euler Characteristic

Multiphase flow in porous media is strongly influenced by the pore-scale arrangement of fluids. Reservoir-scale constitutive relationships capture these effects in a phenomenological way, relying only on fluid saturation to characterize the macroscopic behavior. Working toward a more rigorous framework, we make use of the fact that the momentary state of such a system is uniquely characterized by the geometry of the pore-scale fluid distribution. We consider how fluids evolve as they undergo topological changes induced by pore-scale displacement events. Changes to the topology of an object are fundamentally discrete events. We describe how discontinuities arise, characterize the possible topological transformations and analyze the associated source terms based on geometric evolution equations. Geometric evolution is shown to be hierarchical in nature, with a topological source term that constrains how a structure can evolve with time. The challenge associated with predicting topological changes is addressed by constructing a universal geometric state function that predicts the possible states based on a non-dimensional relationship with two degrees of freedom. The approach is validated using fluid configurations from both capillary and viscous regimes in ten different porous media with porosity between 0.10 and 0.38. We show that the non-dimensional relationship is independent of both the material type and flow regime. We demonstrate that the state function can be used to predict history-dependent behavior associated with the evolution of the Euler characteristic during two-fluid flow.

     

冲击下宏观相边界的传播

研究了具有CdS型相变本构材料的宏观相边界传播规律。相边界包括纯新相和混合相两段。纯新相段可用逐步近似法,混合相段则必须用数值方法求解。给出了三种加卸载应力边界条件下的算例。在突加突卸的应力边界条件下,给出了相边界传播的解析解。在算例中,各种解法得到的结果彼此很好符合。     

Relative Permeability Analysis of Tube Bundle Models,Including Capillary Pressure

The analytical equations for calculating two-phase flow, including local capillary pressures, are developed for the bundle of parallel capillary tubes model. The flow equations that are derived were used to calculate dynamic immiscible displacements of oil by water under the constraint of a constant overall pressure drop across the tube bundle. Expressions for averaged fluid pressure gradients and total flow rates are developed, and relative permeabilities are calculated directly from the two-phase form of Darcy's law. The effects of pressure drop and viscosity ratio on the relative permeabilities are discussed. Capillary pressure as a function of water saturation was delineated for several cases and compared to a steady-state mercury-injection drainage type of capillary pressure profile. The bundle of serial tubes model (a model containing tubes whose diameters change randomly at periodic intervals along the direction of flow), including local Young-Laplace capillary pressures, was analyzed with respect to obtaining relative permeabilities and macroscopic capillary pressures. Relative permeabilities for the bundle of parallel tubes model were seen to be significantly affected by altering the overall pressure drop and the viscosity ratio; relative permeabilities for the bundle of serial tubes were seen to be relatively insensitive to viscosity ratio and pressure, and were consistently X-like in profile. This work also considers the standard Leverett (1941) type of capillary pressure versus saturation profile, where drainage of a wetting phase is completed in a step-wise steady fashion; it was delineated for both tube bundle models. Although the expected increase in capillary pressure at low wetting-phase saturation was produced, comparison of the primary-drainage capillary pressure curves with the pseudo-capillary pressure profiles, that are computed directly using the averaged pressures during the displacements, revealed inconsistencies between the two definitions of capillary pressure.     

On ferroelectric crystals with engineered domain configurations

This paper examines the engineered domain configurations and the macroscopic properties of ferroelectric crystals using an energy minimization theory. The energy minimizing domain configurations have been constructed, and their macroscopic properties have been calculated and compared well with experiments. The optimal domain configurations have also been identified.     

Stability of a stationary steam-water front in a porous medium

The instability of a plane front between two phases of the same fluid (steam and water) in a porous medium is considered. The configuration is taken to be initially stationary with the more dense phase overlying the less dense phase. The frontal region is assumed sharp, so that macroscopic boundary conditions can be utilized. This assumption precludes the existence of dispersion instabilities. The stabilizing influence of phrase transition as well as the implication of different macroscopic pressure boundary conditions on the stability of the front are discussed and illustrated.     

Two-phase boundary layer formation in a semi-infinite porous slab

Similarity profiles of pressure and saturation are analysed which result from one-dimensional planar withdrawal of fluid from a porous region initially containing a two phase mixture of steam and water. Approximate expressions are derived for the evolution of pressure and saturation profiles, and boundary-layer changes in saturation are identified. The existence of a similarity variable implies that the saturation conditions for the reservoir tend with time either to having both phases flowing; or to a single phase vapour. In particular, the nonlinear nature of the governing equations implies that infinitesimal changes in pressure can produce finite changes in saturation. The two mechanisms responsible for saturation changing with time involve local changes in energy storage in rock and fluid; together with spatial variations in flowing enthalpy. The latter mechanism occurred relatively slowly in the examples treated, and was responsible for boundary-layer formation when one phase was initially immobile. Dimensional analysis reveals that when a boundary layer develops, the underlying equations involve essentially only one dimensionless parameter which is typically small, being associated with the ratio of the energy density of the mobile phase relative to the total energy density.     

1D Simulations for Microbial Enhanced Oil Recovery with Metabolite Partitioning

We have developed a mathematical model describing the process of microbial enhanced oil recovery (MEOR). The one-dimensional isothermal model comprises displacement of oil by water containing bacteria and substrate for their feeding. The bacterial products are both bacteria and metabolites. In the context of MEOR modeling, a novel approach is partitioning of metabolites between the oil and the water phases. The partitioning is determined by a distribution coefficient. The transfer part of the metabolite to oil phase is equivalent to its ”disappearance,” so that the total effect from of metabolite in the water phase is reduced. The metabolite produced is surfactant reducing oil–water interfacial tension, which results in oil mobilization. The reduction of interfacial tension is implemented through relative permeability curve modifications primarily by lowering residual oil saturation. The characteristics for the water phase saturation profiles and the oil recovery curves are elucidated. However, the effect from the surfactant is not necessarily restricted to influence only interfacial tension, but it can also be an approach for changing, e.g., wettability. The distribution coefficient determines the time lag, until residual oil mobilization is initialized. It has also been found that the final recovery depends on the distance from the inlet before the surfactant effect takes place. The surfactant effect position is sensitive to changes in maximum growth rate, and injection concentrations of bacteria and substrate, thus determining the final recovery. Different methods for incorporating surfactant-induced reduction of interfacial tension into models are investigated. We have suggested one method, where several parameters can be estimated in order to obtain a better fit with experimental data. For all the methods, the incremental recovery is very similar, only coming from small differences in water phase saturation profiles. Overall, a significant incremental oil recovery can be achieved, when the sensitive parameters in the context of MEOR are carefully dealt with.     

储层含水条件下致密砂岩/页岩无机质纳米孔隙气相渗透率模型

页岩及致密砂岩储层富含纳米级孔隙,且储层条件下页岩孔隙(尤其无机质孔隙)及致密砂岩孔隙普遍含水,因此含水条件下纳米孔隙气体的流动能力的评价对这两类气藏的产能分析及生产预测具有重要意义.本文首先基于纳米孔隙内液态水及汽态水热力学平衡理论,量化了储层孔隙含水饱和度分布特征;进一步在纳米孔隙单相气体传质理论的基础上,考虑了孔隙含水饱和度对气体流动的影响;最终建立了含水饱和度与气相渗透率的关系曲线. 基于本文岩心孔隙分布特征,计算结果表明:储层含水饱和度对气体流动能力的影响不容忽视,在储层含水饱和度20%的情况下,气相流动能力与干燥情况相比将降低约10%;在含水饱和度40% 的情况下,气相流动能力将降低约20%.      

Percolation Approach to the Anisotropy Factor in an Unsaturated Porous Medium

The anisotropy factor is defined as the ratio of the effective (macroscopic) conductivities parallel to the bedding plane and perpendicular to it. The anisotropy factor A(p,a) is a function of both the saturation degree, p, in the void space of the disordered medium and the anisotropy parameter, a, that characterizes the ratio of the local conductivities parallel and normal to the bedding plane. There are two opposite behaviors of the anisotropy factor as a function of the saturation degree described in literature. One presents the anisotropy factor as a curve with a maximum and the other as a curve with a minimum. The main result of calculating the conductivities of a uniaxial percolation anisotropic model is that at the saturation threshold value, p_c, A(p_c, a) = 1, wherefrom it increases at a >1 (or decreases at a < 1) with saturation. An extension of the computed results below the threshold is also proposed.     

Modeling of Two-Phase Flow in Fractured Porous Media on Unstructured Non-Uniformly Coarsened Grids

In this article, we investigate two strategies for coarsening fractured geological models. The first approach, which generates grids that resolve the fractures, is referred to as explicit fracture-matrix separation (EFMS). The second approach is based on a non-uniform coarsening strategy introduced in Aarnes et al. (Adv Water Resour 30(11):2177–2193, 2007a). A series of two-phase flow simulations where the saturation is modeled on the respective coarse grids are performed. The accuracy of the resulting solutions is examined, and the robustness of the two strategies is assessed with respect to number of fractures, degree of coarsening, well locations, phase viscosities, and fracture permeability. The numerical results show that saturation solutions obtained on the non-uniform coarse grids are consistently more accurate than the corresponding saturation solutions obtained on the EFMS grids. The numerical results also reveal that it is much easier to tune the upscaling factor with the non-uniform coarsening approach.     

Experimental study of aerodynamic damping in arrays of vibrating cantilevers

Cantilever structures vibrating in a fluid are encountered in numerous engineering applications. The aerodynamic loading from a fluid can have a large effect on both the resonance frequency and damping, and has been the subject of numerous studies. The aerodynamic loading on a single beam is altered when multiple beams are configured in an array. In such situations, neighboring beams interact through the fluid and their dynamic behavior is modified. In this work, aerodynamic interactions between neighboring cantilever beams operating near their first resonance mode and vibrating at amplitudes comparable to their widths are experimentally explored. The degree to which two beams become coupled through the fluid is found to be sensitive to vibration amplitude and proximity of neighboring components in the array. The cantilever beams considered are slender piezoelectric fans (approximately 6 cm in length), and are caused to vibrate in-phase and out-of-phase at frequencies near their fundamental resonance values. Aerodynamic damping is expressed in terms of the quality factor for two different array configurations and estimated for both in-phase and out-of-phase conditions. The two array configurations considered are for neighboring fans placed face-to-face and edge-to-edge. It is found that the damping is greatly influenced by proximity of neighboring fans and phase difference. For the face-to-face configuration, a reduction in damping is observed for in-phase vibration, while it is greatly increased for out-of-phase vibration; the opposite effect is seen for the edge-to-edge configuration. The resonance frequencies also show a dependence on the phase difference, but these changes are small compared to those observed for damping. Correlations are developed based on the experimental data which can be used to predict the aerodynamic damping in arrays of vibrating cantilevers. The distance at which the beams no longer interact is quantified for both array configurations. Understanding the fluid interactions between neighboring vibrating beams is essential for predicting the dynamic behavior of such arrays and designing them for practical applications.     

A micromechanical study of drying and carbonation effects in cement-based materials

This paper is devoted to a micromechanical study of mechanical properties of cement-based materials by taking into account effects of water saturation degree and carbonation process. To this end, the cement-based materials are considered as a composite material constituted with a cement matrix and aggregates (inclusions). Further, the cement matrix is seen as a porous medium with a solid phase (CSH) and pores. Using a two-step homogenization procedure, a closed-form micromechanical model is first formulated to describe the basic mechanical behavior of materials. This model is then extended to partially saturated materials in order to account for the effects of water saturation degree on the mechanical properties. Finally, considering the solid phase change and porosity variation related to the carbonation process, the micromechanical model is coupled with the chemical reaction and is able to describe the consequences of carbonation on the macroscopic mechanical properties of material. Some comparisons between numerical results and experimental data are presented.